ShantanuT01/DACTYL-Pretraining huggingface dataset:
For a directed graph $G(V_n, E_n)$ on the vertices $V_n = \{1,2, \dots, n\}$, we study the distribution of a Markov chain $\{ {\bf R}^{(k)}: k \geq 0\}$ on $\mathbb{R}^n$ such that the $i$th component of ${\bf R}^{(k)}$, denoted $R_i^{(k)}$, corresponds to the value of the process on vertex $i$ at time $k$. We focus on processes $\{ {\bf R}^{(k)}: k \geq 0\}$ where the value of $R_i^{(k+1)}$ depends only on the values $\{ R_j^{(k)}: j \to i\}$ of its inbound neighbors, and possibly on vertex attributes. We then show that, provided $G(V_n, E_n)$ converges in the local weak sense to a marked Galton-Watson process, the dynamics of the process for a uniformly chosen vertex in $V_n$ can be coupled, for any fixed $k$, to a process $\{ \mathcal{R}_\emptyset^{(r)}: 0 \leq r \leq k\}$ constructed on the limiting marked Galton-Watson tree. Moreover, we derive sufficient conditions under which $\mathcal{R}^{(k)}_\emptyset$ converges, as $k \to \infty$, to a random variable $\mathcal{R}^*$ that can be characterized in terms of the attracting endogenous solution to a branching distributional fixed-point equation. Our framework can also be applied to processes $\{ {\bf R}^{(k)}: k \geq 0\}$ whose only source of randomness comes from the realization of the graph $G(V_n, E_n)$.
Let $X$ be a smooth variety over an algebraically closed field of positive characteristic. An $F$-sandwich of $X$ is a normal variety $Y$ through which the relative Frobenius morphism of $X$ factors as $F:X\rightarrow Y \rightarrow X$. In this paper, we give a classification of globally F-regular $F$-sandwiches of Hirzebruch surfaces.
The growing popularity of remote fitness has increased the demand for highly accurate computer vision models that track human poses. However, the best methods still fail in many real-world fitness scenarios, suggesting that there is a domain gap between current datasets and real-world fitness data. To enable the field to address fitness-specific vision problems, we created InfiniteForm, an open-source synthetic dataset of 60k images with diverse fitness poses (15 categories), both single- and multi-person scenes, and realistic variation in lighting, camera angles, and occlusions. As a synthetic dataset, InfiniteForm offers minimal bias in body shape and skin tone, and provides pixel-perfect labels for standard annotations like 2D keypoints, as well as those that are difficult or impossible for humans to produce like depth and occlusion. In addition, we introduce a novel generative procedure for creating diverse synthetic poses from predefined exercise categories. This generative process can be extended to any application where pose diversity is needed to train robust computer vision models.
We theoretically study the electrical conductivity in a one-dimensional helimagnet whose spin texture changes from helimagnetic to conical magnetic, and to forced ferromagnetic state while increasing the magnetic field along the helical axis. We find that the conductivity in the helimagnetic state at zero field depends on the electron filling and the coefficient of the spin-charge coupling. We also find that the conductivity in the conical magnetic state changes nonlinearly to the applied field, and the magnetoresistance becomes negative and positive depending on the model parameters.
We analyzed available observational data of a sample of dark matter (DM) dominated galaxies and clusters of galaxies and we have found correlations between the virial mass, $M_{vir}$, of halos and basic parameters of their cores, namely, the mean DM density, pressure and entropy. These correlations are a natural consequence of similar evolution of all such objects. It is driven mainly by gravitational interactions what implies a high degree of self similarity of both the process of halos formation and their internal structure.   We confirmed the CDM--like shape of both the small and large scale power spectrum. However, our reconstruction of the evolutionary history of observed objects requires either a multicomponent composition of DM or a more complex primordial power spectrum of density perturbations with significant excess of power at scales of clusters of galaxies and larger. We demonstrated that a model with suitable combination of the heavy DM particles (CDM) and DM particles with large damping scale (HDM) could provide a successful description of the observational data in a wide range of masses.
Recently the use of video surveillance systems is widely increasing. Different places are equipped by camera surveillances such as hospitals, schools, airports, museums and military places in order to ensure the safety and security of the persons and their property. Therefore it becomes significant to guarantee the proper working of these systems. Intelligent video surveillance systems equipped by sophisticated digital camera can analyze video information s and automatically detect doubtful actions. The camera tampering detection algorithms may indicate that accidental or suspicious activities have occurred and that causes the abnormality works of the video surveillance.   Camera Tampering Detection uses several techniques based on image processing and computer vision. In this paper, comparative study of performance of three algorithms that can detect abnormal disturbance for video surveillance is presented.
The possibility for occurrence of a Bose condensate of dibaryons in nuclear matter is investigated within the framework of the Walecka model in the mean-field approximation. Constraints for the omega - and sigma - meson coupling constants with dibaryons following from the requirement of stability of dibaryon matter against compression are derived and the effect of sigma - and pi - meson exchange current contributions to the sigma - dibaryon coupling constant is discussed. The mean-field solutions of the model are constructed. The effective nucleon mass vanishes when the density of dibaryons approaches a critical value about 0.15/fm^3. The Green's functions of the equilibrium binary mixture of nucleons and dibaryons are constructed by solving the Gorkov-Dyson system of equations in the no-loop approximation. We find that when the square of the sound velocity is positive, the dispersion laws for all elementary excitations of the system are real functions. This indicates stability of the ground state of the heterophase nucleon-dibaryon mixture. In the model considered, production of dibaryons becomes energetically favorable at higher densities as compared to estimates based on a model of non-interacting nucleons and dibaryons.
We measure the anomalous Hall effect (AHE) resistivity $\rho_{xy}$ in thin films of the itinerant ferromagnet SrRuO$_{3}$. At low temperatures, the AHE coefficient $R_{s}$ varies with $\rho_{xx}^2$, and at higher temperatures, $R_{s}$ reaches a peak and then changes sign just below $T_{c}$. We find that for all films studied $R_{s}$ scales with resistivity in the entire ferromagnetic phase. We attribute the observed behavior to the contribution of the extrinsic side jumps mechanism and the intrinsic Karplus-Luttinger (Berry phase) mechanism including the effect of finite scattering rates.
Using simulation methods, distortion effects on energy spectra caused by errors in the energy determination have been investigated. For cosmic ray proton spectra, falling steeply with kinetic energy E as E-2.7, significant effects appear. When magnetic spectrometers are used to determine the energy, the relative error increases linearly with the energy and distortions with a sinusoidal form appear starting at an energy that depends significantly on the error distribution but at an energy lower than that corresponding to the Maximum Detectable Rigidity of the spectrometer. The effect should be taken into consideration when comparing data from different experiments, often having different error distributions.
For a random walk on the integer lattice $\mathbb{Z}$ that is attracted to a strictly stable process with index $\alpha\in (1, 2)$ we obtain the asymptotic form of the transition probability for the walk killed when it hits a finite set. The asymptotic forms obtained are valid uniformly in a natural range of the space and time variables. The situation is relatively simple when the limit stable process has jumps in both positive and negative directions; in the other case when the jumps are one sided rather interesting matters are involved and detailed analyses are necessitated.
Recent analysis of both new (1998) and old (1995,1996) data obtained by the NA50 Collaboration on J/Psi suppression in Pb+Pb are examined in light of our already existing calculations with the relativistic heavy ion simulation LUCIFER. In particular we comment on the unexplained change of transverse energy scale by NA50 and the apparent disappearance from the data of discontinuities in the suppression with transverse energy.
In the absence of low-energy supersymmetry, a multiplicity of weak-scale Higgs doublets would require additional fine-tunings unless they formed an irreducible multiplet of a non-abelian symmetry. Remnants of such symmetry typically render some Higgs fields stable, giving several dark matter particles of various masses. The non-abelian symmetry also typically gives simple, testable mass relations.
Images of morphed faces pose a serious threat to face recognition--based security systems, as they can be used to illegally verify the identity of multiple people with a single morphed image. Modern detection algorithms learn to identify such morphing attacks using authentic images of real individuals. This approach raises various privacy concerns and limits the amount of publicly available training data. In this paper, we explore the efficacy of detection algorithms that are trained only on faces of non--existing people and their respective morphs. To this end, two dedicated algorithms are trained with synthetic data and then evaluated on three real-world datasets, i.e.: FRLL-Morphs, FERET-Morphs and FRGC-Morphs. Our results show that synthetic facial images can be successfully employed for the training process of the detection algorithms and generalize well to real-world scenarios.
In this paper we study semi-stable, radially symmetric and decreasing solutions $u\in W^{1,p}(B_1)$ of $-\Delta_p u=g(u)$ in $B_1\setminus\{0\}$, where $B_1$ is the unit ball of $\mathbb{R}^N$, $p>1$, $\Delta_p$ is the $p-$Laplace operator and $g$ is a general locally Lipschitz function. We establish sharp pointwise estimates for such solutions. As an application of these results, we obtain optimal pointwise estimates for the extremal solution and its derivatives (up to order three) of the equation $-\Delta_p u=\lambda f(u)$, posed in $B_1$, with Dirichlet data $u|_{\partial B_1}=0$, where the nonlinearity $f$ is an increasing $C^1$ function with $f(0)>0$ and $\lim_{t\rightarrow+\infty}{\frac{f(t)}{t^{p-1}}}=+\infty.$   In addition, we provide, for $N\geq p+4p/(p-1)$, a large family of semi-stable radially symmetric and decreasing unbounded $W^{1,p}(B_1)$ solutions.
This paper reports the Suzaku results on the northeast shell of RCW 86. With the spatial and spectral analysis, we separated the X-rays into three distinct components; low (kT_e~0.3keV) and high (kT_e~1.8keV) temperature plasmas and a non-thermal component, and discovered their spatial distributions are different from each other. The low temperature plasma is dominated at the east rim, whereas the non-thermal emission is the brightest at the northeast rim which is spatially connected from the east rim. The high temperature plasma, found to contain the ~6.42keV line (K alpha of low-ionized iron), is enhanced at the inward region with respect to the east rim and has no spatial correlation with the non-thermal X-ray (the northeast). The Fe-Kalpha line, therefore, is not related to the non-thermal emission but originates from Fe-rich ejecta heated to the high temperatures by the reverse shock. Since the metal abundances of the low temperature plasma are sub-solar, the most possible origin of this component is interstellar medium heated by a blast wave. The non-thermal X-ray, which has a power-law index of ~2.8, is likely to be synchrotron emission. A possible scenario to explain these morphologies and spectra is: A fast moving blast wave in a thin cavity of OB association collided with a dense interstellar medium or cloud at the east region very recently. As the result, the reverse shock in this interior decelerated, and arrived at the Fe-rich region of the ejecta and heated it. In the northeast rim, on the other hand, the blast wave is still moving fast, and accelerated high energy electrons to emit synchrotron X-rays.
The formation of regular patterns is a common feature of many solidification processes involving cast materials. We describe here how regular patterns can be obtained in porous alumina by controlling the freezing of ceramic slurries followed by subsequent ice sublimation and sintering, leading to multilayered porous alumina structures with homogeneous and well-defined architecture. We discuss the relationships between the experimental results, the physics of ice and the interaction between inert particles and the solidification front during directional freezing. The anisotropic interface kinetics of ice leads to numerous specific morphologies features in the structure. The structures obtained here could have numerous applications including ceramic filters, biomaterials, and could be the basis for dense multilayered composites after infiltration with a selected second phase.
We have synthesized single-layer graphene on Cu foils using chemical vapor deposition method and transferred the graphene to the top of a Si/SiO2 substrate with a pair of prefabricated Ti/Au electrodes. A resistive graphene-based gas sensor prepared in this way revealed n-type oxygen response at room temperature and we have successfully fitted the data obtained with varying oxygen levels using a two-site Langmuir model. P-type oxygen response of our sensor was observed after the temperature was raised to 100 oC, with a reversible transition to n-type behaviour when the temperature was lowered back to room temperature. Such inversion of the gas response type with temperature was interpreted as a result of interplay between the adsorbate-induced charge transfer and charge carrier scattering. The transduction function was derived, which relates the electrical response to surface coverage through both the induced mobility and charge density changes.
We investigate the potential of the galaxy power spectrum to constrain compensated isocurvature perturbations (CIPs), primordial fluctuations in the baryon density that are compensated by fluctuations in CDM density to ensure an unperturbed total matter density. We show that CIPs contribute to the galaxy overdensity at linear order, and if they are close to scale-invariant, their effects are nearly perfectly degenerate with the local PNG parameter $f_{\rm nl}$ if they correlate with the adiabatic perturbations. This degeneracy can however be broken by analyzing multiple galaxy samples with different bias parameters, or by taking CMB priors on $f_{\rm nl}$ into account. Parametrizing the amplitude of the CIP power spectrum as $P_{\sigma\sigma} = A^2P_{\mathcal{R}\mathcal{R}}$ (where $P_{\mathcal{R}\mathcal{R}}$ is the adiabatic power spectrum) we find, for a number of fiducial galaxy samples in a simplified forecast setup, that constraints on $A$, relative to those on $f_{\rm nl}$, of order $\sigma_{A}/\sigma_{f_{\rm nl}} \approx 1-2$ are achievable for CIPs correlated with adiabatic perturbations, and $\sigma_{A}/\sigma_{f_{\rm nl}} \approx 5$ for the uncorrelated case. These values are independent of survey volume, and suggest that current galaxy data are already able to improve significantly on the tightest existing constraints on CIPs from the CMB. Future galaxy surveys that aim to achieve $\sigma_{f_{\rm nl}} \sim 1$ have the potential to place even stronger bounds on CIPs.
The strengthened data processing inequality have been proved. The general theory have been illustrated on the simple example.
We used neutron powder diffraction to obtain the local and long-range structure of La0.5Ca0.5MnO3 at room temperature and 20K. By combining Rietveld and pair distribution function analysis of the total neutron scattering data, we have analyzed the structure of the compound using two competing models describing the low temperature phase: first the charge ordered/orbital ordered model and second the Mn-Mn dimer model. These structural models fit the 20K neutron powder diffraction pattern equally well using Rietveld analysis. Therefore, pair distribution function analysis is used to probe the local and medium-range structure revealing a system with two distinctly distorted Mn octahedra and Mn ions with non-integral valence states. The distorted octahedra differ with the structural model for the Zener polaron type Mn-Mn dimer picture proposed for Pr0.6Ca0.4MnO3 and order in a similar checkerboard configuration associated with the CE-type anti-ferromagnetic structure. Therefore, locally the charge difference and structural ordering between the two Mn is appreciable enough to describe the system at 20K as "partially charge ordered".
We study I-V characteristics of an all-II-VI semiconductor resonant tunneling diode with dilute magnetic impurities in the quantum well layer. Bound magnetic polaron states form in the vicinity of potential fluctuations at the well interface while tunneling electrons traverse these interface quantum dots. The resulting microscopic magnetic order lifts the degeneracy of the resonant tunneling states. Although there is no macroscopic magnetization, the resulting resonant tunneling current is highly spin polarized at zero magnetic field due to the zero field splitting. Detailed modeling demonstrates that the local spin polarization efficiency exceeds 90% without an external magnetic field.
We have studied various classical solutions in $R^2$ cosmology. Especially we have obtained general classical solutions in pure $R^2$\ cosmology. Even in the quantum theory, we can solve the Wheeler-DeWitt equation in pure $R^2$\ cosmology exactly. Comparing these classical and quantum solutions in $R^2$\ cosmology, we have studied the problem of time in general relativity.
With AKARI, we obtain the spatially-resolved near-infrared (2.5 - 5.0 um) spectra for the nearby starburst galaxy M82. These spectra clearly show the absorption features due to interstellar ices. Based on the spectra, we created the column density maps of H_2O and CO_2 ices. As a result, we find that the spatial distribution of H_2O ice is significantly different from that of CO_2 ice; H_2O ice is widely distributed, while CO_2 ice is concentrated near the galactic center. Our result for the first time reveals variations in CO_2/H_2O ice abundance ratio on a galactic scale, suggesting that the ice-forming interstellar environment changes within a galaxy. We discuss the cause of the spatial variations in the ice abundance ratio, utilizing spectral information on the hydrogen recombination Br{\alpha} and Br{\beta} lines and the polycyclic aromatic hydrocarbon 3.3 um emission appearing in the AKARI near-infrared spectra.
In this paper, we show that if $X$ is a smooth variety of general type of dimension $m \geq 2$, for which its canonical map induces a double cover onto $Y$, where $Y$ is a projective bundle over $\mathbf P^1$, or onto a projective space or onto a quadric hypersurface, embedded by a complete linear series, then the general deformation of the canonical morphism of $X$ again is canonical and again induces a double cover. The second part of the article deals with the existence or non existence of canonical double structures on rational varieties. The negative result in this article has consequences for the moduli of varieties of general type of arbitrary dimension. The results here show that there is an entire component, that is hyperelliptic in infinitely many moduli spaces of higher dimensional varieties of general type. This is in sharp contrast with the case of curves or surfaces of lower Kodaira dimensions.
Several previous works have investigated the circumstances under which quantum adiabatic optimization algorithms can tunnel out of local energy minima that trap simulated annealing or other classical local search algorithms. Here we investigate the even more basic question of whether adiabatic optimization algorithms always succeed in polynomial time for trivial optimization problems in which there are no local energy minima other than the global minimum. Surprisingly, we find a counterexample in which the potential is a single basin on a graph, but the eigenvalue gap is exponentially small as a function of the number of vertices. In this counterexample, the ground state wavefunction consists of two "lobes" separated by a region of exponentially small amplitude. Conversely, we prove if the ground state wavefunction is single-peaked then the eigenvalue gap scales at worst as one over the square of the number of vertices.
We study nonequilibrium dephasing in an electronic Mach-Zehnder interferometer. We demonstrate that the shot noise at the beam splitter of the interferometer generates an ensemble of nonequilibrium electron density configurations and that electron interactions induce configuration-specific phase shifts of an interfering electron. The resulting dephasing exhibits two characteristic features, a lobe pattern in the visibility and phase jumps of $\pi$, in good agreement with experimental data.
We study questions surrounding cup-product maps which arise from pairs of non-degenerate line bundles on an abelian variety. Important to our work is Mumford's index theorem which we use to prove that non-degenerate line bundles exhibit positivity analogous to that of ample line bundles. As an application we determine the asymptotic behaviour of families of cup-product maps and prove that vector bundles associated to these families are asymptotically globally generated. To illustrate our results we provide several examples. For instance, we construct families of cup-product problems which result in a zero map on a one dimensional locus. We also prove that the hypothesis of our results can be satisfied, in all possible instances, by a particular class of simple abelian varieties. Finally, we discuss the extent to which Mumford's theta groups are applicable in our more general setting.
We study the problem of determining the minimum number $f(n,k,d)$ of affine subspaces of codimension $d$ that are required to cover all points of $\mathbb{F}_2^n\setminus \{\vec{0}\}$ at least $k$ times while covering the origin at most $k-1$ times. The case $k=1$ is a classic result of Jamison, which was independently obtained by Brouwer and Schrijver for $d = 1$. The value of $f(n,1,1)$ also follows from a well-known theorem of Alon and F\"uredi about coverings of finite grids in affine spaces over arbitrary fields. Here we determine the value of this function exactly in various ranges of the parameters. In particular, we prove that for $k \ge 2^{n-d-1}$ we have $f(n,k,d)=2^d k - \left \lfloor \frac{k}{2^{n-d}} \right \rfloor$, while for $n > 2^{2^d k-k-d+1}$ we have $f(n,k,d)= n + 2^dk-d-2$, and also study the transition between these two ranges. While previous work in this direction has primarily employed the polynomial method, we prove our results through more direct combinatorial and probabilistic arguments, and also exploit a connection to coding theory.
Using the colored quark cluster model, we study magnetic moments of the octet baryons. We give the values of the magnetic moments of baryons $p$, $n$, $\Sigma^+$, $\Sigma^-$, $\Xi^0$, and $\Xi^-$. The results also show that the orbital motion has very significant effects on the spin and magnetic moments of those baryons and the strange component in the proton is very small.
The present paper is devoted to the construction of small reducible quasi--periodic solutions for the completely resonant NLS equations on a $d$--dimensional torus $\T^d$. The main point is to prove that prove that the normal form is reducible, block diagonal and satisfies the second Melnikov condition block wise. From this we deduce the result by a KAM algorithm.