ShantanuT01/DACTYL-Pretraining huggingface dataset:
n this paper, we prove a result linking the square and the rectangular R-transforms, the consequence of which is a surprising relation between the square and rectangular versions the free additive convolutions, involving the Marchenko-Pastur law. Consequences on random matrices, on infinite divisibility and on the arithmetics of the square versions of the free additive and multiplicative convolutions are given.
Real-time object detection is one of the core problems in computer vision. The cascade boosting framework proposed by Viola and Jones has become the standard for this problem. In this framework, the learning goal for each node is asymmetric, which is required to achieve a high detection rate and a moderate false positive rate. We develop new boosting algorithms to address this asymmetric learning problem. We show that our methods explicitly optimize asymmetric loss objectives in a totally corrective fashion. The methods are totally corrective in the sense that the coefficients of all selected weak classifiers are updated at each iteration. In contract, conventional boosting like AdaBoost is stage-wise in that only the current weak classifier's coefficient is updated. At the heart of the totally corrective boosting is the column generation technique. Experiments on face detection show that our methods outperform the state-of-the-art asymmetric boosting methods.
In this paper, we propose a fast and accurate coordinate regression method for face alignment. Unlike most existing facial landmark regression methods which usually employ fully connected layers to convert feature maps into landmark coordinate, we present a structure coherence component to explicitly take the relation among facial landmarks into account. Due to the geometric structure of human face, structure coherence between different facial parts provides important cues for effectively localizing facial landmarks. However, the dense connection in the fully connected layers overuses such coherence, making the important cues unable to be distinguished from all connections. Instead, our structure coherence component leverages a dynamic sparse graph structure to passing features among the most related landmarks. Furthermore, we propose a novel objective function, named Soft Wing loss, to improve the accuracy. Extensive experiments on three popular benchmarks, including WFLW, COFW and 300W, demonstrate the effectiveness of the proposed method, achieving state-of-the-art performance with fast speed. Our approach is especially robust to challenging cases resulting in impressively low failure rate (0% and 2.88%) in COFW and WFLW datasets.
Since conduction electrons of a metal screen effectively the local electric dipole moments, it was widely believed that the ferroelectric-like distortion cannot occur in metals. Recently, metallic LiOsO3, was discovered to be the first clear-cut example of an Anderson-Blount "ferroelectric" metal, which at 140 K undergoes a ferroelectric-like structural transition similar to insulating LiNbO3. This is very surprising because the mechanisms for structural phase transitions are usually quite distinct in metals and insulators. Through performing first principles calculations, here we reveal that the local polar distortion in LiOsO3 is solely due to the instability of the A-site Li atom, in contrast to the LiNbO3 case where the second order Jahn-Teller effect of the B-site Nb ion also plays an additional role. More importantly, the "ferroelectric"-like long range order of the local polar distortion is found to be due to the predominantly ferroelectric short-range pair interactions between the local polar modes which are not screened by conduction electrons. Furthermore, we predict that LiNbO3-type MgReO3 is also a "ferroelectric" metal, but with a much higher structural transition temperature by 391 K than LiOsO3. Our work not only unravels the origin of FE-like distortion in LiNbO3-type "ferroelectric" metals, but also provides clue for designing other multi-functional "ferroelectric" metals.
Smooth solutions to the axially symmetric Navier-Stokes equations obey the following maximum principle:$\|ru_\theta(r,z,t)\|_{L^\infty}\leq\|ru_\theta(r,z,0)\|_{L^\infty}.$ We first prove the global regularity of solutions if $\|ru_\theta(r,z,0)\|_{L^\infty}$ or $ \|ru_\theta(r,z,t)\|_{L^\infty(r\leq r_0)}$ is small compared with certain dimensionless quantity of the initial data. This result improves the one in Zhen Lei and Qi S. Zhang \cite{1}. As a corollary, we also prove the global regularity under the assumption that $|ru_\theta(r,z,t)|\leq\ |\ln r|^{-3/2},\ \ \forall\ 0<r\leq\delta_0\in(0,1/2).$
In this paper it is argued that even invoking the dominant energy condition, the Einstein's field equations admit nonglobally hyperbolic, asymptotically de Sitter spacetimes with locally naked singularities and with Cauchy horizons failing to be surfaces of infinite gravitational blueshift; what is more, it is shown the existence of space-time solutions containing Cauchy horizons expected to be stable against small linear nonstationary axisymmetric perturbations in an open set of the physical parameter space where the positive cosmological constant is nearly zero. The price to pay is a violation at ultrahigh densities of Le Chatelier's principle. Given an equation of state, the line of thought introduces black-hole Cauchy horizon instability criteria in terms of the associated adiabatic index, revealing a connection between this subject and the stability theory of relativistic stars. This is used to put forward a tentative, limited formulation of the strong cosmic censorship principle inside black holes (once called dark stars).
We perform theoretical investigation of the localized state dynamics in the presence of interaction with the reservoir and Coulomb correlations. We analyze kinetic equations for electron occupation numbers with different spins taking into account high order correlation functions for the localized electrons. We reveal that in the stationary state electron occupation numbers with the opposite spins always have the same value - the stationary state is a $"$paramagnetic$"$ one. $"$Magnetic$"$ properties can appear only in the non-stationary characteristics of the single-impurity Anderson model and in the dynamics of the localized electrons second order correlation functions. We found, that for deep energy levels and strong Coulomb correlations, relaxation time for initial $"$magnetic$"$ state can be several orders larger than for $"$paramagnetic$"$ one. So, long-living $"$magnetic$"$ moment can exist in the system. We also found non-stationary spin polarized currents flowing in opposite directions for the different spins in the particular time interval.
A short review on the self-consistent RPA based on a energy-density functional of the Skyrme type is given. We also present an extension of the RPA where the coupling of phonons to the single-particle states is considered. Within this approach we present numerical results which are compared with data. The self-consistent approach is compared with the Landau-Migdal theory. Here we derive from the self-consistent $ph$ interaction, the Landau-Migdal parameters as well as their density dependence. In the Appendix a new derivation of the reduced matrix elements of the $ph$ interaction is presented.
In the Born, Infeld, Bopp, Podolsky and Dirac theories the electron mass is finite (or zero), but gravity effects have not been considered. Shirokov and Fisher showed that in studying of origin of elemental particle masses we can not neglect these effects. Gravity field plays an essential role in interpretation of particle mass. It has been shown that for point-like charge the general solution of gravity and electromagnetic (EM) equations that contains arbitrary function $\mu(r)$, can in special case of this function, describe gravity and EM fields that do not have singularities in full range of $r$ from $0$ to $\infty$. In this paper we are trying to find more general solution.
We investigate the role of the boundary in the symmetric simple exclusion process with competing nonlocal and local hopping events. With open boundaries, the system undergoes a first order phase transition from a finite density phase to an empty road phase as the nonlocal hopping rate increases. Using a cluster stability analysis, we determine the location of such an abrupt nonequilibrium phase transition, which agrees well with numerical results. Our cluster analysis provides a physical insight into the mechanism behind this transition. We also explain why the transition becomes discontinuous in contrast to the case with periodic boundary conditions, in which the continuous phase transition has been observed.
The INTEGRAL satellite has revealed a major population of supergiant High Mass X-ray Binaries in our Galaxy, revolutionizing our understanding of binary systems and their evolution. This population, constituted of a compact object orbiting around a massive and luminous supergiant star, exhibits unusual properties, either being extremely absorbed, or showing very short and intense flares. An intensive set of multi-wavelength observations has led us to reveal their nature, and to show that these systems are wind-fed accretors, closely related to massive star-forming regions. In this paper I describe the characteristics of these sources, showing that this newly revealed population is linked to the evolution of gamma-ray emitting massive stars with a compact companion.
We prove a regularity theorem for the free boundary of minimizers of the two-phase Bernoulli problem, completing the analysis started by Alt, Caffarelli and Friedman in the 80s. As a consequence, we also show regularity of minimizers of the multiphase spectral optimization problem for the principal eigenvalue of the Dirichlet Laplacian.
I extend the calculations represented in \cite{konav} regarding the resistivity in Kondo lattice materials from $3d$ syatem to $2d$ systems. In the present work I consider a 2d system, and memory function is computed. However, results found in 2d case are different from 3d system . I find that in $2d$ in low temperature regime($ k_{B}T\ll \mu_d$) resistivity shows power law($\frac{1}{T}$) behaviour and in the high temeprature regime($ k_{B}T\gg\mu_d$) resistivity varies linearly with temperature. In $3d$ these behaviours are as $\frac{1}{T}$ and as $T^{\frac{3}{2}}$ respectively.
Extended abstract for the workshop "Geophysical Fluid Dynamics " held in Oberwolfach, 17 February - 23 February 2013, to be published by the Mathematisches Forschungsinstitut Oberwolfach in the "Oberwolfach Reports" series.
We report a new manifestation of first-order magnetic transitions in two-dimensional electron systems. This phenomenon occurs in aluminum arsenide quantum wells with sufficiently low carrier densities and appears as a set of hysteretic spikes in the resistance of a sample placed in crossed parallel and perpendicular magnetic fields, each spike occurring at the transition between states with different partial magnetizations. Our experiments thus indicate that the presence of magnetic domains at the transition starkly increases dissipation, an effect also suspected in other ferromagnetic materials. Analysis of the positions of the transition spikes allows us to deduce the change in exchange-correlation energy across the magnetic transition, which in turn will help improve our understanding of metallic ferromagnetism.
We present a spectroscopic study of the inner circumstellar ring around SN 1987A. The aim is to determine the elemental abundances and density structure, with particular emphasis on the abundance of iron. We acquired and analysed optical spectra at the Anglo-Australian Telescope (AAT) between 1400 and 4300 days post-explosion. We also assembled from the literature all available optical/near-IR line fluxes of the inner ring. The observed line light curves were then compared with a photoionisation model for the inner ring. This indicates an iron abundance of (0.20+-0.08) x solar which is lower than that generally seen in the Large Magellanic Cloud (LMC).
When compared to fault-tolerant quantum computational strategies, variational quantum algorithms stand as one of the candidates with the potential of achieving quantum advantage for real-world applications in the near term. However, the optimization of the circuit parameters remains arduous and is impeded by many obstacles such as the presence of barren plateaus, many local minima in the optimization landscape, and limited quantum resources. A non-random initialization of the parameters seems to be key to the success of the parametrized quantum circuits (PQC) training. Drawing and extending ideas from the field of meta-learning, we address this parameter initialization task with the help of machine learning and propose FLIP: a FLexible Initializer for arbitrarily-sized Parametrized quantum circuits. FLIP can be applied to any family of PQCs, and instead of relying on a generic set of initial parameters, it is tailored to learn the structure of successful parameters from a family of related problems which are used as the training set. The flexibility advocated to FLIP hinges in the possibility of predicting the initialization of parameters in quantum circuits with a larger number of parameters from those used in the training phase. This is a critical feature lacking in other meta-learning parameter initializing strategies proposed to date. We illustrate the advantage of using FLIP in three scenarios: a family of problems with proven barren plateaus, PQC training to solve max-cut problem instances, and PQC training for finding the ground state energies of 1D Fermi-Hubbard models.
The KKLT construction of dS vacua relies on an uplift term that arises from an anti-D3-brane. It was argued by Kachru, Pearson and Verlinde that this anti-D3-brane is an excited state in a supersymmetric theory since it can decay to a supersymmetric ground state. Hence the anti-D3-brane breaks supersymmetry spontaneously and one should be able to package all the world-volume fields on the anti-D3-brane into a four dimensional $\cal{N}=1$ supersymmetric action. Here we extend previous results and identify the constrained superfields that correspond to all the degrees of freedom on the anti-D3-brane. In particular, we show explicitly that the four 4D worldvolume spinors give rise to constrained chiral multiplets $S$ and $Y^i$, $i=1,2,3$ that satisfy $S^2=SY^i=0$. We also conjecture (and provide evidence in a forthcoming publication) that the vector field $A_\mu$ and the three scalars $\phi^i$ give rise to a field strength multiplet $W_\alpha$ and three chiral multiplets $H^i$ that satisfy the constraints $S W_\alpha= \bar{D}_{\dot \alpha} (S \bar H^i)=0$. This is the first time that such constrained multiplets appear in string theory constructions.
Octet baryon magnetic moments are calculated within \chiQM, respecting color spin spin forces (Szczepaniak et al., PRL 87, 072001(2001)), incorporating the orbital angular momentum as well as the quark sea contribution through the Cheng and Li mechanism (PRL 80, 2789(1998)). Using configuration mixing generated by color spin spin forces as well as the concept of ``effective'' quark mass to include the effects of confinement, we are able to get an excellent fit to the octet magnetic moments as well as the violation of Coleman Glashow Sum Rule (CGSR) without any further input except for the ones already used in \chiQM as well as in NRQM. Specifically, in the case of p, \Sigma^+, \Xi^o, and violation of CGSR we get a perfect fit whereas in almost all the other cases the results are within 5% of the data.
Synthesis, thermodynamic properties, and microscopic magnetic model of ilinskite-type KCu$_{5}$O$_2$(SeO$_3$)$_2$Cl$_3$ built by corner-sharing Cu$_4$ tetrahedra are reported, and relevant magnetostructural correlations are discussed. Quasi-one-dimensional magnetic behavior with the short-range order around 50\,K and the absence of long-range order down to at least 2\,K is observed experimentally and explained in terms of weakly coupled spin ladders (tubes) with a complex topology formed upon fragmentation of the tetrahedral network. This fragmentation is rooted in the non-trivial effect of the SeO$_3$ groups that render the Cu--O--Cu superexchange strongly ferromagnetic.
We develop a field-theoretic representation for the configurations of an interface between two ordered phases of a q-state Potts model in two dimensions, in the solid-on-solid approximation. The model resembles the field theory of directed percolation and may be analysed using similar renormalisation group methods. In the one-loop approximation these reveal a simple mechanism for the emergence of a critical value q_c, such that for q<q_c the interface becomes a fractal with a vanishing interfacial tension at the critical point, while for q>q_c the interfacial width diverges at a finite value of the tension, indicating a first-order transition. The value of the Widom exponent for q<q_c within this approximation is in fair agreement with known exact values. Some comments are made on the case of quenched randomness. We also show that the q-> minus infinity limit of our model corresponds to directed percolation and that the values for the exponents in the one-loop approximation are in reasonable agreement with accepted values.
Using both numerical and analytical approaches, we demonstrate the existence of an effective power-law relation $L\propto m^p$ between the mean Lyapunov exponent $L$ of stellar orbits chaotically scattered by a supermassive black hole in the center of a galaxy and the mass parameter $m$, i.e. ratio of the mass of the black hole over the mass of the galaxy. The exponent $p$ is found numerically to obtain values in the range $p \approx 0.3$--$0.5$. We propose a theoretical interpretation of these exponents, based on estimates of local `stretching numbers', i.e. local Lyapunov exponents at successive transits of the orbits through the black hole's sphere of influence. We thus predict $p=2/3-q$ with $q\approx 0.1$--$0.2$. Our basic model refers to elliptical galaxy models with a central core. However, we find numerically that an effective power law scaling of $L$ with $m$ holds also in models with central cusp, beyond a mass scale up to which chaos is dominated by the influence of the cusp itself. We finally show numerically that an analogous law exists also in disc galaxies with rotating bars. In the latter case, chaotic scattering by the black hole affects mainly populations of thick tube-like orbits surrounding some low-order branches of the $x_1$ family of periodic orbits, as well as its bifurcations at low-order resonances, mainly the Inner Lindbland resonance and the 4/1 resonance. Implications of the correlations between $L$ and $m$ to determining the rate of secular evolution of galaxies are discussed.
Recent work shows that density functional theory calculations accurately describe materials exhibiting turbostratic disorder between layers of incommensurate constituents. These calculations approximate one of the constituents as a finite island between continuous layers of the other constituent. This island approximation allows equal treatment of all relative angles between the interleaved layers, and it removes the requirement of a unit cell that is commensurate with both layers. The work presented here uses this approximation to search for new layered materials that exhibit turbostratic disorder and magnetic structure. In a first application, the approach finds the recently synthesized SnSe$_2$-VSe$_2$ system. The approach predicts a stable Fe$_3$Ge-VSe$_2$ structure and multiple stable structures that interleave Mn$_x$Se$_y$ layers with VSe$_2$ layers. These Mn$_x$Se$_y$ layers exhibit emergent structures and stability.
We present a novel idea to compute square roots over finite fields, without being given any quadratic nonresidue, and without assuming any unproven hypothesis. The algorithm is deterministic and the proof is elementary. In some cases, the square root algorithm runs in $\tilde{O}(\log^2 q)$ bit operations over finite fields with $q$ elements. As an application, we construct a deterministic primality proving algorithm, which runs in $\tilde{O}(\log^3 N)$ for some integers $N$.
Mass is a fundamental property of galaxy groups and clusters. In theory weak gravitational lensing will enable an approximately unbiased measurement of mass, but parametric methods for extracting cluster masses from data require the additional knowledge of concentration. Measurements of both mass and concentration are limited by the degeneracy between the two parameters, particularly in low mass, high redshift systems where the signal-to-noise is low. In this paper we develop a hierarchical model of mass and concentration for mass inference we test our method on toy data and then apply it to a sample of galaxy groups and poor clusters down to masses of $\sim$ 1e13 M$_\odot$. Our fit and model gives a relationship among masses, concentrations and redshift that allow prediction of these parameters from incomplete and noisy future measurements. Additionally the underlying population can be used to infer an observationally based concentration-mass relation. Our method is equivalent to a quasi- stacking approach with the degree of stacking set by the data. We also demonstrate that mass and concentration derived from pure stacking can be offset from the population mean with differing values depending on the method of stacking.
Two different approximation schemes for the self-consistent solution of the relativistic Brueckner-Hartree-Fock equation for finite nuclei are discussed using realistic One-Boson-Exchange potentials. In a first scheme, the effects of correlations are deduced from a study of nuclear matter and parameterized in terms of an effective $\sigma$, $\omega$ and $\pi$ exchange. Employing this effective interaction relativistic Hartree-Fock equations are solved for finite nuclei \osi , \caf\ and \cafe . In the second approach the effect of correlations are treated in the Brueckner-Hartree-Fock approximation directly for the finite nuclei, but the modifications of the Dirac spinors in the medium are derived from nuclear matter assuming a local-density approximation. Both approaches yield rather similar results for binding energies and radii in fair agreement with experimental data. The importance of the density dependent correlation effects is demonstrated and different ingredients to the spin-orbit splitting in the shell-model of the nucleus are discussed.
A model is presented that explains the `torsional oscillation' pattern of deviations in the solar rotation rate as a geostrophic flow. The flow is driven by temperature variations near the surface due to the enhanced emission of radiation by the small scale magnetic field. The model explains the sign of the flow, its amplitude and the fact that the maxima occur near the boundaries of the main activity belts. The amplitude of the flow decreases with depth from its maximum at the surface but penetrates over much of the depth of the convection zone, in agreement with the data from helioseismology. It predicts that the flow is axisymmetric only on average, and in reality consists of a superposition of circulations around areas of enhanced magnetic activity. It must be accompanied by a meridional flow component, which declines more rapidly with depth.