ShantanuT01/DACTYL-Pretraining huggingface dataset:
Fractional derivatives are nonlocal differential operators of real order that often appear in models of anomalous diffusion and a variety of nonlocal phenomena. Recently, a version of the Schr\"odinger Equation containing a fractional Laplacian has been proposed. In this work, we develop a Fractional Path Integral Monte Carlo algorithm that can be used to study the finite temperature behavior of the time-independent Fractional Schr\"odinger Equation for a variety of potentials. In so doing, we derive an analytic form for the finite temperature fractional free particle density matrix and demonstrate how it can be sampled to acquire new sets of particle positions. We employ this algorithm to simulate both the free particle and $^{4}$He (Aziz) Hamiltonians. We find that the fractional Laplacian strongly encourages particle delocalization, even in the presence of interactions, suggesting that fractional Hamiltonians may manifest atypical forms of condensation. Our work opens the door to studying fractional Hamiltonians with arbitrarily complex potentials that escape analytical solutions.
We propose a generalization of the classical M/M/1 queue process. The resulting model is derived by applying fractional derivative operators to a system of difference-differential equations. This generalization includes both non-Markovian and Markovian properties, which naturally provide greater flexibility in modeling real queue systems than its classical counterpart. Algorithms to simulate M/M/1 queue process and the related linear birth-death process are provided. Closed-form expressions of the point and interval estimators of the parameters of these fractional stochastic models are also presented. These methods are necessary to make these models usable in practice. The proposed fractional M/M/1 queue model and the statistical methods are illustrated using S&P data.
Starting from the (Hubbard) model of an atom, we demonstrate that the uniqueness of the mapping from the interacting to the noninteracting Green's function, $G\to G_0$, is strongly violated, by providing numerous explicit examples of different $G_0$ leading to the same physical $G$. We argue that there are indeed infinitely many such $G_0$, with numerous crossings with the physical solution. We show that this rich functional structure is directly related to the divergence of certain classes of (irreducible vertex) diagrams, with important consequences for traditional many-body physics based on diagrammatic expansions. Physically, we ascribe the onset of these highly non-perturbative manifestations to the progressive suppression of the charge susceptibility induced by the formation of local magnetic moments and/or RVB states in strongly correlated electron systems.
Real-world scenarios pose several challenges to deep learning based computer vision techniques despite their tremendous success in research. Deeper models provide better performance, but are challenging to deploy and knowledge distillation allows us to train smaller models with minimal loss in performance. The model also has to deal with open set samples from classes outside the ones it was trained on and should be able to identify them as unknown samples while classifying the known ones correctly. Finally, most existing image recognition research focuses only on using two-dimensional snapshots of the real world three-dimensional objects. In this work, we aim to bridge these three research fields, which have been developed independently until now, despite being deeply interrelated. We propose a joint Knowledge Distillation and Open Set recognition training methodology for three-dimensional object recognition. We demonstrate the effectiveness of the proposed method via various experiments on how it allows us to obtain a much smaller model, which takes a minimal hit in performance while being capable of open set recognition for 3D point cloud data.
NGC 147 and NGC 185 are two of the most massive satellites of the Andromeda galaxy (M 31). Close together in the sky, of similar mass and morphological type dE, they possess different amounts of interstellar gas and tidal distortion. The question therefore is, how do their histories compare? Here we present the first reconstruction of the star formation histories of NGC 147 and NGC 185 using long-period variable stars. These represent the final phase of evolution of low- and intermediate-mass stars at the asymptotic giant branch, when their luminosity is related to their birth mass. Combining near-infrared photometry with stellar evolution models, we construct the mass function and hence the star formation history. For NGC 185 we found that the main epoch of star formation occurred 8.3 Gyr ago, followed by a much lower, but relatively constant star formation rate. In the case of NGC 147, the star formation rate peaked only 7 Gyr ago, staying intense until ~ 3 Gyr ago, but no star formation has occurred for at least 300 Myr. Despite their similar masses, NGC 147 has evolved more slowly than NGC 185 initially, but more dramatically in more recent times. This is corroborated by the strong tidal distortions of NGC 147 and the presence of gas in the centre of NGC 185.
This paper proposes the CogSense system, which is inspired by sense-making cognition and perception in the mammalian brain to perform perception error detection and perception parameter adaptation using probabilistic signal temporal logic. As a specific application, a contrast-based perception adaption method is presented and validated. The proposed method evaluates perception errors using heterogeneous probe functions computed from the detected objects and subsequently solves a contrast optimization problem to correct perception errors. The CogSense probe functions utilize the characteristics of geometry, dynamics, and detected blob image quality of the objects to develop axioms in a probabilistic signal temporal logic framework. By evaluating these axioms, we can formally verify whether the detections are valid or erroneous. Further, using the CogSense axioms, we generate the probabilistic signal temporal logic-based constraints to finally solve the contrast-based optimization problem to reduce false positives and false negatives.
We present high-resolution long-slit spectroscopy of a Balmer-dominated shock in the northeastern limb of the Cygnus Loop with the Subaru high dispersion spectrograph. By setting the slit angle along the shock normal, we investigate variations of the flux and profile of the H-alpha line from preshock to postshock regions with a spatial resolution of about 4 times 10^{15} cm. The H-alpha line profile can be represented by a narrow (28.9+/-0.7 km/s) Gaussian in a diffuse region ahead of the shock, i.e., a photoionization precursor, and narrow (33.1+/-0.2 km/s) plus broad (130-230 km/s) Gaussians at the shock itself. We find that the width of the narrow component abruptly increases up to 33.1+/-0.2 km/s, or 38.8+/-0.4 km/s if we eliminate projected emission originating from the photoionization precursor, in an unresolved thin layer (< 4 times 10^{15} cm at a distance of 540 pc) at the shock. We show that the sudden broadening can be best explained by heating via damping of Alfven waves in a thin cosmic-ray precursor, although other possibilities are not fully ruled out. The thickness of the cosmic-ray precursor in the Cygnus Loop (a soft gamma-ray emitter) is an order of magnitude thinner than that in Tycho's Knot g (a hard gamma-ray emitter), which may be caused by different energy distribution of accelerated particles between the two sources. In this context, systematic studies might reveal a positive correlation between the thickness of the cosmic-ray precursor and the hardness of the cosmic-ray energy distribution.
JHK_S photometry is presented for a 35 arcmin square field centred on the Sculptor dwarf spheroidal galaxy. With the aid of published kinematic data definite galaxy members are identified and the width in J-K of the colour-magnitude diagram is shown to be consistent with an old population of stars with a large range in metal abundance. We identify two Asymptotic Giant Branch variables, both carbon Miras, with periods of 189 and 554 days, respectively, and discuss their ages, metallicities and mass loss as well as their positions in the Mira period-luminosity diagram. There is evidence for a general period-age relation for Local Group Miras. The mass-loss rate for the 554-day variable, MAG29, appears to be consistent with that found for Miras of comparable period in other Local Group galaxies.
We consider a branching Brownian motion which starts from $0$ with drift $\mu \in \mathbb{R}$ and we focus on the number $Z_x$ of particles killed at $-x$, where $x>0$. Let us call $\mu_0$ the critical drift such that there is a positive probability of survival if and only if $\mu>-\mu_0$. Maillard \cite{maillard2013number} and Berestycki et al. \cite{berestycki2015branching} have study $Z_x$ in the case $\mu \leq -\mu_0$ and $\mu\geq \mu_0$ respectively. We complete the picture by considering the case where $\mu>-\mu_0$ on the extinction event. More precisely we study the asymptotic of $q_i(x):=\mathbb{P}\left(Z_x=i,\zeta_x<\infty\right)$. We show that the radius of convergence $R(\mu)$ of the corresponding power series increases as $\mu$ increases, up until $\mu=\mu_c\in [-\mu_0,+\infty]$ after which it is constant. We also give a necessary and sufficient condition for $\mu_c<+\infty$. In addition, finer asymptotics are also obtained, which highlight three different regimes depending on $\mu<\mu_c$, $\mu=\mu_c$ or $\mu>\mu_c$.
A spin metal-oxide-semiconductor field-effect-transistor (spin MOSFET), which combines a Schottky-barrier MOSFET with ferromagnetic source and drain contacts, is a promising device for spintronic logic. Previous simulation studies predict that this device should display a very high magnetoresistance (MR) ratio (between the cases of parallel and anti-parallel magnetizations) for the case of half-metal ferromagnets (HMF). We use the non-equilibrium Green's function (NEGF) formalism to describe tunneling and carrier transport in this device and to incorporate spin relaxation at the HMF-semiconductor interfaces. Spin relaxation at interfaces results in non-ideal spin injection. Minority spin currents arise and dominate the leakage current for anti-parallel magnetizations. This reduces the MR ratio and sets a practical limit for spin MOSFET performance. We found that MR saturates at a lower value for smaller source-to-drain bias. In addition, spin relaxation at the detector side is found to be more detrimental to MR than that at the injector side, for drain bias less than the energy difference of the minority spin edge and the Fermi level.
The scalars of an N = 1 supersymmetric sigma-model in 4 dimensions parameterize a Kaehler manifold. The transformations of their fermionic superpartners under the isometries are often anomalous. These anomalies can be canceled by introducing additional chiral multiplets with appropriate charges. To obtain the right charges a non-trivial singlet compensating multiplet can be used. However when the topology of the underlying Kaehler manifold is non-trivial, the consistency of this multiplet requires that its charge is quantized. This singlet can be interpreted as a section of a line bundle. We determine the Kaehler potentials corresponding to the minimal non-trivial singlet chiral superfields for any compact Kaehlerian coset space G/H. The quantization condition may be in conflict with the requirement of anomaly cancelation. To illustrate this, we discuss the consistency of anomaly free models based on the coset spaces E_6/SO(10)xU(1) and SU(5)/SU(2)xU(1)xSU(3).
Solar flares are rapid energy release phenomena that appear as bright ribbons in the chromosphere and high-temperature loops in the corona, respectively. Supra-arcade Downflows (SADs) are plasma voids that first come out above the flare loops and then move quickly towards the flare loop top during the decay phase of the flare. In our work, we study 20 SADs appearing in three flares. By differential emission measure (DEM) analysis, we calculate the DEM weighted average temperature and emission measure (EM) of the front region and the main body of SADs. It is found that the temperatures of the SAD front and body tend to increase during the course of SADs flowing downwards. The relationship between the pressure and temperature fits well with the adiabatic equation for both the SAD front and body, suggesting that the heating of SADs is mainly caused by adiabatic compression. Moreover, we also estimate the velocities of SADs via the Fourier Local Correlation Tracking (FLCT) method and find that increase of the temperature of the SAD front presents a correlation with the decrease of the SAD kinetic energy, while the SAD body does not, implying that the viscous process may also heat the SAD front in spite of a limited role.
Determination of the coronal electron density by the inversion of white-light polarized brightness (pB) measurements by coronagraphs is a classic problem in solar physics. An inversion technique based on the spherically symmetric geometry (Spherically Symmetric Inversion, SSI) was developed in the 1950s, and has been widely applied to interpret various observations. However, to date there is no study about uncertainty estimation of this method. In this study we present the detailed assessment of this method using a three-dimensional (3D) electron density in the corona from 1.5 to 4 Rsun as a model, which is reconstructed by tomography method from STEREO/COR1 observations during solar minimum in February 2008. We first show in theory and observation that the spherically symmetric polynomial approximation (SSPA) method and the Van de Hulst inversion technique are equivalent. Then we assess the SSPA method using synthesized pB images from the 3D density model, and find that the SSPA density values are close to the model inputs for the streamer core near the plane of the sky (POS) with differences generally less than a factor of two or so; the former has the lower peak but more spread in both longitudinal and latitudinal directions than the latter. We estimate that the SSPA method may resolve the coronal density structure near the POS with angular resolution in longitude of about 50 degrees. Our results confirm the suggestion that the SSI method is applicable to the solar minimum streamer (belt) as stated in some previous studies. In addition, we demonstrate that the SSPA method can be used to reconstruct the 3D coronal density, roughly in agreement with that by tomography for a period of low solar activity. We suggest that the SSI method is complementary to the 3D tomographic technique in some cases, given that the development of the latter is still an ongoing research effort.
We introduce an architecture for robust and scalable quantum computation using both stationary qubits (e.g. single photon sources made out of trapped atoms, molecules, ions, quantum dots, or defect centers in solids) and flying qubits (e.g. photons). Our scheme solves some of the most pressing problems in existing non-hybrid proposals, which include the difficulty of scaling conventional stationary qubit approaches, and the lack of practical means for storing single photons in linear optics setups. We combine elements of two previous proposals for distributed quantum computing, namely the efficient photon-loss tolerant build up of cluster states by Barrett and Kok [Phys. Rev. A 71, 060310(R) (2005)] with the idea of Repeat-Until-Success (RUS) quantum computing by Lim et al. [Phys. Rev. Lett. 95, 030505 (2005)]. This idea can be used to perform eventually deterministic two-qubit logic gates on spatially separated stationary qubits via photon pair measurements. Under non-ideal conditions, where photon loss is a possibility, the resulting gates can still be used to build graph states for one-way quantum computing. In this paper, we describe the RUS method, present possible experimental realizations, and analyse the generation of graph states.
We report on the experimental investigation of an individual pseudomolecule using trapped ions with adjustable magnetically induced J-type coupling between spin states. Resonances of individual spins are well separated and are addressed with high fidelity. Quantum gates are carried out using microwave radiation in the presence of thermal excitation of the pseudomolecule's vibrations. Demonstrating Controlled-NOT gates between non-nearest neighbors serves as a proof-of-principle of a quantum bus employing a spin chain. Combining advantageous features of nuclear magnetic resonance experiments and trapped ions, respectively, opens up a new avenue towards scalable quantum information processing.
We prove sufficient conditions, ensuring that a sequence of multiple Wiener-It\^{o} integrals (with respect to a general Gaussian process) converges stably to a mixture of normal distributions. Our key tool is an asymptotic decomposition of contraction kernels, realized by means of increasing families of projection operators. We also use an infinite-dimensional Clark-Ocone formula, as well as a version of the correspondence between "abstract" and "concrete" filtered Wiener spaces, in a spirit similar to \"{U}st\"{u}nel and Zakai (1997).
We consider the Cauchy problem for nonlinear Schrodinger equations in the presence of a smooth, possibly unbounded, potential. No assumption is made on the sign of the potential. If the potential grows at most linearly at infinity, we construct solutions in Sobolev spaces (without weight), locally in time. Under some natural assumptions, we prove that the $H^1$-solutions are global in time. On the other hand, if the potential has a super-linear growth, then the Sobolev regularity of positive order is lost instantly, not matter how large it is, unless the initial datum decays sufficiently fast at infinity.
We investigated the magnetotransport in high quality ferromagnetic (Ga,Mn)As films and wires. At low temperature the conductivity decreases with decreasing temperature without saturation down to 20 mK. Here we show, that the conductivity decrease follows a ln($T/T_0$) dependency in 2D films and a $-1/\sqrt{T}$ dependency in 1D wires and is independent of an applied magnetic field. This behavior can be explained by the theory of electron-electron interaction.
The field equations of elementary domains proposed by Yukawa in 1968 are studied from the viewpoint of particle embedded $\mbox{AdS}_5$ spacetime with warp factor. The fifth dimension in $\mbox{AdS}_5$ is known to produce the branes associated with the energy hierarchy as a effect of the warp factor. The particles embedded in this spacetime behave as those in an infinite square well potential due to the boundary conditions in the fifth dimension. Then the superposition of the fields for those particles leads to a Yukawa's domain type of difference equation under some conditions. As a new perspective on AdS spacetime, we investigate the mechanisms that lie between the domain type of field equations in this sense and the spacetime with a compact extra dimension in detail.
We discuss instanton operators in five-dimensional gauge theories. These are defined as disorder operators which create a non-vanishing second Chern class on a four-sphere surrounding their insertion point. As such they may be thought of as higher-dimensional analogues of three-dimensional monopole (or `t Hooft) operators. We argue that they play an important role in the enhancement of the Lorentz symmetry for maximally supersymmetric Yang-Mills to SO(1,5) at strong coupling.
The radio continuum spectra of 14 star-forming galaxies are investigated by fitting nonthermal (synchrotron) and thermal (free-free) radiation laws. The underlying radio continuum measurements cover a frequency range of ~325 MHz to 24.5 GHz (32 GHz in case of M82). It turns out that most of these synchrotron spectra are not simple power-laws, but are best represented by a low-frequency spectrum with a mean slope alpha_nth = 0.59 +/- 0.20 (S_nu ~ nu^-alpha), and by a break or an exponential decline in the frequency range of 1 - 12 GHz. Simple power-laws or mildly curved synchrotron spectra lead to unrealistically low thermal flux densities, and/or to strong deviations from the expected optically thin free-free spectra with slope alpha_th = 0.10 in the fits. The break or cutoff energies are in the range of 1.5 - 7 GeV. We briefly discuss the possible origin of such a cutoff or break. If the low-frequency spectra obtained here reflect the injection spectrum of cosmic-ray electrons, they comply with the mean spectral index of Galactic supernova remnants. A comparison of the fitted thermal flux densities with the (foreground-corrected) Halpha fluxes yields the extinction, which increases with metallicity. The fraction of thermal emission is higher than believed hitherto, especially at high frequencies, and is highest in the dwarf galaxies of our sample, which we interpret in terms of a lack of containment in these low-mass systems, or a time effect caused by a very young starburst.
We report a simple and reproducible method to fabricate two metallic electrodes made of different metals with a nanometer-sized gap. These electrodes are fabricated by defining a pair of gold electrodes lithographically and electrodepositing a second metal onto one of them. The method enables the fabrication of pairs of metallic electrodes that exhibit distinct magnetic properties or work functions. The utility of this technique is demonstrated by making single-electron tunneling devices incorporating 2-nm gold nanocrystals.
Globular clusters (GCs) are found ubiquitously in massive galaxies and due to their old ages, they are regarded as fossil records of galaxy evolution. Spectroscopic studies of GC systems are often limited to the outskirts of galaxies, where GCs stand out against the galaxy background and serve as bright tracers of galaxy assembly. In this work, we use the capabilities of the Multi Unit Explorer Spectrograph (MUSE) to extract a spectroscopic sample of 722 GCs in the inner regions ($\lesssim 3 R_\text{eff}$) of 32 galaxies in the Fornax cluster. These galaxies were observed as part of the Fornax 3D project, a MUSE survey that targets early and late-type galaxies within the virial radius of Fornax. After accounting for the galaxy background in the GC spectra, we extracted line-of-sight velocities and determined metallicities of a sub-sample of 238 GCs. We found signatures of rotation within GC systems, and comparing the GC kinematics and that of the stellar body shows that the GCs trace the spheroid of the galaxies. While the red GCs prove to closely follow the metallicity profile of the host galaxy, the blue GCs show a large spread of metallicities but they are generally more metal-poor than the host.
We prove that the harmonic map flow from the Euclidean space $\mathbb{R}^d$ into the sphere $S^d$ has no equivariant self-similar shrinking solutions in dimensions $d\geq 7$.
Kondo temperature is standardly defined from the local zero-temperature susceptibility in the regime of strong electron correlations as a new scale controlling the low-temperature asymptotics of thermodynamic quantities. We show by using a two-particle self-consistent theory that the Kondo temperature can be identified as a crossover temperature at which the zero-temperature quantum fluctuations equal the thermal ones in the electron-hole correlation function. The high-temperature Curie-Weiss susceptibility is shown to go over to the Pauli one below the Kondo temperature.