ShantanuT01/DACTYL-Pretraining huggingface dataset:
The richness of quantum theory's reversible dynamics is one of its unique operational characteristics, with recent results suggesting deep links between the theory's reversible dynamics, its local state space and the degree of non-locality it permits. We explore the delicate interplay between these features, demonstrating that reversibility places strong constraints on both the local and global state space. Firstly, we show that reversible dynamics are trivial (composed of local transformations and permutations of subsytems) in maximally non-local theories whose local state spaces satisfy a dichotomy criterion; this applies to a range of operational models that have previously been studied, such as d-dimensional "hyperballs" and almost all regular polytope systems. By separately deriving a similar result for odd-sided polygons, we show that classical systems are the only regular polytope state spaces whose maximally non-local composites allow for non-trivial reversible dynamics. Secondly, we show that non-trivial reversible dynamics do exist in maximally non-local theories whose state spaces are reducible into two or more smaller spaces. We conjecture that this is a necessary condition for the existence of such dynamics, but that reversible entanglement generation remains impossible even in this scenario.
This paper is devoted to the study of the stability of limit cycles of a nonlinear delay differential equation with a distributed delay. The equation arises from a model of population dynamics describing the evolution of a pluripotent stem cells population. We study the local asymptotic stability of the unique nontrivial equilibrium of the delay equation and we show that its stability can be lost through a Hopf bifurcation. We then investigate the stability of the limit cycles yielded by the bifurcation using the normal form theory and the center manifold theorem. We illustrate our results with some numerics.
The problem of computing the class expansion of some symmetric functions evaluated in Jucys-Murphy elements appears in different contexts, for instance in the computation of matrix integrals. Recently, M. Lassalle gave a unified algebraic method to obtain some induction relations on the coefficients in this kind of expansion. In this paper, we give a simple purely combinatorial proof of his result. Besides, using the same type of argument, we obtain new simpler formulas. We also prove an analogous formula in the Hecke algebra of $(S_{2n},H_n)$ and use it to solve a conjecture of S. Matsumoto on the subleading term of orthogonal Weingarten function. Finally, we propose a conjecture for a continuous interpolation between both problems.
We consider the effect of mass segregation on the observable integrated properties of star clusters. The measurable properties depend on a combination of the dynamical age of the cluster and the physical age of the stars in the cluster. To investigate all possible combinations of these two quantities we propose an analytical model for the mass function of segregated star clusters that agrees with the results of N-body simulations, in which any combination can be specified. For a realistic degree of mass segregation and a fixed density profile we find with increasing age an increase in the measured core radii and a central surface brightness that decreases in all filters more rapidly than what is expected from stellar evolution alone. Within a Gyr the measured core radius increases by a factor of two and the central surface density in all filters of a segregated cluster will be overestimated by a similar factor when not taking into account mass segregation in the conversion from light to mass. We find that the $V-I$ colour of mass segregated clusters decreases with radius by about 0.1-0.2 mag, which could be observable. From recent observations of partially resolved extra-galactic clusters a decreasing half-light radius with increasing wavelength was observed, which was attributed to mass segregation. These observations can not be reproduced by our models. We find that the differences between measured radii in different filters are always smaller than 5%.
We have studied X-ray spectral state transitions that can be seen in the long- term monitoring light curves of bright X-ray binaries from the All-Sky Monitor (ASM) on board the Rossi X-ray Timing Explorer (RXTE) and the Burst Alert Telescope (BAT) on board Swift during a period of five years from 2005 to 2010. We have applied a program to automatically identify the hard-to-soft (H-S) spectral state transitions in the bright X- ray binaries monitored by the ASM and the BAT. In total we identified 128 hard-to-soft transitions, of which 59 occurred after 2008. We also determined the transition fluxes and the peak fluxes of the following soft states, updated the measurements of the luminosity corresponding to the H-S transition and the peak luminosity of the following soft state in about 30 bright persistent and transient black hole and neutron star binaries following Yu & Yan (2009), and found the luminosity correlation and the luminosity range of spectral transitions in data between 2008-2010 are about the same as those derived from the data before 2008. This further strengthen the idea that the luminosity at which the H-S spectral transition occurs in the Galactic X-ray binaries is determined by non-stationary accretion parameters such as the rate-of-change of the mass accretion rate rather than the mass accretion rate itself. The correlation is also found to hold in data of individual sources 4U 1608-52 and 4U 1636-53.
We find that clouds of optically-thin, pressure-confined gas are prone to fragmentation as they cool below $\sim10^6$ K. This fragmentation follows the lengthscale $\sim{c}_{\text{s}}\,t_{\text{cool}}$, ultimately reaching very small scales ($\sim{0.1} \text{pc}/n$) as they reach the temperature $\sim10^4$ K at which hydrogen recombines. While this lengthscale depends on the ambient pressure confining the clouds, we find that the column density through an individual fragment $N_{\text{cloudlet}}\sim10^{17} \text{cm}^{-3}$ is essentially independent of environment; this column density represents a characteristic scale for atomic gas at $10^4$ K. We therefore suggest that "clouds" of cold, atomic gas may in fact have the structure of a mist or a fog, composed of tiny fragments dispersed throughout the ambient medium. We show that this scale emerges in hydrodynamic simulations, and that the corresponding increase in the surface area may imply rapid entrainment of cold gas. We also apply it to a number of observational puzzles, including the large covering fraction of diffuse gas in galaxy halos, the broad line widths seen in quasar and AGN spectra, and the entrainment of cold gas in galactic winds. While our simulations make a number of assumptions and thus have associated uncertainties, we show that this characteristic scale is consistent with a number of observations, across a wide range of astrophysical environments. We discuss future steps for testing, improving, and extending our model.
Morel's stable connectivity theorems state that for any connective $S^1$-spectrum $F$ of motivic spaces (Nisnevich simplicial sheaves) over an arbitrary field, the spectrum $L_{\mathbb A^1}(F)$ is connective, and the same property for $\mathbb P^1$-spectra of motivic spaces. Here $L_{\mathbb A^1}$ denotes the $\mathbb A^1$-localisation in the category of motivic spectra over a field $k$.   Originally the same property was conjectured for the case of motivic $S^1$-spectra over a base scheme $S$.In view of Ayoub's conterexamples the modified version of conjecture states that $L_{\mathbb A^1}(F)$ is $(-d)$-connective for any connective $F$, where $d=\mathrm{dim} S$ is the Krull dimension. The conjecture is proven under the infiniteness assumption on the residue fields for the cases of Dedekind schemes by J.~Schmidt and F.~Strunk and noetherian domains of arbitrary dimension by N.~Deshmukh, A.~Hogadi, G.~Kulkarni and S.~Yadavand. In the article we prove the result or general base with out the assumption on the residue fields.   So by the result for any smooth scheme $X$ over a base scheme $S$ of Krull dimension $d$ the Nisnevich sheaves of $S^1$-stable motivic homotopy groups $\pi_i^{S^1}(X)$ and $\mathbb P^1$-stable motivic homotopy groups $\pi_{i+j,j}^{\mathbb P^1}(X)$ vanishes for all $i<-d$.
Within both slightly non--extensive statistics and related numerical model, a picture is elaborated to treat self--similar time series as a thermodynamic system. Thermodynamic--type characteristics relevant to temperature, pressure, entropy, internal and free energies are introduced and tested. Predictability conditions of time series analysis are discussed on the basis of Van der Waals model. Maximal magnitude for time interval and minimal resolution scale of the value under consideration are found and analyzed in details. The statistics developed is shown to be governed by effective temperature being exponential measure of the fractal dimension of the time series. Testing of the analytical consideration is based on numerical scheme of non--extensive random walk. A statistical scheme is introduces to present numerical model as a grand canonical ensemble for which entropy and internal energy are calculated as functions of particle number. Effective temperature is found numerically to show that its value is reduced to averaged energy per one degree of freedom.
The vector and tensor analyzing powers as well as the polarization of the outgoing proton are calculated for the exclusive deuteron break-up reaction $\vec{d}p \to \vec{p}pn$ at a deuteron beam energy of 2 GeV. Two component covariant formalism of Stapp has been used to have the completely Lorentz invariant model. In addition to the Impulse Approximation the nucleon-nucleon double-scattering and delta-excitation mechanism have been added coherently. Good agreement with the precise data obtained at Saclay is achieved.
While domain adaptation has been used to improve the performance of object detectors when the training and test data follow different distributions, previous work has mostly focused on two-stage detectors. This is because their use of region proposals makes it possible to perform local adaptation, which has been shown to significantly improve the adaptation effectiveness. Here, by contrast, we target single-stage architectures, which are better suited to resource-constrained detection than two-stage ones but do not provide region proposals. To nonetheless benefit from the strength of local adaptation, we introduce an attention mechanism that lets us identify the important regions on which adaptation should focus. Our method gradually adapts the features from global, image-level to local, instance-level. Our approach is generic and can be integrated into any single-stage detector. We demonstrate this on standard benchmark datasets by applying it to both SSD and YOLOv5. Furthermore, for equivalent single-stage architectures, our method outperforms the state-of-the-art domain adaptation techniques even though they were designed for specific detectors.
We propose an improved discriminative model prediction method for robust long-term tracking based on a pre-trained short-term tracker. The baseline pre-trained short-term tracker is SuperDiMP which combines the bounding-box regressor of PrDiMP with the standard DiMP classifier. Our tracker RLT-DiMP improves SuperDiMP in the following three aspects: (1) Uncertainty reduction using random erasing: To make our model robust, we exploit an agreement from multiple images after erasing random small rectangular areas as a certainty. And then, we correct the tracking state of our model accordingly. (2) Random search with spatio-temporal constraints: we propose a robust random search method with a score penalty applied to prevent the problem of sudden detection at a distance. (3) Background augmentation for more discriminative feature learning: We augment various backgrounds that are not included in the search area to train a more robust model in the background clutter. In experiments on the VOT-LT2020 benchmark dataset, the proposed method achieves comparable performance to the state-of-the-art long-term trackers. The source code is available at: https://github.com/bismex/RLT-DIMP.
We develop a theoretical approach to study the scaling of anomalous Hall effect (AHE) in the insulating regime, which is observed to be $\sigma_{xy}^{AH}\propto\sigma_{xx}^{1.40\sim1.75}$ in experiments over a large range of materials. This scaling is qualitatively different from the ones observed in metals. Basing our theory on the phonon-assisted hopping mechanism and percolation theory, we derive a general formula for the anomalous Hall conductivity, and show that it scales with the longitudinal conductivity as $\sigma_{xy}^{AH}\sim\sigma_{xx}^{\gamma}$ with $\gamma$ predicted to be $1.38\leq\gamma\leq1.76$, quantitatively in agreement with the experimental observations. Our result provides a clearer understanding of the AHE in the insulating regime and completes the scaling phase diagram of the AHE.
The aim of this paper is to compute the Frobenius structures of some cohomological operators of arithmetic $\ms{D}$-modules. To do this, we calculate explicitly an isomorphism between canonical sheaves defined abstractly. Using this calculation, we establish the relative Poincar\'{e} duality in the style of SGA4. As another application, we compare the push-forward as arithmetic $\ms{D}$-modules and the rigid cohomologies taking Frobenius into account. These theorems will lead us to an analog of "Weil II" and a product formula for $p$-adic epsilon factors.
Applying the dynamical coherent potential approximation to a simple model, we have systematically studied the carrier states in $A_{1-x}$Mn$_xB$-type diluted magnetic semiconductors (DMS's). The model calculation was performed for three typical cases of DMS's: The cases with strong and moderate exchange interactions in the absence of nonmagnetic potentials, and the case with strong attractive nonmagnetic potentials in addition to moderate exchange interaction. When the exchange interaction is sufficiently strong, magnetic impurity bands split from the host band. Carriers in the magnetic impurity band mainly stay at magnetic sites, and coupling between the carrier spin and the localized spin is very strong. The hopping of the carriers among the magnetic sites causes ferromagnetism through a {\it double-exchange (DE)-like} mechanism. We have investigated the condition for the DE-like mechanism to operate in DMS's. The result reveals that the nonmagnetic attractive potential at the magnetic site assists the formation of the magnetic impurity band and makes the DE-like mechanism operative by substantially enhancing the effect of the exchange interaction. Using conventional parameters we have studied the carrier states in Ga$_{1-x}$Mn$_x$As. The result shows that the ferromagnetism is caused through the DE-like mechanism by the carriers in the bandtail originating from the impurity states.
We give continued fraction algorithms for a particular class of Fuchsian triangle groups. In particular, we give an explicit form of each such group that is a subgroup of the Hilbert modular group of its trace field and provide an interval map that is piecewise linear fractional, given in terms of group elements. Using natural extensions, we find an ergodic invariant measure for the interval map. We also study diophantine properties of approximation in terms of the continued fractions; and furthermore show that these continued fractions are appropriate to obtain transcendence results.
Canonically, elliptical galaxies might be expected to have a perfect rotational symmetry, making them ideal targets for flexion studies - however, this assumption hasn't been tested. We have undertaken an analysis of low and high redshift galaxy catalogs of known morphological type with a new gravitational lensing code, Lenser. Using color measurements in the u-r band and fit Sersic index values, objects with characteristics consistent with early-type galaxies are found to have a lower intrinsic scatter in flexion signal than late-type galaxies. We find this measured flexion noise can be reduced by more than a factor of two at both low and high redshift.
The abrupt structure change from the nuclei of $N=Z \le 35$ to those of $N=Z \ge 36$ is investigated by means of shell model calculations. The basic features of the even-even and odd-odd nuclei under consideration are nicely reproduced. A sudden jump of nucleons into the upper $g_{9/2}d_{5/2}$ shell at $N=Z=36$ is found to be the main reason that causes the qualitative structure difference. It is argued that the structure change can be viewed as a decisive change of the mean field, or a phase transition, along the $N=Z$ line.
A novel approach for studying phase transitions in systems with quantum degrees of freedom is discussed. Starting from the microscopic hamiltonian of a quantum model, we first derive a set of exact differential equations for the free energy and the correlation functions describing the effects of fluctuations on the thermodynamics of the system. These equations reproduce the full renormalization group structure in the neighborhood of a critical point keeping, at the same time, full information on the non universal properties of the model. As a concrete application we investigate the phase diagram of a Heisenberg antiferromagnet in a staggered external magnetic field. At long wavelengths the known relationship to the Quantum Non Linear Sigma Model naturally emerges from our approach. By representing the two point function in an approximate analytical form, we obtain a closed partial differential equation which is then solved numerically. The results in three dimensions are in good agreement with available Quantum Monte Carlo simulations and series expansions. More refined approximations to the general framework presented here and few applications to other models are briefly discussed.
Jets around low- and intermediate-mass young stellar objects (YSOs) contain a fossil record of the recent accretion and outflow activity of their parent star-forming systems. We aim to understand whether the accretion/ejection process is similar across the entire stellar mass range of the parent YSOs. To this end we have obtained VLT/X-shooter spectra of HH 1042 and HH 1043, two newly discovered jets in the massive star-forming region RCW 36. HH 1042 is associated with the intermediate-mass YSO 08576nr292. Over 90 emission lines are detected in the spectra. High-velocity (up to 220 km/s) blue- and redshifted emission from a bipolar flow is observed in typical shock tracers. Low-velocity emission from the background cloud is detected in nebular tracers, including lines from high ionization species. We applied combined optical and infrared spectral diagnostic tools in order to derive the physical conditions (density, temperature, and ionization) in the jets. The measured mass outflow rates are Mjet ~ 10^-7 Msun/yr. We measure a high accretion rate for HH 1042 (Macc ~ 10^-6 Msun/yr) and Mjet/Macc ~ 0.1, comparable to low-mass sources and consistent with models for magneto-centrifugal jet launching. The knotted structure and velocity spread in both jets are interpreted as fossil signatures of a variable outflow rate. The mean velocities in both lobes of the jets are comparable, but the variations in Mjet and velocity in the two lobes are not symmetric, suggesting that the launching mechanism on either side of the accretion disk is not synchronized. For HH 1042, we have constructed an interpretative physical model with a stochastic or periodic outflow rate and a description of a ballistic flow as its constituents. The knotted structure and velocity spread can be reproduced qualitatively with the model, indicating that the outflow velocity varies on timescales on the order of 100 yr.
Aims. We investigate the dominant formation mechanism of H2CO and CH3OH in the Horsehead PDR and its associated dense core. Methods. We performed deep integrations of several H2CO and CH3OH lines at two positions in the Horsehead, namely the PDR and dense core, with the IRAM-30m telescope. In addition, we observed one H2CO higher frequency line with the CSO telescope at both positions. We determine the H2CO and CH3OH column densities and abundances from the single-dish observations complemented with IRAM-PdBI high-angular resolution maps (6") of both species. We compare the observed abundances with PDR models including either pure gas-phase chemistry or both gas-phase and grain surface chemistry. Results. We derive CH3OH abundances relative to total number of hydrogen atoms of ~1.2e-10 and ~2.3e-10 in the PDR and dense core positions, respectively. These abundances are similar to the inferred H2CO abundance in both positions (~2e-10). We find an abundance ratio H2CO/CH3OH of ~2 in the PDR and ~1 in the dense core. Pure gas-phase models cannot reproduce the observed abundances of either H2CO or CH3OH at the PDR position. Both species are therefore formed on the surface of dust grains and are subsequently photodesorbed into the gas-phase at this position. At the dense core, on the other hand, photodesorption of ices is needed to explain the observed abundance of CH3OH, while a pure gas-phase model can reproduce the observed H2CO abundance. The high-resolution observations show that CH3OH is depleted onto grains at the dense core. CH3OH is thus present in an envelope around this position, while H2CO is present in both the envelope and the dense core itself. Conclusions. Photodesorption is an efficient mechanism to release complex molecules in low FUV-illuminated PDRs, where thermal desorption of ice mantles is ineffective.
We examine the possibility for precise determination of |V_{ts}| (and |V_{td}/V_{ts}|) from the exclusive decays, $B --> K \ell^+ \ell^-, B --> K^* \ell^+ \ell^-$ (and $B --> \pi \ell^+ \ell^-, B --> \rho \ell^+ \ell^-$). We show that the ratio |V_{ts}| can be extracted experimentally with a small theoretical uncertainty from hadronic form--factors, if we {\bf appropriately constrain} kinematical regions of $q^2$. We also give detailed analytical and numerical results on the differential decay width $d\Gamma(B --> K^* \ell^+ \ell^-)/dq^2$, and the ratios of integrated branching fractions, ${\cal B}(B --> \rho \ell^+ \ell^-)/{\cal B}(B --> K^* \ell^+ \ell^-)$. We estimate that one can determine the ratio |V_{ts}| from those decays within theoretical accuracy of $\sim 10%$.
We reexamine here a problem considered in detail before by Waugh and Lake: the solutions of spherically symmetric Einstein's equations with a radial flow of unpolarized radiation (the Vaidya metric) in double-null coordinates. This problem is known to be not analytically solvable, the only known explicit solutions correspond to the constant mass case (Schwarzschild solution in Kruskal-Szekeres form) and the linear and exponential mass functions originally discovered by Waugh and Lake. We present here a semi-analytical approach that can be used to discuss some qualitative and quantitative aspects of the Vaidya metric in double-null coordinates for generic mass functions. We present also a new analytical solution corresponding to $(1/v)$-mass function.