ShantanuT01/DACTYL-Pretraining huggingface dataset:
We apply Renormalization Group (RG) techniques to Classical Information Theory, in the limit of large codeword size $n$. In particular, we apply RG techniques to (1) noiseless coding (i.e., a coding used for compression) and (2) noisy coding (i.e., a coding used for channel transmission). Shannon's "first" and "second" theorems refer to (1) and (2), respectively. Our RG technique uses composition class (CC) ideas, so we call our technique Composition Class Renormalization Group (CCRG). Often, CC's are called "types" instead of CC's, and their theory is referred to as the "Method of Types". For (1) and (2), we find that the probability of error can be expressed as an Error Function whose argument contains variables that obey renormalization group equations. We describe a computer program called WimpyRG-C1.0 that implements the ideas of this paper. C++ source code for WimpyRG-C1.0 is publicly available.
In the consistent histories formalism one specifies a family of histories as an exhaustive set of pairwise exclusive descriptions of the dynamics of a quantum system. We define branching families of histories, which strike a middle ground between the two available mathematically precise definitions of families of histories, viz., product families and Isham's history projector operator formalism. The former are too narrow for applications, and the latter's generality comes at a certain cost, barring an intuitive reading of the ``histories''. Branching families retain the intuitiveness of product families, they allow for the interpretation of a history's weight as a probability, and they allow one to distinguish two kinds of coarse-graining, leading to reconsidering the motivation for the consistency condition.
Inspired by the recent developments of constructing novel Dirac liquid boundary states of the $3d$ topological insulator, we propose one possible $2d$ boundary state of the $3d$ bosonic symmetry protected topological state with $U(1)_e \rtimes Z_2^T \times U(1)_s $ symmetry. This boundary theory is described by a $(2+1)d$ quantum electrodynamics (QED$_3$) with two flavors of Dirac fermions ($N_f = 2$) coupled with a noncompact U(1) gauge field: $ \mathcal{L} = \sum_{j = 1}^2 \bar{\psi}_j \gamma_\mu (\partial_\mu - i a_\mu) \psi_j - i A^{s}_\mu \bar{\psi_i} \gamma_\mu \tau^z_{ij} \psi_j + \frac{i}{2\pi} \epsilon_{\mu\nu\rho} a_\mu \partial_\nu A^{e}_\rho $, where $a_\mu$ is the internal noncompact U(1) gauge field, $A^s_\mu$ and $A^e_\mu$ are two external gauge fields that couple to $U(1)_s$ and $U(1)_e$ global symmetries respectively. We demonstrate that this theory has a "self-dual" structure, which is a fermionic analogue of the self-duality of the noncompact CP$^1$ theory with easy plane anisotropy. Under the self-duality, the boundary action takes exactly the same form except for an exchange between $A^s_\mu$ and $A^e_\mu$. The self-duality may still hold after we break one of the U(1) symmetries (which makes the system a bosonic topological insulator), with some subtleties that will be discussed.
We report on NICER observations of the Magnetar SGR~1935+2154, covering its 2020 burst storm and long-term persistent emission evolution up to $\sim90$ days post outburst. During the first 1120~seconds taken on April 28 00:40:58 UTC we detect over 217 bursts, corresponding to a burst rate of $>0.2$ bursts s$^{-1}$. Three hours later the rate is at 0.008 bursts s$^{-1}$, remaining at a comparatively low level thereafter. The $T_{90}$ burst duration distribution peaks at 840~ms; the distribution of waiting times to the next burst is fit with a log-normal with an average of 2.1 s. The 1-10 keV burst spectra are well fit by a blackbody, with an average temperature and area of $kT=1.7$ keV and $R^2=53$ km$^2$. The differential burst fluence distribution over $\sim3$ orders of magnitude is well modeled with a power-law form $dN/dF\propto F^{-1.5\pm0.1}$. The source persistent emission pulse profile is double-peaked hours after the burst storm. We find that the bursts peak arrival times follow a uniform distribution in pulse phase, though the fast radio burst associated with the source aligns in phase with the brighter peak. We measure the source spin-down from heavy-cadence observations covering days 21 to 39 post-outburst, $\dot\nu=-3.72(3)\times10^{-12}$ Hz s$^{-1}$; a factor 2.7 larger than the value measured after the 2014 outburst. Finally, the persistent emission flux and blackbody temperature decrease rapidly in the early stages of the outburst, reaching quiescence 40 days later, while the size of the emitting area remains unchanged.
It is proved that a general polyhedral perfect conducting obstacle in $\mathbb{R}^3$, possibly consisting of finitely many solid polyhedra, is uniquely determined by the far-field pattern corresponding to a single incident wave. This improves earlier results in the literature to the formally determined case.
In this paper, we briefly introduce the interests and the recent research activities on the \eta -mesic nuclei. We also mention the activities on the \eta ' (958)-mesic nucleus formation.
We examine the the emission from optically bright gamma-ray burst (GRB) afterglows as the Ultraviolet and Optical Telescope (UVOT) on the Neil Gehrels Swift Observatory first begins observing, following the slew to target the GRB, while the pointing of the Swift satellite is still settling. We verify the photometric quality of the UVOT settling data using bright stars in the field of view. In the majority of cases we find no problems with the settling exposure photometry, but in one case we excise the first second of the exposure to mitigate a spacecraft attitude reconstruction issue, and in a second case we exclude the first second of the exposure in which the UVOT photocathode voltage appears to be ramping up. Of a sample of 23 afterglows which have peak V magnitudes <16, we find that all are detected in the settling exposures, when Swift arrives on target. For 9 of the GRBs the UVOT settling exposure took place before the conclusion of the prompt gamma-ray emission. Five of these GRBs have well defined optical peaks after the settling exposures, with rises of >0.5 mag in their optical lightcurves, and there is a marginal trend for these GRBs to have long T90. Such a trend is expected for thick-shell afterglows, but the temporal indices of the optical rises and the timing of the optical peaks appear to rule out thick shells.
The persistent current in two vertically coupled quantum rings containing few electrons is studied. We find that the Coulomb interaction between the rings in the absence of tunneling affects the persistent current in each ring and the ground state configurations. Quantum tunneling between the rings alters significantly the ground state and the persistent current in the system.
PSR J2032+4127 is a radio-loud gamma-ray-emitting pulsar; it is orbiting around a high-mass Be type star with a very long orbital period of 25-50years, and is approaching periastron, which will occur in late 2017/early 2018. This system comprises with a young pulsar and a Be type star, which is similar to the so-called gamma-ray binary PSR~B1259-63/LS2883. It is expected therefore that PSR J2032+4127 shows an enhancement of high-energy emission caused by the interaction between the pulsar wind and Be wind/disk around periastron. Ho et al. recently reported a rapid increase in the X-ray flux from this system. In this paper, we also confirm a rapid increase in the X-ray flux along the orbit, while the GeV flux shows no significant change. We discuss the high-energy emissions from the shock caused by the pulsar wind and stellar wind interaction and examine the properties of the pulsar wind in this binary system. We argue that the rate of increase of the X-ray flux observed by Swift indicates (1) a variation of the momentum ratio of the two-wind interaction region along the orbit, or (2) an evolution of the magnetization parameter of the pulsar wind with the radial distance from the pulsar. We also discuss the pulsar wind/Be disk interaction at the periastron passage, and propose the possibility of formation of an accretion disk around the pulsar. We model high-energy emissions through the inverse-Compton scattering process of the cold-relativistic pulsar wind off soft photons from the accretion disk.
Computing endomorphism rings of supersingular elliptic curves is an important problem in computational number theory, and it is also closely connected to the security of some of the recently proposed isogeny-based cryptosystems. In this paper we give a new algorithm for computing the endomorphism ring of a supersingular elliptic curve $E$ that runs, under certain heuristics, in time $O((\log p)^2p^{1/2})$. The algorithm works by first finding two cycles of a certain form in the supersingular $\ell$-isogeny graph $G(p,\ell)$, generating an order $\Lambda \subseteq \operatorname{End}(E)$. Then all maximal orders containing $\Lambda$ are computed, extending work of Voight. The final step is to determine which of these maximal orders is the endomorphism ring. As part of the cycle finding algorithm, we give a lower bound on the set of all $j$-invariants $j$ that are adjacent to $j^p$ in $G(p,\ell)$, answering a question in arXiv:1909.07779.
For every number field $k$, we construct an affine algebraic surface $X$ over $k$ with a Zariski dense set of $k$-rational points, and a regular function $f$ on $X$ inducing an injective map $X(k)\to k$ on $k$-rational points. In fact, given any elliptic curve $E$ of positive rank over $k$, we can take $X=V\times V$ with $V$ a suitable affine open set of $E$. The method of proof combines value distribution theory for complex holomorphic maps with results of Faltings on rational points in sub-varieties of abelian varieties.
We consider the problem of optimizing signal transmission through multi-channel noisy devices. We investigate an array of bithreshold noisy devices which are connected in parallel and convergent on a summing center. Utilizing the concept of noise-induced linearization we derive an analytical approximation of the normalized power norm and clarify the relation between the optimum threshold and the standard deviation of noises. We show that the optimum threshold value is 0.63 times the standard deviation of the noises. This relation is applicable to both subthreshold and suprathreshold inputs.
The up-dated three-phase concept of nuclear matter evolution in course of cooling down - from the phase of quark-qluon plasma (QGP) through the intermediate phase allowing for massive constituent quarks (valons), pions and kaons (QPK) to the phase of hadronic matter (H) - is exploited for the treatment of relative hadronic yields in the central region of heavy ion collisions. The most attention is paid to the description of the QPK-phase which is argued to be a gaseous one and lasts until the valonic spacing approaches the confinement radius (at the temperature about 110 MeV), when the valons start fusing to be locked, in the end, within the hadrons. The hadronic yields emerged from thermal treatment of QPK-phase and simple combinatorial approach to the hadronization process are shown to fit the available experimental data from AGS, SPS and RHIC quite well. This provides an alternative insight into the real origin of the observed relative hadronic yields which is (to a considerable extent) free of the well known puzzle inherent in some conventional models where the early chemical freeze-out is assumed: namely, why the gaseous thermal approach to actually tightly packed (even overlapping) hadrons seems workable? Many predictions for the other hadronic yields which could be observed at these machines as well as at LHC are given.
In models of galaxy formation, feedback driven both by supernova (SN) and active galactic nucleus (AGN) is not efficient enough to quench star formation in massive galaxies. Models of smaller galaxies have suggested that cosmic rays (CRs) play a major role in expelling material from the star forming regions by diffusing SN energy to the lower density outskirts. We therefore run gas dynamical simulations of galactic outflows from a galaxy contained in a halo with $5\times10^{12}$~M$_{\odot}$ that resembles a local ultraluminous galaxy, including both SN thermal energy and a treatment of CRs using the same diffusion approximation as Salem & Bryan. We find that CR pressure drives a low-density bubble beyond the edge of the shell swept up by thermal pressure, but the main bubble driven by SN thermal pressure overtakes it later, which creates a large-scale biconical outflow. CRs diffusing into the disk are unable to entrain its gas in the outflows, yielding a mass-loading rate of only $\sim0.1~\%$ with varied CR diffusion coefficients. We find no significant difference in mass-loading rates in SN driven outflows with or without CR pressure. Our simulations strongly suggest that it is hard to drive a heavily mass-loaded outflow with CRs from a massive halo potential, although more distributed star formation could lead to a different result.
The perturbative approach to structure formation has recently received a lot of attention in the literature. In such setups the final predictions for observables like the power spectrum is often derived under additional approximations such as a simplified time dependence. Here we provide all-order perturbative integral solutions for density and velocity fields in generalized cosmologies, with a direct application to clustering quintessence. We go beyond the standard results based on extending the EdS-like approximations. As an illustrative example, we apply our findings to the calculation of the one-loop power spectrum of density and momentum fields. We find corrections close to $1\%$ in the mildly non-linear regime of $\Lambda$CDM cosmologies for the density power spectrum, while in the case of the density-momentum power spectrum effects can reach up to $1.5\%$ for $k\sim 0.2h/$Mpc.
In a previous work, it was shown that there is a curious problem with the benchmark ColorChecker dataset for illuminant estimation. To wit, this dataset has at least 3 different sets of ground-truths. Typically, for a single algorithm a single ground-truth is used. But then different algorithms, whose performance is measured with respect to different ground-truths, are compared against each other and then ranked. This makes no sense. We show in this paper that there are also errors in how each ground-truth set was calculated. As a result, all performance rankings based on the ColorChecker dataset - and there are scores of these - are inaccurate.   In this paper, we re-generate a new 'recommended' set of ground-truth based on the calculation methodology described by Shi and Funt. We then review the performance evaluation of a range of illuminant estimation algorithms. Compared with the legacy ground-truths, we find that the difference in how algorithms perform can be large, with many local rankings of algorithms being reversed.   Finally, we draw the readers attention to our new 'open' data repository which, we hope, will allow the ColorChecker set to be rehabilitated and once again to become a useful benchmark for illuminant estimation algorithms.
It has been proposed that a first-order phase transition driven to happen in the metastable region exhibits scaling and universality near an instability point controlled by an instability fixed point of a $\varphi^3$ theory. However, this fixed point has an imaginary value and the renormalization-group flow of the $\varphi^3$ coupling diverges at a finite scale. Here combining a momentum-space RG analysis and a nucleation theory near the spinodal point, we show that imaginary rather than real values are physical counter-intuitively and thus the imaginary fixed point does control the scaling.
The quasi-two-dimensional modeling of the small adiabatic perturbation on the background of the stationary configuration of the selfgravitating gas with the weak transverse nonhomogeneity approximation is presented. The space periodic character of the solution of this system is proofed.
We consider the (discrete) parabolic Anderson model $\partial u(t,x)/\partial t=\Delta u(t,x) +\xi_t(x) u(t,x)$, $t\geq 0$, $x\in \mathbb{Z}^d$, where the $\xi$-field is $\mathbb{R}$-valued and plays the role of a dynamic random environment, and $\Delta$ is the discrete Laplacian. We focus on the case in which $\xi$ is given by a properly rescaled symmetric simple exclusion process under which it converges to an Ornstein--Uhlenbeck process. Scaling the Laplacian diffusively and restricting ourselves to a torus, we show that in dimension $d=3$ upon considering a suitably renormalised version of the above equation, the sequence of solutions converges in law.   As a by-product of our main result we obtain precise asymptotics for the survival probability of a simple random walk that is killed at a scale dependent rate when meeting an exclusion particle. Our proof relies on the discrete theory of regularity structures of \cite{ErhardHairerRegularity} and on novel sharp estimates of joint cumulants of arbitrary large order for the exclusion process. We think that the latter is of independent interest and may find applications elsewhere.
A model is proposed to describe a transition from a charged black hole of mass $M$ and charge $Q$ to one of mass $\bar{M}$ and charge $\bar{Q}$. The basic equations are derived from the non-vacuum Einstein field equations sourced by the Coulomb field and by a null scalar field with a nonvanishing trace anomaly. It is shown that the nonvanishing trace of the energy-momentum tensor prevents the formation of a naked singularity.
Red Dwarfs (main-sequence / dwarf M or dM) stars are the most common stars in the Galaxy. These cool, faint, low mass stars comprise over 75% of all stars. Because of their low luminosities (~0.0008-0.06 of the Sun's luminosity), the circumstellar habitable zones (HZs) of dM stars are located within ~0.05-0.4 AU of the host star. Nevertheless, the prospect of life on a planet located within the HZ of a red dwarf is moderately high, based on the longevity of these stars (>50 Gyr), their constant luminosities and high space densities. Here we describe the aims and early results of the "Living with a Red Dwarf" Program - a study of dM stars that we have been carrying out over the last few years. The primary focus of our research on dM stars is the study of their magnetic dynamos and resulting star spots & coronal X-ray and chromospheric UV emissions as a function of age, rotation and spectral type. This program will provide datasets that can be used as inputs for the study of all aspects of dM stars, along with the planets already discovered hosted by them and the probable hundreds (thousands?) of planets expected to be uncovered in the near future by missions such as Kepler & Darwin/TPF. These datasets will be invaluable to those who model exo-planetary atmospheres, as well as exobiologists & astrobiologists who are studying the possibilities of life elsewhere in the universe. A significant element of our program is the determination of accurate stellar magnetic-driven X-ray-UV (X-UV) irradiances that are generated by the dM stars' vigorous magnetic dynamos. These X-UV irradiances (and flare frequencies) are strongly dependent on rotation, and thus age, and diminish as the stars lose angular momentum and spin-down over time via magnetic braking.
First principles simulation of x-ray photoemission spectroscopy (XPS) is an important tool in the challenging interpretation and assignment of XPS data of metal-organic interfaces. We investigate the origin of the disagreement between XPS simulation and experiment for the azulene molecule adsorbed on Ag(111). We systematically eliminate possible causes for this discrepancy, including errors in the structural model and finite size effects in periodic boundary conditions. By analysis of the electronic structure in the ground-state and the core-hole excited-state, we are able to trace the error back to artificial charge transfer between adsorbed molecule and metal surface. This is caused by the self-interaction error of common exchange-correlation functionals. This error is not remedied by standard hybrid or range-separated hybrid functionals. We employ an ad hoc self-interaction error correction based on molecular orbital projection, that exposes this issue and is able to recover the correct experimental behaviour. The charge transfer artefact also negatively affects the prediction of X-ray absorption spectra for this system. Both the simulated photoemisson and x-ray absorption spectra show a better agreement with experimental data, once the ad hoc correction is employed. Similar core-hole-induced charge artefacts may affect core-level simulations at metal-organic interfaces more generally.
Using far-infrared 240 micron and near-infrared K band data from the COBE/DIRBE instrument, we model the Galactic stellar and dust distribution. Making the assumption that the Galaxy is transparent in the 240 micron band, the dust emission is modeled using the following components: a warped exponential disk of scale length 0.26 R_sun, a spiral arm component as mapped by HII regions, and a feature coinciding with the local (Orion) arm. The dust distribution is used to calculate absorption in the K band, and the stellar emission is likewise modeled with a warped exponential disk, with a scale length of 0.29 R_sun, and a spiral arm component. Models of the K band emission in the Galactic plane indicate that in this waveband a two arm spiral dominates the nonaxisymmetric emission. The warp is evident in both the dust and stellar component, and is found to start within the Solar Circle.
Using some ideas of Modern Kaluza-Klein theory, we examine the evolution of entropy on a 4D Friedmann-Robertson-Walker (FRW) brane from a 5D vacuum state, which is defined on a 5D background Riemann-flat metric. We found that entropy production is sufficiently important during inflation: $S > 10^{90}$, for all the initial values of temperature $T_0 < T_{GU}$.
Quantum interference of helicity amplitudes provides a powerful tool for measuring the spins of new particles. By looking at the azimuthal angular dependence of the differential cross-section in the production followed by decay of a new particle species one can determine its spin by looking at the various cosine modes. The heavy spin-2 Kaluza-Klein (KK) graviton provides a unique signature with a $\cos{(4 \phi)}$ mode. We study the feasibility of this approach to measuring the spin of the KK graviton in the Randall-Sundrum Model at the LHC.
We describe the geometry of the leading singularity locus of the traintrack integral family directly in momentum twistor space. For the two-loop case, known as the elliptic double box, the leading singularity locus is a genus one curve, which we obtain as an intersection of two quadrics in $\mathbb{P}^{3}$. At three loops, we obtain a K3 surface which arises as a branched surface over two genus-one curves in $\mathbb{P}^{1} \times \mathbb{P}^{1}$. We present an analysis of its properties. We also discuss the geometry at higher loops and the supersymmetrization of the construction.
We use a "monodromy" argument to derive new expressions for the ${\bm Z}_2$ invariants of topological insulators with time-reversal symmetry in 2 and 3 dimensions. The derivations and the final expressions do not require any gauge choice and the calculation of the invariants is based entirely on the projectors onto the occupied states. Explicit numerical tests for tight-binding models with strongly broken inversion symmetry are presented in 2 and 3-dimensions.