ShantanuT01/DACTYL-Pretraining huggingface dataset:
The main objective of this paper is to look from the unique point of view at some phenomena arising in different areas of probability theory and mathematical statistics. We will try to understand what is common between classical probabilistic results, such as the law of iterated logarithm for example, and well-known problem in adaptive estimation called price to pay for adaptation. Why exists two different kinds of this price? What relates exponential inequalities for M-estimators, so-called uniform-in-bandwidth consistency in density or regression model and the bounds for modulus of continuity of gaussian random functions defined on a metric space equipped with doubling measure? It turned out that all these and many others problems can be reduced to finding upper functions for a collection real- valued random variables. Each variable is the value of a given sub-additive positive functional of continuous random mapping defined on a totally bounded subset of a metric space.
Results of some recent investigations of democratic three-body decays of nuclear systems are discussed. In particular, we consider experimental studies of three-body ($\alpha+N+N$)-decay of $A=6$ nuclei and $J$-matrix calculations of monopole excitations in $^{12}$C and $E1$ transitions in $^{11}$Li in the three-body-continuum cluster models $\alpha + \alpha + \alpha$ and $^{9}$Li + n + n, respectively.
Nesterenko proved, among other results, the algebraic independence over $\QQ$ of the numbers $\pi,e^{\pi},\Gamma(1/4)$. A very important feature of his proof is a multiplicity estimate for quasi-modular forms associated to $\SL_2(\ZZ)$ which involves profound differential properties of certain non-linear differential systems. The aim of this article is to begin the study of the analogous properties for Hilbert modular and quasi-modular forms, especially those which are associated with the number field $\QQ(\sqrt{5})$. We show that the differential structure of these functions has several analogies with the differential structure of the quasi-modular forms associated to $\SL_2(\ZZ)$.
Stacking Fault Energy (SFE) is an intrinsic alloy property that governs much of the plastic deformation mechanisms observed in fcc alloys. While SFE has been recognized for many years as a key intrinsic mechanical property, its inference via experimental observations or prediction using, for example, computationally intensive first-principles methods is challenging. This difficulty precludes the explicit use of SFE as an alloy design parameter. In this work, we combine DFT calculations (with necessary configurational averaging), machine-learning (ML) and physics-based models to predict the SFE in the fcc CoCrFeMnNiV-Al high-entropy alloy space. The best-performing ML model is capable of accurately predicting the SFE of arbitrary compositions within this 7-element system. This efficient model along with a recently developed model to estimate intrinsic strength of fcc HEAs is used to explore the strength-SFE Pareto front, predicting new-candidate alloys with particularly interesting mechanical behavior.
The dynamics of n slowly moving fundamental monopoles in the SU(n+1) BPS Yang-Mills-Higgs theory can be approximated by geodesic motion on the 4n-dimensional hyperkahler Lee-Weinberg-Yi manifold. In this paper we apply a variational method to construct some scaling geodesics on this manifold. These geodesics describe the scattering of n monopoles which lie on the vertices of a bouncing polyhedron; the polyhedron contracts from infinity to a point, representing the spherically symmetric n-monopole, and then expands back out to infinity. For different monopole masses the solutions generalize to form bouncing nested polyhedra. The relevance of these results to the dynamics of well separated SU(2) monopoles is also discussed.
The transverse momentum distribution of charged particles formed in AuAu collisions at Beam Energy Scan (BES) ($\sqrt{S_{NN}}=$ 7.7, 11.5, 19.6, 27, 39 $\hspace{0.05cm} GeV$) is investigated. In addition, $ P_{T}$ spectra of $\Lambda$ particle at $\sqrt{S_{NN}}$=62.4 $\hspace{0.03cm} GeV$ was examined. Tsallis distribution is used to extract the temperature, volume and the entropic index from the experimental results at mid-rapidity and zero chemical potential. We measure some particle ratios like $ \frac{k^{+}}{\pi^{+}} $ and $ \frac{\Lambda}{\pi^{-}} $ which are puzzling horn in the experiment and in the thermal model. We conclude that the horn vanished when we used Tsallis distribution, but this does not confirm a solution to the puzzle, which is primarily visible in the experimental results.
We apply a formalism accounting for thermal effects (such as modified Sommerfeld effect; Salpeter correction; decohering scatterings; dissociation of bound states), to one of the simplest WIMP-like dark matter models, associated with an "inert" Higgs doublet. A broad temperature range T ~ M/20...M/10^4 is considered, stressing the importance and less-understood nature of late annihilation stages. Even though only weak interactions play a role, we find that resummed real and virtual corrections increase the tree-level overclosure bound by 1...18%, depending on quartic couplings and mass splittings.
We consider locally consistent systems of magnetized D9 branes on an orbifolded six-torus which support N=1 gauge theories. In such realizations, the matter multiplets arise from "twisted" strings connecting different stacks of branes. The introduction of Euclidean 5 branes (E5) wrapped on the six-dimensional compact space leads to instanton effects. For instance, if the system is engineered so as to yield SQCD, a single E5 brane may account for the ADS/TVY superpotential. We discuss the subtle interplay that exists between the annuli diagrams with an E5 boundary and the holomorphicity properties of the effective low-energy action of the N=1 theory. The consistency of this picture allows to obtain information on the Kahler metric of the chiral matter multiplets arising from twisted strings.
In this paper we provide local test vector for Waldspurger's period integral, when the level of the representation $\pi_v$ is sufficiently large compared to the level of the character $\Omega_v$ over quadratic extension, while allowing joint ramifications. The test vectors we shall use are variants of classical newforms, and the size of the resulting local integral is asymptotically the inverse of convexity bound for $L(\Pi\otimes\Omega,1/2)$. Such test vectors are used to recover Gross-Prasad type test vectors. We also get vanishing result for local integral when using other test vectors. This phenomenon is used to prove the mass equidistribution of cuspidal newforms on nonsplit torus in depth aspect.
The rutile TiO$_2$ (110) surface reduced by the bridging oxygen vacancy, bridging hydroxyl group or Ti interstitial atom has been investigated by calculating their electronic structures using the density functional theory plus U method. It is found that defect states located in the forbidden band gap can enhance optical absorption. When the surface is highly reduced, the defect states approach the valence band. More importantly, defects induce a substantial up-shift of the conduction band edge, rendering the reduced surface stronger reducibility. The shifts of both conduction and valence band edges are due to the dipole moments created by these defects.
Learning 3D point sets with rotational invariance is an important and challenging problem in machine learning. Through rotational invariant architectures, 3D point cloud neural networks are relieved from requiring a canonical global pose and from exhaustive data augmentation with all possible rotations. In this work, we introduce a rotational invariant neural network by combining recently introduced vector neurons with self-attention layers to build a point cloud vector neuron transformer network (VNT-Net). Vector neurons are known for their simplicity and versatility in representing SO(3) actions and are thereby incorporated in common neural operations. Similarly, Transformer architectures have gained popularity and recently were shown successful for images by applying directly on sequences of image patches and achieving superior performance and convergence. In order to benefit from both worlds, we combine the two structures by mainly showing how to adapt the multi-headed attention layers to comply with vector neurons operations. Through this adaptation attention layers become SO(3) and the overall network becomes rotational invariant. Experiments demonstrate that our network efficiently handles 3D point cloud objects in arbitrary poses. We also show that our network achieves higher accuracy when compared to related state-of-the-art methods and requires less training due to a smaller number of hyperparameters in common classification and segmentation tasks.
In this work we investigate the so-called model-space Brueckner-Hartree-Fock (MBHF) approach for nuclear matter as well as for neutron matter and the extension of this which includes the particle-particle and hole-hole (PPHH) diagrams. A central ingredient in the model-space approach for nuclear matter is the boundary momentum $k_M$ beyond which the single-particle potential energy is set equal to zero. This is also the boundary of the model space within which the PPHH diagrams are calculated. It has been rather uncertain which value should be used for $k_M$. We have carried out model-space nuclear matter and neutron matter calculations with and without PPHH diagrams for various choices of $k_M$ and using several modern nucleon-nucleon potentials. Our results exhibit a saturation region where the nuclear and neutron matter matter energies are quite stable as $k_M$ varies. The location of this region may serve to determine an "optimum" choice for $k_M$. However, we find that the strength of the tensor force has a significant influence on binding energy variation with $k_M$. The implications for nuclear and neutron matter calculations are discussed.
Let $X$ be an analytic space over a non-Archimedean, complete field $k$ and let $(f_1,..., f_n)$ be a family of invertible functions on $X$. Let $\phi$ the morphism $X\to G_m^n$ induced by the $f_i$'s, and let $t$ be the map $X\to (R^*_+)^n$ induced by the norms of the $f_i$'s. Let us recall two results.   1) The compact set $t(X)$ is a polytope of the $R$-vector space $(R^*_+)^n$ (we use the multiplicative notation) ; this is due to Berkovich in the locally algebraic case, and has been extended to the general case by the author.   2) If moreover $X$ is Hausdorff and $n$-dimensional, then the pre-image under $\phi$ of the skeleton $S_n$ of $G_m^n$ has a piecewise-linear structure making $\phi^{-1}(S_n)\to S_n$ a piecewise immersion ; this is due to the author.   In this article, we improve 1) and 2), and give new proofs of both of them. Our proofs are based upon the model theory of algebraically closed, non-trivially valued fields.   Let us quickly explain what we mean by improving 1) and 2).   - Concerning 1), we also prove that if $x\in X$, there exists a compact analytic neighborhood $U$ of $x$, such that for every compact analytic neighborhood $V$ of $x$ in $X$, the germs of polytopes $(t(U),t(x))$ and $(t(V),t(x))$ coincide.   - Concerning 2), we prove that the piecewise linear structure on $\phi^{-1}(S_n)$ is canonical, that is, doesn't depend on the map we choose to write it as a pre-image of the skeleton; we thus answer a question which was asked to us by Temkin. Moreover, we prove that the pre-image of the skeleton 'stabilizes after a finite, separable ground field extension', and that if $\phi_1,..., \phi_m$ are finitely many morphisms from $X\to G_m^n$, the union $\bigcup \phi_j(S_n)$ also inherits a canonical piecewise-linear structure.
We carry out a thorough study of weight-shifting operators on Hilbert modular forms in characteristic $p$, generalizing the author's prior work with Sasaki to the case where $p$ is ramified in the totally real field $F$. In particular we use the partial Hasse invariants and Kodaira-Spencer filtrations defined by Reduzzi and Xiao to improve on Andreatta and Goren's construction of partial $\Theta$-operators, obtaining ones whose effect on weights is optimal from the point of view of geometric Serre weight conjectures. Furthermore we describe the kernels of partial $\Theta$-operators in terms of images of geometrically constructed partial Frobenius operators. Finally we apply our results to prove a partial positivity result for minimal weights of mod $p$ Hilbert modular forms.
Fission neutron multiplicity distributions are known to be well reproduced by simple Gaussian distributions. Many previous evaluations of multiplicity distributions have adjusted the widths of Gaussian distributions to best fit the measured multiplicity distributions Pn. However, many observables do not depend on the detailed shape of Pn, but depend on the first three factorial moments of the distributions. In the present evaluation, the widths of Gaussians are adjusted to fit the measured 2nd and 3rd factorial moments. The relationships between the first three factorial moments are estimated assuming that the widths of the multiplicity distributions are independent of the initial excitation energy of the fissioning system. These simple calculations are in good agreement with experimental neutron induced fission data up to an incoming neutron energy of 10 MeV.
We present the first calculations of a symmetry conserving configuration mixing method (SCCM) using time-reversal symmetry breaking Hartree-Fock-Bogoliubov (HFB) states with the Gogny D1S interaction. The method includes particle number and tridimensional angular momentum symmetry restorations as well as configuration mixing within the generator coordinate method (GCM) framework. The nucleus $^{32}$Mg is chosen to show the performance and reliability of the calculations. Additionally, $0^{+}_{1}$, $2^{+}_{1}$ and $4^{+}_{1}$ states are computed for the magnesium isotopic chain, where a noticeable compression of the spectrum is obtained by including cranked states, leading to a very good agreement with the known experimental data.
We explore the possibility that the density profiles of elliptical galaxies and cold dark matter (CDM) halos found in cosmological simulations can be understood in terms of the same physical process, collisionless gravitational collapse. To investigate this, we study a simplified model, the collapse of a perfectly cold Plummer sphere. First, we examine an N-body simulation of this model with particles constrained to purely radial orbits. This results in a final state characterized by a profile slightly steeper than \rho \propto r^{-2} at small radii and behaving as \rho \propto r^{-4} at large radii, which can be understood in terms of simple analytic arguments. Next, we repeat our simulation without the restriction of radial orbits. This results in a shallower inner density profile, like those found in elliptical galaxies and CDM halos. We attribute this change to the radial orbit instability (ROI) and propose a form of the distribution function (DF) motivated by a physical picture of collapse. As evidence of the link between our model and CDM halos, we find that our collapse simulation has a final state with pseudo-phase-space density which scales roughly as \rho/\sigma^3 \propto r^{-1.875}, like that observed in CDM halos from cosmological simulations (Navarro et al. 2010). The velocity anisotropy profile is also qualitatively similar to that found near the centers of these halos. We argue that the discrepancy at large radii (where CDM halos scale as \rho \propto r^{-3}) is due to the presence of the cosmological background or continued infall. This leads us to predict that the outer CDM halo density profile is not "universal," but instead depends on cosmological environment (be it an underdense void or overdense region).
We investigate the density of integer solutions to certain binary inhomogeneous quadratic congruences and use this information to detect almost primes on a singular del Pezzo surface of degree 6.
Procedure of finding of the Bogomolny-Prasad-Sommerfield monopole solutions in the Georgi-Glashow model is investigated in detail on the backgrounds of three space models of constant curvature: Euclid, Riemann, Lobachevski's. Classification of possible solutions is given. It is shown that among all solutions there exist just three ones which reasonably and in a one-to-one correspondence can be associated with respective geometries. It is pointed out that the known non-singular BPS-solution in the flat Minkowski space can be understood as a result of somewhat artificial combining the Minkowski space background with a possibility naturally linked up with the Lobachewski geometry. The standpoint is brought forth that of primary interest should be regarded only three specifically distinctive solutions -- one for every curved space background. In the framework of those arguments the generally accepted status of the known monopole BPS-solution should be critically reconsidered and even might be given away.
Finding an intermediate-mass black hole (IMBH) in a globular cluster (or proving its absence) would provide valuable insights into our understanding of galaxy formation and evolution. However, it is challenging to identify a unique signature of an IMBH that cannot be accounted for by other processes. Observational claims of IMBH detection are indeed often based on analyses of the kinematics of stars in the cluster core, the most common signature being a rise in the velocity dispersion profile towards the centre of the system. Unfortunately, this IMBH signal is degenerate with the presence of radially-biased pressure anisotropy in the globular cluster. To explore the role of anisotropy in shaping the observational kinematics of clusters, we analyse the case of omega Cen by comparing the observed profiles to those calculated from the family of LIMEPY models, that account for the presence of anisotropy in the system in a physically motivated way. The best-fit radially anisotropic models reproduce the observational profiles well, and describe the central kinematics as derived from Hubble Space Telescope proper motions without the need for an IMBH.
We study the transverse single spin asymmetry (SSA), A_N, for the single inclusive process l p (transv. polarized) --> h + X, in a perturbative QCD factorization scheme with inclusion of spin and transverse momentum dependent (TMD) distributions. By adopting the relevant TMDs (Sivers and Collins functions) as extracted from semi-inclusive deep inelastic scattering (SIDIS) and e+e- data, predictions for these SSAs are given. A measurement of A_N for this process could then provide a direct test of the validity of the TMD factorization.
We investigate a one-dimensional model that shows several properties of water. The model combines the long-range attraction of the van der Waals model with the nearest-neighbor interaction potential by Ben-Naim, which is a step potential that includes a hard core and a potential well. Starting from the analytical expression for the partition function, we determine numerically the Gibbs energy and other thermodynamic quantities. The model shows two phase transitions, which can be interpreted as the liquid-gas transition and a transition between a high-density and a low-density liquid. At zero temperature, the low-density liquid goes into the crystalline phase. Furthermore, we find several anomalies that are considered characteristic for water. We explore a wide range of pressure and temperature values and the dependence of the results on the depth and width of the potential well.
Building on Schlessinger's work, we define a framework for studying geometric deformation problems which allows us to systematize the relationship between the local and global tangent and obstruction spaces of a deformation problem. Starting from Schlessinger's functors of Artin rings, we proceed in two steps: we replace functors to sets by categories fibered in groupoids, allowing us to keep track of automorphisms, and we work with deformation problems naturally associated to a scheme X, and which naturally localize on X, so that we can formalize the local behavior. The first step is already carried out by Rim in the context of his homogeneous groupoids, but we develop the theory substantially further. In this setting, many statements known for a range of specific deformation problems can be proved in full generality, under very general stack-like hypotheses.
The purpose of this paper is to give some symmetric identities of higher-order degenerate Euler polynomials derived from the symmetric properties of the multivariate p-adic fermionic integrals on Zp.
We report the detection of the GRB 971214 counterpart in the near-infrared by means of two images in the K'-band taken at Calar Alto only ~3.5 and ~5 hours after the gamma-ray event. We detect the transient at K'=18.03+/-0.18 and K'=18.00+/-0.22 respectively. Our data seem to indicate the existence of a plateau with duration ~1.5 < T < 6.7 hours (between 3.5 and 10.2 hours after the high-energy event). Moreover the power-law decline should be steeper than the one given by the index ak'=0.45. There is also a change in the slope of the broad-band spectrum at some wavelength between the J and K' bands (possibly around the H-band).
While preparing the correspondence between Leonhard Euler and Christian Goldbach for publication, Martin Mattmueller asked whether the lemma given in the postscript of Euler's letter dated July 26, 1749, was enough for completing the proof of Fermat's Four Squares Theorem. In this article we will show that Euler's result can in fact be used for proving this result via induction.
Parrondo's games manifest the apparent paradox where losing strategies can be combined to win and have generated significant multidisciplinary interest in the literature. Here we review two recent approaches, based on the Fokker-Planck equation, that rigorously establish the connection between Parrondo's games and a physical model known as the flashing Brownian ratchet. This gives rise to a new set of Parrondo's games, of which the original games are a special case. For the first time, we perform a complete analysis of the new games via a discrete-time Markov chain (DTMC) analysis, producing winning rate equations and an exploration of the parameter space where the paradoxical behaviour occurs.
We compute conformal anomalies for conformal field theories with free conformal scalars and massless spin $1/2$ fields in hyperbolic space $\mathbb{H}^d$ and in the ball $\mathbb{B}^d$, for $2\leq d\leq 7$. These spaces are related by a conformal transformation. In even dimensional spaces, the conformal anomalies on $\mathbb{H}^{2n}$ and $\mathbb{B}^{2n}$ are shown to be identical. In odd dimensional spaces, the conformal anomaly on $\mathbb{B}^{2n+1}$ comes from a boundary contribution, which exactly coincides with that of $\mathbb{H}^{2n+1}$ provided one identifies the UV short-distance cutoff on $\mathbb{B}^{2n+1}$ with the inverse large distance IR cutoff on $\mathbb{H}^{2n+1}$, just as prescribed by the conformal map. As an application, we determine, for the first time, the conformal anomaly coefficients multiplying the Euler characteristic of the boundary for scalars and half-spin fields with various boundary conditions in $d=5$ and $d=7$.
An exact one monopole solution in a uniform self-dual background field is obtained in the BPS limit of the SU(2) Yang-Mills-Higgs theory by using the inverse scattering method.