ShantanuT01/DACTYL-Pretraining huggingface dataset:
We study the convergence of the $M/G/1$ processor-sharing, queue length process in the heavy traffic regime, in the finite variance case. To do so, we combine results pertaining to L\'{e}vy processes, branching processes and queuing theory. These results yield the convergence of long excursions of the queue length processes, toward excursions obtained from those of some reflected Brownian motion with drift, after taking the image of their local time process by the Lamperti transformation. We also show, via excursion theoretic arguments, that this entails the convergence of the entire processes to some (other) reflected Brownian motion with drift. Along the way, we prove various invariance principles for homogeneous, binary Crump-Mode-Jagers processes. In the last section we discuss potential implications of the state space collapse property, well known in the queuing literature, to branching processes.
Let $K/k$ be a finite Galois extension of number fields, and let $H_K$ be the Hilbert class field of $K$. We find a way to verify the nonsplitting of the short exact sequence $$1\to Cl_K\to \text{Gal}(H_K/k)\to\text{Gal}(K/k)\to 1$$ by finite calculation. Our method is based on the study of the principal version of the Chebotarev density theorem, which represents the density of the prime ideals of $k$ that factor into the product of principal prime ideals in $K$. We also find explicit equations to express the principal density in terms of the invariants of $K/k$. In particular, we prove that the group structure of the ideal class group of $K$ can be determined by reading the principal densities.
While the dominant radiation mechanism gamma-ray bursts (GRBs) remains a question of debate, synchrotron emission is one of the foremost candidates to describe the multi-wavelength afterglow observations. As such, it is expected that GRBs should present some degree of polarization across their evolution - presenting a feasible means of probing these bursts' energetic and angular properties. Although obtaining polarization data is difficult due to the inherent complexities regarding GRB observations, advances are being made, and theoretical modeling of synchrotron polarization is now more relevant than ever. In this manuscript, we present the polarization for a fiduciary model where the synchrotron forward-shock emission evolving in the radiative-adiabatic regime is described by a radially stratified off-axis outflow. This is parameterized with a power-law velocity distribution and decelerated in a constant-density and wind-like external environment. We apply this theoretical polarization model for selected bursts presenting evidence of off-axis afterglow emission, including the nearest orphan GRB candidates observed by the Neil Gehrels Swift Observatory and a few Gravitational Wave (GWs) events that could generate electromagnetic emission. In the case of GRB 170817A, we require the available polarimetric upper limits in radio wavelengths to constrain its magnetic field geometry.
The large time behavior of solutions to Cauchy problem for viscous Hamilton-Jacobi equation is classified. The large time asymptotics are given by very singular self-similar solutions on one hand and by self-similar viscosity solutions on the other hand
Let $G$ be a graph with the usual shortest-path metric. A graph is $\delta$-hyperbolic if for every geodesic triangle $T$, any side of $T$ is contained in a $\delta$-neighborhood of the union of the other two sides. A graph is chordal if every induced cycle has at most three edges. A vertex separator set in a graph is a set of vertices that disconnects two vertices. In this paper we study the relation between vertex separator sets, some chordality properties which are natural generalizations of being chordal and the hyperbolicity of the graph. We also give a characterization of being quasi-isometric to a tree in terms of chordality and prove that this condition also characterizes being hyperbolic, when restricted to triangles, and having stable geodesics, when restricted to bigons.
The single particle spectral-weight function (SWF) of the ionic Hubbard model at half filling is calculated in the cluster perturbation theory approximation. An abrupt change of regime in the low-energy region, near the chemical potential, is found at a critical value, $U_{c}$, of the coupling constant (Hubbard $U$). The SWF at the Fermi points $k_{F}$=$\pm{\pi}/2$ jumps, as $U$ increases, from a two-peak structure, the gap edges, to a four-peak structure accompanied by a (non-vanishing) minimum of the charge-gap. The two inner peaks of this structure show very small dispersion (flat bands) away from the Fermi points, whereas the outer peaks mark the edges of the Hubbard bands. No other signatures of abrupt change are detected in the SWF. The two regimes are physically realized in the angle-resolved photoelectron spectra of $(TaSe_{4})_{2}I$, and the blue-bronze $K_{0.3}MoO_{3}$, respectively.
Helium has been proposed as the key element to interpret the observed multiple main sequences (MS), subgiant branches (SGB) and red giant branches (RGB), as well as the complex horizontal branch (HB) morphology in Globular Clusters (GC). However, up to now, He was never directly measured in suitable GC stars (8500<Teff<11500 K) with the purpose of verify this hypothesis. We studied 7 hot blue horizontal branch (BHB) stars (Teff<11500 K) in the GC NGC 6752 with the purpose to measure their Helium content. In addition Fe,Cr,Si,Ti,O,Na, and Ba abundances were measured. We could measure He abundance only for stars warmer than Teff=8500 K. All our targets with measurable He are zero age HB (ZAHB) objects and turned out to have a homogeneous He content with a mean value of Y=0.245+-0.012, compatible with the most recent measurements of the primordial He content of the Universe (Y~0.25). The whole sample of stars have a metallicity of [Fe/H]=-1.56+-0.03 and [alpha/Fe]=+0.21+-0.03. Our HB targets show the same Na-O anticorrelation identified among the TO-SGB-RGB stars. This is the first direct measurement of the He abundance for a significative sample of GC stars in a temperature regime where the He content is not altered by sedimentation processing or extreme mixing as suggested for the hottest, late helium flasher HB stars.
Kolo\u{g}lu, Kopp and Miller compute the limiting spectral distribution of a certain class of real random matrix ensembles, known as $k$-block circulant ensembles, and discover that it is exactly equal to the eigenvalue distribution of an $k \times k$ Gaussian unitary ensemble. We give a simpler proof that under very general conditions which subsume the cases studied by Kolo\u{g}lu-Kopp-Miller, real-symmetric ensembles with periodic diagonals always have limiting spectral distribution equal to the eigenvalue distribution of a finite Hermitian ensemble with Gaussian entries which is a `complex version' of a $k \times k$ submatrix of the ensemble. We also prove an essentially algebraic relation between certain periodic finite Hermitian ensembles with Gaussian entries, and the previous result may be seen as an asymptotic version of this for real-symmetric ensembles. The proofs show that this general correspondence between periodic random matrix ensembles and finite complex Hermitian ensembles is elementary and combinatorial in nature.
Given a marked renewal point process (assuming that the marks are i.i.d.) we say that an unbounded region is stable if it contains finitely many points of the point process with probability one. In this paper we provide algorithms that allow to sample these finitely many points efficiently. We explain how exact simulation of the steady-state measure valued state descriptor of the infinite server queue follows as a simple corollary of our algorithms. We provide numerical evidence supporting that our algorithms are not only theoretically sound but also practical. Finally, having simulation optimization in mind, we also apply our results to gradient estimation of steady-state performance measures.
This paper is devoted to the use of the entropy and duality methods for the existence theory of reaction-cross diffusion systems consisting of two equations, in any dimension of space. Those systems appear in population dynamics when the diffusion rates of individuals of two species depend on the concentration of individuals of the same species (self-diffusion), or of the other species (cross diffusion).
We present a QCD analysis of the cumulative out-of-event-plane momentum distribution in DIS process with emission of high p_t jets. We derive the all-order resummed result to next-to-leading accuracy and estimate the leading power correction. We aim at the same level of accuracy which, in e+e- annihilation, seems to be sufficient for making predictions. As is typical of multi-jet observables, the distribution depends on the geometry of the event and the underlying colour structure. This result should provide a powerful method to study QCD dynamics, in particular to constrain the parton distribution functions, to measure the running coupling and to search for genuine non-perturbative effects.
We report studies of low-field conductivity, sigma, of the orthorhombic TaS_3 samples as a function of strain, epsilon. In the Peierls state the sigma(epsilon) dependencies show hysteresis. A similar hysteresis loop is observed for K_{0.3}MoO_3. For nano-sized TaS_3 samples the sigma(epsilon) curves show step-like changes associated with the "quantization" of the wave vector, q, of the charge-density wave (CDW). The dependences clearly reveal the change of the q-vector with strain. In contrast with the traditional concept, q is found to increase with sample expansion. This means that the stretch-induced anomalies cannot be explained by the transition of the CDW to fourfold commensurability with the pristine lattice (lock-in transition). Alternatively, we suppose, that at the critical stretch a CDW with larger amplitude and modified q-vector forms. Further, the models describing metastable length states and drop of the Young modulus on CDW depinning in terms of longitudinal CDW strain, require reconsideration. Presumably, transverse effects should be taken into account.
In designing an ion trap, geometry and rf source should be optimized such that the trap depth is maximized while the ion remain stable. In a quadrupole linear trap, stable parameters $a$ and $q$ are utilized frequently in describing the stability. However, in a surface trap, the trap have to be mapped to the linear quadrupole trap so that $a$ and $q$ can be evaluated. This work explains how to handle them for surface trap designing and how the geometry and rf source affect it. We conclude that the $q$ parameter should be 0.2~0.22 so that the trap is stable.
One of the main characteristics of the penumbra of sunspots is the radially outward-directed Evershed flow. Only recently have penumbral regions been reported with similar characteristics to normal penumbral filaments, but with an opposite direction of the flow. Such flows directed towards the umbra are known as counter Evershed flows (CEFs). We aim to determine the frequency of occurrence of CEFs in active regions (ARs) and to characterize their lifetime and the prevailing conditions in the ARs. We analysed the continuum images, Dopplergrams, and magnetograms recorded by SDO/HMI of 97 ARs that appeared from 2011 to 2017. We followed the ARs for $9.6\pm1.4$ days on average. We found 384 CEFs in total, with a median value of 6 CEFs per AR. CEFs are a rather common feature, they occur in 83.5% of all ARs regardless of the magnetic complexity of the AR. However, CEFs were observed on average only during 5.9% of the mean total duration of all the observations analyzed here. The lifetime of CEFs follows a log-normal distribution with a median value of 10.6$_{-6.0}^{+12.4}$ hr. In addition, we report two populations of CEFs depending on whether they are associated with light bridges, or not. We explain that the rarity of reports of CEFs in the literature is a result of highly incomplete coverage of ARs with spectropolarimetric data. By using the continuous observations now routinely available from space, we are able to overcome this limitation.
By combining H$\alpha$ flux measurements from the Sloan Digital Sky Survey (SDSS) with UV flux observations from the Galaxy Evolution Explorer (GALEX), we examine the environmental dependence (through central/satellite distinction) of the rapid quenching and rejuvenation of galaxies. H$\alpha$ emissions trace the most massive stars, thereby indicating star-formation on timescales of $\sim 10$ Myr, while UV emission traces star-formation on timescales of $\sim 100$ Myr. These varying timescales are exploited to probe the most recent star-formation histories of galaxies. In this work, we define a class of transient galaxies which have UV emission typical of star-formation but negligible H$\alpha$ emission. We find that the occurrence of these transients has a strong stellar mass dependence in both the satellite and central population. However, while at stellar masses greater than $\sim 10^{10} M_\odot$ they occur with equal frequency regardless of environmental class, at lower stellar masses they are more common in satellites only, with an excess of about 1 percentage point across all low stellar mass galaxies. These satellite transients also have a strong halo mass and group-centric radial dependence suggesting they are driven by an environmental process. Finally, we select a sample of galaxies with H$\alpha$ emission but not UV emission which could contain short-timescale rejuvenating galaxies. These rejuvenating candidates are few in number and do not have a strong difference in their occurrence rate in centrals or satellites. These unique probes point to an environmental quenching mechanism which occurs on short timescales after the satellite has been in the group environment for a significant time - consistent with 'delayed-then-rapid' quenching.
In this paper, a new formula for {\pi}^(2)(N) is formulated, it is a function that counts the number of semi-primes not exceeding a given number N. A semi-prime is a natural number that is the product of precisely two prime numbers, the two primes in the product may equal each other. Semi-prime numbers are also a case of almost primes. Since a formula for this is already known, a new identity that uses the prime counting function is created by equating the two functions.
One of the most intriguing aspects of Quantum Mechanics is the impossibility of measuring at the same time observables corresponding to non-commuting operators. This impossibility can be partially relaxed when considering joint or sequential weak values evaluation. Indeed, weak measurements have been a real breakthrough in the quantum measurement framework that is of the utmost interest from both a fundamental and an applicative point of view. Here we show how we realized, for the first time, a sequential weak value evaluation of two incompatible observables on a single photon.
Recent high-resolution observations from the Solar Dynamics Observatory (SDO) have reawakened interest in the old and fascinating phenomenon of solar tornado-like prominences. This class of prominences was first introduced by Pettit (1932), who studied them over many years. Observations of tornado prominences similar to the ones seen by SDO had already been documented by Secchi (1877) in his famous "Le Soleil". High resolution and high cadence multiwavelength data obtained by SDO reveal that the tornado-like appearance of these prominences is mainly an illusion due to projection effects. We discuss two different cases where prominences on the limb might appear to have a tornado-like behavior. One case of apparent vortical motions in prominence spines and barbs arises from the (mostly) 2D counterstreaming plasma motion along the prominence spine and barbs together with oscillations along individual threads. The other case of apparent rotational motion is observed in prominence cavities and results from the 3D plasma motion along the writhed magnetic fields inside and along the prominence cavity as seen projected on the limb. Thus, the "tornado" impression results either from counterstreaming and oscillations or from the projection on the plane of the sky of plasma motion along magnetic field lines, rather than from a true vortical motion around an (apparent) vertical or horizontal axis. We discuss the link between tornado-like prominences, filament barbs, and photospheric vortices at their base.
The existence and uniqueness of mild solutions are proved for a class of degenerate stochastic differential equations on Hilbert spaces where the drift is Dini continuous in the component with noise and H\"older continuous of order larger than $\ff 2 3$ in the other component.   In the finite-dimensional case the Dini continuity is further weakened. The main results are applied to solve second order stochastic systems driven by space-time white noises.
We discuss the relations between (topological) quantum field theories in 4 dimensions and the theory of 2-knots (embedded 2-spheres in a 4-manifold). The so-called BF theories allow the construction of quantum operators whose trace can be considered as the higher-dimensional generalization of Wilson lines for knots in 3-dimensions. First-order perturbative calculations lead to higher dimensional linking numbers, and it is possible to establish a heuristic relation between BF theories and Alexander invariants. Functional integration-by-parts techniques allow the recovery of an infinitesimal version of the Zamolodchikov tetrahedron equation, in the form considered by Carter and Saito.
Vehicle Re-identification (ReID) is an important yet challenging problem in computer vision. Compared to other visual objects like faces and persons, vehicles simultaneously exhibit much larger intraclass viewpoint variations and interclass visual similarities, making most exiting loss functions designed for face recognition and person ReID unsuitable for vehicle ReID. To obtain a high-performance vehicle ReID model, we present a novel Distance Shrinking with Angular Marginalizing (DSAM) loss function to perform hybrid learning in both the Original Feature Space (OFS) and the Feature Angular Space (FAS) using the local verification and the global identification information. Specifically, it shrinks the distance between samples of the same class locally in the Original Feature Space while keeps samples of different classes far away in the Feature Angular Space. The shrinking and marginalizing operations are performed during each iteration of the training process and are suitable for different SoftMax based loss functions. We evaluate the DSAM loss function on three large vehicle ReID datasets with detailed analyses and extensive comparisons with many competing vehicle ReID methods. Experimental results show that our DSAM loss enhances the SoftMax loss by a large margin on the PKU-VD1-Large dataset: 10.41% for mAP, 5.29% for cmc1, and 4.60% for cmc5. Moreover, the mAP is increased by 9.34% on the PKU-VehicleID dataset and 6.13% on the VeRi-776 dataset. Source code will be released to facilitate further studies in this research direction.
We show that every $4$-chromatic graph on $n$ vertices, with no two vertex-disjoint odd cycles, has an odd cycle of length at most $\tfrac12\,(1+\sqrt{8n-7})$. Let $G$ be a non-bipartite quadrangulation of the projective plane on $n$ vertices. Our result immediately implies that $G$ has edge-width at most $\tfrac12\,(1+\sqrt{8n-7})$, which is sharp for infinitely many values of $n$. We also show that $G$ has face-width (equivalently, contains an odd cycle transversal of cardinality) at most $\tfrac14(1+\sqrt{16 n-15})$, which is a constant away from the optimal; we prove a lower bound of $\sqrt{n}$. Finally, we show that $G$ has an odd cycle transversal of size at most $\sqrt{2\Delta n}$ inducing a single edge, where $\Delta$ is the maximum degree. This last result partially answers a question of Nakamoto and Ozeki.
A recent application of the Kolmogorov-Smirnov test to the WMAP 7 year W-band maps claims evidence that the CMB is "weakly random", and that only 20% of the signal can be explained as a random Gaussian field. I here repeat this analysis, and in contrast to the original result find no evidence for deviation from the standard {\Lambda}CDM model. Instead, the results of the original analysis are consistent with not properly taking into account the correlations of the {\Lambda}CDM power spectrum.
Multipartite entanglement is an essential resource for quantum communication, quantum computing, quantum sensing, and quantum networks. The utility of a quantum state, $|\psi\rangle$, for these applications is often directly related to the degree or type of entanglement present in $|\psi\rangle$. Therefore, efficiently quantifying and characterizing multipartite entanglement is of paramount importance. In this work, we introduce a family of multipartite entanglement measures, called Concentratable Entanglements. Several well-known entanglement measures are recovered as special cases of our family of measures, and hence we provide a general framework for quantifying multipartite entanglement. We prove that the entire family does not increase, on average, under Local Operations and Classical Communications. We also provide an operational meaning for these measures in terms of probabilistic concentration of entanglement into Bell pairs. Finally, we show that these quantities can be efficiently estimated on a quantum computer by implementing a parallelized SWAP test, opening up a research direction for measuring multipartite entanglement on quantum devices.
Let $(K,v)$ be a valued field and let $(K^h,v^h)$ be the henselization determined by the choice of an extension of $v$ to an algebraic closure of $K$. Consider an embedding $v(K^*)\hookrightarrow\Lambda$ of the value group into a divisible ordered abelian group. Let $T(K,\Lambda)$, $T(K^h,\Lambda)$ be the trees formed by all $\Lambda$-valued extensions of $v$, $v^h$ to the polynomial rings $K[x]$, $K^h[x]$, respectively. We show that the natural restriction mapping $T(K^h,\Lambda)\to T(K,\Lambda)$ is an isomorphism of posets.   As a consequence, the restriction mapping $T_v\to T_{v^h}$ is an isomorphism of posets too, where $T_v$, $T_{v^h}$ are the trees whose nodes are the equivalence classes of valuations on $K[x]$, $K^h[x]$ whose restriction to $K$, $K^h$ are equivalent to $v$, $v^h$, respectively.
Digital cameras that use Color Filter Arrays (CFA) entail a demosaicking procedure to form full RGB images. As today's camera users generally require images to be viewed instantly, demosaicking algorithms for real applications must be fast. Moreover, the associated cost should be lower than the cost saved by using CFA. For this purpose, we revisit the classical Hamilton-Adams (HA) algorithm, which outperforms many sophisticated techniques in both speed and accuracy. Inspired by HA's strength and weakness, we design a very low cost edge sensing scheme. Briefly, it guides demosaicking by a logistic functional of the difference between directional variations. We extensively compare our algorithm with 28 demosaicking algorithms by running their open source codes on benchmark datasets. Compared to methods of similar computational cost, our method achieves substantially higher accuracy, Whereas compared to methods of similar accuracy, our method has significantly lower cost. Moreover, on test images of currently popular resolution, the quality of our algorithm is comparable to top performers, whereas its speed is tens of times faster.
Magnetization measurements of Sr{14-x}Ca_xCu_{24}O_{41} with 0 <= x <=12 in magnetic fields up to 16 T show that the low-temperature magnetic response of the CuO_2 spin chains changes strongly upon Ca doping. For x=0 quantum statistical simulations yield that the temperature and field dependence of the magnetization can be well described by an effective Heisenberg model in which the ground state configuration is composed of spin dimers, trimers, and monomers. For x>0 a constant contribution to the low-temperature magnetic susceptibility is observed which cannot be explained in terms of simple chain models. Alternative scenarios are outlined.