ShantanuT01/DACTYL-Pretraining huggingface dataset:
In this paper, we consider the Cauchy problem of local well-posedness of the Chern-Simons-Dirac system in the Lorenz gauge for $B^{\frac14}_{2,1}$ initial data. We improve the low regularity well-posedness, compared to Huh-Oh \cite{huhoh} and Okamoto \cite{oka}, by using the localization of space-time Fourier side and bilinear estimates given by Selberg \cite{selb}, whereas the authors of \cite{huhoh, oka} used global estimates of \cite{danfoselb}. Then we show the Dirac spinor flow of Chern-Simons-Dirac system is not $C^2$ at the origin in $H^s$ if $ s < \frac14$. From this point of view, the space $B_{2,1}^\frac14$ can be regarded as a critical space for the local well-posedness. We apply the argument for failure of smoothness to the Dirac equation decoupled from Chern-Simons-Dirac system and show the flow is not $C^3$ in $H^s, s < 0$.
It has been shown by van den Berg and Steif that the sub-critical Ising model on $\mathbb{Z}^d$ is a finitary factor of a finite-valued i.i.d. process. We strengthen this by showing that the factor map can be made to have finite expected coding volume (in fact, stretched-exponential tails), answering a question of van den Berg and Steif. The result holds at any temperature above the critical temperature. An analogous result holds for Markov random fields satisfying a high-noise assumption and for proper colorings with a large number of colors.
In this report we present the first quantitative determination of the correlations between baryons and anti-baryons induced by local baryon number conservation. This is important in view of the many experimental studies aiming at probing the phase structure of strongly interacting matter. We confront our results with the recent measurements of net-proton fluctuations reported by the CERN ALICE experiment. The role of local baryon number conservation is found to be small on the level of second cumulants.
We investigate the renormalization group optimized perturbation theory (RGOPT) at the next-to-next-to-leading order (NNLO) for the thermal scalar field theory. From comparing three thus available successive RGOPT orders we illustrate the efficient resummation and very good apparent convergence properties of the method. In particular the remnant renormalization scale dependence of thermodynamical quantities is drastically improved as compared to both standard perturbative expansions and other related resummation methods, such as the screened perturbation theory. Our present results thus constitute a useful first NNLO illustration in view of NNLO applications of this approach to the more involved thermal QCD.
We determine the accuracy of galaxy redshift distributions as estimated from photometric redshift probability distributions $p(z)$. Our method utilises measurements of the angular cross-correlation between photometric galaxies and an overlapping sample of galaxies with spectroscopic redshifts. We describe the redshift leakage from a galaxy photometric redshift bin $j$ into a spectroscopic redshift bin $i$ using the sum of the $p(z)$ for the galaxies residing in bin $j$. We can then predict the angular cross-correlation between photometric and spectroscopic galaxies due to intrinsic galaxy clustering when $i \neq j$ as a function of the measured angular cross-correlation when $i=j$. We also account for enhanced clustering arising from lensing magnification using a halo model. The comparison of this prediction with the measured signal provides a consistency check on the validity of using the summed $p(z)$ to determine galaxy redshift distributions in cosmological analyses, as advocated by the Canada-France-Hawaii Telescope Lensing Survey (CFHTLenS). We present an analysis of the photometric redshifts measured by CFHTLenS, which overlaps the Baryon Oscillation Spectroscopic Survey (BOSS). We also analyse the Red-sequence Cluster Lensing Survey (RCSLenS), which overlaps both BOSS and the WiggleZ Dark Energy Survey. We find that the summed $p(z)$ from both surveys are generally biased with respect to the true underlying distributions. If unaccounted for, this bias would lead to errors in cosmological parameter estimation from CFHTLenS by less than $\sim 4\%$. For photometric redshift bins which spatially overlap in 3-D with our spectroscopic sample, we determine redshift bias corrections which can be used in future cosmological analyses that rely on accurate galaxy redshift distributions.
Radio observations of the magnetic chemically peculiar star CU Vir, carried out with the VLA in three different days, show that the radio emission at 20 cm is characterized by a strong enhancement at particular rotational phases. This radio emission is found to be right hand polarized with a degree of polarization close to 100 %. As common for this class of stars, the magnetic axis of CU Vir is oblique with respect to the rotational axis. By comparing the 20 cm radio light curve with the effective magnetic field available from the literature, a coincidence of the main peaks of the radio emission with the magnetic nulls has been found. This happens when the magnetic axis lies in the plane of the sky. We suggest that the high degree of polarization, together with the high directivity of the radiation, can be explained in terms of coherent radio emission. The data have been interpreted on the basis of the Electron Cyclotron Maser Emission from electrons accelerated in current sheets out of the Alfven radius toward the stellar surface and eventually reflected outward by magnetic mirroring.
We study the positive, regular, radially symmetric solutions to the nonlinear biharmonic equation $\Delta^2 \phi = \phi^p$. First, we show that there exists a critical value $p_c$, depending on the space dimension, such that the solutions are linearly unstable if $p<p_c$ and linearly stable if $p\geq p_c$. Then, we focus on the supercritical case $p\geq p_c$ and we show that the graphs of no two solutions intersect one another.
We study a sorting procedure (run-sorting) on permutations, where runs are rearranged in lexicographic order. We describe a rather surprising bijection on permutations on length $n$, with the property that it sends the set of peak-values to the set of peak-values after run-sorting. We also prove that the expected number of descents in a permutation $\sigma \in S_{n}$ after run-sorting is equal to $(n-2)/3$. Moreover, we provide a closed form of the exponential generating function introduced by Nabawanda, Rakotondrajao and Bamunoba in 2020, for the number of run-sorted permutations of $[n]$, ($RSP(n)$) having $k$ runs, which gives a new interpretation to the sequence A124324 in the Online Encyclopedia of Integer Sequences. We show that the descent generating polynomials, $A_{n}(t)$ for $RSP(n)$ are real rooted, and satisfy an interlacing property similar to that satisfied by the Eulerian polynomials.   Finally, we study run-sorted binary words and compute the expected number of descents after run-sorting a binary word of length $n$.
With the development of 3D scanning technologies, 3D vision tasks have become a popular research area. Owing to the large amount of data acquired by sensors, unsupervised learning is essential for understanding and utilizing point clouds without an expensive annotation process. In this paper, we propose a novel framework and an effective auto-encoder architecture named "PSG-Net" for reconstruction-based learning of point clouds. Unlike existing studies that used fixed or random 2D points, our framework generates input-dependent point-wise features for the latent point set. PSG-Net uses the encoded input to produce point-wise features through the seed generation module and extracts richer features in multiple stages with gradually increasing resolution by applying the seed feature propagation module progressively. We prove the effectiveness of PSG-Net experimentally; PSG-Net shows state-of-the-art performances in point cloud reconstruction and unsupervised classification, and achieves comparable performance to counterpart methods in supervised completion.
We present the first version of a new tool to scan the parameter space of generic scalar potentials, ScannerS. The main goal of ScannerS is to help distinguish between different patterns of symmetry breaking for each scalar potential. In this work we use it to investigate the possibility of excluding regions of the phase diagram of several versions of a complex singlet extension of the Standard Model, with future LHC results. We find that if another scalar is found, one can exclude a phase with a dark matter candidate in definite regions of the parameter space, while predicting whether a third scalar to be found must be lighter or heavier. The first version of the code is publicly available and contains various generic core routines for tree level vacuum stability analysis, as well as implementations of collider bounds, dark matter constraints, electroweak precision constraints and tree level unitarity.
The main purpose of this paper is to give an overview over the theory of abelian varieties, with main focus on Jacobian varieties of curves reaching from well-known results till to latest developments and their usage in cryptography. In the first part we provide the necessary mathematical background on abelian varieties, their torsion points, Honda-Tate theory, Galois representations, with emphasis on Jacobian varieties and hyperelliptic Jacobians. In the second part we focus on applications of abelian varieties on cryptography and treating separately, elliptic curve cryptography, genus 2 and 3 cryptography, including Diffie-Hellman Key Exchange, index calculus in Picard groups, isogenies of Jacobians via correspondences and applications to discrete logarithms. Several open problems and new directions are suggested.
We resolve a significant controversy about how to understand and engineer single-shot all-optical switching of magnetization in ferrimagnets using femto- or picosecond-long heat pulses. By realistically modelling a generic ferrimagnet as two coupled macrospins, we comprehensively show that the net magnetization can be reversed via different pathways, using a heat pulse with duration spanning all relevant timescales within the non-adiabatic limit. This conceptual understanding is fully validated by experiments studying the material and optical limits at which the switching process in GdFeCo alloys loses its reliability. Our interpretation and results constitute a blueprint for understanding how deterministic all-optical switching can be achieved in alternative ferrimagnets using short thermal pulses.
In the optically thin regime, the intensity ratio of the two Si IV resonance lines (1394 and 1403 \AA\ ) are theoretically the same as the ratio of their oscillator strengths, which is exactly 2. Here, we study the ratio of the integrated intensity of the Si IV lines ($R=\int I_{1394}(\lambda)\mathrm{d}\lambda/\int I_{1403}(\lambda)\mathrm{d}\lambda$) and the ratio of intensity at each wavelength point ($r(\Delta\lambda)=I_{1394}(\Delta\lambda)/I_{1403}(\Delta\lambda)$) in two solar flares observed by the Interface Region Imaging Spectrograph. We find that at flare ribbons, the ratio $R$ ranges from 1.8 to 2.3 and would generally decrease when the ribbons sweep across the slit position. Besides, the distribution of $r(\Delta\lambda)$ shows a descending trend from the blue wing to the red wing. In loop cases, the Si IV line presents a wide profile with a central reversal. The ratio $R$ deviates little from 2, but the ratio $r(\Delta\lambda)$ can vary from 1.3 near the line center to greater than 2 in the line wings. Hence we conclude that in flare conditions, the ratio $r(\Delta\lambda)$ varies across the line, due to the variation of the opacity at the line center and line wings. We notice that, although the ratio $r(\Delta\lambda)$ could present a value which deviates from 2 as a result of the opacity effect near the line center, the ratio $R$ is still close to 2. Therefore, caution should be taken when using the ratio of the integrated intensity of the Si IV lines to diagnose the opacity effect.
In this article, we prove the existence of weak solutions as well as the existence and uniqueness of strong solutions for McKean-Vlasov multivalued stochastic differential equations with oblique subgradients (MVMSDEswOS, for short) by means of the equations of Euler type and Skorohod's representation theorem. For this type of equation, compared with the method in [19,13], since we can't use the maximal monotony property of its constituent subdifferential operator, some different specific techniques are applied to solve our problems. Afterwards, we give an example for MVMSDEswOS with time-dependent convex constraints, which can be reduced to MVMSDEswOS. Finally, we consider an optimal control problem and establish the dynamic programming principle for the value function.
It is shown that in an anisotropic harmonic trap that rotates with the properly chosen rotation rate, the force of gravity leads to a resonant behavior. Full analysis of the dynamics in an anisotropic, rotating trap in 3D is presented and several regions of stability are identified. On resonance, the oscillation amplitude of a single particle, or of the center of mass of a many-particle system (for example, BEC), grows linearly with time and all particles are expelled from the trap. The resonances can only occur when the rotation axis is tilted away from the vertical position. The positions of the resonances (there are always two of them) do not depend on the mass but only on the characteristic frequencies of the trap and on the direction of the angular velocity of rotation.
Field theory and gauge theory on noncommutative spaces have been established as their own areas of research in recent years. The hope prevails that a noncommutative gauge theory will deliver testable experimental predictions and will thus be a serious candidate for an extension of the Standard Model. This note contains the results for expanded gauge theory actions on a noncommutative space with constant theta, up to second order, together with a discussion of the ambiguities of the expanded theory and how they affect the action.
For a comprehensive characterization of mechanical reliability of metallization layers on polymer substrates both electrical and mechanical degradation should be taken into account. Although it is evident that cracking of a conductive film should lead to electrical degradation, the quantitative relationship between the growth of electric resistance and parameters of the induced crack pattern has remained thus far unexplored. With the help of finite element modelling we were able to find an explicit and concise expression which shows that electrical resistance grows with the fourth order of the crack length and second order of the areal crack density. The discovered relationship was verified by comparison with the experimental results of tensile testing of polymer-supported thin metal films. Presented model is independent of the length scale and can be applied to films with different thicknesses as long as Ohm's law is valid. It is demonstrated that linear crack density is an ambiguous parameter which does not properly capture the development of a crack pattern. For the unambiguous characterization of the intensity of a crack pattern a universal dimensionless factor is proposed. Presented results show that there is a wide range of possible crack patterns which do not lead to electrical failure of a conductive film that can be used for failure-free design of flexible electronic devices.
Using the optical reference geometry approach, we have derived in the following, a general expression for the ellipticity of a slowly rotating fluid configuration using Newtonian force balance equation in the conformally projected absolute 3-space, in the realm of general relativity. Further with the help of Hartle-Thorne (H-T) metric for a slowly rotating compact object, we have evaluated the centrifugal force acting on a fluid element and also evaluated the ellipticity and found that the centrifugal reversal occurs at around $R/R_s \approx 1.45$, and the ellipticity maximum at around $R/R_s \approx 2.75$. The result has been compared with that of Chandrasekhar and Miller which was obtained in the full 4-spacetime formalism.
We present the argument that the past limit of the Trautman-Bondi mass is the ADM mass under weak hypotheses on the decay of the metric towards spatial infinity, without any smallness conditions on the initial data, assuming well defined energy, momentum, center of mass and angular moment. Part of the proof consists of a careful inspection of the proof of stability of Minkowski space-time, which is sketched. This is complemented by an interior gluing result for asymptotically flat initial data with well defined Poincar\'e charges, which is proved in detail.
One method of discriminating between the many Type Ia progenitor scenarios is by searching for contaminating hydrogen and helium stripped from the companion star. We present several high-resolution 2-D numerical simulations of the impact of a Type Ia supernova explosion with hydrogen-rich main sequence, subgiant, and red giant companions. The binary parameters were chosen to represent several classes of single-degenerate Type Ia progenitor models that have been suggested in the literature. We use realistic stellar models and supernova debris profiles to represent each binary system. For each scenario, we explore the hydrodynamics of the supernova-secondary interaction, calculate the amount of stellar material stripped from the secondary and the kick delivered by the impact, and construct the velocity and solid angle distributions of the stripped material. After the impact, the main sequence star is puffed up, much like a pre-main sequence star. The subgiant companion behaves similarly. The secondary will not be contaminated by much supernova debris from the initial impact, but it may accrete low-velocity iron-group elements (or oxygen and silicon if the ejecta is radially mixed) at late times. A He pre-white dwarf will be left behind after a supernova explosion with a red giant companion.
The heavy quark drag and momentum diffusion coefficients in the presence of both the collisional and radiative processes have been studied in a hot viscous QCD medium. The thermal medium effects are incorporated by employing the effective fugacity quasiparticle model based on the lattice QCD equation of state. Viscous effects are embedded into the heavy quark transport through the near-equilibrium distribution functions of the constituent medium particles of the quark-gluon plasma. The viscous corrections to the momentum distributions have been estimated from the effective Boltzmann equation. The effect of shear viscous correction to drag and diffusion is investigated by considering the soft gluon radiation by heavy quarks along with the elastic collisional processes of the heavy quark with the light quarks and gluons within the QGP medium. The momentum and temperature dependence of the heavy quark transport coefficients are seen to be sensitive to the viscous coefficient of the QGP for the collisional and radiative processes. The collisional and radiative energy loss of the heavy quark in the viscous quark-gluon plasma has also been explored.
In this paper, we construct new families of flag-transitive linear spaces with $q^{2n}$ points and $q^{2}$ points on each line that admit a one-dimensional affine automorphism group. We achieve this by building a natural connection with permutation polynomials of $\mathbb{F}_{q^{2}}$ of a particular form and following the scheme of Pauley and Bamberg in [A construction of one-dimensional affine flag-transitive linear spaces, Finite Fields Appl. 14 (2008) 537-548].
I review the application of self-consistent Green's functions methods to study the properties of infinite nuclear systems. Improvements over the last decade, including the consistent treatment of three-nucleon forces and the development of extrapolation methods from finite to zero temperature, have allowed for realistic predictions of the equation of state of infinite symmetric, asymmetric and neutron matter based on chiral interactions. Microscopic properties, like momentum distributions or spectral functions, are also accessible. Using an indicative set of results based on a subset of chiral interactions, I summarise here the first-principles description of infinite nuclear system provided by Green's functions techniques, in the context of several issues of relevance for nuclear theory including, but not limited to, the role of short-range correlations in nuclear systems, nuclear phase transitions and the isospin dependence of nuclear observables.
The restrictions on the topology of nonsingular plane projective real algebraic curves of odd degree, obtained by O. Viro and the author in the paper published in the early 90s, are extended to flexible curves lying on an almost complex four-dimensional manifold. Some examples of real algebraic surfaces and real curves on them prove the sharpness of the obtained inequalities.   In addition, it is proved that a compact Lie group smooth action can be lifted to a cyclic branched covering space $ \tilde{X} $ over a closed four-dimensional manifold, and a sufficient condition for $ H_1(\tilde{X})=0 $ was found.
We consider the Radon transform along lines in an $n$ dimensional vector space over the two element field. It is well known that this transform is injective and highly overdetermined. We classify the minimal collections of lines for which the restricted Radon transform is also injective. This is an instance of I.M.~Gelfand's {\it admissibility problem}. The solution is in stark contrast to the more uniform cases of the affine hyperplane transform and the projective line transform, which are addressed in other papers, \cite{Feld-G,Gr1}. The presentation here is intended to be widely accessible, requiring minimum background.
Ion implantation is an interesting method to dope semiconducting materials such as zinc oxide provided that the implantation-induced defects can be subsequently removed. Nitrogen implantation followed by anneals under O2 were carried out on zinc oxide nanowires in the same conditions as in a previous study on bulk ZnO [J. Appl.Phys. 109, 023513 (2011)], allowing a direct comparison of the defect recovery mechanisms. Transmission electron microscopy and cathodoluminescence were carried out to assess the effects of nitrogen implantation and of subsequent anneals on the structural and optical properties of ZnO nanowires. Defect recovery is shown to be more effective in nanowires compared with bulk material due to the proximity of free surfaces. Nevertheless, the optical emission of implanted and annealed nanowires deteriorated compared to as-grown nanowires, as also observed for unimplanted and annealed nanowires. This is tentatively attributed to the dissociation of excitons in the space charge region induced by O2 adsorption on the nanowire surface.
The solution $\vartheta =(\vartheta_{t})_{t\geq 0}$ of a class of linear stochastic partial differential equations is approximated using Clark's robust representation approach (\cite{c}, \cite{cc}). The ensuing approximations are shown to coincide with the time marginals of solutions of a certain McKean-Vlasov type equation. We prove existence and uniqueness of the solution of the McKean-Vlasov equation. The result leads to a representation of $\vartheta $as a limit of empirical distributions of systems of equally weighted particles. In particular, the solution of the Zakai equation and that of the Kushner-Stratonovitch equation (the two main equations of nonlinear filtering) are shown to be approximated the empirical distribution of systems of particles that have equal weights (unlike those presented in \cite{kj1} and \cite{kj2}) and do not require additional correction procedures (such as those introduced in \cite{dan3}, \cite{dan4}, \cite{dmm}, etc).