ShantanuT01/DACTYL-Pretraining huggingface dataset:
Astrophysical sources of relativistic jets or outflows, such as gamma-ray bursts (GRBs), active galactic nuclei (AGN) or micro-quasars, often show strong time variability. Despite such impulsive behavior, most models of these sources assume a steady state for simplicity. Here I consider a time-dependent outflow that is initially highly magnetized and divided into many well-separated sub-shells, as it experiences impulsive magnetic acceleration and interacts with the external medium. In AGN the deceleration by the external medium is usually unimportant and most of the initial magnetic energy is naturally converted into kinetic energy, leading to efficient dissipation in internal shocks as the sub-shells collide. Such efficient low-magnetization internal shocks can also naturally occur in GRBs, where the deceleration by the external medium can be important. A strong low-magnetization reverse shock can develop, and the initial division into sub-shells allows it to be relativistic and its emission to peak on the timescale of the prompt GRB duration (which is not possible for a single shell). Sub-shells also enable the outflow to reach much higher Lorentz factors that help satisfy existing constraints on GRBs from intrinsic pair opacity and from the afterglow onset time.
In this paper we develop a formalism for incorporating hadron loops in the quark model. We derive expressions for mass shifts, continuum components and mixing amplitudes of "quenched" quark model states due to hadron loops, as perturbation series in the valence-continuum coupling Hamiltonian. We prove three general theorems regarding the effects of hadron loops, which show that given certain constraints on the external "bare" quark model states, the valence-continuum coupling, and the hadrons summed in the loops, the following results hold: (1) The loop mass shifts are identical for all states within a given N,L multiplet. (2) These states have the same total open-flavor decay widths. (3) Loop-induced valence configuration mixing vanishes provided that ${\L}_i \neq \L_f$ or $\S_i \neq \S_f$. The charmonium system is used as a numerical case study, with the $^3\P_0$ decay model providing the valence-continuum coupling. We evaluate the mass shifts and continuum mixing numerically for all 1S, 1P and 2S charmonium valence states due to loops of D, D$^*$, D$_s$ and D$_s^*$ meson pairs. We find that the mass shifts are quite large, but are numerically similar for all the low-lying charmonium states, as suggested by the first theorem. Thus, loop mass shifts may have been "hidden" in the valence quark model by a change of parameters. The two-meson continuum components of the physical charmonium states are also found to be large, creating challenges for the interpretation of the constituent quark model.
We show that an iterative method for computing the center of mass (CM) of q units of mass, placed on a unit interval [0, 1] along the x- axis, give rise to a simple procedure for expanding rational numbers less than unity in powers of r/s < 1, with r, s, integers larger than 0. The method is then extended to all numbers, real or complex, though the procedure for none rational numbers is more time consuming. We also show how our method provides a natural way to generalize Jacobsthal numbers. Moreover, the method provides a way to generate infinitely many sequences of numbers, of which many play an important rule in mathematical sciences and engineering, to name few, Jacobsthal sequence, Fibonacci sequence, and Pell sequence.
In a $(1:b)$ biased Maker-Breaker game, how good a strategy is for a player can be measured by the bias range for which its rival can win, choosing an appropriate counterstrategy. Bednarska and {\L}uczak proved that, in the $H$-subgraph game, the uniformly random strategy for Maker is essentially optimal with high probability. Here we prove an analogous result for the $H$-graph minor game, and we study for which choices of $H$ the random strategy is within a factor of $1+o(1)$ of being optimal.
Let $G$ be a group and let $S$ be an inverse-closed and identity-free generating set of $G$. The \emph{Cayley graph} $\Cay(G,S)$ has vertex-set $G$ and two vertices $u$ and $v$ are adjacent if and only if $uv^{-1}\in S$. Let $CAY_d(n)$ be the number of isomorphism classes of $d$-valent Cayley graphs of order at most $n$. We show that $\log(CAY_d(n))\in\Theta (d(\log n)^2)$, as $n\to\infty$. We also obtain some stronger results in the case $d=3$.
Given a set D of positive integers, the associated distance graph on the integers is the graph with the integers as vertices and an edge between distinct vertices if their difference lies in D. We investigate the chromatic numbers of distance graphs. We show that, if $D = {d_1,d_2,d_3,...}$, with $d_n | d_{n+1}$ for all n, then the distance graph has a proper 4-coloring. We further find the exact chromatic numbers of all such distance graphs. Next, we characterize those distance graphs that have periodic proper colorings and show a relationship between the chromatic number and the existence of periodic proper colorings.
We study a magnetic molecule that exhibits spin tunneling and is free to rotate about its anisotropy axis. Exact low-energy eigenstates of the molecule that are superpositions of spin and rotational states are obtained. We show that parameter $\alpha = 2(\hbar S)^2/(I\Delta)$ determines the ground state of the molecule. Here $\hbar S$ is the spin, $I$ is the moment of inertia, and $\Delta$ is the tunnel splitting. The magnetic moment of the molecule is zero at $\alpha < \alpha_c = [1-1/(2S)^{2}]^{-1}$ and non-zero at $\alpha > \alpha_c$. At $\alpha \to \infty$ the spin of the molecule localizes in one of the directions along the anisotropy axis.
We present a 23 ks XMM-Newton observation of the ULIRG Mrk 273. The hard X-ray spectrum can be modeled by a highly absorbed power law plus an Fe Kalpha emission line. The iron line is broad, suggesting possible superposition of a neutral iron line at 6.4 keV, and a blend of ionized iron lines from Fe XXV and Fe XXVI. Given the relatively short exposure, the three line components can not be singularly resolved with high statistical significance: the neutral component is detected at ~2.5sigma and the Fe XXV line at ~2sigma c.l., while for the Fe XXVI line we can only estimate an upper limit. The broad band spectrum requires, in addition to a highly absorbed power law, at least three collisionally ionized plasma components, which may be associated with star-forming regions. The temperatures of the three plasmas are about 0.3, 0.8 and 6 keV, where the highest of the three is sufficient to produce ionized iron emission lines. An alternative interpretation for the origin of the soft emission might also be given in terms of reflection off some photoionized gas, as has been observed in a number of nearby Compton-thick Seyfert 2 galaxies. A hot gas, photoionized by the primary, continuum can also produce ionized iron lines. Unfortunately, given the limited statistics and the lack of high resolution spectroscopy, it is not possible to distinguish between the two models investigated. We further compare the XMM-Newton findings with the Chandra data obtaining consistent spectral results. The absorption corrected hard X-ray (2-10 keV) luminosity of Mrk 273 corresponds to ~0.2% of the far-IR luminosity, similar to typical values found in pure starbursts. The thermal contribution to the soft X-ray luminosity is ~0.2-0.7x10^42 erg s^-1, comparable to those found in NGC 6240 and other starburst dominated ULIRGs.
In this talk, we describe recent experimental progress in detecting the chiral anomaly in the Dirac semimetal Na$_3$Bi in the presence of a magnetic field. The chiral anomaly, which plays a fundamental role in chiral gauge theories, was predicted to be observable in crystals by Nielsen and Ninomiya in 1983 [1]. Theoretical progress in identifying and investigating Dirac and Weyl semimetals has revived strong interest in this issue [2-6]. In the Dirac semimetal, the breaking of time-reversal symmetry by a magnetic field $\bf B$ splits each Dirac node into two chiral Weyl nodes. If an electric field $\bf E$ is applied parallel to $\bf B$, charge is predicted to flow between the Weyl nodes. We report the observation in the Dirac semimetal Na$_3$Bi of a novel, negative and highly anisotropic magnetoresistance (MR). We show that the enhanced conductivity has the form of a narrowly defined plume that can be steered by the applied field. The novel MR is acutely sensitive to deviations of $\bf B$ from $\bf E$, a feature incompatible with conventional transport. The locking of the current plume to the field appears to be a defining signature of the chiral anomaly.
In this paper a recently developed projector-based renormalization method (PRM) for many-particle Hamiltonians is applied to the periodic Anderson model (PAM) with the aim to describe heavy Fermion behavior. In this method high-energetic excitation operators instead of high energetic states are eliminated. We arrive at an effective Hamiltonian for a quasi-free system which consists of two non-interacting heavy-quasiparticle bands. The resulting renormalization equations for the parameters of the Hamiltonian are valid for large as well as small degeneracy $\nu_f$ of the angular momentum. An expansion in $1/\nu_f$ is avoided. Within an additional approximation which adapts the idea of a fixed renormalized \textit{f} level $\tilde{\epsilon}_{f}$, we obtain coupled equations for $\tilde{\epsilon}_{f}$ and the averaged \textit{f} occupation $<n_{f}>$. These equations resemble to a certain extent those of the usual slave boson mean-field (SB) treatment. In particular, for large $\nu_f$ the results for the PRM and the SB approach agree perfectly whereas considerable differences are found for small $\nu_f$.
The responses of perturbations added into the optically thick, advection-dominated accretion disk (ADAD), what we call the slim disk (SD), are investigated through numerical simulations. Although it is proposed that the SD is thermally stable, I find that a perturbation added into the disk is not rapidly damped and moves through the disk in its free-fall time. After the perturbation moves, the global structure of the disk does not vary very much. These facts may account for the substantial variability of the X-ray luminosities of stellar super-luminal jet sources (SLJSs) and Narrow-Line Seyfert 1s (NLS1s).
We study possible quantum $U(1)$ spin liquids in three dimensions with time-reversal symmetry. We find a total of 7 families of such $U(1)$ spin liquids, distinguished by the properties of their emergent electric/magnetic charges. We show how these spin liquids are related to each other. Two of these classes admit nontrivial protected surface states which we describe. We show how to access all of the 7 spin liquids through slave particle (parton) constructions. We also provide intuitive loop gas descriptions of their ground state wave functions. One of these phases is the `topological Mott insulator' conventionally described as a topological insulator of an emergent fermionic `spinon'. We show that this phase admits a remarkable dual description as a topological insulator of emergent fermionic magnetic monopoles. This results in a new (possibly natural) surface phase for the topological Mott insulator and a new slave particle construction. We describe some of the continuous quantum phase transitions between the different $U(1)$ spin liquids. Each of these seven families of states admits a finer distinction in terms of their surface properties which we determine by combining these spin liquids with symmetry protected topological phases. We discuss lessons for materials such as pyrochlore quantum spin ices which may harbor a $U(1)$ spin liquid. We suggest the topological Mott insulator as a possible ground state in some range of parameters for the quantum spin ice Hamiltonian.
We consider a linear stochastic fluid network under Markov modulation, with a focus on the probability that the joint storage level attains a value in a rare set at a given point in time. The main objective is to develop efficient importance sampling algorithms with provable performance guarantees. For linear stochastic fluid networks without modulation, we prove that the number of runs needed (so as to obtain an estimate with a given precision) increases polynomially (whereas the probability under consideration decays essentially exponentially); for networks operating in the slow modulation regime, our algorithm is asymptotically efficient. Our techniques are in the tradition of the rare-event simulation procedures that were developed for the sample-mean of i.i.d. one-dimensional light-tailed random variables, and intensively use the idea of exponential twisting. In passing, we also point out how to set up a recursion to evaluate the (transient and stationary) moments of the joint storage level in Markov-modulated linear stochastic fluid networks.
An animal is a planar shape formed by attaching congruent regular polygons, known as tiles, along their edges. In this paper, we study extremal animals defined on regular tessellations of the plane. In 1976, Harary and Harborth studied animals in the Euclidean cases, finding extremal values for their vertices, edges, and tiles, when any one of these parameters is fixed. Here, we generalize their results to hyperbolic animals. For each hyperbolic tessellation, we exhibit a sequence of spiral animals and prove that they attain the minimal numbers of edges and vertices within the class of animals with $n$ tiles. In their conclusions, Harary and Harborth also proposed the question of enumerating extremal animals with a fixed number of tiles. This question has previously only been considered for Euclidean animals. As a first step in solving this problem, we find special sequences of extremal animals that are unique extremal animals, in the sense that any animal with the same number of tiles which is distinct up to isometries can't be extremal.
By virtue of barrier arguments we prove $C^\alpha$-regularity up to the boundary for the weak solutions of a non-local nonlinear problem driven by the fractional $p$-Laplacian operator. The equation is boundedly inhomogeneous and the boundary conditions are of Dirichlet type. We employ different methods according to the singular ($p<2$) of degenerate ($p>2$) case.
Video prediction, forecasting the future frames from a sequence of input frames, is a challenging task since the view changes are influenced by various factors, such as the global context surrounding the scene and local motion dynamics. In this paper, we propose a new framework to integrate these complementary attributes to predict complex pixel dynamics through deep networks. We present global context propagation networks that iteratively aggregate the non-local neighboring representations to preserve the contextual information over the past frames. To capture the local motion pattern of objects, we also devise local filter memory networks that generate adaptive filter kernels by storing the prototypical motion of moving objects in the memory. The proposed framework, utilizing the outputs from both networks, can address blurry predictions and color distortion. We conduct experiments on Caltech pedestrian and UCF101 datasets, and demonstrate state-of-the-art results. Especially for multi-step prediction, we obtain an outstanding performance in quantitative and qualitative evaluation.
For any directed graph G with vertex set V, the graph G^(d) is said to be a subset power of G and is defined to have vertex set equal to the set of d-element subsets of V; in G^(d), there is an edge from A to B if and only if we can label the elements of A and B such that there is an edge in G between each pair of corresponding elements. We determine the complete cycle structure of C^(d), where C is a directed cycle of length l.
We show that a blazar classification in BL Lacs and Flat Spectrum Radio Quasars may not be adequate when it relies solely on the equivalent widths (EWs) of optical lines. In fact, depending on redshift, some strong emission lines can fall in the infrared window and be missed. We selected a sample of BL Lacs with firm redshift identification and good visibility from Paranal. We targeted with the X-shooter spectrograph the five BL Lacs with z > 0.7, i.e., those for which the Halpha line, one of the strongest among blazars, falls outside the optical window and determined the EW of emission lines in both the infrared and optical bands. Two out of five sources show an observed Halpha EW > 5A (one has rest frame EW > 5A) and could be classified as FSRQs by one of the classification schemes used in the literature. A third object is border-line with an observed EW of 4.4 +/- 0.5A. In all these cases Halpha is the strongest emission line detected. The Halpha line of the other two blazars is not detected, but in one case it falls in a region strongly contaminated by sky lines and in the other one the spectrum is featureless. We conclude that a blazar classification based on EW width only can be inaccurate and may lead to an erroneous determination of blazar evolution. This effect is more severe for the BL Lac class, since FSRQs can be misclassified as BL Lacs especially at high redshifts (z > 0.7), where the latter are extremely rare.
State-of-the-art deep neural network recognition systems are designed for a static and closed world. It is usually assumed that the distribution at test time will be the same as the distribution during training. As a result, classifiers are forced to categorise observations into one out of a set of predefined semantic classes. Robotic problems are dynamic and open world; a robot will likely observe objects that are from outside of the training set distribution. Classifier outputs in robotic applications can lead to real-world robotic action and as such, a practical recognition system should not silently fail by confidently misclassifying novel observations. We show how a deep metric learning classification system can be applied to such open set recognition problems, allowing the classifier to label novel observations as unknown. Further to detecting novel examples, we propose an open set active learning approach that allows a robot to efficiently query a user about unknown observations. Our approach enables a robot to improve its understanding of the true distribution of data in the environment, from a small number of label queries. Experimental results show that our approach significantly outperforms comparable methods in both the open set recognition and active learning problems.
Galaxy clusters are the most massive systems in the known universe. They host relativistic cosmic ray populations and are thought to be gravitationally bound by large amounts of Dark Matter, which under the right conditions could yield to a detectable $\gamma$-ray flux. Prior to the launch of the Fermi satellite, predictions were optimistic that Galaxy clusters would be established as $\gamma$-ray bright objects by observations through its prime instrument, the Large Area Telescope (LAT). Yet, despite numerous efforts, even a single cluster detection is still pending.
In the present paper we consider the functional dissipativity of the Dirichlet problem for systems of partial differential operators of the form $\partial_{h} ({\mathop{\mathscr A}\nolimits}^{hk}(x)\partial_{k})$ (${\mathop{\mathscr A}\nolimits}^{hk}$ being $m\times m$ matrices with complex valued $L^{1}_{\text{loc}}$ entries). In the particular case of the operator $\partial_{h} ({\mathop{\mathscr A}\nolimits}^{h}(x)\partial_{h})$ (where ${\mathop{\mathscr A}\nolimits}^{h}$ are $m\times m$ matrices) we obtain algebraic necessary and sufficient conditions. We give also three different notions of functional ellipticity and investigate the relations between them and the functional dissipativity for the operators in question.
The thermodynamic uncertainty relation, which establishes a universal trade-off between nonequilibrium current fluctuations and dissipation, has been found for various Markovian systems. However, this relation has not been revealed for non-Markovian systems; therefore, we investigate the thermodynamic uncertainty relation for time-delayed Langevin systems. We prove that the fluctuation of arbitrary dynamical observables is constrained by the Kullback--Leibler divergence between the distributions of the forward path and its reversed counterpart. Specifically, for observables that are antisymmetric under time reversal, the fluctuation is bounded from below by a function of a quantity that can be identified as a generalization of the total entropy production in Markovian systems. We also provide a lower bound for arbitrary observables that are odd under position reversal. The term in this bound reflects the extent to which the position symmetry has been broken in the system and can be positive even in equilibrium. Our results hold for finite observation times and a large class of time-delayed systems because detailed underlying dynamics are not required for the derivation. We numerically verify the derived uncertainty relations using two single time-delay systems and one distributed time-delay system.
We consider permutations avoiding a pattern of length three under the family of Mallows distributions. In particular, for any pattern $\tau\in S_3-\{321\}$, we obtain rather precise results on the asymptotic probability as $n\to\infty$ that a permutation $\sigma\in S_n$ under the Mallows distribution with parameter $q\in(0,1)$ avoids the pattern. By a duality between the parameters $q$ and $\frac1q$, we also obtain rather precise results on the above probability for $q>1$ and any pattern $\tau\in S_3-\{123\}$.
We show that the exact solution of the two_superbody problem in N=2 Chern Simons Supergravity in 2+1 dimensions leads to a supermultiplet of space-times. This supersymmetric space-time is characterized by the two gauge invariant observables of the super Poincare' group, which may be viewed as the Casimir invariants of an equivalent one-superbody state. The metric of this space-time supermultiplet can be cast into the form of the metric for a spinning cone in which the coordinates do not commute or for a spinning cone with an additional finite discrete dimension. Some of the interesting features of this universe and their possible physical implications are discussed in the light of a corresponding observation by Witten.
We study the strong solvability of the nonstationary Stokes problem with non-zero divergence in a bounded domain.
Particle and pairing densities in spherical even-even neutron-rich nuclei are studied within the Skyrme-Hartree-Fock-Bogoliubov approach with the density-dependent pairing interaction. The influence of the density dependence of the pairing interaction on asymptotic properties of nucleonic distributions are analyzed. It is demonstrated that the size of the neutron halo dramatically depends on the behavior of the pairing interaction at low density.