ShantanuT01/DACTYL-Pretraining huggingface dataset:
Let $c_{kl} \in W^{1,\infty}(\Omega, \mathbb{C})$ for all $k,l \in \{1, \ldots, d\}$ and $\Omega \subset \mathbb{R}^d$ be open with Lipschitz boundary. We consider the divergence form operator $ A_p = - \sum_{k,l=1}^d \partial_l (c_{kl} \, \partial_k) $ in $L_p(\Omega)$ when the coefficient matrix satisfies $(C(x) \, \xi, \xi) \in \Sigma_\theta$ for all $x \in \Omega$ and $\xi \in \mathbb{C}^d$, where $\Sigma_\theta$ be the sector with vertex 0 and semi-angle $\theta$ in the complex plane. We show that a sectorial estimate hold for $A_p$ for all $p$ in a suitable range. We then apply these estimates to prove that the closure of $-A_p$ generates a holomorphic semigroup under further assumptions on the coefficients. The contractivity and consistency properties of these holomorphic semigroups are also considered.
Universality properties of the distribution of the generalized eigenvalues of a pencil of random Hankel matrices, arising in the solution of the exponential interpolation problem of a complex discrete stationary process, are proved under the assumption that every finite set of random variables of the process have a multivariate spherical distribution. An integral representation of the condensed density of the generalized eigenvalues is also derived. The asymptotic behavior of this function turns out to depend only on stationarity and not on the specific distribution of the process.
The recently developed auxiliary field diffusion Monte Carlo method is applied to compute the equation of state and the compressibility of neutron matter. By combining diffusion Monte Carlo for the spatial degrees of freedom and auxiliary field Monte Carlo to separate the spin-isospin operators, quantum Monte Carlo can be used to simulate the ground state of many nucleon systems $(A\alt 100)$. We use a path constraint to control the fermion sign problem. We have made simulations for realistic interactions, which include tensor and spin--orbit two--body potentials as well as three-nucleon forces. The Argonne $v_8'$ and $v_6'$ two nucleon potentials plus the Urbana or Illinois three-nucleon potentials have been used in our calculations. We compare with fermion hypernetted chain results. We report results of a Periodic Box--FHNC calculation, which is also used to estimate the finite size corrections to our quantum Monte Carlo simulations. Our AFDMC results for $v_6$ models of pure neutron matter are in reasonably good agreement with equivalent Correlated Basis Function (CBF) calculations, providing energies per particle which are slightly lower than the CBF ones. However, the inclusion of the spin--orbit force leads to quite different results particularly at relatively high densities. The resulting equation of state from AFDMC calculations is harder than the one from previous Fermi hypernetted chain studies commonly used to determine the neutron star structure.
In this note, we give a positive answer to a question addressed in \cite{Nad-Per-Tan}. Precisely we prove that, for any kernel and any slope at the origin, there do exist travelling wave solutions (actually those which are "rapid") of the nonlocal Fisher equation that connect the two homogeneous steady states 0 (dynamically unstable) and 1. In particular this allows situations where 1 is unstable in the sense of Turing. Our proof does not involve any maximum principle argument and applies to kernels with {\it fat tails}.
Experiments with evanescent modes and tunneling particles have shown that i) their signal velocity may be faster than light, ii) they are described by virtual particles, iii) they are nonlocal and act at a distance, iv) experimental tunneling data of phonons, photons, and electrons display a universal scattering time at the tunneling barrier front, and v) the properties of evanescent, i.e. tunneling modes is not compatible with the special theory of relativity.
In robotic applications, we often face the challenge of discovering new objects while having very little or no labelled training data. In this paper we explore the use of self-supervision provided by a robot traversing an environment to learn representations of encountered objects. Knowledge of ego-motion and depth perception enables the agent to effectively associate multiple object proposals, which serve as training data for learning object representations from unlabelled images. We demonstrate the utility of this representation in two ways. First, we can automatically discover objects by performing clustering in the learned embedding space. Each resulting cluster contains examples of one instance seen from various viewpoints and scales. Second, given a small number of labeled images, we can efficiently learn detectors for these labels. In the few-shot regime, these detectors have a substantially higher mAP of 0.22 compared to 0.12 of off-the-shelf standard detectors trained on this limited data. Thus, the proposed self-supervision results in effective environment specific object discovery and detection at no or very small human labeling cost.
We present an analytical model for describing highly relativistic acceleration of magnetically driven jets, within the framework of ideal MHD for cold, stationary and axisymmetric outflows. Our novel procedure is to treat the wind equation as an algebraic relation between the relativistic Alfv\'{e}n Mach-number and the poloidal electric to toroidal magnetic field amplitudes ratio $\xi$.   This allows us to obtain easily the wind solutions for trans-fast-magnetosonic flows, together with the required range of   $\xi$. Then, to determine the spatial variation of $\xi$, we solve approximately the Grad-Shafranov equation applied to a jet flow ejected with a very large total specific energy $E$ and confined within a very small opening angle. Our trans-fast-magnetosonic model provides a closed-form expression for the transition from a magnetically dominated flow to a kinetic-energy dominated one, which occurs in the sub-asymptotic region far beyond the light cylinder of the radius   $R_{\rm L}$. Importantly, we find that the equipartition between magnetic and kinetic energies is realized at a cylindrical radius of order of   $R_{\rm L}E/c^{2}$, and confirm that the further conversion of magnetic to kinetic energy proceeds logarithmically with distance in the asymptotic region. Finally, we discuss briefly the astrophysical implications of our model for jets originating from active galactic nuclei.
With the help of some techniques based on certain inverse pairs of symbolic operators, the authors investigated several decomposition formulas associated with Srivastava's Hypergeometric functions of three variables. Some operator identities have been constructed in this matter. With the help these operator forms 15 decompositions are found which are expressed through product of Hypergeometric Gauss and Appell's functions.
In position space the interaction terms of soft-collinear effective theory must be multipole-expanded to obtain interaction terms with homogeneous scaling behaviour. In this note we provide a manifestly gauge-invariant formulation of the theory after this expansion in the presence of non-abelian gauge fields, extending our previous result. We give the effective Lagrangian (including the Yang-Mills Lagrangian for collinear and ultrasoft gluons) and heavy-to-light transition currents to second order in the power expansion, paying particular attention to the field redefinitions that lead to the gauge symmetries of the effective Lagrangian.
Let $p\equiv 8\mod 9$ be a prime. In this paper we give a sufficient condition such that at least one of $p$ and $p^2$ is the sum of two rational cubes. This is the first general result on the $8$ case of the so-called Sylvester conjecture.
As part of the SINS/zC-SINF surveys of high-z galaxy kinematics, we derive the radial distributions of H-alpha surface brightness, stellar mass surface density, and dynamical mass at ~2 kpc resolution in 19 z~2 star-forming disks with deep SINFONI AO spectroscopy at the ESO VLT. From these data we infer the radial distribution of the Toomre Q-parameter for these main-sequence star forming galaxies (SFGs), covering almost two decades of stellar mass (10^9.6 to 10^11.5 solar masses). In more than half of our SFGs, the H-alpha distributions cannot be fit by a centrally peaked distribution, such as an exponential, but are better described by a ring, or the combination of a ring and an exponential. At the same time the kinematic data indicate the presence of a mass distribution more centrally concentrated than a single exponential distribution for 5 of the 19 galaxies. The resulting Q-distributions are centrally peaked for all, and significantly exceed unity there for three quarters of the SFGs. The occurrence of H-alpha rings and of large nuclear Q-values is strongly correlated, and is more common for the more massive SFGs. While our sample is small and there remain substantial uncertainties and caveats, our observations are consistent with a scenario in which cloud fragmentation and global star formation are secularly suppressed in gas rich high-z disks from the inside out, as the central stellar mass density of the disks grows.
In this paper, we continue the study in \cite{MiaoTX:DNLS:Stab}. We use the perturbation argument, modulational analysis and the energy argument in \cite{MartelMT:Stab:gKdV, MartelMT:Stab:NLS} to show the stability of the sum of two solitary waves with weak interactions for the generalized derivative Schr\"{o}dinger equation (gDNLS) in the energy space. Here (gDNLS) hasn't the Galilean transformation invariance, the pseudo-conformal invariance and the gauge transformation invariance, and the case $\sigma>1$ we considered corresponds to the $L^2$-supercritical case.
We argue that the appearance of the Landau pole in the running coupling of QCD introduces 1/Q^2 power corrections in current correlation functions. These terms are not accounted for by the standard operator product expansion and is the price to be paid for the lack of a unique definition of the running coupling at the 1/Q^2 level. We review also possible phenomenological implications of the 1/Q^2 terms in an alternative language of the ultraviolet renormalon.
Let V^{r}_{d,g, \delta} be the Hilbert scheme of nodal curves in P^r of degree d and arithmetic genus g with \delta nodes. Under suitable numerical assumptions on d and g, for every 0 \le \delta \le g we construct an irreducible component of V^{r}_{d,g, \delta} having the expected number of moduli.
One of the central goals of multi-wavelength galaxy cluster cosmology is to unite all cluster observables to form a consistent understanding of cluster mass. Here, we study the impact of systematic effects from optical cluster catalogs on stacked SZ signals. We show that the optically predicted Y-decrement can vary by as much as 50% based on the current 2 sigma systematic uncertainties in the observed mass-richness relationship. Mis-centering and impurities will suppress the SZ signal compared to expectations for a clean and perfectly centered optical sample, but to a lesser degree. We show that the level of these variations and suppression is dependent on the amount of systematics in the optical cluster catalogs. We also study X-ray luminosity-dependent sub-sampling of the optical catalog and find that it creates Malmquist bias increasing the observed Y-decrement of the stacked signal. We show that the current Planck measurements of the Y-decrement around SDSS optical clusters and their X-ray counterparts are consistent with expectations after accounting for the 1 sigma optical systematic uncertainties using the Johnston mass richness relation.
One of the unique features of Dirac Fermions is pseudo-diffusive transport by evanescent modes at low Fermi energies when the disorder is low. At higher Fermi energies i.e. carrier densities, the electrical transport is diffusive in nature and the propagation occurs via plane-waves. In this study, we report the detection of such evanescent modes in the surface states of topological insulator through 1/f noise. While signatures of pseudo-diffusive transport have been seen experimentally in graphene, such behavior is yet to be observed explicitly in any other system with a Dirac dispersion. To probe this, we have studied 1/f noise in topological insulators as a function of gate-voltage, and temperature. Our results show a non-monotonic behavior in 1=f noise as the Fermi energy is varied, suggesting a crossover from pseudo-diffusive to diffusive transport regime in mesoscopic topological insulators. The temperature dependence of noise points towards conductance fluctuations from quantum interference as the dominant source of the noise in these samples.
Let $p\in[1,\infty]$. Consider the projection of a uniform random vector from a suitably normalized $\ell^p$ ball in $\mathbb{R}^n$ onto an independent random vector from the unit sphere. We show that sequences of such random projections, when suitably normalized, satisfy a large deviation principle (LDP) as the dimension $n$ goes to $\infty$, which can be viewed as an annealed LDP. We also establish a quenched LDP (conditioned on a fixed sequence of projection directions) and show that for $p\in(1,\infty]$ (but not for $p=1$), the corresponding rate function is "universal", in the sense that it coincides for "almost every" sequence of projection directions. We also analyze some exceptional sequences of directions in the "measure zero" set, including the directions corresponding to the classical Cram\'er's theorem, and show that those directions yield LDPs with rate functions that are distinct from the universal rate function of the quenched LDP. Lastly, we identify a variational formula that relates the annealed and quenched LDPs, and analyze the minimizer of this variational formula. These large deviation results complement the central limit theorem for convex sets, specialized to the case of sequences of $\ell^p$ balls.
GRB 160325A is the only bright burst detected by AstroSat CZT Imager in its primary field of view to date. In this work, we present the spectral and polarimetric analysis of the prompt emission of the burst using AstroSat, Fermi and Niel Gehrels Swift observations. The prompt emission consists of two distinct emission episodes separated by a few seconds of quiescent/ mild activity period. The first emission episode shows a thermal component as well as a low polarisation fraction of $PF < 37\, \%$ at $1.5\, \sigma$ confidence level. On the other hand, the second emission episode shows a non-thermal spectrum and is found to be highly polarised with $PF > 43\, \%$ at $1.5 \sigma$ confidence level. We also study the afterglow properties of the jet using {\it Swift}/XRT data. The observed jet break suggests that the jet is pointed towards the observer and has an opening angle of $1.2^{\circ}$ for an assumed redshift, $z = 2$. With composite modelling of polarisation, spectrum of the prompt emission and the afterglow, we infer that the first episode of emission originates from the photosphere with localised dissipation happening below it, and the second from the optically thin region above the photosphere. The photospheric emission is generated mainly by inverse Compton scattering, whereas the emission in the optically thin region is produced by the synchrotron process. The low radiation efficiency of the burst suggests that the outflow remains baryonic dominated throughout the burst duration with only a subdominant Poynting flux component, and the kinetic energy of the jet is likely dissipated via internal shocks which evolves from an optically thick to optically thin environment within the jet.
Frame difference families, which can be obtained via a careful use of cyclotomic conditions attached to strong difference families, play an important role in direct constructions for resolvable balanced incomplete block designs. We establish asymptotic existences for several classes of frame difference families. As corollaries new infinite families of 1-rotational $(pq+1,p+1,1)$-RBIBDs over $\mathbb{F}_{p}^+ \times \mathbb{F}_{q}^+$ are derived, and the existence of $(125q+1,6,1)$-RBIBDs is discussed. We construct $(v,8,1)$-RBIBDs for $v\in\{624,1576,2976,5720,5776,10200,14176,24480\}$, whose existence were previously in doubt. As applications, we establish asymptotic existences for an infinite family of optimal constant composition codes and an infinite family of strictly optimal frequency hopping sequences.
We investigate the probabilistic cloning and purification of quantum states. The performance of these probabilistic operations is quantified by the average fidelity between the ideal and actual output states. We provide a simple formula for the maximal achievable average fidelity and we explictly show how to construct a probabilistic operation that achieves this fidelity. We illustrate our method on several examples such as the phase covariant cloning of qubits, cloning of coherent states, and purification of qubits transmitted via depolarizing channel and amplitude damping channel. Our examples reveal that the probabilistic cloner may yield higher fidelity than the best deterministic cloner even when the states that should be cloned are linearly dependent and are drawn from a continuous set.
Despite being robust to small amounts of label noise, convolutional neural networks trained with stochastic gradient methods have been shown to easily fit random labels. When there are a mixture of correct and mislabelled targets, networks tend to fit the former before the latter. This suggests using a suitable two-component mixture model as an unsupervised generative model of sample loss values during training to allow online estimation of the probability that a sample is mislabelled. Specifically, we propose a beta mixture to estimate this probability and correct the loss by relying on the network prediction (the so-called bootstrapping loss). We further adapt mixup augmentation to drive our approach a step further. Experiments on CIFAR-10/100 and TinyImageNet demonstrate a robustness to label noise that substantially outperforms recent state-of-the-art. Source code is available at https://git.io/fjsvE
Classical lattice simulations of the Abelian Higgs model are used to investigate small scale structure and loop distributions in cosmic string networks. Use of the field theory ensures that the small-scale physics is captured correctly. The results confirm analytic predictions of Polchinski & Rocha [1] for the two-point correlation function of the string tangent vector, with a power law from length scales of order the string core width up to horizon scale with evidence to suggest that the small scale structure builds up from small scales. An analysis of the size distribution of string loops gives a very low number density, of order 1 per horizon volume, in contrast with Nambu-Goto simulations. Further, our loop distribution function does not support the detailed analytic predictions for loop production derived by Dubath et al. [2]. Better agreement to our data is found with a model based on loop fragmentation [3], coupled with a constant rate of energy loss into massive radiation. Our results show a strong energy loss mechanism which allows the string network to scale without gravitational radiation, but which is not due to the production of string width loops. From evidence of small scale structure we argue a partial explanation for the scale separation problem of how energy in the very low frequency modes of the string network is transformed into the very high frequency modes of gauge and Higgs radiation. We propose a picture of string network evolution which reconciles the apparent differences between Nambu-Goto and field theory simulations.
It has been realized for a long time that knowing the eta and eta^prime wave functions in terms of quark and gluon components probes our understanding of non-perturbative QCD dynamics. Great effort has been given to this challenge -- yet no clear picture has emerged even with the most recent KLOE data. We point out which measurements would be most helpful in arriving at a more definite conclusion. A better knowledge of these wave functions will significantly help to disentangle the weight of different decay subprocesses in semi-leptonic decays of D+, Ds^+ and B+ mesons. The resulting insights will be instrumental in treating even non-leptonic B transitions involving eta and eta^prime and their CP asymmetries; thus they can sharpen the case for or against New Physics intervening there.
We consider loop-erased random walk (LERW) running between two boundary points of a square grid approximation of a planar simply connected domain. The LERW Green's function is the probability that the LERW passes through a given edge in the domain. We prove that this probability, multiplied by the inverse mesh size to the power 3/4, converges in the lattice size scaling limit to (a constant times) an explicit conformally covariant quantity which coincides with the SLE(2) Green's function.   The proof does not use SLE techniques and is based on a combinatorial identity which reduces the problem to obtaining sharp asymptotics for two quantities: the loop measure of random walk loops of odd winding number about a branch point near the marked edge and a "spinor" observable for random walk started from one of the vertices of the marked edge.
we study the statistical properties of inhomogenous Poisson networks. we perform a detailed analysis of the statistical properties of Poisson networks and show that the topological properties of random cellular structures, can be derived from these models of random networks. we study both two and three dimensional networks with non uniform density and show that with a class of symmetric distribution $P(\lambda_{1}, \lambda_{2}, ..., \lambda_{N})$ Lewis and Aboav-Weaire laws are obeyed in these networks.
On the base of potential theory of light nuclei cluster photodisintegration the characteristics of Lithium nuclei cluster photodisintegration reactions are considered in the range of low and intermediate energies. For the inverse reaction the interference has an opposite character: in forward semisphere it is deconstructive, and in backward semisphere it is constructive. In the energy range above several MeV the E2-multipole becomes dominating. The effect of appearance of the node structure of the wave function of relative motion has been considered in the characteristics of Li cluster photodisintegration reaction with polarized and non-polarized photons.
We prove that the maximum size of a simple binary matroid of rank $r \geq 5$ with no AG(3,2)-minor is $\binom{r+1}{2}$ and characterise those matroids achieving this bound. When $r \geq 6$, the graphic matroid $M(K_{r+1})$ is the unique matroid meeting the bound, but there are a handful of smaller examples. In addition, we determine the size function for non-regular simple binary matroids with no AG(3,2)-minor and characterise the matroids of maximum size for each rank.
We review the formalism of the effective average action in quantum field theory which corresponds to a coarse grained free energy in statistical mechanics. The associated exact renormalization group equation and possible nonperturbative approximations for its solution are discussed. This is applied to QCD where one observes the consecutive emergence of mesonic bound states and spontaneous chiral symmetry breaking as the coarse graining scale is lowered. We finally present a study of the phenomenological importance of non--renormalizable terms in the effective linear meson model.
We apply elliptical isothermal mass models to reproduce the point source properties, i.e. image positions, flux density ratios and time delay ratios, of the quadruple lens B1608+656. A wide set of suitable solutions is found, showing that models that only fit the properties of point sources are under-constrained and can lead to a large uncertainty in the prediction of Ho. We present two examples of models predicting Ho=100 km/(s Mpc) (chi^2=4) and Ho=69 km/(s Mpc) (chi^2=24).