ShantanuT01/DACTYL-Pretraining huggingface dataset:
Reservoir Computing is a type of recursive neural network commonly used for recognizing and predicting spatio-temporal events relying on a complex hierarchy of nested feedback loops to generate a memory functionality. The Reservoir Computing paradigm does not require any knowledge of the reservoir topology or node weights for training purposes and can therefore utilize naturally existing networks formed by a wide variety of physical processes. Most efforts prior to this have focused on utilizing memristor techniques to implement recursive neural networks. This paper examines the potential of skyrmion fabrics formed in magnets with broken inversion symmetry that may provide an attractive physical instantiation for Reservoir Computing.
I revue the so called Wilson loop approach to bound state problem in QCD. I shall show how using appropriate path integral representations for the quark propagator in an external field it is possible to obtain corresponding path integral representations for various types of gauge invariant Green functions which have the important feature of involving the gauge field only trough Wilson loop correlators or their generalizations. Two different kinds of representations are used, one given in the form of a semi-relativistic expansion, the second completely relativistic of the Feynmann-Schwinger type. In this way starting from reasonable ansatz on the non perturbative part of the Wilson correlator one can obtain: expressions for the semi relativistic (spin dependent and momentum dependent) q \bar q and 3q potentials, a ``second order'' q \bar q Bethe-Salpeter equation and and a related Dyson-Schwinger equation. I shall concentrate on the three quark potential for which new controversial results have been obtained by lattice numerical simulations and on a three dimensional reduction of the BS equation obtained in the form of the eigenvalue equation of of a squared or a usual mass operator. We shall report on a numerical resolution of such equations which seems to give a comprehensive reproduction of the entire meson spectrum with the exception of light pseudo-scalar bound states for which a complete four dimensional treatment should be necessary.
We show that a recent purported correction to the effects of Doppler boosting of flux density in an erstwhile published formula for calculating the observer's motion from the cosmic radio dipole in sky brightness is erroneous. The thereby computed downward correction in the estimated magnitude for the observer's motion needs to be scrapped and the results derived therefore need to be reverted back to their erstwhile values.
Quantum algorithms have the potential to provide exponential speedups over some of the best known classical algorithms. These speedups may enable quantum devices to solve currently intractable problems such as those in the fields of optimization, material science, chemistry, and biology. Thus, the realization of large-scale, reliable quantum-computers will likely have a significant impact on the world. For this reason, the focus of this dissertation is on the development of quantum-computing applications and robust, scalable quantum-architectures. I begin by presenting an overview of the language of quantum computation. I then, in joint work with Ojas Parekh, analyze the performance of the quantum approximate optimization algorithm (QAOA) on a graph problem called Max Cut. Next, I present a new stabilizer simulation algorithm that gives improved runtime performance for topological stabilizer codes. After that, in joint work with Andrew Landahl, I present a new set of procedures for performing logical operations called "color-code lattice-surgery." Finally, I describe a software package I developed for studying, developing, and evaluating quantum error-correcting codes under realistic noise.
Let $E$ be a CM number field and $F$ its maximal real subfield. We prove a level-raising result for regular algebraic conjugate self-dual automorphic representations of $GL_n(\mathbb{A}_E)$. This generalizes previously known results of Thorne by removing certain hypotheses occurring in that work. In particular, the level-raising prime $p$ is allowed to be unramified as opposed to inert in $F$, the field $E/F$ is not assumed to be everywhere unramified, and the field $E$ is allowed to be a general CM field.
We use dimensional regularization to evaluate quantum mechanical path integrals in arbitrary curved spaces on an infinite time interval. We perform 3-loop calculations in Riemann normal coordinates, and 2-loop calculations in general coordinates. It is shown that one only needs a covariant two-loop counterterm (V_{DR} = R/8) to obtain the same results as obtained earlier in other regularization schemes. It is also shown that the mass term needed in order to avoid infrared divergences explicitly breaks general covariance in the final result.
We investigate the temperature and voltage dependence of the quantum interference in an electronic Mach-Zehnder interferometer using edge channels in the integer quantum-Hall-regime. The amplitude of the interference fringes is significantly smaller than expected from theory; nevertheless the functional dependence of the visibility on temperature and bias voltage agrees very well with theoretical predictions. Superimposed on the Aharonov-Bohm (AB) oscillations, a conductance oscillation with six times smaller period is observed. The latter depends only on gate voltage and not on the AB-phase, and may be related to single electron charging.
We study, from the perspective of large financial markets, the asymptotic arbitrage opportunities in a sequence of binary markets approximating the fractional Black-Scholes model. This approximating sequence was introduced by Sottinen and named fractional binary market. The large financial market under consideration does not satisfy the standard assumptions of the theory of asymptotic arbitrage. For this reason, we follow a constructive approach to show first that a strong type of asymptotic arbitrage exists in the large market without transaction costs. Indeed, with the help of an appropriate version of the law of large numbers and a stopping time procedure, we construct a sequence of self-financing strategies, which leads to the desired result. Next, we introduce, in each small market, proportional transaction costs, and we construct, following a similar argument, a sequence of self-financing strategies providing a strong asymptotic arbitrage when the transaction costs converge fast enough to 0.
We study Nahm transformation for parabolic Higgs bundles on the projective line \PP^1, with logarithmic singularities on a finite set P. Such a Higgs bundle can be given by its spectral data: a Hirzebruch surface Z together with a coherent sheaf M on Z, supported in dimension 1 and away from infinity. We describe the transform in terms of these data. The main technical tool is the notion of proper transform of a coherent sheaf with respect to a blow-up. Finally, we prove the main properties of the induced map on moduli spaces: involutibility and preservation of the hyper-Kaehler structure.
We propose novel mixed states in two qubits, ``maximally entangled mixed states'', which have a property that the amount of entanglement of these states cannot be increased further by applying any unitary operations. The property is proven when the rank of the states is less than 4, and confirmed numerically in the other general cases. The corresponding entanglement of formation specified by its eigenvalues gives an upper bound of that for density matrices with same eigenvalues.
$K\pi$ scattering and $K_{\mu 4}$ decays are studied at leading order of improved chiral perturbation theory. It is shown that high precision $K_{\mu 4}$ experiments at, e.g., DA$\Phi$NE should allow for a direct measurement of the quark mass ratio $m_s$/${\hat m}$.
In this paper we discuss some aspects of N=1 type I-heterotic string duality in four dimensions. We consider a particular example of a (weak-weak) dual pair where on the type I side there are only D9-branes corresponding to perturbative heterotic description in a certain region of the moduli space. We match the perturbative type I and heterotic tree-level massless spectra via giving certain scalars appropriate vevs, and point out the crucial role of the perturbative superpotential (on the heterotic side) for this matching. We also discuss the role of anomalous U(1) gauge symmetry present in both type I and heterotic models. In the perturbative regime we match the (tree-level) moduli spaces of these models. Since both type I and heterotic models can be treated perturbatively, we are able to discuss a dictionary that in generic models maps type I description onto heterotic one, and vice-versa. Finally, we discuss possible directions to study perturbative quantum corrections to the moduli space, as well as outline ways to learn about the non-perturbative effects in both descriptions.
We use a large N-body simulation to examine the detectability of HI in emission at redshift z ~ 1, and the constraints imposed by current observations on the neutral hydrogen mass function of galaxies at this epoch. We consider three different models for populating dark matter halos with HI, designed to encompass uncertainties at this redshift. These models are consistent with recent observations of the detection of HI in emission at z ~ 0.8. Whilst detection of 21 cm emission from individual halos requires extremely long integrations with existing radio interferometers, such as the Giant Meter Radio Telescope (GMRT), we show that the stacked 21 cm signal from a large number of halos can be easily detected. However, the stacking procedure requires accurate redshifts of galaxies. We show that radio observations of the field of the DEEP2 spectroscopic galaxy redshift survey should allow detection of the HI mass function at the 5-12 sigma level in the mass range 10^(11.4) M_sun/h < M_halo < 10^(12.5)M_sun/h, with a moderate amount of observation time. Assuming a larger noise level that corresponds to an upper bound for the expected noise for the GMRT, the detection significance for the HI mass function is still at the 1.7-3 sigma level. We find that optically undetected satellite galaxies enhance the HI emission profile of the parent halo, leading to broader wings as well as a higher peak signal in the stacked profile of a large number of halos. We show that it is in principle possible to discern the contribution of undetected satellites to the total HI signal, even though cosmic variance limitation make this challenging for some of our models.
We have considered a new type of 'XY' model where spins are placed on concentric ring with constant spin density in every ring. The spin executes continuous rotation under a modified Shore-Zwanzig Hamiltonian (J. Chem. Phys. 63, 5445 (1975)). We have performed Monte Carlo simulation using Glauber acceptance criteria. Computations of Binder's cumulant, specific heat and magnetic susceptibility all show presence of a finite temperature order-disorder phase transition in this spin system. The system size dependence of Binder's cumulant suggests the existence of a phase transition with a transition temperature of T* = 1.2. However, we have found no signature of the occurrence of vortex in our SOR model. The absence of hysteresis rules out the possibility of first order phase transition. We have found two "stable" states for T* = 0 phase. The perfectly ordered true ground state is obtained by gradual cooling of the system, while the other is obtained by starting the simulation with a random configuration at T* = 0. This second state has higher energy than the perfectly aligned ground state.
Parameters and abundances have been derived for 435 Cepheids based on an analysis of 1127 spectra. Results from five or more phases are available for 52 of the program stars. The latter set of stars span periods between 1.5 and 68 days. The parameters and abundances show excellent consistency across phase. For iron, the average range in the determined abundance is 0.11 from these 52 stars. For 163 stars with more than one phase available the average range is 0.07. The variation in effective temperature tracks well with phase, as does the total broadening velocity. The gravity and microturbulent velocity follow phase, but with less variation and regularity.   Abundance gradients have been derived using GAIA DR2 parallax data (GAIA Collaboration et al. 2016, 2018), as well as Bayesian distance estimates based upon GAIA DR2 from Bailer-Jones et al. (2018). The abundance gradient derived for iron is d[Fe/H]/dR = -0.05 dex/kpc, similar to gradients derived in previous studies.
We study Le Potier's strange duality conjecture for moduli spaces of sheaves over generic abelian surfaces. We prove the isomorphism for abelian surfaces which are products of elliptic curves, when the moduli spaces consist of sheaves of equal ranks and fiber degree 1. The birational type of the moduli space of sheaves is also investigated. Generalizations to arbitrary product elliptic surfaces are given.
The unitarity equations for the boson interaction amplitudes in the superstring theory are used to calculate the interaction amplitudes including the Ramond states, which are 10-fermion and Ramond bosons. The n-loop, 4-point amplitude with two massless Neveu-Schwarz bosons and two massless Ramond states is obtained explicitly. It is shown that, in addition, the unitarity equations require some integral relations for local functions determining the amplitude. For the tree amplitude the validness of the above integral relations is verified.
In this work, we adopt first-principle calculations based on density functional theory and Kinetic Monte Carlo simulations to investigate the adsorption and diffusion of lithium in bilayer graphene (BLG) as anodes in lithium-ion batteries. Based on energy barriers directly obtained from first-principle calculations for single-Li and two-Li intercalated BLG, a new equation was deduced for predicting energy barriers considering Li's interactions for multi-Li intercalated BLG. Our calculated results indicate that Li energetically prefers to intercalate within rather than adsorb outside the bilayer graphene. Additionally, lithium exists in cationic state in the bilayer graphene. More excitingly, ultrafast Li diffusion coefficient, within AB-stacked BLG near room temperature was obtained, which reproduces the ultrafast Li diffusion coefficient measured in recent experiment. However, ultrafast Li diffusion was not found within AA-stacked BLG near room temperature. The analyses of potential distribution indicate that the stacking structure of BLG greatly affects its height of potential well within BLG, which directly leads to the large difference in Li diffusion. Furthermore, it is found that both the interaction among Li ions and the stacking, structure cause Li diffusion within AB-stacked BLG to exhibit directional preference. Finally, the temperature dependence of Li diffusion is described by the Arrhenius law. These findings suggest that the stacking structure of BLG has an important influence on Li diffusion within BLG, and changing the stacking structure of BLG is one possible way to greatly improve Li diffusion rate within BLG. At last, it is suggested that AB-stacked BLG can be an excellent candidate for anode material in Lithium-ion batteries.
The lifetime of statistical system is introduced. It is supposed that the nonequilibrium statistical operator implicitly contains the lifetime. The operations of taking of invariant part, averaging on initial conditions used in works of D.N. Zubarev, temporary coarse-graining (Kirkwood), choose of the direction of time are replaced by averaging on lifetime distribution. The expression for lifetime change at transitions from quasi-equilibrium system to nonequilibrium one is derived. A sort of the nonequilibrium statistical operator for systems of the finite sizes is suggested.
We prove that, as $n$ approaches infinity, the proportion of $n$-element matroids that are representable tends to zero.
We present quasi-elastic neutrino-nucleus cross sections in the energy range from 150 MeV up to 5 GeV for the target nuclei 12C and 56Fe. A relativistic description of the nuclear dynamics and the neutrino-nucleus coupling is adopted. For the treatment of final-state interactions (FSI) we rely on two frameworks succesfully applied to exclusive electron-nucleus scattering: a relativistic optical potential and a relativistic multiple-scattering Glauber approximation. At lower energies, the optical-potential approach is considered to be the optimum choice, whereas at high energies a Glauber approach is more natural. Comparing the results of both calculations, it is found that the Glauber approach yields valid results down to the remarkably small nucleon kinetic energies of 200 MeV. We argue that the nuclear transparencies extracted from A(e,e'p) measurements can be used to obtain realistic estimates of the effect of FSI mechanisms on quasi-elastic neutrino-nucleus cross sections. We present two independent relativistic plane-wave impulse approximation (RPWIA) calculations of quasi-elastic neutrino-nucleus cross sections. They agree at the percent level, showing the reliability of the numerical techniques adopted and providing benchmark RPWIA results.
In this work, a new algorithm is proposed to compute single particle (infinite dilution) thermodiffusion using Non-Equilibrium Molecular Dynamics simulations through the estimation of the thermophoretic force that applies on a solute particle. This scheme is shown to provide consistent results for simple Lennard-Jones fluids and for model nanofluids (spherical non-metallic nanoparticles + Lennard-Jones fluid) where it appears that thermodiffusion amplitude, as well as thermal conductivity, decrease with nanoparticles concentration. Then, in nanofluids in the liquid state, by changing the nature of the nanoparticle (size, mass and internal stiffness) and of the solvent (quality and viscosity) various trends are exhibited. In all cases the single particle thermodiffusion is positive, i.e. the nanoparticle tends to migrate toward the cold area. The single particle thermal diffusion 2 coefficient is shown to be independent of the size of the nanoparticle (diameter of 0.8 to 4 nm), whereas it increases with the quality of the solvent and is inversely proportional to the viscosity of the fluid. In addition, this coefficient is shown to be independent of the mass of the nanoparticle and to increase with the stiffness of the nanoparticle internal bonds. Besides, for these configurations, the mass diffusion coefficient behavior appears to be consistent with a Stokes-Einstein like law.
Under minimal condition, we prove the local convergence of a critical multi-type Galton-Watson tree conditioned on having a large total progeny by types towards a multi-type Kesten's tree. We obtain the result by generalizing Neveu's strong ratio limit theorem for aperiodic random walks on Z^d .
We give a survey on some aspects of deformations of isolated singularities. In addition to the presentation of the general theory, we report on the question of the smoothability of a singularity and on relations between different invariants, such as the Milnor number, the Tjurina number, and the dimension of a smoothing component.
Horizontal gene transfer consists in exchanging genetic materials between microorganisms during their lives. This is a major mechanism of bacterial evolution and is believed to be of main importance in antibiotics resistance. We consider a stochastic model for the evolution of a discrete population structured by a trait taking finitely many values, with density-dependent competition. Traits are vertically inherited unless a mutation occurs, and can also be horizontally transferred by unilateral conjugation with frequency dependent rate. Our goal is to analyze the trade-off between natural evolution to higher birth rates on one side, and transfer which drives the population towards lower birth rates on the other side. Simulations show that evolutionary outcomes include evolutionary suicide or cyclic re-emergence of small populations with well-adapted traits. We focus on a parameter scaling where individual mutations are rare but the global mutation rate tends to infinity. This implies that negligible sub-populations may have a strong contribution to evolution. Our main result quantifies the asymptotic dynamics of subpopulation sizes on a logarithmic scale. We characterize the possible evolutionary outcomes with explicit criteria on the model parameters. An important ingredient for the proofs lies in comparisons of the stochastic population process with linear or logistic birth-death processes with immigration. For the latter processes, we derive several results of independent interest.
The purpose of this White Paper is to review recent progress towards elucidating and evaluating string amplitudes, relating them to quantum field theory amplitudes, applying their predictions to string dualities, exploring their connection with gravitational physics, and deepening our understanding of their mathematical structure. We also present a selection of targets for future research.
We present a new class of magnetic brane solutions in $(n+1)$-dimensional Brans-Dicke-Maxwell theory in the presence of a quadratic potential for the scalar field. These solutions are neither asymptotically flat nor (anti)-de Sitter. Our strategy for constructing these solutions is applying a conformal transformation to the corresponding solutions in dilaton gravity. This class of solutions represents a spacetime with a longitudinal magnetic field generated by a static brane. They have no curvature singularity and no horizons but have a conic geometry with a deficit angle $\delta$. We generalize this class of solutions to the case of spinning magnetic brane with all rotation parameters. We also use the counterterm method and calculate the conserved quantities of the solutions.
The plastic flow of a polycrystal is analyzed assuming grains as fine that the rate limiting process is grain boundary sliding, and grains readily accommodate their shapes by slip to preserve spatial continuity. It is shown that thinking of a polycrystal with randomly oriented grains as an homogeneous and isotropic continuum when dealing with it as a dynamical medium, even in a scale much larger than the grain size, leads to gross errors. The polyhedral nature of grains influences the plastic flow in a radical manner, as the relative velocity of adjacent grains is constrained to the common boundary plane, and only the in--plane shear stress contributes to their relative motion. This constriction determines that the divergency of the velocity field of the material medium does not vanish, and plastic deformation necessarily involves grain volume variations, which can only be elastic. As this has a limit, fracture follows as a necessary step of plastic flow. A theoretical approach to plastic flow is developed, and emphasis is done in superplastic deformation, from zero to fracture strain. The theory allows to quantitatively explain the observed features of superplastic materials and responds to many open questions in the field.
Let $\Delta_{k}(n)$ denote the number of $k$-broken diamond partitions of $n$. Quite recently, the second author proved an infinite family of congruences modulo 25 for $\Delta_{k}(n)$ with the help of modular forms. In this paper, we aim to provide an elementary proof of this result.
We generalize the covariant c-map found in hep-th/0701214 including perturbative quantum corrections. We also perform explicitly the superconformal quotient from the hyperkahler cone obtained by the quantum c-map to the quaternion-Kahler space, which is the moduli space of hypermultiplets. As a result, the perturbatively corrected metric on the moduli space is found in a simplified form comparing to the expression known in the literature.