ShantanuT01/DACTYL-Pretraining huggingface dataset:
High-energy cosmic rays (CRs) can be accelerated in the relativistic jets of Active Galactic Nuclei (AGNs) powered by supermassive black holes. The baryon loading efficiency onto relativistic CR baryons from the accreting black holes is poorly constrained by observations so far. In this paper, we suggest that the $\gamma$-ray emission of galaxy clusters can be used to study the baryon loading factor of AGN jets, since CRs injected by AGN jets are completely confined in the galaxy clusters and sufficiently interact with intra-cluster medium via hadronic process, producing diffuse $\gamma$-rays. We study the propagation of CRs in the galaxy clusters and calculate the radial distribution of the gamma-rays in the galaxy cluster with different injection rates from AGNs. By comparison with the $\gamma$-ray flux and upper limits of the Coma cluster measured by $Fermi$-LAT and VERITAS, we find the upper limit of the average baryon loading factor {(defined as the efficiency with which the gravitational energy is converted into relativistic particles)} to be $\eta_{p, \mathrm{grav}} < 0.1$. The upper limit is much lower than that required to account for diffuse neutrino flux in the conventional blazar models.
The detection of x-ray afterglows of gamma-ray burst (GRB) sources has enabled the optical discovery that GRBs are at cosmological distances, which confirms that the enormous luminosities required must produce a relativistically expanding fireball. It is not yet clear if this expansion is quasi-spherical or beamed, or if the beaming differs between the prompt GRB and afterglow, although the differences for both source emission and population models are profound. We show that relative beaming (prompt vs. afterglow) may be constrained by analysis of the "fast transient" x-ray sources catalogued by Pye and McHardy (1983) from the Ariel V survey as well as several other (e.g. HEAO-A1/A2) surveys. After removing contamination from likely stellar transients, and scaling from x-ray/$\gamma$-ray fluence ratios recently derived from Ginga and BeppoSAX, approximately half of the sources were possible prompt emission or afterglows from GRBs with gamma-ray fluence of >~1.2 X 10$^{-5} /erg-cm^2. Since the rate of these candidate afterglow events, 0.15 /day, is consistent with the BATSE logN-logS distribution, no difference in prompt vs. afterglow beaming is required. However more sensitive x-ray monitors or hard x-ray imaging surveys, with better temporal and spatial resolution, could provide strong constraints on GRBs and beaming.
A square-free integer is a positive integer that is not divisible by the square of any prime. Merten's function, $M(x)$ is defined as the difference between the number of square free integers with an even number of prime factors and the number of those with an odd number of prime factors up to $x$. It's well known that $M(x)=O(x^{1/2+\epsilon})$ is equivalent to Riemann Hypothesis. In this paper, we derive a new equation involving Merten's function that leads to a promising technique for Riemann Hypothesis.
In this article, the author proposes a new approach for the estimating of the number of edges in induced subgraphs of a special distance graph. Author significantly improves previous estimates and suggests a new approach to obtaining better ones.
The Mott-Hubbard transition is studied in the context of the two-dimensional Hubbard model. Analytical calculations show the existence of a critical value Uc of the potential strength which separates a paramagnetic metallic phase from a paramagnetic insulating phase. Calculations of the density of states and double occupancy show that the ground state in the insulating phase contains always a small fraction of empty and doubly occupied sites. The structure of the ground state is studied by considering the probability amplitude of intersite hopping. The results indicate that the ground state of the Mott insulator is characterized by a local antiferromagnetic order; the electrons keep some mobility, but this mobility must be compatible with the local ordering. The vanishing of some intersite probability amplitudes at U=Uc puts a constrain on the electron mobility. It is suggested that such quantities might be taken as the quantities which control the order in the insulating phase.
The dynamics of a one dimensional growth model involving attachment and detachment of particles is studied in the presence of a localized growth inhomogeneity along with anchored boundary conditions. At large times, the latter enforce an equilibrium stationary regime which allows for an exact calculation of roughening exponents. The stochastic evolution is related to a spin Hamiltonian whose spectrum gap embodies the dynamic scaling exponent of late stages. For vanishing gaps the interface can exhibit a slow morphological transition followed by a change of scaling regimes which are studied numerically. Instead, a faceting dynamics arises for gapful situations.
We investigate the dynamics of cellular solidification patterns using three-dimensional phase-field simulations. The cells can organize into stable hexagonal patterns or exhibit unsteady evolutions. We identify the relevant secondary instabilities of regular hexagonal arrays and find that the stability boundaries depend significantly on the strength of crystalline anisotropy. We also find multiplet states that can be reached by applying well-defined perturbations to a pre-existing hexagonal array.
A family of loss functions built on pair-based computation have been proposed in the literature which provide a myriad of solutions for deep metric learning. In this paper, we provide a general weighting framework for understanding recent pair-based loss functions. Our contributions are three-fold: (1) we establish a General Pair Weighting (GPW) framework, which casts the sampling problem of deep metric learning into a unified view of pair weighting through gradient analysis, providing a powerful tool for understanding recent pair-based loss functions; (2) we show that with GPW, various existing pair-based methods can be compared and discussed comprehensively, with clear differences and key limitations identified; (3) we propose a new loss called multi-similarity loss (MS loss) under the GPW, which is implemented in two iterative steps (i.e., mining and weighting). This allows it to fully consider three similarities for pair weighting, providing a more principled approach for collecting and weighting informative pairs. Finally, the proposed MS loss obtains new state-of-the-art performance on four image retrieval benchmarks, where it outperforms the most recent approaches, such as ABE\cite{Kim_2018_ECCV} and HTL by a large margin: 60.6% to 65.7% on CUB200, and 80.9% to 88.0% on In-Shop Clothes Retrieval dataset at Recall@1. Code is available at https://github.com/MalongTech/research-ms-loss.
Linear and angular momenta of a soliton in a ferromagnet are commonly derived through the application of Noether's theorem. We show that these quantities exhibit unphysical behavior: they depend on the choice of a gauge potential in the spin Lagrangian and can be made arbitrary. To resolve this problem, we exploit a similarity between the dynamics of a ferromagnetic soliton and that of a charged particle in a magnetic field. For the latter, canonical momentum is also gauge-dependent and thus unphysical; the physical momentum is the generator of magnetic translations, a symmetry combining physical translations with gauge transformations. We use this analogy to unambiguously define conserved momenta for ferromagnetic solitons. General considerations are illustrated on simple models of a domain wall in a ferromagnetic chain and of a vortex in a thin film.
High number of writers, small number of training samples per writer with high intra-class variability and heavily imbalanced class distributions are among the challenges and difficulties of the offline Handwritten Signature Verification (HSV) problem. A good alternative to tackle these issues is to use a writer-independent (WI) framework. In WI systems, a single model is trained to perform signature verification for all writers from a dissimilarity space generated by the dichotomy transformation. Among the advantages of this framework is its scalability to deal with some of these challenges and its ease in managing new writers, and hence of being used in a transfer learning context. In this work, we present a white-box analysis of this approach highlighting how it handles the challenges, the dynamic selection of references through fusion function, and its application for transfer learning. All the analyses are carried out at the instance level using the instance hardness (IH) measure. The experimental results show that, using the IH analysis, we were able to characterize "good" and "bad" quality skilled forgeries as well as the frontier region between positive and negative samples. This enables futures investigations on methods for improving discrimination between genuine signatures and skilled forgeries by considering these characterizations.
An example is presented when decoherence and quantum interference gives rise to narrow eigenstates (in coordinate representation) for the reduced density matrix of macroscopic quantum systems. On the basis of modal interpretations this means the emergence of classical properties.
We consider a subcarrier wave quantum key distribution (QKD) system, where the quantum en- coding is carried by weak sidebands generated to a coherent optical beam by means of an electrooptic phase modulation. We study the security of two protocols, B92 and BB84, against one of the most powerful attacks on the systems of this class: the collective beam splitting attack. We show that a subcarrier wave QKD system with realistic parameters is capable of distributing a cryptographic key over large distances. We show also that a modification of the BB84 protocol, with discrimina- tion of only one state in each basis, performs not worse than the original BB84 protocol for this class of QKD systems, which brings a significant simplification to the development of cryprographic networks on the basis of considered technique.
Geometrical structures of quantum mechanics provide us with new insightful results about the nature of quantum theory. In this work we consider mixed quantum states represented by finite rank density operators. We review our geometrical framework that provide the space of density operators with Riemannian and symplectic structures, and we derive a geometric uncertainty relation for observables acting on mixed quantum states. We also give an example that visualizes the geometric uncertainty relation for spin-$\frac{1}{2}$ particles.
The processes of star formation are fundamentally different from those of planet formation. Since the mass of a very-low-mass object alone doesn't allow us to uniquely determine its basic nature, we have to look at its other characteristics, such as its motion, its age, its atmospheric composition, its internal structure and composition, etc., in order to ascertain its formation mechanism.
We produce an edge-coloring of the complete 3-uniform hypergraph on n vertices with $e^{O(\sqrt {log log n})}$ colors such that the edges spanned by every set of five vertices receive at least three distinct colors. This answers the first open case of a question of Conlon-Fox-Lee-Sudakov [1] who asked whether such a coloring exists with $(log n)^{o(1)}$ colors.
The running BFKL equation gives rise to a series of moving poles in the complex $j$-plane. The first nodes for all subleading solutions (color dipole cross sections) accumulate at $r_1\sim 0.1 fm$.Therefore the processes dominated by the dipole sizes $r\sim r_1 $ are free of subleading BFKL corrections. An example - the leptoproduction of charm. The calculated $F_2^{cc}$ is exhausted by the leading BFKL pole and gives a perfect description of the experimental data. The logarithmic slope of the subleading structure functions, $dF_2^{(n)}/d\log Q^2$, at small $Q^2$ is small compared to $dF_2^{(0)}/d\log Q^2$ due to the presence of nodes. This observation provides an explanation for the observed $x$/$Q^2$ dependence of the derivative of the proton structure function $dF_2/d\log Q^2$.
We study the edge states in graphene in the presence of a magnetic field perpendicular to the plane of the lattice. Most of the works done so far discuss the edge states in either zigzag or armchair edge graphene considering an isotropic electron hopping. In practice, graphene can have mixture of armchair and zigzag edges and the electron hopping can be anisotropic, which is the subject of this article. We predict that the mixed edges smear the enhanced local density of states (LDOS) at E=0 of the zigzag edge and, on the other hand, the anisotropic hopping gives rise to the enhanced LDOS at E=0 in the armchair edge. The behavior of the LDOS can be studied using scanning tunneling microscopy (STM) experiments. We suggest that care must be taken while interpreting the STM data. It is because the clear distinction between the zigzag edge (enhanced LDOS at E=0) and armchair edge (suppressed LDOS at E=0) can be lost if the hopping is not isotropic and if the edges are mixed.
Massive starburst galaxies in the early Universe are estimated to have depletion times of $\sim 100$ Myr and thus be able to convert their gas very quickly into stars, possibly leading to a rapid quenching of their star formation. For these reasons, they are considered progenitors of massive early-type galaxies (ETGs). In this paper, we study two high-$z$ starbursts, AzTEC/C159 ($z\simeq 4.57$) and J1000+0234 ($z\simeq 4.54$), observed with ALMA in the [CII] 158-$\mu$m emission line. These observations reveal two massive and regularly rotating gaseous discs. A 3D modelling of these discs returns rotation velocities of about $500$ km/s and gas velocity dispersions as low as $\approx 20$ km/s, leading to very high ratios between regular and random motion ($V/\sigma {\lower.7ex\hbox{$\;\stackrel{\textstyle>}{\sim}\;$}} 20$), at least in AzTEC/C159. The mass decompositions of the rotation curves show that both galaxies are highly baryon-dominated with gas masses of $\approx 10^{11}M_{\odot}$, which, for J1000+0234, is significantly higher than previous estimates. We show that these high-$z$ galaxies overlap with $z=0$ massive ETGs in the ETG analogue of the stellar-mass Tully-Fisher relation once their gas is converted into stars. This provides dynamical evidence of the connection between massive high-$z$ starbursts and ETGs, although the transformation mechanism from fast rotating to nearly pressure-supported systems remains unclear.
We have calculated the E1 and E2 contributions to the low-energy B-8 + Pb-208 -> p + Be-7 + Pb-208 Coulomb dissociation cross sections using the kinematics of a recent experiment at RIKEN. Using a potential model description of the Be-7 (p,gamma) B-8 reaction, we find that the E2 contributions cannot a priori be ignored in the analysis of the data. Its inclusion reduces the extracted Be-7 (p,gamma) B-8 S-factor at solar energies by about 25%.
We investigate a minimal model for cell propagation involving migration along self-generated signaling gradients and cell division, which has been proposed in an earlier study. The model consists in a system of two coupled parabolic diffusion-advection-reaction equations. Because of a discontinuous advection term, the Cauchy problem should be handled with care. We first establish existence and uniqueness locally in time through the reduction of the problem to the well-posedness of an ODE, under a monotonicity condition on the signaling gradient. Then, we carry out an asymptotic analysis of the system. All positive and bounded traveling waves of the system are computed and an explicit formula for the minimal wave speed is deduced. An analysis on the inside dynamics of the wave establishes a dichotomy between pushed and pulled waves depending on the strength of the advection. We identified the minimal wave speed as the biologically relevant speed, in a weak sense, that is, the solution propagates slower, respectively faster, than the minimal wave speed, up to time extraction. Finally, we extend the study to a hyperbolic two-velocity model with persistence.
Let G be a complex semi-simple linear algebraic group without G_2 factors, B a Borel subgroup of G and T a maximal torus in B. The flag variety G/B is a projective G-homogeneous variety whose tangent space at the identity coset is isomorphic, as a B-module, to Lie(G)/Lie(B). Recall that if w is an element of the Weyl group W of the pair (G,T), the Schubert variety X(w) in G/B is by definition the closure of the Bruhat cell BwB. In this note we prove that X(w) is non-singular iff the following two conditions hold: 1) its Poincar\'e polynomial is palindromic and 2) the tangent space TE(X(w)) to the set T-stable curves in X(w) through the identity is a $B$-submodule of Lie(G)/Lie(B). This gives two criteria in terms of the combinatorics of W which are necessary and sufficient for X(w) to be smooth: \sum_{x\le w} t^{\ell(x)} is palindromic, and every root of (G,T) in the convex hull of the set of negative roots whose reflection is less than w (in the Bruhat order on W) has the property that its T-weight space (in Lie(G)/Lie(B)) is contained in TE(X(w)). However, as we show by example, these conditions don't characterize the smooth Schubert varieties when G has type G_2.
The behavior of several nuclear properties with temperature is analyzed within the framework of the Finite Temperature Hartree-Fock-Bogoliubov (FTHFB) theory with the Gogny force and large configuration spaces. Thermal shape fluctuations in the quadrupole degree of freedom, around the mean field solution, are taken into account with the Landau prescription. As representative examples the nuclei $^{164}$Er, $^{152}$Dy and $^{192}$Hg are studied. Numerical results for the superfluid to normal and deformed to spherical shape transitions are presented. We found a substantial effect of the fluctuations on the average value of several observables. In particular, we get a decrease in the critical temperature ($T_c$) for the shape transition as compared with the plain FTHFB prediction as well as a washing out of the shape transition signatures. The new values of $T_c$ are closer to the ones found in Strutinsky calculations and with the Pairing Plus Quadrupole model Hamiltonian.
This paper investigates the influence of charge on physical features of gravastars in the framework of energy-momentum squared gravity. A gravastar is an alternate model to a black hole that comprises of three distinct regions, namely the intermediate shell, inner and outer sectors. Different values of the barotropic equation of state parameter provide the mathematical formulation for these regions. We construct the structure of a gravastar admitting conformal motion for a specific model of energy-momentum squared gravity. The field equations are formulated for a spherically symmetric spacetime with charged perfect matter distribution. For the smooth matching of external and internal spacetimes, we use Israel matching criteria. Various physical attributes of gravastars such as the equation of state parameter, proper length, entropy and energy are investigated (in the presence of charge) versus thickness of the shell. The charge in the inner core of gravastars preserves the state of equilibrium by counterbalancing the inward gravitational force. It is concluded that the non-singular solutions of charged gravastar are physically viable in the background of energy-momentum squared gravity.
In the context of quantum information theory, "quantization" of various mathematical and computational constructions is said to occur upon the replacement, at various points in the construction, of the classical randomization notion of probability distribution with higher order randomization notions from quantum mechanics such as quantum superposition with measurement. For this to be done "properly", a faithful copy of the original construction is required to exist within the new "quantum" one, just as is required when a function is extended to a larger domain. Here procedures for extending history dependent Parrondo games, Markov processes and multiplexing circuits to their "quantum" versions are analyzed from a game theoretic viewpoint, and from this viewpoint, proper quantizations developed.
We consider the topological string partition function, including the Nekrasov deformation, for type IIB geometries with an A_{n-1} singularity over a Riemann surface. These models realize the N=2 SU(n) superconformal gauge systems recently studied by Gaiotto and collaborators. Employing large N dualities we show why the partition function of topological strings in these backgrounds is captured by the chiral blocks of A_{n-1} Toda systems and derive the dictionary recently proposed by Alday, Gaiotto and Tachikawa. For the case of genus zero Riemann surfaces, we show how these systems can also be realized by Penner-like matrix models with logarithmic potentials. The Seiberg-Witten curve can be understood as the spectral curve of these matrix models which arises holographically at large N. In this context the Nekrasov deformation maps to the beta-ensemble of generalized matrix models, that in turn maps to the Toda system with general background charge. We also point out the notion of a double holography for this system, when both n and N are large.
We present a new, open source, free semi-analytic model (SAM) of galaxy formation, Shark, designed to be highly flexible and modular, allowing easy exploration of different physical processes and ways of modelling them. We introduce the philosophy behind Shark and provide an overview of the physical processes included in the model. Shark is written in C++11 and has been parallelized with OpenMP. In the released version (v1.1), we implement several different models for gas cooling, active galactic nuclei, stellar and photo-ionisation feedback, and star formation (SF). We demonstrate the basic performance of Shark using the Planck15 cosmology SURFS simulations, by comparing against a large set of observations, including: the stellar mass function (SMF) and stellar-halo mass relation at z=0-4; the cosmic evolution of the star formation rate density (SFRD), stellar mass, atomic and molecular hydrogen; local gas scaling relations; and structural galaxy properties, finding excellent agreement. Significant improvements over previous SAMs are seen in the mass-size relation for disks/bulges, the gas-stellar mass and stellar mass-metallicity relations. To illustrate the power of Shark in exploring the systematic effects of the galaxy formation modelling, we quantify how the scatter of the SF main sequence and the gas scaling relations changes with the adopted SF law, and the effect of the starbursts H$_2$ depletion timescale on the SFRD and $\Omega_{\rm H_2}$. We compare Shark with other SAMs and the hydrodynamical simulation EAGLE, and find that SAMs have a much higher halo baryon fractions due to large amounts of intra-halo gas, which in the case of EAGLE is in the intergalactic medium.
One of the central issues in extremal set theory is Sperner's theorem and its generalizations. Among such generalizations is the best-known BLYM inequality and the Ahlswede--Zhang (AZ) identity which surprisingly generalizes the BLYM inequality into an identity. Sperner's theorem and the BLYM inequality has been also generalized to a wide class of posets. Another direction in this research was the study of more part Sperner systems. In this paper we derive AZ type identities for regular posets. We also characterize all maximum 2-part Sperner systems for a wide class of product posets.