ShantanuT01/DACTYL-Pretraining huggingface dataset:
Eye movements play a vital role in perceiving the world. Eye gaze can give a direct indication of the users point of attention, which can be useful in improving human-computer interaction. Gaze estimation in a non-intrusive manner can make human-computer interaction more natural. Eye tracking can be used for several applications such as fatigue detection, biometric authentication, disease diagnosis, activity recognition, alertness level estimation, gaze-contingent display, human-computer interaction, etc. Even though eye-tracking technology has been around for many decades, it has not found much use in consumer applications. The main reasons are the high cost of eye tracking hardware and lack of consumer level applications. In this work, we attempt to address these two issues. In the first part of this work, image-based algorithms are developed for gaze tracking which includes a new two-stage iris center localization algorithm. We have developed a new algorithm which works in challenging conditions such as motion blur, glint, and varying illumination levels. A person independent gaze direction classification framework using a convolutional neural network is also developed which eliminates the requirement of user-specific calibration.   In the second part of this work, we have developed two applications which can benefit from eye tracking data. A new framework for biometric identification based on eye movement parameters is developed. A framework for activity recognition, using gaze data from a head-mounted eye tracker is also developed. The information from gaze data, ego-motion, and visual features are integrated to classify the activities.
We study the dynamics of gas and dust in a protoplanetary disk in the presence of embedded planets. We investigate the conditions for dust-gap formation in terms of particle size and planetary mass. We also monitor the amount of dust that is accreted by the planet relative to the amount of gas, which is an important parameter in determining the enrichment of solids in giant planets compared to the solid content of the central star. We use a new two-fluid hydrodynamics code to solve the flow equations for both gas and dust. For the gas, we use a Godunov-type scheme with an approximate Riemann solver (the Roe solver). The dust is treated as a pressureless fluid by essentially the same numerical method as is used for the gas. We find that it only takes a planet of 0.05 Jupiter masses to open up a gap in a disk with a significant population of mm-sized particles. Dust particles larger than 150 micron participate in gap formation. We also find that the formation of the gap severely slows down dust accretion compared to that in the gas. Therefore, it is not possible to enrich a newly formed giant planet in solids, if these solids are contained in particles with sizes from 150 micron to approximately 10 cm.
We study the critical behavior and phase diagram of the $d$-dimensional random field O(N) model by means of the nonperturbative functional renormalization group approach presented in the preceding paper. We show that the dimensional reduction predictions, obtained from conventional perturbation theory, break down below a critical dimension $d_{DR}(N)$ and we provide a description of criticality, ferromagnetic ordering and quasi-long range order in the whole $(N,d)$ plane. Below $d_{DR}(N)$, our formalism gives access to both the typical behavior of the system, controlled by zero-temperature fixed points with a nonanalytic dimensionless effective action, and to the physics of rare low-energy excitations ("droplets"), described at nonzero temperature by the rounding of the nonanalyticity in a thermal boundary layer.
We consider a fractional Schr\"odinger-Poisson system in the whole space $\mathbb R^{N}$ in presence of a positive potential and depending on a small positive parameter $\varepsilon.$ We show that, for suitably small $\varepsilon$ (i.e. in the "semiclassical limit") the number of positive solutions is estimated below by the Ljusternick-Schnirelmann category of the set of minima of the potential.
This paper consists of two halves.   In the first half of the paper, we consider real-valued functions $f$ whose domain is the vertex set of a graph $G$ and that are Lipschitz with respect to the graph distance. By placing a uniform distribution on the vertex set, we treat $f$ as a random variable. We investigate the link between the isoperimetric function of $G$ and the functions $f$ that have maximum variance or meet the bound established by the subgaussian inequality. We present several results describing the extremal functions, and use those results to resolve: (A) a conjecture by Bobkov, Houdr\'e, and Tetali characterizing the extremal functions of the subgaussian inequality of the odd cycle, and (B) a conjecture by Alon, Boppana, and Spencer on the relationship between maximum variance functions and the isoperimetric function of product graphs.   While establishing a discrete analogue of the curved Brunn-Minkowski inequality for the discrete hypercube, Ollivier and Villani suggested several avenues for research. We resolve them in second half of the paper as follows. (1) They propose that a bound on $t$-midpoints can be obtained by repeated application of the bound on midpoints, if the original sets are convex. We construct a specific example where this reasoning fails, and then prove our construction is general by characterizing the convex sets in the discrete hypercube. (2) A second proposed technique to bound $t$-midpoints involves new results in concentration of measure. We follow through on this proposal, with heavy use on results from the first half of the paper. (3) We show that the curvature of the discrete hypercube is not positive or zero.
As a natural extension of the Four Color Theorem, Haj\'{o}s conjectured that graphs containing no $K_5$-subdivision are 4-colorable. Any possible counterexample to this conjecture with minimum number of vertices is called a {\it Haj\'{o}s graph}. Previous results show that Haj\'{o}s graphs are 4-connected but not 5-connected. A $k$-separation in a graph $G$ is a pair $(G_1,G_2)$ of edge-disjoint subgraphs of $G$ such that $|V(G_1\cap G_2)|=k$, $G=G_1\cup G_2$, and $G_i\not\subseteq G_{3-i}$ for $i=1,2$. In this paper, we show that Haj\'{o}s graphs do not admit a 4-separation $(G_1,G_2)$ such that $|V(G_1)|\ge 6$ and $G_1$ can be drawn in the plane with no edge crossings and all vertices in $V(G_1\cap G_2)$ incident with a common face. This is a step in our attempt to reduce Haj\'{o}s' conjecture to the Four Color Theorem.
We quantitatively study the probability distribution function (PDF) of cosmological nonlinear density fluctuations from N-body simulations with Gaussian initial condition. In particular, we examine the validity and limitations of one-point and two-point log-normal PDF models against those directly estimated from the simulations. We find that the one-point log-normal PDF describes very accurately the cosmological density distribution even in the nonlinear regime (the rms variance \sigma_{nl} \simlt 4 and the over-density \delta \simlt 100). Furthermore the two-point log-normal PDFs are also in good agreement with the simulation data from linear to fairly nonlinear regime, while slightly deviate from them for \delta \simlt -0.5. Thus the log-normal PDF can be used as a useful empirical model for the cosmological density fluctuations. While this conclusion is fairly insensitive to the shape of the underlying power spectrum of density fluctuations P(k), models with substantial power on large scales, i.e., n\equiv d\ln P(k)/d \ln k \simlt -1, are better described by the log-normal PDF. On the other hand, we note that the one-to-one mapping of the initial and the evolved density fields consistent with the log-normal model does not approximate the broad distribution of their mutual correlation even on average. Thus the origin of the phenomenological log-normal PDF approximation still remains to be understood.
We review the application of Migdal's "Theory of Finite Fermi System" to the structure of deformed nuclei, approaches beyond the conventional linear response, and microscopic calculations of the Migdal-parameters.
Clusters of galaxies, the largest collapsed structures in the Universe, are located at the intersection of extended filaments of baryons and dark matter. Cosmological accretion onto clusters through large scale filaments adds material at cluster outskirts. Kinetic energy in the form of bulk motions and turbulence due to this accretion provides a form of pressure support against gravity, supplemental to thermal pressure. Significant amount of non-thermal pressure support could bias cluster masses derived assuming hydrostatic equilibrium, the primary proxy for cluster cosmology studies. Sensitive measurements of Doppler broadening and shift of astrophysical lines, and the relative fluctuations in thermodynamical quantities (e.g., density, pressure, and entropy) are primary diagnostic tools. Forthcoming planned and proposed X-ray (with large etendue, throughput, and high spectral resolution) and SZ observatories will provide crucial information on the assembly and virialisation processes of clusters, involving turbulent eddies cascading at various spatial scales and larger gas bulk motions in their external regions to the depth or their potential wells.
Using the recently discovered strong negative dependence properties of the symmetric exclusion process, we derive general conditions for when the normalized current of particles between regions converges to the Gaussian distribution. The main novelty is that the results do not assume any translation invariance, and hold for most initial configurations.
The renormalization of EFT for nucleon-nucleon scattering in nonperturbative regimes is investigated in a compact parametrization of the $T$-matrix. The key difference between perturbative and nonperturbative renormalization is clarified. The underlying theory perspective and the 'fixing' of the prescriptions for the $T$-matrix from physical boundary conditions are stressed.
The weak tensor product was introduced by Snevily as a way to construct new graphs that admit $\alpha$-labelings from a pair of known $\alpha$-graphs. In this article, we show that this product and the application to $\alpha$-labelings can be generalized by considering as a second factor of the product, a family $\Gamma$ of bipartite $(p,q)$-graphs, $p$ and $q$ fixed. The only additional restriction that we should consider is that for every $F\in \Gamma$, there exists and $\alpha$-labeling $f_F$ with $f_F(V(F))=L\cup H$, where $L,H \subset [0,q]$ are the stable sets induced by the characteristic of $f_F$ and they do not depend on $F$. We also obtain analogous applications to near $\alpha$-labelings and bigraceful labelings.
We have found the fluorine lines [F IV] 3996.92A,4059.90A in the extremely metal-poor ([Ar/H] = -2.10+/-0.21) halo planetary nebula (PN) BoBn 1 in high-dispersion spectra from the 8.2-m VLT/UVES archive. Chemical abundance analysis shows that the fluorine abundance is [F/H] = +1.06+/-0.08, making BoBn 1 the most fluorine-enhanced and metal-poor PN among fluorine-detected PNe and providing new evidence that fluorine is enhanced by nucleosynthesis in low mass metal-poor stars. A comparison with the abundances of carbon-enhanced metal-poor (CEMP) stars suggests that BoBn 1 shares their origin and evolution with CEMP-s stars such as HE1305+0132. BoBn 1 might have evolved from a binary consisting of ~2 Msun primary and ~0.8 Msun secondary stars.
We describe a graph reduction operation, generalizing three graph reduction operations related to gene assembly in ciliates. The graph formalization of gene assembly considers three reduction rules, called the positive rule, double rule, and negative rule, each of which removes one or two vertices from a graph. The graph reductions we define consist precisely of all compositions of these rules. We study graph reductions in terms of the adjacency matrix of a graph over the finite field with two elements, and show that they are path invariant, in the sense that the result of a sequence of graph reductions depends only on the vertices removed. The binary rank of a graph is the rank of its adjacency matrix over the finite field with two elements. We show that the binary rank of a graph determines how many times the negative rule is applied in any sequence of positive, double, and negative rules reducing the graph to the empty graph, resolving two open problems posed by Harju, Li, and Petre. We also demonstrate the close relation between graph reductions and the matrix pivot operation, both of which can be studied in terms of the poset of subsets of vertices of a graph that can be removed by a graph reduction.
The sigma-omega model in mean-field approximation where the meson fields are treated classically, describes much of observed nuclear structure and has been employed to describe the nuclear equation of state up to the quark-gluon phase transition. The acceleration of the meson sources, for example, in relativistic heavy-ion collisions, should result in bremsstrahlung-like radiation of the meson fields. The many mesons emitted serve to justify the use of classical meson fields. The slowing of the nuclei during the collision is modeled here as a smooth transition from initial to final velocity. Under ultra-relativistic conditions, vector radiation dominates. The angular distribution of energy flux shows a characteristic shape. It appears that if the vector meson field couples to the conserved baryon current, independent of the baryonic degrees of freedom, this mechanism will contribute to the radiation seen in relativistic heavy-ion collisions. The possible influence of the quark-gluon plasma is also considered.
Using exact diagonalizations, we investigate the T=0 phase diagram of the Multi-Spin Exchange (MSE) model on the triangular lattice: we find a transition separating a ferromagnetic phase from a non-magnetic gapped Spin Liquid phase. Systems far enough from the ferromagnetic transition have a metamagnetic behavior with magnetization plateaus at m/m_sat=0 and 1/2. The MSE has been proposed to describe solid 3He films adsorbed onto graphite, thus we compute the MSE heat capacity for parameters in the low density range of the 2nd layer and find a double-peak structure.
The lattice model of principal chiral field interacting with the gauge fields, which have no kinetic term, is considered. This model can be regarded as a strong coupling limit of lattice gauge theory at finite temperature. The complete set of equations for collective field variables is derived in the large N limit and the phase structure of the model is studied.
The goal of this paper is to generalize and refine the classical ramification theory of complete discrete valuation rings to more general valuation rings, in the case of Artin-Schreier extensions. We define refined versions of invariants of ramification in the classical ramification theory and compare them. Furthermore, we can treat the defect case.
We report on the observation of temperature and field dependent anomalous Nernst effect (ANE) in Ni-rich bulk Ni-Co-Mn-Sn full Heusler alloy. A large change in the transverse Nernst coefficient (N) is obtained across the first order magnetostructural transition from a tetragonal martensite to a cubic austenite phase. The saturation of ANE and magnetic data appear to depend largely on the magnetic anisotropy of the device. Such change in the Nernst co-efficient may prove to be useful for switching applications controlled by temperature and magnetic field changes.
Exchangeable sequences of random probability measures (partitions of mass) and their corresponding exchangeable bridges play an important role in a variety of areas in probability, statistics and related areas, including Bayesian statistics, physics, finance and machine learning. An area of theoretical as well as practical interest, is the study of coagulation and fragmentation operators on partitions of mass. In this regard, an interesting but formidable question is the identification of operators and distributional families on mass partitions that exhibit interesting duality relations. In this paper we identify duality relations for a large sub-class of mixed Poisson-Kingman models generated by a stable subordinator. Our results are natural generalizations of the duality relations developed in Pitman, Bertoin and Goldschmidt, and Dong, Goldschmidt and Martin for the two-parameter Poisson Dirichlet family. These results are deduced from results for corresponding bridges.
A relativistic kinetic description for the irreversible thermodynamic process of gravitationally induced particle production is proposed in the context of an expanding Friedmann-Robertson-Walker (FRW) geometry. We show that the covariant thermodynamic treatment referred to as "adiabatic" particle production provoked by the cosmic time-varying gravitational field has a consistent kinetic counterpart. The variation of the distribution function is associated to a non-collisional kinetic term of quantum-gravitational origin which is proportional to the ratio $\Gamma/H$, where $\Gamma$ is the gravitational particle production rate and H is the Hubble parameter. For $\Gamma << H$ the process is negligible and as should be expected it also vanishes (regardless of the value of $\Gamma$) in the absence of gravitation. The resulting non-equilibrium distribution function has the same functional form of equilibrium with the evolution laws corrected by the particle production process. The macroscopic temperature evolution law is also kinetically derived for massive and massless particles. The present approach points to the possibility of an exact (semi-classical) quantum-gravitational kinetic treatment by incorporating back-reaction effects in the cosmic background.
In this paper, we study the characters of homogeneous monotonic P-polynomial table algebras with finite dimension d>=5. We then apply them to association schemes. To this end, we develop some methods using tridiagonal matrices and Z-transform. Moreover, we calculate the eigenvalues of a special tridiagonal matrix which is found through the first intersection matrix of P-polynomial table algebras.
We study a $R^{2}$ model of gravity with torsion in a closed Friedmann-Robertson-Walker universe. The model is cast in Hamiltonian form subtracting from the original Lagrangian the total time derivative of $f_{K}f_{R}$, where $f_{K}$ is proportional to the trace of the extrinsic curvature tensor, and $f_{R}$ is obtained differentiating the Lagrangian with respect to the highest derivative. Torsion is found to lead to a primary constraint linear in the momenta and a secondary constraint quadratic in the momenta, and the full field equations are finally worked out in detail. Problems to be studied for further research are the solution of these equations and the quantization of the model. One could then try to study a new class of quantum cosmological models with torsion.
In this paper, we study moments of the central values of quartic Dirichlet $L$-functions and establish quantitative non-vanishing result for these $L$-values.
Given a unirational parameterization of a surface, we present a general algorithm to determine a birational parameterization without using parameterization algorithms. Additionally, if the surface is assumed to have a birational parametrization with empty base locus, and the input parametrization is transversal, the degree of the solution is determined in advance and the dimension of the space of solutions is reduced. As a consequence, for these cases, we present a second faster algorithm.
A negative result is when the outcome of an experiment or a model is not what is expected or when a hypothesis does not hold. Despite being often overlooked in the scientific community, negative results are results and they carry value. While this topic has been extensively discussed in other fields such as social sciences and biosciences, less attention has been paid to it in the computer vision community. The unique characteristics of computer vision, particularly its experimental aspect, call for a special treatment of this matter. In this paper, I will address what makes negative results important, how they should be disseminated and incentivized, and what lessons can be learned from cognitive vision research in this regard. Further, I will discuss issues such as computer vision and human vision interaction, experimental design and statistical hypothesis testing, explanatory versus predictive modeling, performance evaluation, model comparison, as well as computer vision research culture.
In this paper, we consider a stochastic system described by a differential equation admitting a spatially varying random coefficient.   The differential equation has been employed to model various static physics systems such as elastic deformation, water flow, electric-magnetic fields, temperature distribution, etc.   A random coefficient is introduced to account for the system's uncertainty and/or imperfect measurements.   This random coefficient is described by a Gaussian process (the input process) and thus the solution to the differential equation (under certain boundary conditions) is a complexed functional of the input Gaussian process.   In this paper, we focus the analysis on the one-dimensional case and derive asymptotic approximations of the tail probabilities of the solution to the equation that has various physics interpretations under different contexts.   This analysis rests on the literature of the extreme analysis of Gaussian processes (such as the tail approximations of the supremum) and extends the analysis to more complexed functionals.
Using the light front wave functions for the nucleons in a quark model in AdS/QCD, we calculate the nucleon electromagnetic form factors. The flavor decompositions of the nucleon form factors are calculated from the GPDs in this model. We show that the nucleon form factors and their flavor decompositions calculated in AdS/QCD are in agreement with experimental data.
Superradiance is the enhanced emission of photons from quantum emitters collectively coupling to the same optical mode. However, disorder in the resonant frequencies of the quantum emitters can perturb this effect. In this paper, we study the interplay between superradiance and spectral disorder in a dynamically modulated Tavis-Cummings model. Through numerical simulations and analytical calculations, we show that the effective cooperativity of the superradiant mode, which is always formed over an extensive number of emitters, can be multiplicatively enhanced with a quantum control protocol modulating the resonant frequency of the optical mode. Our results are relevant to experimental demonstration of superradiant effects in solid-state quantum optical systems, wherein the spectral disorder is a significant technological impediment towards achieving photon-mediated emitter-emitter couplings.
We consider the height process of a Levy process with no negative jumps, and its associated continuous tree representation. Using Levy snake tools developed by Duquesne and Le Gall, with an underlying Poisson process, we construct a fragmentation process, which in the stable case corresponds to the self-similar fragmentation described by Miermont. For the general fragmentation process we compute a family of dislocation measures as well as the law of the size of a tagged fragment. We also give a special Markov property for the snake which is interesting in itself.