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Loday's dendriform algebras and its siblings pre-Lie and zinbiel have received attention over the past two decades. In recent literature, there has been interest in a generalization of these types of algebra in which each individual operation is replaced by a family of operations indexed by a fixed semigroup $S$. The purpose of this note is twofold. First, we add to the existing work by showing that a similar extension is possible already for the most familiar types of algebra: commutative, associative, and Lie. Second, we show that these concepts arise naturally and in a unified manner from a categorical perspective. For this, one simply has to consider the standard types of algebra but in reference to the monoidal category of $S$-graded vector spaces. | Dendriform Algebras Relative to a Semigroup |
The transport properties of a large-spin molecule strongly coupled to ferromagnetic leads in the presence of transverse magnetic anisotropy are studied theoretically. The relevant spectral functions, linear-response conductance and the tunnel magnetoresistance are calculated by means of the numerical renormalization group method. We study the dependence of transport characteristics on orbital level position, uniaxial and transverse anisotropies, external magnetic field and temperature. It is shown that while uniaxial magnetic anisotropy leads to the suppression of the Kondo effect, finite transverse anisotropy can restore the Kondo resonance. The effect of Kondo peak restoration strongly depends on the magnetic configuration of the device and leads to nontrivial behavior of the tunnel magnetoresistance. We show that the temperature dependence of the conductance at points where the restoration of the Kondo effect occurs is universal and shows a scaling typical for usual spin-one-half Kondo effect. | Transverse anisotropy effects on spin-resolved transport through large-spin molecules |
The neural network with $1$-Lipschitz property based on $\ell_\infty$-dist neuron has a theoretical guarantee in certified $\ell_\infty$ robustness. However, due to the inherent difficulties in the training of the network, the certified accuracy of previous work is limited. In this paper, we propose two approaches to deal with these difficuties. Aiming at the characteristics of the training process based on $\ell_\infty$-norm neural network, we introduce the EMA method to improve the training process. Considering the randomness of the training algorithm, we propose an ensemble method based on trained base models that have the $1$-Lipschitz property and gain significant improvement in the small parameter network. Moreover, we give the theoretical analysis of the ensemble method based on the $1$-Lipschitz property on the certified robustness, which ensures the effectiveness and stability of the algorithm. Our code is available at https://github.com/Theia-4869/EMA-and-Ensemble-Lip-Networks. | Boosting Certified $\ell_\infty$ Robustness with EMA Method and Ensemble Model |
We have developed a powerful method for crystal structure prediction from "scratch" through particle swarm optimization (PSO) algorithm within the evolutionary scheme. PSO technique is dramatically different with the genetic algorithm and has apparently avoided the use of evolution operators (e.g., crossover and mutation). The approach is based on a highly efficient global minimization of free energy surfaces merging total-energy calculations via PSO technique and requires only chemical compositions for a given compound to predict stable or metastable structures at given external conditions (e.g., pressure). A particularly devised geometrical structure factor method which allows the elimination of similar structures during structure evolution was implemented to enhance the structure search efficiency. The application of designed variable unit cell size technique has greatly reduced the computational cost. Moreover, the symmetry constraint imposed in the structure generation enables the realization of diverse structures, leads to significantly reduced search space and optimization variables, and thus fastens the global structural convergence. The PSO algorithm has been successfully applied to the prediction of many known systems (e.g., elemental, binary and ternary compounds) with various chemical bonding environments (e.g., metallic, ionic, and covalent bonding). The remarkable success rate demonstrates the reliability of this methodology and illustrates the great promise of PSO as a major technique on crystal structure determination. | Crystal Structure Prediction via Particle Swarm Optimization |
The metric projection onto an order nonnegative cone from the metric projection onto the corresponding order cone is derived. Particularly, we can use Pool Adjacent Violators-type algorithms developed for projecting onto the monotone cone for projecting onto the monotone nonnegative cone too. | How to project onto the monotone nonnegative cone using Pool Adjacent Violators type algorithms |
This paper gives an overview of Demaq, an XML message processing system operating on the foundation of transactional XML message queues. We focus on the syntax and semantics of its fully declarative, rule-based application language and demonstrate our message-based programming paradigm in the context of a case study. Further, we discuss optimization opportunities for executing Demaq programs. | Demaq: A Foundation for Declarative XML Message Processing |
Despite of achieving great success in real-world applications, Deep Reinforcement Learning (DRL) is still suffering from three critical issues, i.e., data efficiency, lack of the interpretability and transferability. Recent research shows that embedding symbolic knowledge into DRL is promising in addressing those challenges. Inspired by this, we introduce a novel deep reinforcement learning framework with symbolic options. Our framework features a loop training procedure, which enables guiding the improvement of policy by planning with planning models (including action models and hierarchical task network models) and symbolic options learned from interactive trajectories automatically. The learned symbolic options alleviate the dense requirement of expert domain knowledge and provide inherent interpretability of policies. Moreover, the transferability and data efficiency can be further improved by planning with the symbolic planning models. To validate the effectiveness of our framework, we conduct experiments on two domains, Montezuma's Revenge and Office World, respectively. The results demonstrate the comparable performance, improved data efficiency, interpretability and transferability. | Creativity of AI: Hierarchical Planning Model Learning for Facilitating Deep Reinforcement Learning |
The object of the present paper is to characterize two classes of almost Kenmotsu manifolds admitting Ricci-Yamabe soliton. It is shown that a $(k,\mu)'$-almost Kenmotsu manifold admitting a Ricci-Yamabe soliton or gradient Ricci-Yamabe soliton is locally isometric to the Riemannian product $\mathbb{H}^{n+1}(-4) \times \mathbb{R}^n$. For the later case, the potential vector field is pointwise collinear with the Reeb vector field. Also, a $(k,\mu)$-almost Kenmotsu manifold admitting certain Ricci-Yamabe soliton with the curvature property $Q \cdot P = 0$ is locally isometric to the hyperbolic space $\mathbb{H}^{2n+1}(-1)$ and the non-existense of the curvature property $Q \cdot R = 0$ is proved. | Almost Kenmotsu metric as Ricci-Yamabe soliton |
This article contains a noncommutative generalization of the topological path lifting problem. Noncommutative geometry has no paths and even points. However there are paths of *-automorphisms. It is proven that paths of *-automorphisms comply with unique path lifting. | The Unique Path Lifting for Noncommutative Covering Projections |
In this article, we study the dynamics of marking in football matches. To do this, we surveyed and analyzed a database containing the trajectories of players from both teams on the field of play during three professional games. We describe the dynamics through the construction of temporal bipartite networks of proximity. Based on the introduced concept of proximity, the nodes are the players, and the links are defined between opponents that are close enough to each other at a given moment. By studying the evolution of the heterogeneity parameter of the networks during the game, we characterized a scaling law for the average shape of the fluctuations, unveiling the emergence of complexity in the system. Moreover, we proposed a simple model to simulate the players' motion in the field from where we obtained the evolution of a synthetic proximity network. We show that the model captures with a remarkable agreement the complexity of the empirical case, hence it proves to be helpful to elucidate the underlying mechanisms responsible for the observed phenomena. | Complexity emerges in measures of the marking dynamics in football games |
We present a lattice calculation of the Hadronic Vacuum Polarization (HVP) contribution of the strange and charm quarks to the anomalous magnetic moment of the muon including leading-order electromagnetic corrections. We employ the gauge configurations generated by the European Twisted Mass Collaboration (ETMC) with $N_f = 2+1+1$ dynamical quarks at three values of the lattice spacing ($a \simeq 0.062, 0.082, 0.089$ fm) with pion masses in the range $M_\pi \simeq 210 - 450$ MeV. The strange and charm quark masses are tuned at their physical values. Neglecting disconnected diagrams and after the extrapolations to the physical pion mass and to the continuum limit we obtain: $a_\mu^s(\alpha_{em}^2) = (53.1 \pm 2.5) \cdot 10^{-10}$, $a_\mu^s(\alpha_{em}^3) = (-0.018 \pm 0.011) \cdot 10^{-10}$ and $a_\mu^c(\alpha_{em}^2) = (14.75 \pm 0.56) \cdot 10^{-10}$, $a_\mu^c(\alpha_{em}^3) = (-0.030 \pm 0.013) \cdot 10^{-10}$ for the strange and charm contributions, respectively. | Strange and charm HVP contributions to the muon ($g - 2)$ including QED corrections with twisted-mass fermions |
It is shown that nonlinear electrodynamics of the Born--Infeld theory type may be exploited to shed insight into a few fundamental problems in theoretical physics, including rendering electromagnetic asymmetry to energetically exclude magnetic monopoles, achieving finite electromagnetic energy to relegate curvature singularities of charged black holes, and providing theoretical interpretation of equations of state of cosmic fluids via k-essence cosmology. Also discussed are some nonlinear differential equation problems. | Nonlinear Problems Inspired by the Born--Infeld Theory of Electrodynamics |
Period doubling H\'enon renormalization of strongly dissipative maps is generalized in arbitrary finite dimension. In particular, a small perturbation of toy model maps with dominated splitting has invariant $C^r$ surfaces embedded in higher dimension and the Cantor attractor has unbounded geometry with respect to full Lebesgue measure on the parameter space. It is an extension of dynamical properties of three dimensional infinitely renormalizable H\'enon-like map in arbitrary finite dimension. | Renormalization of H\'enon map in arbitrary dimension I : Universality and reduction of ambient space |
Framing is a process of emphasizing a certain aspect of an issue over the others, nudging readers or listeners towards different positions on the issue even without making a biased argument. {Here, we propose FrameAxis, a method for characterizing documents by identifying the most relevant semantic axes ("microframes") that are overrepresented in the text using word embedding. Our unsupervised approach can be readily applied to large datasets because it does not require manual annotations. It can also provide nuanced insights by considering a rich set of semantic axes. FrameAxis is designed to quantitatively tease out two important dimensions of how microframes are used in the text. \textit{Microframe bias} captures how biased the text is on a certain microframe, and \textit{microframe intensity} shows how actively a certain microframe is used. Together, they offer a detailed characterization of the text. We demonstrate that microframes with the highest bias and intensity well align with sentiment, topic, and partisan spectrum by applying FrameAxis to multiple datasets from restaurant reviews to political news.} The existing domain knowledge can be incorporated into FrameAxis {by using custom microframes and by using FrameAxis as an iterative exploratory analysis instrument.} Additionally, we propose methods for explaining the results of FrameAxis at the level of individual words and documents. Our method may accelerate scalable and sophisticated computational analyses of framing across disciplines. | FrameAxis: Characterizing Microframe Bias and Intensity with Word Embedding |
Instance-based methods are a specific class of methods for automated proof search in first-order logic. This article provides an overview of the major methods in the area and discusses their properties and relations to the more established resolution methods. It also discusses some recent trends on refinements and applications. This overview is rather brief and informal, but we provide a comprehensive literature list to follow-up on the details. | Instance Based Methods --- A Brief Overview |
In this paper, we present recent results about the developement of a semiclassical approach in the setting of nilpotent Lie groups and nilmanifolds. We focus on two-step nilmanifolds and exhibit some properties of the weak limits of sequence of densities associated with eigenfunctions of a sub-Laplacian. We emphasize the influence of the geometry on these properties. | Some remarks on semi-classical analysis on two-step Nilmanifolds |
Split manufacturing (SM) and layout camouflaging (LC) are two promising techniques to obscure integrated circuits (ICs) from malicious entities during and after manufacturing. While both techniques enable protecting the intellectual property (IP) of ICs, SM can further mitigate the insertion of hardware Trojans (HTs). In this paper, we strive for the "best of both worlds," that is we seek to combine the individual strengths of SM and LC. By jointly extending SM and LC techniques toward 3D integration, an up-and-coming paradigm based on stacking and interconnecting of multiple chips, we establish a modern approach to hardware security. Toward that end, we develop a security-driven CAD and manufacturing flow for 3D ICs in two variations, one for IP protection and one for HT prevention. Essential concepts of that flow are (i) "3D splitting" of the netlist to protect, (ii) obfuscation of the vertical interconnects (i.e., the wiring between stacked chips), and (iii) for HT prevention, a security-driven synthesis stage. We conduct comprehensive experiments on DRC-clean layouts of multi-million-gate DARPA and OpenCores designs (and others). Strengthened by extensive security analysis for both IP protection and HT prevention, we argue that entering the third dimension is eminent for effective and efficient hardware security. | A Modern Approach to IP Protection and Trojan Prevention: Split Manufacturing for 3D ICs and Obfuscation of Vertical Interconnects |
Electromagnetic properties provide information about the structure of strongly interacting systems and allow for independent tests of hadronic models. The radiative decay of the Delta(1700) is studied, which appears dynamically generated in a coupled channel approach from the rescattering of the (3/2^+) decuplet of baryons with the (0^-) octet of pseudoscalar mesons. The radiative decay is predicted from the well-known couplings of the photon to the mesons and hadrons which constitute this resonance in the dynamical picture. | Radiative decay of the Delta(1700) |
We investigate the phase diagram of a quarter filled Hubbard ladder with nearest-neighbor Coulomb repulsion using bosonization and renormalization group approach. Focusing on the strong-repulsion regime, we discuss the effect of an interchain exchange interaction J and interchain repulsion V on the possible ground states of the system and charge order configurations. Since the spin excitations always possess a gap, we find competing bond-order wave and charge density wave phases as possible ground states of the ladder model. We discuss the elementary excitations in these various phases and point an analogy between the excitations on some of these phases and those of a Kondo-Heisenberg insulator. We also study the order of the quantum phase transitions between the different ground states of the system. We obtain second order transitions in the Ising or SU(2)_2 universality class or first order transitions. We map the complete phase diagram in the J-V plane by integrating perturbative renormalization-group equations. Finally, we discuss the effect of doping away from half-filling and the effect of an applied magnetic field. | Charge Density Waves and Bond Order Waves in a quarter filled extended Hubbard ladder |
The Lie algebra of the group SU(2) is constructed from two deformed oscillator algebras for which the deformation parameter is a root of unity. This leads to an unusual quantization scheme, the {J2,Ur} scheme, an alternative to the familiar {J2,Jz} quantization scheme corresponding to common eigenvectors of the Casimir operator J2 and the Cartan operator Jz. A connection is established between the eigenvectors of the complete set of commuting operators {J2,Ur} and mutually unbiased bases in spaces of constant angular momentum. | Angular Momentum and Mutually Unbiased Bases |
The classical Riemann-Hilbert correspondence establishes an equivalence between the triangulated category of regular holonomic D-modules and that of constructible sheaves. In this paper, we prove a Riemann-Hilbert correspondence for holonomic D-modules which are not necessarily regular. The construction of our target category is based on the theory of ind-sheaves by Kashiwara-Schapira and influenced by Tamarkin's work. Among the main ingredients of our proof is the description of the structure of flat meromorphic connections due to Mochizuki and Kedlaya. | Riemann-Hilbert correspondence for holonomic D-modules |
The concept of random deaths in a computational model for population dynamics is critically examined. We claim that it is just an artifact, albeit useful, of computational models to limit the size of the populations and has no biological foundation. Alternative implementations of random deaths strategies are discussed and compared. | Random deaths in a computational model for age-structured populations |
The Sphynx project was an exploratory study to discover what might be done to improve the heavy replication of in- structions in independent instruction caches for a massively parallel machine where a single program is executing across all of the cores. While a machine with only many cores (fewer than 50) might not have any issues replicating the instructions for each core, as we approach the era where thousands of cores can be placed on one chip, the overhead of instruction replication may become unacceptably large. We believe that a large amount of sharing should be possible when the ma- chine is configured for all of the threads to issue from the same set of instructions. We propose a technique that allows sharing an instruction cache among a number of independent processor cores to allow for inter-thread sharing and reuse of instruction memory. While we do not have test cases to demonstrate the potential magnitude of performance gains that could be achieved, the potential for sharing reduces the die area required for instruction storage on chip. | Sphynx: A Shared Instruction Cache Exporatory Study |
Let $p$ be prime, let $K$ be a non-archimedean local field of characteristic $p$ and let $C_p^3$ denote the elementary abelian group of order $p^3$. We give a complete classification of Hopf orders in the $K$-Hopf algebra $(K[C_p^3])^*$ and under a mild condition compute their dual Hopf orders in the group ring $K[C_p^3]$. | Hopf orders in $K[C_p^3]$ in characteristic $p$ |
This paper considers the beamforming design for a multiuser multiple-input single-output (MISO) downlink with an arbitrary number of (context-specific) shaping constraints. In this setup, the state-of-the-art beamforming schemes cannot attain the well-known performance bound promised by the semidefinite program (SDP) relaxation technique. To close the gap, we propose a redundant-signal embedded linear beamforming (REEL-BF) scheme, where each user is assigned with one information beamformer and several shaping beamformers. It is shown that the proposed REEL-BF scheme can perform general rank-$K$ beamforming for user symbols in a low-complexity and structured manner. In addition, sufficient conditions are derived to guarantee that the REEL-BF scheme always achieves the SDP bound for linear beamforming schemes. Based on such conditions, an efficient algorithm is then developed to obtain the optimal REEL-BF solution in polynomial time. Numerical results demonstrate that the proposed scheme enjoys substantial performance gains over the existing alternatives. | REEL-BF Design: Achieving the SDP Bound for Downlink Beamforming with Arbitrary Shaping Constraints |
The LCLS beam is meant for a single user, but the baseline undulator is long enough to serve two users simultaneously. To this end, we propose a setup composed of two elements: an X-ray mirrors pair for X-ray beam deflection, and a 4 m-long magnetic chicane, which creates an offset for mirrors pair installation in the middle of the baseline undulator. The insertable mirrors pair can separate spatially the X-ray beams generated in the first and in the second half of the baseline undulator. Rapid switching of the FEL amplification process allows deactivating one half and activating another half of the undulator. As proposed elsewhere, using a kicker installed upstream of the LCLS baseline undulator and an already existing corrector in the first half of the undulator, it is possible to rapidly switch the X-ray beam from one user to another. We present simulation results for the LCLS baseline, and show that it is possible to generate two saturated SASE X-ray beams in the whole 0.8-8 keV photon energy range in the same baseline undulator. These can serve two users. Our technique does not perturb the baseline mode of operation of the LCLS undulator. Also, the magnetic chicane setup is very flexible, and can be used as a self-seeding setup too. We present simulation results for the LCLS baseline undulator with SHAB. One can produce monochromatic radiation at the 2nd harmonic as well as at the 1st. We describe an efficient way for obtaining multi-user operation at the LCLS hard X-ray FEL. To this end, a photon beam distribution system based on the use of crystals in the Bragg reflection geometry is proposed. The reflectivity of crystal deflectors can be switched fast enough by flipping the crystals with piezoelectric devices. Monochromatic hard X-rays can then be distributed among 6 independent experiments, thereby enabling 6 users to work in parallel in the near and far experimental halls. | Way to increase the user access at the LCLS baseline |
We examine the connectivity fluctuations across networks obtained when the horizontal visibility (HV) algorithm is used on trajectories generated by nonlinear circle maps at the quasiperiodic transition to chaos. The resultant HV graph is highly anomalous as the degrees fluctuate at all scales with amplitude that increases with the size of the network. We determine families of Pesin-like identities between entropy growth rates and generalized graph-theoretical Lyapunov exponents. An irrational winding number with pure periodic continued fraction characterizes each family. We illustrate our results for the so-called golden, silver and bronze numbers. | Quasiperiodic graphs at the onset of chaos |
Learning accurate predictive models of real-world dynamic phenomena (e.g., climate, biological) remains a challenging task. One key issue is that the data generated by both natural and artificial processes often comprise time series that are irregularly sampled and/or contain missing observations. In this work, we propose the Neural Continuous-Discrete State Space Model (NCDSSM) for continuous-time modeling of time series through discrete-time observations. NCDSSM employs auxiliary variables to disentangle recognition from dynamics, thus requiring amortized inference only for the auxiliary variables. Leveraging techniques from continuous-discrete filtering theory, we demonstrate how to perform accurate Bayesian inference for the dynamic states. We propose three flexible parameterizations of the latent dynamics and an efficient training objective that marginalizes the dynamic states during inference. Empirical results on multiple benchmark datasets across various domains show improved imputation and forecasting performance of NCDSSM over existing models. | Neural Continuous-Discrete State Space Models for Irregularly-Sampled Time Series |
We prove a Davies type double integral estimate for the heat kernel $H(y,t;x,l)$ under the Ricci flow. As a result, we give an affirmative answer to a question proposed by Chow etc.. Moreover, we apply the Davies type estimate to provide a new proof of the Gaussian upper and lower bounds of $H(y,t;x,l)$ which were first shown by Chau-Tam-Yu. | Davies type estimate and the heat kernel bound under the Ricci flow |
A polycrystalline graphene consists of perfect domains tilted at angle {\alpha} to each other and separated by the grain boundaries (GB). These nearly one-dimensional regions consist in turn of elementary topological defects, 5-pentagons and 7-heptagons, often paired up into 5-7 dislocations. Energy G({\alpha}) of GB computed for all range 0<={\alpha}<=Pi/3, shows a slightly asymmetric behavior, reaching ~5 eV/nm in the middle, where the 5's and 7's qualitatively reorganize in transition from nearly armchair to zigzag interfaces. Analysis shows that 2-dimensional nature permits the off-plane relaxation, unavailable in 3-dimensional materials, qualitatively reducing the energy of defects on one hand while forming stable 3D-landsapes on the other. Interestingly, while the GB display small off-plane elevation, the random distributions of 5's and 7's create roughness which scales inversely with defect concentration, h ~ n^(-1/2) | Cones, pringles, and grain boundary landscapes in graphene topology |
Cascading failures in power systems exhibit non-local propagation patterns which make the analysis and mitigation of failures difficult. In this work, we propose a distributed control framework inspired by the recently proposed concepts of unified controller and network tree-partition that offers strong guarantees in both the mitigation and localization of cascading failures in power systems. In this framework, the transmission network is partitioned into several control areas which are connected in a tree structure, and the unified controller is adopted by generators or controllable loads for fast timescale disturbance response. After an initial failure, the proposed strategy always prevents successive failures from happening, and regulates the system to the desired steady state where the impact of initial failures are localized as much as possible. For extreme failures that cannot be localized, the proposed framework has a configurable design, that progressively involves and coordinates more control areas for failure mitigation and, as a last resort, imposes minimal load shedding. We compare the proposed control framework with Automatic Generation Control (AGC) on the IEEE 118-bus test system. Simulation results show that our novel framework greatly improves the system robustness in terms of the N-1 security standard, and localizes the impact of initial failures in majority of the load profiles that are examined. Moreover, the proposed framework incurs significantly less load loss, if any, compared to AGC, in all of our case studies. | Less is More: Real-time Failure Localization in Power Systems |
We present an analysis of the time-averaged spectrum of the Seyfert-2 active galaxy NGC 4388, obtained by NICER. The intrinsic strength of the reflection spectrum in NGC 4388, the large collecting area and favorable pass band of NICER, and a net exposure of 105.6 ks yielded an exceptionally sensitive spectrum. Using two independent families of models, the intrinsic spectrum from the central engine is found to be highly obscured but not Compton-thick. Enforcing physical self-consistency within each model, the independent treatments give formally consistent results: N_H = 2.67 (-0.03,+0.02) E+23 cm^-2 or N_H = 2.64 (-0.03, +0.03) E+23 cm^-2. Past measurements made with Suzaku and XMM-Newton are in broad agreement with these column density values. A more recent measurement with NuSTAR (in late 2013) recorded a column density about twice as large; the robustness of this variability is reinforced by the use of consistent models and procedures. The neutral Fe K-alpha line in the NICER spectrum is nominally resolved and consistent with an origin in the optical broad line region (BLR). The data also require ionized absorption in the Fe K band, similar to the "warm absorbers" detected in Seyfert-1 active galactic nuclei (AGN). The low-energy spectrum is consistent with a set of ionized plasma components. We discuss these findings and note that the geometric inferences that derive from this analysis can be tested with XRISM and Athena. | A NICER Look at Strong X-ray Obscuration in the Seyfert-2 Galaxy NGC 4388 |
The non-equilibrium structural and dynamical properties of flexible polymers confined in a square microchannel and exposed to a Poiseuille flow are investigated by mesoscale simulations. The chain length and the flow strength are systematically varied. Two transport regimes are identified, corresponding to weak and strong confinement. For strong confinement, the transport properties are independent of polymer length. The analysis of the long-time tumbling dynamics of short polymers yields non-periodic motion with a sublinear dependence on the flow strength. We find distinct differences for conformational as well as dynamical properties from results obtained for simple shear flow. | Mesoscale simulations of polymer dynamics in microchannel flows |
A fascinating conjectural connection between statistical mechanics and combinatorics has in the past five years led to the publication of a number of papers in various areas, including stochastic processes, solvable lattice models and supersymmetry. This connection, known as the Razumov-Stroganov conjecture, expresses eigenstates of physical systems in terms of objects known from combinatorics, which is the mathematical theory of counting. This note intends to explain this connection in light of the recent papers by Zinn-Justin and Di Francesco. | The Razumov-Stroganov conjecture: Stochastic processes, loops and combinatorics |
A new method that enables easy and convenient discretization of partial differential equations with derivatives of arbitrary real order (so-called fractional derivatives) and delays is presented and illustrated on numerical solution of various types of fractional diffusion equation. The suggested method is the development of Podlubny's matrix approach (Fractional Calculus and Applied Analysis, vol. 3, no. 4, 2000, 359--386). Four examples of numerical solution of fractional diffusion equation with various combinations of time/space fractional derivatives (integer/integer, fractional/integer, integer/fractional, and fractional/fractional) with respect to time and to the spatial variable are provided in order to illustrate how simple and general is the suggested approach. The fifth example illustrates that the method can be equally simply used for fractional differential equations with delays. A set of MATLAB routines for the implementation of the method as well as sample code used to solve the examples have been developed. | Matrix approach to discrete fractional calculus II: partial fractional differential equations |
In this paper a class of single machine scheduling problems is considered. It is assumed that job processing times and due dates can be uncertain and they are specified in the form of discrete scenario set. A probability distribution in the scenario set is known. In order to choose a schedule some risk criteria such as the value at risk (VaR) an conditional value at risk (CVaR) are used. Various positive and negative complexity results are provided for basic single machine scheduling problems. In this paper new complexity results are shown and some known complexity results are strengthen. | Risk averse single machine scheduling - complexity and approximation |
Let X be a minimal surface of general type with positive geometric genus ($b_+ > 1$) and let $K^2$ be the square of its canonical class. Building on work of Khodorovskiy and Rana, we prove that if X develops a Wahl singularity of length $\ell$ in a Q-Gorenstein degeneration, then $\ell \leq 4K^2 + 7$. This improves on the current best-known upper bound due to Lee ($\ell \leq 400(K^2)^4$). Our bound follows from a stronger theorem constraining symplectic embeddings of certain rational homology balls in surfaces of general type. In particular, we show that if the rational homology ball $B_{p,1}$ embeds symplectically in a quintic surface, then $p \leq 12$, partially answering the symplectic version of a question of Kronheimer. | Bounds on Wahl singularities from symplectic topology |
Broad absorption signatures from alkali metals, such as the sodium (Na I) and potassium (K I) resonance doublets, have long been predicted in the optical atmospheric spectra of cloud-free irradiated gas-giant exoplanets1,2,3. However, observations have only revealed the narrow cores of these features rather than the full pressure-broadened profiles4-6. Cloud and haze opacity at the day-night planetary terminator are considered responsible for obscuring the absorption-line wings, which hinders constraints on absolute atmospheric abundances7-9. Here we present an optical transmission spectrum for the 'hot-Saturn' WASP-96b obtained with the Very Large Telescope, which exhibits the complete pressure-broadened profile of the sodium absorption feature. The spectrum is in excellent agreement with cloud-free, solar-abundance models assuming chemical equilibrium. We are able to measure a precise, absolute sodium abundance of log\epsilon_Na=6.9+0.6-0.4, and use it as a proxy to the planet's atmospheric metallicity relative to the solar value (Z_p/Z_\star=2.3+8.9/--1.7). This result is consistent with the mass-metallicity trend observed for solar-system planets and exoplanets10-12. | An absolute sodium abundance for a cloud-free 'hot Saturn' exoplanet |
The stellar wind around the compact object in luminous wind-accreting high mass X-ray binaries is expected to be strongly ionized with the X-rays coming from the compact object. The stellar wind of hot stars is mostly driven by light absorption in lines of heavier elements, and X-ray photo-ionization significantly reduces the radiative force within the so-called Stroemgren region leading to wind stagnation around the compact object. In close binaries like Vela X-1 this effect might alter the wind structure throughout the system. Using the spectral data from Monitor of All-sky X-ray Image (MAXI), we study the observed dependence of the photoelectric absorption as function of orbital phase in Vela X-1, and find that it is inconsistent with expectations for a spherically-symmetric smooth wind. Taking into account previous investigations we develop a simple model for wind structure with a stream-like photoionization wake region of slower and denser wind trailing the neutron star responsible for the observed absorption curve. | Footprints in the wind of Vela X-1 traced with MAXI |
Travel time estimation is a fundamental problem in transportation science with extensive literature. The study of these techniques has intensified due to availability of many publicly available large trip datasets. Recently developed deep learning based models have improved the generality and performance and have focused on estimating times for individual sub-trajectories and aggregating them to predict the travel time of the entire trajectory. However, these techniques ignore the road network information. In this work, we propose and study techniques for incorporating road networks along with historical trips' data into travel time prediction. We incorporate both node embeddings as well as road distance into the existing model. Experiments on large real-world benchmark datasets suggest improved performance, especially when the train data is small. As expected, the proposed method performs better than the baseline when there is a larger difference between road distance and Vincenty distance between start and end points. | Map Enhanced Route Travel Time Prediction using Deep Neural Networks |
Spin-dependent exchange-correlation energy functionals in use today depend on the charge density and the magnetization density: $E_{\rm xc}[\rho,{\bf m}]$. However, it is also correct to define the functional in terms of the curl of ${\bf m}$ for physical external fields: $E_{\rm xc}[\rho,\nabla\times{\bf m}]$. The exchange-correlation magnetic field, ${\bf B}_{\rm xc}$, then becomes source-free. We study this variation of the theory by uniquely removing the source term from local and generalized gradient approximations to the functional. By doing so, the total Kohn-Sham moments are improved for a wide range of materials for both functionals. Significantly, the moments for the pnictides are now in good agreement with experiment. We also predict dramatic differences in the spatial geometry of ${\bf B}_{\rm xc}$ for the pnictides. Our source-free method is simple to implement in all existing density functional theory codes. | Source-free exchange-correlation magnetic fields in density functional theory |
We describe a scheme for the teleportation of entanglements of zero- and one-photon running-wave field states. In addition to linear optical elements, Kerr nonlinearity is also employed so as to achieve a 100% probability of success in the ideal case. A comprehensive phenomenological treatment of errors in the domain of running-wave physics, for linear and nonlinear optical elements, is also given, making it possible to calculate the fidelity of the teleportation process. A strategy for carrying out the Bell-type measurement which is able to probe the absorption of photons in the optical elements is adopted. Such strategy, combined with usually small damping constants characterizing the optical devices, results in a high fidelity for the teleportation process. The feasibility of the proposed scheme relies on the fact that the Kerr nonlinearity it demands can be achieved through the recently reported ultraslow light propagation in cold atomic media [Phys. Rev. Lett. 84, 1419 (2000); Phys. Rev. A 65, 033833 (2002)]. | High-fidelity teleportation of entanglements of running-wave field states |
The mean shift iterative algorithm was proposed in 2006, for using the entropy as a stopping criterion. From then on, a theoretical base has been developed and a group of applications has been carried out using this algorithm. This paper proposes a new stopping criterion for the mean shift iterative algorithm, where stopping threshold via entropy is used now, but in another way. Many segmentation experiments were carried out by utilizing standard images and it was verified that a better segmentation was reached, and that the algorithm had better stability. An analysis on the convergence, through a theorem, with the new stopping criterion was carried out. The goal of this paper is to compare the new stopping criterion with the old criterion. For this reason, the obtained results were not compared with other segmentation approaches, since with the old stopping criterion were previously carried out. | A new stopping criterion for the mean shift iterative algorithm |
We present a new implementation of the NNLO QCD corrections to three-jet final states and related event-shape observables in electron--positron annihilation. Our implementation is based on the antenna subtraction method, and is performed in the NNLOJET framework. The calculation improves upon earlier results by taking into account the full kinematical information on the initial state momenta, thereby allowing the event orientation to be computed to NNLO accuracy. We find the event-orientation distributions at LEP and SLC to be very robust under higher order QCD corrections. | NNLO QCD corrections to event orientation in e+e- annihilation |
We report on NICER X-ray monitoring of the magnetar SGR 1830-0645 covering 223 days following its October 2020 outburst, as well as Chandra and radio observations. We present the most accurate spin ephemerides of the source so far: $\nu=0.096008680(2)$~Hz, $\dot{\nu}=-6.2(1)\times10^{-14}$~Hz~s$^{-1}$, and a significant second and third frequency derivative terms indicative of non-negligible timing noise. The phase-averaged 0.8--7~keV spectrum is well fit with a double-blackbody (BB) model throughout the campaign. The BB temperatures remain constant at 0.46 and 1.2 keV. The areas and flux of each component decreased by a factor of 6, initially through a steep decay trend lasting about 46 days followed by a shallow long-term one. The pulse shape in the same energy range is initially complex, exhibiting three distinct peaks, yet with clear continuous evolution throughout the outburst towards a simpler, single-pulse shape. The rms pulsed fraction is high and increases from about 40% to 50%. We find no dependence of pulse shape or fraction on energy. These results suggest that multiple hotspots, possibly possessing temperature gradients, emerged at outburst-onset, and shrank as the outburst decayed. We detect 84 faint bursts with \nicer, having a strong preference for occurring close to the surface emission pulse maximum the first time this phenomenon is detected in such a large burst sample. This likely implies a very low altitude for the burst emission region, and a triggering mechanism connected to the surface active zone. Finally, our radio observations at several epochs and multiple frequencies reveal no evidence of pulsed or burst-like radio emission. | X-ray burst and persistent emission properties of the magnetar SGR 1830-0645 in outburst |
As scientific frameworks become sophisticated, so do their data structures. Current data structures are no longer simple in design and they have been progressively complicated. The typical trend in designing data structures in scientific applications are basically nested data structures: pointing to a data structure within another one. Managing nested data structures on a modern heterogeneous system requires tremendous effort due to the separate memory space design. In this paper, we will discuss the implications of deep copy on data transfers on current heterogeneous. Then, we will discuss the two options that are currently available to perform the memory copy operations on complex structures and will introduce pointerchain directive that we proposed. Afterwards, we will introduce a set of extensive benchmarks to compare the available approaches. Our goal is to make our proposed benchmarks a basis to examine the efficiency of upcoming approaches that address the challenge of deep copy operations. | Assessing Performance Implications of Deep Copy Operations via Microbenchmarking |
Using one arm of the Michelson interferometer and the power recycling mirror of the interferometric gravitational wave detector GEO600, we created a Fabry-Perot cavity with a length of 1200 m. The main purpose of this experiment was to gather first experience with the main optics, its suspensions and the corresponding control systems. The residual displacement of a main mirror is about 150 nm rms. By stabilising the length of the 1200 m long cavity to the pre-stabilised laser beam we achieved an error point frequency noise of 0.1 mHz/sqrt(Hz) at 100 Hz Fourier frequency. In addition we demonstrated the reliable performance of all included subsystems by several 10-hour-periods of continuous stable operation. Thus the full frequency stabilisation scheme for GEO600 was successfully tested. | Performance of a 1200m long suspended Fabry-Perot cavity |
Static word embeddings encode word associations, extensively utilized in downstream NLP tasks. Although prior studies have discussed the nature of such word associations in terms of biases and lexical regularities captured, the variation in word associations based on the embedding training procedure remains in obscurity. This work aims to address this gap by assessing attributive word associations across five different static word embedding architectures, analyzing the impact of the choice of the model architecture, context learning flavor and training corpora. Our approach utilizes a semi-supervised clustering method to cluster annotated proper nouns and adjectives, based on their word embedding features, revealing underlying attributive word associations formed in the embedding space, without introducing any confirmation bias. Our results reveal that the choice of the context learning flavor during embedding training (CBOW vs skip-gram) impacts the word association distinguishability and word embeddings' sensitivity to deviations in the training corpora. Moreover, it is empirically shown that even when trained over the same corpora, there is significant inter-model disparity and intra-model similarity in the encoded word associations across different word embedding models, portraying specific patterns in the way the embedding space is created for each embedding architecture. | Model Choices Influence Attributive Word Associations: A Semi-supervised Analysis of Static Word Embeddings |
We have carried out optical spectroscopy with the Anglo-Australian Telescope for 24,726 objects surrounding a sample of 19 Giant Radio Galaxies (GRGs) selected to have redshifts in the range 0.05 to 0.15 and projected linear sizes from 0.8 to 3.2 Mpc. Such radio galaxies are ideal candidates to study the Warm-Hot Intergalactic Medium (WHIM) because their radio lobes extend beyond the ISM and halos of their host galaxies, and into the tenuous IGM. We were able to measure redshifts for 9,076 galaxies. Radio imaging of each GRG, including high-sensitivity, wideband radio observations from the Australia Telescope Compact Array for 12 GRGs and host optical spectra (presented in a previous paper, Malarecki et al. 2013), is used in conjunction with the surrounding galaxy redshifts to trace large-scale structure. We find that the mean galaxy number overdensity in volumes of ~700 Mpc$^3$ near the GRG host galaxies is ~70 indicating an overdense but non-virialized environment. A Fourier component analysis is used to quantify the anisotropy in the surrounding galaxy distribution. For GRGs with radio components offset from the radio axis, there is a clear influence of the environment with lobes appearing to be deflected away from overdensities in the surrounding medium. Furthermore, the GRG lobes tend to be normal to the plane defined by the galaxy neighbourhood close to the host. This indicates the tendency for lobes to grow to giant sizes in directions that avoid dense regions on both small and large scales. | Giant radio galaxies - II. Tracers of large-scale structure |
We study the transport properties of a superconducting Nb film with a square lattice of artificial pinning centers (APCs) as a function of dc current, at a temperature close to the superconducting transition temperature of the film. We find that, at low dc currents, the differential resistance of the film shows the standard matching field anomaly, that is, the differential resistance has a local minimum at magnetic fields corresponding to an integer number of flux lines per APC. However, at higher dc currents, the differential resistance at each matching field turns to a local maximum, which is exactly opposite to the low current behavior. This novel effect might indicate that the flux lines in the APC system change their flow mode as the dc current is increased. | Novel pinning phenomena in a superconducting film with a square lattice of artificial pinning centers |
We show that finite index subgroups of the handlebody group are rigid in their ambient mapping class group: any injective map of a finite index subgroup of the genus $g$ handlebody group into the genus $g$ mapping class group is conjugation by a mapping class group element. On the other hand, we construct an injection of the genus $g$ handlebody group into a genus $h>g$ mapping class group which is not conjugate into a handlebody group. | Rigidity and Flexibility for Handlebody Groups |
Most recent approaches to bilingual dictionary induction find a linear alignment between the word vector spaces of two languages. We show that projecting the two languages onto a third, latent space, rather than directly onto each other, while equivalent in terms of expressivity, makes it easier to learn approximate alignments. Our modified approach also allows for supporting languages to be included in the alignment process, to obtain an even better performance in low resource settings. | Generalizing Procrustes Analysis for Better Bilingual Dictionary Induction |
We calculate recently observed $d$-wave Feshbach resonance [Phys. Rev. Lett. {\bf 119}, 203402 (2017)] and associated triplet structure in $^{87}$Rb-$^{85}$Rb cold collisions. We resort to a computational technique combining some features of close-coupling (CC) and $R$-matrix theory. In the long-range part, we numerically calculate a pair of base or reference functions for each channel ignoring all interchannel couplings, ensuring the linear independence of these base functions. The short-range part of the wave function is calculated by CC method. The multichannel wave functions are obtained by matching the short- and long-range parts at a suitably chosen matching point. We first verify the method by calculating cold collisional properties of $^{85}$Rb and $^6$Li in the presence of external magnetic fields tuned across specific $s$-wave Feshbach resonances and thereby reproducing known results. Our numerical results on the $d$-wave resonance agree reasonably well with the experimental ones. Furthermore, our method enables one to readily construct the real space Green functions in order to calculate perturbatively the effects of any residual inter-channel couplings in the long range. | Calculation of $d$-wave Feshbach resonance in $^{87}$Rb-$^{85}$Rb cold collisions by a multichannel computational method |
The bound that arises out of sparse recovery analysis in compressed sensing involves input signal sparsity and some property of the sensing matrix. An effort has therefore been made in the literature to optimize sensing matrices for optimal recovery using this property. We discover, in the specific case of optimizing codes for the CACTI camera, that the popular method of mutual coherence minimization does not produce optimal results: codes designed to optimize effective dictionary coherence often perform worse than random codes in terms of mean squared reconstruction error. This surprising phenomenon leads us to investigate the reliability of the coherence bound for matrix optimization, in terms of its looseness. We examine, on simulated data, the looseness of the bound as it propagates across various steps of the inequalities in a derivation leading to the final bound. We then similarly examine an alternate bound derived by Tang, G. et al, based on the $\ell_1/\ell_{\infty}$ notion of sparsity, which is a compromise between coherence and the restricted isometry constant (RIC). Moreover, we also perform a bound looseness analysis for the RIC as derived by Cai, T. et al. The conclusion of these efforts is that coherence optimization is problematic not only because of the coherence bound on the RIC, but also the RIC bound itself. These negative results imply that despite the success of previous work in designing sensing matrices based on optimization of a matrix quality factor, one needs to exercise caution in using them for practical sensing matrix design. We then introduce a paradigm for optimizing sensing matrices that overcomes the looseness of compressed sensing upper bounds using an average case error approach. We show a proof-of-concept design using this paradigm that performs convincingly better than coherence-based design in the CACTI case, and no worse for general matrices. | Optimizing Matrices For Compressed Sensing Using Existing Goodness Measures: Negative Results, And An Alternative |
In this paper we consider modification of electronic properties of graphene-based topological insulator in the presence of wedge disclination and magnetic field by adopting the Kane-Mele model with intrinsic spin-orbit coupling. Using the properly defined Dirac-Weyl equation for this system, an exact solution for the Landau levels is obtained. The influence of the topological defect on the evolution of Landau levels is discussed. | Evolution of Landau levels in graphene-based topological insulators in the presence of wedge disclinations |
An interpretation of non-relativistic quantum mechanics is presented in the spirit of Erwin Madelung's hydrodynamic formulation of QM and Louis de Broglie's and David Bohm's pilot wave models. The aims of the approach are as follows: 1) to have a clear ontology for QM, 2) to describe QM in a causal way, 3) to get rid of the wave-particle dualism in pilot wave theories, 4) to provide a theoretical framework for describing creation and annihilation of particles, and 5) to provide a possible connection between particle QM and virtual particles in QFT. These goals are achieved, if the wave function is replaced by a fluid of so called virtual particles. It is also assumed that in this fluid of virtual particles exist a few real particles and that only these real particles can be directly observed. This has relevance for the measurement problem in QM and it is found that quantum probabilities arise in a very natural way from the structure of the theory. The model presented here is very similar to a recent computational model of quantum physics and recent Bohmian models of QFT. | Virtual Particle Interpretation of Quantum Mechanics - a non-dualistic model of QM with a natural probability interpretation |
Professional athletes increasingly use automated analysis of meta- and signal data to improve their training and game performance. As in other related human-to-human research fields, signal data, in particular, contain important performance- and mood-specific indicators for automated analysis. In this paper, we introduce the novel data set SCORE! to investigate the performance of several features and machine learning paradigms in the prediction of the sex and immediate stroke success in tennis matches, based only on vocal expression through players' grunts. The data was gathered from YouTube, labelled under the exact same definition, and the audio processed for modelling. We extract several widely used basic, expert-knowledge, and deep acoustic features of the audio samples and evaluate their effectiveness in combination with various machine learning approaches. In a binary setting, the best system, using spectrograms and a Convolutional Recurrent Neural Network, achieves an unweighted average recall (UAR) of 84.0 % for the player sex prediction task, and 60.3 % predicting stroke success, based only on acoustic cues in players' grunts of both sexes. Further, we achieve a UAR of 58.3 %, and 61.3 %, when the models are exclusively trained on female or male grunts, respectively. | Predicting Sex and Stroke Success -- Computer-aided Player Grunt Analysis in Tennis Matches |
In this paper, a class of time inconsistent linear quadratic optimal control problems of mean-field stochastic differential equations (SDEs) is considered under Markovian framework. Open-loop equilibrium controls and their particular closed-loop representations are introduced and characterized via variational ideas. Several interesting features are revealed and a system of coupled Riccati equations is derived. In contrast with the analogue optimal control problems of SDEs, the mean-field terms in state equation, which is another reason of time inconsistency, prompts us to define above two notions in new manners. An interesting result, which is almost trivial in the counterpart problems of SDEs, is given and plays significant role in the previous characterizations. As application, the uniqueness of open-loop equilibrium controls is discussed. | Characterizations of equilibrium controls in time inconsistent mean-field stochastic linear quadratic problems. I |
In this dissertation, we study the implications generated by the Lorentz breaking symmetry in quantum electrodynamics. We analyze fermions interacting with an electromagnetic field in the contexts of quantum mechanics and make radiative corrections. In quantum mechanics, the terms of the Lorentz breaking symmetry were treated as perturbations to the Dirac equation, and their expected values were obtained in a vacuum. In the radiative corrections, the Lorentz breaking symmetry was introduced in this interaction for the Chern-Simons like term could be induced in (3 +1) dimensions. We also discussed the consequences generated by this term on the propagation speeds of classic photons. | Lorentz Symmetry Breaking in Quantum Electrodynamics |
We consider a task of surveillance-evading path-planning in a continuous setting. An Evader strives to escape from a 2D domain while minimizing the risk of detection (and immediate capture). The probability of detection is path-dependent and determined by the spatially inhomogeneous surveillance intensity, which is fixed but a priori unknown and gradually learned in the multi-episodic setting. We introduce a Bayesian reinforcement learning algorithm that relies on a Gaussian Process regression (to model the surveillance intensity function based on the information from prior episodes), numerical methods for Hamilton-Jacobi PDEs (to plan the best continuous trajectories based on the current model), and Confidence Bounds (to balance the exploration vs exploitation). We use numerical experiments and regret metrics to highlight the significant advantages of our approach compared to traditional graph-based algorithms of reinforcement learning. | Surveillance Evasion Through Bayesian Reinforcement Learning |
The number of clinical citations received from clinical guidelines or clinical trials has been considered as one of the most appropriate indicators for quantifying the clinical impact of biomedical papers. Therefore, the early prediction of the clinical citation count of biomedical papers is critical to scientific activities in biomedicine, such as research evaluation, resource allocation, and clinical translation. In this study, we designed a four-layer multilayer perceptron neural network (MPNN) model to predict the clinical citation count of biomedical papers in the future by using 9,822,620 biomedical papers published from 1985 to 2005. We extracted ninety-one paper features from three dimensions as the input of the model, including twenty-one features in the paper dimension, thirty-five in the reference dimension, and thirty-five in the citing paper dimension. In each dimension, the features can be classified into three categories, i.e., the citation-related features, the clinical translation-related features, and the topic-related features. Besides, in the paper dimension, we also considered the features that have previously been demonstrated to be related to the citation counts of research papers. The results showed that the proposed MPNN model outperformed the other five baseline models, and the features in the reference dimension were the most important. | Predicting the clinical citation count of biomedical papers using multilayer perceptron neural network |
We introduce a method for using Fizeau interferometry to measure the intrinsic resolving power of a diffraction grating. This method is more accurate than traditional techniques based on a long-trace profiler (LTP), since it is sensitive to long-distance phase errors not revealed by a d-spacing map. We demonstrate 50,400 resolving power for a mechanically ruled XUV grating from Inprentus, Inc. | Intrinsic resolving power of XUV diffraction gratings measured with Fizeau interferometry |
The authors compute the long-time asymptotics for solutions of the NLS equation just under the assumption that the initial data lies in a weighted Sobolev space. In earlier work (see e.g. [DZ1],[DIZ]) high orders of decay and smoothness are required for the initial data. The method here is a further development of the steepest descent method of [DZ1], and replaces certain absolute type estimates in [DZ1] with cancellation from oscillations. | Long-time asymptotics for solutions of the NLS equation with initial data in a weighted Sobolev space |
Let $A$ be the coordinate ring of a projective smooth curve over a finite field minus a closed point. For a nontrivial ideal $I \subset A$, Drinfeld defined the notion of structure of level $I$ on a Drinfeld module. We extend this to that of level $N$, where $N$ is a finitely generated torsion $A$-module. The case where $N=(I^{-1}/A)^d$, where $d$ is the rank of the Drinfeld module,coincides with the structure of level $I$. The moduli functor is representable by a regular affine scheme. The automorphism group $\mathrm{Aut}_{A}(N)$ acts on the moduli space. Our theorem gives a class of subgroups for which the quotient of the moduli scheme is regular. Examples include generalizations of $\Gamma_0$ and of $\Gamma_1$. We also show that parabolic subgroups appearing in the definition of Hecke correspondences are such subgroups. | Regularity of quotients of Drinfeld modular schemes |
Our aim is to find and classify OB stars in Sextans A, to later determine accurate stellar parameters of these blue massive stars in this low metallicity region $(Z \sim 0.1 \rm Z_{\odot})$. Using UBV photometry, the reddening-free index Q and GALEX imaging, we built a list of blue massive star candidates in Sextans A. We obtained low resolution (R $\sim$ 1000) GTC-OSIRIS spectra for a fraction of them and carried out spectral classification. For the confirmed O-stars we derive preliminary stellar parameters. The target selection criteria and observations were successful and have produced the first spectroscopic atlas of OB-type stars in Sextans A. From the whole sample of 18 observed stars, 12 were classified as early OB-types, including 5 O-stars. The radial velocities of all target stars are in agreement with their Sextans A membership, although three of them show significant deviations. We determined the stellar parameters of the O-type stars using the stellar atmosphere code FASTWIND, and revisited the sub-SMC temperature scale. Two of the O-stars are consistent with relatively strong winds and enhanced helium abundances, although results are not conclusive. We discuss the position of the OB stars in the HRD. Initial stellar masses run from slightly below 20 up to 40 solar masses. The target selection method worked well for Sextans A, confirming the procedure developed in Garcia \& Herrero (2013). The stellar temperatures are consistent with findings in other galaxies. Some of the targets deserve follow-up spectroscopy because of indications of a runaway nature, an enhanced helium abundance or a relatively strong wind. We observe a correlation between HI and OB associations similar to the irregular galaxy IC1613, confirming the previous result that the most recent star formation of Sextans A is currently on-going near the rim of the H\,{\sc I} cavity. | OB stars at the lowest Local Group metallicity: GTC-OSIRIS observations of Sextans A |
Antiferromagnetic topological insulator (AFTI) is a topological matter that breaks time-reversal symmetry. Since its proposal, explorations of AFTI in strong-correlated systems are still lacking. In this paper, we show for the first time that a novel AFTI phase can be realized in three-dimensional topological Kondo insulator (TKI). In a wide parameter region, the ground states of TKI undergo a second-order transition to antiferromagnetic insulating phases which conserve a combined symmetry of time reversal and a lattice translation, allowing us to derive a $\mathcal{Z}_2$-classification formula for these states. By calculating the $\mathcal{Z}_2$ index, the antiferromagnetic insulating states are classified into (AFTI) or non-topological antiferromagnetic insulator (nAFI) in different parameter regions. On the antiferromagnetic surfaces in AFTI, we find topologically protected gapless Dirac cones inside the bulk gap, leading to metallic Fermi rings exhibiting helical spin texture with weak spin-momentum locking. Depending on model parameters, the magnetic transitions take place either between AFTI and strong topological insulator, or between nAFI and weak topological insulator. By varying some model parameters, we find a topological transition between AFTI and nAFI, driving by closing of bulk gap. Our work may account for the pressure-induced magnetism in TKI compound SmB$_6$, and helps to explore richer AFTI phases in heavy-fermion systems as well as in other strong-correlated systems. | $\mathcal{Z}_2$ classification for a novel antiferromagnetic topological insulating phase in three-dimensional topological Kondo insulator |
We present a robust framework to perform linear regression with missing entries in the features. By considering an elliptical data distribution, and specifically a multivariate normal model, we are able to conditionally formulate a distribution for the missing entries and present a robust framework, which minimizes the worst case error caused by the uncertainty about the missing data. We show that the proposed formulation, which naturally takes into account the dependency between different variables, ultimately reduces to a convex program, for which a customized and scalable solver can be delivered. In addition to a detailed analysis to deliver such solver, we also asymptoticly analyze the behavior of the proposed framework, and present technical discussions to estimate the required input parameters. We complement our analysis with experiments performed on synthetic, semi-synthetic, and real data, and show how the proposed formulation improves the prediction accuracy and robustness, and outperforms the competing techniques. Missing data is a common problem associated with many datasets in machine learning. With the significant increase in using robust optimization techniques to train machine learning models, this paper presents a novel robust regression framework that operates by minimizing the uncertainty associated with missing data. The proposed approach allows training models with incomplete data, while minimizing the impact of uncertainty associated with the unavailable data. The ideas developed in this paper can be generalized beyond linear models and elliptical data distributions. | RIGID: Robust Linear Regression with Missing Data |
Metal halide perovskite-based materials have emerged over the past few decades as remarkable solution-processable opto-electronic materials with many intriguing properties and potential applications. These emerging materials have recently been considered for their promise in low-energy memory and information processing applications. In particular, their large optical cross-sections, high photoconductance contrast, large carrier diffusion lengths, and mixed electronic/ionic transport mechanisms are attractive for enabling memory elements and neuromorphic devices that are written and/or read in the optical domain. Here, we review recent progress toward memory and neuromorphic functionality in metal halide perovskite materials and devices where photons are used as a critical degree of freedom for switching, memory, and neuromorphic functionality. | Optical Memory, Switching, and Neuromorphic Functionality in Metal Halide Perovskite Materials and Devices |
We study the virtual effects of unparticle physics in the lepton flavor violating processes $M^0\to l^+l'^-$ and $e^+e^-\to l^+l'^-$ scattering, where $M^0$ denotes the pseudoscalar mesons: $\pi^0,K_L, D_0,B_0,B_s^0$ and $l,l'$ denote two different lepton flavors. For the decay of $B^0\to l^+l'^-$, there is no constraint from the current experimental upper bounds on the vector unparticle coupling with leptons. The constraint on the coupling constant between scalar unparticle field and leptons is sensitive to the scaling dimension of the unparticle $d_{\cal U}$. For the scattering process $e^-e^+\to l^-l'^+$, there is only constraint from experiments on the vector unparticle couplings with leptons but no constraint on the scalar unparticle. We study the $\sqrt s$ dependence of the cross section $ \frac{1}{\sigma} \frac{d\sigma}{d\sqrt s}$ of $e^+e^-\to l^-l'^+$ with different values of $d_{\cal U}$. If $d_{\cal U}=1.5$, the cross section is independent on the center mass energy. For $d_{\cal U}>1.5$, the cross section increases with $\sqrt s$. | Lepton flavor violating processes in unparticle physics |
The study of the neutrinoless double beta ($0 \beta\beta$) decay mode can provide us with important information on the neutrino properties, particularly on the electron neutrino absolute mass. In this work we revise the present constraints on the neutrino mass parameters derived from the $0 \beta\beta$ decay analysis of the experimentally interesting nuclei. We use the latest results for the phase space factors (PSFs) and nuclear matrix elements (NMEs), as well as for the experimental lifetimes limits. For the PSFs we use values computed with an improved method reported very recently. For the NMEs we use values chosen from literature on a case-by-case basis, taking advantage of the consensus reached by the community on several nuclear ingredients used in their calculation. Thus, we try to restrict the range of spread of the NME values calculated with different methods and, hence, to reduce the uncertainty in deriving limits for the Majorana neutrino mass parameter. Our results may be useful to have an up-date image on the present neutrino mass sensitivities associated with $0 \beta\beta$ measurements for different isotopes and to better estimate the range of values of the neutrino masses that can be explored in the future double beta decay (DBD) experiments. | Constraints on light neutrino parameters derived from the study of neutrinoless double beta decay |
The TRAPPIST-1 planetary system provides an unprecedented opportunity to study terrestrial exoplanet evolution with the James Webb Space Telescope (JWST) and ground-based observatories. Since M dwarf planets likely experience extreme volatile loss, the TRAPPIST-1 planets may have highly-evolved, possibly uninhabitable atmospheres. We used a versatile, 1D terrestrial-planet climate model with line-by-line radiative transfer and mixing length convection (VPL Climate) coupled to a terrestrial photochemistry model to simulate environmental states for the TRAPPIST-1 planets. We present equilibrium climates with self-consistent atmospheric compositions, and observational discriminants of post-runaway, desiccated, 10-100 bar O2- and CO2-dominated atmospheres, including interior outgassing, as well as for water-rich compositions. Our simulations show a range of surface temperatures, most of which are not habitable, although an aqua-planet TRAPPIST-1 e could maintain a temperate surface given Earth-like geological outgassing and CO2. We find that a desiccated TRAPPIST-1 h may produce habitable surface temperatures beyond the maximum greenhouse distance. Potential observational discriminants for these atmospheres in transmission and emission spectra are influenced by photochemical processes and aerosol formation, and include collision-induced oxygen absorption (O2-O2), and O3, CO, SO2, H2O, and CH4 absorption features, with transit signals of up to 200 ppm. Our simulated transmission spectra are consistent with K2, HST, and Spitzer observations of the TRAPPIST-1 planets. For several terrestrial atmospheric compositions, we find that TRAPPIST-1 b is unlikely to produce aerosols. These results can inform JWST observation planning and data interpretation for the TRAPPIST-1 system and other M dwarf terrestrial planets. | Evolved Climates and Observational Discriminants for the TRAPPIST-1 Planetary System |
Perivolaropoulos has recently proposed a position-deformed Heisenberg algebra which includes a maximal length [Phys.Rev.95, 103523 (2017)]. He has shown that this length scale naturally emerges in the context of cosmological particle's horizon or cosmic topology. Following this work, we propose a new deformed algebra and derive the maximal length uncertainty and its corresponding minimal momentum uncertainty from the generalized uncertainty principle. We also construct the corresponding Fourier transform and its inverse representations. Finally, we propose n-dimensional representation of this algebra | Hilbert space representation of maximal length and minimal momentum uncertainties |
If neutrinos get mass via the seesaw mechanism the mixing matrix describing neutrino oscillations can be effectively non-unitary. We show that in this case the neutrino appearance probabilities involve a new CP phase, phi, associated to non-unitarity. This leads to an ambiguity in extracting the "standard" three--neutrino phase delta_CP, which can survive even after neutrino and antineutrino channels are combined. Its existence should be taken into account in the planning of any oscillation experiment aiming at a robust measurement of delta_CP. | New ambiguity in probing CP violation in neutrino oscillations |
Multiple testing plagues many important questions in finance such as fund and factor selection. We propose a new way to calibrate both Type I and Type II errors. Next, using a double-bootstrap method, we establish a t-statistic hurdle that is associated with a specific false discovery rate (e.g., 5%). We also establish a hurdle that is associated with a certain acceptable ratio of misses to false discoveries (Type II error scaled by Type I error), which effectively allows for differential costs of the two types of mistakes. Evaluating current methods, we find that they lack power to detect outperforming managers. | False (and Missed) Discoveries in Financial Economics |
Annotation is the labeling of data by human effort. Annotation is critical to modern machine learning, and Bloomberg has developed years of experience of annotation at scale. This report captures a wealth of wisdom for applied annotation projects, collected from more than 30 experienced annotation project managers in Bloomberg's Global Data department. | Best Practices for Managing Data Annotation Projects |
In this paper we introduce a flexible HJM-type framework that allows for consistent modelling of intraday, spot, futures, and option prices. This framework is based on stochastic processes with economic interpretations and consistent with the initial term structure given in the form of a price forward curve. Furthermore, the framework allows for existing day-ahead spot price models to be used in an HJM setting. We include several explicit examples of classical spot price models but also show how structural models and factor models can be formulated within the framework. | A structural Heath-Jarrow-Morton framework for consistent intraday, spot, and futures electricity prices |
We demonstrate the local control of up to eight two-level systems interacting strongly with a microwave cavity. Following calibration, the frequency of each individual two-level system (qubit) is tunable without influencing the others. Bringing the qubits one by one on resonance with the cavity, we observe the collective coupling strength of the qubit ensemble. The splitting scales up with the square root of the number of the qubits, which is the hallmark of the Tavis-Cummings model. The local control circuitry causes a bypass shunting the resonator, and a Fano interference in the microwave readout, whose contribution can be calibrated away to recover the pure cavity spectrum. The simulator's attainable size of dressed states with up to five qubits is limited by reduced signal visibility, and -- if uncalibrated -- by off-resonance shifts of sub-components. Our work demonstrates control and readout of quantum coherent mesoscopic multi-qubit system of intermediate scale under conditions of noise. | Probing the Tavis-Cummings level splitting with intermediate-scale superconducting circuits |
A two-dimensional lattice hard-core boson system with a small fraction of bosonic or fermionic impurity particles is studied. The impurities have the same hopping and interactions as the dominant bosons and their effects are solely due to quantum statistics. Quantum Monte Carlo simulations are carried out in which paths of the dominant boson species are sampled and a summation is performed over all second-species paths compatible with the permutation cycles. Both kinds of impurities reduce modestly and equally the Kosterliz-Thouless superfluid transition temperature. However, the effective impurity interactions are found to be qualitatively different at lower temperatures; fermions are repulsive and further suppress superfluidity at low temperatures. | Quantum Monte Carlo simulations of bosonic and fermionic impurities in a two-dimensional hard-core boson system |
We consider weak solutions with finite entropy production to the scalar conservation law \begin{equation} \partial_t u+\mathrm{div}_x F(u)=0 \quad \mbox{in }(0,T)\times \mathbb{R}^d. \end{equation} Building on the kinetic formulation we prove under suitable nonlinearity assumption on $f$ that the set of non Lebesgue points of $u$ has Hausdorff dimension at most $d$. A notion of Lagrangian representation for this class of solutions is introduced and this allows for a new interpretation of the entropy dissipation measure. | On the structure of weak solutions to scalar conservation laws with finite entropy production |
Increasing accessibility of data to researchers makes it possible to conduct massive amounts of statistical testing. Rather than follow a carefully crafted set of scientific hypotheses with statistical analysis, researchers can now test many possible relations and let P-values or other statistical summaries generate hypotheses for them. Genetic epidemiology field is an illustrative case in this paradigm shift. Driven by technological advances, testing a handful of genetic variants in relation to a health outcome has been abandoned in favor of agnostic screening of the entire genome, followed by selection of top hits, e.g., by selection of genetic variants with the smallest association P-values. At the same time, nearly total lack of replication of claimed associations that has been shaming the field turned to a flow of reports whose findings have been robustly replicating. Researchers may have adopted better statistical practices by learning from past failures, but we suggest that a steep increase in the amount of statistical testing itself is an important factor. Regardless of whether statistical significance has been reached, an increased number of tested hypotheses leads to enrichment of smallest P-values with genuine associations. In this study, we quantify how the expected proportion of genuine signals (EPGS) among top hits changes with an increasing number of tests. When the rate of occurrence of genuine signals does not decrease too sharply to zero as more tests are performed, the smallest P-values are increasingly more likely to represent genuine associations in studies with more tests. | The more you test, the more you find: Smallest P-values become increasingly enriched with real findings as more tests are conducted |
We prove the stability conjecture of $\imath$canonical bases, which was raised by Huanchen Bao and Weiqiang Wang in 2016, for all locally finite types. To this end, we characterize the trivial module over the $\imath$quantum groups of such type at $q = \infty$. This result can be seen as a very restrictive version of the $\imath$crystal base theory for locally finite types. | Stability of $\imath$canonical bases of locally finite type |
Quantum computation started to become significant field of studies as it hold great promising towards the upgrade of our current computational power. Studying the evolution of quantum states serves as a good fundamental in understanding quantum information which lead to quantum computation. This was assisted with the respective mathematical tools such as Lie group and Lie algebra. In this study, the Lie algebra of $\mathfrak{su}(8)$ is represented in tensor product between three Pauli matrices. This is done by constructing the generalized Gell-Mann matrices and compared to the Pauli basis. This study will explicitly shows the one-to-one correlation of Gell-Mann matrices with the Pauli basis resembled change of coordinates. This is particularly useful when dealing with quantum circuit problems. | Representation of $\mathfrak{su}(8)$ in Pauli Basis |
The CEM2k and LAQGSM codes have been recently developed at Los Alamos National Laboratory to simulate nuclear reactions for a number of applications. We have benchmarked our codes against most available measured data at incident particle energies from 10 MeV to 800 GeV and have compared our results with predictions of other current models used by the nuclear community. Here, we present a brief description of our codes and show illustrative results to show that CEM2k and LAQGSM can be used as reliable event generators for space-radiation-shielding, cosmic-ray-propagation, and other astrophysical applications. Finally, we show the use of our calculated cross sections together with experimental data from our LANL T-16 compilation to produce evaluated files which we use in the GALPROP model of galactic particle propagation to better constrain the size of the CR halo. | CEM2k and LAQGSM as Event Generators for Space-Radiation-Shielding and Cosmic-Ray-Propagation Applications |
A set of vertices $S$ \emph{resolves} a graph $G$ if every vertex is uniquely determined by its vector of distances to the vertices in $S$. The \emph{metric dimension} of a graph $G$ is the minimum cardinality of a resolving set. In this paper we study the metric dimension of infinite graphs such that all its vertices have finite degree. We give necessary conditions for those graphs to have finite metric dimension and characterize infinite trees with finite metric dimension. We also establish some results about the metric dimension of the cartesian product of finite and infinite graphs, and give the metric dimension of the cartesian product of several families of graphs. | On the Metric Dimension of Infinite Graphs |
We consider sets of trace-normalized non-negative operators in Hilbert-Schmidt balls that maximize their mutual Hilbert-Schmidt distance; these are optimal arrangements in the sets of purity-limited classical or quantum states on a finite-dimensional Hilbert space. Classical states are understood to be represented by diagonal matrices, with the diagonal entries forming a probability vector. We also introduce the concept of spectrahedron arrangements which provides a unified framework for classical and quantum arrangements and the flexibility to define new types of optimal packings. Continuing a prior work, we combine combinatorial structures and line packings associated with frames to arrive at optimal arrangements of higher-rank quantum states. One new construction that is presented involves generating an optimal arrangement we call a Gabor-Steiner equiangular tight frame as the orbit of a projective representation of the Weyl-Heisenberg group over any finite abelian group. The minimal sets of linearly dependent vectors, the so-called binder, of the Gabor-Steiner equiangular tight frames are then characterized; under certain conditions these form combinatorial block designs and in one case generate a new class of block designs. The projections onto the span of minimal linearly dependent sets in the Gabor-Steiner equiangular tight frame are then used to generate further optimal spectrahedron arrangements. | Optimal arrangements of classical and quantum states with limited purity |
The $Z_N$-invariant chiral Potts model is considered as a perturbation of a $Z_N$ conformal field theory. In the self-dual case the renormalization group equations become simple, and yield critical exponents and anisotropic scaling which agree with exact results for the super-integrable lattice models. Although the continuum theory is not Lorentz invariant, it respects a novel type of space-time symmetry which allows for the observed spontaneous breaking of translational symmetry in the ground state. The continuum theory is shown to possess an infinite number of conserved charges on the self-dual line, which remain conserved when the theory is perturbed by the energy operator. | Critical Exponents of the Chiral Potts Model from Conformal Field Theory |
The form and evolution of multi-phase biomembranes is of fundamental importance in order to understand living systems. In order to describe these membranes, we consider a mathematical model based on a Canham--Helfrich--Evans two-phase elastic energy, which will lead to fourth order geometric evolution problems involving highly nonlinear boundary conditions. We develop a parametric finite element method in an axisymmetric setting. Using a variational approach, it is possible to derive weak formulations for the highly nonlinear boundary value problems such that energy decay laws, as well as conservation properties, hold for spatially discretised problems. We will prove these properties and show that the fully discretised schemes are well-posed. Finally, several numerical computations demonstrate that the numerical method can be used to compute complex, experimentally observed two-phase biomembranes. | Structure preserving discretisations of gradient flows for axisymmetric two-phase biomembranes |
A recent paper [J. A. Evans, D. Kamensky, Y. Bazilevs, "Variational multiscale modeling with discretely divergence-free subscales", Computers & Mathematics with Applications, 80 (2020) 2517-2537] introduced a novel stabilized finite element method for the incompressible Navier-Stokes equations, which combined residual-based stabilization of advection, energetic stability, and satisfaction of a discrete incompressibility condition. However, the convergence analysis and numerical tests of the cited work were subject to the restrictive assumption of a divergence-conforming choice of velocity and pressure spaces, where the pressure space must contain the divergence of every velocity function. The present work extends the convergence analysis to arbitrary inf-sup-stable velocity-pressure pairs (while maintaining robustness in the advection-dominated regime) and demonstrates the convergence of the method numerically, using both the traditional and isogeometric Taylor-Hood elements. | Variational multiscale modeling with discretely divergence-free subscales: Non-divergence-conforming discretizations |
We have assembled 21-cm linewidths for 376 of the 732 galaxies in a magnitude-limited redshift survey of the the Perseus-Pisces region. We analyze a distance limited subset of 271 galaxies (131 widths) to examine the relationship between linewidth and local density. The sample indicates that galaxies with linewidths $\gtrsim 480$ km/s are absent from regions where the galaxy density is $\lesssim 0.03$ galaxies Mpc$^{-3}$ ($M_{B(0)}< -18.3$). This effect is in the direction predicted by standard CDM models. Galaxies with linewidths $\lesssim$ 480 km/s appear throughout the sample. The observational constraints could be substantially improved with a larger sample, IR photometry, and more uniform 21-cm data. | The Rotation Velocity - Density Relation |
It has long been realized that dark matter halos formed in cosmological N-body simulations are characterized by density profiles rho(r) that, when suitably scaled, have similar shapes. Additionally, combining the density and velocity dispersion profiles sigma(r), each of which have decidedly nonpower-law shapes, leads to quantity rho/(sigma^3) that is a power-law in radius over 3 orders of magnitude in radius. Halos' velocity anisotropy profiles beta(r) vary from isotropic near the centers of halos to quite radially anisotropic near the virial radius. Finally, there appears to be a nearly linear correlation between beta and the logarithmic density slope gamma for a wide variety of halos. This work is part of a continuing investigation of the above interrelationships and their origins using analytical and semi-analytical techniques. Our finding suggest that the nearly linear beta--gamma relationship is not just another expression of scale-free rho/(sigma^3) behavior. We also note that simultaneously reproducing density and anisotropy profiles like those found in simulations requires beta(r) and gamma(r) to have similar shapes, leading to nearly linear beta--gamma correlations. This work suggests that the beta--gamma and power-law rho/(sigma^3) relations have distinct physical origins. | Density Profiles of Collisionless Equilibria. II. Anisotropic Spherical Systems |
Massive vector fields feature in several areas of particle physics, e.g., as carriers of weak interactions, dark matter candidates, or as an effective description of photons in a plasma. Here we investigate vector fields with self-interactions by replacing the mass term in the Proca equation with a general potential. We show that this seemingly benign modification inevitably introduces ghost instabilities of the same kind as those recently identified for vector-tensor theories of modified gravity (but in this simpler, minimally coupled theory). It has been suggested that nonperturbative dynamics may drive systems away from such instabilities. We demonstrate that this is not the case by evolving a self-interacting Proca field on a Kerr background, where it grows due to the superradiant instability. The system initially evolves as in the massive case, but instabilities are triggered in a finite time once the self-interaction becomes significant. These instabilities have implications for the formation of condensates of massive, self-interacting vector bosons, the possibility of spin-one bosenovae, vector dark matter models, and effective models for interacting photons in a plasma. | The problem with Proca: ghost instabilities in self-interacting vector fields |
Thin, Keplerian accretion disks generically become gravitationally unstable at large radius. I investigate the nonlinear outcome of such instability in cool disks using razor-thin, local, numerical models. Cooling, characterized by a constant cooling time t_c, drives the instability. I show analytically that, if the disk can reach a steady state in which heating by dissipation of turbulence balances cooling, then the dimensionless angular momentum flux density \alpha = ((9/4) \gamma (\gamma-1) \Omega t_c)^{-1}. Numerical experiments show that: (1) if t_c \gtrsim 3\Omega^{-1} then the disk reaches a steady, gravito-turbulent state in which Q \sim 1 and cooling is balanced by heating due to dissipation of turbulence; (2) if t_c \lesssim 3\Omega^{-1}, then the disk fragments, possibly forming planets or stars; (3) in a steady, gravito-turbulent state, surface density structures have a characteristic physical scale \sim 64 G \Sigma/\Omega^2 that is independent of the size of the computational domain. | Nonlinear Outcome of Gravitational Instability in Cooling, Gaseous Disks |
Let $U:\mathcal{C}\rightarrow\mathcal{D}$ be a strong monoidal functor between abelian monoidal categories admitting a right adjoint $R$, such that $R$ is exact, faithful and the adjunction $U\dashv R$ is coHopf. Building on the work of Balan, we show that $R$ is separable (resp., special) Frobenius monoidal if and only if $R(\mathbb{1}_{\mathcal{D}})$ is a separable (resp., special) Frobenius algebra in $\mathcal{C}$. If further, $\mathcal{C},\mathcal{D}$ are pivotal (resp., ribbon) categories and $U$ is a pivotal (resp., braided pivotal) functor, then $R$ is a pivotal (resp., ribbon) functor if and only if $R(\mathbb{1}_{\mathcal{D}})$ is a symmetric Frobenius algebra in $\mathcal{C}$. As an application, we construct Frobenius monoidal functors going into the Drinfeld center $\mathcal{Z}(\mathcal{C})$, thereby producing Frobenius algebras in it. | Frobenius monoidal functors from (co)Hopf adjunctions |
In this article, we develop a simple mathematical GNU Octave/MATLAB code that is easy to modify for the simulation of mathematical models governed by fractional-order differential equations, and for the resolution of fractional-order optimal control problems through Pontryagin's maximum principle (indirect approach to optimal control). For this purpose, a fractional-order model for the respiratory syncytial virus (RSV) infection is considered. The model is an improvement of one first proposed by the authors in [Chaos Solitons Fractals 117 (2018), 142--149]. The initial value problem associated with the RSV infection fractional model is numerically solved using Garrapa's fde12 solver and two simple methods coded here in Octave/MATLAB: the fractional forward {Euler's} method and the predict-evaluate-correct-evaluate (PECE) method of Adams--Bashforth--Moulton. A fractional optimal control problem is then formulated having treatment as the control. The fractional Pontryagin maximum principle is used to characterize the fractional optimal control and the extremals of the problem are determined numerically through the implementation of the forward-backward PECE method. The implemented algorithms are available on GitHub and, at the end of the paper, in appendixes, both for the uncontrolled initial value problem as well as for the fractional optimal control problem, using the free GNU Octave computing software and assuring compatibility with~MATLAB. | Numerical Fractional Optimal Control of Respiratory Syncytial Virus Infection in Octave/MATLAB |
Employing the $G_0W_0$ approximation of Hedin's $GW$ approach one can obtain quasi-particle energies of extended systems and molecules with good accuracy. However, for many materials, semi-local exchange-correlation functionals are unsatisfactory starting points for $G_0W_0$ calculations. Hybrid functionals often improve upon them, but at a substantially higher computational cost. As an alternative, we suggest the LDA-1/2 method, which provides reasonable band gaps, without being computationally involved. In this work, we systematically compare 3 starting points for $G_0W_0$: LDA, PBE0, and LDA-1/2. A selection of solids is chosen for this benchmark: C, Si, SiC, AlP, LiF, MgO, Ne, Ar, GaN, GaAs, CdS, ZnS, and ZnO. We demonstrate that LDA-1/2 is a good starting point in most cases, reducing the mean absolute error of band gaps by 50% when compared to the other 2 functionals. | Probing the LDA-1/2 method as a starting point for $G_0W_0$ calculations |
Several years ago Linial and Meshulam introduced a model called X_d(n,p) of random n-vertex d-dimensional simplicial complexes. The following question suggests itself very naturally: What is the threshold probability p=p(n) at which the d-dimensional homology of such a random d-complex is, almost surely, nonzero? Here we derive an upper bound on this threshold. Computer experiments that we have conducted suggest that this bound may coincide with the actual threshold, but this remains an open question. | When does the top homology of a random simplicial complex vanish? |
Using a constrained formalism for Einstein equations in Dirac gauge, we propose to compute excised quasistationary initial data for black hole spacetimes in full general relativity. Vacuum spacetime settings are numerically constructed by using the isolated horizon formalism; we especially tackle the conformal metric part of our equations, assuming global stationarity. We show that a no-boundary treatment can be used on the horizon for the equation related to the conformal metric. We relate this finding to previous suggestions in the literature, and use our results to assess the widely used conformally flat approximation for computing black hole initial data. | Isolated horizons in numerical relativity: constructing the excised Kerr spacetime in Dirac gauge |
We consider a ferromagnetic/antiferromagnetic bilayer on a triangular lattice in the framework of the planar Heisenberg model. The impact of the geometrical frustration in this system on the magnetization curves and the exchange bias phenomenon is studied. The magnetization curves and the phase diagram for such systems are obtained. We observe horizontal plateaus and a split of the hysteresis loop on the magnetization curves. It is shown that the shift of the hysteresis loop (exchange bias) occurs for the systems with a magnetically hard antiferromagnet. | Magnetization curves of geometrically frustrated exchange-biased FM/AFM bilayers |
Contrastive pretraining techniques for text classification has been largely studied in an unsupervised setting. However, oftentimes labeled data from related tasks which share label semantics with current task is available. We hypothesize that using this labeled data effectively can lead to better generalization on current task. In this paper, we propose a novel way to effectively utilize labeled data from related tasks with a graph based supervised contrastive learning approach. We formulate a token-graph by extrapolating the supervised information from examples to tokens. Our formulation results in an embedding space where tokens with high/low probability of belonging to same class are near/further-away from one another. We also develop detailed theoretical insights which serve as a motivation for our method. In our experiments with $13$ datasets, we show our method outperforms pretraining schemes by $2.5\%$ and also example-level contrastive learning based formulation by $1.8\%$ on average. In addition, we show cross-domain effectiveness of our method in a zero-shot setting by $3.91\%$ on average. Lastly, we also demonstrate our method can be used as a noisy teacher in a knowledge distillation setting to significantly improve performance of transformer based models in low labeled data regime by $4.57\%$ on average. | Supervised Graph Contrastive Pretraining for Text Classification |
We study the high energy behaviour of elastic scattering amplitudes within the leading logarithm approximation. In particular, we cast the amplitude in a form which allows us to study the internal dynamics of the BFKL Pomeron for general momentum transfer. We demonstrate that the momentum transfer acts as an effective infrared cut-off which ensures that the dominant contribution arises from short distance physics. | Diffusion and the BFKL Pomeron |
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