ShantanuT01/DACTYL-Pretraining huggingface dataset:
Characterizing the glass state remains elusive since its distinction from a liquid state is not obvious. Glasses are liquids whose viscosity has increased so much that they cannot flow. Accordingly there have been many attempts to define a static length-scale associated with the dramatic slowing down of supercooled liquid with decreasing temperature. Here we present a simple method to extract the desired length-scale which is highly accessible both for experiments and for numerical simulations. The fundamental idea is that low lying vibrational frequencies come in two types, those related to elastic response and those determined by plastic instabilities. The minimal observed frequency is determined by one or the other, crossing at a typical length-scale which is growing with the approach of the glass transition. This length-scale characterizes the correlated disorder in the system, where on longer length-scales the details of the disorder become irrelevant, dominated by the Debye model of elastic modes.
The initial value problem for the homogeneous Schr\"odinger equation is investigated for radially symmetric initial data with slow decay rates and not too wild oscillations. Our global wellposedness results apply to initial data for which Strichartz estimates fail.
In a recent preprint, Hearin et al. (2012,H12) suggest that the halo mass-richness calibration of clusters can be improved by using the difference in the magnitude of the brightest and the second brightest galaxy (magnitude gap) as an additional observable. They claim that their results are at odds with the results from Paranjape & Sheth (2012, PS12) who show that the magnitude distribution of the brightest and second brightest galaxies can be explained based on order statistics of luminosities randomly sampled from the total galaxy luminosity function. We find that a conditional luminosity function (CLF) for galaxies which varies with halo mass, in a manner which is consistent with existing observations, naturally leads to a magnitude gap distribution which changes as a function of halo mass at fixed richness, in qualitative agreement with H12. We show that, in general, the luminosity distribution of the brightest and the second brightest galaxy depends upon whether the luminosities of galaxies are drawn from the CLF or the global luminosity function. However, we also show that the difference between the two cases is small enough to evade detection in the small sample investigated by PS12. This shows that the luminosity distribution is not the appropriate statistic to distinguish between the two cases, given the small sample size. We argue in favor of the CLF (and therefore H12) based upon its consistency with other independent observations, such as the kinematics of satellite galaxies, the abundance and clustering of galaxies, and the galaxy-galaxy lensing signal from the Sloan Digital Sky Survey.
The limits of scaled relative entropies between probability distributions associated with N-particle weakly interacting Markov processes are considered. The convergence of such scaled relative entropies is established in various settings. The analysis is motivated by the role relative entropy plays as a Lyapunov function for the (linear) Kolmogorov forward equation associated with an ergodic Markov process, and Lyapunov function properties of these scaling limits with respect to nonlinear finite-state Markov processes are studied in the companion paper [6].
In this short paper, periodic homogenization of a steady heat flow in two-component media with highly adhesive contact is performed via the two-scale convergence technique. Our micro-model is based on mass conservation for the heat flow in each phase with interfacial contact of adhesive type between these constituents. It is shown that the macroscopic model is a single phase elliptic equation.
We construct, in D=3,4,6 and 10 space-time dimensions, supersymmetric Lagrangians for free massless higher spin fields which belong to reducible representations of the Poincare group.The fermionic part of these models consists of spinor-tensor fields which are totally symmetrical with respect to their tensor indices, while the bosonic part contains totally symmetric tensor fields as well as the simplest mixed-symmetry fields. A peculiar feature of these models is that they describe higher- and lower-spin supermultiplets in different dimensions in a uniform way.
A century after its conception, quantum mechanics still hold surprises that contradict many "common sense" notions. The contradiction is especially sharp in case one consider trajectories of truly quantum objects such as single photons. From a classical point of view, trajectories are well defined for particles, but not for waves. The wave-particle duality forces a breakdown of this dichotomy and quantum mechanics resolves this in a remarkable way: Trajectories can be well defined, but they are utterly different from classical trajectories. Here, we give an operational definition to the trajectory of a single photon by introducing a novel technique to mark its path using its spectral composition. The method demonstrates that the frequency degree of freedom can be used as a bona fide quantum measurement device (meter). The analysis of a number of setups, using our operational definition, leads to anomalous trajectories which are non-continuous and in some cases do not even connect the source of the photon to where it is detected. We carried out an experimental demonstration of these anomalous trajectories using a nested interferometer. We show that the Two-state vector formalism provides a simple explanation for the results.
We report a simultaneous ground and space-based photometric study of the Beta Cephei star Nu Eridani. Half a year of observations have been obtained by four of the five satellites constituting BRITE-Constellation, supplemented with ground-based photoelectric photometry. We show that carefully combining the two data sets virtually eliminates the aliasing problem that often hampers time-series analyses. We detect 40 periodic signals intrinsic to the star in the light curves. Despite a lower detection limit we do not recover all the pressure and mixed modes previously reported in the literature, but we newly detect six additional gravity modes. This behaviour is a consequence of temporal changes in the pulsation amplitudes that we also detected for some of the p modes. We point out that the dependence of theoretically predicted pulsation amplitude on wavelength is steeper in visual passbands than those observationally measured, to the extent that the three dominant pulsation modes of Nu Eridani would be incorrectly identified using data in optical filters only. We discuss possible reasons for this discrepancy.
Multi-particle form factors of local operators in integrable models in two dimensions seem to have the property that they factorize when one subset of the particles in the external states are boosted by a large rapidity with respect to the others. This remarkable property, which goes under the name of form factor clustering, was first observed by Smirnov in the O(3) non-linear sigma-model and has subsequently found useful applications in integrable models without internal symmetry structure. In this paper we conjecture the nature of form factor clustering for the general O(n) sigma-model and make some tests in leading orders of the 1/n expansion and for the special cases n=3,4.
Physical arguments related with the existence of black hole solutions having a non trapping interior are discussed. Massive scalar fields interacting with gravity are considered. Interior asymptotic solutions showing a scalar field approaching a constant value at the horizon are given. It is argued that the coupled Einstein-Klein-Gordon equations can be satisfied in the sense of the generalized functions after removing a particular regularization designed for matching the interior solution with an external Scwartzschild spacetime. The scalar field appears as just avoiding the appearance of closed trapped surfaces while coming from the exterior region. It also follows that the usual space integral over the temporal- temporal components of energy-momnetum tensor in the internal region just gives the total proper mass associated to the external Schwartzschild solution, as it should be expected.
Photometric observations of HD~217522 in 1981 revealed only one pulsation frequency $\nu_1=1.21529$~mHz. Subsequent observations in 1989 showed the presence of an additional frequency $\nu_2=2.0174$~mHz. New observations in 2008 confirm the presence of the mode with $\nu_2=2.0174$~mHz. Examination of the 1989 data shows amplitude modulation over a time scale of the order of a day, much shorter than what has been observed in other roAp stars. High spectral and time resolution data obtained using the VLT in 2008 confirm the presence of $\nu_2$ and short term modulations in the radial velocity amplitudes of rare earth elements. This suggests growth and decay times shorter than a day, more typical of solar-like oscillations. The driving mechanism of roAp stars and the Sun are different, and the growth and decay seen in the Sun are due to stochastic nature of the driving mechanism. The driving mechanism in roAp stars usually leads to mode stability on a longer time-scale than in the Sun. We interpret the reported change in $\nu_1$ between the 1982 and 1989 data as part of the general frequency variability observed in this star on many time scales.
We review the theory of vortices in trapped dilute Bose-Einstein condensates and compare theoretical predictions with existing experiments. Mean-field theory based on the time-dependent Gross-Pitaevskii equation describes the main features of the vortex states, and its predictions agree well with available experimental results. We discuss various properties of a single vortex, including its structure, energy, dynamics, normal modes and stability, as well as vortex arrays. When the nonuniform condensate contains a vortex, the excitation spectrum includes unstable (``anomalous'') mode(s) with negative frequency. Trap rotation shifts the normal-mode frequencies and can stabilize the vortex. We consider the effect of thermal quasiparticles on vortex normal modes as well as possible mechanisms for vortex dissipation. Vortex states in mixtures and spinor condensates are also discussed.
Period analysis of CCD photometry of V1493 Aql (Nova Aql 1999 no. 1) performed during 12 nights through I and R filters a few weeks after maximum is presented. The PDM method for period analysis (Stellingwerf 1978) is used. The photometric data is modulated with a period of 0.156 +- 0.001 d. Following the sinusoidal shape of the phased light curve, we interpret this periodicity as possibly orbital in nature which is consistent with a cataclysmic variable above the period gap.
There exists a variety of coloring problems for plane graphs, involving vertices, edges, and faces in all possible combinations. For instance, in the \emph{entire coloring} of a plane graph we are to color these three sets so that any pair of adjacent or incident elements get different colors. We study here some problems of this type from algebraic perspective, focusing on the \emph{facial} variant. We obtain several results concerning the \emph{Alon-Tarsi number} of various graphs derived from plane embeddings. This allows for extensions of some previous results for \emph{choosability} of these graphs to the game theoretic variant, know as \emph{paintability}. For instance, we prove that every plane graph is facially entirely \emph{$8$-paintable}, which means (metaphorically) that even a color-blind person can facially color the entire graph form lists of size $8$.
Observations of CO+ suggest column densities on the order 10^12 cm^-2 that can not be reproduced by many chemical models. CO+ is more likely to be destroyed than excited in collisions with hydrogen. An anomalous excitation mechanism may thus have to be considered when interpreting CO^+ observations. Chemical models are used to perform a parameter study of CO^+ abundances. Line fluxes are calculated for N(CO+)=10^12 cm^-2 and different gas densities and temperatures using a non-LTE escape probability method. The chemical formation and destruction rates are considered explicitly in the detailed balance equations of the radiative transfer. In addition, the rotational levels of CO+ are assumed to be excited upon chemical formation according to a formation temperature. It is found, that chemical models are generally able to produce high fractional CO+ abundances (x(CO+) =10^-10). In a far-ultraviolet (FUV) dominated environment, however, high abundances of CO+ are only produced in regions with a Habing field G0 > 100 and T(kin) > 600 K, posing a strong constraint on the gas temperature. For gas densities >10^6 cm^-3 and temperatures > 600 K, the combination of chemical and radiative transfer analysis shows little effect on intensities of CO+ lines with upper levels N_up <= 3. Significantly different line fluxes are calculated with an anomalous excitation mechanism, however, for transitions with higher upper levels and densities >10^6 cm ^ -3. The Herschel Space Observatory is able to reveal such effects in the terahertz wavelength regime. Ideal objects to observe are protoplanetary disks with densities 10^6 cm^-3. It is finally suggested that the CO+ chemistry may be well understood and that the abundances observed so far can be explained with a high enough gas temperature and a proper geometry.
We have examined theoretically the spontaneous thinning process of tip-suspended nanowires, and subsequently studied the structure and stability of the monatomic gold wires recently observed by Transmission Electron Microscopy (TEM). The methods used include thermodynamics, classical many-body force simulations, Local Density (LDA) and Generalized Gradient (GGA) electronic structure calculations as well as ab-initio simulations including the two tips. The wire thinning is well explained in terms of a thermodynamic tip suction driving migration of surface atoms from the wire to the tips. For the same reason the monatomic wire becomes progressively stretched. Surprisingly, however, all calculations so far indicate that the stretched monatomic gold wire should be unstable against breaking, contrary to the apparent experimental stability. The possible reasons for the observed stability are discussed.
With the development of the Generative Adversarial Networks (GANs) and DeepFakes, AI-synthesized images are now of such high quality that humans can hardly distinguish them from real images. It is imperative for media forensics to develop detectors to expose them accurately. Existing detection methods have shown high performance in generated images detection, but they tend to generalize poorly in the real-world scenarios, where the synthetic images are usually generated with unseen models using unknown source data. In this work, we emphasize the importance of combining information from the whole image and informative patches in improving the generalization ability of AI-synthesized image detection. Specifically, we design a two-branch model to combine global spatial information from the whole image and local informative features from multiple patches selected by a novel patch selection module. Multi-head attention mechanism is further utilized to fuse the global and local features. We collect a highly diverse dataset synthesized by 19 models with various objects and resolutions to evaluate our model. Experimental results demonstrate the high accuracy and good generalization ability of our method in detecting generated images. Our code is available at https://github.com/littlejuyan/FusingGlobalandLocal.
Pure quantum spin-$s$ states can be represented by $2s$ points on the sphere, as shown by Majorana in 1932 --- the description has proven particularly useful in the study of rotational symmetries of the states, and a host of other properties, as the points rotate rigidly on the sphere when the state undergoes an $SU(2)$ transformation in Hilbert space. At the same time, the Wilzcek-Zee effect, which involves the cyclic evolution of a degenerate $k$-dimensional linear subspace of the Hilbert space, and the associated holonomy dictated by Schroedinger's equation, have been proposed as a fault-tolerant mechanism for the implementation of logical gates, with applications in quantum computing. We show, in this paper, how to characterize such subspaces by Majorana-like sets of points on the sphere, that also rotate rigidly under $SU(2)$ transformations --- the construction is actually valid for arbitrary totally antisymmetric $k$-partite qudit states.
I provide a brief, and therefore necessarily biased, review of the application of effective field theory to electromagnetic processes on the deuteron. Electron-deuteron scattering is discussed for virtual photon momenta up to 700 MeV, and photon-deuteron scattering is examined for incident photon energies of order the pion mass.
The task of image captioning implicitly involves gender identification. However, due to the gender bias in data, gender identification by an image captioning model suffers. Also, the gender-activity bias, owing to the word-by-word prediction, influences other words in the caption prediction, resulting in the well-known problem of label bias. In this work, we investigate gender bias in the COCO captioning dataset and show that it engenders not only from the statistical distribution of genders with contexts but also from the flawed annotation by the human annotators. We look at the issues created by this bias in the trained models. We propose a technique to get rid of the bias by splitting the task into 2 subtasks: gender-neutral image captioning and gender classification. By this decoupling, the gender-context influence can be eradicated. We train the gender-neutral image captioning model, which gives comparable results to a gendered model even when evaluating against a dataset that possesses a similar bias as the training data. Interestingly, the predictions by this model on images with no humans, are also visibly different from the one trained on gendered captions. We train gender classifiers using the available bounding box and mask-based annotations for the person in the image. This allows us to get rid of the context and focus on the person to predict the gender. By substituting the genders into the gender-neutral captions, we get the final gendered predictions. Our predictions achieve similar performance to a model trained with gender, and at the same time are devoid of gender bias. Finally, our main result is that on an anti-stereotypical dataset, our model outperforms a popular image captioning model which is trained with gender.
We theoretically study the orbital magnetic susceptibility produced by electron states near a crossing point of two band-contact lines in a crystal. It is shown that this susceptibility can have an unusual dependence on the Fermi level and can change noticeably with the temperature when the Fermi level is in the vicinity of the crossing point. These features of the magnetic susceptibility can be useful in detecting the crossing points in crystal. The obtained results explain the well-known temperature dependence of the magnetic susceptibility of V$_3$Si.
In many dynamical systems in nature, the law of the dynamics changes along with the temporal evolution of the system. These changes are often associated with the occurrence of certain events. The timing of occurrence of these events depends, in turn, on the trajectory of the dynamical system itself, making the dynamics of the system and the timing of a change in the dynamics strongly coupled. Naturally, trajectories that take longer to satisfy the event will last longer. Therefore, we expect to observe more frequently the dominant dynamics, the ones that take longer to change in the long run. This article proposes a Markov chain model, called Self-Switching Markov Chain (SSMC), in which the emergence of dominant dynamics can be rigorously addressed. We present conditions and scaling in the SSMC under which we observe with probability one only the subset of dominant dynamics, and we characterize these dominant dynamics. Furthermore, we show that the switching between dynamics exhibits metastability-like property.
The Fe-Cu intersite charge transfer and Fe charge disproportionation are interesting phenomena observed in some LnCu3Fe4O12 (Ln: Lanthanides) compounds containing light and heavy Ln atoms, respectively. We show that a change in the spin state is responsible for the intersite charge transfer in the light Ln compounds. At the high spin state, such systems prefer an unusual Cu-d^8 configuration, whereas at the low spin state they retreat to the normal Cu-d^9 configuration through a charge transfer from Fe to Cu-3d_{xy} orbital. We find that the strength of the crystal field splitting and the relative energy ordering between Cu-3d_{xy} and Fe-3d states are the key parameters, determining the intersite charge transfer (charge disproportionation) in light (heavy) Ln compounds. It is further proposed that the size of Ln affects the onsite interaction strength of Cu-3d states, leading to a strong modification of the Cu-L_3 edge spectrum, as observed by the X-ray absorption spectroscopy.
We prove that there exists a pencil of Enriques surfaces defined over $\mathbb{Q}$ with non-algebraic integral Hodge classes of non-torsion type. This gives the first example of a threefold with the trivial Chow group of zero-cycles on which the integral Hodge conjecture fails. As an application, we construct a fourfold which gives the negative answer to a classical question of Murre on the universality of the Abel-Jacobi maps in codimension three.
We show how the interface curvature autocorrelation function (ICAF) and associated structure factor (ICSF), of relevance in non-equilibrium pattern-formation problems where sharp interfaces are present, provide new and interesting information on domain structure, as yet not visible via the order-parameter structure factor (OPSF). This is done by discussing numerical simulations of model A (non-conserved relaxational phase-ordering kinetics) in two-dimensional systems. The ICAF is Gaussian over short distances and exhibits dynamical scaling and $t^{1/2}$ power-law growth. We use it to show what the typical length-scale in the model A dynamics corresponds to physically and how it can be obtained uniquely, rather than simply within a multiplicative constant. Experimental methods to measure the ICAF and/or ICSF are still needed at this point.
The paper formulates a precise relationship between the Tate-Shafarevich group of an elliptic curve $E$ over ${\mathbb Q}$ with a quotient of the classgroup of ${\mathbb Q}(E[p])$ on which $Gal({\mathbb Q}(E[p]/{\mathbb Q}) = GL_2({\mathbb Z}/p)$ operates by its standard 2 dimensional representation over ${\mathbb Z}/p$. We establish such a relationship in most cases.
We show the existence of a self-similar solution for a We prove the uniqueness of the self-similar profile solution for a modified Boltzmann equation describing probabilistic ballistic annihilation. Such a model describes a system of hard spheres such that, whenever two particles meet, they either annihilate with probability $\alpha \in (0,1)$ or they undergo an elastic collision with probability $1-\alpha$. The existence of a self-similar profile for $\alpha$ smaller than an explicit threshold value $\underline{\alpha}_1$ has been obtained in our previous contribution (J. Differential Equations, 254, 3023--3080, 2013). . We complement here our analysis of such a model by showing that, for some $\alpha^{\sharp} $ explicit, the self-similar profile is unique for $\alpha \in (0,\alpha^{\sharp})$.