ShantanuT01/DACTYL-Pretraining huggingface dataset:
Scalar conservation laws with non-convex fluxes have shock wave solutions that violate the Lax entropy condition. In this paper, such solutions are selected by showing that some of them have corresponding traveling waves for the equation supplemented with dissipative and dispersive higher-order terms. For a cubic flux, traveling waves can be calculated explicitly for linear dissipative and dispersive terms. Information about their existence can be used to solve the Riemann problem, in which we find solutions for some data that are different from the classical Lax-Oleinik construction. We consider dispersive terms of a BBM type and show that the calculation of traveling waves is somewhat more intricate than for a KdV-type dispersion. The explicit calculation is based upon the calculation of parabolic invariant manifolds for the associated ODE describing traveling waves. The results extend to the p-system of one-dimensional elasticity with a cubic stress-strain law.
We present the main results on the energy spectrum and composition of the highest energy cosmic rays of energy exceeding 10$^{18}$ eV obtained by the High Resolution Fly's Eye and the Southern Auger Observatory. The current results are somewhat contradictory and raise interesting questions about the origin and character of these particles.
The known solutions to the zero-sound dispersion equation are considered as placed on the physical and unphysical sheets in the complex plane of frequency.
We continue the study by Melo and Winter [arXiv:1712.01763, 2017] on the possible intersection sizes of a $k$-dimensional subspace with the vertices of the $n$-dimensional hypercube in Euclidean space. Melo and Winter conjectured that all intersection sizes larger than $2^{k-1}$ (the "large" sizes) are of the form $2^{k-1}+2^i$. We show that this is almost true: the large intersection sizes are either of this form or of the form $35\cdot 2^{k-6}$. We also disprove a second conjecture of Melo and Winter by proving that a positive fraction of the "small" values is missing.
It is well-known that the space group selection rule constrains the interactions of closed strings on orbifolds. For some examples, this rule has been described by an effective Abelian symmetry that combines with a permutation symmetry to a non-Abelian flavor symmetry like $D_4$ or $\Delta(54)$. However, the general case of the effective Abelian symmetries was not yet fully understood. In this work, we formalize the computation of the Abelian symmetry that results from the space group selection rule by imposing two conditions only: (i) well-defined discrete charges and (ii) their conservation. The resulting symmetry, which we call the space group flavor symmetry $D_S$, is uniquely specified by the Abelianization of the space group. For all Abelian orbifolds with $N=1$ supersymmetry we compute $D_S$ and identify new cases, for example, where $D_S$ contains a $Z_2$ dark matter-parity with charges 0 and 1 for massless and massive strings, respectively.
L\'evy walks represent a class of stochastic models (space-time coupled continuous time random walks) with applications ranging from the laser cooling to the description of animal motion. The initial model was intended for the description of turbulent dispersion as given by the Richardson's law. The existence of this Richardson's regime in the original model was recently challenged in the work by T. Albers and G. Radons, Phys. Rev. Lett. 120, 104501 (2018): the mean squared displacement (MSD) in this model diverges, i.e. does not exist, in the regime, where it presumably should reproduce the Richardson's law. In the supplemental material to this work the authors present (but do not investigate in detail) a generalized model interpolating between the original one and the Drude-like models known to show no divergences. In the present work we give a detailed investigation of the ensemble MSD in this generalized model, show that the behavior of the MSD in this model is the same (up to prefactiors) as in the original one in the domains where the MSD in the original model does exist, and investigate the conditions under which the MSD in the generalized model does exist or diverges. Both ordinary and aged situations are considered.
We define matrix groups $FG_n(P)$ for each natural number $n$ and finite set of primes $P$, such that every rational-valued upper triangular matrix group is a (possibly distorted) subgroup. Brofferio and Schapira [Brofferio2011poisson], described the \PF boundary of $GL_n (\mathbb{Q})$ for measures of finite first moment with respect to adelic length. We show that adelic length is a word metric estimate on $FG_n(P)$ by constructing another, intermediate, word metric estimate which can be easily computed from the entries of any matrix in the group. In particular, finite first moment of a probability measure with respect to adelic length is an equivalent condition to requiring finite first moment with respect to word length in $FG_n(P)$.   We also investigate random walks in the case that $P$ is a length one sequence. Conditions for pointwise convergence in $\mathbb{R}$ or $\mathbb{Q}_p$ are given. When these conditions are satisfied, we give path estimates from boundary points, discuss boundary triviality, show that the resulting space is a $\mu$-boundary and give cases where the $\mu$-boundary is the \PF boundary, as conjectured by Kaimanovich.
In the present work we study how the standard homogenization commutator, a random field that plays a central role in the theory of fluctuations, quantitatively decorrelates on large scales.
The renormalization-group properties of transverse-momentum dependent parton distribution functions in the light-cone gauge with the Mandelstam-Leibbrandt prescription for the gluon propagator are addressed. An expression for the transverse component of the gauge field at light-cone infinity, which plays a crucial role in the description of the final-/initial-state interactions in the light-cone axial gauge, is obtained. The leading-order anomalous dimension is calculated in this gauge and the relation to the results obtained in other gauges is worked out. It is shown that, using the Mandelstam-Leibbrandt prescription, the ensuing anomalous dimension does not receive contributions from extra rapidity divergences related to a cusped junction point of the Wilson lines.
We present and perform a detailed analysis of multi-wavelength observations of \thisgrb, an optical bright GRB with an observed reverse shock (RS) signature. Observations of this GRB were acquired with the BOOTES-4 robotic telescope, the \fermi, and the \swift missions. Time-resolved spectroscopy of the prompt emission shows that changes to the peak energy (\Ep) tracks intensity and the low-energy spectral index seems to follow the intensity for the first episode, whereas this tracking behavior is less clear during the second episode. The fit to the afterglow light curves shows that the early optical afterglow can be described with RS emission and is consistent with the thin shell scenario of the constant ambient medium. The late time afterglow decay is also consistent with the prediction of the external forward shock (FS) model. We determine the properties of the shocks, Lorentz factor, magnetization parameters, and ambient density of \thisgrb, and compare these parameters with another 12 GRBs, consistent with having RS produced by thin shells in an ISM-like medium. The value of the magnetization parameter ($R_{\rm B} \approx 18$) indicates a moderately magnetized baryonic dominant jet composition for \thisgrb. We also report the host galaxy photometric observations of \thisgrb obtained with 10.4m GTC, 3.5m CAHA, and 3.6m DOT telescopes and find the host (photo $z$ = $2.8^{+0.7}_{-0.9}$) to be a high mass, star-forming galaxy with a star formation rate of $20 \pm 10 \msun$ $\rm yr^{-1}$.
Let $\mathcal{P}(n)$ denote the power set of $[n]$, ordered by inclusion, and let $\mathcal{P}(n,p)$ be obtained from $\mathcal{P}(n)$ by selecting elements from $\mathcal{P}(n)$ independently at random with probability $p$. A classical result of Sperner asserts that every antichain in $\mathcal{P}(n)$ has size at most that of the middle layer, $\binom{n}{\lfloor n/2 \rfloor}$. In this note we prove an analogous result for $\mathcal{P} (n,p)$: If $pn \rightarrow \infty$ then, with high probability, the size of the largest antichain in $\mathcal{P}(n,p)$ is at most $(1+o(1)) p \binom{n}{\lfloor n/2 \rfloor}$. This solves a conjecture of Osthus who proved the result in the case when $pn/\log n \rightarrow \infty$. Our condition on $p$ is best-possible. In fact, we prove a more general result giving an upper bound on the size of the largest antichain for a wider range of values of $p$.
We construct the transversal and longitudinal 4-vector potentials and strengths F^{\mu\nu} in the momentum representation on using the second-type 4-spinors recently proposed by Ahluwalia. Questions of relevance of this kind of theories to the correct photon statistics are briefly discussed.
Various features of the mass yields in heavy ion collisions are studied. The mass yields are discussed in terms of iterative one dimensional discrete maps. These maps are shown to produce orbits for a monomer or for a nucleus which generate the mass yields and the distribution of cluster sizes. Simple Malthusian dynamics and non-linear Verhulst dynamics are used to illustrate the approach. Nuclear cobwebbing, attractors of the dynamics, and Lyapanov exponents are discussed for the mass distribution. The self-similar property of the Malthusian orbit offers a new variable for the study of scale invariance using power moments of the mass distribution. Correlation lengths, exponents and dimensions associated with scaling relations are developed. Fourier transforms of the mass distribution are used to obtain power spectra which are investigated for a $1/f^{\beta}$ behavior.
An antiferromagnetic Hund coupling in multiorbital Hubbard systems induces orbital freezing and an associated superconducting instability, as well as unique composite orders in the case of an odd number of orbitals. While the rich phase diagram of the half-filled three-orbital model has recently been explored in detail, the properties of the doped system remain to be clarified. Here, we complement the previous studies by computing the entropy of the half-filled model, which exhibits an increase in the orbital-frozen region, and a suppression in the composite ordered phase. The doping dependent phase diagram shows that the composite ordered state can be stabilized in the doped Mott regime, if conventional electronic orders are suppressed by frustration. While antiferro orbital order dominates the filling range $2\lesssim n \le 3$, and ferro orbital order the strongly interacting region for $1\lesssim n < 2$, we find superconductivity with a remarkably high $T_c$ around $n=1.5$ (quarter filling). Also in the doped system, there is a close connection between the orbital freezing crossover and superconductivity.
We examined the temperature (T) evolution of the optical conductivity spectra of Sr$_3$Ir$_2$O$_7$ over a wide range of 10-400 K. The system was barely insulating, exhibiting a small indirect bandgap of $\sim$0.1 eV. The low-energy features of the optical d-d excitation (${\hbar}{\omega}$ $<$ 0.3 eV) evolved drastically, whereas such evolution was not observed for the O K-edge X-ray absorption spectra. This suggests that the T evolution in optical spectra is not caused by a change in the bare (undressed) electronic structure, but instead, presumably originates from an abundance of phonon-assisted indirect excitations. Our results showed that the low-energy excitations were dominated by phonon-absorption processes which involve, in particular, the optical phonons. This implies that phonon-assisted processes significantly facilitate the charge dynamics in barely insulating Sr$_3$Ir$_2$O$_7$.
We consider a two-phase heat conductor in $\mathbb R^N$ with $N \geq 2$ consisting of a core and a shell with different constant conductivities. We study the role played by radial symmetry for overdetermined problems of elliptic and parabolic type. First of all, with the aid of the implicit function theorem, we give a counterexample to radial symmetry for some two-phase elliptic overdetermined boundary value problems of Serrin-type. Afterwards, we consider the following setting for a two-phase parabolic overdetermined problem. We suppose that, initially, the conductor has temperature 0 and, at all times, its boundary is kept at temperature 1. A hypersurface in the domain has the constant flow property if at every of its points the heat flux across surface only depends on time. It is shown that the structure of the conductor must be spherical, if either there is a surface of the constant flow property in the shell near the boundary or a connected component of the boundary of the heat conductor is a surface of the constant flow property. Also, by assuming that the medium outside the conductor has a possibly different conductivity, we consider a Cauchy problem in which the conductor has initial inside temperature $0$ and outside temperature $1$. We then show that a quite similar symmetry result holds true.
The concept of partial symmetry is introduced for an interacting fermion system. The associated Hamiltonians are shown to be closely related to a realistic nuclear quadrupole-quadrupole interaction. An application to $^{12}$C is presented.
We present a practical framework to prove, in a simple way, two-terms asymptotic expansions for Fourier integrals $$ {\mathcal I}(t) = \int_{\mathbb R}({\rm e}^{it\phi(x)}-1) {\rm d} \mu(x) $$ where $\mu$ is a probability measure on $\mathbb{R}$ and $\phi$ is measurable. This applies to many basic cases, in link with Levy's continuity theorem. We present applications to limit laws related to rational continued fractions coefficients.
The purpose of this article is to investigate the intersection cohomology for algebraic varieties with torus action. Given an algebraic torus $\mathbb{T}$, one of our result determines the intersection cohomology Betti numbers of any normal projective $\mathbb{T}$-variety admitting an algebraic curve as global quotient. The calculation is expressed in terms of a combinatorial description involving a divisorial fan which is the analogous of the defining fan of a toric variety. Our main tool to obtain this computation is a description of the decomposition theorem in this context.
The role of photon angular momentum in laser-induced demagnetization of Nickel thin films is investigated by means of pump-probe time-resolved magneto-optical Kerr effect in the polar geometry. The recorded data display a strong dependency on pump helicity during pump-probe temporal overlap, which is shown to be of non-magnetic origin. By accurately fitting the demagnetization curves we also show that demagnetization time and electron-phonon equilibration time are not affected by pump-helicity. Thereby our results do not support direct transfer of angular momentum between photons and spins to be relevant for the demagnetization process. This suggests, in agreement with the microscopic model that we recently presented, that the source of angular momentum could be phonons or impurities rather than laser photons as required in the microscopic model proposed by Zhang and Huebner.
A signed graph has edge signs. A gain graph has oriented edge gains drawn from a group. We define the combination of the two for the abelian case, in which each oriented edge of a signed graph has a gain from an abelian group, concentrating on the case of the additive group of a field. We develop the elementary graph properties, the associated matroid, and the vector and hyperplanar representations.
Deep convolution neural networks (CNN) have demonstrated advanced performance on single-label image classification, and various progress also have been made to apply CNN methods on multi-label image classification, which requires to annotate objects, attributes, scene categories etc. in a single shot. Recent state-of-the-art approaches to multi-label image classification exploit the label dependencies in an image, at global level, largely improving the labeling capacity. However, predicting small objects and visual concepts is still challenging due to the limited discrimination of the global visual features. In this paper, we propose a Regional Latent Semantic Dependencies model (RLSD) to address this problem. The utilized model includes a fully convolutional localization architecture to localize the regions that may contain multiple highly-dependent labels. The localized regions are further sent to the recurrent neural networks (RNN) to characterize the latent semantic dependencies at the regional level. Experimental results on several benchmark datasets show that our proposed model achieves the best performance compared to the state-of-the-art models, especially for predicting small objects occurred in the images. In addition, we set up an upper bound model (RLSD+ft-RPN) using bounding box coordinates during training, the experimental results also show that our RLSD can approach the upper bound without using the bounding-box annotations, which is more realistic in the real world.
Quantum emitters (QEs) coupled to structured baths can localize multiple photons around them and form qubit-photon bound states. In the Markovian or weak coupling regime, the interaction of QEs through these single-photon bound states is known to lead to effective many-body QE Hamiltonians with tuneable but yet perturbative interactions. In this work we study the emergence of such models in the non-Markovian or strong coupling regime in different excitation subspaces. The effective models for the non-Markovian regime with up to three excitations are characterized using analytical methods, uncovering the existence of doublons or triplon states. Furthermore, we provide numerical results for systems with multiple excitations and demonstrate the emergence of polariton models with optically tuneable interactions, whose many-body ground state exhibits a superfluid-Mott insulator transition.
Quantum resources, such as entanglement, can decrease the uncertainty of a parameter-estimation procedure beyond what is classically possible. This phenomenon is well described for noiseless systems with asymptotically many measurement resources by the Quantum Cramer-Rao Bound, but no general description exists for the regime of limited measurement resources. We address this problem by defining a Bayesian quantifier for uncertainty suitable for the regime of limited resources, and by developing a mathematical description for a parameter-estimation procedure which uses qubit probes to estimate a rotation angle induced on them. We simulate the qubit estimation scheme in the regime of limited resources using a single class of probe states. We find that, in noiseless systems, entanglement between qubits always decreases the uncertainty of the estimation; however, the quantum advantage decreases as fewer qubits are used in the estimation. We also find that the presence of strong dephasing noise removes the quantum advantage completely, regardless of the number of qubit probes used.
It has been shown that quantum paradoxes have followed from one special assumption, i.e., from attributing basic physical meaning to Hamiltonian eigenfunctions and representing all physical states by vectors of the Hilbert space spanned on these eigenfunctions. However, any paradoxical properties disappear if the physical states are represented by vectors from the extended Hilbert space on which the scattering theory of Lax and Phillips has been based. On the other side, all stationary characteristics and experimentally verified quantum-mechanical predictions remain the same. The extended mathematical model is also in full agreement with results of EPR experiments, if one takes into account that a further assumption (in addition to locality condition) is involved in derivation of Bell's inequalities as shown recently (see: quant-ph/9808005).
In this paper we study classical general relativistic static wormhole configurations with pseudo-spherical symmetry. We show that in addition to the hyperbolic wormhole solutions discussed by Lobo and Mimoso in the Ref. Phys.\ Rev.\ D {\bf 82}, 044034 (2010), there exists another wormhole class, which is truly pseudo-spherical counterpart of spherical Morris-Thorne wormhole (contrary to the Lobo-Mimoso wormhole class), since all constraints originally defined by Morris and Thorne for spherically symmetric wormholes are satisfied. We show that, for both classes of hyperbolic wormholes the energy density, at the throat, is always negative, while the radial pressure is positive, contrary to the spherically symmetric Morris-Thorne wormhole. Specific hyperbolic wormholes are constructed and discussed by imposing different conditions for the radial and lateral pressures, or by considering restricted choices for the redshift and the shape functions. In particular, we show that an hyperbolic wormhole can not be sustained at the throat by phantom energy, and that there are pseudo-spherically symmetric wormholes supported by matter with isotropic pressure and characterized by space sections with an angle deficit (or excess).
We use the functional form of the QCD running coupling to modify the conformal metric in AdS/CFT mapping the fifth-dimensional z-coordinate to the energy scale in the four-dimensional QCD. The resulting type-0 string theory in five dimensions is solved with the Nambu-Goto action giving good agreement with the Coulombic and confinement $Q \bar Q$ potential.
The aim of this paper is to examine some obtained exact solutions of the Einstein-Maxwell equations, especially their properties from a chronological point of view. Each our spacetime is stationary cylindrically symmetric and it is filled up with an perfect fluid that is electrically charged. There are two classes of solutions and examples of each of them are investigated. We give examples of the first class both for the vanishing as well as for the non-vanishing Lorentz force.
The Halting problem of a quantum computer is considered. It is shown that if halting of a quantum computer takes place the associated dynamics is described by an irreversible operator.
In this work we establish conditions which guarantee the existence of (strictly) positive steady states of a nonlinear structured population model. In our framework the steady state formulation amounts to recasting the nonlinear problem as a family of eigenvalue problems combined with a fixed point problem. Amongst other things our formulation requires us to control the growth behaviour of the spectral bound of a family of linear operators along positive rays. For the specific class of model we consider here, this presents a considerable challenge. We are going to show that the spectral bound of the family of operators, arising from the steady state formulation, can be controlled by perturbations in the domain of the generators (only). These new boundary perturbation results are particularly important for models exhibiting fertility controlled dynamics. As an important by-product of the application of the boundary perturbation results we employ here we recover (using a recent theorem by H.R. Thieme) the familiar net reproduction number (or function) for models with single state at birth, which include for example the classic McKendrick (linear) and Gurtin-McCamy (non-linear) age-structured models.