ShantanuT01/DACTYL-Pretraining huggingface dataset:
We present a numerical and partially analytical study of classical particles obeying a Langevin equation that describes diffusion on a surface modeled by a two dimensional potential. The potential may be either periodic or random. Depending on the potential and the damping, we observe superdiffusion, large-step diffusion, diffusion, and subdiffusion. Superdiffusive behavior is associated with low damping and is in most cases transient, albeit often long. Subdiffusive behavior is associated with highly damped particles in random potentials. In some cases subdiffusive behavior persists over our entire simulation and may be characterized as metastable. In any case, we stress that this rich variety of behaviors emerges naturally from an ordinary Langevin equation for a system described by ordinary canonical Maxwell-Boltzmann statistics.
We prove that the enumerative polynomials of generalized Stirling permutations by the statistics of plateaux, descents and ascents are partial $\gamma$-positive. Specialization of our result to the Jacobi-Stirling permutations confirms a recent partial $\gamma$-positivity conjecture due to Ma, Yeh and the second named author. Our partial $\gamma$-positivity expansion, as well as a combinatorial interpretation for the corresponding $\gamma$-coefficients, are obtained via the machine of context-free grammars and a group action on generalized Stirling permutations. Besides, we also provide an alternative approach to the partial $\gamma$-positivity from the stability of certain multivariate polynomials.
All-electrical control of a dynamic magnetoelectric effect is demonstrated in a classical multiferroic manganite DyMnO3, a material containing coupled antiferromagnetic and ferroelectric orders. Due to intrinsic magnetoelectric coupling with electromagnons a linearly polarized terahertz light rotates upon passing through the sample. The amplitude and the direction of the polarization rotation are defined by the orientation of ferroelectric domains and can be switched by static voltage. These experiments allow the terahertz polarization to be tuned using the dynamic magnetoelectric effect.
We study the possible existence of static traversable wormholes without invoking exotic matter in the framework of the Einstein--Cartan theory. A family of exact static, spherically symmetric wormhole solutions with an arbitrary throat radius, with flat or AdS asymptotic behavior, has been obtained with sources in the form of two noninteracting scalar fields with nonzero potentials. Both scalar fields are canonical (that is, satisfy the weak energy condition), one is minimally and the other nonminimally coupled to gravity, and the latter is a source of torsion.
The short and intermediate range order of an amorphous Ge$_{30}$Se$_{70}$ alloy produced by Mechanical Alloying were studied by Reverse Monte Carlo simulations of its x-ray total structure factor, Raman scattering and differential scanning calorimetry. The simulations were used to compute the $G^{\text{RMC}}_{\text{Ge-Ge}}(r)$, $G^{\text{RMC}}_{\text{Ge-Se}}(r)$ and $G^{\text{RMC}}_{\text{Se-Se}}(r)$ partial distribution functions and the ${\cal S}^{\text{RMC}}_{\text{Ge-Ge}}(K)$, ${\cal S}^{\text{RMC}}_{\text{Ge-Se}}(K)$ and ${\cal S}^{\text{RMC}}_{\text{Se-Se}}(K)$ partial structure factors. We calculated the coordination numbers and interatomic distances for the first and second neighbors and the bond-angle distribution functions $\Theta_{ijl}(\cos\theta)$. The data obtained indicate that the structure of the alloy has important differences when compared to alloys prepared by other techniques. There are a high number of Se-Se pairs in the first shell, and some of the tetrahedral units formed seemed to be connected by Se-Se bridges.
An adequate classification of proximal femur fractures from X-ray images is crucial for the treatment choice and the patients' clinical outcome. We rely on the commonly used AO system, which describes a hierarchical knowledge tree classifying the images into types and subtypes according to the fracture's location and complexity. In this paper, we propose a method for the automatic classification of proximal femur fractures into 3 and 7 AO classes based on a Convolutional Neural Network (CNN). As it is known, CNNs need large and representative datasets with reliable labels, which are hard to collect for the application at hand. In this paper, we design a curriculum learning (CL) approach that improves over the basic CNNs performance under such conditions. Our novel formulation reunites three curriculum strategies: individually weighting training samples, reordering the training set, and sampling subsets of data. The core of these strategies is a scoring function ranking the training samples. We define two novel scoring functions: one from domain-specific prior knowledge and an original self-paced uncertainty score. We perform experiments on a clinical dataset of proximal femur radiographs. The curriculum improves proximal femur fracture classification up to the performance of experienced trauma surgeons. The best curriculum method reorders the training set based on prior knowledge resulting into a classification improvement of 15%. Using the publicly available MNIST dataset, we further discuss and demonstrate the benefits of our unified CL formulation for three controlled and challenging digit recognition scenarios: with limited amounts of data, under class-imbalance, and in the presence of label noise. The code of our work is available at: https://github.com/ameliajimenez/curriculum-learning-prior-uncertainty.
We study branes moving in an AdS Schwarzschild black hole background. When the brane tension exceeds a critical value, the induced metric on the brane is of FRW type and asymptotically de Sitter. We discuss the relevance of such configurations to dS/CFT correspondence. When the black hole mass reaches a critical value that depends on the brane tension, the brane interpolates in the infinite past and future between a dS space and a finite space of zero Hubble constant. This corresponds to a cosmological evolution without a Big Bang or a Big Crunch. Moreover, the central charge of the CFT dual to the dS brane enters the Cardy-Verlinde formula that gives the entropy of the thermal CFT dual to the bulk AdS black hole.
We consider scaling of the entanglement entropy across a topological quantum phase transition in one dimension. The change of the topology manifests itself in a sub-leading term, which scales as $L^{-1/\alpha}$ with the size of the subsystem $L$, here $\alpha$ is the R\'{e}nyi index. This term reveals the universal scaling function $h_\alpha(L/\xi)$, where $\xi$ is the correlation length, which is sensitive to the topological index.
Using a part of XJC-correspondence by Pirio and Russo, we classify cubic forms $f$ whose Hessian matrices induce matrix factorizations of themselves. When it defines a reduced hypersurface, it satisfies the "secant-singularity" correspondence, that is, it coincides with the secant locus of its singular locus. In particular, when $f$ is irreducible, its singular locus is either one of four Severi varieties.
Generation of magnetic field energy, without mean field generation, is studied. Isotropic mirror-symmetric turbulence of a conducting fluid amplifies the energy of small-scale magnetic perturbations if the magnetic Reynolds number is high, and the dimensionality of space d satisfies 2.103 < d <8.765. The result does not depend on the model of turbulence, incompressibility and isotropy being the only requirements.
Due to the finite size effects, the localisation of the phase transition in finite systems and the determination of its order, become an extremely difficult task, even in the simplest known cases. In order to identify and locate the finite volume transition point $T_{0}(V)$ of the QCD deconfinement phase transition to a Colorless QGP, we have developed a new approach using the finite size cumulant expansion of the order parameter and the $L_{mn}$-method. The first six cumulants $C_{1,2,3,4,5,6}$ with the corresponding under-normalized ratios(skewness $\Sigma$, kurtosis $\kappa$ ,pentosis $\Pi_{\pm}$ and hexosis $\mathcal{H}_{1,2,3}$) and three unnormalized combinations of them ($\mathcal{O}={\mathcal{\sigma }^{2} \mathcal{\kappa } }{\mathbf{\Sigma }^{-1} }$, $\mathcal{U} ={\mathcal{\sigma }^{-2} \mathbf{\Sigma }^{-1} }$, $\mathcal{N} = \mathcal{\sigma }^{2} \mathcal{\kappa }$) are calculated and studied as functions of $(T,V)$. A new approach, unifying in a clear and consistent way the definitions of cumulant ratios, is proposed. A numerical FSS analysis of the obtained results has allowed us to locate accurately the finite volume transition point. The extracted transition temperature value $T_{0}(V)$ agrees with that expected $T_{0}^{N}(V)$ from the order parameter and the thermal susceptibility $\chi _{T}\left( T,V\right)$, according to the standard procedure of localization to within about $2\%$. In addition to this, a very good correlation factor is obtained proving the validity of our cumulants method. The agreement of our results with those obtained by means of other models is remarkable.
We analyze the hydrodynamic behavior of the porous medium model in a discrete space $\{0,\ldots, n\}$, where the sites $0$ and $n$ stand for reservoirs. Our strategy relies on the entropy method of Guo, Papanicolau and Varadhan. However, this method cannot be straightforwardly applied, since there are configurations that do not evolve according to the dynamics (blocked configurations). In order to avoid this problem, we slightly perturbed the dynamics in such a way that the macroscopic behavior of the system keeps following the porous medium equation, but with boundary conditions which depend on the reservoirs strength's.
Magnetic, linear thermal expansion (LTE), anisotropic ($\lambda_t$) and volume ($\omega $) magnetostriction properties of Pr$_{0.5}$Sr$_{0.5}$MnO$_3$ were investigated. The LTE decreases smoothly from 300 K without a clear anomaly either around the Curie (T$_C$ = 270 K) or the Neel temperature (T$_N$ = 100 K) and it exhibits hysteresis over a wide temperature range (60 K-270 K) upon warming. Isothermal magnetization study suggests that 13 % of the ferromagnetic phase coexists with 87 % of the antiferromagnetic phase at 25 K. The parallel and perpendicular magnetostrictions undergo rapid changes during the metamagnetic transition. Contrary to the isotropic giant volume magnetostriction reported in manganites so far, this compound exhibits a giant anisotropic magnetostriction ($\lambda_t \approx 10^{-3}$) and smaller volume ($\omega \approx 10^{-4}$) magnetostrictions below T$_N$. We suggest that the field induced antiferromagnetic to ferromagnetic transition is accompanied by a structural transition from the d$_{x^2-y^2}$ orbital ordered antiferromagnetic (orthorhombic) to the orbital disordered ferromagnetic (tetragonal) phase. The metamagnetic transition proceeds through nucleation and growth of the ferromagnetic domains at the expense of the antiferromagnetic phase. The preferential orientation of the ferromagnetic (tetragonal) domains along the field direction increases the linear dimension of the sample in the field direction and decreases in the orthogonal direction leading to the observed giant anisotropic magnetostriction effect. Our study also suggests that nanodomains of the low temperature antiferromagnetic phase possibly exist in the temperature region T$_N$ < T < T$_C$.
The transverse momentum dependent gluon density obtained with CCFM evolution is determined from a fit to the latest combined HERA structure function measurements.
We propose a CNN-based approach for multi-camera markerless motion capture of the human body. Unlike existing methods that first perform pose estimation on individual cameras and generate 3D models as post-processing, our approach makes use of 3D reasoning throughout a multi-stage approach. This novelty allows us to use provisional 3D models of human pose to rethink where the joints should be located in the image and to recover from past mistakes. Our principled refinement of 3D human poses lets us make use of image cues, even from images where we previously misdetected joints, to refine our estimates as part of an end-to-end approach. Finally, we demonstrate how the high-quality output of our multi-camera setup can be used as an additional training source to improve the accuracy of existing single camera models.
We analyze 24 binary radio pulsars in the North American Nanohertz Observatory for Gravitational Waves (NANOGrav) nine-year data set. We make fourteen significant measurements of Shapiro delay, including new detections in four pulsar-binary systems (PSRs J0613$-$0200, J2017+0603, J2302+4442, and J2317+1439), and derive estimates of the binary-component masses and orbital inclination for these MSP-binary systems. We find a wide range of binary pulsar masses, with values as low as $m_{\rm p} = 1.18^{+0.10}_{-0.09}\text{M}_{\odot}$ for PSR J1918$-$0642 and as high as $m_{\rm p} = 1.928^{+0.017}_{-0.017}\text{M}_{\odot}$ for PSR J1614$-$2230 (both 68.3\% credibility). We make an improved measurement of the Shapiro timing delay in the PSR J1918$-$0642 and J2043+1711 systems, measuring the pulsar mass in the latter system to be $m_{\rm p} = 1.41^{+0.21}_{-0.18}\text{M}_{\odot}$ (68.3\% credibility) for the first time. We measure secular variations of one or more orbital elements in many systems, and use these measurements to further constrain our estimates of the pulsar and companion masses whenever possible. In particular, we used the observed Shapiro delay and periastron advance due to relativistic gravity in the PSR J1903+0327 system to derive a pulsar mass of $m_{\rm p} = 1.65^{+0.02}_{-0.02}\text{M}_{\odot}$ (68.3\% credibility). We discuss the implications that our mass measurements have on the overall neutron-star mass distribution, and on the "mass/orbital-period" correlation due to extended mass transfer.
In this work we explore the compositions of non-stoichiometric intermediate phases formed by diffusion reactions: a mathematical framework is developed and tested against the specific case of Nb3Sn superconductors. In the first part, the governing equations for the bulk diffusion and inter-phase interface reactions during the growth of a compound are derived, numerical solutions to which give both the composition profile and growth rate of the compound layer. The analytic solutions are obtained with certain approximations made. In the second part, we explain an effect that the composition characteristics of compounds can be quite different depending on whether it is the bulk diffusion or grain boundary diffusion that dominates in the compounds, and that frozen bulk diffusion leads to unique composition characteristics quite distinct from equilibrium expectations; then the model is modified for the case of grain boundary diffusion. Finally, we apply this model to the Nb3Sn superconductors and propose the approaches to control their compositions.
Trapped ions are among the most promising platforms for quantum technologies. They are at the heart of the most precise clocks and sensors developed to date, which exploit the quantum coherence of a single electronic or motional degree of freedom of an ion. However, future high precision quantum metrology will require the use of entangled states of several degrees of freedom. Here we propose a protocol capable of generating high N00N states where the entanglement is shared between the motion of a trapped ion and an electromagnetic cavity mode, a so called hybrid configuration. We prove the feasibility of the proposal in a platform consisting of a trapped ion excited to its circular Rydberg state manifold, coupled to the modes of a high Q microwave cavity. This compact hybrid architecture has the advantage that it can couple to signals of very different nature, which modify either the ions motion or the cavity modes. Moreover, the exact same setup can be used right after the state preparation phase to implement the interferometer required for quantum metrology.
The future of high-precision electroweak physics lies in e+e- collider measurements of properties of the Z boson, the W boson, the Higgs boson, and the top quark. We estimate the expected performance of three possible future colliders: the ILC, FCC-ee (formerly known as TLEP), and CEPC. In particular, we present the first estimates of the possible reach of CEPC, China's proposed Circular Electron-Positron Collider, for the oblique parameters S and T and for seven-parameter fits of Higgs couplings. These results allow the physics potential for CEPC to be compared with that of the ILC and FCC-ee. We also show how the constraints on S and T would evolve as the uncertainties on each of the most important input measurements change separately. This clarifies the basic physics goals for future colliders. To improve on the current precision, the highest priorities are improving the uncertainties on the W mass and effective weak mixing angle. At the same time, improved measurements of the top mass, the Z mass, the running of alpha, and the Z width will offer further improvement which will determine the ultimate reach. Each of the possible future colliders we consider has strong prospects for probing TeV-scale electroweak physics.
Despite its success in the weak gravity regime, General Relativity (GR) has yet to be verified in the regime of strong gravity. In this paper, we present the results of detailed ray tracing simulations aiming at clarifying if the combined information from X-ray spectroscopy, timing, and polarization observations of stellar mass and supermassive black holes can be used to test GR's no-hair theorem. The latter states that stationary astrophysical black holes are described by the Kerr-family of metrics with the black hole mass and spin being the only free parameters. We use four "non-Kerr metrics", some phenomenological in nature and others motivated by alternative theories of gravity, and study the observational signatures of deviations from the Kerr metric. Particular attention is given to the case when all the metrics are set to give the same Innermost Stable Circular Orbit (ISCO) in quasi-Boyer Lindquist coordinates. We give a detailed discussion of similarities and differences of the observational signatures predicted for BHs in the Kerr metric and the non-Kerr metrics. We emphasize that even though some regions of the parameter space are nearly degenerate even when combining the information from all observational channels, X-ray observations of very rapidly spinning black holes can be used to exclude large regions of the parameter space of the alternative metrics. Although it proves difficult to distinguish between the Kerr and non-Kerr metrics for some portions of the parameter space, the observations of very rapidly spinning black holes like Cyg X-1 can be used to rule out large regions for several black hole metrics.
Deep neural networks (DNNs) have recently been applied and used in many advanced and diverse tasks, such as medical diagnosis, automatic driving, etc. Due to the lack of transparency of the deep models, DNNs are often criticized for their prediction that cannot be explainable by human. In this paper, we propose a novel Morphological Fragmental Perturbation Pyramid (MFPP) method to solve the Explainable AI problem. In particular, we focus on the black-box scheme, which can identify the input area that is responsible for the output of the DNN without having to understand the internal architecture of the DNN. In the MFPP method, we divide the input image into multi-scale fragments and randomly mask out fragments as perturbation to generate a saliency map, which indicates the significance of each pixel for the prediction result of the black box model. Compared with the existing input sampling perturbation method, the pyramid structure fragment has proved to be more effective. It can better explore the morphological information of the input image to match its semantic information, and does not need any value inside the DNN. We qualitatively and quantitatively prove that MFPP meets and exceeds the performance of state-of-the-art (SOTA) black-box interpretation method on multiple DNN models and datasets.
A formulation of quantum mechanics based on an operational definition of state is presented. This formulation, which includes explicitly the macroscopic systems, assumes the probabilistic interpretation and is nevertheless objective. The classical paradoxes of quantum mechanics are analyzed and their origin is found to be the fictitious properties that are usually attributed to quantum-mechanical states. The hypothesis that any mixed state can always be considered as an incoherent superposition of pure states is found to contradict quantum mechanics. A solution of EPR paradox is proposed. It is shown that entanglement of quantum states is compatible with realism and locality of events, but implies non-local encoding of information.
The backreaction term ${\cal Q}_\CD$ and the averaged spatial Ricci scalar $\average{\CR}$ in the spatially averaged inhomogeneous Universe can be used to combine into effective perfect fluid energy density $\varrho_{\rm eff}^{\CD}$ and pressure $p_{\rm eff}^{\CD}$ that can be regarded as new effective sources for the backreaction effects. In order to model the realistic evolution of backreaction, we adopt the Chevallier-Polarski-Linder(CPL) parameterizations of the equation of state(EoS) of the effective perfect fluid. To deal with observations in the backreaction context, in this paper, we employ two metrics to describe the the late time Universe, one of them is the standard Friedmann-Lema\^{\i}tre-Robertson-Walker(FLRW) metric, and the other is a template metric with an evolving curvature parameter introduced by Larena et. al. in \cite{larena2009testing}. We also fit the CPL backreaction model using type Ia supernova(SN Ia) data and observational Hubble parameter data(OHD) with these two metrics, and find out that parameter tensions between two different data sets are larger when the backreaction model is equipped with the template metric, therefore we conclude that the prescription of the geometrical instantaneous spatially-constant curvature $\kappa_{\CD}$ needs to be modified.
We propose a simple model of dynamical supersymmetry breaking in the context of minimal supergravity with gauged $U(1)_R$ symmetry. The model is based on the gauge group $SU(2) \times U(1)_R$ with three matters. Since the $U(1)_R$ symmetry is gauged, the Fayet-Iliopoulos D-term appears due to the symmetry of supergravity. On the other hand, the superpotential generated dynamically by the SU(2) gauge dynamics leads to run away potential. Since the supersymmetric vacuum condition required by the D-term potential contradicts the one required by the superpotential, supersymmetry is broken. The supersymmetry breaking scale is controlled by the dynamical scale of the SU(2) gauge interaction. We can choose the parameters in our model for vanishing cosmological constant. Our model is phenomenologically viable with the gravitino mass of order 1 TeV or 10 TeV.
The Thue colouring of a graph is a colouring such that the sequence of vertex colours of any path of even and finite length in $G$ is non-repetitive. The change in the Thue number, $\pi(G)$, as edges are iteratively removed from a graph $G$ is studied. The notion of the $\tau$-index denoted, $\tau(G)$, of a graph $G$ is introduced as well. $\tau(G)$ serves as a measure for the efficiency of edge deletion to reduce the Thue chromatic number of a graph.