ShantanuT01/DACTYL-Pretraining huggingface dataset:
We exhibit a sufficient condition in terms of decay at infinity of the initial data for the finite time blowup of strong solutions to the Camassa--Holm equation: a wave breaking will occur as soon as the initial data decay faster at infinity than the solitons. In the case of data decaying slower than solitons we provide persistence results for the solution in weighted $L^p$-spaces, for a large class of moderate weights. Explicit asymptotic profiles illustrate the optimality of these results.
We investigate theoretically the interplay between the effects of a perpendicular electric field and incommensurability at the interface on the electronic properties of a heterostructure of bilayer graphene and a semiconducting substrate with a unit cell almost three times larger then that of graphene. It is known that the former introduces an asymmetry in the distribution of the electronic wave function between the layers and opens a band gap in the electronic spectrum. The latter generates a long wavelength periodic moir\'{e} perturbation of graphene electrons which couples states in inequivalent graphene Brillouin zone corners and leads to the formation of minibands. We show that, depending on the details of the moir\'{e} perturbation, the miniband structure can be tuned from that with a single band gap at the neutrality point and over-lapping minibands on the conduction/valence band side to a situation where a single narrow miniband is separated by gaps from the rest of the spectrum.
We first use five non-spinning and two mildly spinning (chi_i \simeq -0.44, +0.44) numerical-relativity waveforms of black-hole binaries and calibrate an effective-one-body (EOB) model for non-precessing spinning binaries, notably its dynamics and the dominant (2,2) gravitational-wave mode. Then, we combine the above results with recent outcomes of small-mass-ratio simulations produced by the Teukolsky equation and build a prototype EOB model for detection purposes, which is capable of generating inspiral-merger-ringdown waveforms for non-precessing spinning black-hole binaries with any mass ratio and individual black-hole spins -1 \leq chi_i \lesssim 0.7. We compare the prototype EOB model to two equal-mass highly spinning numerical-relativity waveforms of black holes with spins chi_i = -0.95, +0.97, which were not available at the time the EOB model was calibrated. In the case of Advanced LIGO we find that the mismatch between prototype-EOB and numerical-relativity waveforms is always smaller than 0.003 for total mass 20-200 M_\odot, the mismatch being computed by maximizing only over the initial phase and time. To successfully generate merger waveforms for individual black-hole spins chi_i \gtrsim 0.7, the prototype-EOB model needs to be improved by (i) better modeling the plunge dynamics and (ii) including higher-order PN spin terms in the gravitational-wave modes and radiation-reaction force.
In the context of 2D/3D registration, this paper introduces an approach that allows to match features detected in two different modalities: photographs and 3D models, by using a common 2D reprensentation. More precisely, 2D images are matched with a set of depth images, representing the 3D model. After introducing the concept of curvilinear saliency, related to curvature estimation, we propose a new ridge and valley detector for depth images rendered from 3D model. A variant of this detector is adapted to photographs, in particular by applying it in multi-scale and by combining this feature detector with the principle of focus curves. Finally, a registration algorithm for determining the correct viewpoint of the 3D model and thus the pose is proposed. It is based on using histogram of gradients features adapted to the features manipulated in 2D and in 3D, and the introduction of repeatability scores. The results presented highlight the quality of the features detected, in term of repeatability, and also the interest of the approach for registration and pose estimation.
This paper is devoted to a statistical analysis of the velocity fluctuations arising from a random distribution of point vortices in two-dimensional turbulence. Exact results are derived for the correlations in the velocities occurring at two points separated by an arbitrary distance. We find that the spatial correlation function decays extremely slowly with the distance. We discuss the analogy with the statistics of the gravitational field in stellar systems.
We present the fabrication and exploration of arrays of nanodots of $SrRuO_3$ with dot sizes between 500 nm and 15 nm. Down to the smallest dot size explored, the samples were found to be magnetic with a maximum of the Curie temperature $T_C$ achieved by dots of 30 nm diameter. This peak in $T_C$ is associated with a dot-size-induced relief of the epitaxial strain, as evidenced by scanning transmission electron microscopy.
We show that optical second-harmonic generation (SHG) can be observed from individual single-walled carbon nanotubes (SWCNTs) and, furthermore, allows imaging of individual tubes. Detailed analysis of our results suggests that the structural noncentrosymmetry, as required for SHG, arises from the non-zero chiral angle of the SWCNT. SHG thus has potential as a fast, non-destructive, and simple method for imaging of individual nanomolecules and for probing their chiral properties. Even more, it opens the possibility to optically determine the handedness of individual SWCNTs.
We consider a mixed stochastic differential equation driven by possibly dependent fractional Brownian motion and Brownian motion. Under mild regularity assumptions on the coefficients, it is proved that the equation has a unique solution.
Deep convolutional neural networks (CNNs) have shown appealing performance on various computer vision tasks in recent years. This motivates people to deploy CNNs to realworld applications. However, most of state-of-art CNNs require large memory and computational resources, which hinders the deployment on mobile devices. Recent studies show that low-bit weight representation can reduce much storage and memory demand, and also can achieve efficient network inference. To achieve this goal, we propose a novel approach named BWNH to train Binary Weight Networks via Hashing. In this paper, we first reveal the strong connection between inner-product preserving hashing and binary weight networks, and show that training binary weight networks can be intrinsically regarded as a hashing problem. Based on this perspective, we propose an alternating optimization method to learn the hash codes instead of directly learning binary weights. Extensive experiments on CIFAR10, CIFAR100 and ImageNet demonstrate that our proposed BWNH outperforms current state-of-art by a large margin.
An exactly solvable model describing the dilute spin-3/2 fermion gas in one-dimensional optical trap is proposed. The diagonalization of the model Hamiltonian is derived by means of the Bethe ansatz method. Exotic spin excitations such as the heavy spinon with fractional spin 3/2, the neutral spinon with spin zero and the dressed spinon with spin 1/2 are found based on the exact solution.
Cylindric Young tableaux are combinatorial objects that first appeared in the 1990s. A natural extension of the classical notion of a Young tableau, they have since been used several times, most notably by Gessel and Krattenthaler and by Alexander Postnikov. Despite this, relatively little is known about cylindric Young tableaux. This paper is an investigation of the properties of this object. In this paper, we extend the Robinson-Schensted-Knuth Correspondence, a well-known and very useful bijection concerning regular Young tableaux, to be a correspondence between pairs of cylindric tableaux. We use this correspondence to reach further results about cylindric tableaux. We then establish an interpretation of cylindric tableaux in terms of a game involving marble-passing. Next, we demonstrate a generic method to use results concerning cylindric tableaux in order to prove results about skew Young tableaux. We finish with a note on Knuth equivalence and its analog for cylindric tableaux.
The results and conclusions by Ponomarev and Vdovin [Phys. Rev. C {\bf 72}, 034309 (2005)] are inadequate to judge the applicability of the modified BCS because they were obtained either in the temperature region, where the use of zero-temperature single-particle spectra is no longer justified, or in too limited configuration spaces.
We analyze polarization phenomena for pseudoscalar and vector mesons production in nucleon-nucleon collisions. We identify three energy regions corresponding to different physics and different approaches in the analysis of polarization effects. In the threshold region, characterized by the S-wave production for all final particles, the general symmetry properties of strong interaction can be applied. The region of intermediate energies, T=2-4 GeV, is characterized by the essential role of central i.e. non-peripheral collisions, where only a small number of s-channel states with definite quantum numbers, ${\cal J}^P=1^-$ and $2^+$, contribute. At higher energies, T $\ge $10 GeV, the leading mechanism is the diffractive dissociation and it is especially interesting for baryon spectroscopy. The transition to this region is an open field for experimental research at the Nuclotron.
Existing person re-identification (re-id) methods mostly rely on supervised model learning from a large set of person identity labelled training data per domain. This limits their scalability and usability in large scale deployments. In this work, we present a novel selective tracklet learning (STL) approach that can train discriminative person re-id models from unlabelled tracklet data in an unsupervised manner. This avoids the tedious and costly process of exhaustively labelling person image/tracklet true matching pairs across camera views. Importantly, our method is particularly more robust against arbitrary noisy data of raw tracklets therefore scalable to learning discriminative models from unconstrained tracking data. This differs from a handful of existing alternative methods that often assume the existence of true matches and balanced tracklet samples per identity class. This is achieved by formulating a data adaptive image-to-tracklet selective matching loss function explored in a multi-camera multi-task deep learning model structure. Extensive comparative experiments demonstrate that the proposed STL model surpasses significantly the state-of-the-art unsupervised learning and one-shot learning re-id methods on three large tracklet person re-id benchmarks.
We study perverse coherent sheaves on the resolution of rational double points. As examples, we consider rational double points on 2-dimensional moduli spaces of stable sheaves on K3 and elliptic surfaces. Then we show that perverse coherent sheaves appears in the theory of Fourier-Mukai transforms. As an application, we generalize the Fourier-Mukai duality for K3 surfaces to our situation.
This paper is concerned with modeling the dynamics of social outbursts of activity, such as protests or rioting activity. In this sequel to our work in \cite{Berestycki2014}, written in collaboration with J-P. Nadal, we model the effect of restriction of information and explore the effects that it has on the existence of {\it upheaval waves}. The systems involve the coupling of an explicit variable representing the intensity of rioting activity and an underlying (implicit) field of social tension. We prove the existence of global solutions to the Cauchy problem in $\mathbb{R}^d$ as well as the existence of {\it traveling wave solutions} under certain parameter regimes. We furthermore explore the effects of heterogeneities in the environment with the help of numerical simulations, which leads to pulsating waves in certain cases. We analyze the effects of periodic domains as well as the {\it barrier} problem with the help of numerical simulations and discuss many open problems.
We analyze data on pulsation amplitudes and phases for two $\beta$ Cephei stars, $\delta$ Cet and $\nu$ Eri. Str\"omgren photometry and radial velocity measurements are used simultaneously to obtain constraints on mean parameters of the stars and identification of the excited modes. The inference about the radial mode order and mean star parameters is based on comparison of certain complex parameter, $f$, determined from data, with its counterpart derived from linear nonadiabatic modelling of stellar oscillations. The theoretical $f$ values are very sensitive to the adopted opacity data. In our modelling we rely on the data from OPAL and OP projects. Significant differences were found. New seismic models of $\nu$ Eri were constructed with both the OPAL and OP opacities.
We study flux tubes (strings) on the Higgs branches in supersymmetric gauge theories. In generic vacua on the Higgs branches strings were shown to develop long-range "tails" associated with massless fields, a characteristic feature of the Higgs branch (the only exception is the vacuum at the base of the Higgs branch). A natural infrared regularization for the above tails is provided by a finite string length L. We perform a numerical study of these strings in generic vacua. We focus on the simplest example of strings in N=1 supersymmetric QED with the Fayet-Iliopoulos term. In particular, we examine the accuracy of a logarithmic approximation (proposed earlier by Evlampiev and Yung) for the tension of such string solutions. In the Evlampiev-Yung formula the dependence of tension on the string length is logarithmic and the dependence on the geodesic length from the base of the Higgs branch is quadratic. We observe a remarkable agreement of our numerical results for the string tension with the Evlampiev-Yung analytic expression.
We present the most accurate measurement to date of cosmological evolution of the near-infrared galaxy luminosity function, from the local Universe out to z~4. The analysis is based on a large and highly complete sample of galaxies selected from the first data release of the UKIDSS Ultra Deep Survey. Exploiting a master catalogue of K- and z-band selected galaxies over an area of 0.7 square degrees, we analyse a sample of ~50,000 galaxies, all with reliable photometry in 16-bands from the far-ultraviolet to the mid-infrared. The unique combination of large area and depth provided by the Ultra Deep Survey allows us to trace the evolution of the K-band luminosity function with unprecedented accuracy. In particular, via a maximum likelihood analysis we obtain a simple parameterization for the luminosity function and its cosmological evolution, including both luminosity and density evolution, which provides an excellent description of the data from z =0 up to z~4. We find differential evolution for galaxies dependent on galaxy luminosity, revealing once again the ``down-sizing behaviour'' of galaxy formation. Finally, we compare our results with the predictions of the latest theoretical models of galaxy formation, based both on semi-analytical prescriptions, and on full hydrodynamical simulations.
In this article, we prove that small localized data yield solutions to Kawahara type equation which have linear dispersive decay on a finite time. We use the similar method used to derive the dispersive decay bound of the solutions to the KdV equation, with some steps being simpler. This result is expected to be the first result of the small data global bounds of the fifth-order dispersive equations with quadratic nonlinearity.
Capacitance of a nanoscale system is usually thought of having two contributions, a classical electrostatic contribution and a quantum contribution dependent on the density of states and/or molecular orbitals close to the Fermi energy. In this letter we demonstrate that in molecular nano-magnets and other magnetic nanoscale systems, the quantum part of the capacitance becomes spin-dependent, and is tunable by an external magnetic field. This molecular magnetocapacitance can be realized using single molecule nano-magnets and/or other nano-structures that have antiferromagnetic ground states. As a proof of principle, first-principles calculation of the nano-magnet [Mn3O(sao)3(O2CMe)(H2O)(py)3] shows that the charging energy of the high-spin state is 260 meV lower than that of the low-spin state, yielding a 6% difference in capacitance. A magnetic field of ~40T can switch the spin state, thus changing the molecular capacitance. A smaller switching field may be achieved using nanostructures whose physical properties such as magnetic moment are size-dependent. Molecular magnetocapacitance may lead to revolutionary device designs, e.g., by exploiting the Coulomb blockade magnetoresistance whereby a small change in capacitance can lead to a huge change in resistance.
We present a scheme to extend the halo mass resolution of N-body simulations of the hierarchical clustering of dark matter. The method uses the density field of the simulation to predict the number of sub-resolution dark matter haloes expected in different regions. The technique requires as input the abundance of haloes of a given mass and their average clustering, as expressed through the linear and higher order bias factors. These quantities can be computed analytically or, more accurately, derived from a higher resolution simulation as done here. Our method can recover the abundance and clustering in real- and redshift-space of haloes with mass below $\sim 7.5 \times 10^{13}h^{-1}M_{\odot}$ at $z=0$ to better than 10%. We demonstrate the technique by applying it to an ensemble of 50 low resolution, large-volume $N$-body simulations to compute the correlation function and covariance matrix of luminous red galaxies (LRGs). The limited resolution of the original simulations results in them resolving just two thirds of the LRG population. We extend the resolution of the simulations by a factor of 30 in halo mass in order to recover all LRGs. With existing simulations it is possible to generate a halo catalogue equivalent to that which would be obtained from a $N$-body simulation using more than 20 trillion particles; a direct simulation of this size is likely to remain unachievable for many years. Using our method it is now feasible to build the large numbers of high-resolution large volume mock galaxy catalogues required to compute the covariance matrices necessary to analyse upcoming galaxy surveys designed to probe dark energy.
One of the key requirements for good thermoelectric materials is a low lattice thermal conductivity. Here we present a combined neutron scattering and theoretical investigation of the lattice dynamics in the type I clathrate system Ba-Ge-Ni, which fulfills this requirement. We observe a strong hybridization between phonons of the Ba guest atoms and acoustic phonons of the Ge-Ni host structure over a wide region of the Brillouin zone which is in contrast with the frequently adopted picture of isolated Ba atoms in Ge-Ni host cages. It occurs without a strong decrease of the acoustic phonon lifetime which contradicts the usual assumption of strong anharmonic phonon--phonon scattering processes. Within the framework of ab-intio density functional theory calculations we interpret these hybridizations as a series of an ti-crossings which act as a low pass filter, preventing the propagation of acoustic phonons. To highlight the effect of such a phononic low pass filter on the thermal transport, we compute the contribution of acoustic phonons to the thermal conductivity of Ba$_8$Ge$_{40}$Ni$_{6}$ and compare it to those of pure Ge and a Ge$_{46}$ empty-cage model system.
We discuss the problem of gauge fixing for the partition function in generalized quantum (or trace) dynamics, deriving analogs of the De Witt-Faddeev-Popov procedure and of the BRST invariance familiar in the functional integral context.
We consider off-diagonal correlation functions of impenetrable bosons on a lattice. By using the Jordan-Wigner transformation the one-body density matrix is represented as (Toeplitz) determinant of a matrix of fermionic Green functions. Using the replica method we calculate exactly the full long-range asymptotic behaviour of the one-body density matrix. We discuss how subleading oscillating terms, originating from short-range correlations give rise to interesting features in the momentum distribution.
The effects of fluctuating initial conditions are studied in the context of relativistic heavy ion collisions where a rapidly evolving system is formed. Two particle correlation analysis is applied to events generated with the NEXSPHERIO hydrodynamic code, starting with fluctuating non-smooth initial conditions (IC). Results show that the non-smoothness in the IC survives the hydro-evolution and can be seen as topological features of the angular correlation function of the particles emerging from the evolving system. A long range correlation is observed in the longitudinal direction and in the azimuthal direction a double peak structure is observed in the opposite direction to the trigger particle. This analysis provides clear evidence that these are signatures of the combined effect of tubular structures present in the IC and the proceeding collective dynamics of the hot and dense medium.
A formalism to evaluate the resonant states produced by two particles moving outside a closed shell core is presented. The two particle states are calculated by using a single particle representation consisting of bound states, Gamow resonances and scattering states in the complex energy plane (Berggren representation). Two representative cases are analysed corresponding to whether the Fermi level is below or above the continuum threshold. It is found that long lived two-body states (including bound states) are mostly determined by either bound single-particle states or by narrow Gamow resonances. However, they can be significantly affected by the continuum part of the spectrum.
We study the evolution of Milky Way thick and thin discs in the light of the most recent observational data. In particular, we analyze abundance gradients of O, N, Fe and Mg along the thin disc as well as the [Mg/Fe] vs. [Fe/H] relations and the metallicity distribution functions at different Galactocentric distances. We run several models starting from the two-infall paradigm, assuming that the thick and thin discs formed by means of two different infall episodes, and we explore several physical parameters, such as radial gas flows, variable efficiency of star formation, different times for the maximum infall onto the disc, different distributions of the total surface mass density of the thick disc and enriched gas infall. Our best model suggests that radial gas flows and variable efficiency of star formation should be acting together with the inside-out mechanism for the thin disc formation. The timescale for maximum infall onto the thin disc, which determines the gap between the formation of the two discs, should be $t_{max}\simeq 3.25$ Gyr. The thick disc should have an exponential, small scale length density profile and gas infall on the inner thin disc should be enriched. We compute also the evolution of Gaia-Enceladus system and study the effects of possible interactions with the thick and thin discs. We conclude that the gas lost by Enceladus or even part of it could have been responsible for the formation of the thick disc but not the thin disc.