ShantanuT01/DACTYL-Pretraining huggingface dataset:
Matrix exponentiation (ME) is widely used in various fields of science and engineering. For example, the unitary dynamics of quantum systems is described by exponentiation of Hamiltonian operators. However, despite a significant attention, the numerical evaluation of ME remains computationally expensive, particularly for large dimensions. Often this process becomes a bottleneck in algorithms requiring iterative evaluation of ME. Here we propose a method for approximating ME of a single operator with a bounded coefficient into a product of certain discrete operators. This approach, which we refer to as Rapid Exponentiation using Discrete Operators (REDO), is particularly efficient for iterating ME over large numbers. We describe REDO in the context of a quantum system with a constant as well as a time-dependent Hamiltonian, although in principle, it can be adapted in a more general setting. As concrete examples, we choose two applications. First, we incorporate REDO in optimal quantum control algorithms and report a speed-up of several folds over a wide range of system size. Secondly, we propose REDO for numerical simulations of quantum dynamics. In particular, we study exotic quantum freezing with noisy drive fields.
We study constraints on the Chern classes of a vector bundle on a singular variety. We use this constraint to study a variety which carries a Hodge cycle that are not a linear combination of Chern classes of vector bundles on it.
The virtual geometry of the moduli space of stable quotients is used to obtain Chow relations among the kappa classes on the moduli space of nonsingular genus g curves. In a series of steps, the stable quotient relations are rewritten in successively simpler forms. The final result is the proof of the Faber-Zagier relations (conjectured in 2000).
We have used the Australia Telescope Compact Array to measure the absorption from the 2(0) - 3(-1}E 12.2 GHz transition of methanol towards the z=0.89 lensing galaxy in the PKS B 1830-211 gravitational lens system. Comparison of the velocity of the main absorption feature with the published absorption spectrum from the 1(0) - 2(-1)E transition of methanol shows that they differ by -0.6 +/- 1.6 km/s . We can use these observations to constrain the changes in the proton-to-electron mass ratio from z=0.89 to the present to 0.8 +/- 2.1 x 10^-7. This result is consistent, and of similar precision to recent observations at z = 0.68 achieved through comparison of a variety of rotational and inversion transitions, and approximately a factor of 2 better than previous constraints obtained in this source. Future more sensitive observations which incorporate additional rotational methanol transitions offer the prospect of improving current results by a factor of 5-10.
We derive a formula for the Bondi mass aspect in terms of asymptotic data of the Bondi-Sachs metric in the affine gauge. We prove the positivity of the total energy of a regular null cone in agreement with a recent result of Chru\'{s}ciel and Paetz.
There is a growing trend in placing video advertisements on social platforms for online marketing, which demands automatic approaches to understand the contents of advertisements effectively. Taking the 2021 TAAC competition as an opportunity, we developed a multimodal system to improve the ability of structured analysis of advertising video content. In our framework, we break down the video structuring analysis problem into two tasks, i.e., scene segmentation and multi-modal tagging. In scene segmentation, we build upon a temporal convolution module for temporal modeling to predict whether adjacent frames belong to the same scene. In multi-modal tagging, we first compute clip-level visual features by aggregating frame-level features with NeXt-SoftDBoF. The visual features are further complemented with textual features that are derived using a global-local attention mechanism to extract useful information from OCR (Optical Character Recognition) and ASR (Audio Speech Recognition) outputs. Our solution achieved a score of 0.2470 measured in consideration of localization and prediction accuracy, ranking fourth in the 2021 TAAC final leaderboard.
Quantum systems often contain negative energy densities. In general relativity, negative energies lead to time advancement, rather than the usual time delay. As a result, some Casimir systems appear to violate energy conditions that would protect against exotic phenomena such as closed timelike curves and superluminal travel. However, when one examines a variety of Casimir systems using self-consistent approximations in quantum field theory, one finds that a particular energy condition is still obeyed, which rules out exotic phenomena. I will discuss the methods and results of these calculations in detail and speculate on their potential implications in general relativity.
The theory of Ihara zeta functions is extended to non-compact arithmetic quotients of Bruhat-Tits trees. This new zeta function turns out to be a rational function, despite the infinite-dimensional setting. In general it has zeros and poles, in contrast to the compact case. The determinant formulas of Bass and Ihara hold true if one defines the determinant as limit of all finite principal minors. From this analysis, a prime geodesic theorem is derived, which, applied to special arithmetic groups, yields new asymptotic assertions on class numbers of orders in global fields.
Derivation and experimental violation of Bell-like inequalities involve the measurement of in-compatible observables. Simple complementarity forbids the existence of such joint probabilitydistribution. Moreover, the measurement of incompatible observables requires different experimen-tal procedures, which no necessarily must share a common joint statistics. In this work, we avoidthese difficulties by proposing a joint simultaneous measurement experiment. We can obtain theexact individual statistics of all the observables involved in the Bell inequalities after a suitable datainversion. A lack of positivity or any other pathology of the so retrieved joint distribution is then asignature of nonclassical behavior.
Given a permutation polynomial of a large finite field, finding its inverse is usually a hard problem. Based on a piecewise interpolation formula, we construct the inverses of cyclotomic mapping permutation polynomials of arbitrary finite fields.
The contact mechanics of individual, very small particles with other particles and walls is studied using a nanoindenter setup that allows normal and lateral displacement control and measurement of the respective forces. The sliding, rolling and torsional forces and torques are tested with borosilicate microspheres, featuring radii of about 10$\mu$m. The contacts are with flat silicon substrates of different roughness for pure sliding and rolling and with silicon based, ion-beam crafted rail systems for combined rolling and torsion.   The experimental results are discussed and compared to various analytical predictions and contact models, allowing for two concurrent interpretations of the effects of surface roughness, plasticity and adhesion. This enables us to determine both rolling and torsion friction coefficients together with their associated length scales. Interestingly, even though normal contacts behave elastically (Hertzian), all other modes of motion display effects due to surface roughness and consequent plastic deformation. The influence of adhesion is interpreted in the framework of different models and is very different for different degrees of freedom, being largest for rolling.
Based on tests of a tentative detector for observing geo-synchrotron hard X-rays generated by primary electrons, we study the feasibility of probing cosmic electrons above a few TeV to over 10 TeV. Such high energy electrons are expected to give proof of sources near the Earth (e.g. supernova remnants such as Vela: age < ~10^5 years located within <~1kpc). The idea itself is rather old; a high energy electron emits synchrotron X-rays successively in the geomagnetic field and thus gives several X-rays aligned on a meter scale. This feature is a clue to overcome the background problem encountered in other traditional observation methods. We critically examine the feasibility of this approach assuming a satellite altitudes observation, and find that it is difficult to derive a precise energy spectrum of electrons but is possible to get a clear signal of the existence of several TeV electrons if the flux is comparable to the level predicted by a class of plausible models. For such observations, an exposure >1 m^2year would be needed. It would be attractive to incorporate the present scheme in the gamma-ray burst observations.
This article is an attempt to generalize the classical theory of reversible computing, principally developed by Bennet [IBM J. Res. Develop., 17(1973)] and by Fredkin and Toffoli [Internat. J. Theoret. Phys., 21(1982)], to the quantum case. This is a fundamental step towards the construction of a quantum computer because a time efficient quantum computation is a reversible physical process. The paper is organized as follows. The first section reviews the classical theory of reversible computing. In the second section it is showed that the designs used in the classical framework to decrease the consumption of space cannot be generalized to the quantum case; it is also suggested that quantum computing is generally more demanding of space than classical computing. In the last section a new model of fully quantum and reversible automaton is proposed. The computational power of this automaton is at least equal to that of classical automata. Some conclusion are drawn in the last section.
The Kolmogorov equation associated to a stochastic 2D Euler equations with transport type noise and random initial conditions is studied by a direct approach, based on Fourier analysis, Galerkin approximation and Wiener chaos methods. The method allows us to generalize previous results and to understand the role of the regularity of the noise, in relation to a limiting value of roughness.
We developed the theory of finite volume form factors in the presence of integrable defects. These finite volume form factors are expressed in terms of the infinite volume form factors and the finite volume density of states and incorporate all polynomial corrections in the inverse of the volume. We tested our results, in the defect Lee-Yang model, against numerical data obtained by truncated conformal space approach (TCSA), which we improved by renormalization group methods adopted to the defect case. To perform these checks we determined the infinite volume defect form factors in the Lee-Yang model exactly, including their vacuum expectation values. We used these data to calculate the two point functions, which we compared, at short distance, to defect CFT. We also derived explicit expressions for the exact finite volume one point functions, which we checked numerically. In all of these comparisons excellent agreement was found.
We present very-high-resolution 1D MHD simulations of the late-stage supernova remnants (SNR). In the post-adiabatic stage the magnetic field has an important and significant dynamical effect on the shock dynamics, the flow structure, and hence the acceleration and emission of cosmic rays. We find that the tangential component of the magnetic field provides pressure support that to a fair degree prevents the collapse of the radiative shell and thus limits the total compression ratio of the partially or fully radiative forward shock. A consequence is that the spectra of cosmic rays would not be as hard as in hydrodynamic simulations. We also investigated the effect on the flow profiles of the magnetic-field inclination and a large-scale gradient in the gas density and/or the magnetic field. A positive density gradient shortens the evolutionary stages whereas a shock obliquity lowers the shock compression. The compression of the tangential component of the magnetic field leads to its dominance in the downstream region of post-adiabatic shocks for a wide range of orientation of the upstream field, which may explain why one preferentially observes tangential radio polarization in old SNRs. As most cosmic rays are produced at late stages of SNR evolution, the post-adiabatic phase and the influence of the magnetic field during it are most important for modeling the cosmic-ray acceleration at old SNRs and the gamma-ray emission from late-stage SNRs interacting with clouds.
(Abridged) We use a high-resolution spectrum of the quasar HE0001-2340 observed with the UVES/VLT to measure Mg isotope abundances in the intervening absorption-line systems at high redshifts. Line profiles are prepared accounting for possible shifts between the individual exposures. Due to unique composition of the selected systems - the presence of several transitions of the same ion - we can test the local accuracy of the wavelength scale calibration which is the main source of errors in the sub-pixel line position measurements. In the system at zabs = 0.45 which is probably a fragment of the outflow caused by SN Ia explosion of high-metallicity white dwarf(s) we measured velocity shifts of MgII and MgI lines relative to other lines (FeI, FeII, CaI, CaII): Delta V(MgII) = -0.44 +/- 0.05 km/s and Delta V(MgI) = -0.17 +/- 0.17$ km/s. This translates into the isotopic ratio 24Mg:25Mg:26Mg = (19 +/- 11):(22 +/- 13):(59 +/- 6) with a strong relative overabundance of heavy Mg isotopes, (25Mg+26Mg)/24Mg = 4, as compared to the solar ratio 24Mg:25Mg:26Mg = 79:10:11, and (25Mg+26Mg)/24Mg = 0.3. At zabs = 1.58, we put a strong constraint on a putative variation of alpha: Delta alpha/alpha = (-1.5 +/- 2.6)x10^{-6} which is one of the most stringent limits obtained from optical spectra of QSOs. We reveal that the wavelength calibration in the range above 7500 A is subject to systematic wavelength-dependent drifts.
e have developed a simple process to obtain large magnetoresistance (MR) in perovskite manganite thin films by a combination of focused ion beam (FIB) milling and 120 keV H$_{2}^{+}$ ion implantation. Metal slits about 70 nm in width were printed by 30 kV focused Ga ion beam nanolithography on a 4 mm track, and the materials in these slits are then irradiated by the accelerated H$_{2}^{+}$ ions. Using this method, in a magnetic field of 5 T we can get a MR${>}$60% over a 230 K temperature scope, with a maximum value of 95% at around 70 K. This technique is very promising in terms of its simplicity and flexibility of fabrication and has potential for high-density integration.
The Lorentz factor (LF) of gamma-ray burst (GRB) ejecta may be constrained by observations of high-energy (HE) spectral attenuation. The recent Fermi-LAT observations of prompt GeV emission from several bright GRBs have leaded to conclusions of unexpectedly large LFs, $\Gamma>10^3$. Here we revisit this problem with two main concerns. (1) With one-zone assumption where all photons are assumed to be generated in the same region (radius) and time, we {\em self-consistently} calculate the $\gamma\gamma$ optical depth by adopting a target photon spectrum with HE cutoff. We find that this might be important when the GRB LF is below a few hundreds. (2) Recent Fermi-LAT observations suggest that the bulk MeV-range and HE ($\ga100$ MeV) emission may arise from different regions. We then consider a two-zone case where HE emission is generated in much larger radii than that of the MeV-range emission. We find that the HE emission may be mainly attenuated by MeV-range emission and that the attenuated HE spectrum does not show an exponential spectral cutoff but a slight steepening. This suggests that there may be no abrupt cutoff due to $\gamma\gamma$ attenuation if relaxing the one-zone assumption. By studying the spectra of three bright Fermi-LAT GRBs 080916C, 090510 and 090902B, we show that a bulk LF of\textbf{ $\Gamma\sim600$ }can be consistent with observations in the two-zone case. Even lower LFs can be obtained in the multi-zone case.
Monocular depth estimation and semantic segmentation are two fundamental goals of scene understanding. Due to the advantages of task interaction, many works study the joint task learning algorithm. However, most existing methods fail to fully leverage the semantic labels, ignoring the provided context structures and only using them to supervise the prediction of segmentation split, which limit the performance of both tasks. In this paper, we propose a network injected with contextual information (CI-Net) to solve the problem. Specifically, we introduce self-attention block in the encoder to generate attention map. With supervision from the ideal attention map created by semantic label, the network is embedded with contextual information so that it could understand scene better and utilize correlated features to make accurate prediction. Besides, a feature sharing module is constructed to make the task-specific features deeply fused and a consistency loss is devised to make the features mutually guided. We evaluate the proposed CI-Net on the NYU-Depth-v2 and SUN-RGBD datasets. The experimental results validate that our proposed CI-Net could effectively improve the accuracy of semantic segmentation and depth estimation.
Electrons are indistinguishable, but the energy of each electron is different in different materials and if we can exploit this energy, then we can systematically study the changes of electronic properties in non free-electron metals.
In this article, we study the existence/multiplicity results for the following variable order nonlocal Choquard problem with variable exponents \begin{equation*} \begin{array}{rl} (-\Delta)_{p(\cdot)}^{s(\cdot)}u(x)&=\lambda|u(x)|^{\alpha(x)-2}u(x)+\left(\DD\int_\Omega\frac{F(y,u(y))}{|x-y|^{\mu(x,y)}}dy\right)f(x,u(x)),\\ &~\hspace{6cm} x\in \Omega, \\ u(x)&=0 ,\hspace{20mm} x\in \Omega^c:=\mathbb R^N\setminus\Omega, \end{array} \end{equation*} where $\Om\subset\mathbb R^N$ is a smooth and bounded domain, $N\geq 2$, $p,s,\mu$ and $\alpha$ are continuous functions on $\mathbb R^N\times\mathbb R^N$ and $f(x,t)$ is continuous function with $F(x,t):=\displaystyle\int_{0}^{t} f(x,s)ds$. Under suitable assumption on $s,p,\mu,\alpha$ and $f(x,t)$, first we study the analogous Hardy-Sobolev-Littlewood-type result for variable exponents suitable for the fractional Sobolev space with variable order and variable exponents. Then we give the existence/multiplicity results for the above equation.
Monolayer AlB$_2$ is composed of two atomic layers: honeycomb borophene and triangular aluminum. In contrast with the bulk phase, monolayer AlB$_2$ is predicted to be a superconductor with a high critical temperature. Here, we demonstrate that monolayer AlB$_2$ can be synthesized on Al(111) via molecular beam epitaxy. Our theoretical calculations revealed that the monolayer AlB$_2$ hosts several Dirac cones along the $\Gamma$--M and $\Gamma$--K directions; these Dirac cones are protected by crystal symmetries and are thus resistant to external perturbations. The extraordinary electronic structure of the monolayer AlB$_2$ was confirmed via angle-resolved photoemission spectroscopy measurements. These results are likely to stimulate further research interest to explore the exotic properties arising from the interplay of Dirac fermions and superconductivity in two-dimensional materials.
In this paper we consider the existence of weakly c\`adl\`ag versions of a solution to a linear equation in a Hilbert space $H$, driven by a Levy process taking values in a Hilbert space $U$. In particular we are interested in diagonal type processes, where process on coordinates are functionals of independent $\alpha$ stable symmetric process. We give the if and only if characterization in this case. We apply the same techniques to obtain a sufficient condition for existence of a c\`adl\`ag versions of stable processes described as integrals of deterministic functions with respect to symmetric $\alpha$-stable random measures with $\alpha\in[1,2)$.
In this paper uniquely list colorable graphs are studied. A graph G is called to be uniquely k-list colorable if it admits a k-list assignment from which G has a unique list coloring. The minimum k for which G is not uniquely k-list colorable is called the M-number of G. We show that every triangle-free uniquely vertex colorable graph with chromatic number k+1, is uniquely k-list colorable. A bound for the M-number of graphs is given, and using this bound it is shown that every planar graph has M-number at most 4. Also we introduce list criticality in graphs and characterize all 3-list critical graphs. It is conjectured that every $\chi_\ell$-critical graph is $\chi'$-critical and the equivalence of this conjecture to the well known list coloring conjecture is shown.
[abridged] The galactic field's late-type stellar single and binary population is calculated on the supposition that all stars form as binaries in embedded star clusters. A recently developed tool (Marks, Kroupa & Oh) is used to evolve the binary star distributions in star clusters for a few Myr so that a particular mixture of single and binary stars is achieved. On cluster dissolution the population enters the galactic field with these characteristics. The different contributions of single stars and binaries from individual star clusters which are selected from a power-law embedded star cluster mass function are then added up. This gives rise to integrated galactic field binary distribution functions (IGBDFs) resembling a galactic field's stellar content (Dynamical Population Synthesis). It is found that the binary proportion in the galactic field of a galaxy is larger the lower the minimum cluster mass, the lower the star formation rate, the steeper the embedded star cluster mass function and the larger the typical size of forming star clusters in the considered galaxy. In particular, period-, mass-ratio- and eccentricity IGBDFs for the Milky Way are modelled. The afore mentioned theoretical IGBDFs agree with independently observed distributions. Of all late-type binaries, 50% stem from M<300M_sun clusters, while 50% of all single stars were born in M>10^4M_sun clusters. Comparison of the G-dwarf and M-dwarf binary population indicates that the stars formed in mass-segregated clusters. In particular it is pointed out that although in the present model all M-dwarfs are born in binary systems, in the Milky Way's Galactic field the majority ends up being single stars. This work predicts that today's binary frequency in elliptical galaxies is lower than in spiral and in dwarf-galaxies. The period and mass-ratio distributions in these galaxies are explicitly predicted.
In this paper, we will give a series of non-congruent numbers with $\equiv3\pmod8$ prime factors.