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Planning with partial observation is a central challenge in embodied AI. A majority of prior works have tackled this challenge by developing agents that physically explore their environment to update their beliefs about the world state.In contrast, humans can $\textit{imagine}$ unseen parts of the world through a mental exploration and $\textit{revise}$ their beliefs with imagined observations. Such updated beliefs can allow them to make more informed decisions, without necessitating the physical exploration of the world at all times. To achieve this human-like ability, we introduce the $\textit{Generative World Explorer (Genex)}$, an egocentric world exploration framework that allows an agent to mentally explore a large-scale 3D world (e.g., urban scenes) and acquire imagined observations to update its belief. This updated belief will then help the agent to make a more informed decision at the current step. To train $\textit{Genex}$, we create a synthetic urban scene dataset, Genex-DB. Our experimental results demonstrate that (1) $\textit{Genex}$ can generate high-quality and consistent observations during long-horizon exploration of a large virtual physical world and (2) the beliefs updated with the generated observations can inform an existing decision-making model (e.g., an LLM agent) to make better plans.
arXiv
I model a rational agent who spends resources between the current time and some fixed future deadline. Opportunities to spend resources arise randomly according to a Poisson process, and the quality of each opportunity follows a uniform distribution. The agent values their current resource stock at exactly the sum of expected utility from all future spending opportunities. Unlike in traditional discounted expected utility models, the agent exhibits correlation aversion, static (but not dynamic) preference reversals, and monotonicity with respect to payment timing. Connecting the agent's risk and time preference is intuitive, and doing so leads to a new model of procrastination where the agent misperceives their general attitude toward spending resources.
arXiv
A full set of optimized observables is measured in an angular analysis of the decay B$^0$ $\to$ K$^*$(892)$^0\mu^+\mu^-$ using a sample of proton-proton collisions at $\sqrt{s}$ = 13 TeV, collected with the CMS detector at the LHC, corresponding to an integrated luminosity of 140 fb$^{-1}$. The analysis is performed in six bins of the squared invariant mass of the dimuon system, $q^2$, over the range 1.1 $\lt$ $q^2$ $\lt$ 16 GeV$^2$. The results are among the most precise experimental measurements of the angular observables for this decay and are compared to a variety of predictions based on the standard model.
arXiv
Differential equations are derived which show how generalized Euler vector representations of the Euler rotation axis and angle for a rigid body evolve in time; the Euler vector is also known as a rotation vector or axis-angle vector. The solutions can exhibit interesting rotational features in this non-abstract, visualizable setting, including spinor-like behavior and quasiperiodicity. The equations are well-behaved at zero, reducing to the simple infinitesimal case there. One of them is equivalent to a known quaternion differential equation. The simple geometric derivation does not depend on Euler's rotation theorem, and yields a proof of Euler's theorem using only infinitesimal motions. With mild regularity conditions on the angular velocity function, there is a continuous evolution of the normalized axis and angle for all time. Dynamical systems properties are discussed, and numerical solutions are used to investigate them when the angular velocity is itself rotating, and the Euler vector trajectory traces out a torus-like shape, with a strobe plot that densely fills in a closed curve.
arXiv
This paper describes two C++/Open Motion Planning Library implementations of the recently developed motion planning algorithms HyRRT arXiv:2210.15082v1 [cs.RO] and HySST arXiv:2305.18649v1 [cs.RO]. Specifically, cHyRRT, an implementation of the HyRRT algorithm, is capable of generating a solution to a motion planning problem for hybrid systems with probabilistically completeness, while cHySST, an implementation of the asymptotically near-optimal HySST algorithm, is capable of computing a trajectory to solve the optimal motion planning problem for hybrid systems. cHyRRT is suitable for motion planning problems where an optimal solution is not required, whereas cHySST is suitable for such problems that prefer optimal solutions, within all feasible solutions. The structure, components, and usage of the two tools are described. Examples are included to illustrate the main capabilities of the toolbox.
arXiv
Federated learning (FL) is an emerging paradigm for training machine learning models across distributed clients. Traditionally, in FL settings, a central server assigns training efforts (or strategies) to clients. However, from a market-oriented perspective, clients may independently choose their training efforts based on rational self-interest. To explore this, we propose a potential game framework where each client's payoff is determined by their individual efforts and the rewards provided by the server. The rewards are influenced by the collective efforts of all clients and can be modulated through a reward factor. Our study begins by establishing the existence of Nash equilibria (NEs), followed by an investigation of uniqueness in homogeneous settings. We demonstrate a significant improvement in clients' training efforts at a critical reward factor, identifying it as the optimal choice for the server. Furthermore, we prove the convergence of the best-response algorithm to compute NEs for our FL game. Finally, we apply the training efforts derived from specific NEs to a real-world FL scenario, validating the effectiveness of the identified optimal reward factor.
arXiv
High penetration from volatile renewable energy resources in the grid and the varying nature of loads raise the need for frequent line switching to ensure the efficient operation of electrical distribution networks. Operators must ensure maximum load delivery, reduced losses, and the operation between voltage limits. However, computations to decide the optimal feeder configuration are often computationally expensive and intractable, making it unfavorable for real-time operations. This is mainly due to the existence of binary variables in the network reconfiguration optimization problem. To tackle this issue, we have devised an approach that leverages machine learning techniques to reshape distribution networks featuring multiple substations. This involves predicting the substation responsible for serving each part of the network. Hence, it leaves simple and more tractable Optimal Power Flow problems to be solved. This method can produce accurate results in a significantly faster time, as demonstrated using the IEEE 37-bus distribution feeder. Compared to the traditional optimization-based approaches, a feasible solution is achieved approximately ten times faster for all the tested scenarios.
arXiv
Tuning the density of resident electrons or holes in semiconductors provides crucial insight into the composition of excitonic complexes that are observed as absorption or photoluminescence resonances in optical studies. Moreover, we can change the way these resonances shift and broaden in energy by controlling the quantum numbers of the resident carriers with magnetic fields and doping levels, and by selecting the quantum numbers of the photoexcited or recombining electron-hole (e-h) pair through optical polarization. We discuss the roles of distinguishability and optimality of excitonic complexes, showing them to be key ingredients that determine the energy shifts and broadening of optical resonances in charge-tunable semiconductors. A distinguishable e-h pair means that the electron and hole undergoing photoexcitation or recombination have quantum numbers that are not shared by any of the resident carriers. An optimal excitonic complex refers to a complex whose particles come with all available quantum numbers of the resident carriers. All optical resonances may be classified as either distinct or indistinct depending on the distinguishability of the e-h pair, and the underlying excitonic complex can be classified as either optimal or suboptimal. The universality of these classifications, inherited from the fundamental Pauli exclusion principle, allows us to understand how optical resonances shift in energy and whether they should broaden as doping is increased. This understanding is supported by conclusive evidence that the decay of optical resonances cannot be simply attributed to enhanced screening when resident carriers are added to a semiconductor. Finally, applying the classification scheme in either monolayer or moire heterobilayer systems, we relate the energy shift and amplitude of the neutral exciton resonance to the compressibility of the resident carrier gas.
arXiv
Blockchain networks are facing increasingly heterogeneous computational demands, and in response, protocol designers have started building specialized infrastructure to supply that demand. This paper introduces Resoonance: a new kind of transaction fee mechanism that operates in a general two-sided marketplace setting with extreme preference heterogeneity on both sides of the market. We allow users submitting transactions to have arbitrary valuations for inclusion, nodes responsible for executing transactions to incur arbitrary net costs for executing any bundle, and further allow for arbitrary constraints in allocation validity. These constraints, for example, may range from representing an individual node's specialized hardware constraints to denoting the fact that transactions may not be executed in parallel across different nodes if they utilize the same part of the network's state. Transactions may even require multiple nodes for execution. Resonance's design utilizes competition among sophisticated brokers to find idiosyncratic prices. We show that at pure Nash equilibria, Resonance finds an efficient outcome and minimizes the need for strategization by users and nodes. It is also budget-balanced, individually rational for all parties, and computationally tractable.
arXiv
In this paper we prove that Schr\"{o}dinger's equation with a Hamiltonian of the form $H=-\Delta+i(A \nabla + \nabla A) + V$, which includes a magnetic potential $A$, has the same dispersive and solution decay properties as the free Schr\"{o}dinger equation. In particular, we prove $L^1 \to L^\infty$ decay and some related estimates for the wave equation. The potentials $A$ and $V$ are short-range and $A$ has four derivatives, but they can be arbitrarily large. All results hold in three space dimensions.
arXiv
A generative adversarial network (GAN) has been a representative backbone model in generative artificial intelligence (AI) because of its powerful performance in capturing intricate data-generating processes. However, the GAN training is well-known for its notorious training instability, usually characterized by the occurrence of mode collapse. Through the lens of gradients' variance, this work particularly analyzes the training instability and inefficiency in the presence of mode collapse by linking it to multimodality in the target distribution. To ease the raised training issues from severe multimodality, we introduce a novel GAN training framework that leverages a series of tempered distributions produced via convex interpolation. With our newly developed GAN objective function, the generator can learn all the tempered distributions simultaneously, conceptually resonating with the parallel tempering in Statistics. Our simulation studies demonstrate the superiority of our approach over existing popular training strategies in both image and tabular data synthesis. We theoretically analyze that such significant improvement can arise from reducing the variance of gradient estimates by using the tempered distributions. Finally, we further develop a variant of the proposed framework aimed at generating fair synthetic data which is one of the growing interests in the field of trustworthy AI.
arXiv
In 1975, Erd\H{o}s and Sauer asked to estimate, for any constant $r$, the maximum number of edges an $n$-vertex graph can have without containing an $r$-regular subgraph. In a recent breakthrough, Janzer and Sudakov proved that any $n$-vertex graph with no $r$-regular subgraph has at most $C_r n \log \log n$ edges, matching an earlier lower bound by Pyber, R\"odl and Szemer\'edi and thereby resolving the Erd\H{o}s-Sauer problem up to a constant depending on $r$. We prove that every $n$-vertex graph without an $r$-regular subgraph has at most $Cr^2 n \log \log n$ edges. This bound is tight up to the value of $C$ for $n\geq n_0(r)$ and hence resolves the Erd\H{o}s-Sauer problem up to an absolute constant. Moreover, we obtain similarly tight results for the whole range of possible values of $r$ (i.e., not just when $r$ is a constant), apart from a small error term at a transition point near $r\approx \log n$, where, perhaps surprisingly, the answer changes. More specifically, we show that every $n$-vertex graph with average degree at least $\min(Cr\log(n/r),Cr^2 \log\log n)$ contains an $r$-regular subgraph. The bound $Cr\log(n/r)$ is tight for $r\geq \log n$, while the bound $Cr^2 \log \log n$ is tight for $r<(\log n)^{1-\Omega(1)}$. These results resolve a problem of R\"odl and Wysocka from 1997 for almost all values of $r$. Among other tools, we develop a novel random process that efficiently finds a very nearly regular subgraph in any almost-regular graph. A key step in our proof uses this novel random process to show that every $K$-almost-regular graph with average degree $d$ contains an $r$-regular subgraph for some $r=\Omega_K(d)$, which is of independent interest.
arXiv
Quantum computing architectures based on neutral atoms offer large scales and high-fidelity operations. They can be heterogeneous, with different zones for storage, entangling operations, and readout. Zoned architectures improve computation fidelity by shielding idling qubits in storage from side-effect noise, unlike monolithic architectures where all operations occur in a single zone. However, supporting these flexible architectures with efficient compilation remains challenging. In this paper, we propose ZAC, a scalable compiler for zoned architectures. ZAC minimizes data movement overhead between zones with qubit reuse, i.e., keeping them in the entanglement zone if an immediate entangling operation is pending. Other innovations include novel data placement and instruction scheduling strategies in ZAC, a flexible specification of zoned architectures, and an intermediate representation for zoned architectures, ZAIR. Our evaluation shows that zoned architectures equipped with ZAC achieve a 22x improvement in fidelity compared to monolithic architectures. Moreover, ZAC is shown to have a 10% fidelity gap on average compared to the ideal solution. This significant performance enhancement enables more efficient and reliable quantum circuit execution, enabling advancements in quantum algorithms and applications. ZAC is open source at https://github.com/UCLA-VAST/ZAC
arXiv
Motivated by knot theory, it is natural to define the orientation-reversal of a quandle orbit by inverting all the translations given by elements of that orbit. In this short note we observe that this natural notion is unsuited to medial quandles.
arXiv
We consider the dynamics of a continuously monitored qubit in the limit of strong measurement rate where the quantum trajectory is described by a stochastic master equation with Poisson noise. Such limits are expected to give rise to quantum jumps between the pointer states associated with the non-demolition measurement. A surprising discovery in earlier work [Tilloy et al., Phys. Rev. A 92, 052111 (2015)] on quantum trajectories with Brownian noise was the phenomena of spikes observed in between the quantum jumps. Here, we show that spikes are observed also for Poisson noise. We consider three cases where the non-demolition is broken by adding, to the basic strong measurement dynamics, either unitary evolution or thermal noise or additional measurements. We present a complete analysis of the spike and jump statistics for all three cases using the fact that the dynamics effectively corresponds to that of stochastic resetting. We provide numerical results to support our analytic results.
arXiv
Coherent perfect absorption (CPA) has been a topic of considerable contemporary research interest. However, its implementation in practical applications has been limited, since it has been demonstrated only for plane waves till now. The issue for beams with finite confinement -- characterized by a collection of plane waves -- is that complete destructive interference is not feasible for all the plane waves simultaneously. In this paper, we study the absorption characteristics of two counter-propagating structured beams, e.g., Gaussian and Laguerre-Gaussian (LG) beams with and without orbital angular momentum respectively, incident normally on a composite slab from both sides by fulfilling the CPA condition exclusively for the central plane waves. We show that though perfect absorption is not achievable, there can be a substantial reduction of the scattered light. We also consider CPA for oblique incidence and discuss the difficulties.
arXiv
We investigate prophet inequalities with competitive ratios approaching $1$, seeking to generalize $k$-uniform matroids. We first show that large girth does not suffice: for all $k$, there exists a matroid of girth $\geq k$ and a prophet inequality instance on that matroid whose optimal competitive ration is $\frac{1}{2}$. Next, we show $k$-fold matroid unions do suffice: we provide a prophet inequality with competitive ratio $1-O(\sqrt{\frac{\log k}{k}})$ for any $k$-fold matroid union. Our prophet inequality follows from an online contention resolution scheme. The key technical ingredient in our online contention resolution scheme is a novel bicriterion concentration inequality for arbitrary monotone $1$-Lipschitz functions over independent items which may be of independent interest. Applied to our particular setting, our bicriterion concentration inequality yields "Chernoff-strength" concentration for a $1$-Lipschitz function that is not (approximately) self-bounding.
arXiv
We prove upper bounds which are independent of the dimension of the ambient space, on the number of realizable zero-nonzero patterns as well as sign conditions (when the field of coefficients is ordered) of a finite set of polynomials $\mathcal{P}$ restricted to some algebraic subset $V$.Our bounds (which are tight) depend on the number and the degrees of the polynomials in $\mathcal{P}$, as well as the degree (of the embedding) of $V$ and the dimension of $V$, but are independent of the dimension of the space in which $V$ is embedded. This last feature of our bounds is useful in situations where the ambient dimension could be much larger than $\dim V$. We give several applications of our results. We generalize existing results on bounding the speeds of algebraically defined classes of graphs, as well as lower bounds in terms of the number of connected components for testing membership in semi-algebraic sets using algebraic computation trees. Motivated by quantum complexity theory we introduce a notion of relative rank (additive as well as multiplicative) in finite dimensional vector spaces and algebras relative to a fixed algebraic subset in the vector space or algebra -- which generalizes the classical definition of ranks of tensors. We prove a very general lower bound on the maximum relative rank of finite subsets relative to algebraic subsets of bounded degree and dimension which is independent of the dimension of the vector space or algebra. We show how our lower bound implies a quantum analog of a classical lower bound result of Shannon for Boolean circuits -- that almost all Boolean functions require (classical) circuits of size at least $\Omega(2^n/n)$.
arXiv
Aligning diffusion models with downstream objectives is essential for their practical applications. However, standard alignment methods often struggle with step generalization when directly applied to few-step diffusion models, leading to inconsistent performance across different denoising step scenarios. To address this, we introduce Stepwise Diffusion Policy Optimization (SDPO), a novel alignment method tailored for few-step diffusion models. Unlike prior approaches that rely on a single sparse reward from only the final step of each denoising trajectory for trajectory-level optimization, SDPO incorporates dense reward feedback at every intermediate step. By learning the differences in dense rewards between paired samples, SDPO facilitates stepwise optimization of few-step diffusion models, ensuring consistent alignment across all denoising steps. To promote stable and efficient training, SDPO introduces an online reinforcement learning framework featuring several novel strategies designed to effectively exploit the stepwise granularity of dense rewards. Experimental results demonstrate that SDPO consistently outperforms prior methods in reward-based alignment across diverse step configurations, underscoring its robust step generalization capabilities. Code is avaliable at https://github.com/ZiyiZhang27/sdpo.
arXiv
The Vol-Det Conjecture, formulated by Champanerkar, Kofman and Purcell, states that there exists a specific inequality connecting the hyperbolic volume of an alternating link and its determinant. Among the classes of links for which this conjecture holds are all knots with at most 16 crossings, 2-bridge links, and links that are closures of 3-strand braids. In the present paper, Burton's bound on the number of crossings for which the Vol-Det Conjecture holds is improved for links with more than eight twists. In addition, Stoimenow's inequalities between hyperbolic volumes and determinants are improved for alternating and alternating arborescent links with more than eight twists.
arXiv
We prove that for every compact, convex subset $K\subset\mathbb{R}^2$ the operator system $A(K)$, consisting of all continuous affine functions on $K$, is hyperrigid in the C*-algebra $C(\mathrm{ex}(K))$. In particular, this result implies that the weak and strong operator topologies coincide on the set $$ \{ T\in\mathcal{B}(H);\ T\ \mathrm{normal}\ \mathrm{and}\ \sigma(T)\subset \mathrm{ex}(K) \}. $$ Our approach relies on geometric properties of $K$ and generalizes previous results by Brown.
arXiv
This paper explores quadratic forms over finite fields with associated Artin-Schreier curves. Specifically, we investigate quadratic forms of $\mathbb F_{q^n}/\mathbb F_q$ represented by polynomials over $\mathbb F_{q^n}$ with $q$ odd, characterizing them using certain matrices defined by coefficients of the polynomials. In particular, a comprehensive treatment will be given for those polynomials whose coefficients all lie in $\mathbb F_q$. Afterwards, the results on quadratic forms will be applied to get maximal and minimal Artin-Schreier curves explicitly.
arXiv
We are interested in the nonlinear damped Klein-Gordon equation \[ \partial_t^2 u+2\alpha \partial_t u-\Delta u+u-|u|^{p-1}u=0 \] on $\mathbb{R}^d$ for $2\le d\le 5$ and energy sub-critical exponents $2 < p < \frac{d+2}{d-2}$. We construct multi-solitons, that is, solutions which behave for large times as a sum of decoupled solitons, in various configurations with symmetry: this includes multi-solitons whose soliton centers lie at the vertices of an expanding regular polygon (with or without a center), of a regular polyhedron (with a center), or of a higher dimensional regular polytope. We give a precise description of these multi-solitons: in particular the interaction between nearest neighbour solitons is asymptotic to $\ln (t)$ as $t \to +\infty$. We also prove that in any multi-soliton, the solitons can not all share the same sign. Both statements generalize and precise results from \cite{F98}, \cite{Nak} and are based on the analysis developed in \cite{CMYZ,CMY}.
arXiv
The personalization techniques of diffusion models succeed in generating specific concepts but also pose threats to copyright protection and illegal use. Model Watermarking is an effective method to prevent the unauthorized use of subject-driven or style-driven image generation, safeguarding concept copyrights. However, under the goal of concept-oriented protection, current watermarking schemes typically add watermarks to all images rather than applying them in a refined manner targeted at specific concepts. Additionally, the personalization techniques of diffusion models can easily remove watermarks. Existing watermarking methods struggle to achieve fine-grained watermark embedding with a few images of specific concept and prevent removal of watermarks through personalized fine-tuning. Therefore, we introduce a novel concept-oriented watermarking framework that seamlessly embeds imperceptible watermarks into the concept of diffusion models. We conduct extensive experiments and ablation studies to verify our framework. Our code is available at https://anonymous.4open.science/r/Conceptwm-4EB3/.
arXiv
We critically review the evidence for time-varying dark energy from recent Baryon Acoustic Oscillations (BAO) and Supernova (SN) observations. First, we show that such evidence is present at the 3$\sigma$ level, even without the new BAO data from the dark energy Spectroscopic Instrument (DESI), by instead using BAO data from the dark energy Survey (DES), combined with the DES5Y supernovae and Planck CMB data. Next, we examine the role of the DES5Y supernova dataset, showing that the preference for time-varying dark energy is driven by the low redshift supernovae common to both the DES5Y and Pantheon+ compilations. We find that combining Pantheon+ and DES5Y supernovae by removing the common supernovae leads to two different results, depending on whether they are removed from the DES5Y or the Pantheon+ catalog, leading to stronger or weaker exclusion of $\Lambda$CDM, at the (3.8$\sigma$) and (2.5$\sigma$) level, respectively. These common supernovae have smaller error bars in DES5Y compared to Pantheon+, and, as recently pointed out, there is an offset in magnitude in DES5Y between supernovae at ($z > 0.1$), where almost all the measurements taken during the full five years of DES are, and the low-redshift ones ($z < 0.1$), where all the historical set of nearby supernovae lies. We show that marginalizing over such an offset in DES5Y would lead to significantly weaker evidence for evolving dark energy.
arXiv
The abundant chemical compositions in ternary hydrides bring much more possibility to explore high temperature superconductors under lower pressure. Here we constructed 115 ternary hydrides on the basis of the elements substitution using 16 metal elements within 5 reported prototype structures. We conducted a three-step approach to screen and study these candidate structures in the aspects of dynamical stability, formation energy and relative enthalpy, respectively. Based on this approach, we found three meta-stable compounds with hydrogen clathrate cages in the space group of P-3m1, including Y2CdH18, Y2InH18 and Ca2SnH18. All of the structures are superconductive under high pressure with Tc above 110 K, which is larger than the superconductive temperature of liquid nitrogen. Our study enriches the database of novel ternary hydrides under high pressure, and provides insight for future theoretical and experimental researches.
arXiv
The variation of the physical conditions across the three dimensions of our Galaxy is a major source of complexity for the modelling of the foreground signal facing the cosmic microwave background (CMB). In the present work, we demonstrate that the spin-moment expansion formalism provides a powerful framework to model and understand this complexity, with a special focus on that arising from variations of the physical conditions along each line-of-sight on the sky. We perform the first application of the moment expansion to reproduce a thermal dust model largely used by the CMB community, demonstrating its power as a minimal tool to compress, understand and model the information contained within any foreground model. Furthermore, we use this framework to produce new models of thermal dust emission containing the maximal amount of complexity allowed by the current data, remaining compatible with the observed angular power-spectra by the $Planck$ mission. By assessing the impact of these models on the performance of component separation methodologies, we conclude that the additional complexity contained within the third dimension could represent a significant challenge for future CMB experiments and that different component separation approaches are sensitive to different properties of the moments.
arXiv
Ashkin-Teller model is a two-layer lattice model where spins in each layer interact ferromagnetically with strength $J$, and the spin-dipoles (product of spins) interact with neighbors with strength $\lambda.$ The model exhibits simultaneous magnetic and electric transitions along a self-dual line on the $\lambda$-$J$ plane with continuously varying critical exponents. In this article, we investigate the percolation of geometric clusters of spins and spin-dipoles denoted respectively as magnetic and electric clusters. We find that the largest cluster in both cases becomes macroscopic in size and spans the lattice when interaction exceeds a critical threshold given by the same self-dual line where magnetic and electric transitions occur. The fractal dimension of the critical spanning clusters is related to order parameter exponent $\beta_{m,e}$ as $D_{m,e}=d-\frac{5}{12}\frac{\beta_{m,e}}\nu,$ where $d=2$ is the spatial dimension and $\nu$ is the correlation length exponent. This relation determines all other percolation exponents and their variation wrt $\lambda.$ We show that for magnetic Percolation, the Binder cumulant, as a function of $\xi_2/L$ with $\xi_2$ being the second-moment correlation length, remains invariant all along the critical line and matches with that of the spin-percolation in the usual Ising model. The function also remains invariant for the electric percolation, forming a new superuniversality class of percolation transition.
arXiv
We study the dynamics of synthetic molecules whose architectures are generated by space transformations from a point group acting on seed resonators. We show that the dynamical matrix of any such molecule can be reproduced as the left regular representation of a self-adjoint element from the stabilized group's algebra. Furthermore, we use elements of representation theory and K-theory to rationalize the dynamical features supported by such synthetic molecules up to topological equivalences. These tools enable us to identify a set of fundamental models which generate by superposition all possible dynamical matrices up to homotopy equivalences. Interpolations between these fundamental models give rise to topological spectral flows.
arXiv
We prove a version of Jordan's classification theorem for finite subgroups of $\mathrm{GL}_{n}(K)$ that is at the same time quantitatively explicit, CFSG-free, and valid for arbitrary $K$. This is the first proof to satisfy all three properties at once. Our overall strategy follows Larsen and Pink [24], with explicit computations based on techniques developed by the authors and Helfgott [2, 3], particularly in relation to dimensional estimates.
arXiv
We consider two supersymmetric M5 brane probe solutions in $\textrm{AdS}_7 \times S^4$ and one in $\textrm{AdS}_4 \times S^7$ that all have the $\textrm{AdS}_3 \times S^3$ world-volume geometry. The values of the classical action of the first two M5 probes (with $S^3$ in $\textrm{AdS}_7$ or in $S^4$) are related to the leading $N^2$ parts in the anomaly b-coefficient in the (2,0) theory corresponding to a spherical surface defect in symmetric or antisymmetric $SU(N)$ representations. We present a detailed computation of the corresponding one-loop M5 brane partition functions finding that they vanish (in a particular regularization). This implies the vanishing of the order $N^0$ part in the b-anomaly coefficients, in agreement with earlier predictions for their exact values. It remains, however, a puzzle of how to reproduce the non-vanishing order $N$ terms in these coefficients within the semiclassical M5-brane probe setup.
arXiv
Determining potential probability distributions with a given causal graph is vital for causality studies. To bypass the difficulty in characterizing latent variables in a Bayesian network, the nested Markov model provides an elegant algebraic approach by listing exactly all the equality constraints on the observed variables. However, this algebraically motivated causal model comprises distributions outside Bayesian networks, and its physical interpretation remains vague. In this work, we inspect the nested Markov model through the lens of generalized probabilistic theory, an axiomatic framework to describe general physical theories. We prove that all the equality constraints defining the nested Markov model hold valid theory-independently. Yet, we show this model generally contains distributions not implementable even within such relaxed physical theories subjected to merely the relativity principles and mild probabilistic rules. To interpret the origin of such a gap, we establish a new causal model that defines valid distributions as projected from a high-dimensional Bell-type causal structure. The new model unveils inequality constraints induced by relativity principles, or equivalently high-dimensional conditional independences, which are absent in the nested Markov model. Nevertheless, we also notice that the restrictions on states and measurements introduced by the generalized probabilistic theory framework can pose additional inequality constraints beyond the new causal model. As a by-product, we discover a new causal structure exhibiting strict gaps between the distribution sets of a Bayesian network, generalized probabilistic theories, and the nested Markov model. We anticipate our results will enlighten further explorations on the unification of algebraic and physical perspectives of causality.
arXiv
In this paper, we construct new t-server Private Information Retrieval (PIR) schemes with communication complexity subpolynomial in the previously best known, for all but finitely many t. Our results are based on combining derivatives (in the spirit of Woodruff-Yekhanin) with the Matching Vector based PIRs of Yekhanin and Efremenko. Previously such a combination was achieved in an ingenious way by Dvir and Gopi, using polynomials and derivatives over certain exotic rings, en route to their fundamental result giving the first 2-server PIR with subpolynomial communication. Our improved PIRs are based on two ingredients: - We develop a new and direct approach to combine derivatives with Matching Vector based PIRs. This approach is much simpler than that of Dvir-Gopi: it works over the same field as the original PIRs, and only uses elementary properties of polynomials and derivatives. - A key subproblem that arises in the above approach is a higher-order polynomial interpolation problem. We show how "sparse S-decoding polynomials", a powerful tool from the original constructions of Matching Vector PIRs, can be used to solve this higher-order polynomial interpolation problem using surprisingly few higer-order evaluations. Using the known sparse S-decoding polynomials, in combination with our ideas leads to our improved PIRs. Notably, we get a 3-server PIR scheme with communication $2^{O^{\sim}( (\log n)^{1/3}) }$, improving upon the previously best known communication of $2^{O^{\sim}( \sqrt{\log n})}$ due to Efremenko.
arXiv
Large double-logarithmic corrections are induced by soft gluon emissions near threshold in the semi-inclusive $e^+e^-$ annihilation (SIA) distributions, and must be resummed to all-orders in perturbation theory for reliable theoretical predictions. Building on strategy developed for threshold resummation for DIS structure function in momentum space using soft-collinear effective theory (SCET), we present the explicit formalism for SIA cross section. We then perform the resummation directly in momentum space for $\gamma^* \to q \bar q$, $H \to gg$ and $H \to b\bar b$ to N$^4$LL accuracy and demonstrate good convergence. We anticipate that these results will benefit the extraction of the light-quark, the heavy-quark as well as the gluon fragmentation functions.
arXiv
This paper studies the distributed bandit convex optimization problem with time-varying inequality constraints, where the goal is to minimize network regret and cumulative constraint violation. To calculate network cumulative constraint violation, existing distributed bandit online algorithms solving this problem directly use the clipped constraint function to replace its original constraint function. However, the use of the clipping operation renders Slater condition (i.e, there exists a point that strictly satisfies the inequality constraints at all iterations) ineffective to achieve reduced network cumulative constraint violation. To tackle this challenge, we propose a new distributed bandit online primal-dual algorithm. If local loss functions are convex, we show that the proposed algorithm establishes sublinear network regret and cumulative constraint violation bounds. When Slater condition holds, the network cumulative constraint violation bound is reduced. In addition, if local loss functions are strongly convex, for the case where strongly convex parameters are unknown, the network regret bound is reduced. For the case where strongly convex parameters are known, the network regret and cumulative constraint violation bounds are further reduced. To the best of our knowledge, this paper is among the first to establish reduced (network) cumulative constraint violation bounds for (distributed) bandit convex optimization with time-varying constraints under Slater condition. Finally, a numerical example is provided to verify the theoretical results.
arXiv
This paper studies observability inequalities for heat equations on both bounded domains and the whole space $\mathbb{R}^d$. The observation sets are measured by log-type Hausdorff contents, which are induced by certain log-type gauge functions closely related to the heat kernel. On a bounded domain, we derive the observability inequality for observation sets of positive log-type Hausdorff content. Notably, the aforementioned inequality holds not only for all sets with Hausdorff dimension $s$ for any $s\in (d-1,d]$, but also for certain sets of Hausdorff dimension $d-1$. On the whole space $\mathbb{R}^d$, we establish the observability inequality for observation sets that are thick at the scale of the log-type Hausdorff content. Furthermore, we prove that for the 1-dimensional heat equation on an interval, the Hausdorff content we have chosen is an optimal scale for the observability inequality. To obtain these observability inequalities, we use the adapted Lebeau-Robiano strategy from \cite{Duyckaerts2012resolvent}. For this purpose, we prove the following results at scale of the log-type Hausdorff content, the former being derived from the latter: We establish a spectral inequality/a Logvinenko-Sereda uncertainty principle; we set up a quantitative propagation of smallness of analytic functions; we build up a Remez' inequality; and more fundamentally, we provide an upper bound for the log-type Hausdorff content of a set where a monic polynomial is small, based on an estimate in Lubinsky \cite{Lubinsky1997small}, which is ultimately traced back to the classical Cartan Lemma. In addition, we set up a capacity-based slicing lemma (related to the log-type gauge functions) and establish a quantitative relationship between Hausdorff contents and capacities. These tools are crucial in the studies of the aforementioned propagation of smallness in high-dimensional situations.
arXiv
Bonne and Censor-Hillel (ICALP 2019) initiated the study of distributed subgraph finding in dynamic networks of limited bandwidth. For the case where the target subgraph is a clique, they determined the tight bandwidth complexity bounds in nearly all settings. However, several open questions remain, and very little is known about finding subgraphs beyond cliques. In this work, we consider these questions and explore subgraphs beyond cliques. For finding cliques, we establish an $\Omega(\log \log n)$ bandwidth lower bound for one-round membership-detection under edge insertions only and an $\Omega(\log \log \log n)$ bandwidth lower bound for one-round detection under both edge insertions and node insertions. Moreover, we demonstrate new algorithms to show that our lower bounds are tight in bounded-degree networks when the target subgraph is a triangle. Prior to our work, no lower bounds were known for these problems. For finding subgraphs beyond cliques, we present a complete characterization of the bandwidth complexity of the membership-listing problem for every target subgraph, every number of rounds, and every type of topological change: node insertions, node deletions, edge insertions, and edge deletions. We also show partial characterizations for one-round membership-detection and listing.
arXiv
In this paper, we study the componentwise linearity of symbolic powers of edge ideals. We propose the conjecture that all symbolic powers of the edge ideal of a cochordal graph are componentwise linear. This conjecture is verified for some families of cochordal graphs, including complements of block graphs and complements of proper interval graphs. As a corollary, Minh's conjecture is established for such families. Moreover, we show that $I(G)^{(2)}$ is componentwise linear, for any cochordal graph $G$.
arXiv
The Schrieffer-Wolff transformation (SWT) is an important perturbative method in quantum mechanics used to simplify Hamiltonians by decoupling low- and high-energy subspaces. Existing methods for implementing the SWT often lack general applicability to arbitrary perturbative systems or fail to provide a closed-form solution for the SWT generator. In this article, we present a systematic and unified framework for the SWT that addresses these shortcomings. Specifically, we derive a closed-form solution for the SWT generator that is universally applicable to any system that satisfies the conditions required to be perturbatively treated. Furthermore, we extend this solution to time-dependent systems with periodic perturbations, covering all frequency regimes. The effectiveness of this approach is then demonstrated by applying it to analyze the dispersive shift of an anharmonic resonator coupled to a two-level system with time-dependent coupling.
arXiv
The James Webb Space Telescope has uncovered a puzzling population of UV-faint broad-line active galactic nuclei (AGN), nicknamed ``Little Red Dots'' (LRD) owing to their compact morphology and red rest-frame optical colours. Interpreted as dust attenuated AGN, their inferred intrinsic luminosities and supermassive black hole (SMBH) masses rival those of UV-luminous quasars, although they are $>100$ times more abundant. If LRDs and quasars are members of the same underlying population, they should inhabit comparable mass dark matter halos, traced by similar overdensities of galaxies. Otherwise, they represent distinct populations with different physical properties and formation histories. Characterizing LRD environments thus provides a critical test of their nature. Here, we report the discovery of a LRD at $z=7.3$, attenuated by moderate amounts of dust, $A_V = {3.26}\,\rm{mag}$, with an intrinsic bolometric luminosity of $10^{46.7}\,\rm{erg}\,\rm{s}^{-1}$ and a SMBH mass of $7\times10^8\,\rm{M}_\odot$. Most notably, this object is embedded in an overdensity of eight nearby galaxies, allowing us to calculate the first spectroscopic estimate of the clustering of galaxies around LRDs. We find a LRD-galaxy cross-correlation length of $r_0\!=\!9\pm2\,\rm{h}^{-1}\,\rm{cMpc}$, comparable to that of $z\!\sim\!6$ UV-luminous quasars. The resulting estimate of their minimum dark matter halo mass of $\log_{10}(M_{\rm{halo, min}}/\rm{M}_{\odot})= 12.3_{-0.8}^{+0.7}$ indicates that nearly all halos above this mass must host actively accreting SMBHs at $z\approx7$, in strong contrast with the far smaller duty cycle of luminous quasars ($<1\%$). Our results, taken at face value, motivate a picture in which LRDs are the obscured counterparts of UV-luminous quasars, which provides a natural explanation for the short UV-luminous lifetimes inferred from both quasar clustering and quasar proximity zones.
arXiv
The rapid development of large language models (LLMs) with advanced programming capabilities has paved the way for innovative approaches in software testing. Fuzz testing, a cornerstone for improving software reliability and detecting vulnerabilities, often relies on manually written fuzz drivers, limiting scalability and efficiency. To address this challenge, we propose CodeGraphGPT, a novel system that integrates code knowledge graphs with an LLM-powered intelligent agent to automate the fuzz driver generation process. By framing fuzz driver creation as a code generation task, CodeGraphGPT leverages program analysis to construct a knowledge graph of code repositories, where nodes represent code entities, such as functions or files, and edges capture their relationships. This enables the system to generate tailored fuzz drivers and input seeds, resolve compilation errors, and analyze crash reports, all while adapting to specific API usage scenarios. Additionally, querying the knowledge graph helps identify precise testing targets and contextualize the purpose of each fuzz driver within the fuzzing loop. We evaluated CodeGraphGPT on eight open-source software projects, achieving an average improvement of 8.73\% in code coverage compared to state-of-the-art methods. Moreover, it reduced the manual workload in crash case analysis by 84.4\% and identified 11 real-world bugs, including nine previously unreported ones. This work highlights how integrating LLMs with code knowledge graphs enhances fuzz driver generation, offering an efficient solution for vulnerability detection and software quality improvement.
arXiv
In this paper we present an approach to reduce hallucinations in Large Language Models (LLMs) by incorporating Knowledge Graphs (KGs) as an additional modality. Our method involves transforming input text into a set of KG embeddings and using an adapter to integrate these embeddings into the language model space, without relying on external retrieval processes. To facilitate this, we created WikiEntities, a dataset containing over 3 million Wikipedia texts annotated with entities from Wikidata and their corresponding embeddings from PyTorch-BigGraph. This dataset serves as a valuable resource for training Entity Linking models and adapting the described method to various LLMs using specialized adapters. Our method does not require fine-tuning of the language models themselves; instead, we only train the adapter. This ensures that the model's performance on other tasks is not affected. We trained an adapter for the Mistral 7B, LLaMA 2-7B (chat), and LLaMA 3-8B (instruct) models using this dataset and demonstrated that our approach improves performance on the HaluEval, True-False benchmarks and FEVER dataset. The results indicate that incorporating KGs as a new modality can effectively reduce hallucinations and improve the factual accuracy of language models, all without the need for external retrieval.
arXiv
Massive Open Online Courses (MOOCs) have greatly contributed to making education more accessible.However, many MOOCs maintain a rigid, one-size-fits-all structure that fails to address the diverse needs and backgrounds of individual learners.Learning path personalization aims to address this limitation, by tailoring sequences of educational content to optimize individual student learning outcomes.Existing approaches, however, often require either massive student interaction data or extensive expert annotation, limiting their broad application.In this study, we introduce a novel data-efficient framework for learning path personalization that operates without expert annotation.Our method employs a flexible recommender system pre-trained with reinforcement learning on a dataset of raw course materials.Through experiments on semi-synthetic data, we show that this pre-training stage substantially improves data-efficiency in a range of adaptive learning scenarios featuring new educational materials.This opens up new perspectives for the design of foundation models for adaptive learning.
arXiv
E-commerce app users exhibit behaviors that are inherently logically consistent. A series of multi-scenario user behaviors interconnect to form the scene-level all-domain user moveline, which ultimately reveals the user's true intention. Traditional CTR prediction methods typically focus on the item-level interaction between the target item and the historically interacted items. However, the scene-level interaction between the target item and the user moveline remains underexplored. There are two challenges when modeling the interaction with preceding all-domain user moveline: (i) Heterogeneity between items and scenes: Unlike traditional user behavior sequences that utilize items as carriers, the user moveline utilizes scenes as carriers. The heterogeneity between items and scenes complicates the process of aligning interactions within a unified representation space. (ii) Temporal misalignment of linked scene-level and item-level behaviors: In the preceding user moveline with a fixed sampling length, certain critical scene-level behaviors are closely linked to subsequent item-level behaviors. However, it is impossible to establish a complete temporal alignment that clearly identifies which specific scene-level behaviors correspond to which item-level behaviors. To address these challenges and pioneer modeling user intent from the perspective of the all-domain moveline, we propose All-domain Moveline Evolution Network (AMEN). AMEN not only transfers interactions between items and scenes to homogeneous representation spaces, but also introduces a Temporal Sequential Pairwise (TSP) mechanism to understand the nuanced associations between scene-level and item-level behaviors, ensuring that the all-domain user moveline differentially influences CTR predictions for user's favored and unfavored items. Online A/B testing demonstrates that our method achieves a +11.6% increase in CTCVR.
arXiv
While AI models have demonstrated remarkable capabilities in constrained domains like game strategy, their potential for genuine creativity in open-ended domains like art remains debated. We explore this question by examining how AI can transcend human cognitive limitations in visual art creation. Our research hypothesizes that visual art contains a vast unexplored space of conceptual combinations, constrained not by inherent incompatibility, but by cognitive limitations imposed by artists' cultural, temporal, geographical and social contexts. To test this hypothesis, we present the Alien Recombination method, a novel approach utilizing fine-tuned large language models to identify and generate concept combinations that lie beyond human cognitive availability. The system models and deliberately counteracts human availability bias, the tendency to rely on immediately accessible examples, to discover novel artistic combinations. This system not only produces combinations that have never been attempted before within our dataset but also identifies and generates combinations that are cognitively unavailable to all artists in the domain. Furthermore, we translate these combinations into visual representations, enabling the exploration of subjective perceptions of novelty. Our findings suggest that cognitive unavailability is a promising metric for optimizing artistic novelty, outperforming merely temperature scaling without additional evaluation criteria. This approach uses generative models to connect previously unconnected ideas, providing new insight into the potential of framing AI-driven creativity as a combinatorial problem.
arXiv
We establish the profound equivalence between measures of genuine multipartite entanglement(GME) and their corresponding coherence measures. Initially we construct two distinct classes of measures for genuine multipartite entanglement utilizing real symmetric concave functions and the convex roof technique. We then demonstrate that all coherence measures for any qudit states, defined through the convex roof approach, are identical to our two classes of GME measures of the states combined with an incoherent ancilla under a unitary incoherent operation. This relationship implies that genuine multipartite entanglement can be generated from the coherence inherent in an initial state through the unitary incoherent operations. Furthermore, we explore the interplay between coherence and other forms of genuine quantum correlations, specifically genuine multipartite steering and genuine multipartite nonlocality. In the instance of special three-qubit X-states (only nonzero elements of X-state are diagonal or antidiagonal when written in an orthonormal basis), we find that genuine multipartite steering and nonlocality are present if and only if the coherence exists in the corresponding qubit states.
arXiv
Uncertainty persists over how and why some countries become democratic and others do not, or why some countries remain democratic and others 'backslide' toward autocracy. Furthermore, while scholars generally agree on the nature of 'democracy' and 'autocracy', the nature of regimes in-between, and changes between them, are much less clear. By applying the spectral dimensionality-reduction technique Diffusion Map to political-science data from the V-Dem project for the period 1900 to 2021, we identify a low-dimensional non-linear manifold on which all electoral regimes move. Using the diffusion equation from statistical physics, we measure the time scale on which countries change their degree of electoral quality, freedom of association, and freedom of expression depending on their position on the manifold. By quantifying the coefficients of the diffusion equation for each country and over time, we show that democracies behave like sub-diffusive (i.e. slow spreading) particles and that autocracies on the verge of collapse behave like super-diffusive (i.e. fast spreading) particles. We show that regimes in-between exhibit diffusion dynamics distinct from autocracies and democracies, and an overall higher instability. Furthermore, we show that a country's position on the manifold and its dynamics are linked to its propensity for civil conflict. Our study pioneers the use of statistical physics in the analysis of political regimes. Our results provide a quantitative foundation for developing theories about what changes during democratization and democratic backsliding, as well as a new framework for regime-transformation and risk-of-conflict assessment.
arXiv
Given a closed subset $K$ in $\mathbb{R}$, the rational $K$-truncated moment problem ($K$-RTMP) asks to characterize the existence of a positive Borel measure $\mu$, supported on $K$, such that a linear functional $\mathcal{L}$, defined on all rational functions of the form $\frac{f}{q}$, where $q$ is a fixed polynomial with all real zeros of even order and $f$ is any real polynomial of degree at most $2k$, is an integration with respect to $\mu$. The case of a compact set $K$ was solved by Chandler in 1994, but there is no argument that ensures that $\mu$ vanishes on all real zeros of $q$. An obvious necessary condition for the solvability of the $K$-RTMP is that $\mathcal{L}$ is nonnegative on every $f$ satisfying $f|_{K}\geq 0$. If $\mathcal{L}$ is strictly positive on every $0\neq f|_{K}\geq 0$, we add the missing argument from Chandler's solution and also bound the number of atoms in a minimal representing measure. We show by an example that nonnegativity of $\mathcal{L}$ is not sufficient and add the missing conditions to the solution. We also solve the $K$-RTMP for unbounded $K$ and derive the solutions to the strong truncated Hamburger moment problem and the truncated moment problem on the unit circle as special cases.
arXiv
This work investigates the effects of tangent polar activity on the conformational and dynamic properties of entangled polymer melts through Langevin molecular dynamics simulations. We examine systems composed of all self-propelled, monodisperse linear chains, so that constraint release is considered. The range of activities explored here includes values where the active reptation theory is applicable, as well as higher activities that challenge the validity of the theory. Chain conformations exhibit a moderate increase in coil size increase, which becomes more pronounced at higher activity levels. Under these conditions, a local bond alignment along the chain contour appears together with a non-homogeneous segmental stretching, and orientation and stretching of the tube. Dynamically, polar activity induces a molecular-weight-independent diffusion coefficient, a transient superdiffusive behavior, and an end-to-end relaxation time inversely proportional to the molecular weight. Finally, our results are summarized in a diagram that classifies the various regimes of behavior observed in the simulations. Overall, these findings provide valuable insights into the complex interplay between activity and entanglements, advancing our understanding of active polymer systems and their potential applications across various fields.
arXiv
Depth estimation is an essential task toward full scene understanding since it allows the projection of rich semantic information captured by cameras into 3D space. While the field has gained much attention recently, datasets for depth estimation lack scene diversity or sensor modalities. This work presents the ADUULM-360 dataset, a novel multi-modal dataset for depth estimation. The ADUULM-360 dataset covers all established autonomous driving sensor modalities, cameras, lidars, and radars. It covers a frontal-facing stereo setup, six surround cameras covering the full 360-degree, two high-resolution long-range lidar sensors, and five long-range radar sensors. It is also the first depth estimation dataset that contains diverse scenes in good and adverse weather conditions. We conduct extensive experiments using state-of-the-art self-supervised depth estimation methods under different training tasks, such as monocular training, stereo training, and full surround training. Discussing these results, we demonstrate common limitations of state-of-the-art methods, especially in adverse weather conditions, which hopefully will inspire future research in this area. Our dataset, development kit, and trained baselines are available at https://github.com/uulm-mrm/aduulm_360_dataset.
arXiv
Migration is a key ingredient for the formation of close-in super-Earth and mini-Neptune systems, as it sets in which resonances planets can be trapped. Slower migration rates result in wider resonance configurations compared to higher migration rates. We investigate the influence of different migration rates, set by the disc's viscosity, on the structure of multi-planet systems growing by pebble accretion via N-body simulations. Planets in low viscosity environments migrate slower due to partial gap opening. Thus systems formed in low viscosity environments tend to have planets trapped in wider resonant configurations (typically 4:3, 3:2 and 2:1), compared to their high viscosity counterparts (mostly 7:6, 5:4 and 4:3 resonances). After gas disc dissipation, the damping forces cease and the systems can undergo instabilities, rearranging their configurations and breaking the resonance chains. The low viscosity discs naturally account for the resonant chains like Trappist-1, TOI-178 and Kepler-223, unlike high viscosity simulations which produce relatively more compact chains. About 95% of our low viscosity resonant chains became unstable, experiencing giant impacts. Dynamical instabilities in our low viscosity simulations are more violent than those of high viscosity simulations due to the effects of leftover external perturbers (P>200 days). About 50% of our final system ended with no planets within 200 days, while all our systems have remaining outer planets. We speculate that this process could be qualitatively consistent with the lack of inner planets in a large fraction of Sun-like stars. Systems produced in low viscosity simulations alone do not match the overall period ratio distribution of observations, but give a better match to the period distributions of chains, which may suggest that systems of super-Earths and mini-Neptunes form in natal discs with a diversity of viscosities.
arXiv
Recently, the Large High-Altitude Air Shower Observatory (LHAASO) collaboration has obtained a measurement of the gamma-ray diffuse emission in the ultra-high energy range, $10-10^3$ TeV after masking the contribution of known sources. The measurement appears to be 2-3 times higher than the gamma-ray signal expected from the hadronic interactions of diffuse cosmic rays with the interstellar medium, potentially suggesting a contribution from unresolved sources. However, estimates of the diffuse emission are affected by large uncertainties that must be accounted for. In this work, we calculate the hadronic gamma-ray diffuse emission including uncertainties in the gas content of the Galactic disk, in the energy and spatial distribution of cosmic rays as well as in the hadronic interaction cross-section. We show that the LHAASO data above $\sim 30$ TeV are consistent with the gamma-ray diffuse emission model when all these uncertainties are taken into account. This implies that, with the current data in this energy range, there is no need to invoke a cosmic ray spectral variation toward the Galactic center, nor a dominant contribution from unresolved sources.
arXiv
A large host of scientific journals and conferences solicit peer reviews from multiple reviewers for the same submission, aiming to gather a broader range of perspectives and mitigate individual biases. In this work, we reflect on the role of diversity in the slate of reviewers assigned to evaluate a submitted paper as a factor in diversifying perspectives and improving the utility of the peer-review process. We propose two measures for assessing review utility: review coverage -- reviews should cover most contents of the paper -- and review redundancy -- reviews should add information not already present in other reviews. We hypothesize that reviews from diverse reviewers will exhibit high coverage and low redundancy. We conduct a causal study of different measures of reviewer diversity on review coverage and redundancy using observational data from a peer-reviewed conference with approximately 5,000 submitted papers. Our study reveals disparate effects of different diversity measures on review coverage and redundancy. Our study finds that assigning a group of reviewers that are topically diverse, have different seniority levels, or have distinct publication networks leads to broader coverage of the paper or review criteria, but we find no evidence of an increase in coverage for reviewer slates with reviewers from diverse organizations or geographical locations. Reviewers from different organizations, seniority levels, topics, or publications networks (all except geographical diversity) lead to a decrease in redundancy in reviews. Furthermore, publication network-based diversity alone also helps bring in varying perspectives (that is, low redundancy), even within specific review criteria. Our study adopts a group decision-making perspective for reviewer assignments in peer review and suggests dimensions of diversity that can help guide the reviewer assignment process.
arXiv
Graph augmentation is a fundamental and well-studied problem that arises in network optimization. We consider a new variant of this model motivated by reconfigurable communication networks. In this variant, we consider a given physical network and the measured communication demands between the nodes. Our goal is to augment the given physical network with a matching, so that the shortest path lengths in the augmented network, weighted with the demands, are minimal.We prove that this problem is NP-hard, even if the physical network is a cycle. We then use results from demand-aware network design to provide a constant-factor approximation algorithm for adding a matching in case that only a few nodes in the network cause almost all the communication. For general real-world communication patterns, we design and evaluate a series of heuristics that can deal with arbitrary graphs as the underlying network structure. Our algorithms are validated experimentally using real-world traces (from e.g., Facebook) of data centers.
arXiv
Recent advances in Large Language Models (LLMs) have enabled them to overcome their context window limitations, and demonstrate exceptional retrieval and reasoning capacities on longer context. Quesion-answering systems augmented with Long-Context Language Models (LCLMs) can automatically search massive external data and incorporate it into their contexts, enabling faithful predictions and reducing issues such as hallucinations and knowledge staleness. Existing studies targeting LCLMs mainly concentrate on addressing the so-called lost-in-the-middle problem or improving the inference effiencicy, leaving their privacy risks largely unexplored. In this paper, we aim to bridge this gap and argue that integrating all information into the long context makes it a repository of sensitive information, which often contains private data such as medical records or personal identities. We further investigate the membership privacy within LCLMs external context, with the aim of determining whether a given document or sequence is included in the LCLMs context. Our basic idea is that if a document lies in the context, it will exhibit a low generation loss or a high degree of semantic similarity to the contents generated by LCLMs. We for the first time propose six membership inference attack (MIA) strategies tailored for LCLMs and conduct extensive experiments on various popular models. Empirical results demonstrate that our attacks can accurately infer membership status in most cases, e.g., 90.66% attack F1-score on Multi-document QA datasets with LongChat-7b-v1.5-32k, highlighting significant risks of membership leakage within LCLMs input contexts. Furthermore, we examine the underlying reasons why LCLMs are susceptible to revealing such membership information.
arXiv
We elaborate on and further develop an approach to determining the teleparallel analogue of spacetimes in General Relativity (GR) by studying the Teleparallel analogue of pp-Wave (TppW) spacetimes. This relies on using the fact that these solutions belong to the Vanishing Scalar Invariant (VSI) subclass for which the explicit forms of the frame and spin-connection are known. By identifying the pp-wave (ppW) metric within this class, we are able to use frame based symmetry methods and the Cartan-Karlhede (CK) algorithm to determine the necessary form for the frame. Through this analysis we find two overlooked solutions that are permitted in teleparallel gravity (TPG) and in GR.
arXiv
Let $k$ be an uncountable algebraically closed filed of positive characteristic and let $S_0$ be a connected smooth projective surface over $k$. We extend the theorem on the Gysin kernel from [28, Theorem 5.1] to also be true over $k$, where it was proved over $\mathbb{C}$. This is done by showing that almost all results still hold true over $k$ via the same argument or by using \'{e}tale base arguments and then use a lift with the Comparison theorem [22, Theorems 21.1 & 20.5] as needed.
arXiv
In this study, we introduced a simple yet innovative method to trigger turbulence in a channel flow to achieve statistically stationary flow conditions. We compare this new method based on synthetically generated three-dimensional turbulence with two other well-established methods, namely, linear profile superposed with random noise and descending counter-rotating vortices and log-law profile superposed with random noise and descending counter-rotating vortices. We found that synthetically generated three-dimensional turbulence provides a computationally cheap and effective way to reduce simulation spin-up to achieve statistically stationary flow conditions when a precursor turbulent initial condition is not available. At a one-time cost of less than 1 CPU hour to generate the synthetic turbulent initial condition, the flow becomes statistically stationary within 3 eddy turnovers for all the parameters of interest in wall-bounded pressure-driven channel flow simulations when compared to other alternatives that can take more than 10 eddy turnovers resulting in substantial savings in the computational cost.
arXiv
In this paper, we prove several new infinite families of Ramanujan--like congruences satisfied by the coefficients of the generating function $U_t(a,q)$ which is an extension of MacMahon's generalized sum-of-divisors function. As a by-product, we also show that, for all $n\geq 0$, $\overline{B}_3(15n+7)\equiv 0 \pmod{5}$ where $\overline{B}_3(n)$ is the number of almost $3$-regular overpartitions of $n$.
arXiv
Bell scenarios are multipartite scenarios that exclude any communication between parties. This constraint leads to a strict hierarchy of correlation sets in such scenarios, namely, classical, quantum, and nonsignaling. However, without any constraints on communication between the parties, they can realize arbitrary correlations by exchanging only classical systems. Here we consider a multipartite scenario where the parties can engage in at most a single round of communication, i.e., each party is allowed to receive a system once, implement any local intervention on it, and send out the resulting system once. While no global assumption about causal relations between parties is assumed in this scenario, we do make a causal assumption local to each party, i.e., the input received by it causally precedes the output it sends out. We then introduce antinomicity, a notion of nonclassicality for correlations in such scenarios, and prove the existence of a strict hierarchy of correlation sets classified by their antinomicity. Antinomicity serves as a generalization of Bell nonlocality: when all the parties discard their output systems (i.e., in a nonsignaling scenario), it is mathematically equivalent to Bell nonlocality. Like Bell nonlocality, it can be understood as an instance of fine-tuning, one that is necessary in any classical model of cyclic causation that avoids time-travel antinomies but allows antinomic correlations. Furthermore, antinomicity resolves a long-standing puzzle, i.e., the failure of causal inequality violations as device-independent witnesses of nonclassicality. Antinomicity implies causal inequality violations, but not conversely.
arXiv
The rapid advancement of face forgery techniques has introduced a growing variety of forgeries. Incremental Face Forgery Detection (IFFD), involving gradually adding new forgery data to fine-tune the previously trained model, has been introduced as a promising strategy to deal with evolving forgery methods. However, a naively trained IFFD model is prone to catastrophic forgetting when new forgeries are integrated, as treating all forgeries as a single ''Fake" class in the Real/Fake classification can cause different forgery types overriding one another, thereby resulting in the forgetting of unique characteristics from earlier tasks and limiting the model's effectiveness in learning forgery specificity and generality. In this paper, we propose to stack the latent feature distributions of previous and new tasks brick by brick, $\textit{i.e.}$, achieving $\textbf{aligned feature isolation}$. In this manner, we aim to preserve learned forgery information and accumulate new knowledge by minimizing distribution overriding, thereby mitigating catastrophic forgetting. To achieve this, we first introduce Sparse Uniform Replay (SUR) to obtain the representative subsets that could be treated as the uniformly sparse versions of the previous global distributions. We then propose a Latent-space Incremental Detector (LID) that leverages SUR data to isolate and align distributions. For evaluation, we construct a more advanced and comprehensive benchmark tailored for IFFD. The leading experimental results validate the superiority of our method.
arXiv
From an architectural perspective with the main goal of reducing the effective traffic load in the network and thus gaining more operational efficiency, optical networks have been essentially remained the same in the recent two decades since the year 2000s with the success and then dominance of optical-bypass mode. In the optical-bypass-enabled network, the add/drop and cross-connect functions constitute the fundamental operations in handling the traffic at the optical layer, whose the underlying principle lies in the fact that in cross-connecting in-transit lightpaths over an intermediate node, such lightpaths must be guarded from each other in a certain dimension, be it the time, frequency or spatial domain, to avoid interference, which is treated as destructive. In view of the rapid progresses in the realm of optical computing enabling the precisely controlled interference between optical channels for various computing capabilities, we envision a different perspective to turn the long-established wisdom in optical-bypass network around by putting the optical channel interference to a good use, resulting into the so-called optical-computing-enabled network. This paper presents two illustrative examples based on the optical aggregation and optical XOR operations which have been progressively maturing and thus, could be feasibly integrated into the current legacy infrastructure with possibly minimal disruptions. We then propose a detailed case study in formulating and solving the network coding-enabled optical networks, demonstrating the efficacy of the optical-computing-enabled network, and highlighting the unique challenges tied with greater complexities in network design problems, compared to optical-bypass counterpart
arXiv
Recent advancements in medical image analysis have predominantly relied on Convolutional Neural Networks (CNNs), achieving impressive performance in chest X-ray classification tasks, such as the 92% AUC reported by AutoThorax-Net and the 88% AUC achieved by ChexNet in classifcation tasks. However, in the medical field, even small improvements in accuracy can have significant clinical implications. This study explores the application of Vision Transformers (ViT), a state-of-the-art architecture in machine learning, to chest X-ray analysis, aiming to push the boundaries of diagnostic accuracy. I present a comparative analysis of two ViT-based approaches: one utilizing full chest X-ray images and another focusing on segmented lung regions. Experiments demonstrate that both methods surpass the performance of traditional CNN-based models, with the full-image ViT achieving up to 97.83% accuracy and the lung-segmented ViT reaching 96.58% accuracy in classifcation of diseases on three label and AUC of 94.54% when label numbers are increased to eight. Notably, the full-image approach showed superior performance across all metrics, including precision, recall, F1 score, and AUC-ROC. These findings suggest that Vision Transformers can effectively capture relevant features from chest X-rays without the need for explicit lung segmentation, potentially simplifying the preprocessing pipeline while maintaining high accuracy. This research contributes to the growing body of evidence supporting the efficacy of transformer-based architectures in medical image analysis and highlights their potential to enhance diagnostic precision in clinical settings.
arXiv
Nuclear magnetic resonance instruments are becoming available to the do-it-yourself community. The challenges encountered in the endeavor to build a magnetic resonance imaging instrument from scratch were confronted in a four-day hackathon at Singapore University of Technology and Design in spring 2024. One day was devoted to educational lectures and three days to system construction and testing. Seventy young researchers from all parts of the world formed six teams focusing on magnet, gradient coil, RF coil, console, system integration, and design, which together produced a working MRI instrument in three days. The different steps, encountered challenges, and their solutions are reported.
arXiv
We describe an algorithm to compute the stable multiplicity of a family of irreducible representations in the cohomology of ordered configuration space of the plane. Using this algorithm, we compute the stable multiplicities of all families of irreducibles given by Young diagrams with $23$ boxes or less up to cohomological degree $50$. In particular, this determines the stable cohomology in cohomological degrees $0 \leq i \leq 11$. We prove related qualitative results and formulate some conjectures.
arXiv
Amongst the issues plaguing the Standard Model (SM) are questions pertaining to neutrino masses and mixings, the anomalous magnetic moment of the electron and muon and the problem of a suitable dark matter (DM) candidate. All the three issues can be addressed at once by extending the SM with two generations of vector-like fermions and an inert scalar doublet, all odd under a Z2 symmetry. The light neutrino masses and mixings are generated radiatively while maintaining consistency with bounds on lepton flavor violation. Loop diagrams with the very same fields also serve to explain the anomalous magnetic moments. Similarly, the correct dark matter relic abundance is reproduced without coming into conflict with direct detection constraints, or those from big bang nucleosynthesis or the cosmic microwave observations. Finally, prospective signatures at the LHC are discussed.
arXiv
Machine learning is an important tool for analyzing high-dimension hyperspectral data; however, existing software solutions are either closed-source or inextensible research products. In this paper, we present cuvis.ai, an open-source and low-code software ecosystem for data acquisition, preprocessing, and model training. The package is written in Python and provides wrappers around common machine learning libraries, allowing both classical and deep learning models to be trained on hyperspectral data. The codebase abstracts processing interconnections and data dependencies between operations to minimize code complexity for users. This software package instantiates nodes in a directed acyclic graph to handle all stages of a machine learning ecosystem, from data acquisition, including live or static data sources, to final class assignment or property prediction. User-created models contain convenient serialization methods to ensure portability and increase sharing within the research community. All code and data are available online: https://github.com/cubert-hyperspectral/cuvis.ai
arXiv
In this paper, we propose a conceptual framework for personalized brain-computer interface (BCI) applications, which can offer an enhanced user experience by customizing services to individual preferences and needs, based on endogenous electroencephalography (EEG) paradigms including motor imagery (MI), speech imagery (SI), and visual imagery. The framework includes two essential components: user identification and intention classification, which enable personalized services by identifying individual users and recognizing their intended actions through EEG signals. We validate the feasibility of our framework using a private EEG dataset collected from eight subjects, employing the ShallowConvNet architecture to decode EEG features. The experimental results demonstrate that user identification achieved an average classification accuracy of 0.995, while intention classification achieved 0.47 accuracy across all paradigms, with MI demonstrating the best performance. These findings indicate that EEG signals can effectively support personalized BCI applications, offering robust identification and reliable intention decoding, especially for MI and SI.
arXiv
This paper presents an accelerated spherical K-means clustering algorithm for large-scale and high-dimensional sparse document data sets. We design an algorithm working in an architecture-friendly manner (AFM), which is a procedure of suppressing performance-degradation factors such as the numbers of instructions, branch mispredictions, and cache misses in CPUs of a modern computer system. For the AFM operation, we leverage unique universal characteristics (UCs) of a data-object and a cluster's mean set, which are skewed distributions on data relationships such as Zipf's law and a feature-value concentration phenomenon. The UCs indicate that the most part of the number of multiplications for similarity calculations is executed regarding terms with high document frequencies (df) and the most part of a similarity between an object- and a mean-feature vector is obtained by the multiplications regarding a few high mean-feature values. Our proposed algorithm applies an inverted-index data structure to a mean set, extracts the specific region with high-df terms and high mean-feature values in the mean-inverted index by newly introduced two structural parameters, and exploits the index divided into three parts for efficient pruning. The algorithm determines the two structural parameters by minimizing the approximate number of multiplications related to that of instructions, reduces the branch mispredictions by sharing the index structure including the two parameters with all the objects, and suppressing the cache misses by keeping in the caches the frequently used data in the foregoing specific region, resulting in working in the AFM. We experimentally demonstrate that our algorithm efficiently achieves superior speed performance in large-scale documents compared with algorithms using the state-of-the-art techniques.
arXiv
Quantum secure direct communication (QSDC) enables the message sender to directly send secure messages to the receiver through the quantum channel without keys. Device-independent (DI) and measurement-device-independent (MDI) QSDC protocols can enhance QSDC's practical security in theory. DI QSDC requires extremely high global detection efficiency and has quite low secure communication distance. DI and MDI QSDC both require high-quality entanglement. Current entanglement sources prepare entangled photon pairs with low efficiency, largely reducing their practical communication efficiency. In the paper, we propose a single-photon-based receiver-device-independent (RDI) QSDC protocol. It only relies on the trusted single-photon source, which is nearly on-demand under current technology, and treats all the receiving devices in both communication parties as ``black-boxes''. The parties ensure the message security only from the observed statistics. We develop a numerical method to simulate its performance in practical noisy communication situation. RDI QSDC provides the same security level as MDI QSDC. Compared with DI and MDI QSDC, RDI QSDC has some advantages. First, it uses the single-photon source and single-photon measurement, which makes it obtain the practical communication efficiency about 3415 times of that in DI QSDC and easy to implement. The whole protocol is feasible with current technology. Second, it has higher photon loss robustness and noise tolerance than DI QSDC, which enables it to have a secure communication distance about 26 times of that in DI QSDC. Based on above features, the RDI QSDC protocol makes it possible to achieve highly-secure and high-efficient QSDC in the near future.
arXiv
It is proved that the Chebyshev's method applied to an entire function $f$ is a rational map if and only if $f(z) = p(z) e^{q(z)}$, for some polynomials $p$ and $q$. These are referred to as rational Chebyshev maps, and their fixed points are discussed in this article. It is seen that $\infty$ is a parabolic fixed point with multiplicity one bigger than the degree of $q$. Considering $q(z)=p(z)^n+c$, where $p$ is a linear polynomial, $n \in \mathbb{N}$ and $c$ is a non-zero constant, we show that the Chebyshev's method applied to $pe^q$ is affine conjugate to that applied to $z e^{z^n}$. We denote this by $C_n$. All the finite extraneous fixed points of $C_n$ are shown to be repelling. The Julia set $\mathcal{J}(C_n)$ of $C_n$ is found to be preserved under rotations of order $n$ about the origin. For each $n$, the immediate basin of $0$ is proved to be simply connected. For all $n \leq 16$, we prove that $\mathcal{J}(C_n)$ is connected. The Newton's method applied to $ze^{z^n}$ is found to be conjugate to a polynomial, and its dynamics is also completely determined.
arXiv
Currently, deep learning-based instance segmentation for various applications (e.g., Agriculture) is predominantly performed using a labor-intensive process involving extensive field data collection using sophisticated sensors, followed by careful manual annotation of images, presenting significant logistical and financial challenges to researchers and organizations. The process also slows down the model development and training process. In this study, we presented a novel method for deep learning-based instance segmentation of apples in commercial orchards that eliminates the need for labor-intensive field data collection and manual annotation. Utilizing a Large Language Model (LLM), we synthetically generated orchard images and automatically annotated them using the Segment Anything Model (SAM) integrated with a YOLO11 base model. This method significantly reduces reliance on physical sensors and manual data processing, presenting a major advancement in "Agricultural AI". The synthetic, auto-annotated dataset was used to train the YOLO11 model for Apple instance segmentation, which was then validated on real orchard images. The results showed that the automatically generated annotations achieved a Dice Coefficient of 0.9513 and an IoU of 0.9303, validating the accuracy and overlap of the mask annotations. All YOLO11 configurations, trained solely on these synthetic datasets with automated annotations, accurately recognized and delineated apples, highlighting the method's efficacy. Specifically, the YOLO11m-seg configuration achieved a mask precision of 0.902 and a mask mAP@50 of 0.833 on test images collected from a commercial orchard. Additionally, the YOLO11l-seg configuration outperformed other models in validation on 40 LLM-generated images, achieving the highest mask precision and mAP@50 metrics. Keywords: YOLO, SAM, SAMv2, YOLO11, YOLOv11, Segment Anything, YOLO-SAM
arXiv
A \emph{conforming partition} of a rectilinear $ n $-gon\bastien{I change from ``a polygon'', otherwise $ n $ is not defined.} $ P $ is a partition of $ P $ into rectangles without using Steiner points (i.e., all corners of all rectangles must lie on\bastien{Maybe add: the boundary of} $ P $). The stabbing number of such a partition is the maximum number of rectangles intersected by an axis-aligned segment lying in the interior of $ P $. In this paper, we examine the problem of computing conforming partitions with low stabbing number. We show that computing a conforming partition with stabbing number at most~$ 4 $ is $ NP $-hard, which strengthens a previously known hardness result [Durocher \& Mehrabi, Theor. Comput. Sci. 689: 157-168 (2017)] and eliminates the possibility for fixed-parameter-tractable algorithms parameterized by the stabbing number unless $ P = NP $. In contrast, we give (i) an $ O ( n \log n ) $-time\bastien{Reviewer request: changed from "linearithmic".} algorithm to decide whether a conforming partition with stabbing number~$ 2 $ exists, (ii) a fixed-parameter-tractable algorithm parameterized by both the stabbing number and treewidth of the pixelation of the polygon, and (iii) a fixed-parameter-tractable algorithm parameterized by the stabbing number for simple polygons in general position.
arXiv
We consider estimating the shared mean of a sequence of heavy-tailed random variables taking values in a Banach space. In particular, we revisit and extend a simple truncation-based mean estimator by Catoni and Giulini. While existing truncation-based approaches require a bound on the raw (non-central) second moment of observations, our results hold under a bound on either the central or non-central $p$th moment for some $p > 1$. In particular, our results hold for distributions with infinite variance. The main contributions of the paper follow from exploiting connections between truncation-based mean estimation and the concentration of martingales in 2-smooth Banach spaces. We prove two types of time-uniform bounds on the distance between the estimator and unknown mean: line-crossing inequalities, which can be optimized for a fixed sample size $n$, and non-asymptotic law of the iterated logarithm type inequalities, which match the tightness of line-crossing inequalities at all points in time up to a doubly logarithmic factor in $n$. Our results do not depend on the dimension of the Banach space, hold under martingale dependence, and all constants in the inequalities are known and small.
arXiv
In Radio Super Novae (RSNe) a magnetic field of $(B \, \times \, r) \, = \, 10^{16.0 \pm 0.12} \, {\rm Gauss \, \times \, cm}$ is observed; these are the same numbers for Blue Super Giant (BSG) star explosions as for Red Super Giant (RSG) star explosions, despite their very different wind properties. The EHT data for M87 as well for low power radio galaxies all show consistency with just this value of the quantity $(B \, \times \, r )$, key for angular momentum and energy transport, and can be derived from the radio jet data. We interpret this as a property of the near surroundings of a black hole (BH) at near maximal rotation, independent of BH mass. In the commonly used green onion model, in which a $2 \, \pi$ flow changes over to a jet flow we interpret this as a wind emanating from the BH/accretion disk system and its surroundings. Near the BH collisions in the wind can produce a large fraction of anti-protons. In this scenario the cosmic Ray (CR) population from the wind/jet is proposed to be visible as EeV protons and anti-protons in the CR data to EeV energy, with a $E^{-7/3}$ spectrum. This can be connected to a concept of inner and outer Penrose zones in the ergo-region. The observed numbers for the magnetic field imply the Planck time as the governing time scale: A BH rotating near maximum can accept a proton per log bin of energy in an extended spectrum with the associated pions every Planck time.
arXiv
Aggregators of distributed energy resources are increasingly encouraged to participate in wholesale market bidding. However, the delivery of the power they are awarded can result in over-voltage or congestion issues within the distribution network (DN). The opportunity to lease energy storage from the utility that manages the DN provides the aggregator with a means to mitigate these issues, while also benefiting the utility in terms of additional lease revenue. Nevertheless, this leasing opportunity considerably complicates the aggregator's offer-making process, as it requires the consideration of market uncertainties, uncertain power injection at DN buses, and the strategic interactions between the aggregator and the utility. This paper presents a stochastic Stackelberg game model that effectively captures the interactions between the aggregator and the utility, ensuring DN security across all potential uncertainty scenarios. Furthermore, in light of the privacy concerns of both the aggregator and the utility, two distributed solution methods are proposed. The first method follows a traditional predict-then-optimize framework and has been validated to achieve the game equilibrium. The second method employs an end-to-end framework, which has been empirically shown to yield superior economic results. Case studies conducted on 69 and 533-bus DNs illustrate the efficacy of the proposed methods.
arXiv
Convection in planets and stars is predicted to occur in the "ultimate regime'' of diffusivity-free, rapidly rotating turbulence, in which flows are characteristically unaffected by viscous and thermal diffusion. Boundary layer diffusion, however, has historically hindered experimental study of this regime. Here, we utilize the boundary-independent oscillatory thermal-inertial mode of rotating convection to realize the diffusivity-free scaling in liquid metal laboratory experiments. This oscillatory style of convection arises in rotating liquid metals (low Prandtl number fluids) and is driven by the temperature gradient in the fluid bulk, thus remaining independent of diffusive boundary dynamics. We triply verify the existence of the diffusivity-free regime via measurements of heat transfer efficiency $Nu$, dimensionless flow velocities $Re$, and internal temperature anomalies $\theta$, all of which are in quantitative agreement with planar asymptotically-reduced models. Achieving the theoretical diffusivity-free scalings in desktop-sized laboratory experiments provides the validation necessary to extrapolate and predict the convective flows in remote geophysical and astrophysical systems.
arXiv
Pre-trained vision-language models provide a robust foundation for efficient transfer learning across various downstream tasks. In the field of video action recognition, mainstream approaches often introduce additional parameter modules to capture temporal information. While the increased model capacity brought by these additional parameters helps better fit the video-specific inductive biases, existing methods require learning a large number of parameters and are prone to catastrophic forgetting of the original generalizable knowledge. In this paper, we propose a simple yet effective Multi-modal Spatio-Temporal Adapter (MSTA) to improve the alignment between representations in the text and vision branches, achieving a balance between general knowledge and task-specific knowledge. Furthermore, to mitigate over-fitting and enhance generalizability, we introduce a spatio-temporal description-guided consistency constraint. This constraint involves feeding template inputs (i.e., ``a video of $\{\textbf{cls}\}$'') into the trainable language branch, while LLM-generated spatio-temporal descriptions are input into the pre-trained language branch, enforcing consistency between the outputs of the two branches. This mechanism prevents over-fitting to downstream tasks and improves the distinguishability of the trainable branch within the spatio-temporal semantic space. We evaluate the effectiveness of our approach across four tasks: zero-shot transfer, few-shot learning, base-to-novel generalization, and fully-supervised learning. Compared to many state-of-the-art methods, our MSTA achieves outstanding performance across all evaluations, while using only 2-7\% of the trainable parameters in the original model. Code will be avaliable at https://github.com/chenhaoxing/ETL4Video.
arXiv
Most robotics applications are typically accompanied with safety restrictions that need to be satisfied with a high degree of confidence even in environments under uncertainty. Controlling the state distribution of a system and enforcing such specifications as distribution constraints is a promising approach for meeting such requirements. In this direction, covariance steering (CS) is an increasingly popular stochastic optimal control (SOC) framework for designing safe controllers via explicit constraints on the system covariance. Nevertheless, a major challenge in applying CS methods to systems with the nonlinear dynamics and chance constraints common in robotics is that the approximations needed are conservative and highly sensitive to the point of approximation. This can cause sequential convex programming methods to converge to poor local minima or incorrectly report problems as infeasible due to shifting constraints. This paper presents a novel algorithm for solving chance-constrained nonlinear CS problems that directly addresses this challenge. Specifically, we propose an operator-splitting approach that temporarily separates the main problem into subproblems that can be solved in parallel. The benefit of this relaxation lies in the fact that it does not require all iterates to satisfy all constraints simultaneously prior to convergence, thus enhancing the exploration capabilities of the algorithm for finding better solutions. Simulation results verify the ability of the proposed method to find higher quality solutions under stricter safety constraints than standard methods on a variety of robotic systems. Finally, the applicability of the algorithm on real systems is confirmed through hardware demonstrations.
arXiv
In this article, we study the FitzHugh-Nagumo $(1,1)$--fast-slow system where the vector fields associated to the slow/fast equations come from the reduction of the Hodgin-Huxley model for the nerve impulse. After deriving dynamical properties of the singular and regular cases, we perform a bifurcation analysis and we investigate how the parameters (of the affine slow equation) impact the dynamics of the system. The study of codimension one bifurcations and the numerical locus of canards concludes this case-study. All theoretical results are numerically illustrated.
arXiv
Let $p$ be an odd prime and $k$ be an algebraically closed field with characteristic $p$. Booher and Cais showed that the $a$-number of a $\mathbb Z/p \mathbb Z$-Galois cover of curves $\phi: Y \to X$ must be greater than a lower bound determined by the ramification of $\phi$. In this paper, we provide evidence that the lower bound is optimal by finding examples of Artin-Schreier curves that have $a$-number equal to its lower bound for all $p$. Furthermore we use formal patching to generate infinite families of Artin-Schreier curves with $a$-number equal to the lower bound in any characteristic.
arXiv
Because of the rapid development and increasing public availability of Generative Artificial Intelligence (GenAI) models and tools, educational institutions and educators must immediately reckon with the impact of students using GenAI. There is limited prior research on computing students' use and perceptions of GenAI. In anticipation of future advances and evolutions of GenAI, we capture a snapshot of student attitudes towards and uses of yet emerging GenAI, in a period of time before university policies had reacted to these technologies. We surveyed all computer science majors in a small engineering-focused R1 university in order to: (1) capture a baseline assessment of how GenAI has been immediately adopted by aspiring computer scientists; (2) describe computing students' GenAI-related needs and concerns for their education and careers; and (3) discuss GenAI influences on CS pedagogy, curriculum, culture, and policy. We present an exploratory qualitative analysis of this data and discuss the impact of our findings on the emerging conversation around GenAI and education.
arXiv
In a system of two-dimensional electrons, a combination of broken symmetry, interactions, and nontrivial topology can conspire to give rise to a nonlinear transport regime, where electric current density scales as the square of electric field. This regime has become a venue for exciting discoveries such as the nonlinear Hall effect and diode-like nonreciprocal transport. However, interpretation of experimental data is challenging in the nonlinear regime as DC transport is described by a rank-3 conductivity tensor with 6 free parameters. Here, we resolve this challenge by analytically solving for the nonlinear potential distribution across the disk sample for an arbitrary linear and nonlinear conductivity tensors. This allows us to unambiguously extract all components of the nonlinear tensor from experimental measurement. Using this novel tool, we identify giant nonlinear Hall effect in Bernal bilayer graphene. Our methodology provides the first systematic framework for interpreting nonlinear transport and uncovers a new route towards understanding quasi-2D materials.
arXiv
This work investigates the self-organization of multi-agent systems into closed trajectories, a common requirement in unmanned aerial vehicle (UAV) surveillance tasks. In such scenarios, smooth, unbiased control signals save energy and mitigate mechanical strain. We propose a decentralized control system architecture that produces a globally stable emergent structure from local observations only; there is no requirement for agents to share a global plan or follow prescribed trajectories. Central to our approach is the formulation of an injective virtual embedding induced by rotations from the actual agent positions. This embedding serves as a structure-preserving map around which all agent stabilize their relative positions and permits the use of well-established linear control techniques. We construct the embedding such that it is topologically equivalent to the desired trajectory (i.e., a homeomorphism), thereby preserving the stability characteristics. We demonstrate the versatility of this approach through implementation on a swarm of Quanser QDrone quadcopters. Results demonstrate the quadcopters self-organize into the desired trajectory while maintaining even separation.
arXiv
For a positive integer $k \ge 1$, a $k$-star ($k^+$-star, $k^-$-star, respectively) is a connected graph containing a degree-$\ell$ vertex and $\ell$ degree-$1$ vertices, where $\ell = k$ ($\ell \ge k$, $1 \le \ell \le k$, respectively). The $k^+$-star packing problem is to cover as many vertices of an input graph $G$ as possible using vertex-disjoint $k^+$-stars in $G$; and given $k > t \ge 1$, the $k^-/t$-star packing problem is to cover as many vertices of $G$ as possible using vertex-disjoint $k^-$-stars but no $t$-stars in $G$. Both problems are NP-hard for any fixed $k \ge 2$. We present a $(1 + \frac {k^2}{2k+1})$- and a $\frac 32$-approximation algorithms for the $k^+$-star packing problem when $k \ge 3$ and $k = 2$, respectively, and a $(1 + \frac 1{t + 1 + 1/k})$-approximation algorithm for the $k^-/t$-star packing problem when $k > t \ge 2$. They are all local search algorithms and they improve the best known approximation algorithms for the problems, respectively.
arXiv
We consider the problem of allocating heterogeneous and indivisible goods among strategic agents, with preferences over subsets of goods, when there is no medium of exchange. This model captures the well studied problem of fair allocation of indivisible goods. Serial-quota mechanisms are allocation mechanisms where there is a predefined order over agents, and each agent in her turn picks a predefined number of goods from the remaining goods. These mechanisms are clearly strategy-proof, non-bossy, and neutral. Are there other mechanisms with these properties? We show that for important classes of strict ordinal preferences (as lexicographic preferences, and as the class of all strict preferences), these are the only mechanisms with these properties. Importantly, unlike previous work, we can prove the claim even for mechanisms that are not Pareto-efficient. Moreover, we generalize these results to preferences that are cardinal, including any valuation class that contains additive valuations. We then derive strong negative implications of this result on truthful mechanisms for fair allocation of indivisible goods to agents with additive valuations.
arXiv
We participated in track 2 of the VoiceMOS Challenge 2024, which aimed to predict the mean opinion score (MOS) of singing samples. Our submission secured the first place among all participating teams, excluding the official baseline. In this paper, we further improve our submission and propose a novel Pitch-and-Spectrum-aware Singing Quality Assessment (PS-SQA) method. The PS-SQA is designed based on the self-supervised-learning (SSL) MOS predictor, incorporating singing pitch and spectral information, which are extracted using pitch histogram and non-quantized neural codec, respectively. Additionally, the PS-SQA introduces a bias correction strategy to address prediction biases caused by low-resource training samples, and employs model fusion technology to further enhance prediction accuracy. Experimental results confirm that our proposed PS-SQA significantly outperforms all competing systems across all system-level metrics, confirming its strong sing quality assessment capabilities.
arXiv
We investigate the degrees of freedom of New General Relativity. This theory is a three-parameter theory and is classified into nine irreducible types according to the rotation symmetry of $SO(3)$ on each leaf of ADM-foliation. In the previous work~[{\it 2410.15056[gr-qc]}], we investigated the degrees of freedom in types of NGR that are interests for describing gravity: Type 2, Type 3, Type 5, and Type 8. In this work, we focus on unveiling those numbers in all other types to complete the analysis of NGR. After providing the Hamiltonian formulation of NGR, we perform the analysis on Type 4, Type 7, and Type 9 according to the method that is provided in the previous work~[{\it 2410.15056[gr-qc]}]. Then we unveil that the degrees of freedom of Type 4, Type 7, and Type 9 are five, null, and three, respectively. Type 4 and Type 9 have second-class constraint densities only. Type 7 has first-class constraint densities only, but which is over constraint. In every type, no bifurcation occurs unlikely to Type 8 in the previous work~[2410.15056[gr-qc]]. Finally, we summarize this work and give a concluding remark for this series of works.
arXiv
Abundant geomorphological and geochemical evidence of liquid water on the surface of early Mars during the late Noachian and early Hesperian periods needs to be reconciled with a fainter young Sun. While a dense CO2 atmosphere and related warming mechanisms are potential solutions to the early Mars climate problem, further investigation is warranted. Here, we complete a comprehensive survey of the warming potential of all known greenhouse gases and perform detailed calculations for 15 different minor gas species under early Martian conditions. We find that of these 15 species, H2O2, HNO3, NH3, SO2, and C2H4 cause significant greenhouse warming at concentrations of ~0.1 ppmv or greater. However, the most highly effective greenhouse gas species also tend to be more condensable, soluble and vulnerable to photolytic destruction. To provide a reference for future atmospheric evolution and photochemical studies, we have made our warming potential database freely available online.
arXiv
The accurate segmentation of retinal blood vessels plays a crucial role in the early diagnosis and treatment of various ophthalmic diseases. Designing a network model for this task requires meticulous tuning and extensive experimentation to handle the tiny and intertwined morphology of retinal blood vessels. To tackle this challenge, Neural Architecture Search (NAS) methods are developed to fully explore the space of potential network architectures and go after the most powerful one. Inspired by neuronal diversity which is the biological foundation of all kinds of intelligent behaviors in our brain, this paper introduces a novel and foundational approach to neural network design, termed ``neuron programming'', to automatically search neuronal types into a network to enhance a network's representation ability at the neuronal level, which is complementary to architecture-level enhancement done by NAS. Additionally, to mitigate the time and computational intensity of neuron programming, we develop a hypernetwork that leverages the search-derived architectural information to predict optimal neuronal configurations. Comprehensive experiments validate that neuron programming can achieve competitive performance in retinal blood segmentation, demonstrating the strong potential of neuronal diversity in medical image analysis.
arXiv
In a setting where segmentation models have to be built for multiple datasets, each with its own corresponding label set, a straightforward way is to learn one model for every dataset and its labels. Alternatively, multi-task architectures with shared encoders and multiple segmentation heads or shared weights with compound labels can also be made use of. This work proposes a novel label sharing framework where a shared common label space is constructed and each of the individual label sets are systematically mapped to the common labels. This transforms multiple datasets with disparate label sets into a single large dataset with shared labels, and therefore all the segmentation tasks can be addressed by learning a single model. This eliminates the need for task specific adaptations in network architectures and also results in parameter and data efficient models. Furthermore, label sharing framework is naturally amenable for incremental learning where segmentations for new datasets can be easily learnt. We experimentally validate our method on various medical image segmentation datasets, each involving multi-label segmentation. Furthermore, we demonstrate the efficacy of the proposed method in terms of performance and incremental learning ability vis-a-vis alternative methods.
arXiv
The coefficient algebra of a finite-dimensional Lie algebra with respect to a faithful representation is defined as the subalgebra generated by all coefficients of the corresponding characteristic polynomial. We establish a connection between classical invariant theory and the coefficient algebras of finite-dimensional complex Lie algebras. Specifically, we prove that with respect to any symmetric power of the standard representation: (1) the coefficient algebra of the upper triangular solvable complex Lie algebra is isomorphic to the algebra of symmetric polynomials; (2) the coefficient algebra of the general linear complex Lie algebra is the invariant ring of the general linear group with the conjugacy action on the full space of matrices; and (3) the coefficient algebra of the special linear complex Lie algebra can be generated by classical trace functions. As an application, we exactly exhibit the characteristic polynomial of the special linear complex Lie algebra.
arXiv
Let $M_n$ be the algebra of $n \times n$ complex matrices and $\mathcal{T}_n \subseteq M_n$ the corresponding upper-triangular subalgebra. In their influential work, Petek and \v{S}emrl characterize Jordan automorphisms of $M_n$ and $\mathcal{T}_n$, when $n \geq 3$, as (injective in the case of $\mathcal{T}_n$) continuous commutativity and spectrum preserving maps $\phi : M_n \to M_n$ and $\phi : \mathcal{T}_n \to \mathcal{T}_n$. Recently, in a joint work with Petek, the authors extended this characterization to the maps $\phi : \mathcal{A} \to M_n$, where $\mathcal{A}$ is an arbitrary subalgebra of $M_n$ that contains $\mathcal{T}_n$. In particular, any such map $\phi$ is a Jordan embedding and hence of the form $\phi(X)=TXT^{-1}$ or $\phi(X)=TX^tT^{-1}$, for some invertible matrix $T\in M_n$. In this paper we further extend the aforementioned results in the context of structural matrix algebras (SMAs), i.e. subalgebras $\mathcal{A}$ of $M_n$ that contain all diagonal matrices. More precisely, we provide both a necessary and sufficient condition for an SMA $\mathcal{A}\subseteq M_n$ such that any injective continuous commutativity and spectrum preserving map $\phi: \mathcal{A} \to M_n$ is necessarily a Jordan embedding. In contrast to the previous cases, such maps $\phi$ no longer need to be multiplicative/antimultiplicative, nor rank-one preservers.
arXiv
Expanding reinforcement learning (RL) to offline domains generates promising prospects, particularly in sectors where data collection poses substantial challenges or risks. Pivotal to the success of transferring RL offline is mitigating overestimation bias in value estimates for state-action pairs absent from data. Whilst numerous approaches have been proposed in recent years, these tend to focus primarily on continuous or small-scale discrete action spaces. Factorised discrete action spaces, on the other hand, have received relatively little attention, despite many real-world problems naturally having factorisable actions. In this work, we undertake a formative investigation into offline reinforcement learning in factorisable action spaces. Using value-decomposition as formulated in DecQN as a foundation, we present the case for a factorised approach and conduct an extensive empirical evaluation of several offline techniques adapted to the factorised setting. In the absence of established benchmarks, we introduce a suite of our own comprising datasets of varying quality and task complexity. Advocating for reproducible research and innovation, we make all datasets available for public use alongside our code base.
arXiv
The prevailing of artificial intelligence-of-things calls for higher energy-efficient edge computing paradigms, such as neuromorphic agents leveraging brain-inspired spiking neural network (SNN) models based on spatiotemporally sparse binary activations. However, the lack of efficient and high-accuracy deep SNN learning algorithms prevents them from practical edge deployments with a strictly bounded cost. In this paper, we propose a spatiotemporal orthogonal propagation (STOP) algorithm to tack this challenge. Our algorithm enables fully synergistic learning of synaptic weights as well as firing thresholds and leakage factors in spiking neurons to improve SNN accuracy, while under a unified temporally-forward trace-based framework to mitigate the huge memory requirement for storing neural states of all time-steps in the forward pass. Characteristically, the spatially-backward neuronal errors and temporally-forward traces propagate orthogonally to and independently of each other, substantially reducing computational overhead. Our STOP algorithm obtained high recognition accuracies of 99.53%, 94.84%, 74.92%, 98.26% and 77.10% on the MNIST, CIFAR-10, CIFAR-100, DVS-Gesture and DVS-CIFAR10 datasets with adequate SNNs of intermediate scales from LeNet-5 to ResNet-18. Compared with other deep SNN training works, our method is more plausible for edge intelligent scenarios where resources are limited but high-accuracy in-situ learning is desired.
arXiv
High annotation costs from hiring or crowdsourcing complicate the creation of large, high-quality datasets needed for training reliable text classifiers. Recent research suggests using Large Language Models (LLMs) to automate the annotation process, reducing these costs while maintaining data quality. LLMs have shown promising results in annotating downstream tasks like hate speech detection and political framing. Building on the success in these areas, this study investigates whether LLMs are viable for annotating the complex task of media bias detection and whether a downstream media bias classifier can be trained on such data. We create annolexical, the first large-scale dataset for media bias classification with over 48000 synthetically annotated examples. Our classifier, fine-tuned on this dataset, surpasses all of the annotator LLMs by 5-9 percent in Matthews Correlation Coefficient (MCC) and performs close to or outperforms the model trained on human-labeled data when evaluated on two media bias benchmark datasets (BABE and BASIL). This study demonstrates how our approach significantly reduces the cost of dataset creation in the media bias domain and, by extension, the development of classifiers, while our subsequent behavioral stress-testing reveals some of its current limitations and trade-offs.
arXiv
The demand for deploying deep convolutional neural networks (DCNNs) on resource-constrained devices for real-time applications remains substantial. However, existing state-of-the-art structured pruning methods often involve intricate implementations, require modifications to the original network architectures, and necessitate an extensive fine-tuning phase. To overcome these challenges, we propose a novel method that, for the first time, incorporates the concepts of charge and electrostatic force from physics into the training process of DCNNs. The magnitude of this force is directly proportional to the product of the charges of the convolution filter and the source filter, and inversely proportional to the square of the distance between them. We applied this electrostatic-like force to the convolution filters, either attracting filters with opposite charges toward non-zero weights or repelling filters with like charges toward zero weights. Consequently, filters subject to repulsive forces have their weights reduced to zero, enabling their removal, while the attractive forces preserve filters with significant weights that retain information. Unlike conventional methods, our approach is straightforward to implement, does not require any architectural modifications, and simultaneously optimizes weights and ranks filter importance, all without the need for extensive fine-tuning. We validated the efficacy of our method on modern DCNN architectures using the MNIST, CIFAR, and ImageNet datasets, achieving competitive performance compared to existing structured pruning approaches.
arXiv
We report the detection of an extreme stellar prominence eruption on the M dwarf LAMOST J044431.62+235627.9, observed through time-domain H$\alpha$ spectroscopy with the Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST). This prominence eruption was accompanied by a superflare lasting over 160.4 minutes. The H$\alpha$ line profile exhibits significant blue-wing enhancement during the impulsive phase and near the flare peak, with a projected bulk blueshift velocity of $-228\pm11$~km~s$^{-1}$ and a maximum blueshift velocity reaching $-605\pm15$~km~s$^{-1}$. Velocity analysis of the eruptive prominence at various heights above the stellar surface indicates that some of the projected ejection velocities along the line of sight exceed the corresponding escape velocities, suggesting a potential coronal mass ejection (CME). The equivalent width (EW) of the H$\alpha$ blue-wing enhancement in this eruption appears to be the largest observed to date and is comparable to the EW of the H$\alpha$ line profile during the quiescent phase of the host star. We performed a two-cloud modeling for the prominence and the associated flare, which suggests that the eruptive prominence has a mass ranging from $1.6 \times 10^{19}~\text{g}$ to $7.2 \times 10^{19}~\text{g}$. More importantly, the mass ratio of the erupting prominence to its host star is the largest among all reported stellar prominence eruptions/CMEs.
arXiv
Subspace clustering seeks to identify subspaces that segment a set of n data points into k (k<<n) groups, which has emerged as a powerful tool for analyzing data from various domains, especially images and videos. Recently, several studies have demonstrated the great potential of subspace clustering models for partitioning vertices in attributed graphs, referred to as SCAG. However, these works either demand significant computational overhead for constructing the nxn self-expressive matrix, or fail to incorporate graph topology and attribute data into the subspace clustering framework effectively, and thus, compromise result quality. Motivated by this, this paper presents two effective and efficient algorithms, S2CAG and M-S2CAG, for SCAG computation. Particularly, S2CAG obtains superb performance through three major contributions. First, we formulate a new objective function for SCAG with a refined representation model for vertices and two non-trivial constraints. On top of that, an efficient linear-time optimization solver is developed based on our theoretically grounded problem transformation and well-thought-out adaptive strategy. We then conduct an in-depth analysis to disclose the theoretical connection of S2CAG to conductance minimization, which further inspires the design of M-S2CAG that maximizes the modularity. Our extensive experiments, comparing S2CAG and M-S2CAG against 17 competitors over 8 benchmark datasets, exhibit that our solutions outperform all baselines in terms of clustering quality measured against the ground truth while delivering high efficiency
arXiv
By the end of 2023, renewable sources cover 63.4% of the total electric power demand of Chile, and in line with the global trend, photovoltaic (PV) power shows the most dynamic increase. Although Chile's Atacama Desert is considered the sunniest place on Earth, PV power production, even in this area, can be highly volatile. Successful integration of PV energy into the country's power grid requires accurate short-term PV power forecasts, which can be obtained from predictions of solar irradiance and related weather quantities. Nowadays, in weather forecasting, the state-of-the-art approach is the use of ensemble forecasts based on multiple runs of numerical weather prediction models. However, ensemble forecasts still tend to be uncalibrated or biased, thus requiring some form of post-processing. The present work investigates probabilistic forecasts of solar irradiance for Regions III and IV in Chile. For this reason, 8-member short-term ensemble forecasts of solar irradiance for calendar year 2021 are generated using the Weather Research and Forecasting (WRF) model, which are then calibrated using the benchmark ensemble model output statistics (EMOS) method based on a censored Gaussian law, and its machine learning-based distributional regression network (DRN) counterpart. Furthermore, we also propose a neural network-based post-processing method resulting in improved 8-member ensemble predictions. All forecasts are evaluated against station observations for 30 locations, and the skill of post-processed predictions is compared to the raw WRF ensemble. Our case study confirms that all studied post-processing methods substantially improve both the calibration of probabilistic- and the accuracy of point forecasts. Among the methods tested, the corrected ensemble exhibits the best overall performance. Additionally, the DRN model generally outperforms the corresponding EMOS approach.
arXiv
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