ShantanuT01/DACTYL-Pretraining huggingface dataset:
For a given orthonormal basis $(f_n)$ on a probability measure space, we want to describe all Markov operators which have the $f_n$ as eigenvectors. We introduce for that what we call the hypergroup property. We study this property in three different cases. On finite sets, this property appears as the dual of the GKS property linked with correlation inequalities in statistical mechanics. The representation theory of groups provides generic examples where these two properties are satisfied, although this group structure is not necessary in general. The hypergroup property also holds for Sturm--Liouville bases associated with log-concave symmetric measures on a compact interval, as stated in Achour--Trim\`eche's theorem. We give some criteria to relax this symmetry condition in view of extensions to a more general context. In the case of Jacobi polynomials with non-symmetric parameters, the hypergroup property is nothing else than Gasper's theorem. The proof we present is based on a natural interpretation of these polynomials as harmonic functions and is related to analysis on spheres. The proof relies on the representation of the polynomials as the moments of a complex variable.
We study supernova-driven galactic outflows as a mechanism for injecting turbulence in the intergalactic medium (IGM) far from galaxies. To this aim we follow the evolution of a 10^13 Msun galaxy along its merger tree, with carefully calibrated prescriptions for star formation and wind efficiencies. At z~3 the majority of the bubbles around galaxies are old (ages >1Gyr), i.e. they contain metals expelled by their progenitors at earlier times; their filling factor increases with time reaching about 10% at z<2. The energy deposited by these expanding shocks in the IGM is predominantly in kinetic form (mean energy density of 1 \mu eV cm^-3, about 2-3 x the thermal one), which is rapidly converted in disordered motions by instabilities, finally resulting in a fully developed turbulent spectrum whose evolution is followed through a spectral transfer function approach. The derived mean IGM turbulent Doppler parameter, b_t, peaks at z~1 at about 1.5 km/s with maximum b_t = 25 km/s. The shape of the b_t distribution does not significantly evolve with redshift but undergoes a continuous shift towards lower b_t values with time, as a result of bubble aging. We find also a clear trend of decreasing b_t with N_HI and a more complex dependence on R_s resulting from the age spread of the bubbles. We have attempted a preliminary comparison with the data, hampered by the scarcity of the latter and by the challenge provided by the subtraction of peculiar and thermal motions. Finally we comment on the implications of turbulence for various cosmological studies.
A theory for chemical reaction dynamics in condensed phase systems based on the generalized Langevin formalism of Grote and Hynes is presented. A microscopic approach to calculate the dynamic friction is developed within the framework of a combination of kinetic and mode-coupling theories. The approach provides a powerful analytic tool to study chemical reactions in realistic condensed phase environments. The accuracy of the approach is tested for a model isomerization reaction in a Lennard-Jones fluid. Good agreement is obtained for the transmission coefficient at different solvent densities, in comparison with numerical simulations based on the reactive-flux approach.
The current discrepancy in $R_{D^{(*)}}=BR(\bar{B} \to D^{(*)}\tau\bar{\nu})/BR(\bar{B}\to D^{(*)} \ell \bar{\nu})$ where $\ell=e,\,\mu$ may imply a know particle with the mass around the order of TeV. Therefore it is well motivated to test those scenarios at the large hadron collider. Thanks to the size of the discrepancy and the analysis based on the effective field theory, the variety of the possible new physics candidates is limited. We focus on the charged Higgs and leptoquark possibility and discuss the collider physics.
We propose to replace Ga in (Ga,Mn)As with Li and Zn as a route to high Curie temperature, carrier mediated ferromagnetism in a dilute moment n-type semiconductor. Superior material characteristics, rendering Li(Zn,Mn)As a realistic candidate for such a system, include unlimited solubility of the isovalent substitutional Mn impurity and carrier concentration controlled independently of Mn doping by adjusting Li-(Zn,Mn) stoichiometry. Our predictions are anchored by detail ab initio calculations and comparisons with the familiar and directly related (Ga,Mn)As, by the microscopic physical picture we provide for the exchange interaction between Mn local moments and electrons in the conduction band, and by analysis of prospects for the controlled growth of Li(Zn,Mn)As materials.
We study the uniqueness of higher-spin algebras which are at the core of higher-spin theories in AdS and of CFTs with exact higher-spin symmetry, i.e. conserved tensors of rank greater than two. The Jacobi identity for the gauge algebra is the simplest consistency test that appears at the quartic order for a gauge theory. Similarly, the algebra of charges in a CFT must also obey the Jacobi identity. These algebras are essentially the same. Solving the Jacobi identity under some simplifying assumptions spelled out, we obtain that the Eastwood-Vasiliev algebra is the unique solution for d=4 and d>6. In 5d there is a one-parameter family of algebras that was known before. In particular, we show that the introduction of a single higher-spin gauge field/current automatically requires the infinite tower of higher-spin gauge fields/currents. The result implies that from all the admissible non-Abelian cubic vertices in AdS(d), that have been recently classified for totally symmetric higher-spin gauge fields, only one vertex can pass the Jacobi consistency test. This cubic vertex is associated with a gauge deformation that is the germ of the Eastwood-Vasiliev's higher-spin algebra.
This paper studies the dimension of secant varieties to Segre varieties. The problem is cast both in the setting of tensor algebra and in the setting of algebraic geometry. An inductive procedure is built around the ideas of successive specializations of points and projections. This reduces the calculation of the dimension of the secant variety in a high dimensional case to a sequence of calculations of partial secant varieties in low dimensional cases. As applications of the technique: We give a complete classification of defective $t$-secant varieties to Segre varieties for t < 7. We generalize a theorem of Catalisano-Geramita-Gimigliano on non-defectivity of tensor powers of P^n. We determine the set of p for which unbalanced Segre varieties have defective p-secant varieties. In addition, we show that the Segre varieties P^1 x P^1 x P^n x P^n and P^2 x P ^3 x P^3 are deficient and completely describe the dimensions of their secant varieties. In the final section we propose a series of conjectures about defective Segre varieties.
A review on some recent developments in gamma ray astrophysics with particular emphasis on the role of relativistic bulk motion in nonthermal gamma ray sources, radiation processes in AGN jets, high-energy neutrino astronomy and the use of gamma rays in the energy range 10 GeV - 50 TeV as a probe of the diffuse IR-UV radiation field at cosmic distances.
We study the orbital entanglement in a biased Aharonov-Bohm ring connected in a four-terminal setup. We find that the concurrence achieves a maximum when the magnetic flux B coincides with an integer number of a half flux quantum 0 /2. We show that this behavior is a consequence of the existence of degenerate states of the ring having opposite chirality. We also analyze the behavior of the noise as a function of and discuss the reliability of this quantity as evidence of entanglement.
We have numerically investigated statistical properties of the so-called interoccurrence time or the waiting time, i.e., the time interval between successive earthquakes, based on the two-dimensional (2-D) spring-block (Burridge-Knopoff) model, selecting the velocity-weakening property as the constitutive friction law. The statistical properties of frequency distribution and the cumulative distribution of the interoccurrence time are discussed by tuning the dynamical parameters, namely, a stiffness and frictional property of a fault. We optimize these model parameters to reproduce the interoccurrence time statistics in nature; the frequency and cumulative distribution can be described by the power law and Zipf-Mandelbrot type power law, respectively. In an optimal case, the b-value of the Gutenberg-Richter law and the ratio of wave propagation velocity are in agreement with those derived from real earthquakes. As the threshold of magnitude is increased, the interoccurrence time distribution tends to follow an exponential distribution. Hence it is suggested that a temporal sequence of earthquakes, aside from small-magnitude events, is a Poisson process, which is observed in nature. We found that the interoccurrence time statistics derived from the 2-D BK (original) model can efficiently reproduce that of real earthquakes, so that the model can be recognized as a realistic one in view of interoccurrence time statistics.
We prove that whenever A is a 3-conservative relational structure with only binary and unary relations then the algebra of polymorphisms of A either has no Taylor operation (i.e. CSP(A) is NP-complete), or generates a congruence meet semidistributive variety (i.e. CSP(A) has bounded width).
We present hydrodynamical models of the grand design spiral M51 (NGC 5194), and its interaction with its companion NGC 5195. Despite the simplicity of our models, our simulations capture the present day spiral structure of M51 remarkably well, and even reproduce details such as a kink along one spiral arm, and spiral arm bifurcations. We investigate the offset between the stellar and gaseous spiral arms, and find at most times (including the present day) there is no offset between the stars and gas to within our error bars. We also compare our simulations with recent observational analysis of M51. We compute the pattern speed versus radius, and like the observations, find no single global pattern speed. We also show that the spiral arms cannot be fitted well by logarithmic spirals. We interpret these findings as evidence that M51 does not exhibit a quasi-steady density wave, as would be predicted by density wave theory. The internal structure of M51 derives from the complicated and dynamical interaction with its companion, resulting in spiral arms showing considerable structure in the form of short-lived kinks and bifurcations. Rather than trying to model such galaxies in terms of global spiral modes with fixed pattern speeds, it is more realistic to start from a picture in which the spiral arms, while not being simple material arms, are the result of tidally induced kinematic density `waves' or density patterns, which wind up slowly over time.
Recently Ooguri and Yamazaki proposed a statistical model of melting crystals to count BPS bound states of certain D-brane configurations on toric Calabi--Yau manifolds [arXiv:0811.2801]. This construction relied on a set of consistency conditions on the corresponding brane tiling, and in this note I show that these conditions are satisfied for any physical brane tiling; they follow from the conformality of the low energy field theory on the D-branes. As a byproduct I also provide a simple direct proof that any physical brane tiling has a perfect matching.
In 1975, Erd\H{o}s asked the following question: what is the smallest function $f(n)$ for which all graphs with $n$ vertices and $f(n)$ edges contain two edge-disjoint cycles $C_1$ and $C_2$, such that the vertex set of $C_2$ is a subset of the vertex set of $C_1$ and their cyclic orderings of the vertices respect each other? We prove the optimal linear bound $f(n)=O(n)$ using sublinear expanders.
The relation between thermodynamic phase transitions in classical systems and topology changes in their state space is discussed for systems in which equivalence of statistical ensembles does not hold. As an example, the spherical model with mean field-type interactions is considered. Exact results for microcanonical and canonical quantities are compared with topological properties of a certain family of submanifolds of the state space. Due to the observed ensemble inequivalence, a close relation is expected to exist only between the topological approach and one of the statistical ensembles. It is found that the observed topology changes can be interpreted meaningfully when compared to microcanonical quantities.
The idea of Verlinde that gravity is an entropic force caused by information changes associated with the positions of material bodies, is used in the present work for the FRW model of the Universe. Using modified Hawking temperature, the Friedmann equations are derived on any horizon. For the validity of the first law of thermodynamics (i.e., Clausius relation) it is found that there is modification of Bekenstein entropy on the horizon. However, using equipartition law of energy, Bekenstein entropy is recovered.
In this work, we study the topological phases of the dimerized square lattice in the presence of an external magnetic field. The dimerization pattern in the lattice's hopping amplitudes can induce a series of bulk energy gap openings in the Hofstadter spectrum at certain fractional fillings, giving rise to various topological phases. In particular, we show that at $\frac{1}{2}$-filling the topological quadrupole insulator phase with a quadrupole moment quantized to $\frac{e}{2}$ and associated corner-localized mid-gap states exists in certain parameter regime for all magnetic fluxes. At $\frac{1}{4}$ filling, the system can host obstructed atomic limit phases or Chern insulator phases. For those configurations gapped at fillings below $\frac{1}{4}$, the system is in Chern insulator phases of various non-vanishing Chern numbers. Across the phase diagram, both bulk-obstructed and boundary-obstructed topological phase transitions exist in this model.
The stochastic method based on the influence functional formalism introduced in an earlier paper to treat particle creation in near-uniformly accelerated detectors and collapsing masses is applied here to treat thermal and near-thermal radiance in certain types of cosmological expansions. It is indicated how the appearance of thermal radiance in different cosmological spacetimes and in the two apparently distinct classes of black hole and cosmological spacetimes can be understood under a unifying conceptual and methodological framework.
We studied the properties of the low-frequency quasi-periodic oscillations detected in a sample of six black hole candidates (XTE J1550-564, H 1743-322, XTE J1859+226, 4U 1630-47,GX 339-4, XTE J1650-500) observed by the Rossi XTE satellite. We analyzed the relation between the full width half maximum and the frequency of all the narrow peaks detected in power density spectra where a type-C QPO is observed. Our goal was to understand the nature of the modulation of the signal by comparing the properties of different harmonic peaks in the power density spectrum. We find that for the sources in our sample the width of the fundamental and of the first harmonic are compatible with a frequency modulation, while that of the sub-harmonic is independent of frequency, possibly indicating the presence of an additional modulation in amplitude. We compare our results with those obtained earlier from GRS 1915+105 and XTE J1550-564.
An interplay of magnetic fields and gravitation drives accretion and outflows near black holes. However, a specific mechanism is still a matter of debate; it is very likely that different processes dominate under various conditions. In particular, for the acceleration of particles and their collimation in jets, an ordered component of the magnetic field seems to be essential. Here we discuss the role of large-scale magnetic fields in transporting the charged particles and dust grains from the bound orbits in the equatorial plane of a rotating (Kerr) black hole and the resulting acceleration along trajectories escaping the system in a direction parallel to the symmetry axis (perpendicular to the accretion disk). We consider a specific scenario of destabilization of circular geodesics of initially neutral matter by charging (e.g., due to photoionization). Some particles may be set on escaping trajectories and attain relativistic velocity. The case of charged particles differs from charged dust grains by their charge-to-mass ratio, but the acceleration mechanism operates in a similar manner. It appears that the chaotic dynamics controls the outflow and supports the formation of near-horizon escape zones. We employ the technique of recurrence plots to characterize the onset of chaos in the outflowing medium. We investigate the system numerically and construct the basin-boundary plots, which show the location and the extent of the escape zones. The effects of black hole spin and magnetic field strength on the formation and location of escape zones are discussed, and the maximal escape velocity is computed.
We have obtained a 12.5 ksec image of the Hercules Cluster, A2151, with the {\it ROSAT} PSPC. Comparison of the optical and X-ray data suggest the presence of at least three distinct subclusters in A2151. The brightest X-ray emission coincides with the highest-density peak in the galaxy distribution, and is bimodal. The northern subclump, distinct in position and velocity, has {\it no} detectable X-ray gas. The eastern subclump, apparent in the optical contour map, is indistinguishable from the main clump in velocity space but is clearly visible in the X-ray image. X-ray spectra derived from the central peak of emission yield a best-fit temperature of 1.6 keV. The emission coincident with the eastern clump of galaxies is cooler, 0.8 keV, and is outside the 90\% confidence intervals of the central peak temperature. We suggest that the eastern and central subclusters have recently undergone a merger event. The lack of X-ray emission to the north suggests that those galaxies do not form a physically-distinct structure (i.e. they are not located within a distinct gravitational potential), but rather that they are falling into the cluster core along the filament defined by the Hercules Supercluster.
Context: During solar flares a large number of charged particles are accelerated to high energies, but the exact mechanism responsible for this is, so far, still unclear. Acceleration in collapsing magnetic traps is one of the mechanisms proposed.   Aims: In the present paper we want to extend previous 2D models for collapsing magnetic traps to 3D models and to 2D models with shear flow.   Methods: We use analytic solutions of the kinematic magnetohydrodynamic (MHD) equations to construct the models. Particle orbits are calculated using the guiding centre approximation.   Results: We present a general theoretical framework for constructing kinematic MHD models of collapsing magnetic traps in 3D and in 2D with shear flow. A few illustrative examples of collapsing trap models are presented, together with some preliminary studies of particle orbits. For these example orbits, the energy increases roughly by a factor of 5 or 6, which is consistent with the energy increase found in previous 2D models.
Every adapted absolutely continuous process has a predictable density. The set of adapted absolutely continuous processes equals the set of time integrals of progressive or predictable pathwise locally integrable processes.
As an emerging field of robotics, magnetic-field-controlled soft microrobot has broad application prospects for its flexibility, locomotion diversity as well as remote controllability. Magnetic soft microrobots can perform multimodal locomotion under the control of a magnetic field, which may have potential applications in precision medicine. However, previous researches mainly focus on new locomotion in a relatively ideal environment, lacking exploration on the ability of magnetic microrobot locomotion to resist external disturbances and proceed in a nonideal environment. Here, a porous silica-doped soft magnetic microrobot is constructed for enhanced stability of multimodal locomotion in the nonideal biological environment. Porous silica spheres are doped into NdFeB-silicone elastomer base, improving adhesion properties as well as refining the comprehensive mechanical properties of the microrobot. Multimodal locomotions are achieved, and the influence of porous silica doping on the stability of each locomotion in nonideal environment is explored in depth. Motions in nonideal circumstances such as climbing, loading, current rushing, wind blowing, and obstacle hindering are conducted successfully with porous silica doping. Such a stability-enhanced multimodal locomotion system can be used in biocatalysis as well as thrombus removal, and its prospect for precision medicine is highlighted by in vivo demonstration of multimodal locomotion with nonideal disturbance.
We prove that the neighborly cubical polytopes studied by G"unter M. Ziegler and the first author arise as a special case of neighborly cubical spheres constructed by Babson, Billera, and Chan. By relating the two constructions we obtain an explicit description of a non-polytopal neighborly cubical sphere and, further, a new proof of the fact that the cubical equivelar surfaces of McMullen, Schulz, and Wills can be embedded into R^3.
In this work, we propose a novel Spatial-Temporal Attention (STA) approach to tackle the large-scale person re-identification task in videos. Different from the most existing methods, which simply compute representations of video clips using frame-level aggregation (e.g. average pooling), the proposed STA adopts a more effective way for producing robust clip-level feature representation. Concretely, our STA fully exploits those discriminative parts of one target person in both spatial and temporal dimensions, which results in a 2-D attention score matrix via inter-frame regularization to measure the importances of spatial parts across different frames. Thus, a more robust clip-level feature representation can be generated according to a weighted sum operation guided by the mined 2-D attention score matrix. In this way, the challenging cases for video-based person re-identification such as pose variation and partial occlusion can be well tackled by the STA. We conduct extensive experiments on two large-scale benchmarks, i.e. MARS and DukeMTMC-VideoReID. In particular, the mAP reaches 87.7% on MARS, which significantly outperforms the state-of-the-arts with a large margin of more than 11.6%.