ShantanuT01/DACTYL-Pretraining huggingface dataset:
We model the acceleration of electrons at a shock front in a relativistic blazar jet and compute the radiation they emit in a post-shock region which contains a homogeneous magnetic field. The full space, time and momentum dependence of the electron distribution is used in this calculation. It is shown that the "homogeneous" synchrotron model is recovered, provided the downstream speed of the plasma away from the shock front is nonrelativistic, and provided that the light travel times across the face of the shock front is unimportant. By varying the rate at which particles are picked up by the acceleration process, we calculate the time-dependence of the spectra. Since the magnetic field strength is assumed constant within the emission region, each frequency band can be identified with electrons of a particular energy. We find that for a band in which the electrons are accelerated rapidly compared to the rate at which they cool, the spectra typically harden during phases of rising flux, and soften during phases of falling flux, as has been observed in the objects PKS 2155-304 and Mkn 421. However, in a frequency band in which the timescales are comparable, the reverse behaviour is to be expected. We discuss the extent to which observations of both the stationary spectrum and the spectral variability of the synchrotron component of blazar emission can be used to constrain the model.
In this paper, we prove the strong unique continuation property at the origin for solutions of the following scaling critical parabolic differential inequality   \[   |\operatorname{div} (A(x,t) \nabla u) - u_t| \leq \frac{M}{|x|^{2}} |u|,\ \ \ \   \]   where the coefficient matrix $A$ is Lipschitz continuous in $x$ and $t$. Our main result sharpens a previous one of Vessella concerned with the subcritical case as well as extends a recent result of one of us with Garofalo and Manna for the heat operator.
Within the framework of exact quantum electrodynamics in dispersing and absorbing media, we have studied the emission from an initially in the upper state prepared emitter in a high quality cavity in the case, when there are two cavity modes that resonantly interact with the emitter. In particular, when one of the modes is in resonance with the emitter transition and the other mode is tuned to the frequency equal to the Rabi splitting of the first mode, the effect of Rabi resonance is observed.
Let k be a field. In this paper, we find necessary and sufficient conditions for a noncommutative curve of genus zero over k to be a noncommutative P^1-bundle. This result can be considered a noncommutative, one-dimensional version of Tsen's theorem. By specializing this theorem, we show that every arithmetic noncommutative projective line is a noncommutative curve, and conversely we characterize exactly those noncommutative curves of genus zero which are arithmetic. We then use this characterization, together with results regarding arithmetic noncommutative projective lines, to address some problems posed by D. Kussin.
A $k$-orbit maniplex is one that has $k$ orbits of flags under the action of its automorphism group. In this paper we extend the notion of symmetry type graphs of maps to that of maniplexes and polytopes and make use of them to study $k$-orbit maniplexes, as well as fully-transitive 3-maniplexes. In particular, we show that there are no fully-transtive $k$-orbit 3-mainplexes with $k > 1$ an odd number, we classify 3-orbit mainplexes and determine all face transitivities for 3- and 4-orbit maniplexes. Moreover, we give generators of the automorphism group of a polytope or a maniplex, given its symmetry type graph. Finally, we extend these notions to oriented polytopes, in particular we classify oriented 2-orbit maniplexes and give generators for their orientation preserving automorphism group.
Motivated by the recent experimental observations of the DNA loop extrusion by protein motors, in this paper we investigate the statistical properties of the growing polymer loops within the ideal chain model. The loop conformation is characterized statistically by the mean gyration radius and the pairwise contact probabilities. It turns out that a single dimensionless parameter, which is given by the ratio of the loop relaxation time over the time elapsed since the start of extrusion, controls the crossover between near-equilibrium and highly non-equilibrium asymptotics in statistics of the extruded loop. Besides, we show that two-sided and one-sided loop extruding motors produce the loops with almost identical properties. Our predictions are based on two rigorous semi-analytical methods accompanied by asymptotic analysis of slow and fast extrusion limits.
We discuss 3D simulations of relativistic collisionless shocks in electron-positron pair plasmas using the particle-in-cell (PIC) method. The shock structure is mainly controlled by the shock's magnetization ("sigma" parameter). We demonstrate how the structure of the shock varies as a function of sigma for perpendicular shocks. At low magnetizations the shock is mediated mainly by the Weibel instability which generates transient magnetic fields that can exceed the initial field. At larger magnetizations the shock is dominated by magnetic reflections. We demonstrate where the transition occurs and argue that it is impossible to have very low magnetization collisionless shocks in nature (in more than one spatial dimension). We further discuss the acceleration properties of these shocks, and show that higher magnetization perpendicular shocks do not efficiently accelerate nonthermal particles in 3D. Among other astrophysical applications, this may pose a restriction on the structure and composition of gamma-ray bursts and pulsar wind outflows.
This paper reports the results of a survey of Doppler shift oscillations measured during solar flares in emission lines of S XV and Ca XIX with the Bragg Crystal Spectrometer (BCS) on Yohkoh. Data from 20 flares that show oscillatory behavior in the measured Doppler shifts have been fitted to determine the properties of the oscillations. Results from both BCS channels show average oscillation periods of 5.5 +/- 2.7 minutes, decay times of 5.0 +/-2.5 minutes, amplitudes of 17.1 +/- 17.0 km/s, and inferred displacements of 1070 +/- 1710 km, where the listed errors are the standard deviations of the sample means. For some of the flares, intensity fluctuations are also observed. These lag the Doppler shift oscillations by 1/4 period, strongly suggesting that the oscillations are standing slow mode waves. The relationship between the oscillation period and the decay time is consistent with conductive damping of the oscillations.
We prove a boundedness result for klt pairs $(X,B)$ such that $K_X+B\equiv 0$ and $B$ is big. As a consequence we obtain a positive answer to the Effective Iitaka Fibration Conjecture for klt pairs with big boundary.
Strong gravitational lensing by galaxy clusters has become a powerful tool for probing the high-redshift Universe, magnifying distant and faint background galaxies. Reliable strong lensing (SL) models are crucial for determining the intrinsic properties of distant, magnified sources and for constructing their luminosity function. We present here the first SL analysis of MACS J0308.9+2645 and PLCK G171.9-40.7, two massive galaxy clusters imaged with the Hubble Space Telescope in the framework of the Reionization Lensing Cluster Survey (RELICS). We use the Light-Traces-Mass modeling technique to uncover sets of multiply imaged galaxies and constrain the mass distribution of the clusters. Our SL analysis reveals that both clusters have particularly large Einstein radii ($\theta_E>30"$ for a source redshift of $z_s=2$), providing fairly large areas with high magnifications, useful for high-redshift galaxy searches ($\sim2$ arcmin$^{2}$ with $\mu>5$ to $\sim1$ arcmin$^{2}$ with $\mu>10$, similar to a typical \textit{Hubble Frontier Fields} cluster). We also find that MACS J0308.9+2645 hosts a promising, apparently bright (J$\sim23.2-24.6$ AB), multiply imaged high-redshift candidate at $z\sim6.4$. These images are amongst the brightest high-redshift candidates found in RELICS. Our mass models, including magnification maps, are made publicly available for the community through the Mikulski Archive for Space Telescopes.
We use high-resolution relativistic MHD simulations coupled with a radiative transfer code to compute multiwavelength afterglow light curves of magnetized ejecta of gamma-ray bursts interacting with a uniform circumburst medium. The aim of our study is to determine how the magnetization of the ejecta at large distance from the central engine influences the afterglow emission, and to assess whether observations can be reliably used to infer the strength of the magnetic field. We find that, for typical parameters of the ejecta, the emission from the reverse shock peaks for magnetization $\sigma_0 \sim 0.01 - 0.1$ of the flow, and that it is greatly suppressed for higher $\sigma_0$. The emission from the forward shock shows an achromatic break shortly after the end of the burst marking the onset of the self-similar evolution of the blast wave. Fitting the early afterglow of GRB 990123 and 090102 with our numerical models we infer respective magnetizations of $\sigma_0 \sim 0.01$ and $\sigma_0 \sim 0.1$ for these bursts. We argue that the lack of observed reverse shock emission from the majority of the bursts can be understood if $\sigma_0 \simmore 0.1$, since we obtain that the luminosity of the reverse shock decreases significantly for $\sigma_0 \sim 1$. For ejecta with $\sigma_0 \simmore 0.1$ our models predict that there is sufficient energy left in the magnetic field, at least during an interval of ~10 times the burst duration, to produce a substantial emission if the magnetic energy can be dissipated (for instance, due to resistive effects) and radiated away.
Motivated by the flavored Peccei-Quinn symmetry for unifying the flavor physics and string theory, we construct an explicit model by introducing a $U(1)$ symmetry such that the $U(1)_X$-$[gravity]^2$ anomaly-free condition together with the standard model flavor structure demands additional sterile neutrinos as well as no axionic domain-wall problem. Such additional sterile neutrinos play the role of a realization of baryogenesis via a new Affleck-Dine leptogenesis. We provide grounds for that the $U(1)_X$ symmetry could be interpreted as a fundamental symmetry of nature. The model will resolve rather recent, but fast-growing issues in astro-particle physics, including leptonic mixings and CP violation in neutrino oscillation, high-energy neutrinos, QCD axion, and axion cooling of stars. The QCD axion decay constant, through its connection to the astrophysical constraints of stellar evolution and the SM fermion masses, is shown to be fixed at $F_A=1.30^{+0.66}_{-0.54}\times10^{9}$ GeV (consequently, its mass is $m_a=4.34^{+3.37}_{-1.49}$ meV and axion-photon coupling is $|g_{a\gamma\gamma}|=1.30^{+1.01}_{-0.45}\times10^{-12}\,{\rm GeV}^{-1}$). Interestingly enough, we show that neutrino oscillations at low energies could be connected to astronomical-scale baseline neutrino oscillations. The model predicts non-observational neutrinoless double beta ($0\nu\beta\beta$) decay rate as well as a remarkable pattern between leptonic Dirac CP phase ($\delta_{CP}$) and atmospheric mixing angle ($\theta_{23}$); {\it e.g.} $\delta_{CP}\simeq220^{\circ}-240^{\circ}$, $120^{\circ}-140^{\circ}$ for $\theta_{23}=42.3^{\circ}$ for normal mass ordering, and $\delta_{CP}\simeq283^{\circ},250^{\circ},100^{\circ},70^{\circ}$ for $\theta_{23}=49.5^{\circ}$ for inverted one.
An analytical expression for the third coefficient of the Jones Polynomial $P_J[\gamma,\, {\em e}^q]$ in the variable $q$ is reported. Applications of the result in Quantum Gravity are considered.
Motivated by recent experiments on rotating Bose-Einstein condensates, we investigate a rotating, polarized Fermi gas trapped in an anharmonic potential. We apply a semiclassical expansion of the density of states in order to determine how the thermodynamic properties depend on the rotation frequency. The accuracy of the semiclassical approximation is tested and shown to be sufficient for describing typical experiments. At zero temperature, rotating the gas above a given frequency $\Omega_{\rm DO}$ leads to a `donut'-shaped cloud which is analogous to the hole found in two-dimensional Bose-Einstein condensates. The free expansion of the gas after suddenly turning off the trap is considered and characterized by the time and rotation frequency dependence of the aspect ratio. Temperature effects are also taken into account and both low- and high-temperature expansions are presented for the relevant thermodynamical quantities. In the high-temperature regime a virial theorem approach is used to study the delicate interplay between rotation and anharmonicity.
We define the center of mass and spin of an isolated system in General Relativity. The resulting relationships between these variables and the total linear and angular momentum of the gravitational system are remarkably similar to their Newtonian counterparts, though only variables at the null boundary of an asymptotically flat spacetime are used for their definition. We also derive equations of motion linking their time evolution to the emitted gravitational radiation. The results are then compared to other approaches. In particular one obtains unexpected similarities as well as some differences with results obtained in the Post Newtonian literature . These equations of motion should be useful when describing the radiation emitted by compact sources such as coalescing binaries capable of producing gravitational kicks, supernovas, or scattering of compact objects.
We analyze numerically the out-of-equilibrium relaxation dynamics of a long-range Hamiltonian system of $N$ fully coupled rotators. For a particular family of initial conditions, this system is known to enter a particular regime in which the dynamic behavior does not agree with thermodynamic predictions. Moreover, there is evidence that in the thermodynamic limit, when $N\to \infty$ is taken prior to $t\to \infty$, the system will never attain true equilibrium. By analyzing the scaling properties of the two-time autocorrelation function we find that, in that regime, a very complex dynamics unfolds in which {\em aging} phenomena appear. The scaling law strongly suggests that the system behaves in a complex way, relaxing towards equilibrium through intricate trajectories. The present results are obtained for conservative dynamics, where there is no thermal bath in contact with the system. This is the first time that aging is observed in such Hamiltonian systems.
We develop a time dependent random matrix theory describing the influence of a time-dependent perturbation on mesoscopic conductance fluctuations in open quantum dots. The effect of external field is taken into account to all orders of perturbation theory, and our results are applicable to both weak and strong fields. We obtain temperature and magnetic field dependences of conductance fluctuations. The amplitude of conductance fluctuations is determined by electron temperature in the leads rather than by the width of electron distribution function in the dot. The asymmetry of conductance with respect to inversion of applied magnetic field is the main feature allowing to distinguish the effect of direct suppression of quantum interference from the simple heating if the frequency of external radiation is larger than the temperature of the leads $\hbar\omega \gg T$.
In this note, we give a formulation of log structures for derived stacks using Olsson's log stack. The derived cotangent complex is then Olsson's logarithmic cotangent complex, which (unlike Gabber's) is just given by log differential forms in the log smooth case. The derived moduli stack of log stable maps then produces the desired virtual tangent space and obstruction theory on the underlying underived stack.
Estimating depth from RGB images can facilitate many computer vision tasks, such as indoor localization, height estimation, and simultaneous localization and mapping (SLAM). Recently, monocular depth estimation has obtained great progress owing to the rapid development of deep learning techniques. They surpass traditional machine learning-based methods by a large margin in terms of accuracy and speed. Despite the rapid progress in this topic, there are lacking of a comprehensive review, which is needed to summarize the current progress and provide the future directions. In this survey, we first introduce the datasets for depth estimation, and then give a comprehensive introduction of the methods from three perspectives: supervised learning-based methods, unsupervised learning-based methods, and sparse samples guidance-based methods. In addition, downstream applications that benefit from the progress have also been illustrated. Finally, we point out the future directions and conclude the paper.
Detailed imaging and spectroscopic analysis of the centers of nearby S0 and spiral galaxies shows the existence of "composite bulges", where both classical bulges and disky pseudobulges coexist in the same galaxy. As part of a search for supermassive black holes in nearby galaxy nuclei, we obtained VLT-SINFONI observations in adaptive-optics mode of several of these galaxies. Schwarzschild dynamical modeling enables us to disentangle the stellar orbital structure of the different central components, and to distinguish the differing contributions of kinematically hot (classical bulge) and kinematically cool (pseudobulge) components in the same galaxy.
Simultaneous neutron-scattering and thermal expansion measurements on the heavy-fermion superconductor URu2Si2 under hydrostatic pressure of 0.67 GPa have been performed in order to detect the successive paramagnetic, hidden order, and large moment antiferromagnetic phases on cooling. The temperature dependence of the sharp low energy excitation at the wavevector Q_0=(100) shows that this excitation is clearly a signature of the hidden order state. In the antiferromagnetic phase, this collective mode disappears. The higher energy excitation at the incommensurate wavevector Q_1=(1.4,0,0) persists in the antiferromagnetic phase but increases in energy. The collapse of the inelastic neutron scattering at Q_0 coincides with the previous observation of the disappearance of superconductivity.
Model learning from class imbalanced training data is a long-standing and significant challenge for machine learning. In particular, existing deep learning methods consider mostly either class balanced data or moderately imbalanced data in model training, and ignore the challenge of learning from significantly imbalanced training data. To address this problem, we formulate a class imbalanced deep learning model based on batch-wise incremental minority (sparsely sampled) class rectification by hard sample mining in majority (frequently sampled) classes during model training. This model is designed to minimise the dominant effect of majority classes by discovering sparsely sampled boundaries of minority classes in an iterative batch-wise learning process. To that end, we introduce a Class Rectification Loss (CRL) function that can be deployed readily in deep network architectures. Extensive experimental evaluations are conducted on three imbalanced person attribute benchmark datasets (CelebA, X-Domain, DeepFashion) and one balanced object category benchmark dataset (CIFAR-100). These experimental results demonstrate the performance advantages and model scalability of the proposed batch-wise incremental minority class rectification model over the existing state-of-the-art models for addressing the problem of imbalanced data learning.
The electronic structures of four semiconductor compounds BaCu2S2, BaCu2Se2, BaAg2S2, and BaAg2Se2 are studied by density functional theory using both semi-local and hybrid functionals. The ionization energies and electron affinities were determined by aligning the electronic states with the vacuum level by calculating the electrostatic profile within a supercell slab model. The ionization energy and electron affinity of the compounds were calculated using the Heyd-Scuseria-Ernzerhof (HSE) functionals and range from 4.5 to 5.4 eV and 3.1 to 3.4 eV, respectively. The replacement of Cu by Ag slightly increases the ionization energy and electron affinity, while the replacement of S by Se decreases the ionization energy but slightly increases the electron affinity. Overall, the low ionization energies and small electron affinities suggest that these compounds possess good p-type doping propensities. The band gaps are somewhat small to be ideal candidates for transparent semiconducting behavior. The replacement of Cu with Ag in the barium sulfide compounds can increase the band gap from 1.62 eV to 2.01 eV.
In this review we focus on electronic transport through semiconductor nanostructures which are driven by ac fields. Along the review we describe the available experimental information on different nanostructures, like resonant tunneling diodes, superlattices or quantum dots, together with the theoretical tools needed to describe the observed features. These theoretical tools such as, for instance, the Floquet formalism, the non-equilibrium Green's function technique or the density matrix technique, are suitable for tackling with photon-assisted transport problems where the interplay of different aspects like nonequilibrium, nonlinearity, quantum confinement or electron-electron interactions gives rise to many intriguing new phenomena. Along the review we give many examples which demonstrate the possibility of using appropriate ac fields to control/manipulate coherent quantum states in semiconductor nanostructures.
We evaluate the non-equilibrium single particle Green's functions in the steady state of the interacting resonant level model (IRLM) under the effect of an applied bias voltage. Employing the so-called auxiliary master equation approach, we present accurate nonperturbative results for the non-equilibrium spectral and effective distribution functions, as well as for the current-voltage characteristics. We find a drastic change of these spectral properties between the regimes of low and high bias voltages and discuss the relation of these changes to the negative differential conductance (NDC), a prominent feature in the non-equilibrium IRLM. The anomalous evolution of the distribution function next to the impurity shown by our calculations suggests a mechanism whereby the impurity gets effectively decoupled from the leads at voltages where the NDC sets in, in agreement with previous renormalization group approaches. This scenario is qualitatively confirmed by a Hartree-Fock treatment of the model.
Let $G$ be a cubic graph which has a decomposition into a spanning tree $T$ and a $2$-regular subgraph $C$, i.e. $E(T) \cup E(C) = E(G)$ and $E(T) \cap E(C) = \emptyset$. We provide an answer to the following question: which lengths can the cycles of $C$ have if $G$ is a snark? Note that $T$ is a hist (i.e. a spanning tree without a vertex of degree two) and that every cubic graph with a hist has the above decomposition.
We show that certain linear elliptic equations (and systems) in divergence form with almost periodic coefficients have bounded, almost periodic correctors. This is proved under a new condition we introduce which quantifies the almost periodic assumption and includes (but is not restricted to) the class of smooth, quasiperiodic coefficient fields which satisfy a Diophantine-type condition previously considered by Kozlov. The proof is based on a quantitative ergodic theorem for almost periodic functions combined with the new regularity theory recently introduced by the first author and Shen for equations with almost periodic coefficients. This yields control on spatial averages of the gradient of the corrector, which is converted into estimates on the size of the corrector itself via a multiscale Poincar\'e-type inequality.