ShantanuT01/DACTYL-Pretraining huggingface dataset:
We examine recent developments in the cluster cooling flow scenario following recent observations by Chandra and XMM-Newton. We show that the distribution of gas emissivity verses temperature determined by XMM-Newton gratings observations demonstrates that the central gas in cooling flow clusters cannot be in simple steady-state. Combining this result with the lack of spectroscopic evidence for gas below one-third of the ambient cluster temperature is strong evidence that the gas is heated intermittently. While the old steady-state isobaric cooling flow model is incompatible with recent observations, a "moderate cooling flow model", in which the gas undergoes intermittent heating that effectively reduces the age of a cooling flow is consistent with observations. Most of the gas within cooling flows resides in the hottest gas, which is prevented from cooling continuously and attaining a steady-state configuration. This results in a mass cooling rate that decreases with decreasing temperature, with a much lower mass cooling rate at the lowest temperatures. The present paper strengthens the moderate cooling flow model, which can accommodate the unique activities observed in cooling flow clusters.
Motivated by the magnetic properties of the spin-chain compounds LiCuSbO$_4$$\equiv$LiSbCuO$_4$ and Rb$_2$Cu$_2$Mo$_3$O$_{12}$, we study the ground state of the Heisenberg chain with dimerized nearest-neighbor ferromagnetic (FM)($J_1, J_1^\prime<0$) and next-nearest-neighbor antiferromagnetic ($J_2>0$) couplings. Using the density-matrix renormalization group technique and spin-wave theory we find a first-order transition between a fully-polarized FM and an incommensurate spiral state at $2\alpha=\beta/(1+\beta)$, where $\alpha$ is the frustration ratio $J_2/|J_1|$ and $\beta$ the degree of dimerization $J_1^\prime/J_1$.In the singlet spiral state the spin-gap is vanishingly small in the vicinity of the FM transition, corresponding to a situation of LiCuSbO$_4$. For larger $\alpha$, corresponding to Rb$_2$Cu$_2$Mo$_3$O$_{12}$, and smaller $\beta$ there is a crossover from this frustration induced incommensurate state to an Affleck-Lieb-Kennedy-Tasaki-type valence bond solid state with substantial spin-gaps.
We address the problem of the post-prior equivalence in inclusive breakup reactions induced by weakly-bound nuclei. The problem is studied within the DWBA model of Ichimura, Austern, Vincent [Phys. Rev. C32, 431 (1985)]. The post and prior formulas obtained in this model are briefly recalled, and applied to several breakup reactions induced by deuterons and $^6$Li projectiles, to test their actual numerical equivalence. The different contributions of the prior-form formula are also discussed. A critical comparison with the prior-form distorted-wave Born approximation (DWBA) model of Udagawa and Tamura [Phys. Rev. C24, 1348 (1981)] is also provided.
We aim to explore the relationship between globular cluster total number, $N_{\rm GC}$, and central black hole mass, $M_\bullet$, in spiral galaxies, and compare it with that recently reported for ellipticals. We present results for the Sbc galaxy NGC 4258, from Canada France Hawaii Telescope data. Thanks to water masers with Keplerian rotation in a circumnuclear disk, NGC 4258 has the most precisely measured extragalactic distance and supermassive black hole mass to date. The globular cluster (GC) candidate selection is based on the ($u^*\ -\ i^\prime$) vs. ($i^\prime\ -\ K_s$) diagram, which is a superb tool to distinguish GCs from foreground stars, background galaxies, and young stellar clusters, and hence can provide the best number counts of GCs from photometry alone, virtually free of contamination, even if the galaxy is not completely edge-on. The mean optical and optical-near infrared colors of the clusters are consistent with those of the Milky Way and M 31, after extinction is taken into account. We directly identify 39 GC candidates; after completeness correction, GC luminosity function extrapolation and correction for spatial coverage, we calculate a total $N_{\rm GC} = 144\pm31^{+38}_{-36}$ (random and systematic uncertainties, respectively). We have thus increased to 6 the sample of spiral galaxies with measurements of both $M_\bullet$ and $N_{\rm GC}$. NGC 4258 has a specific frequency $S_{\rm N} = 0.4\pm0.1$ (random uncertainty), and is consistent within 2$\sigma$ with the $N_{\rm GC}$ vs. $M_\bullet$ correlation followed by elliptical galaxies. The Milky Way continues to be the only spiral that deviates significantly from the relation.
This paper is an attempt to survey the current state of our knowledge on the Caccetta-Haggkvist conjecture and related questions. In January 2006 there was a workshop hosted by the American Institute of Mathematics in Palo Alto, on the Caccetta-Haggkvist conjecture, and this paper partly originated there, as a summary of the open problems and partial results presented at the workshop. This summary includes results and open problems related to Caccetta-Haggkvist, Seymour's Second Neighborhood Conjecture, the k/2 Conjecture (for nonedges), and connections with algebraic number theory through Cayley graphs, along with a number of other related topics.
Let $X,X_1,...,X_n$ be independent identically distributed random variables. In this paper we study the behavior of the concentration functions of the weighted sums $\sum\limits_{k=1}^{n}a_k X_k$ with respect to the arithmetic structure of coefficients $a_k$. Such concentration results recently became important in connection with investigations about singular values of random matrices. In this paper we formulate and prove some refinements of a result of Vershynin (R. Vershynin, Invertibility of symmetric random matrices, arXiv:1102.0300. (2011). Published in Random Structures and Algorithms, v. 44, no. 2, 135--182 (2014)).
Landau-Ginzburg mirror symmetry studies isomorphisms between A- and B-models, which are graded Frobenius algebras that are constructed using a weighted homogeneous polynomial $W$ and a related group of symmetries $G$ of $W$. It is known that given two polynomials $W_{1}$, $W_{2}$ with the same weights and same group $G$, the corresponding A-models built with ($W_{1}$,$G$) and ($W_{2}$,$G$) are isomorphic. Though the same result cannot hold in full generality for B-models, which correspond to orbifolded Milnor rings, we provide a partial analogue. In particular, we exhibit conditions where isomorphisms between unorbifolded B-models (or Milnor rings) can extend to isomorphisms between their corresponding orbifolded B-models (or orbifolded Milnor rings).
We study phase diagram of the dense holographic gauge matter in the Sakai-Sugimoto model in the presence of the magnetic field above the deconfinement temperature. Even above the deconfinement, quarks could form colour bound states through the remaining strong interaction if the density is large. We demonstrate that in the presence of the magnetic field for a sufficiently large baryon density, the multiquark-pion gradient (MQ-$\mathcal{5}\phi$) phase is more thermodynamically preferred than the chiral-symmetric quark-gluon plasma. The phase diagrams between the holographic multiquark and the chiral-symmetric quark-gluon plasma phase are obtained at finite temperature and magnetic field. In the mixed MQ-$\mathcal{5}\phi$ phase, the pion gradient induced by the external magnetic field is found to be a linear response for small and moderate field strengths. Its population ratio decreases as the density is raised and thus the multiquarks dominate the phase. Temperature dependence of the baryon chemical potential, the free energy and the linear pion gradient response of the multiquark phase are well approximated by a simple analytic function $\sqrt{1-\frac{T^{6}}{T^{6}_{0}}}$ inherited from the metric of the holographic background.
We show that partial mass concentration can happen for stationary solutions of aggregation-diffusion equations with homogeneous attractive kernels in the fast diffusion range. More precisely, we prove that the free energy admits a radial global minimizer in the set of probability measures which may have part of its mass concentrated in a Dirac delta at a given point. In the case of the quartic interaction potential, we find the exact range of the diffusion exponent where concentration occurs in space dimensions $N\geq6$. We then provide numerical computations which suggest the occurrence of mass concentration in all dimensions $N\geq3$, for homogeneous interaction potentials with higher power.
We introduce an algorithm for the uniform generation of infinite runs in concurrent systems under a partial order probabilistic semantics. We work with trace monoids as concurrency models. The algorithm outputs on-the-fly approximations of a theoretical infinite run, the latter being distributed according to the exact uniform probability measure. The average size of the approximation grows linearly with the time of execution of the algorithm. The execution of the algorithm only involves distributed computations, provided that some - costly - precomputations have been done.
The arbitrary mass scale in the spectral action for the Dirac operator in the spectral action is made dynamical by introducing a dilaton field. We evaluate all the low-energy terms in the spectral action and determine the dilaton couplings. These results are applied to the spectral action of the noncommutative space defined by the standard model. We show that the effective action for all matter couplings is scale invariant, except for the dilaton kinetic term and Einstein-Hilbert term. The resulting action is almost identical to the one proposed for making the standard model scale invariant as well as the model for extended inflation and has the same low-energy limit as the Randall-Sundrum model. Remarkably, all desirable features with correct signs for the relevant terms are obtained uniquely and without any fine tuning.
The quantum object is in general considered as displaying both wave and particle nature. By particle is understood an item localized in a very small volume of the space, and which cannot be simultaneously in two disjoint regions of the space. By wave, to the contrary, is understood a distributed item, occupying in some cases two or more disjoint regions of the space. The quantum formalism did not explain until today the so called "collapse" of the wave function, i.e. the shrinking of the wave function to one small region of the space, when a macroscopic object is encountered. This seems to happen in "which way" experiments. A very appealing explanation for this behavior is the idea of a particle, localized in some limited part of the wave-function. The present article challenges the concept of particle. It proves in base of a variant of the Tan, Walls and Collett experiment, that this concept leads to a situation in which the particle has to be simultaneously in two places distant from one another, situation that contradicts the very definition of a particle. Another argument is based on a modified version of the Afshar experiment, showing that the concept of particle is problematic. The concept of particle makes additional difficulties when the wave-function passes through fields. An unexpected possibility to solve these difficulties seems to arise from the cavity quantum electrodynamics studies done recently by S. Savasta and his collaborators. It involves virtual particles. One of these studies is briefly described here. Though, experimental results are expected, so that it is too soon to draw conclusions whether it speaks in favor, or against the concept of particle.
The LAT instrument on the Fermi Gamma-Ray Space Telescope is performing an all-sky survey from 20 MeV to 300 GeV with unprecedented statistics and angular resolution. This is providing a wealth of new information on the non-thermal emission from the Galactic interstellar medium with implications for cosmic rays and Galactic structure. First results at intermediate latitudes have already shown good agreement with predictions based on direct measurements of cosmic rays, suggesting that at least the local (within about 1 kpc from the Sun) gamma-ray emission is understood. We will present the first spectra from regions over the sky using the LAT data, and profiles for selected energies. The aim here is to evaluate the agreement with the models and assess what we can expect to learn as this analysis matures.
We present a detailed theory of spectacular semiclassical catastrophes happening during the time evolution of a kicked quantum rotor (Phys.Rev. Lett. {\bf 87}, 163601 (2001)). Both two- and three-dimensional rotational systems are analyzed. It is shown that the wave function of the rotor develops a {\em cusp} at a certain delay after a kick, which results in a sharply focused rotational wave packet. The {\em cusp} is followed by a fold-type catastrophe manifested in the {\em rainbow}-like moving angular singularities. In the three-dimensional case, the rainbows are accompanied by additional singular features similar to {\em glory} structures known in wave optics. These catastrophes in the time-dependent angular wave function are well described by the appropriate tools of the quasiclassical wave mechanics, i.e. by Airy and Bessel approximations and Pearcey's functions. A scenario of "accumulative squeezing" is also presented in which a specially designed train of short kicks produces an unlimited narrowing of the rotor angular distribution. This scenario is relevant for the molecular alignment by short laser pulses, and also for atom lithography schemes in which cold atoms are focused by an optical standing wave.
We study whether the individual violation of the lepton numbers L_{e,mu,tau} in the charged sector can lead to measurable rates for BR(mu->e gamma) and BR(tau->mu gamma). We consider three different scenarios, the fist one corresponds to the Minimal Supersymmetric Standard Model with non-universal soft terms. In the other two cases the violation of flavor in the leptonic charged sector is associated to the neutrino problem in models with a see-saw mechanism and with R-parity violation respectively.
An examples of a Ricci-flat of four-dimensional spaces with a Walker metrics and their generalizations are constructed. The properties of corresponding geodesic equations are discussed.
We theoretically investigate spin-polarized transport in a system composed of a ferromagnetic Scanning Tunneling Microscope (STM) tip coupled to an adsorbed atom (adatom) on a host surface. Electrons can tunnel directly from the tip to the surface or via the adatom. Since the tip is ferromagnetic and the host surface (metal or semiconductor) is non-magnetic we obtain a spin-diode effect when the adatom is in the regime of single occupancy. This effect leads to an unpolarized current for direct bias (V > 0) and polarized current for reverse (V < 0) bias voltages, if the tip is nearby the adatom. Within the nonequilibrium Keldysh technique we analyze the interplay between the lateral displacement of the tip and the intra adatom Coulomb interaction on the spindiode effect. As the tip moves away from the adatom the spin-diode effect vanishes and the currents become polarized for both V > 0 and V < 0. We also find an imbalance between the up and down spin populations in the adatom, which can be tuned by the tip position and the bias. Finally, due to the presence of the adsorbate on the surface, we observe spin-resolved Friedel oscillations in the current, which reflects the oscillations in the calculated LDOS of the subsystem surface+adatom.
We show that monomials and sums of pairwise coprime monomials in four or more variables have Waring rank less than the generic rank, with a short list of exceptions. We asymptotically compare their ranks with the generic rank.
We present the Herschel SPIRE Fourier Transform Spectroscopy (FTS) atlas for a complete flux limited sample of local Ultra-Luminous Infra-Red Galaxies as part of the HERschel ULIRG Survey (HERUS). The data reduction is described in detail and was optimized for faint FTS sources with particular care being taken with the subtraction of the background which dominates the continuum shape of the spectra. Special treatment in the data reduction has been given to any observation suffering from artefacts in the data caused by anomalous instrumental effects to improve the final spectra. Complete spectra are shown covering $200 - 671\mu$m with photometry in the SPIRE bands at 250$\mu$m, 350$\mu$m and 500$\mu$m. The spectra include near complete CO ladders for over half of our sample, as well as fine structure lines from [CI] 370 $\mu$m, [CI] 609 $\mu$m, and [NII] 205 $\mu$m. We also detect H$_{2}$O lines in several objects. We construct CO Spectral Line Energy Distributions (SLEDs) for the sample, and compare their slopes with the far-infrared colours and luminosities. We show that the CO SLEDs of ULIRGs can be broadly grouped into three classes based on their excitation. We find that the mid-J (5$<$J$<$8) lines are better correlated with the total far-infrared luminosity, suggesting that the warm gas component is closely linked to recent star-formation. The higher J transitions do not linearly correlate with the far-infrared luminosity, consistent with them originating in hotter, denser gas unconnected to the current star-formation. {\bf We conclude that in most cases more than one temperature components are required to model the CO SLEDs.}
Predictive coding theories suggest that the brain learns by predicting observations at various levels of abstraction. One of the most basic prediction tasks is view prediction: how would a given scene look from an alternative viewpoint? Humans excel at this task. Our ability to imagine and fill in missing information is tightly coupled with perception: we feel as if we see the world in 3 dimensions, while in fact, information from only the front surface of the world hits our retinas. This paper explores the role of view prediction in the development of 3D visual recognition. We propose neural 3D mapping networks, which take as input 2.5D (color and depth) video streams captured by a moving camera, and lift them to stable 3D feature maps of the scene, by disentangling the scene content from the motion of the camera. The model also projects its 3D feature maps to novel viewpoints, to predict and match against target views. We propose contrastive prediction losses to replace the standard color regression loss, and show that this leads to better performance on complex photorealistic data. We show that the proposed model learns visual representations useful for (1) semi-supervised learning of 3D object detectors, and (2) unsupervised learning of 3D moving object detectors, by estimating the motion of the inferred 3D feature maps in videos of dynamic scenes. To the best of our knowledge, this is the first work that empirically shows view prediction to be a scalable self-supervised task beneficial to 3D object detection.
We consider additive functionals of stationary Markov processes and show that under Kipnis-Varadhan type conditions they converge in rough path topology to a Stratonovich Brownian motion, with a correction to the Levy area that can be described in terms of the asymmetry (non-reversibility) of the underlying Markov process. We apply this abstract result to three model problems: First we study random walks with random conductances under the annealed law. If we consider the Ito rough path, then we see a correction to the iterated integrals even though the underlying Markov process is reversible. If we consider the Stratonovich rough path, then there is no correction. The second example is a non-reversible Ornstein-Uhlenbeck process, while the last example is a diffusion in a periodic environment.   As a technical step we prove an estimate for the p-variation of stochastic integrals with respect to martingales that can be viewed as an extension of the rough path Burkholder-Davis-Gundy inequalities for local martingale rough paths of Friz et al to the case where only the integrator is a local martingale.
Recently there is a lot of attention given to manipulation of heat by constructing thermal devices such as thermal diodes, transistors and logic gates. Many of the models proposed have an asymmetry which leads to the desired effect. Presence of non-linear interactions among the particles is also essential. But, such models lack analytical understanding. Here we propose a simple, analytically solvable model of a thermal diode. Our model consists of classical spins in contact with multiple heat baths and constant external magnetic fields. Interestingly the magnetic field is the only parameter required to get the effect of heat rectification.
We consider the voter model on Z, starting with all 1's to the left of the origin and all 0's to the right of the origin. It is known that if the associated random walk kernel p has zero mean and a finite r-th moment for any r>3, then the evolution of the boundaries of the interface region between 1's and 0's converge in distribution to a standard Brownian motion (B_t)_{t>0} under diffusive scaling of space and time. This convergence fails when p has an infinite r-th moment for any r<3, due to the loss of tightness caused by a few isolated 1's appearing deep within the regions of all 0's (and vice versa) at exceptional times. In this note, we show that as long as p has a finite second moment, the measure-valued process induced by the rescaled voter model configuration is tight, and converges weakly to the measure-valued process 1_{x<B_t}dx, t>0.
We present independent measurements of the masses of the galaxy clusters in the local universe by employing the Dynamical Mass Estimator (DME) originally developed by Falco et al in 2014. In the catalog of the galaxy groups/clusters constructed by Tempel et al. from the Sloan Digital Sky Survey Data Release 10, we search for those as the targets around which the neighbor galaxies constitute thin straight filamentary structures in the configuration space spanned by the redshifts and the projected distances. Out of the $29$ Sloan clusters that have $100$ or more member galaxies, a total of six targets are found to have filamentary structures in their bound zones. For each of the six targets, we construct the profile of the recession velocities of the filament galaxies, which depends on the cluster mass and the angle of the filament relative the line of the sight direction. Fitting the constructed profile to the universal formula with constant amplitude and slope, we statistically determine the dynamical mass of each cluster and compare it with the previous estimates made by a conventional method. The weak and strong points of the DME as well as its prospect for the measurements of the dynamical masses of the high-$z$ clusters are discussed.
We study the hypernuclei of C and B isotopes by Hartree-Fock model with Skyrme-type nucleon-nucleon and nucleon-hyperon interactions. The calculated $\Lambda$ binding energies agree well with the available experiment data. We found halo structure in the hyperon $1p$-state with extended wave function beyond nuclear surface in the light C and B isotopes. We also found the enhanced electric dipole transition between $1p$- and $1s$-hyperon states, which could be the evidence for this hyperon halo structure.