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|---|---|---|---|---|
2109.01435
|
Chekanov torus and Gelfand--Zeitlin torus in $S^2 \times S^2$
|
The Chekanov torus was the first known \emph{exotic} torus, a monotone Lagrangian torus that is not Hamiltonian isotopic to the standard monotone Lagrangian torus. We explore the relationship between the Chekanov torus in $S^2 \times S^2$ and a monotone Lagrangian torus which had been introduced before Chekanov's construction \cite{Chekanov}. We prove that the monotone Lagrangian torus fiber in a certain Gelfand--Zeitlin system is Hamiltonian isotopic to the Chekanov torus in $S^2 \times S^2$.
|
[
"Mathematics Archive->math.SG"
] | 2021-09-03T10:55:33Z |
1706.05549
|
A Large-Scale CNN Ensemble for Medication Safety Analysis
|
Revealing Adverse Drug Reactions (ADR) is an essential part of post-marketing drug surveillance, and data from health-related forums and medical communities can be of a great significance for estimating such effects. In this paper, we propose an end-to-end CNN-based method for predicting drug safety on user comments from healthcare discussion forums. We present an architecture that is based on a vast ensemble of CNNs with varied structural parameters, where the prediction is determined by the majority vote. To evaluate the performance of the proposed solution, we present a large-scale dataset collected from a medical website that consists of over 50 thousand reviews for more than 4000 drugs. The results demonstrate that our model significantly outperforms conventional approaches and predicts medicine safety with an accuracy of 87.17% for binary and 62.88% for multi-classification tasks.
|
[
"Computer Science Archive->cs.CL",
"Computer Science Archive->cs.IR"
] | 2017-06-17T15:06:58Z |
1410.6382
|
Attribute Efficient Linear Regression with Data-Dependent Sampling
|
In this paper we analyze a budgeted learning setting, in which the learner can only choose and observe a small subset of the attributes of each training example. We develop efficient algorithms for ridge and lasso linear regression, which utilize the geometry of the data by a novel data-dependent sampling scheme. When the learner has prior knowledge on the second moments of the attributes, the optimal sampling probabilities can be calculated precisely, and result in data-dependent improvements factors for the excess risk over the state-of-the-art that may be as large as $O(\sqrt{d})$, where $d$ is the problem's dimension. Moreover, under reasonable assumptions our algorithms can use less attributes than full-information algorithms, which is the main concern in budgeted learning settings. To the best of our knowledge, these are the first algorithms able to do so in our setting. Where no such prior knowledge is available, we develop a simple estimation technique that given a sufficient amount of training examples, achieves similar improvements. We complement our theoretical analysis with experiments on several data sets which support our claims.
|
[
"Computer Science Archive->cs.LG",
"Statistics Archive->stat.ML"
] | 2014-10-23T14:55:09Z |
0903.3624
|
Distributed and Adaptive Algorithms for Vehicle Routing in a Stochastic and Dynamic Environment
|
In this paper we present distributed and adaptive algorithms for motion coordination of a group of m autonomous vehicles. The vehicles operate in a convex environment with bounded velocity and must service demands whose time of arrival, location and on-site service are stochastic; the objective is to minimize the expected system time (wait plus service) of the demands. The general problem is known as the m-vehicle Dynamic Traveling Repairman Problem (m-DTRP). The best previously known control algorithms rely on centralized a-priori task assignment and are not robust against changes in the environment, e.g. changes in load conditions; therefore, they are of limited applicability in scenarios involving ad-hoc networks of autonomous vehicles operating in a time-varying environment. First, we present a new class of policies for the 1-DTRP problem that: (i) are provably optimal both in light- and heavy-load condition, and (ii) are adaptive, in particular, they are robust against changes in load conditions. Second, we show that partitioning policies, whereby the environment is partitioned among the vehicles and each vehicle follows a certain set of rules in its own region, are optimal in heavy-load conditions. Finally, by combining the new class of algorithms for the 1-DTRP with suitable partitioning policies, we design distributed algorithms for the m-DTRP problem that (i) are spatially distributed, scalable to large networks, and adaptive to network changes, (ii) are within a constant-factor of optimal in heavy-load conditions and stabilize the system in any load condition. Simulation results are presented and discussed.
|
[
"Computer Science Archive->cs.RO"
] | 2009-03-20T22:48:08Z |
1308.5534
|
Maxima of Weibull-like distributions and the Lambert W function
|
The Weibull--like distributions form a large class of probability distributions that belong to the domain of attraction for the maxima of the Gumbel law. Besides the Weibull distribution, it includes important distributions as the Gamma laws and, in particular, the $\chi^2$ distributions. In order to have explicit expressions of the norming constants for the maxima it is necessary to solve asymptotically a nonlinear equation; however, for some members of that family, numerical and simulation studies show that the constants that are usual suggested are inaccurate for moderate or even large sample sizes. In this paper we propose other norming constants computed with the asymptotics of the Lambert W function that significantly improve the accuracy of the approximation to the Gumbel law. These results are applied to the computation of the constants for the maxima of Gamma random variables that appear in some applied problems.
|
[
"Mathematics Archive->math.ST",
"Statistics Archive->stat.TH"
] | 2013-08-26T10:20:22Z |
1503.02568
|
High pressure floating zone growth and structural properties of ferrimagnetic quantum paraelectric BaFe$_{12}$O$_{19}$
|
High quality single crystals of BaFe$_{12}$O$_{19}$ were grown using the floating zone technique in flowing oxygen pressurized to 100 atm. Single crystal neutron diffraction was used to determine the nuclear and magnetic structure of BaFe$_{12}$O$_{19}$ at 4 K and 295 K. At both temperatures, there exist local electric dipoles formed by the off-mirror-plane displacements of magnetic Fe$^{3+}$ ions at the bipyramidal sites. The displacement at 4 K is about half of that at room temperature. The temperature dependence of the specific heat shows no anomaly associated with long range polar ordering in the temperature range from 1.90-300 K. The inverse dielectric permittivity, $1/\varepsilon$, along the c-axis shows a $T^2$ temperature dependence between 10 K and 20 K, with a significantly reduced temperature dependence displayed below 10 K. Moreover, as the sample is cooled below 1.4 K there is an anomalous sharp upturn in $1/\varepsilon$. These features resemble those of classic quantum paraelectrics such as SrTiO$_3$. The presence of the upturn in $1/\varepsilon$ indicates that BaFe$_{12}$O$_{19}$ is a critical quantum paraelectric system with Fe$^{3+}$ ions involved in both magnetic and electric dipole formation.
|
[
"Physics Archive->cond-mat->cond-mat.mtrl-sci",
"Physics Archive->cond-mat->cond-mat.str-el"
] | 2015-03-09T17:32:26Z |
nucl-th/9804009
|
The neutron charge form factor in helium-3
|
In order to measure the charge form factor of the neutron, $G^n_E(Q^2)$, one needs to use a neutron bound in a nuclear target. We calculate the change in the form factor for a neutron bound in $^3He$, with respect to the free case, using several versions of the quark meson coupling model. It is found that the form factor may be suppressed by as much as 12% at $Q^2 = 0.5{GeV}^2$ with respect to that of the free neutron.
|
[
"Physics Archive->hep->hep-ph",
"Physics Archive->nucl->nucl-ex",
"Physics Archive->nucl->nucl-th"
] | 1998-04-06T09:56:25Z |
2211.09304
|
Spectral conditions for $k$-extendability and $k$-factors of bipartite graphs
|
Let $G$ be a connected graph. If $G$ contains a matching of size $k$, and every matching of size $k$ is contained in a perfect matching of $G$, then $G$ is said to be \emph{$k$-extendable}. A $k$-regular spanning subgraph of $G$ is called a \textit{$k$-factor}. In this paper, we provide spectral conditions for a (balanced bipartite) graph with minimum degree $\delta$ to be $k$-extendable, and for the existence of a $k$-factor in a balanced bipartite graph, respectively. Our results generalize some previous results on perfect matchings of graphs, and extend the results in \cite{D.F} and \cite{W.L} to $k$-extendable graphs. Furthermore, our results generalize the result of Lu, Liu and Tian \cite{Lu-Liu} to general regular factors. Additionally, using the equivalence of $k$ edge-disjoint perfect matchings and $k$-factors in balanced bipartite graphs, our results can derive a spectral condition for the existence of $k$ edge-disjoint perfect matchings in balanced bipartite graphs.
|
[
"Mathematics Archive->math.CO"
] | 2022-11-17T02:45:09Z |
0810.2208
|
Multipath Channels of Unbounded Capacity
|
The capacity of discrete-time, noncoherent, multipath fading channels is considered. It is shown that if the variances of the path gains decay faster than exponentially, then capacity is unbounded in the transmit power.
|
[
"Computer Science Archive->cs.IT",
"Mathematics Archive->math.IT"
] | 2008-10-13T11:21:01Z |
0801.0859
|
Evolution of Massive Blackhole Triples II -- The effect of the BH triples dynamics on the structure of the galactic nuclear
|
In this paper, we investigate the structures of galaxies which either have or have had three BHs using $N$-body simulations, and compare them with those of galaxies with binary BHs. We found that the cusp region of a galaxy which have (or had) triple BHs is significantly larger and less dense than that of a galaxy with binary BHs of the same mass. Moreover, the size of the cusp region depends strongly on the evolution history of triple BHs, while in the case of binary BHs, the size of the cusp is determined by the mass of the BHs. In galaxies which have (or had) three BHs, there is a region with significant radial velocity anisotropy, while such a region is not observed in galaxies with binary BH. These differences come from the fact that with triple BHs the energy deposit to the central region of the galaxy can be much larger due to multiple binary-single BH scatterings. Our result suggests that we can discriminate between galaxies which experienced triple BH interactions with those which did not, through the observable signatures such as the cusp size and velocity anisotropy.
|
[
"Physics Archive->astro-ph"
] | 2008-01-06T13:15:00Z |
cond-mat/0601648
|
Colloidal glass transition observed in confinement
|
We study a colloidal suspension confined between two quasi-parallel walls as a model system for glass transitions in confined geometries. The suspension is a mixture of two particle sizes to prevent wall-induced crystallization. We use confocal microscopy to directly observe the motion of colloidal particles. This motion is slower in confinement, thus producing glassy behavior in a sample which is a liquid in an unconfined geometry. For higher volume fraction samples (closer to the glass transition), the onset of confinement effects occurs at larger length scales.
|
[
"Physics Archive->cond-mat->cond-mat.mtrl-sci",
"Physics Archive->cond-mat->cond-mat.soft"
] | 2006-01-28T22:04:24Z |
2101.04279
|
Enhanced Information Fusion Network for Crowd Counting
|
In recent years, crowd counting, a technique for predicting the number of people in an image, becomes a challenging task in computer vision. In this paper, we propose a cross-column feature fusion network to solve the problem of information redundancy in columns. We introduce the Information Fusion Module (IFM) which provides a channel for information flow to help different columns to obtain significant information from another column. Through this channel, different columns exchange information with each other and extract useful features from the other column to enhance key information. Hence, there is no need for columns to pay attention to all areas in the image. Each column can be responsible for different regions, thereby reducing the burden of each column. In experiments, the generalizability of our model is more robust and the results of transferring between different datasets acheive the comparable results with the state-of-the-art models.
|
[
"Computer Science Archive->cs.CV"
] | 2021-01-12T03:35:22Z |
1712.08487
|
Features of Neutrino Mixing
|
The elements (squared) of the neutrino mixing matrix are found to satisfy, as functions of the induced mass, a set of differential equations. They show clearly the dominance of pole terms when the neutrino masses "cross". Using the known vacuum mixing parameters as initial conditions, it is found that these equations have very good approximate solutions, for all values of the induced mass. The results are applicable to Long Baseline Experiments (LBL).
|
[
"Physics Archive->hep->hep-ph"
] | 2017-12-22T15:02:35Z |
1703.06292
|
Hydrodynamic limit for the Ginzburg-Landau $\nabla\phi$ interface model with non-convex potential
|
Hydrodynamic limit for the Ginzburg-Landau $\nabla\phi$ interface model was established in [Nishikawa, 2003] under the Dirichlet boundary conditions. This paper studies the similar problem, but with non-convex potentials. Because of the lack of strict convexity, a lot of difficulties arise, especially, on the identification of equilibrium states. We give a proof of the equivalence between the stationarity and the Gibbs property under quite general settings, and as its conclusion, we complete the identification of equilibrium states under the high temparature regime in [Deuschel and Cotar, 2008]. We also establish some uniform estimates for variances of extremal Gibbs measures under quite general settings.
|
[
"Mathematics Archive->math.PR"
] | 2017-03-18T12:41:55Z |
hep-ex/0011014
|
Jet energy scale setting with "photon+Jet" events at LHC energies. Selection of events with a clean "photon+Jet" topology and photon Pt - jet Pt disbalance
|
It is shown in the paper that Pt activity limitation (modulus of the vector sum) of all particle beyond "photon+Jet" system Pt^out leads to the noticeable photon Pt - jet Pt disbalance decreasing. On a simultaneous restriction of the cluster Pt and Pt^out from above it is possible to reach an acceptable balance between photon Pt - jet Pt with a sufficient number of the photon Pt - jet Pt events for the jet energy scale setting and hadron calorimeter calibratiom of the CMS detector at LHC.
|
[
"Physics Archive->hep->hep-ex"
] | 2000-11-03T17:06:58Z |
1412.1616
|
A solution to Ahmed's Integral(II)
|
In the year 2000, Ahmed proposed a family of integrals in the American Mathematical Monthly which invoked a considerable response then. Here I would like to present another solution to this family of integrals. I propose to call this as Ahmed's Integral (II) in the light of the well known Ahmed's Integral.
|
[
"Mathematics Archive->math.HO"
] | 2014-12-04T10:52:49Z |
hep-th/0512005
|
Generalised T-Duality and Non-Geometric Backgrounds
|
We undertake a systematic analysis of non-geometric backgrounds in string theory by seeking stringy liftings of a class of gauged supergravity theories. In addition to conventional flux compactifications and non-geometric T-folds with T-duality transition functions, we find a new class of non-geometric backgrounds with non-trivial dependence on the dual coordinates that are conjugate to the string winding number. We argue that T-duality acts in our class of theories, including those cases without isometries in which the conventional Buscher rules cannot be applied, and that these generalised T-dualities can take T-folds or flux compactifications on twisted tori to examples of the new non-geometric backgrounds. We show that the new class of non-geometric backgrounds and the generalised T-dualities arise naturally in string field theory, and are readily formulated in terms of a doubled geometry, related to generalised geometry. At special points in moduli space, some of the non-geometric constructions become equivalent to asymmetric orbifolds which are known to provide consistent string backgrounds. We construct the bosonic sector of the corresponding gauged supergravity theories and show that they have a universal form in any dimension, and in particular construct the scalar potential. We apply this to the supersymmetric WZW model, giving the complete non-linear structure for a class of WZW-model deformations.
|
[
"Physics Archive->hep->hep-th"
] | 2005-12-01T05:33:05Z |
1205.4018
|
Global status of neutrino oscillation parameters after Neutrino-2012
|
Here we update the global fit of neutrino oscillations in arXiv:1103.0734 and arXiv:1108.1376 including the recent measurements of reactor antineutrino disappearance reported by the Double Chooz, Daya Bay and RENO experiments, together with latest MINOS and T2K appearance and disappearance results, as presented at the Neutrino-2012 conference. We find that the preferred global fit value of $\theta_{13}$ is quite large: $\sin^2\theta_{13} \simeq 0.025$ for normal and inverted neutrino mass ordering, with $\theta_{13} = 0$ now excluded at more than 10$\sigma$. The impact of the new $\theta_{13}$ measurements over the other neutrino oscillation parameters is discussed as well as the role of the new long-baseline neutrino data and the atmospheric neutrino analysis in the determination of a non-maximal atmospheric angle $\theta_{23}$.
|
[
"Physics Archive->hep->hep-ex",
"Physics Archive->hep->hep-ph"
] | 2012-05-17T19:55:01Z |
1812.03203
|
Synthetic Dynamic PMU Data Generation: A Generative Adversarial Network Approach
|
This paper concerns with the production of synthetic phasor measurement unit (PMU) data for research and education purposes. Due to the confidentiality of real PMU data and no public access to the real power systems infrastructure information, the lack of credible realistic data becomes a growing concern. Instead of constructing synthetic power grids and then producing synthetic PMU measurement data by time simulations, we propose a model-free approach to directly generate synthetic PMU data. we train the generative adversarial network (GAN) with real PMU data, which can be used to generate synthetic PMU data capturing the system dynamic behaviors. To validate the sequential generation by GAN to mimic PMU data, we theoretically analyze GAN's capacity of learning system dynamics. Further by evaluating the synthetic PMU data by a proposed quantitative method, we verify GAN's potential to synthesize realistic samples and meanwhile realize that GAN model in this paper still has room to improve. Moreover it is the first time that such generative model is applied to synthesize PMU data.
|
[
"Computer Science Archive->cs.LG",
"Electrical Engineering and Systems Science Archive->eess.SP"
] | 2018-12-07T20:14:01Z |
0910.1549
|
Classical limit of non-Hermitian quantum dynamics - a generalised canonical structure
|
We investigate the classical limit of non-Hermitian quantum dynamics arising from a coherent state approximation, and show that the resulting classical phase space dynamics can be described by generalised "canonical" equations of motion, for both conservative and dissipative motion. The dynamical equations combine a symplectic flow associated with the Hermitian part of the Hamiltonian with a metric gradient flow associated with the anti-Hermitian part of the Hamiltonian. We derive this structure of the classical limit of quantum systems in the case of a Euclidean phase space geometry. As an example we show that the classical dynamics of a damped and driven oscillator can be linked to a non-Hermitian quantum system, and investigate the quantum classical correspondence. Furthermore, we present an example of an angular momentum system whose classical phase space is spherical and show that the generalised canonical structure persists for this nontrivial phase space geometry.
|
[
"Mathematics Archive->math.MP",
"Physics Archive->math-ph",
"Physics Archive->quant-ph"
] | 2009-10-08T16:51:51Z |
quant-ph/0408137
|
Eigenvalue Estimation of Differential Operators
|
We demonstrate how linear differential operators could be emulated by a quantum processor, should one ever be built, using the Abrams-Lloyd algorithm. Given a linear differential operator of order 2S, acting on functions psi(x_1,x_2,...,x_D) with D arguments, the computational cost required to estimate a low order eigenvalue to accuracy Theta(1/N^2) is Theta((2(S+1)(1+1/nu)+D)log N) qubits and O(N^{2(S+1)(1+1/nu)} (D log N)^c) gate operations, where N is the number of points to which each argument is discretized, nu and c are implementation dependent constants of O(1). Optimal classical methods require Theta(N^D) bits and Omega(N^D) gate operations to perform the same eigenvalue estimation. The Abrams-Lloyd algorithm thereby leads to exponential reduction in memory and polynomial reduction in gate operations, provided the domain has sufficiently large dimension D > 2(S+1)(1+1/nu). In the case of Schrodinger's equation, ground state energy estimation of two or more particles can in principle be performed with fewer quantum mechanical gates than classical gates.
|
[
"Physics Archive->quant-ph"
] | 2004-08-20T18:58:19Z |
1605.02014
|
Existence of invariant measures for the stochastic damped Schr\"odinger equation
|
In this paper, we address the long time behaviour of solutions of the stochastic Schrodinger equation in $\mathbb{R}^d$. We prove the existence of an invariant measure and establish asymptotic compactness of solutions, implying in particular the existence of an ergodic measure.
|
[
"Mathematics Archive->math.AP"
] | 2016-05-06T17:50:39Z |
nucl-th/0701081
|
Exotic modes of excitation in atomic nuclei far from stability
|
We review recent studies of the evolution of collective excitations in atomic nuclei far from the valley of $\beta$-stability. Collective degrees of freedom govern essential aspects of nuclear structure, and for several decades the study of collective modes such as rotations and vibrations has played a vital role in our understanding of complex properties of nuclei. The multipole response of unstable nuclei and the possible occurrence of new exotic modes of excitation in weakly-bound nuclear systems, present a rapidly growing field of research, but only few experimental studies of these phenomena have been reported so far. Valuable data on the evolution of the low-energy dipole response in unstable neutron-rich nuclei have been gathered in recent experiments, but the available information is not sufficient to determine the nature of observed excitations. Even in stable nuclei various modes of giant collective oscillations had been predicted by theory years before they were observed, and for that reason it is very important to perform detailed theoretical studies of the evolution of collective modes of excitation in nuclei far from stability. We therefore discuss the modern theoretical tools that have been developed in recent years for the description of collective excitations in weakly-bound nuclei. The review focuses on the applications of these models to studies of the evolution of low-energy dipole modes from stable nuclei to systems near the particle emission threshold, to analyses of various isoscalar modes, those for which data are already available, as well as those that could be observed in future experiments, to a description of charge-exchange modes and their evolution in neutron-rich nuclei, and to studies of the role of exotic low-energy modes in astrophysical processes.
|
[
"Physics Archive->nucl->nucl-ex",
"Physics Archive->nucl->nucl-th"
] | 2007-01-26T16:53:35Z |
1808.10420
|
A concise frictional contact formulation based on surface potentials and isogeometric discretization
|
This work presents a concise theoretical and computational framework for the finite element formulation of frictional contact problems with arbitrarily large deformation and sliding. The aim of this work is to extend the contact theory based on surface potentials (Sauer and De Lorenzis, 2013) to account for friction. Coulomb friction under isothermal conditions is considered here. For a consistent friction formulation, we start with the first and second laws of thermodynamics and derive the governing equations at the contact interface. A so-called interacting gap can then be defined as a kinematic variable unifying both sliding/sticking and normal/tangential contact. A variational principle for the frictional system can then be formulated based on a purely kinematical constraint. The direct elimination approach applied to the tangential part of this constraint leads to the so-called moving friction cone approach of Wriggers and Haraldsson (2003). Compared with existing friction formulations, our approach reduces the theoretical and computational complexity. Several numerical examples are presented to demonstrate the accuracy and robustness of the proposed friction formulation.
|
[
"Computer Science Archive->cs.CE"
] | 2018-08-30T17:40:40Z |
1805.06861
|
Answer Set Programming Modulo `Space-Time'
|
We present ASP Modulo `Space-Time', a declarative representational and computational framework to perform commonsense reasoning about regions with both spatial and temporal components. Supported are capabilities for mixed qualitative-quantitative reasoning, consistency checking, and inferring compositions of space-time relations; these capabilities combine and synergise for applications in a range of AI application areas where the processing and interpretation of spatio-temporal data is crucial. The framework and resulting system is the only general KR-based method for declaratively reasoning about the dynamics of `space-time' regions as first-class objects. We present an empirical evaluation (with scalability and robustness results), and include diverse application examples involving interpretation and control tasks.
|
[
"Computer Science Archive->cs.AI"
] | 2018-05-17T17:05:30Z |
astro-ph/0301466
|
Towards a self-consistent relativistic model of the exterior gravitational field of rapidly rotating neutron stars
|
We present a self-consistent, relativistic model of rapidly rotating neutron stars describing their exterior gravitational field. This is achieved by matching the new solution of Einstein's field equations found by Manko et al. (2000) and the numerical results for the interior of neutron stars with different equations of state calculated by Cook et al. (1994). This matching process gives constraints for the choice of the five parameters of the vacuum solution. Then we investigate some properties of the gravitational field of rapidly rotating neutron stars with these fixed parameters.
|
[
"Physics Archive->astro-ph"
] | 2003-01-23T09:44:34Z |
1901.00638
|
Dependence of Solutions and Eigenvalues of Third Order Linear Measure Differential Equations on Measures
|
This paper deals with a complex third order linear measure differential equation \begin{equation*} i\mathrm{d}\left( y^{\prime }\right) ^{\bullet }+2iq\left( x\right) y^{\prime }\mathrm{d}x+y\left( i\mathrm{d}q\left( x\right) +\mathrm{d}p\left( x\right) \right) = \lambda y\mathrm{d}x \end{equation*} on a bounded interval with boundary conditions presenting a mixed aspect of the Dirichlet and the periodic problems. The dependence of eigenvalues on the coefficients $p$, $q$ is investigated. We prove that the $n$-th eigenvalue is continuous in $p$, $q$ when the norm topology of total variation and the weak$^*$ topology are considered. Moreover, the Fr\'{e}chet differentiability of the $n$-th eigenvalue in $p$, $q$ with the norm topology of total variation is also considered. To deduce these conclusions, we investigate the dependence of solutions of the above equation on the coefficients $p$, $q$ with different topologies and establish the counting lemma of eigenvalues according to the estimates of solutions.
|
[
"Mathematics Archive->math.SP"
] | 2019-01-03T07:36:15Z |
1710.09217
|
Unramified 2-extensions of totally imaginary number fields and 2-adic analytic groups
|
- Let K be a totally imaginary number field. Denote by G ur K (2) the Galois group of the maximal unramified pro-2 extension of K. By comparing cup-products in {\'e}tale cohomology of SpecO K and cohomology of uniform pro-2 groups, we obtain situations where G ur K (2) has no non-trivial uniform analytic quotient, proving some new special cases of the unramified Fontaine-Mazur conjecture. For example, in the family of imaginary quadratic fields K for which the 2-rank of the class group is equal to 5, we obtain that for at least 33.12% of such K, the group G ur K (2) has no non-trivial uniform analytic quotient.
|
[
"Mathematics Archive->math.NT"
] | 2017-10-25T13:11:12Z |
1812.08089
|
Inference for Heterogeneous Effects using Low-Rank Estimation of Factor Slopes
|
We study a panel data model with general heterogeneous effects where slopes are allowed to vary across both individuals and over time. The key dimension reduction assumption we employ is that the heterogeneous slopes can be expressed as having a factor structure so that the high-dimensional slope matrix is low-rank and can thus be estimated using low-rank regularized regression. We provide a simple multi-step estimation procedure for the heterogeneous effects. The procedure makes use of sample-splitting and orthogonalization to accommodate inference following the use of penalized low-rank estimation. We formally verify that the resulting estimator is asymptotically normal allowing simple construction of inferential statements for {the individual-time-specific effects and for cross-sectional averages of these effects}. We illustrate the proposed method in simulation experiments and by estimating the effect of the minimum wage on employment.
|
[
"Mathematics Archive->math.ST",
"Statistics Archive->stat.TH"
] | 2018-12-19T17:05:26Z |
2310.16331
|
Brain-Inspired Reservoir Computing Using Memristors with Tunable Dynamics and Short-Term Plasticity
|
Recent advancements in reservoir computing research have created a demand for analog devices with dynamics that can facilitate the physical implementation of reservoirs, promising faster information processing while consuming less energy and occupying a smaller area footprint. Studies have demonstrated that dynamic memristors, with nonlinear and short-term memory dynamics, are excellent candidates as information-processing devices or reservoirs for temporal classification and prediction tasks. Previous implementations relied on nominally identical memristors that applied the same nonlinear transformation to the input data, which is not enough to achieve a rich state space. To address this limitation, researchers either diversified the data encoding across multiple memristors or harnessed the stochastic device-to-device variability among the memristors. However, this approach requires additional pre-processing steps and leads to synchronization issues. Instead, it is preferable to encode the data once and pass it through a reservoir layer consisting of memristors with distinct dynamics. Here, we demonstrate that ion-channel-based memristors with voltage-dependent dynamics can be controllably and predictively tuned through voltage or adjustment of the ion channel concentration to exhibit diverse dynamic properties. We show, through experiments and simulations, that reservoir layers constructed with a small number of distinct memristors exhibit significantly higher predictive and classification accuracies with a single data encoding. We found that for a second-order nonlinear dynamical system prediction task, the varied memristor reservoir experimentally achieved a normalized mean square error of 0.0015 using only five distinct memristors. Moreover, in a neural activity classification task, a reservoir of just three distinct memristors experimentally attained an accuracy of 96.5%.
|
[
"Computer Science Archive->cs.LG"
] | 2023-10-25T03:27:43Z |
1409.5418
|
Decoherence imaging of spin ensembles using a scanning single-electron spin in diamond
|
The nitrogen-vacancy (NV) defect center in diamond has demonstrated great capability for nanoscale magnetic sensing and imaging for both static and periodically modulated target fields. However, it remains a challenge to detect and image randomly fluctuating magnetic fields. Recent theoretical and numerical works have outlined detection schemes that exploit changes in decoherence of the detector spin as a sensitive measure for fluctuating fields. Here we experimentally monitor the decoherence of a scanning NV center in order to image the fluctuating magnetic fields from paramagnetic impurities on an underlying diamond surface. We detect a signal corresponding to roughly 800 ${\mu}_B$ in 2 s of integration time, without any control on the target spins, and obtain magnetic-field spectral information using dynamical decoupling techniques. The extracted spatial and temporal properties of the surface paramagnetic impurities provide insight to prolonging the coherence of near-surface qubits for quantum information and metrology applications.
|
[
"Physics Archive->cond-mat->cond-mat.mes-hall"
] | 2014-09-18T19:31:40Z |
1405.7536
|
The relative sizes of sumsets and difference sets
|
Let A be a finite subset of a commutative additive group Z. The sumset and difference set of A are defined as the sets of pairwise sums and differences of elements of A, respectively. The well-known inequality $\sigma(A)^{1/2} \leq \delta(A) \leq \sigma(A)^2,$ where $\sigma(A)=\frac{|A+A|}{|A|}$ is the doubling constant of A and $\delta(A)=\frac{|A-A|}{|A|}$ is the difference constant of A, relates the relative sizes of the sumset and difference set of A. The exponent 2 in this inequality is known to be optimal, for the exponent 1/2 this is unknown. We determine those sets for which equality holds in the above inequality. We find that equality holds if and only if A is a coset of some finite subgroup of Z or, equivalently, if and only if both the doubling constant and difference constant are equal to 1. This implies that there is space for possible improvement of the exponent 1/2 in the inequality. We then use the derived methods to show that Pl\"unnecke's inequality is strict when the doubling constant is larger than 1.
|
[
"Mathematics Archive->math.CO"
] | 2014-05-29T12:34:34Z |
2002.06111
|
Shape dependence of renormalized holographic entanglement entropy
|
We study the holographic entanglement entropy of deformed entangling regions in three-dimensional CFTs dual to Einstein-AdS gravity, using a renormalization scheme based on the addition of extrinsic counterterms. In this prescription, when even-dimensional manifolds are considered, the universal contribution to the entanglement entropy is identified as the renormalized volume of the Ryu-Takayanagi hypersurface, which is written as the sum of a topological and a curvature term. It is shown that the change in the renormalized entanglement entropy due to the deformation of the entangling surface is encoded purely in the curvature contribution. In turn, as the topological part is given by the Euler characteristic of the Ryu-Takayanagi surface, it remains shape independent. Exploiting the covariant character of the extrinsic counterterms, we apply the renormalization scheme for the case of deformed entangling regions in AdS$_4$/CFT$_3$, recovering the results found in the literature. Finally, we provide a derivation of the relation between renormalized entanglement entropy and Willmore energy. The presence of a lower bound of the latter makes manifest the relation between the AdS curvature of the Ryu-Takayanagi surface and the strong subadditivity property.
|
[
"Physics Archive->gr-qc",
"Physics Archive->hep->hep-th"
] | 2020-02-14T16:29:00Z |
2105.10555
|
Inverting catalecticants of ternary quartics
|
We study the reciprocal variety to the linear space of symmetric matrices (LSSM) of catalecticant matrices associated with ternary quartics. With numerical tools, we obtain 85 to be its degree and 36 to be the ML-degree of the LSSM. We provide a geometric explanation to why equality between these two invariants is not reached, as opposed to the case of binary forms, by describing the intersection of the reciprocal variety and the orthogonal of the LSSM in the rank loci. Moreover, we prove that only the rank-$1$ locus, namely the Veronese surface $\nu_4(\mathbb{P}^2)$, contributes to the degree of the reciprocal variety.
|
[
"Mathematics Archive->math.AG"
] | 2021-05-21T20:07:58Z |
0911.4041
|
Singularly perturbed degenerated parabolic equations and application to seabed morphodynamics in tided environment
|
In this paper we build models for short-term, mean-term and long-term dynamics of dune and megariple morphodynamics. They are models that are degenerated parabolic equations which are, moreover, singularly perturbed. We, then give an existence and uniqueness result for the short-term and mean-term models. This result is based on a time-space periodic solution existence result for degenerated parabolic equation that we set out. Finally the short-term model is homogenized.
|
[
"Mathematics Archive->math.AP"
] | 2009-11-20T13:21:23Z |
1804.00203
|
U-cross Gram matrices and their invertibility
|
The Gram matrix is defined for Bessel sequences by combining synthesis with subsequent analysis operators. If different sequences are used and an operator U is inserted we reach so called U-cross Gram matrices. This can be seen as reinterpretation of the matrix representation of operators using frames. In this paper we investigate some necessary or sufficient conditions for Schatten p-class properties and the invertibility of U-cross Gram matrices. In particular, we show that under mild conditions the pseudo-inverse of a U-cross Gram matrix can always be represented as a U-cross Gram matrix with dual frames of the given ones. We link some properties of U-cross Gram matrices to approximate duals. Finally, we state several stability results. More precisely, it is shown that the invertibility of U-cross Gram matrices is preserved under small perturbations.
|
[
"Mathematics Archive->math.FA"
] | 2018-03-31T18:42:05Z |
1704.01206
|
Observation of Efimov molecules created from a resonantly interacting Bose gas
|
We convert a strongly interacting ultracold Bose gas into a mixture of atoms and molecules by sweeping the interactions from resonant to weak. By analyzing the decay dynamics of the molecular gas, we show that in addition to Feshbach dimers it contains Efimov trimers. Typically around 8\% of the total atomic population is bound into trimers, identified by their density-independent lifetime of about 100~$\mu$s. The lifetime of the Feshbach dimers shows a density dependence due to inelastic atom-dimer collisions, in agreement with theoretical calculations. We also vary the density of the gas across a factor of 250 and investigate the corresponding atom loss rate at the interaction resonance.
|
[
"Physics Archive->cond-mat->cond-mat.quant-gas",
"Physics Archive->quant-ph"
] | 2017-04-04T22:26:23Z |
1707.09546
|
The Separable Quotient Problem for Topological Groups
|
The famous Banach-Mazur problem, which asks if every infinite-dimensional Banach space has an infinite-dimensional separable quotient Banach space, has remained unsolved for 85 years, though it has been answered in the affirmative for reflexive Banach spaces and even Banach spaces which are duals. The analogous problem for locally convex spaces has been answered in the negative, but has been shown to be true for large classes of locally convex spaces including all non-normable Fr\'echet spaces. In this paper the analogous problem for topological groups is investigated. Indeed there are four natural analogues: Does every non-totally disconnected topological group have a separable quotient group which is (i) non-trivial; (ii) infinite; (iii) metrizable; (iv) infinite metrizable. All four questions are answered here in the negative. However, positive answers are proved for important classes of topological groups including (a) all compact groups; (b) all locally compact abelian groups; (c) all $\sigma$-compact locally compact groups; (d) all abelian pro-Lie groups; (e) all $\sigma$-compact pro-Lie groups; (f) all pseudocompact groups. Negative answers are proved for precompact groups.
|
[
"Mathematics Archive->math.GN"
] | 2017-07-29T18:05:33Z |
1409.2876
|
Secular- and merger-built bulges in barred galaxies
|
(Abridged) We study the incidence, as well as the nature, of composite bulges in a sample of 10 face-on barred galaxies to constrain the formation and evolutionary processes of the central regions of disk galaxies. We analyze the morphological, photometric, and kinematic properties of each bulge. Then, by using a case-by-case analysis we identify composite bulges and classify every component into a classical or pseudobulge. In addition, bar-related boxy/peanut (B/P) structures were also identified and characterised. We find only three galaxies hosting a single-component bulge (two pseudobulges and one classical bulge). We find evidence of composite bulges coming in two main types based on their formation: secular-built and merger- and secular-built. We call secular-built to composite bulges made of entirely by structures associated with secular processes such as pseudo bulges, central disks, or B/P bulges. We find four composite bulges of this kind in our sample. On the other hand, merger- and secular-built bulges are those where structures with different formation paths coexist within the same galaxy, i.e., a classical bulge coexisting with a secular-built structure (pseudobulge, central disk, or B/P). Three bulges of this kind were found in the sample. We remark on the importance of detecting kinematic structures such as sigma-drops to identify composite bulges. A large fraction (80%) of galaxies were found to host sigma-drops or sigma-plateaus in our sample revealing their high incidence in barred galaxies. The high frequency of composite bulges in barred galaxies points towards a complex formation and evolutionary scenario. Moreover, the evidence for coexisting merger- and secular-built bulges reinforce this idea. We discuss how the presence of different bulge types, with different formation histories and timescales, can constrain current models of bulge formation.
|
[
"Physics Archive->astro-ph->astro-ph.GA"
] | 2014-09-09T20:00:14Z |
2103.13145
|
Unsupervised collaborative learning using privileged information
|
In the collaborative clustering framework, the hope is that by combining several clustering solutions, each one with its own bias and imperfections, one will get a better overall solution. The goal is that each local computation, quite possibly applied to distinct data sets, benefits from the work done by the other collaborators. This article is dedicated to collaborative clustering based on the Learning Using Privileged Information paradigm. Local algorithms weight incoming information at the level of each observation, depending on the confidence level of the classification of that observation. A comparison between our algorithm and state of the art implementations shows improvement of the collaboration process using the proposed approach.
|
[
"Computer Science Archive->cs.LG"
] | 2021-03-24T12:43:49Z |
2308.00727
|
Adaptive Semantic Consistency for Cross-domain Few-shot Classification
|
Cross-domain few-shot classification (CD-FSC) aims to identify novel target classes with a few samples, assuming that there exists a domain shift between source and target domains. Existing state-of-the-art practices typically pre-train on source domain and then finetune on the few-shot target data to yield task-adaptive representations. Despite promising progress, these methods are prone to overfitting the limited target distribution since data-scarcity and ignore the transferable knowledge learned in the source domain. To alleviate this problem, we propose a simple plug-and-play Adaptive Semantic Consistency (ASC) framework, which improves cross-domain robustness by preserving source transfer capability during the finetuning stage. Concretely, we reuse the source images in the pretraining phase and design an adaptive weight assignment strategy to highlight the samples similar to target domain, aiming to aggregate informative target-related knowledge from source domain. Subsequently, a semantic consistency regularization is applied to constrain the consistency between the semantic features of the source images output by the source model and target model. In this way, the proposed ASC enables explicit transfer of source domain knowledge to prevent the model from overfitting the target domain. Extensive experiments on multiple benchmarks demonstrate the effectiveness of the proposed ASC, and ASC provides consistent improvements over the baselines. The source code will be released.
|
[
"Computer Science Archive->cs.CV"
] | 2023-08-01T15:37:19Z |
1703.05929
|
Completely regular codes by concatenating Hamming codes
|
We construct new families of completely regular codes by concatenation methods. By combining parity check matrices of cyclic Hamming codes, we obtain families of completely regular codes. In all cases, we compute the intersection array of these codes. We also study when the extension of these codes gives completely regular codes. Some of these new codes are completely transitive.
|
[
"Mathematics Archive->math.CO"
] | 2017-03-17T09:07:59Z |
1506.02443
|
Consistency of pipi phase shift analyses with rho^0(770)-f_0(980) spin mixing in pi(-)p->pi(-)pi(+)n
|
We have performed two analytical pipi phase shift analyses using a Standard amplitude analysis of the CERN data on pi(-)p->pi(-)pi(+)n on polarized target at 17.2 GeV/c and a more recent analysis of the same data using Spin Mixing Mechanism (SMM). There are two solutions for helicity amplitudes labeled (1,1) and (2,2) in the Standard analysis and SpinMixing and S-Matrix in the SMM analysis which are related to the pipi scattering amplitudes. Our first phase shift analysis is an elastic scattering analysis below KKbar threshold. Our second analysis is a joint pipi phase shift analysis of pi(-)pi(+) and pi(0)pi(0) data below 1080 MeV. Our elastic Solution (2,2)1 and elastic Solution SpinMixing 1 for delta^0_S are in a remarkable agreement with the 1997 Cracow Solution Down-flat using the same CERN data on polarized target. Our joint Solution (2,2) and joint Solution SpinMixing are also in a remarkable agreement with the 2002 joint Cracow Solution Down-flat. Solutions elastic (1,1) and joint (1,1) agree with the Cracow Solutions Up-flat and are rejected. Model independent amplitude analyses of measurements of pi(-)p->pi(-)pi(+)n at 17.2 and 1.78 GeV/c and pi(+)n->pi(+)pi(-)p at 5.98 and 11.85 GeV/c reveal evidence for rho^0(770)-f_0(980) spin mixing in the S-wave transversity amplitudes. These transversity amplitudes define single-flip helicity amplitudes which have been related to pipi scattering amplitudes. Our key observation is that the presented and the Cracow solutions are consistent with the evidence for rho^0(770)-f_0(980) spin mixing in the measured transversity amplitudes from which all these phase shifts ultimately arise.
|
[
"Physics Archive->hep->hep-ph"
] | 2015-06-08T11:29:49Z |
2009.12948
|
Finding Matrix Sequences with a High Asymptotic Growth Rate for Linear Constrained Switching Systems
|
Linear constrained switching systems are linear switched systems whose switching sequences are constrained by a deterministic finite automaton. This work investigates how to generate a sequence of matrices with an asymptotic growth rate close to the constrained joint spectral radius (CJSR) for constrained switching systems, based on our previous result that reveals the equivalence of a constrained switching system and a lifted arbitrary switching system. By using the dual solution of a sum-of-squares optimization program, an algorithm is designed for the lifted arbitrary switching system to produce a sequence of matrices with an asymptotic growth rate that is close to the CJSR of the original constrained switching system. It is also shown that a type of existing algorithms designed for arbitrary switching systems can be applied to the lifted system such that the desired sequence of matrices can be generated for the constrained switching system. Several numerical examples are provided to illustrate the better performance of the proposed algorithms compared with existing ones.
|
[
"Computer Science Archive->cs.SY",
"Electrical Engineering and Systems Science Archive->eess.SY",
"Mathematics Archive->math.OC"
] | 2020-09-27T20:52:04Z |
1108.2015
|
Models for unitary black hole disintegration
|
Simple models for unitary black hole evolution are given in an effective Hilbert-space description, parameterizing a possible minimal relaxation of locality, with respect to semiclassical black hole geometry.
|
[
"Physics Archive->gr-qc",
"Physics Archive->hep->hep-th"
] | 2011-08-09T19:26:31Z |
2005.11756
|
Reliability and Performance Assessment of Federated Learning on Clinical Benchmark Data
|
As deep learning have been applied in a clinical context, privacy concerns have increased because of the collection and processing of a large amount of personal data. Recently, federated learning (FL) has been suggested to protect personal privacy because it does not centralize data during the training phase. In this study, we assessed the reliability and performance of FL on benchmark datasets including MNIST and MIMIC-III. In addition, we attempted to verify FL on datasets that simulated a realistic clinical data distribution. We implemented FL that uses a client and server architecture and tested client and server FL on modified MNIST and MIMIC-III datasets. FL delivered reliable performance on both imbalanced and extremely skewed distributions (i.e., the difference of the number of patients and the characteristics of patients in each hospital). Therefore, FL can be suitable to protect privacy when applied to medical data.
|
[
"Computer Science Archive->cs.CR",
"Computer Science Archive->cs.LG"
] | 2020-05-24T14:36:44Z |
1403.3985
|
BICEP2 I: Detection Of B-mode Polarization at Degree Angular Scales
|
(abridged for arXiv) We report results from the BICEP2 experiment, a cosmic microwave background (CMB) polarimeter specifically designed to search for the signal of inflationary gravitational waves in the B-mode power spectrum around $\ell\sim80$. The telescope comprised a 26 cm aperture all-cold refracting optical system equipped with a focal plane of 512 antenna coupled transition edge sensor 150 GHz bolometers each with temperature sensitivity of $\approx300\mu\mathrm{K}_\mathrm{CMB}\sqrt{s}$. BICEP2 observed from the South Pole for three seasons from 2010 to 2012. A low-foreground region of sky with an effective area of 380 square deg was observed to a depth of 87 nK deg in Stokes $Q$ and $U$. We find an excess of $B$-mode power over the base lensed-LCDM expectation in the range $30< \ell< 150$, inconsistent with the null hypothesis at a significance of $> 5\sigma$. Through jackknife tests and simulations we show that systematic contamination is much smaller than the observed excess. We also examine a number of available models of polarized dust emission and find that at their default parameter values they predict power $\sim(5-10)\times$ smaller than the observed excess signal. However, these models are not sufficiently constrained to exclude the possibility of dust emission bright enough to explain the entire excess signal. Cross correlating BICEP2 against 100 GHz maps from the BICEP1 experiment, the excess signal is confirmed and its spectral index is found to be consistent with that of the CMB, disfavoring dust at $1.7\sigma$. The observed $B$-mode power spectrum is well fit by a lensed-LCDM + tensor theoretical model with tensor-to-scalar ratio $r=0.20^{+0.07}_{-0.05}$, with $r=0$ disfavored at $7.0\sigma$. Accounting for the contribution of foreground dust will shift this value downward by an amount which will be better constrained with upcoming data sets.
|
[
"Physics Archive->astro-ph->astro-ph.CO",
"Physics Archive->gr-qc",
"Physics Archive->hep->hep-ph",
"Physics Archive->hep->hep-th"
] | 2014-03-17T02:14:52Z |
2009.12703
|
An Adaptive EM Accelerator for Unsupervised Learning of Gaussian Mixture Models
|
We propose an Anderson Acceleration (AA) scheme for the adaptive Expectation-Maximization (EM) algorithm for unsupervised learning a finite mixture model from multivariate data (Figueiredo and Jain 2002). The proposed algorithm is able to determine the optimal number of mixture components autonomously, and converges to the optimal solution much faster than its non-accelerated version. The success of the AA-based algorithm stems from several developments rather than a single breakthrough (and without these, our tests demonstrate that AA fails catastrophically). To begin, we ensure the monotonicity of the likelihood function (a the key feature of the standard EM algorithm) with a recently proposed monotonicity-control algorithm (Henderson and Varahdan 2019), enhanced by a novel monotonicity test with little overhead. We propose nimble strategies for AA to preserve the positive definiteness of the Gaussian weights and covariance matrices strictly, and to conserve up to the second moments of the observed data set exactly. Finally, we employ a K-means clustering algorithm using the gap statistic to avoid excessively overestimating the initial number of components, thereby maximizing performance. We demonstrate the accuracy and efficiency of the algorithm with several synthetic data sets that are mixtures of Gaussians distributions of known number of components, as well as data sets generated from particle-in-cell simulations. Our numerical results demonstrate speed-ups with respect to non-accelerated EM of up to 60X when the exact number of mixture components is known, and between a few and more than an order of magnitude with component adaptivity.
|
[
"Computer Science Archive->cs.LG",
"Statistics Archive->stat.ML"
] | 2020-09-26T22:55:44Z |
2001.02645
|
Excitations with projected entangled pair states using the corner transfer matrix method
|
We present an extension of a framework for simulating single quasiparticle or collective excitations on top of strongly correlated quantum many-body ground states using infinite projected entangled pair states, a tensor network ansatz for two-dimensional wave functions in the thermodynamic limit. Our approach performs a systematic summation of locally perturbed states in order to obtain excited eigenstates localized in momentum space, using the corner transfer matrix method, and generalizes the framework to arbitrary unit cell sizes, the implementation of global Abelian symmetries and fermionic systems. Results for several test cases are presented, including the transverse Ising model, the spin-$\frac{1}{2}$ Heisenberg model and a free fermionic model, to demonstrate the capability of the method to accurately capture dispersions. We also provide insight into the nature of excitations at the $k=(\pi,0)$ point of the Heisenberg model.
|
[
"Physics Archive->cond-mat->cond-mat.str-el"
] | 2020-01-08T17:42:34Z |
1912.03789
|
Feature Engineering Combined with 1 D Convolutional Neural Network for Improved Mortality Prediction
|
The intensive care units (ICUs) are responsible for generating a wealth of useful data in the form of Electronic Health Record (EHR). This data allows for the development of a prediction tool with perfect knowledge backing. We aimed to build a mortality prediction model on 2012 Physionet Challenge mortality prediction database of 4000 patients admitted in ICU. The challenges in the dataset, such as high dimensionality, imbalanced distribution, and missing values were tackled with analytical methods and tools via feature engineering and new variable construction. The objective of the research is to utilize the relations among the clinical variables and construct new variables which would establish the effectiveness of 1-Dimensional Convolutional Neural Network (1- D CNN) with constructed features. Its performance with the traditional machine learning algorithms like XGBoost classifier, Support Vector Machine (SVM), K-Neighbours Classifier (K-NN), and Random Forest Classifier (RF) is compared for Area Under Curve (AUC). The investigation reveals the best AUC of 0.848 using 1-D CNN model.
|
[
"Computer Science Archive->cs.LG",
"Statistics Archive->stat.ML"
] | 2019-12-08T23:52:58Z |
2105.07085
|
MutualNet: Adaptive ConvNet via Mutual Learning from Different Model Configurations
|
Most existing deep neural networks are static, which means they can only do inference at a fixed complexity. But the resource budget can vary substantially across different devices. Even on a single device, the affordable budget can change with different scenarios, and repeatedly training networks for each required budget would be incredibly expensive. Therefore, in this work, we propose a general method called MutualNet to train a single network that can run at a diverse set of resource constraints. Our method trains a cohort of model configurations with various network widths and input resolutions. This mutual learning scheme not only allows the model to run at different width-resolution configurations but also transfers the unique knowledge among these configurations, helping the model to learn stronger representations overall. MutualNet is a general training methodology that can be applied to various network structures (e.g., 2D networks: MobileNets, ResNet, 3D networks: SlowFast, X3D) and various tasks (e.g., image classification, object detection, segmentation, and action recognition), and is demonstrated to achieve consistent improvements on a variety of datasets. Since we only train the model once, it also greatly reduces the training cost compared to independently training several models. Surprisingly, MutualNet can also be used to significantly boost the performance of a single network, if dynamic resource constraint is not a concern. In summary, MutualNet is a unified method for both static and adaptive, 2D and 3D networks. Codes and pre-trained models are available at \url{https://github.com/taoyang1122/MutualNet}.
|
[
"Computer Science Archive->cs.CV"
] | 2021-05-14T22:30:13Z |
2311.12765
|
Power saving for the Brown-Erd\H{o}s-S\'os problem
|
Let $f(n, v, e)$ denote the maximum number of edges in a 3-uniform hypergraph on $n$ vertices which does not contain $v$ vertices spanning at least $e$ edges. A central problem in extremal combinatorics, famously posed by Brown, Erd\H{o}s and S\'os in 1973, asks whether $f(n, e+3, e)=o(n^2)$ for every $e \ge 3$. A classical result of S\'ark\"ozy and Selkow states that $f(n, e+\lfloor \log_2 e\rfloor+2, e)=o(n^{2})$ for every $e \ge 3$. This bound was recently improved by Conlon, Gishboliner, Levanzov and Shapira. Motivated by applications to other problems, Gowers and Long made the striking conjecture that $f(n, e+4, e)=O(n^{2-\varepsilon})$ for some $\varepsilon=\varepsilon(e)>0$. Conlon, Gishboliner, Levanzov and Shapira, and later, Shapira and Tyomkyn reiterated the following approximate version of this problem. What is the smallest $d(e)$ for which $f(n, e+d(e), e)=O(n^{2-\varepsilon})$ for some $\varepsilon=\varepsilon(e)>0$? In this paper, we prove that for each $e\geq 3$ we have $f(n, e+\lfloor \log_2 e\rfloor +38, e)=O(n^{2-\varepsilon})$ for some $\varepsilon>0$. This shows that one can already obtain power saving near the S\'ark\"ozy-Selkow bound at the cost of a small additive constant.
|
[
"Mathematics Archive->math.CO"
] | 2023-11-21T18:20:59Z |
1807.10776
|
Two Different Grain Size Distributions within the Protoplanetary Disk around HD 142527 Revealed by ALMA Polarization Observation
|
The origin of polarized emission from protoplanetary disks is uncertain. Three mechanisms have been proposed for such polarized emission: grain alignment with magnetic fields, grain alignment with radiation gradients, and self-scattering of thermal dust emission. Aiming to observationally identify the polarization mechanisms, we present ALMA polarization observations of the 0.87 mm dust continuum emission toward the circumstellar disk around HD 142527 with high spatial resolution. We confirm that the polarization vectors in the northern region are consistent with self-scattering. Furthermore, we show that the polarization vectors in the southern region are consistent with grain alignment by magnetic fields, although self-scattering cannot be ruled out. To understand the differences between the polarization mechanisms, we propose a simple grain size segregation model: small dust grains ($\lesssim$ 100 microns) are dominant and aligned with magnetic fields in the southern region, and middle-sized ($\sim100$ microns) grains in the upper layer emit self-scattered polarized emission in the northern region. The grain size near the middle plane in the northern region cannot be measured because the emission at 0.87 mm is optically thick. However, it can be speculated that larger dust grains ($\gtrsim$ cm) may accumulate near this plane. These results are consistent with those of a previous analysis of the disk, in which large grain accumulation and optically thick emission from the northern region were found. This model is also consistent with theories where smaller dust grains are aligned with magnetic fields. The magnetic fields are toroidal, at least in the southern region.
|
[
"Physics Archive->astro-ph->astro-ph.EP"
] | 2018-07-27T18:00:05Z |
1702.02806
|
de Sitter spacetime with a Becchi-Rouet-Stora quartet
|
We generalize the topological model recently proposed and investigate the cosmological perturbations of the model. The model has an exact de Sitter background solution associated with a Becchi-Rouet-Stora(BRS) quartet terms which are regarded as a Lagrangian density of the topological field theory. The de Sitter solution can be selected without spontaneously breaking the BRS symmetry, and be interpreted as a gauge fixing of de Sitter spacetime. The BRS symmetry is preserved for the perturbations around the de Sitter background before we solve the constraints of general relativity. We derive action to the second order of the perturbations and confirm that even after solving the constraints, we have the BRS symmetry at least for the second order action. We construct the cosmological perturbation theory involving the BRS sector, and obtain the two point correlation functions for the curvature perturbation and the isocurvature perturbations which compose the BRS sector. Our result gives a new description for de Sitter spacetime and the quantum field theory in de Sitter spacetime.
|
[
"Physics Archive->gr-qc",
"Physics Archive->hep->hep-th"
] | 2017-02-09T12:29:30Z |
2302.11440
|
De Rham algebras of closed quasiregularly elliptic manifolds are Euclidean
|
We show that, if a closed, connected, and oriented Riemannian $n$-manifold $N$ admits a non-constant quasiregular mapping from the Euclidean $n$-space $\mathbb R^n$, then the de Rham cohomology algebra $H_{\mathrm{dR}}^*(N)$ of $N$ embeds into the exterior algebra ${\bigwedge}^*\mathbb R^n$. As a consequence, we obtain a homeomorphic classification of closed simply connected quasiregularly elliptic $4$-manifolds.
|
[
"Mathematics Archive->math.CV",
"Mathematics Archive->math.DG"
] | 2023-02-22T15:22:50Z |
1105.2135
|
Confidence bands for Horvitz-Thompson estimators using sampled noisy functional data
|
When collections of functional data are too large to be exhaustively observed, survey sampling techniques provide an effective way to estimate global quantities such as the population mean function. Assuming functional data are collected from a finite population according to a probabilistic sampling scheme, with the measurements being discrete in time and noisy, we propose to first smooth the sampled trajectories with local polynomials and then estimate the mean function with a Horvitz-Thompson estimator. Under mild conditions on the population size, observation times, regularity of the trajectories, sampling scheme, and smoothing bandwidth, we prove a Central Limit theorem in the space of continuous functions. We also establish the uniform consistency of a covariance function estimator and apply the former results to build confidence bands for the mean function. The bands attain nominal coverage and are obtained through Gaussian process simulations conditional on the estimated covariance function. To select the bandwidth, we propose a cross-validation method that accounts for the sampling weights. A simulation study assesses the performance of our approach and highlights the influence of the sampling scheme and bandwidth choice.
|
[
"Mathematics Archive->math.ST",
"Statistics Archive->stat.ME",
"Statistics Archive->stat.TH"
] | 2011-05-11T09:20:57Z |
gr-qc/0512152
|
Supersymmetry Breaking Casimir Warp Drive
|
Within the framework of brane-world models it is possible to account for the cosmological constant by assuming supersymmetry is broken on the 3-brane but preserved in the bulk. An effective Casimir energy is induced on the brane due to the boundary conditions imposed on the compactified extra dimensions. It will be demonstrated that modification of these boundary conditions allows a spacecraft to travel at any desired speed due to a local adjustment of the cosmological constant which effectively contracts/expands space-time in the front/rear of the ship resulting in motion potentially faster than the speed of light as seen by observers outside the disturbance.
|
[
"Physics Archive->gr-qc"
] | 2005-12-27T05:31:21Z |
1401.0748
|
Completely bounded isomorphisms of operator algebras and similarity to complete isometries
|
A well-known theorem of Paulsen says that if $\mathcal{A}$ is a unital operator algebra and $\phi:\mathcal{A}\to B(\mathcal{H})$ is a unital completely bounded homomorphism, then $\phi$ is similar to a completely contractive map $\phi'$. Motivated by classification problems for Hilbert space contractions, we are interested in making the inverse $\phi'^{-1}$ completely contractive as well whenever the map $\phi$ has a completely bounded inverse. We show that there exist invertible operators $X$ and $Y$ such that the map $$ XaX^{-1}\mapsto Y\phi(a)Y^{-1} $$ is completely contractive and is "almost" isometric on any given finite set of elements from $\mathcal{A}$ with non-zero spectrum. Although the map cannot be taken to be completely isometric in general, we show that this can be achieved if $\mathcal{A}$ is completely boundedly isomorphic to either a $C^*$-algebra or a uniform algebra. In the case of quotient algebras of $H^\infty$, we translate these conditions in function theoretic terms and relate them to the classical Carleson condition.
|
[
"Mathematics Archive->math.FA",
"Mathematics Archive->math.OA"
] | 2014-01-03T22:44:12Z |
1311.5764
|
Dark Matter or Neutrino recoil? Interpretation of Recent Experimental Results
|
The elastic nuclear recoil signal, being under intense scrutiny by multiple underground experiments, can be interpreted either as coming from the interaction of nuclei with WIMP dark matter or from the scattering of new species of MeV-energy neutrinos. The most promising model for the latter case is a neutrino $\nu_b$ that interacts with baryon number, and with a flux sourced by the oscillations of regular solar $^8$B neutrinos. We re-analyze this model in light of the latest experimental results. In contrast to the light-DM interpretation of various tentative positive signals (anomalies) that is now seriously challenged by the negative results of the LUX experiment, the neutrino interpretation remains a viable explanation to most of the anomalies. Considering future prospects, we show that the superCDMS experiment alone, when equipped with Ge and Si detectors, will be able to detect $\nu_b$ and discriminate the model from a light DM interpretation. In addition, we also provide the forecast for the new CRESST-II run that now operates with new detectors and diminished backgrounds.
|
[
"Physics Archive->hep->hep-ph"
] | 2013-11-22T14:35:02Z |
alg-geom/9607006
|
Plane curves with a big fundamental group of the complement
|
Let $C \s \pr^2$ be an irreducible plane curve whose dual $C^* \s \pr^{2*}$ is an immersed curve which is neither a conic nor a nodal cubic. The main result states that the Poincar\'e group $\pi_1(\pr^2 \se C)$ contains a free group with two generators. If the geometric genus $g$ of $C$ is at least 2, then a subgroup of $G$ can be mapped epimorphically onto the fundamental group of the normalization of $C$, and the result follows. To handle the cases $g=0,1$, we construct universal families of immersed plane curves and their Picard bundles. This allows us to reduce the consideration to the case of Pl\"ucker curves. Such a curve $C$ can be regarded as a plane section of the corresponding discriminant hypersurface (cf. [Zar, DoLib]). Applying Zariski--Lefschetz type arguments we deduce the result from `the bigness' of the $d$-th braid group $B_{d,g}$ of the Riemann surface of $C$.
|
[
"Mathematics Archive->math.AG"
] | 1996-07-04T12:40:41Z |
1906.02232
|
Weighted Irrigation Plans
|
We model an irrigation network where lower branches must be thicker in order to support the weight of the higher ones. This leads to a countable family of ODEs, one for each branch, that must be solved by backward induction. Having introduced conditions that guarantee the existence and uniqueness of solutions, our main result establishes the lower semicontinuity of the corresponding cost functional, w.r.t. pointwise convergence of the irrigation plans. In turn, this yields the existence of an optimal irrigation plan, in the presence of these additional weights.
|
[
"Mathematics Archive->math.OC"
] | 2019-06-05T18:15:19Z |
quant-ph/9506035
|
Values and the Quantum Conception of Man
|
Classical mechanics is based upon a mechanical picture of nature that is fundamentally incorrect. It has been replaced at the basic level by a radically different theory: quantum mechanics. This change entails an enormous shift in our basic conception of nature, one that can profoundly alter the scientific image of man himself. Self-image is the foundation of values, and the replacement of the mechanistic self-image derived from classical mechanics by one concordant with quantum mechanics may provide the foundation of a moral order better suited to our times, a self-image that endows human life with meaning, responsibility, and a deeper linkage to nature as a whole.
|
[
"Physics Archive->quant-ph"
] | 1995-06-21T15:27:30Z |
2109.13919
|
A Remark on Mathieu's Series
|
We establish a new lower bound for Mathieu's series and present a new derivation of its expansions in terms of Riemann Zeta functions.
|
[
"Mathematics Archive->math.NT"
] | 2021-09-23T03:47:15Z |
2108.13419
|
Lightweight self-conjugate nucleus $^{80}$Zr
|
Protons and neutrons in the atomic nucleus move in shells analogous to the electronic shell structures of atoms. Nuclear shell structure varies across the nuclear landscape due to changes of the nuclear mean field with the number of neutrons $N$ and protons $Z$. These variations can be probed with mass differences. The $N=Z=40$ self-conjugate nucleus $^{80}$Zr is of particular interest as its proton and neutron shell structures are expected to be very similar, and its ground state is highly deformed. In this work, we provide evidence for the existence of a deformed double shell closure in $^{80}$Zr through high precision Penning trap mass measurements of $^{80-83}$Zr. Our new mass values show that $^{80}$Zr is significantly lighter, and thus more bound than previously determined. This can be attributed to the deformed shell closure at $N=Z=40$ and the large Wigner energy. Our statistical Bayesian model mixing analysis employing several global nuclear mass models demonstrates difficulties with reproducing the observed mass anomaly using current theory.
|
[
"Physics Archive->nucl->nucl-ex",
"Physics Archive->nucl->nucl-th"
] | 2021-08-30T15:09:38Z |
hep-ph/0011371
|
Renormalization Group Flow Equations For The Scalar O(N) Theory
|
Self-consistent new renormalization group flow equations for an O(N)-symmetric scalar theory are approximated in next-to-leading order of the derivative expansion. The Wilson-Fisher fixed point in three dimensions is analyzed in detail and various critical exponents are calculated.
|
[
"Physics Archive->hep->hep-ph"
] | 2000-11-29T18:07:31Z |
1712.07047
|
Duality and the universality class of the three-state Potts antiferromagnet on plane quadrangulations
|
We provide a new criterion based on graph duality to predict whether the 3-state Potts antiferromagnet on a plane quadrangulation has a zero- or finite-temperature critical point, and its universality class. The former case occurs for quadrangulations of self-dual type, and the zero-temperature critical point has central charge $c=1$. The latter case occurs for quadrangulations of non-self-dual type, and the critical point belongs to the universality class of the 3-state Potts ferromagnet. We have tested this criterion against high-precision computations on four lattices of each type, with very good agreement. We have also found that the Wang-Swendsen-Koteck\'y algorithm has no critical slowing-down in the former case, and critical slowing-down in the latter.
|
[
"Physics Archive->cond-mat->cond-mat.stat-mech"
] | 2017-12-19T17:02:32Z |
1507.08168
|
Electroweak baryogenesis in the framework of the effective field theory
|
We study the electroweak baryogenesis in the framework of the effective field theory. Our study shows that by introducing a light singlet scalar particle and a dimension-5 operator, it can provide the strong first order phase transition and the source of the CP-violation during the phase transition, and then produce abundant particle phenomenology at zero temperature. We also show the constraints on the new physics scale from the observed baryon-to-photon ratio, the low-energy experiments, and the LHC data.
|
[
"Physics Archive->hep->hep-ph"
] | 2015-07-29T14:48:43Z |
1208.3176
|
Magneto-elastic coupling and competing entropy changes in substituted CoMnSi metamagnets
|
We use neutron diffraction, magnetometry and low temperature heat capacity to probe giant magneto-elastic coupling in CoMnSi-based antiferromagnets and to establish the origin of the entropy change that occurs at the metamagnetic transition in such compounds. We find a large difference between the electronic density of states of the antiferromagnetic and high magnetisation states. The magnetic field-induced entropy change is composed of this contribution and a significant counteracting lattice component, deduced from the presence of negative magnetostriction. In calculating the electronic entropy change, we note the importance of using an accurate model of the electronic density of states, which here varies rapidly close to the Fermi energy.
|
[
"Physics Archive->cond-mat->cond-mat.mtrl-sci",
"Physics Archive->cond-mat->cond-mat.str-el"
] | 2012-08-15T18:43:18Z |
2210.02825
|
Logarithmic base change theorem and smooth descent of positivity of log canonical divisor
|
We prove a logarithmic base change theorem for pushforwards of pluri-canonical bundles and use it to deduce that positivity properties of log canonical divisors descend via smooth projective morphisms. As an application, for a surjective morphism $f:X\to Y$ with $\kappa(X)\ge 0$ and $-K_Y$ big, we prove $Y\setminus \Delta(f)$ is of log general type, where $\Delta(f)$ is the discriminant locus. In particular, when $Y=\mathbb{P}^n$ we have $\dim \Delta(f)=n-1$ and $\mathrm{deg}\,\Delta(f)\ge n+2$, generalizing the case $n=1$ proved by Viehweg-Zuo. In addition, we prove Popa's conjecture on the superadditivity of the logarithmic Kodaira dimension of smooth algebraic fiber spaces over bases of dimension at most three and analyze related problems.
|
[
"Mathematics Archive->math.AG"
] | 2022-10-06T11:29:51Z |
1211.0084
|
A simple model of pointlike spacetime defects and implications for photon propagation
|
A model in which pointlike defects are randomly embedded in Minkowski spacetime is considered. The distribution of spacetime defects is constructed to be Lorentz-invariant. It does not introduce a preferred reference frame, because it is based on a sprinkling process. A field-theoretic action for the photon and a fermion is set up, in which the photon is assumed not to couple to the defects directly, but via a scalar field. We are interested in signs for Lorentz violation caused by the spacetime defects, which are expected to reveal themselves in the photon sector. A modification of the photon dispersion relation may result as a quantum effect and we compute it at leading order perturbation theory. The outcome of the calculation is that the photon dispersion law remains conventional, if the defect distribution is dense, homogeneous, and isotropic. This result sheds some new light on Lorentz violation in the framework of a small-scale structure of spacetime. It shows that Lorentz invariance can be preserved even in the presence of a spacetime structure that is supposed to emerge at the Planck scale. This conclusion has already been drawn on general grounds in other publications, where the current paper delivers a demonstration by a direct computation in a simple model.
|
[
"Physics Archive->hep->hep-th"
] | 2012-11-01T03:50:09Z |
1506.03421
|
Almost-rigidity and the extinction time of positively curved Ricci flows
|
We prove that Ricci flows with almost maximal extinction time must be nearly round, provided that they have positive isotropic curvature when crossed with $\mathbb{R}^{2}$. As an application, we show that positively curved metrics on $S^{3}$ and $RP^{3}$ with almost maximal width must be nearly round.
|
[
"Mathematics Archive->math.AP",
"Mathematics Archive->math.DG"
] | 2015-06-10T18:34:32Z |
math/0511534
|
The generating hypothesis in the derived category of R-modules
|
In this paper, we prove a version of Freyd's generating hypothesis for triangulated categories: if D is a cocomplete triangulated category and S is an object in D whose endomorphism ring is graded commutative and concentrated in degree zero, then S generates (in the sense of Freyd) the thick subcategory determined by S if and only if the endomorphism ring of S is von Neumann regular. As a corollary, we obtain that the generating hypothesis is true in the derived category of a commutative ring R if and only if R is von Neumann regular. We also investigate alternative formulations of the generating hypothesis in the derived category. Finally, we give a characterization of the Noetherian stable homotopy categories in which the generating hypothesis is true.
|
[
"Mathematics Archive->math.AT"
] | 2005-11-21T23:15:25Z |
0805.2539
|
A method for the quantitative study of atomic transitions in a magnetic field based on an atomic vapor cell with L=lambda
|
We describe the so-called "Lambda-Zeeman method" to investigate individual hyperfine transitions between Zeeman sublevels of atoms in an external magnetic field of 0.1 mT - 0.25 T. Atoms are confined in a nanocell with thickness L = Lambda, where Lambda is the resonant wavelength (794 nm or 780 nm for D1 or D2 line of Rb). Narrow resonances in the transmission spectrum of the nanocell are split into several components in a magnetic field; their frequency positions and probabilities depend on the B-field. Possible applications are described, such as magnetometers with nanometric spatial resolution and tunable atomic frequency references.
|
[
"Physics Archive->physics->physics.atom-ph"
] | 2008-05-16T14:00:33Z |
2108.10052
|
Integrating LSTMs and GNNs for COVID-19 Forecasting
|
The spread of COVID-19 has coincided with the rise of Graph Neural Networks (GNNs), leading to several studies proposing their use to better forecast the evolution of the pandemic. Many such models also include Long Short Term Memory (LSTM) networks, a common tool for time series forecasting. In this work, we further investigate the integration of these two methods by implementing GNNs within the gates of an LSTM and exploiting spatial information. In addition, we introduce a skip connection which proves critical to jointly capture the spatial and temporal patterns in the data. We validate our daily COVID-19 new cases forecast model on data of 37 European nations for the last 472 days and show superior performance compared to state-of-the-art graph time series models based on mean absolute scaled error (MASE). This area of research has important applications to policy-making and we analyze its potential for pandemic resource control.
|
[
"Computer Science Archive->cs.AI",
"Computer Science Archive->cs.LG"
] | 2021-07-14T14:14:33Z |
1506.05898
|
Hydrodynamics in 1+1 dimensions from Maxwell-Chern-Simons theory in AdS_3
|
In this presentation we review our work on Abelian Maxwell-Chern-Simons theory in three-dimensional AdS black brane backgrounds, with both integer and non-integer Chern-Simons coupling. Such theories can be derived from several string theory constructions, and we found exact solutions in the low frequency, low momentum limit (omega, k << T, the hydrodynamic limit). Our results are translated into correlation functions of vector operators in the dual strongly coupled 1+1-dimensional quantum field theory with a chiral anomaly at non-zero temperature T, via the holographic correspondence. The applicability of the hydrodynamic limit is discussed, together with the comparison between an exact field theoretic computation and the found holographic correlation functions in the conformal case.
|
[
"Physics Archive->hep->hep-th"
] | 2015-06-19T08:00:34Z |
physics/0505076
|
Phase Contrast technique: a broader approach
|
The treatment found on most general optics textbooks related to the phase contrast technique imposes limitations on the filter phase and object phase variations in order to mathematically explain it in a simple manner. We consider that this simplified treatment can be misleading in terms of the concept the student may develop and also about the potential applications of the phase contrast technique. In this paper we describe a broader and yet simple explanation of the phase contrast process, creating a parallelism between optical image processing and interferometry.
|
[
"Physics Archive->physics->physics.optics"
] | 2005-05-11T01:26:30Z |
1702.03026
|
Bound States in Nanoscale Graphene Quantum Dots in a Continuous Graphene Sheet
|
Considerable efforts have been made to trap massless Dirac fermions in graphene monolayer, but only quasi-bound states are realized in continuous graphene sheets up to now. Here, we demonstrate the realization of bound states in nanoscale graphene quantum dots (GQDs) in a continuous graphene sheet. The GQDs are electronically isolated from the surrounding continuous graphene sheet by circular boundaries, which are generated by strong coupling between graphene and substrate. By using scanning tunneling microscopy (STM), we observe single-electron charging states of the GQDs, seen as Coulomb oscillations in the tunneling conductance. Evolution of single-electron tunneling of the GQDs between the Coulomb blockade regime and the Coulomb staircase regime is observed by tuning the STM tip-sample distances. Spatial maps of the local electronic densities reveal concentric rings inside the GQDs with each ring corresponding to a single Coulomb oscillation of the tunneling spectra. These results indicate explicitly that the electrons are completely trapped inside the nanoscale GQDs.
|
[
"Physics Archive->cond-mat->cond-mat.mes-hall"
] | 2017-02-10T00:51:28Z |
2112.04296
|
Analytic long-lived modes in charged critical plasma
|
Fluctuations around critical behavior of a holographic charged plasmas are investigated by studying quasi-normal modes of the corresponding black branes in 5D Einstein-Maxwell-Dilaton gravity. The near horizon geometry of black branes approaches the well-known 2D charged string black hole in the critical limit, for which a world-sheet description is available, and the corresponding quasi-normal modes can be obtained analytically from the reflection amplitude of the 2D black hole geometry. We find two distinct set of modes: a purely imaginary ``decoupled'' set, directly following from the reflection amplitude, and a ``non-decoupled'' set that was already identified in the neutral holographic plasma in \cite{Betzios:2018kwn}. In the extremal limit, the former set of imaginary quasi-normal modes coalesce on a branch cut starting from the the origin, signaling breakdown of hydrodynamic approximation. We further complete the black brane geometry with a slice of AdS near the boundary, to allow for a holographic construction, and find another set of modes localized in the UV. Finally, we develop an alternative WKB method to obtain the quasi-normal modes in the critical limit and apply this method to study the spectrum of hyperscaling-violating Lifshitz black branes. The critical limit of the plasma we consider in this paper is in one-to-one correspondence with the large D limit of Einstein's gravity which allows for an alternative interesting interpretation of our findings.
|
[
"Physics Archive->hep->hep-th"
] | 2021-12-08T14:11:34Z |
2003.09679
|
On the Diagonal Stability of $k$-Positive Linear Systems
|
We consider $k$-positive linear systems, that is, systems that map the set of vectors with up to $k-1$ sign variations to itself. For $k=1$, this reduces to positive linear systems. It is well-known that stable positive linear time invariant (LTI) systems admit a diagonal Lyapunov function. This property has many important implications. A natural question is whether stable $k$-positive systemsalso admit a diagonal Lyapunov function. This paper shows that, in general, the answer is no. However, for both continuous-time and discrete-time $n$-dimensional systems that are $(n-1)$-positive we provide a sufficient condition for diagonal stability.
|
[
"Mathematics Archive->math.DS"
] | 2020-03-21T15:16:36Z |
0802.1817
|
Comments to the review "Nonthermal phenomena in clusters of galaxies" by Y.Rephaeli et al. that will appear on the book: Clusters of galaxies: beyond the thermal view
|
Comments to the review "Nonthermal Phenomena in Clusters of Galaxies" by Y.Rephaeli et al. (arXiv:0801.0982 [astro-ph]) that regard the presence of a hard X-ray excess in the Coma cluster, A2199, A2163 and the Bullet cluster.
|
[
"Physics Archive->astro-ph"
] | 2008-02-13T13:03:04Z |
quant-ph/0009081
|
Homodyne characterization of active optical media
|
An effective maximum likelihood method is suggested to characterize the absorption/amplification properties of active optical media through homodyne detection.
|
[
"Physics Archive->quant-ph"
] | 2000-09-20T15:31:15Z |
2105.05994
|
Neural Trajectory Fields for Dynamic Novel View Synthesis
|
Recent approaches to render photorealistic views from a limited set of photographs have pushed the boundaries of our interactions with pictures of static scenes. The ability to recreate moments, that is, time-varying sequences, is perhaps an even more interesting scenario, but it remains largely unsolved. We introduce DCT-NeRF, a coordinatebased neural representation for dynamic scenes. DCTNeRF learns smooth and stable trajectories over the input sequence for each point in space. This allows us to enforce consistency between any two frames in the sequence, which results in high quality reconstruction, particularly in dynamic regions.
|
[
"Computer Science Archive->cs.CV"
] | 2021-05-12T22:38:30Z |
hep-ph/9803404
|
Phenomenology of $SU(3) \otimes SU(2) \otimes U(1)$ supersymmetric model with Dirac neutrino masses
|
We consider supersymmetric extension of standard electroweak model with Dirac neutrino masses. In such model for significant region of the parameters right-handed tau sneutrino is the lightest superparticle and right-handed charged tau slepton is the next to lightest superparticle. Due to the smallness of the neutrino masses the right-handed tau slepton is long-lived particle that changes the standard signatures used in the search for supersymmetry at supercolliders. The most striking signatures of such scenario is the existence of highly ionizing tracks and excess of multilepton events that is similar to the phenomenology of gauge-mediated supersymmetry breaking models
|
[
"Physics Archive->hep->hep-ph"
] | 1998-03-20T14:05:14Z |
cond-mat/0005335
|
Scaling behavior for finite O(n) systems with long-range interaction
|
A detailed investigation of the scaling properties of the fully finite ${\cal O}(n)$ systems with long-range interaction, decaying algebraically with the interparticle distance $r$ like $r^{-d-\sigma}$, below their upper critical dimension is presented. The computation of the scaling functions is done to one loop order in the non-zero modes. The results are obtained in an expansion of powers of $\sqrt\epsilon$, where $\epsilon=2\sigma-d$ up to ${\cal O}(\epsilon^{3/2})$. The thermodynamic functions are found to be functions the scaling variable $z=RL^{2-\eta-\epsilon/2}U^{-1/2}$, where $R$ and $U$ are the coupling constants of the constructed effective theory, and $L$ is the linear size of the system. Some simple universal results are obtained.
|
[
"Physics Archive->cond-mat->cond-mat.stat-mech"
] | 2000-05-20T05:41:40Z |
1210.2345
|
Achieving steady-state entanglement of remote micromechanical oscillators by cascaded cavity coupling
|
In this paper, we propose a scheme for generating steady-state entanglement of remote micromechanical oscillators in unidirectionally-coupled cavities. For the system of two mechanical oscillators, we show that when two cavity modes in each cavity are driven at red- and blue-detuned sidebands, respectively, a stationary two-mode squeezed vacuum state of the two mechanical oscillators can be generated with the help of the cavity dissipation. The degree of squeezing is controllable by adjusting the relative strength of the pump lasers. Our calculations also show that the achieved mechanical entanglement is robust against thermal fluctuations of phononic environments. For the case of multiple mechanical oscillators, we find that the steady-state genuine multipartite entanglement can also be built up among the remote mechanical oscillators by the cavity dissipation. The present scheme does not require nonclassical light input or conditional quantum measurements, and it can be realized with current experimental technology.
|
[
"Physics Archive->quant-ph"
] | 2012-10-08T17:16:02Z |
2308.09418
|
Geometric monodromies, mixed Hodge numbers of motivic Milnor fibers and Newton polyhedra
|
We introduce the theory of geometric monodromies in various situations, focusing on its relations with toric geometry and motivic Milnor fibers, and moreover in the modern languages of nearby and vanishing cycle sheaves. Equivariant mixed Hodge numbers of motivic Milnor fibers will be described in terms of Newton polyhedra of polynomials.
|
[
"Mathematics Archive->math.AG"
] | 2023-08-18T09:34:14Z |
1708.05707
|
A String Theory Which Isn't About Strings
|
Quantization of closed string proceeds with a suitable choice of worldsheet vacuum. A priori, the vacuum may be chosen independently for left-moving and right-moving sectors. We construct {\sl ab initio} quantized bosonic string theory with left-right asymmetric worldsheet vacuum and explore its consequences and implications. We critically examine the validity of new vacuum and carry out first-quantization using standard operator formalism. Remarkably, the string spectrum consists only of a finite number of degrees of freedom: string gravity (massless spin-two, Kalb-Ramond and dilaton fields) and two massive spin-two Fierz-Pauli fields. The massive spin-two fields have negative norm, opposite mass-squared, and provides a Lee-Wick type extension of string gravity. We compute two physical observables: tree-level scattering amplitudes and one-loop cosmological constant. Scattering amplitude of four dilatons is shown to be a rational function of kinematic invariants, and in $D=26$ factorizes into contributions of massless spin-two and a pair of massive spin-two fields. The string one loop partition function is shown to perfectly agree with one loop Feynman diagram of string gravity and two massive spin-two fields. In particular, it does not exhibit modular invariance. We critically compare our construction with recent studies and contrast differences.
|
[
"Physics Archive->hep->hep-th"
] | 2017-08-18T17:52:41Z |
1501.02985
|
The Herschel Comprehensive (U)LIRG Emission Survey (HerCULES): CO Ladders, fine structure lines, and neutral gas cooling
|
(Ultra) Luminous Infrared Galaxies ((U)LIRGs) are objects characterized by their extreme infrared (8-1000 $\mu$m) luminosities ($L_{LIRG}>10^{11} $L$_\odot$ and $L_{ULIRG}>10^{12}$ L$_\odot$). The Herschel Comprehensive ULIRG Emission Survey (HerCULES; PI van der Werf) presents a representative flux-limited sample of 29 (U)LIRGs that spans the full luminosity range of these objects (10$^{11}\leq L_\odot \geq10^{13}$). With the \emph{Herschel Space Observatory}, we observe [CII] 157 $\mu$m, [OI] 63 $\mu$m, and [OI] 145 $\mu$m line emission with PACS, CO J=4-3 through J=13-12, [CI] 370 $\mu$m, and [CI] 609 $\mu$m with SPIRE, and low-J CO transitions with ground-based telescopes. The CO ladders of the sample are separated into three classes based on their excitation level. In 13 of the galaxies, the [OI] 63 $\mu$m emission line is self absorbed. Comparing the CO excitation to the IRAS 60/100 $\mu$m ratio and to far infrared luminosity, we find that the CO excitation is more correlated to the far infrared colors. We present cooling budgets for the galaxies and find fine-structure line flux deficits in the [CII], [SiII], [OI], and [CI] lines in the objects with the highest far IR fluxes, but do not observe this for CO $4\leq J_{upp}\leq13$. In order to study the heating of the molecular gas, we present a combination of three diagnostic quantities to help determine the dominant heating source. Using the CO excitation, the CO J=1-0 linewidth, and the AGN contribution, we conclude that galaxies with large CO linewidths always have high-excitation CO ladders, and often low AGN contributions, suggesting that mechanical heating is important.
|
[
"Physics Archive->astro-ph->astro-ph.GA"
] | 2015-01-13T13:03:27Z |
2102.07324
|
Multifractal analysis in non-uniformly hyperbolic interval maps
|
In this paper, we study the Hausdorff dimension of the generalized intrinsic level set with respect to the given ergodic meausre in a class of non-uniformly hyperbolic interval maps with finitely many branches.
|
[
"Mathematics Archive->math.DS"
] | 2021-02-15T03:33:15Z |
2103.04831
|
Semantic Models for the First-stage Retrieval: A Comprehensive Review
|
Multi-stage ranking pipelines have been a practical solution in modern search systems, where the first-stage retrieval is to return a subset of candidate documents, and latter stages attempt to re-rank those candidates. Unlike re-ranking stages going through quick technique shifts during past decades, the first-stage retrieval has long been dominated by classical term-based models. Unfortunately, these models suffer from the vocabulary mismatch problem, which may block re-ranking stages from relevant documents at the very beginning. Therefore, it has been a long-term desire to build semantic models for the first-stage retrieval that can achieve high recall efficiently. Recently, we have witnessed an explosive growth of research interests on the first-stage semantic retrieval models. We believe it is the right time to survey current status, learn from existing methods, and gain some insights for future development. In this paper, we describe the current landscape of the first-stage retrieval models under a unified framework to clarify the connection between classical term-based retrieval methods, early semantic retrieval methods and neural semantic retrieval methods. Moreover, we identify some open challenges and envision some future directions, with the hope of inspiring more researches on these important yet less investigated topics.
|
[
"Computer Science Archive->cs.IR"
] | 2021-03-08T15:36:09Z |
0711.1649
|
Systematic study of multi-quark states I. qq-qq-\bar{q} configuration
|
Group theoretic method for the systematic study of multi-quark states is developed. The calculation of matrix elements of many body Hamiltonian is simplified by transforming the physical bases (quark cluster bases) to symmetry bases (group chain classified bases), where the fractional parentage expansion method can be used. Five quark system is taken as example in this study. The Jaffe-Wilczek $qq-qq-\bar{q}$ configuration is chosen as one of examples to construct the physical bases and the transformation coefficients between physical bases and symmetry ones are shown to be related to the ${SU}_{mn}\supset{SU}_m\times{SU}_n$ isoscalar factors and a complete transformation coefficients table is given. The needed isoscalar factors and fractional parentage coefficients had been calculated with our new group representation theory and published before. Three quark models, the naive Glashow-Isgur, Salamanca and quark delocalization color screening, are used to show the general applicability of the new multi-quark calculation method and general results of constituent quark models for five-quark states are given.
|
[
"Physics Archive->hep->hep-ph"
] | 2007-11-11T11:06:44Z |
1708.05996
|
Solar Surface Magnetic Field Simulation Enabled Prediction of the Large-Scale Coronal Structure of the 21 August 2017 Great American Eclipse: An Assessment of Model Predictions and Observations
|
On 21 August 2017 a total solar eclipse swept across the contiguous United States providing excellent opportunities for diagnostics of the Sun's corona. The Sun's coronal structure is notoriously difficult to observe except during solar eclipses; thus theoretical models must be relied upon for inferring the underlying magnetic structure of the Sun's outer atmosphere. These models are necessary for understanding the role of magnetic fields in the heating of the corona to a million degrees and generation of severe space weather. Here we present a methodology for predicting the structure of the coronal field based on long-term surface flux transport simulations whose output is utilized to extrapolate the coronal magnetic field structures. This prescription was applied to the 21 August 2017 solar eclipse. Post-eclipse analysis shows good agreement between model simulated and observed coronal structures and their locations on the limb. We demonstrate that slow changes in the Sun's surface magnetic field distribution driven by long-term flux emergence and evolution govern large-scale coronal structures with a (plausibly cycle-phase dependent) dynamical memory timescale on the order of few solar rotations -- opening up the possibility of large-scale, global corona predictions at least a month in advance.
|
[
"Physics Archive->astro-ph->astro-ph.SR"
] | 2017-08-20T17:26:01Z |
2311.02463
|
Effect of streaks on hypersonic boundary layer instability
|
Hypersonic boundary layers exhibit diverse transition pathways, influenced by various flow conditions and environments. Non-modal mechanisms, such as the lift-up effect, are recognized as pivotal contributors to transition, particularly over complex geometries like rough walls or blunted forebodies. In this study, we investigate the impact of steady streaks on the transition to turbulence in hypersonic boundary layers. Streaky baseflows are generated using optimal disturbances at the inlet, forming the basis for our analysis. We conduct linearized direct numerical simulations on these baseflows at Mach number $M_\infty=6.0$, using white noise forcing to trigger instabilities. An efficient extension of the SPOD method is applied to identify and track the instabilities originating from the broadband forcing on the 3D non-homogeneous baseflows. The results highlight the dominant influence of low-frequency first-mode instabilities and streak-associated instabilities in the linear regime. These findings emphasize the critical role of streaks in hypersonic boundary layer transition and provide valuable insights into this complex phenomenon.
|
[
"Physics Archive->physics->physics.flu-dyn"
] | 2023-11-04T17:52:05Z |
1803.06643
|
The Web as a Knowledge-base for Answering Complex Questions
|
Answering complex questions is a time-consuming activity for humans that requires reasoning and integration of information. Recent work on reading comprehension made headway in answering simple questions, but tackling complex questions is still an ongoing research challenge. Conversely, semantic parsers have been successful at handling compositionality, but only when the information resides in a target knowledge-base. In this paper, we present a novel framework for answering broad and complex questions, assuming answering simple questions is possible using a search engine and a reading comprehension model. We propose to decompose complex questions into a sequence of simple questions, and compute the final answer from the sequence of answers. To illustrate the viability of our approach, we create a new dataset of complex questions, ComplexWebQuestions, and present a model that decomposes questions and interacts with the web to compute an answer. We empirically demonstrate that question decomposition improves performance from 20.8 precision@1 to 27.5 precision@1 on this new dataset.
|
[
"Computer Science Archive->cs.AI",
"Computer Science Archive->cs.CL",
"Computer Science Archive->cs.LG"
] | 2018-03-18T11:28:12Z |
0908.1002
|
Temperature dependence of critical velocities and long time decay of supercurrents
|
We show that a microscopic theory of superfluidity, based on the properties of the many-body spectrum of a superfluid, can explain naturally the temperature dependence of critical velocities and the long time decay of supercurrents.
|
[
"Physics Archive->cond-mat->cond-mat.supr-con"
] | 2009-08-07T08:33:28Z |
1502.00648
|
Sign Structure of Susceptibilities of Conserved Charges in the (2+1) Polyakov Quark Meson Model
|
The sign structure of correlations of conserved charges are investigated in a QCD like model: the (2+1) flavor Polyakov Quark Meson model. We compute all susceptibilities of the conserved charges on the $(\mu_{B}-T)$ plane up to fourth order and a few at higher order as well. By varying the mass of the sigma meson, we are able to study and compare scenarios with as well as without a critical point. In the hadron-quark transition regime we identify certain correlations that turn negative unlike expectation from ideal hadron resonance gas calculations. The striking feature being that these remain negative deep into the hadronic side and thus could be measured in experiments. Measurement of such quantities in heavy ion collision experiments can elucidate the location of the QCD transition curve and possibly the critical point.
|
[
"Physics Archive->hep->hep-lat",
"Physics Archive->hep->hep-ph",
"Physics Archive->nucl->nucl-th"
] | 2015-02-02T21:10:40Z |
1001.0904
|
A new approach for doing theoretical and numeric work with Lemaitre-Tolman-Bondi dust models
|
We introduce quasi-local integral scalar variables for the study of spherically symmetric Lemaitre-Tolman-Bondi (LTB) dust models. Besides providing a covariant, and theoretically appealing, interpretation for the parameters of these models, these variables allow us to study their dynamics (in their full generality) by means of fluid flow evolution equations that can be handled with simple numerical techniques and has a significant potential for astrophysical and cosmological applications. These evolution equations can also be understood in the framework of a gauge invariant and covariant formalism of spherical non-linear perturbations on a FLRW background. The covariant time splitting associated with the new variables leads, in a natural way, to rephrase the known analytic solutions within an initial value framework in which covariant scalars are given by simple scaling laws. By using this re-parametrization of the analytic solutions, we re-examine and provide an alternative outlook to various theoretical issues already treated in the literature: regularity conditions, an Omega parameter, as well as the fitting of a given LTB model to radial profiles of density or velocity at different cosmic times. Other theoretical issues and numeric applications will be examined in separate articles.
|
[
"Physics Archive->astro-ph->astro-ph.CO",
"Physics Archive->gr-qc"
] | 2010-01-06T15:09:53Z |
quant-ph/0703237
|
The Multiplicative Quantum Adversary
|
We present a new variant of the quantum adversary method. All adversary methods give lower bounds on the quantum query complexity of a function by bounding the change of a progress function caused by one query. All previous variants upper-bound the_difference_ of the progress function, whereas our new variant upper-bounds the_ratio_ and that is why we coin it the multiplicative adversary. The new method generalizes to all functions the new quantum lower-bound method by Ambainis [Amb05, ASW06] based on the analysis of eigenspaces of the density matrix. We prove a strong direct product theorem for all functions that have a multiplicative adversary lower bound.
|
[
"Physics Archive->quant-ph"
] | 2007-03-26T19:08:19Z |
1908.05985
|
One-proton and one-neutron knockout reactions from $N = Z = 28$ $^{56}$Ni to the $A = 55$ mirror pair $^{55}$Co and $^{55}$Ni
|
We present a high-resolution in-beam $\gamma$-ray spectroscopy study of excited states in the mirror nuclei $^{55}$Co and $^{55}$Ni following one-nucleon knockout from a projectile beam of $^{56}$Ni. The newly determined partial cross sections and the $\gamma$-decay properties of excited states provide a test of state-of-the-art nuclear structure models and probe mirror symmetry in unique ways. A mirror asymmetry for the partial cross sections leading to the two lowest $3/2^-$ states in the $A = 55$ mirror pair was identified as well as a significant difference in the $E1$ decays from the $1/2^+_1$ state to the same two $3/2^-$ states. The mirror asymmetry in the partial cross sections cannot be reconciled with the present shell-model picture or small mixing introduced in a two-state model. The observed mirror asymmetry in the $E1$ decay pattern, however, points at stronger mixing between the two lowest $3/2^-$ states in $^{55}$Co than in its mirror $^{55}$Ni.
|
[
"Physics Archive->nucl->nucl-ex",
"Physics Archive->nucl->nucl-th"
] | 2019-08-16T14:24:58Z |
1805.00471
|
"I ain't tellin' white folks nuthin": A quantitative exploration of the race-related problem of candour in the WPA slave narratives
|
From 1936-38, the Works Progress Administration interviewed thousands of former slaves about their life experiences. While these interviews are crucial to understanding the "peculiar institution" from the standpoint of the slave himself, issues relating to bias cloud analyses of these interviews. The problem I investigate is the problem of candour in the WPA slave narratives: it is widely held in the historical community that the strict racial caste system of the Deep South compelled black ex-slaves to tell white interviewers what they thought they wanted to hear, suggesting that there was a significant difference candour depending on whether their interviewer was white or black. In this work, I attempt to quantitatively characterise this race-related problem of candour. Prior work has either been of an impressionistic, qualitative nature, or utilised exceedingly simple quantitative methodology. In contrast, I use more sophisticated statistical methods: in particular word frequency and sentiment analysis and comparative topic modelling with LDA to try and identify differences in the content and sentiment expressed by ex-slaves in front of white interviewers versus black interviewers. While my sentiment analysis methodology was ultimately unsuccessful due to the complexity of the task, my word frequency analysis and comparative topic modelling methods both showed strong evidence that the content expressed in front of white interviewers was different from that of black interviewers. In particular, I found that the ex-slaves spoke much more about unfavourable aspects of slavery like whipping and slave patrollers in front of interviewers of their own race. I hope that my more-sophisticated statistical methodology helps improve the robustness of the argument for the existence of this problem of candour in the slave narratives, which some would seek to deny for revisionist purposes.
|
[
"Computer Science Archive->cs.CL"
] | 2018-05-01T05:24:40Z |
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