ShantanuT01/DACTYL-Pretraining huggingface dataset:
We address a simple connection between results of Hamiltonian nonlinear dynamical theory and thermostatistics. Using a properly defined dynamical temperature in low-dimensional symplectic maps, we display and characterize long-standing quasi-stationary states that eventually cross over to a Boltzmann-Gibbs-like regime. As time evolves, the geometrical properties (e.g., fractal dimension) of the phase space change sensibly, and the duration of the anomalous regime diverges with decreasing chaoticity. The scenario that emerges is consistent with the nonextensive statistical mechanics one.
On the basis of the density functional calculations in combination with the supercell approach, we report on a complete study of the influences of atomic arrangement and Ni substitution for Al on the ground state structural and magnetic properties for Fe$_2$Ni$_{1+x}$Al$_{1-x}$ Heusler alloys. We discuss systematically the competition between five cubic Heusler-type structures formed by shuffles of Fe and Ni atoms to reveal routes for improving the phase stability and magnetic properties, in particular magnetocrystalline anisotropy~(MAE). We predict that in case of Fe$_2$NiAl the ground state cubic structure with alternated layers of Fe and Ni possesses the highest uniaxial MAE which twice larger than that for the tetragonal L1$_0$ FeNi. The successive Ni doping at Al sublattice leads to a change of ground state structure and to reduce of the MAE. In addition, the phase stability against the decomposition into the stable systems at finite-temperatures is discussed. All~Ni-rich Fe$_2$Ni$_{1+x}$Al$_{1-x}$ are turned to be decomposed into a dual-phase consisting of Fe$_2$NiAl and FeNi.
Several polytopes arise from finite graphs. For edge and symmetric edge polytopes, in particular, exhaustive computation of the Ehrhart polynomials not merely supports the conjecture of Beck {\it et al.}\ that all roots $\alpha$ of Ehrhart polynomials of polytopes of dimension $D$ satisfy $-D \le \Re(\alpha) \le D - 1$, but also reveals some interesting phenomena for each type of polytope. Here we present two new conjectures: (1) the roots of the Ehrhart polynomial of an edge polytope for a complete multipartite graph of order $d$ lie in the circle $|z+\tfrac{d}{4}| \le \tfrac{d}{4}$ or are negative integers, and (2) a Gorenstein Fano polytope of dimension $D$ has the roots of its Ehrhart polynomial in the narrower strip $-\tfrac{D}{2} \leq \Re(\alpha) \leq \tfrac{D}{2}-1$. Some rigorous results to support them are obtained as well as for the original conjecture. The root distribution of Ehrhart polynomials of each type of polytope is plotted in figures.
There are two types of Belyi's Theorem for curves defined over finite fields of characteristic p, namely the Wild and the Tame p-Belyi Theorems. In this paper, we discuss them in the language of function fields. We provide a self-contained proof for the Wild p-Belyi Theorem for any prime p and the Tame 2-Belyi Theorem.
I review various phenomena associated with mass-accreting white dwarfs (WDs) in relation to progenitors of type Ia supernovae (SNe Ia). The WD mass can be estimated from light curve analysis in multiwavelength bands based on the optically thick wind theory. In the single degenerate scenario of SNe Ia, two main channels are known, i.e., WD + main sequence (MS) channel and WD + red giant (RG) channel. In each channel, a typical binary undergoes three evolutional stages before explosion, i.e., the wind phase, supersoft X-ray source (SSS) phase, and recurrent nova phase in order of time because the accretion rate decreases with time as the companion mass decreases. We can specify some accreting WDs as the corresponding stage of evolution. Intermittent supersoft X-ray source like RX J0513.9-6951 and V Sge are corresponding to the wind phase objects. For the SSS phase Cal 87-type objects correspond to the WD+MS channel. For the WD + RG channel, soft X-ray observations of early type galaxies gave a statistical evidence of SSS phase binaries. Recurrent novae of U Sco-type and RS Oph-type correspond to the WD + MS channel and WD + RG channel, respectively. Majority of recurrent novae host a very massive WD (~> 1.35 Mo) and often show a plateau phase in optical light curve correspondingly to the long lasted supersoft X-ray phase: These properties are indications of increasing WD masses.
Chen, Apalkov, and Chakraborty (Phys. Rev. Lett. 98, 186803 (2007)) have computed Fock-Darwin levels of a graphene dot by including only basis states with energies larger than or equal to zero. We show that their results violate the Hellman-Feynman theorem. A correct treatment must include both positive and negative energy basis states. Additional basis states lead to new energy levels in the optical spectrum and anticrossings between optical transition lines.
We say that a group G acts infinitely transitively on a set X if for every integer m the induced diagonal action of G is transitive on the cartesian mth power of X with the diagonals removed. We describe three classes of affine algebraic varieties such that their automorphism groups act infinitely transitively on their smooth loci. The first class consists of affine cones over flag varieties, the second of non-degenerate affine toric varieties, and the third of iterated suspensions over affine varieties with infinitely transitive automorphism groups of a reinforced type.
Cardiac Magnetic Resonance (CMR) is the most effective tool for the assessment and diagnosis of a heart condition, which malfunction is the world's leading cause of death. Software tools leveraging Artificial Intelligence already enhance radiologists and cardiologists in heart condition assessment but their lack of transparency is a problem. This project investigates if it is possible to discover concepts representative for different cardiac conditions from the deep network trained to segment crdiac structures: Left Ventricle (LV), Right Ventricle (RV) and Myocardium (MYO), using explainability methods that enhances classification system by providing the score-based values of qualitative concepts, along with the key performance metrics. With introduction of a need of explanations in GDPR explainability of AI systems is necessary. This study applies Discovering and Testing with Concept Activation Vectors (D-TCAV), an interpretaibilty method to extract underlying features important for cardiac disease diagnosis from MRI data. The method provides a quantitative notion of concept importance for disease classified. In previous studies, the base method is applied to the classification of cardiac disease and provides clinically meaningful explanations for the predictions of a black-box deep learning classifier. This study applies a method extending TCAV with a Discovering phase (D-TCAV) to cardiac MRI analysis. The advantage of the D-TCAV method over the base method is that it is user-independent. The contribution of this study is a novel application of the explainability method D-TCAV for cardiac MRI anlysis. D-TCAV provides a shorter pre-processing time for clinicians than the base method.
We succeed in deriving an exact expression for the magnetic interaction of neutrons and electrons including magneto-electric operators, allowed in the absence of a centre of inversion symmetry. Central characters are a spin anapole and an orbital (toroidal) analogue, in addition to familiar parity-even operators. A simulation of neutron diffraction by antiferromagnetic copper oxide makes full use of information inferred from a thorough investigation with resonant x-ray Bragg diffraction.
On the example of topologically massive gauge field theory we find the origin of possible inconsistency of working with gauge fixing terms (together with relevant ghost sector)
We consider the possibility that one extra $Z\equiv Z'$ exists with arbitrary mass and fermion couplings that do not violate (charged) lepton universality. We show that, in such a situation, a functional relationship is generated between the \underline{deviations} from the SM values of three leptonic observables of two-fermion production at future $e^+e^-$ colliders that is completely independent of the values of the $Z'$ mass and couplings. This selects a certain region in the 3-d space of the deviations that is \underline{characteristic} of the model ($Z'$ "reservation"). As a specific and relevant example, we show the picture that would emerge at LEP2 under realistic experimental conditions.
We use self-consistent Hartree-Fock calculations performed in the full $\pi$-band Hilbert space to assess the nature of the recently discovered correlated insulator states in magic-angle twisted bilayer graphene (TBG). We find that gaps between the flat conduction and valence bands open at neutrality over a wide range of twist angles, sometimes without breaking the system's valley projected ${\cal C}_{2}{\cal T}$ symmetry. Broken spin/valley flavor symmetries then enable gapped states to form not only at neutrality, but also at total moir\'e band filling $n = \pm p/4$ with integer $p = 1, 2, 3$, when the twist angle is close to the magic value at which the flat bands are most narrow. Because the magic-angle flat band quasiparticles are isolated from remote band quasiparticles only for effective dielectric constants larger than $ \sim 20$, the gapped states do not necessarily break \CT symmetry and as a consequence the insulating states at $n = \pm 1/4$ and $n = \pm 3/4$ need not exhibit a quantized anomalous Hall effect.
We investigate a problem considered by Zagier and Elkies, of finding large integral points on elliptic curves. By writing down a generic polynomial solution and equating coefficients, we are led to suspect four extremal cases that still might have nondegenerate solutions. Each of these cases gives rise to a polynomial system of equations, the first being solved by Elkies in 1988 using the resultant methods of~\Macsyma, with there being a unique rational nondegenerate solution. For the second case we found that resultants and/or Gr\"obner bases were not very efficacious. Instead, at the suggestion of Elkies, we used multidimensional $p$-adic Newton iteration, and were able to find a nondegenerate solution, albeit over a quartic number field. Due to our methodology, we do not have much hope of proving that there are no other solutions. For the third case we found a solution in a nonic number field, but we were unable to make much progress with the fourth case. We make a few concluding comments and include an appendix from Elkies regarding his calculations and correspondence with Zagier.
We define, and obtain the meromorphic continuation of, shifted Rankin-Selberg convolutions in one and two variables. As sample applications, this continuation is used to obtain estimates for single and double shifted sums and a Burgess-type bound for $L$-series associated to modular forms of arbitrary central character. Further applications are furnished by subsequent works by the authors and their colleagues.
We study the kinematics of emission lines that arise from many physical processes in NGC 6153 based upon deep, spatially-resolved, high resolution spectra acquired with the UVES spectrograph at the ESO VLT. Our most basic finding is that the plasma in NGC 6153 is complex, especially its temperature structure. The kinematics of most emission lines defines a classic expansion law, with the outer part expanding fastest (normal nebular plasma). However, the permitted lines of \ion{O}{1}, \ion{C}{2}, \ion{N}{2}, \ion{O}{2}, and \ion{Ne}{2} present a constant expansion velocity that defines a second kinematic component (additional plasma component). The physical conditions imply two plasma components, with the additional plasma component having lower temperature and higher density. The [\ion{O}{2}] density and the [\ion{N}{2}] temperature are anomalous, but may be understood considering the contribution of recombination to these forbidden lines. The two plasma components have very different temperatures. The normal nebular plasma appears to be have temperature fluctuations in part of its volume (main shell), but only small fluctuations elsewhere. The additional plasma component contains about half of the mass of the N$^{2+}$ and O$^{2+}$ ions, but only $3-5$\% of the mass of H$^+$ ions, so the two plasma components have very different chemical abundances. We estimate abundances of $12+\log(\mathrm O^{2+}/\mathrm H^+)\sim 9.2$\,dex and $\mathrm{He}/\mathrm H\sim 0.13$. Although they are all complications, multiple plasma components, temperature fluctuations, and the contributions of multiple physical processes to a given emission line are all part of the reality in NGC 6153, and should generally be taken into account.
Fast radio bursts (FRBs) represent one of the most exciting astrophysical discoveries of the recent past. The study of their low-frequency emission, which was only effectively picked up about ten years after their discovery, has helped shape the field thanks to some of the most important detections to date. Observations between 400 and 800 MHz, carried out by the CHIME/FRB telescope, in particular, have led to the detection of ~500 FRBs in little more than 1 year and, among them, ~20 repeating sources. Detections at low frequencies have uncovered a nearby population that we can study in detail via continuous monitoring and targeted campaigns. The latest, most important discoveries include: periodicity, both at the days level in repeaters and at the millisecond level in apparently non-repeating sources; the detection of an FRB-like burst from a galactic magnetar; and the localisation of an FRB inside a globular cluster in a nearby galaxy. The systematic study of the population at low frequencies is important for the characterisation of the environment surrounding the FRBs and, at a global level, to understand the environment of the local universe. This review is intended to give an overview of the efforts leading to the current rich variety of low-frequency studies and to put into a common context the results achieved in order to trace a possible roadmap for future progress in the field.
We prove that, for each nonnegative integer k and each matroid N, if M is a 3-connected matroid containing N as a minor, and the the branch width of M is sufficiently large, then there is a k-element subset X of E(M) such that one of M\X and M/X is 3-connected and contains N as a minor.
Fix a positive integer k. In this paper, we give a formula in closed form for all k-polygonal numbers that are also centered k-polygonal.
Weakly supervised temporal action localization, which aims at temporally locating action instances in untrimmed videos using only video-level class labels during training, is an important yet challenging problem in video analysis. Many current methods adopt the "localization by classification" framework: first do video classification, then locate temporal area contributing to the results most. However, this framework fails to locate the entire action instances and gives little consideration to the local context. In this paper, we present a novel architecture called Cascaded Pyramid Mining Network (CPMN) to address these issues using two effective modules. First, to discover the entire temporal interval of specific action, we design a two-stage cascaded module with proposed Online Adversarial Erasing (OAE) mechanism, where new and complementary regions are mined through feeding the erased feature maps of discovered regions back to the system. Second, to exploit hierarchical contextual information in videos and reduce missing detections, we design a pyramid module which produces a scale-invariant attention map through combining the feature maps from different levels. Final, we aggregate the results of two modules to perform action localization via locating high score areas in temporal Class Activation Sequence (CAS). Extensive experiments conducted on THUMOS14 and ActivityNet-1.3 datasets demonstrate the effectiveness of our method.
We present results of calculations of $n{-}{^6\rm He}$ elastic scattering phase shifts and resonances in ${^7\rm He}$. The calculations utilize the SS-HORSE method combined with ab initio no-core shell model calculations of the ${^7\rm He}$ and ${^6\rm He}$ nuclei with Daejeon16 and the JISP16 $NN$ interactions.
Recently, occluded person re-identification(Re-ID) remains a challenging task that people are frequently obscured by other people or obstacles, especially in a crowd massing situation. In this paper, we propose a self-supervised deep learning method to improve the location performance for human parts through occluded person Re-ID. Unlike previous works, we find that motion information derived from the photos of various human postures can help identify major human body components. Firstly, a motion-aware transformer encoder-decoder architecture is designed to obtain keypoints heatmaps and part-segmentation maps. Secondly, an affine transformation module is utilized to acquire motion information from the keypoint detection branch. Then the motion information will support the segmentation branch to achieve refined human part segmentation maps, and effectively divide the human body into reasonable groups. Finally, several cases demonstrate the efficiency of the proposed model in distinguishing different representative parts of the human body, which can avoid the background and occlusion disturbs. Our method consistently achieves state-of-the-art results on several popular datasets, including occluded, partial, and holistic.
We construct a compactification of the universal moduli space of semistable principal $G$-bundles over $\overline{\textrm{M}}_{g}$, the fibers of which over singular curves are the moduli spaces of $\delta$-semistable singular principal G-bundles.
The Keller-Segel system describes the collective motion of cells that are attracted by a chemical substance and are able to emit it. In its simplest form, it is a conservative drift-diffusion equation for the cell density coupled to an elliptic equation for the chemo-attractant concentration. This paper deals with the rate of convergence towards a unique stationary state in self-similar variables, which describes the intermediate asymptotics of the solutions in the original variables. Although it is known that solutions globally exist for any mass less $8\pi $, a smaller mass condition is needed in our approach for proving an exponential rate of convergence in self-similar variables.
In this work, we explore the properties of the matrix method for black hole quasinormal modes on the nonuniform grid. In particular, the method is implemented to be adapted to the Chebyshev grid, aimed at effectively suppressing Runge's phenomenon. It is found that while such an implementation is favorable from a mathematical point of view, in practice, the increase in precision does not necessarily compensate for the penalty in computational time. On the other hand, the original matrix method, though subject to Runge's phenomenon, is shown to be reasonably robust and suffices for most applications with a moderate grid number. In terms of computational time and obtained significant figures, we carried out an analysis regarding the trade-off between the two aspects. The implications of the present study are also addressed.
We derive four sum-rule expressions for spectra measured in electron energy-loss near edge structure experiments. These sum-rules permit the determination spin and orbital magnetic moments, spin-orbit interaction and number of states, analogously to the sum rules of x-ray magnetic circular dichroism. The derivation of the sum-rules is based on dynamical electron diffraction theory and the properties of the mixed dynamic form-factor. The accuracy of the sum-rules is tested by a complete evaluation of the thickness dependent electron energy-loss spectra for iron, cobalt, and nickel crystals. We find that the sum-rules reproduce both spin and orbital moments with very good accuracy. Our results provide a foundation for the use of the energy loss magnetic chiral dichroism technique as a quantitative probe of element specific magnetic properties.
We propose a robust and decoherence insensitive scheme to generate controllable entangled states of two three-level atoms interacting with an optical cavity and a laser beam. Losses due to atomic spontaneous transitions and to cavity decay are efficiently suppressed by employing fractional adiabatic passage and appropriately designed atom-field couplings. In this scheme the two atoms traverse the cavity-mode and the laser beam in opposite directions as opposed to other entanglement schemes in which the atoms are required to have fixed locations inside a cavity. We also show that the coherence of a traveling atom can be transferred to the other one without populating the cavity-mode.
We discuss an extension of the Coyote emulator to predict non-linear matter power spectra of dark energy (DE) models with a scale factor dependent equation of state of the form w = w_0 + ( 1 - a )w_a . The extension is based on the mapping rule between non-linear spectra of DE models with constant equation of state and those with time varying one originally introduced in ref. [40]. Using a series of N-body simulations we show that the spectral equivalence is accurate to sub-percent level across the same range of modes and redshift covered by the Coyote suite. Thus, the extended emulator provides a very efficient and accurate tool to predict non-linear power spectra for DE models with w_0 - w_a parametrization. According to the same criteria we have developed a numerical code, and we have implemented in a dedicated module for the CAMB code, that can be used in combination with the Coyote Emulator in likelihood analyses of non-linear matter power spectrum measurements. All codes can be found at https://github.com/luciano-casarini/PKequal
We consider the well-posedness of models involving age structure and non-linear diffusion. Such problems arise in the study of population dynamics. It is shown how diffusion and age boundary conditions can be treated that depend non-linearly and possibly non-locally on the density itself. The abstract approach is depicted with examples.
Four parallel workshops were organized at the 1996 Girona Conference, "Blazars, Black Holes, and Jets", with conference attendees free to choose which session they would like to attend. The chosen topics were ``Jet Models'', ``Multi-Frequency Support for High-Energy Observations'', ``Monitoring of Blazars'', and ``Host Galaxies and Environments''. While the individual sessions focused on their assigned topic, the goals of all the sessions were to identify points of agreement in the field and to set a course for future research. Following several hours of lively discussions, each session chair presented to the entire conference a summary of their own group's discussion. In this collective summary we have tried to reproduce the main opinions and ideas that were generated during the workshops.
In a recent paper \cite{CHR16}, Chandra, Hu and Rosalsky introduced the notion of a sequence of random variables being uniformly nonintegrable, and presented a list of interesting results on this uniform nonintegrability. In this note, we introduce a weaker definition on uniform nonintegrability (W-UNI for short) of random variables, present a necessary and sufficient condition for W-UNI, and give two equivalent characterizations of W-UNI, one of which is a W-UNI analogue of the celebrated de La Vall\'{e}e Poussin criterion for uniform integrability. In addition, we give some remarks, one of which gives a negative answer to the open problem raised in \cite{CHR16}.
The Bethe-Salpeter (BS) amplitude for $\pi N$ scattering is evaluated at the off mass shell points corresponding to the Low Energy Theorems (LET) based on PCAC and current algebra. The results suggest a way of maintaining consistency between BS equation and LET.