ShantanuT01/DACTYL-Pretraining huggingface dataset:
Baryon-strangeness correlations ($C_{BS}$) are studied with a hadron/string transport approach (UrQMD) and a dynamical quark recombination model (quark molecular dynamics, qMD) for various energies from $E_{lab}=4A$ GeV to $\sqrt{s_{NN}}=200$ GeV. As expected, we find that the hadron/string dynamics shows correlations similar to a simple hadron gas. In case of the quark molecular dynamics, we find that initially the $C_{BS}$ correlation is that of a weakly interacting QGP but changes in the process of hadronization also to the value for a hadron gas. Therefore, we conclude that the hadronization process itself makes the initial baryon strangeness correlation unobservable. To make an experimental study of this observable more feasible, we also investigate how a restriction to only charged kaons and $\Lambda$'s (instead of all baryons and all strange particles) influences the theoretical result on $C_{BS}$. We find that a good approximation of the full result can be obtained in this limit in the present simulation.
We prove a central limit theorem for an additive functional of the $d$-dimensional fractional Brownian motion with Hurst index $H\in(\frac{1}{2+d},\frac{1}{d})$, using the method of moments, extending the result by Papanicolaou, Stroock and Varadhan in the case of the standard Brownian motion.
We perform a systematic study of in-plane and out-of-plane proton and neutron flow from nucleus-nucleus collisions within the BUU transport approach employing different parameter sets for the mean-field potentials that can be characterized by the nuclear incompressibility and the stiffness of the momentum-dependent potential. We find that a simultaneous description of the experimental data from the BEVALAC and the SIS on both the nucleon squeeze-out $v_2$ and the in-plane flow $F$ at beam energies $E_{lab} = 0.15 \div 2$ AGeV requires a mean field with strong momentum dependence, i.e. an effective Landau mass $m^* \simeq 0.68 m_0$ at normal nuclear matter density $\rho_0=0.17$ fm$^{-3}$, where $m_0=0.938$ GeV is the bare nucleon mass. Some experimental data on the squeeze-out require an even stiffer momentum dependence ($m^* \approx 0.62 m_0$). All systems investigated are found to be compatible with $m^*/m_0 = 0.65 \pm 0.03$.
A graph $G$ is called uniquely k-list colorable (U$k$LC) if there exists a list of colors on its vertices, say $L=\lbrace S_v \mid v \in V(G) \rbrace $, each of size $k$, such that there is a unique proper list coloring of $G$ from this list of colors. A graph $G$ is said to have property $M(k)$ if it is not uniquely $k$-list colorable. Mahmoodian and Mahdian characterized all graphs with property $M(2)$. For $k\geq 3$ property $M(k)$ has been studied only for multipartite graphs. Here we find bounds on $M(k)$ for graphs embedded on surfaces, and obtain new results on planar graphs. We begin a general study of bounds on $M(k)$ for regular graphs, as well as for graphs with varying list sizes.
Let $E$ be an elliptic curve defined over $\mathbb{Q}$, and let $\rho_E\colon {\rm Gal}(\overline{\mathbb{Q}}/\mathbb{Q})\to {\rm GL}(2,\widehat{ \mathbb{Z} })$ be the adelic representation associated to the natural action of Galois on the torsion points of $E(\overline{\mathbb{Q}})$. By a theorem of Serre, the image of $\rho_{E}$ is open, but the image is always of index at least $2$ in ${\rm GL}(2,\widehat{\mathbb{Z}})$ due to a certain quadratic entanglement amongst division fields. In this paper, we study other types of abelian entanglements. More concretely, we classify the elliptic curves $E/\mathbb{Q}$, and primes $p$ and $q$ such that $\mathbb{Q}(E[p])\cap \mathbb{Q}(\zeta_{q^k})$ is non-trivial, and determine the degree of the coincidence. As a consequence, we classify all elliptic curves $E/\mathbb{Q}$ and integers $m,n$ such that the $m$-th and $n$-th division fields coincide, i.e., when $\mathbb{Q}(E[n])=\mathbb{Q}(E[m])$, when the division field is abelian.
We show in the smooth category that the heat trace asymptotics and the heat content asymptotics can be made to grow arbitrarily rapidly. In the real analytic context, however, this is not true and we establish universal bounds on their growth.
For linear multivariate purely second order highla degenerated parabolic equations with univariate convex data, monotonicity of the coefficent matrices implies monotonicity of the related value functions under usual regularity and growth assumptions for the data and the coefficients. The comparison result is applied to a new product, i.e., symmetric passport options.
We investigate hadronic particle spectra and flow characteristics of heavy-ion reactions in the FAIR/NICA energy range of $1\ A{\rm GeV} \le E_{\rm lab} \le 10\ A{\rm GeV}$ within a relativistic ideal hydrodynamic one-fluid approach. The particlization is realized by sampling the Cooper-Frye distribution for a grand canonical hadron gas on a hypersurface of constant energy density. Results of the hydrodynamic calculations for different underlying equations of state are presented and compared with experimental data and microscopic transport simulations. The sensitivity of the approach to physical model inputs concerning the initial state and the particlization is studied.
Let $f\in \mathbb{Z}\lbrack x\rbrack$ be a polynomial of degree $d\geq 3$ without roots of multiplicity $d$ or $(d-1)$. Erd\H{o}s conjectured that, if $f$ satisfies the necessary local conditions, then $f(p)$ is free of $(d-1)$th powers for infinitely many primes $p$. This is proved here for all $f$ with sufficiently high entropy.   The proof serves to demonstrate two innovations: a strong repulsion principle for integer points on curves of positive genus, and a number-theoretical analogue of Sanov's theorem from the theory of large deviations.
An edge-colored graph $G$ is rainbow connected if any two vertices are connected by a path whose edges have distinct colors. The rainbow connection number of a connected graph $G$, denoted $rc(G)$, is the smallest number of colors that are needed in order to make $G$ rainbow connected. We prove if $G$ is a connected strongly $r$-regular graph and $r\geq 600$, then $rc(G)\leq3$. Specially, there is a constant $c$ such that $rc(G)\leq c$ for any connected strongly regular graph $G$.
The paper is concerned with the IBVP of the Navier-Stokes equations. The result of the paper is in the wake of analogous results obtained by the authors in previous articles [4, 5]. The goal is to estimaste the possible gap between the energy equality and the energy inequality deduced for a weak solution.
We propose a particular encoding for bipartite entangled states derived from multipartite cluster-type entangled coherent states (CTECSs). We investigate the effects of amplitude damping on the entanglement content of this bipartite state, as well as its usefulness as a quantum channel for teleportation. We find interesting relationships among the amplitude of the coherent states constituting the CTECSs, the number of subsystems forming the logical qubits (redundancy), and the extent to which amplitude damping affects the entanglement of the channel. For instance, in the sense of sudden death of entanglement, given a fixed value of the initial coherent state amplitude, the entanglement life span is shortened if redundancy is increased.
Beyond possessing large enough size to feed data hungry machines (eg, transformers), what attributes measure the quality of a dataset? Assuming that the definitions of such attributes do exist, how do we quantify among their relative existences? Our work attempts to explore these questions for video action detection. The task aims to spatio-temporally localize an actor and assign a relevant action class. We first analyze the existing datasets on video action detection and discuss their limitations. Next, we propose a new dataset, Multi Actor Multi Action (MAMA) which overcomes these limitations and is more suitable for real world applications. In addition, we perform a biasness study which analyzes a key property differentiating videos from static images: the temporal aspect. This reveals if the actions in these datasets really need the motion information of an actor, or whether they predict the occurrence of an action even by looking at a single frame. Finally, we investigate the widely held assumptions on the importance of temporal ordering: is temporal ordering important for detecting these actions? Such extreme experiments show existence of biases which have managed to creep into existing methods inspite of careful modeling.
We investigate the presence of off-diagonal long-range order in a harmonically confined two-dimensional Bose gas. In the noninteracting case, an analytical calculation of the the finite-temperature one-particle density martix provides an exact description of the spatial correlations known to be associated with the existence of a Bose-Einstein condensate below the transition temperature $T^{(0)}_c$. We treat the effects of repulsive interactions within the semiclassical Hartree-Fock-Bogliubov approximation and find that even though the system remains in the same {\em uncondensed phase} for all $T \geq 0$, there appears to be a revival of off-diagonal long-range order for temperatures $T < T^{(0)}_c$. We suggest that this reentrant order is related to a phase transition in the system which {\em is not} the BEC state.
I provide additional arguments for refuting Vaidmans weak value analysis of the path of a particle in a nested Mach-Zehnder interferometer. The argument uses sequential weak values to supplement my previous analysis according to which even weak measurements disturb the system to such an extent that projector weak values cannot be considered representative for the undisturbed system.
We describe the potential of high resolution imaging spectroscopy with the SXS on ASTRO-H to advance our understanding of the interstellar- and circumgalactic media of our own Galaxy, and other galaxies. Topics to be addressed range from absorption spectroscopy of dust in the Galactic interstellar medium, to observations to constrain the total mass-, metal-, and energy flow out of starburst galaxies.
A simple formula for the ratio of the number of odd- and even-parity states as a function of temperature is derived. This formula is used to calculate the ratio of level densities of opposite parities as a function of excitation energy. We test the formula with quantum Monte Carlo shell model calculations in the $(pf+g_{9/2})$-shell. The formula describes well the transition from low excitation energies where a single parity dominates to high excitations where the two densities are equal.
In quantum field theory, there exist states in which the expectation value of the energy density for a quantized field is negative. These negative energy densities lead to many problems. Although quantum field theory introduces negative energies, it also provides constraints in the form of quantum inequalities (QI's). These uncertainty principle-type relations limit the magnitude and duration of any negative energy. We derive a general form of the QI on the energy density for both the quantized scalar and electromagnetic fields in static curved spacetimes. In the case of the scalar field, the QI can be written as the Euclidean wave operator acting on the Euclidean Green's function. Additionally, a small distance expansion on the Green's function is used to derive the QI in the short sampling time limit. It is found that the QI in this limit reduces to the flat space form with subdominant correction terms which depend on the spacetime geometry.   Several example spacetimes are studied in which exact forms of the QI's can be found. These include the three- and four-dimensional static Robertson-Walker spacetimes, flat space with perfectly reflecting mirrors, Rindler and static de Sitter space, and the spacetime outside a black hole. Finally, the application of the quantum inequalities to the Alcubierre warp drive spacetime leads to strict constraints on the thickness of the negative energy region needed to maintain the warp drive. Under these constraints, we discover that the total negative energy required exceeds the total mass of the visible universe by a hundred billion times.
Let $X_1, X_2, ..., X_n, ... $ be a sequence of iid random variables with values in a finite alphabet $\{1,...,m\}$. Let $LI_n$ be the length of the longest increasing subsequence of $X_1, X_2, ..., X_n.$ We express the limiting distribution of $LI_n$ as functionals of $m$ and $(m-1)$-dimensional Brownian motions. These expressions are then related to similar functionals appearing in queueing theory, allowing us to further establish asymptotic behaviors as $m$ grows. The finite alphabet results are then used to treat the countable (infinite) alphabet.
The exact analytic solutions of the Maxwell equations in the exterior of a boosted rotating black hole immersed in an external magnetic field are obtained. The effect of boost as well as electromagnetic field on charged particle motion and energy extraction process -- magnetic Penrose process around black hole is studied. It justifies however the well known statement that magnetic field greatly increases efficiency of energy extraction which is further boosted by the boost velocity.
We give a short review of our recent works on the first-order quantum phase transitions in frustrated spin chains with orthogonal-dimer structure. When the ratio of the competing antiferromagnetic exchange couplings is varied, a first-order transition occurs between the dimer phase and the plaquette phase, which is accompanied by the discontinuity in the spin excitation gap. We further show that strong frustration triggers the phase transitions in a magnetic field, which exhibit plateaus and jumps in the magnetization curve. The hole-doping effect is also addressed for the orthogonal-dimer chain with linked-tetrahedra structure. It is found that the competing antiferromagnetic interactions result in a first-order metal-insulator transition upon hole doping.
We prove that all open string theory disc amplitudes in a flat background obey Britto-Cachazo-Feng-Witten (BCFW) on-shell recursion relations, up to a possible reality condition on a kinematic invariant. Arguments that the same holds for tree level closed string amplitudes are given as well. Non-adjacent BCFW-shifts are related to adjacent shifts through monodromy relations for which we provide a novel CFT based derivation. All possible recursion relations are related by old-fashioned string duality. The field theory limit of the analysis for amplitudes involving gluons is explicitly shown to be smooth for both the bosonic string as well as the superstring. In addition to a proof a less rigorous but more powerful argument based on the underlying CFT is presented which suggests that the technique may extend to a much more general setting in string theory. This is illustrated by a discussion of the open string in a constant B-field background and the closed string on the level of the sphere.
Due to the advent of antiferromagnetic (AF) spintronics there is a burgeoning interest in AF materials for a wide range of potential and actual applications. Generally, AFs are characterized via the ordering at the Neel temperature (TN) but, to have a stable AF configuration, it is necessary that the material have a sufficient level of anisotropy so as to maintain the orientation of the given magnetic state fixed in one direction. Unlike the case for ferromagnets there is little established data on the anisotropy of AFs and in particular its origins and those factors which control it. In this paper these factors are reviewed in the light of recent and established experimental data. Additionally, there is no recognized technique for the first principle determination of the anisotropy of an AF which can only be found indirectly via the exchange bias phenomenon. This technique is reviewed and in particular the implications for the nature of the anisotropy that is measured and its distribution. Finally, a strategy is proposed that would allow for the development of AF materials with controlled anisotropy for future applications.
We investigate strong lensing by a spherically symmetric mass distribution in the framework of the Einstein-Straus solution with positive cosmological constant and concentrate on the case of a spatially closed Universe ($k=+1$). We develop a method based on integration of differential equations in order to make possible the computation of light deflection and time delay. By applying our results to the lensed quasar SDSS J1004+4112, we find that the bending of light and time delay depend on wether the present value of the scale factor $a_0$ is or is not much smaller than a value close to $9.1 \cdot 10^{26} \mbox{m}$. Beyond this value, the results are almost the same as for the spatially flat Universe. Moreover, it turns out that a positive cosmological constant attenuates the light bending in agreament with Rindler and Ishak's finding.
It has been conjectured that the velocity of sound in any medium is smaller than the velocity of light in vacuum divided by $\sqrt{3}$. Simple arguments support this bound in non-relativistic and/or weakly coupled theories. The bound has been demonstrated in several classes of strongly coupled theories with gravity duals and is saturated only in conformal theories. We point out that the existence of neutron stars with masses around two solar masses combined with the knowledge of the equation of state of hadronic matter at "low" densities is in strong tension with this bound.
We use dwarf spheroidal galaxies as a tool to attempt to put precise lower limits on the mass of the dark matter particle, assuming it is a sterile neutrino. We begin by making cored dark halo fits to the line of sight velocity dispersions as a function of projected radius (taken from Walker et al. 2007) for six of the Milky Way's dwarf spheroidal galaxies. We test Osipkov-Merritt velocity anisotropy profiles, but find that no benefit is gained over constant velocity anisotropy. In contrast to previous attempts, we do not assume any relation between the stellar velocity dispersions and the dark matter ones, but instead we solve directly for the sterile neutrino velocity dispersion at all radii by using the equation of state for a partially degenerate neutrino gas (which ensures hydrostatic equilibrium of the sterile neutrino halo). This yields a 1:1 relation between the sterile neutrino density and velocity dispersion, and therefore gives us an accurate estimate of the Tremaine-Gunn limit at all radii. By varying the sterile neutrino particle mass, we locate the minimum mass for all six dwarf spheroidals such that the Tremaine-Gunn limit is not exceeded at any radius (in particular at the centre). We find sizeable differences between the ranges of feasible sterile neutrino particle mass for each dwarf, but interestingly there exists a small range 270-280eV which is consistent with all dSphs at the 1-$\sigma$ level.
We study the 3-form flux $H_{\m\n\l}$ associated with the semi-classical geometry of $G/H$ gauged WZW models. We derive a simple, general expression for the flux in an orthonormal frame and use it to explicitly verify conformal invariance to the leading order in $\a'$. For supersymmetric models, we briefly revisit the conditions for enhanced supersymmetry. We also discuss some examples of non-abelian cosets with flux.
Let $S$ be a surface isogenous to a product of curves of unmixed type. After presenting several results useful to study the cohomology of $S$ we prove a structure theorem for the cohomology of regular surfaces isogenous to a product of unmixed type with $\chi (\mathcal{O}_S)=2$. In particular we found two families of surfaces of general type with maximal Picard number.
With the goal of providing constraints on the nature of the progenitors of core-collapse supernovae, we compare their radial distribution within their spiral host galaxies with the distributions of stars and ionized gas in the spiral disks. The normalized radial distribution of all CCSNe is consistent with an exponential law, with a possible depletion of CCSNe within one-fifth of the isophotal radius. The scale length of the distribution of type II SNe appears to be significantly larger than that of the stellar disks of their host galaxies, but consistent with the scale lengths of Freeman disks. SNe Ib/c have a significantly smaller scale length than SNe II, with little difference between types Ib and Ic. The radial distribution of type Ib/c SNe is more centrally concentrated than that of the stars in a Freeman disk, but is similar to the stellar disk distribution that we infer for the host galaxies. The scale length of the CCSN radial distribution shows no significant correlation with the host galaxy morphological type, or the presence of bars. However, low luminosity as well as inclined hosts have a less concentrated distribution of CCSNe, which are probably a consequence of metallicity and selection effects, respectively. The exponential distribution of CCSNe shows a scale length consistent with that of the ionized gas confirming the generally accepted hypothesis that the progenitors of these SNe are young massive stars. Given the lack of correlation of the normalized radial distances of CCSNe with the morphological type of the host galaxy, we conclude that the more concentrated distribution of SNe Ib/c relative to SNe II must arise from the higher metallicity of their progenitors or possibly from a shallower initial mass function in the inner regions of spirals.
We demonstrate suppression and enhancement of spontaneous parametric down- conversion via quantum interference with two weak fields from a local oscillator (LO). Pairs of LO photons are observed to upconvert with high efficiency for appropriate phase settings, exhibiting an effective nonlinearity enhanced by at least 10 orders of magnitude. This constitutes a two-photon switch, and promises to be useful for a variety of nonlinear optical effects at the quantum level.
We prove the existence of a family $\mathcal{X}\rightarrow B$ of smooth projective fourfolds, such that the very general fiber $\mathcal{X}_t$ is not stably rational (a fortiori not rational), but some special fibers $\mathcal{X}_t$ are rational (a fortiori stably rational).
We describe and demonstrate a new technique for parallel collection of x-ray reflectivity data, compatible with monochromatic synchrotron radiation and flat substrates, and apply it to the in-situ observation of thin-film growth. The method employs a polycapillary x-ray optic to produce a converging fan of radiation incident onto a sample surface, and an area detector to simultaneously collect the XRR signal over an angular range matching that of the incident fan. Factors determining the range and instrumental resolution of the technique in reciprocal space, in addition to the signal-to-background ratio, are described in detail. Our particular implementation records $\sim$5\degree{} in $2\theta$ and resolves Kiessig fringes from samples with layer thicknesses ranging from 3 to 76 nm. Finally, we illustrate the value of this approach by showing in-situ XRR data obtained with 100 ms time resolution during the growth of epitaxial \ce{La_{0.7}Sr_{0.3}MnO3} on \ce{SrTiO3} by Pulsed Laser Deposition (PLD) at the Cornell High Energy Synchrotron Source (CHESS). Compared to prior methods for parallel XRR data collection, ours is the first method that is both sample-independent and compatible with highly collimated, monochromatic radiation typical of 3rd generation synchrotron sources. Further, our technique can be readily adapted for use with laboratory-based sources.
From an analysis of the specific heat of one of the cuprate superconductors it is shown, that even if a large part of the experimental specific heat associated with the superconducting phase transition is due to fluctuations, this part must be counted when one tries to extract the condensation energy from the data. Previous work by Chakravarty, Kee and Abrahams, where the fluctuation part was subtracted, has resulted in an incorrect estimation of the condensation energy.