ShantanuT01/DACTYL-Pretraining huggingface dataset:
We show that the $\gamma$-vector of the order complex of any polytope is the f-vector of a balanced simplicial complex. This is done by proving this statement for a subclass of Stanley's S-shellable spheres which includes all polytopes. The proof shows that certain parts of the cd-index, when specializing $c=1$ and considering the resulted polynomial in $d$, are the f-polynomials of simplicial complexes that can be colored with "few" colors. We conjecture that the cd-index of a regular CW-sphere is itself the flag f-vector of a colored simplicial complex in a certain sense.
A statistical mechanism is proposed for symmetrization of an extra space. The conditions and rate of attainment of a symmetric configuration and, as a consequence, the appearance of gauge invariance in low-energy physics is discussed. It is shown that, under some conditions, this situation occurs only after completion of the inflationary stage. The dependence of the constants $\hbar$ and G on the geometry of the extra space and the initial parameters of the Lagrangian of the gravitational field with higher derivatives are analyzed.
We present a new framework for calculating multi-jet observables through resummation. The framework is based on the factorisation of scattering amplitudes in an asymptotic limit. By imposing simple constraints on the analytic behaviour of the result when applied away from this limit, we get good agreement with the known lowest order perturbative behaviour of the scattering amplitude, and predictions for the behaviour to all orders in the perturbative series. As an example of application we study predictions for Higgs Boson production through gluon fusion at the LHC in association with at least two jets.
We find new solutions to the Einstein-Maxwell equations in the presence of mimetic field in $ D $ dimensions, all of which are asymptotically Antide Sitter. We derive the solutions in five-dimensional spacetime, in detail. By extending the calculations to six and seven dimensions, we obtain a general form for solutions in dimensions larger than four. The results describe electrically charged static and rotating solutions, which have spherical, toroidal or cylindrical horizons. The solutions, depending on their global identifications, can be regarded as black holes, or black strings/branes. Some physical properties of solutions such as horizons, singularities as well as entropy, mass, and angular momenta of rotating solutions are also investigated.
Quite unexpectedly, kinetic theory is found to specify the correct definition of average value to be employed in nonextensive statistical mechanics. It is shown that the normal average is consistent with the generalized Stosszahlansatz (i.e., molecular chaos hypothesis) and the associated H-theorem, whereas the q-average widely used in the relevant literature is not. In the course of the analysis, the distributions with finite cut-off factors are rigorously treated. Accordingly, the formulation of nonextensive statistical mechanics is amended based on the normal average. In addition, the Shore-Johnson theorem, which supports the use of the q-average, is carefully reexamined, and it is found that one of the axioms may not be appropriate for systems to be treated within the framework of nonextensive statistical mechanics.
The effect of surface curvature on the law relating frictional forces F with normal load L is investigated by molecular dynamics simulations as a function of surface symmetry, adhesion, and contamination. Curved, non-adhering, dry, commensurate surfaces show a linear dependency, F proportional to L, similar to dry flat commensurate or amorphous surfaces and macroscopic surfaces. In contrast, curved, non-adhering, dry, amorphous surfaces show F proportional to L^(2/3) similar to friction force microscopes. In our model, adhesive effects are most adequately described by the Hertz plus offset model, as the simulations are confined to small contact radii. Curved lubricated or contaminated surfaces show again different behavior; details depend on how much of the contaminant gets squeezed out of the contact. Also, it is seen that the friction force in the lubricated case is mainly due to atoms at the entrance of the tip.
The existence of Dark Matter (DM) is a well established fact since many decades, thanks to the observation of the effects of its gravitational interaction with the ordinary matter in the Universe. However, our knowledge of the Dark Matter features is still rather scarce. Indeed, one of the biggest quests in fundamental science today is the investigation of Dark Matter nature, from its origin to its composition, and the way its constituents interact with the ordinary matter, apart from gravity. Huge and ambitious efforts have been spent in the last years into its identification, concentrating especially on the search of viable Weakly Interacting Massive Particle candidates. However, no positive results have been achieved so far along this direction. On the other hand, many fascinating new ideas and models for its interpretation have been blooming: among them, an intriguing hypothesis is that the Dark Matter constituents could be neutral under Standard Model interactions, but they could interact through a new, still unknown, force under a "hidden" charge. This new hidden symmetry would be mediated by a massive gauge boson, the dark photon, which is expected to couple to the Standard Model via a kinetic mixing. The search for such a massive mediator has been pursued with large enthusiasm and dedication in the latest years, as its observation could be within the reach of many already existing experimental facilities, both based on accelerators
Given two elliptic curves defined over a number field K, not both with j-invariant zero, we show that there are infinitely many $D\in K^\times$ with pairwise distinct image in $ K^\times/{K^\times}^2 $, such that the quadratic twist of both curves by D have positive Mordell-Weil rank. The proof depends on relating the values of pairs of cubic polynomials to rational points on another elliptic curve, and on a fiber product construction.
We present a new photometric catalog of 326 candidate globular clusters (GCs) in the nearby spiral galaxy M101, selected from B, V, and I Hubble Space Telescope Advanced Camera for Surveys images. The luminosity function (LF) of these clusters has an unusually large number of faint sources compared with GCLFs in many other spiral galaxies. Accordingly, we separate and compare the properties of "bright" (M_V < -6.5) versus "faint" (M_V > -6.5; one magnitude fainter than the expected GC peak) clusters within our sample. The LF of the bright clusters is well fit by a peaked distribution similar to those observed in the Milky Way (MW) and other galaxies. These bright clusters also have similar size (r_{eff}) and spatial distributions as MW GCs. The LF of the faint clusters, on the other hand, is well described by a power law, dN(L_V)/dL_V proportional to L_V^alpha with alpha = -2.6 plus or minus 0.3, similar to those observed for young and intermediate-age cluster systems in star forming galaxies. We find that the faint clusters have larger typical r_{eff} than the bright clusters, and have a flatter surface density profile, being more evenly distributed, as we would expect for clusters associated with the disk. We use the shape of the LF and predictions for mass-loss driven by two-body relaxation to constrain the ages of the faint clusters. Our results are consistent with two populations of old star clusters in M101: a bright population of halo clusters and a fainter, possibly younger, population of old disk clusters.
We introduce a likelihood analysis of multi-epoch stellar line-of-sight velocities to constrain the binary fractions and binary period distributions of dwarf spheroidal galaxies. This method is applied to multi-epoch data from the Magellan/MMFS survey of the Carina, Fornax, Sculptor and Sextans dSph galaxies, after applying a model for the measurement errors that accounts for binary orbital motion. We find that the Fornax, Sculptor, and Sextans dSphs are consistent with having binary populations similar to that of Milky Way field binaries to within 68% confidence limits, whereas the Carina dSph is remarkably deficient in binaries with periods less than ~10 years. If Carina is assumed to have a period distribution identical to that of the Milky Way field, its best-fit binary fraction is 0.14^{+0.28}_{-0.05}, and is constrained to be less than 0.5 at the 90% confidence level; thus it is unlikely to host a binary population identical to that of the Milky Way field. By contrast, the best-fit binary fraction of the combined sample of all four galaxies is 0.46^{+0.13}_{-0.09}, consistent with that of Milky Way field binaries. More generally, we infer probability distributions in binary fraction, mean orbital period, and dispersion of periods for each galaxy in the sample. Looking ahead to future surveys, we show that the allowed parameter space of binary fraction and period distribution parameters in dSphs will be narrowed significantly by a large multi-epoch survey. However, there is a degeneracy between the parameters that is unlikely to be broken unless the measurement error is of order ~0.1 km/s or smaller, presently attainable only by a high-resolution spectrograph.
We define Gaussian assignment process, determine the asymptotic behavior of its maximum's expectation and suggest an explicit strategy that attains the corresponding asymptotics.
In this study, we address the issue of a spherically symmetrical interior solution to the quadratic form of $f\mathcal{(T)}=\mathcal{T}+\epsilon \mathcal{T}^2$ gravitational theory using a physical tetrad that provides vanishing components of the off-components of the field equation, in contrast to what exists in the current literature. To be able to formulate the resulting differential equation in a closed form, we employ the Krori-Barua (KB) ansatz. Using the KB spacetime form, we derive the analytic form of the energy-density, radial, and tangential pressures and the anisotropic form. All of these quantities are affected by the dimensional parameter $\epsilon$, which causes them to have a noted difference from those given in the frame of Einstein general relativity. The derived model of this study exhibits a non-trivial form of torsion scalar, and it also contains three constants that we drew from the matching of the boundary condition with a line element that also features a non-trivial form of torsion scalar. Having established the physical conditions that are needed for any real stellar, we check our model and show in detail that it bypasses all of these. Finally, we analyze the model's stability utilizing the Tolman-Oppenheimer-Volkoff equation and adiabatic index and show that our model satisfies these.
Similarly to the larger Galactic ridge, the Galactic center region presents a hard diffuse emission whose origin has been strongly debated for the past two decades: does this emission result from the contribution of numerous, yet unresolved, discrete point sources ? Or does it originate in a truly diffuse, hot plasma ?   The Galactic center region (GC) is however different on many respects from the outer parts of the Galaxy, which makes the diffuse emission issue at the Galactic center unique. Although recent observations seem to favour a point sources origin in the far Galactic ridge, the situation is still unclear at the GC and new observations are required.   Here we present results on the modeling of the truly diffuse plasma. Interestingly, such a plasma would strongly affect the dynamics of orbiting molecular clouds and thus the central engine activity. Discriminating between the two hypothesis has thus become a crucial issue in the understanding of this central region that makes the link between the inner small accretion disk and the large scale Galactic dynamics. We investigate the new inputs we can expect from Simbol-X on this matter.
This article is an extended version of a talk given in Oxford in June 2021 as part of an online meeting `Ninety minutes of CCC' to mark the 90th birthday of Sir Roger Penrose. I assemble some questions that I have been asked or have asked myself about CCC.
We report numerical simulations of a strongly biased diffusion process on a one-dimensional substrate with directed shortcuts between randomly chosen sites, i.e. with a small-world-like structure. We find that, unlike many other dynamical phenomena on small-world networks, this process exhibits non-monotonic dependence on the density of shortcuts. Specifically, the diffusion time over a finite length is maximal at an intermediate density. This density scales with the length in a nontrivial manner, approaching zero as the length grows. Longer diffusion times for intermediate shortcut densities can be ascribed to the formation of cyclic paths where the diffusion process becomes occasionally trapped.
Formation mechanism of fragments with strangeness in collisions of antiprotons on nuclei has been investigated within the Lanzhou quantum molecular dynamics (LQMD) transport approach combined with a statistical model (GEMINI) for describing the decays of excited fragments. Production of strange particles in the antiproton induced nuclear reactions is modeled within the LQMD model, in which all possible reaction channels such as elastic scattering, annihilation, charge exchange and inelastic scattering in antibaryon-baryon, baryon-baryon and meson-baryon collisions have been included. A coalescence approach is developed for constructing hyperfragments in phase space after de-excitation of nucleonic fragments. The combined approach could describe the production of fragments in low-energy antiproton induced reactions. Hyperfragments are formed within the narrower rapidities and lower kinetic energies. It has advantage to produce heavier hyperfragments and hypernuclides with strangeness s=-2 (double-$\Lambda$ fragments) and s=1 ($\overline{\Lambda}$-fragments) in antiproton induced reactions.
The occurence of spin-polarization at ZrO$_{2}$, Al$_{2}$O$_{3}$ and MgO surfaces is proved by means of \textit{ab-initio} calculations within the density functional theory. Large spin moments, as high as 1.56 $\mu_B$, develop at O-ended polar terminations, transforming the non-magnetic insulator into a half-metal. The magnetic moments mainly reside in the surface oxygen atoms and their origin is related to the existence of $2p$ holes of well-defined spin polarization at the valence band of the ionic oxide. The direct relation between magnetization and local loss of donor charge makes possible to extend the magnetization mechanism beyond surface properties.
The implications of the most recent experimental results in the B and K meson systems on the CKM paradigm are investigated by means of a global fit to the theoretical predictions of the Standard Model. We advocate the frequentist approach Rfit, which is implemented in the CKMFitter package. Within this approach, constraints on the CKM parameters and other quantities of interest are obtained, and extensions of the Standard Model are investigated.
We present model spectra of stellar populations with variable chemical composition. We derived the [alpha/Fe] abundance ratio of the stars of the most important libraries (ELODIE, CFLIB and MILES) using full spectrum fitting and we generated PEGASE.HR models resolved in [\alpha/Fe]. We used a semi-empirical approach that combines the observed spectra with synthetic stellar spectra. We tested the models using them to derive [\alpha/Fe] in galaxies and star clusters using full spectrum fitting. The present models are available from http://ulyss.univ-lyon1.fr
We develop the complete theory for the collective plasmon modes of an interacting electron system in the presence of explicit mass (or velocity) anisotropy in the corresponding non-interacting situation, with the effective Fermi velocity being different along different axes. Such effective mass anisotropy is common in solid state materials (e.g., silicon or germanium), where the Fermi surface is often not spherical. We find that the plasmon dispersion itself develops significant anisotropy in such systems, and the commonly used isotropic approximation of using a density of states or optical effective mass does not work for the anisotropic system. We predict a qualitatively new phenomenon in anisotropic systems with no corresponding isotropic analog, where the plasmon mode along one direction decays into electron-hole pairs through Landau damping while the mode remains undamped and stable along a different directions
Let $\mu$ be a metric on a set T, and let c be a nonnegative function on the unordered pairs of elements of a superset $V\supseteq T$. We consider the problem of minimizing the inner product $c\cdot m$ over all semimetrics m on V such that m coincides with $\mu$ within T and each element of V is at zero distance from T (a variant of the {\em multifacility location problem}). In particular, this generalizes the well-known multiterminal multiway) cut problem. Two cases of metrics $\mu$ have been known for which the problem can be solved in polynomial time: (a) $\mu$ is a modular metric whose underlying graph $H(\mu)$ is hereditary modular and orientable (in a certain sense); and (b) $\mu$ is a median metric. In the latter case an optimal solution can be found by use of a cut uncrossing method. \Xcomment{We give a common generalization for both cases by proving that the problem is in P for any modular metric $\mu$ whose all orbit graphs are hereditary modular and orientable. To this aim, we show the existence of a retraction of the Cartesian product of the orbit graphs to $H(\mu)$, which enables us to elaborate an analog of the cut uncrossing method for such metrics $\mu$.} In this paper we generalize the idea of cut uncrossing to show the polynomial solvability for a wider class of metrics $\mu$, which includes the median metrics as a special case. The metric uncrossing method that we develop relies on the existence of retractions of certain modular graphs. On the negative side, we prove that for $\mu$ fixed, the problem is NP-hard if $\mu$ is non-modular or $H(\mu)$ is non-orientable.
We phenomenologically build a neutrino mass matrix obeying $\mu-\tau$ symmetry with only two parameters, Cabibbo angle $(\lambda)$ and a flavour twister parameter $(\eta)$. For vanishing $\eta$, the model assumes TBM mixing. When $\eta=\lambda$, the model generates a solar mixing angle and solar mass squared difference that coincide with the experimental best-fits. It motivates us to propose a mixing matrix in the neutrino sector with $ sin\theta_{12}<\frac{1}{\sqrt{3}}$, $\theta_{13}=0$ and $\theta_{23}=\pi/4$. The corrections in $\theta_{13}$ and $\theta_{23}$ are conducted following the breaking of $\mu-\tau$ symmetry, by choosing a proper unitary diagonalizing charged lepton matrix, and this ensures that $\theta_{23}$ lies within the first octant. The Cabibbo angle $(\lambda=\sin\theta_{c})$ plays the role of a guiding parameter in both neutrino as well as leptonic sector. The effect of the Dirac CP violating phase $\delta_{cp}$ is also studied when it enters either through the charged lepton diagonalizing matrix or through neutrino mixing matrix.
Very recently Spitler et al. (2016) and Scholz et al. (2016) reported their detections of sixteen additional bright bursts from the direction of the fast radio burst (FRB) 121102. This repeating FRB is inconsistent with all the catastrophic event models put forward previously for hypothetically non-repeating FRBs. Here we propose a different model, in which highly magnetized pulsars travel through asteroid belts of other stars. We show that a repeating FRB could originate from such a pulsar encountering lots of asteroids in the belt. During each pulsar-asteroid impact, an electric field induced outside the asteroid has such a large component parallel to the stellar magnetic field that electrons are torn off the asteroidal surface and accelerated to ultra-relativistic energies instantaneously. Subsequent movement of these electrons along magnetic field lines will cause coherent curvature radiation, which can account for all the properties of an FRB. In addition, this model can self-consistently explain the typical duration, luminosity, and repetitive rate of the seventeen bursts of FRB 121102. The predicted occurrence rate of repeating FRB sources may imply that our model would be testable in the next few years.
Zero-shot domain adaptation (ZSDA) is a category of domain adaptation problems where neither data sample nor label is available for parameter learning in the target domain. With the hypothesis that the shift between a given pair of domains is shared across tasks, we propose a new method for ZSDA by transferring domain shift from an irrelevant task (IrT) to the task of interest (ToI). Specifically, we first identify an IrT, where dual-domain samples are available, and capture the domain shift with a coupled generative adversarial networks (CoGAN) in this task. Then, we train a CoGAN for the ToI and restrict it to carry the same domain shift as the CoGAN for IrT does. In addition, we introduce a pair of co-training classifiers to regularize the training procedure of CoGAN in the ToI. The proposed method not only derives machine learning models for the non-available target-domain data, but also synthesizes the data themselves. We evaluate the proposed method on benchmark datasets and achieve the state-of-the-art performances.
We derive formulas for the cd-index and the toric h-vector of a convex polytope P from a sweeping by a hyperplane. These arise from interpreting the corresponding S-shelling of the dual of P. We describe a partition of the faces of the complete truncation of P to reflect explicitly the nonnegativity of its cd-index and what its components are counting. One corollary is a quick way to compute the toric h-vector directly from the cd-index. We also propose an "extended toric" h-vector that fully captures the information in the flag h-vector.
In Monstrous moonshine, genus 0 property and the notion of replicability are strongly connected. With regards to recent developments of moonshine, we investigate a higher genus generalization of replicability for a general automorphic form. Specifically, we extend the definitions of replicates and a Hecke operator to harmonic Maass functions on modular curves of higher genera to obtain number theoretic generalizations of important results in Monstrous moonshine. Furthermore, we show the utility of the extended notions in yielding uniform proofs for numerous arithmetic properties of Fourier coefficients of modular functions of arbitrary level, which have been proved only for special cases of curves of genus zero or small prime levels.
This paper proposes to use keypoints as a self-supervision clue for learning depth map estimation from a collection of input images. As ground truth depth from real images is difficult to obtain, there are many unsupervised and self-supervised approaches to depth estimation that have been proposed. Most of these unsupervised approaches use depth map and ego-motion estimations to reproject the pixels from the current image into the adjacent image from the image collection. Depth and ego-motion estimations are evaluated based on pixel intensity differences between the correspondent original and reprojected pixels. Instead of reprojecting the individual pixels, we propose to first select image keypoints in both images and then reproject and compare the correspondent keypoints of the two images. The keypoints should describe the distinctive image features well. By learning a deep model with and without the keypoint extraction technique, we show that using the keypoints improve the depth estimation learning. We also propose some future directions for keypoint-guided learning of structure-from-motion problems.