ShantanuT01/DACTYL-Pretraining huggingface dataset:
Inspired by Aldous' conjecture for the spectral gap of the interchange process and its recent resolution by Caputo, Liggett and Richthammer, we define an associated order on the irreducible representations of S_n. Aldous' conjecture is equivalent to certain representations being comparable in this order, and hence determining the "Aldous order" completely is a generalized question. We show a few additional entries in this order.
The spectrum-generating algebra (SGA) for charged superstrings placed in constant background magnetic fields is constructed. Contrary to the neutral string this algebra is characteristic of including the cyclotron frequency. The Regge intercept and superconformal anomalies are calculated to be shifted by the cyclotron frequency and D-brane parameters from the conventional values.
We illustrate the use of the statistical method of moments for determining the position and momentum distributions of a quantum object from the statistics of a single measurement. The method is used for three different, though related, models; the sequential measurement model, the Arthurs-Kelly model and the eight-port homodyne detection model. In each case, the method of moments gives the position and momentum distribution for a large class of initial states, the relevant condition being the exponential boundedness of the distributions.
A complete analysis of all heterotic Calabi-Yau compactifications based on positive two-term monad bundles over favourable complete intersection Calabi-Yau threefolds is performed. We show that the original data set of about 7000 models contains 91 standard-like models which we describe in detail. A closer analysis of Wilson-line breaking for these models reveals that none of them gives rise to precisely the matter field content of the standard model. We conclude that the entire set of positive two-term monads on complete intersection Calabi-Yau manifolds is ruled out on phenomenological grounds. We also take a first step in analyzing the larger class of non-positive monads. In particular, we construct a supersymmetric heterotic standard model within this class. This model has the standard model gauge group and an additional U(1)_{B-L} symmetry, precisely three families of quarks and leptons, one pair of Higgs doublets and no anti-families or exotics of any kind.
For a set of non-negative integers $L$, the $L$-intersection number of a graph is the smallest number $l$ for which there is an assignment on the vertices to subsets $A_v \subseteq \{1,\dots, l\}$, such that every two vertices $u,v$ are adjacent if and only if $|A_u \cap A_v|\in L$. The bipartite $L$-intersection number is defined similarly when the conditions are considered only for the vertices in different parts. In this paper, some lower bounds for the (bipartite) $L$-intersection number of a graph for various types $L$ in terms of the minimum rank of graph are obtained.
A thermodynamic model describing phase transitions with thermal memory, in terms of an entropy equation and a momentum balance for the microforces, is adressed. Convergence results and error estimates are proved for the related integrodifferential system of PDE as the sequence of memory kernels converges to a multiple of a Dirac delta, in a suitable sense.
We have performed resonant X-ray diffraction experiments on the antiferromagnet GdRu$_{2}$Al$_{10}$ and have clarified that the magnetic structure in the ordered state is cycloidal with the moments lying in the $bc$ plane and propagating along the $b$ axis. The propagation vector shows a similar temperature dependence to the magnetic order parameter, which can be interpreted as being associated with the gap opening in the conduction band and the resultant change in the magnetic exchange interaction. Although the $S=7/2$ state of Gd is almost isotropic, the moments show slight preferential ordering along the $b$ axis. The $c$ axis component in the cycloid develops with decreasing temperature through a tiny transition in the ordered phase. We also show that the scattering involves the $\sigma$-$\sigma'$ process, which is forbidden in normal $E1$-$E1$ resonance of magnetic dipole origin. We discuss the possibility of the $E1$-$E2$ resonance originating from a toroidal moment due to the lack of inversion symmetry at the Gd site. The spin-flop transition in a magnetic field is also described in detail.
We prove a sufficient set of conditions for a sequence of finite measures on the space of cadlag measure-valued paths to converge to the canonical measure of super-Brownian motion in the sense of convergence of finite-dimensional distributions. The conditions are convergence of the Fourier transform of the $r$-point functions and perhaps convergence of the ``survival probabilities.'' These conditions have recently been shown to hold for a variety of statistical mechanical models, including critical oriented percolation, the critical contact process and lattice trees at criticality, all above their respective critical dimensions.
The diffusion of a molecular motor in the presence of a constant external force is considered on the basis of a simple theoretical model. The motor is represented by a Brownian particle moving in a series of parabolic potentials placed periodically on a line, and the potential is switched stochastically from one parabola to another by a chemical reaction, which corresponds to the ATP hydrolysis or synthesis in motor proteins. It is found that the diffusion coefficient as a function of the force exhibits peaks. The mechanism of this diffusion enhancement and the possibility of observing it in F1-ATPase, a biological rotary motor, are discussed.
We consider Gibbs' definition of chemical equilibrium and connect it with dynamic equilibrium, in terms of no substance formed. We determine the activity coefficient as a function of temperature and pressure, in reactions with or without interaction of a solvent, incorporating the error terms from Raoult's Law and Henry's Law, if necessary. We compute the maximal reaction paths and apply the results to electrochemistry, using the Nernst equation.
Single crystal elastic constants of bcc iron and bct FeC and FeN alloys, martensites, have been evaluated by ab initio calculations based on the density functional theory. The energy of a strained crystal has been computed using the supercell method at several values of the strain intensity, and the stiffness coefficient has been determined from the slope of the energy versus square of strain relation. Some of the third order elastic constants have also been evaluated. The absolute magnitudes of the calculated values for bcc iron are in fair agreement with experiment, including the third order constants, although the computed elastic anisotropy is much weaker than measured. The tetragonally distorted dilute FeC and FeN alloys exhibit lower stiffness than bcc iron, particularly in the tensor component C33, while the elastic anisotropy is virtually the same. Average values of elastic moduli for polycrystalline aggregates are also computed. Youngs modulus and the rigidity modulus, as well as the bulk modulus, are decreased by about 10 per cent by the addition of C or N to 3.7 atomic per cent, which agrees with the experimental data for FeC martensite.
A certain sector of the matrix model for M-theory on a plane wave background has recently been shown to produce the transverse five-brane. We consider this theory at finite temperature. We find that, at a critical temperature it has a Gross-Witten phase transition which corresponds to deconfinement of the matrix model gauge theory. We interpret the phase transition as the Hagedorn transition of M-theory and of type II string theory in the five-brane background. We also show that there is no Hagedorn behaviour in the transverse membrane background case.
Neutral diboson processes are precise probes of the Standard Model (SM) of particle physics, which entail high sensitivity to new physics effects. We identify in terms of dimension-8 effective operators the leading departures from the SM that survive in neutral diboson processes at high-energy, and which interfere with the unsuppressed SM helicity contributions. We describe symmetries and selections rules that single out those operators, both for weakly and strongly coupled physics beyond the SM. Finally, we show that unitarity and causality enforce, via dispersion relations, positivity constraints on the coefficients of these effective operators, reducing the parameter space which is theoretically allowed.
Motivated by an emerging theory of robust low-rank matrix representation, in this paper, we introduce a novel solution for online rigid-body motion registration. The goal is to develop algorithmic techniques that enable a robust, real-time motion registration solution suitable for low-cost, portable 3-D camera devices. Assuming 3-D image features are tracked via a standard tracker, the algorithm first utilizes Robust PCA to initialize a low-rank shape representation of the rigid body. Robust PCA finds the global optimal solution of the initialization, while its complexity is comparable to singular value decomposition. In the online update stage, we propose a more efficient algorithm for sparse subspace projection to sequentially project new feature observations onto the shape subspace. The lightweight update stage guarantees the real-time performance of the solution while maintaining good registration even when the image sequence is contaminated by noise, gross data corruption, outlying features, and missing data. The state-of-the-art accuracy of the solution is validated through extensive simulation and a real-world experiment, while the system enjoys one to two orders of magnitude speed-up compared to well-established RANSAC solutions. The new algorithm will be released online to aid peer evaluation.
We give details on how to calculate spectral functions and Green's functions for finite systems using the Chebyshev polynomial expansion method. We apply the method to a finite Anderson impurity system, and furthermore give details on how to exploit its symmetry to transform the system into smaller orthogonal subsystems. We also consider systems connected to infinite leads, which we study by approximating the unknown self-energy with an exact self-energy for a finite system. As our test case, we consider the single-impurity Anderson model, where we find that we can capture some aspects of Kondo physics.
We present a fully nonlinear hydrodynamic 'shallow water' model of the solar tachocline. The model consists of a global spherical shell of differentially rotating fluid, which has a deformable top, thus allowing motions in radial directions along with latitude and longitude directions. When the system is perturbed, in the course of its nonlinear evolution it can generate unstable low-frequency shallow-water shear modes from the differential rotation, high-frequency gravity waves, and their interactions. Radiative and overshoot tachoclines are characterized in this model by high and low effective gravity values respectively. Building a semi-implicit spectral scheme containing very low numerical diffusion, we perform nonlinear evolution of shallow-water modes. Our first results show that, (i) high latitude jets or polar spin-up occurs due to nonlinear evolution of unstable hydrodynamic shallow-water disturbances and differential rotation, (ii) Reynolds stresses in the disturbances together with changing shell-thickness and meridional flow are responsible for the evolution of differential rotation, (iii) disturbance energy primarily remains concentrated in the lowest longitudinal wavenumbers, (iv) an oscillation in energy between perturbed and unperturbed states occurs due to evolution of these modes in a nearly dissipation-free system, and (v) disturbances are geostrophic, but occasional nonadjustment in geostrophic balance can occur, particularly in the case of high effective gravity, leading to generation of gravity waves. We also find that a linearly stable differential rotation profile remains nonlinearly stable.
Deep neural networks have become the default choice for many applications like image and video recognition, segmentation and other image and video related tasks.However, a critical challenge with these models is the lack of explainability.This requirement of generating explainable predictions has motivated the research community to perform various analysis on trained models.In this study, we analyze the learned feature maps of trained models using MNIST images for achieving more explainable predictions.Our study is focused on deriving a set of primitive elements, here called visual concepts, that can be used to generate any arbitrary sample from the data generating distribution.We derive the primitive elements from the feature maps learned by the model.We illustrate the idea by generating visual concepts from a Variational Autoencoder trained using MNIST images.We augment the training data of MNIST dataset by adding about 60,000 new images generated with visual concepts chosen at random.With this we were able to reduce the reconstruction loss (mean square error) from an initial value of 120 without augmentation to 60 with augmentation.Our approach is a first step towards the final goal of achieving trained deep neural network models whose predictions, features in hidden layers and the learned filters can be well explained.Such a model when deployed in production can easily be modified to adapt to new data, whereas existing deep learning models need a re training or fine tuning. This process again needs a huge number of data samples that are not easy to generate unless the model has good explainability.
Radial similarity flow offers a rare instance where concrete inviscid, multi-dimensional, compressible flows can be studied in detail. In particular, there are flows of this type that exhibit imploding shocks and cavities. In such flows the primary flow variables (density, velocity, pressure, temperature) become unbounded at time of collapse. In both cases the solution can be propagated beyond collapse by having an expanding shock wave reflect off the center of motion.   These types of flows are of relevance in bomb-making and inertial confinement fusion, and also as benchmarks for computational codes; they have been investigated extensively in the applied literature. However, despite their obvious theoretical interest as examples of unbounded solutions to the multi-dimensional Euler system, the existing literature does not address to what extent such solutions are bona fide weak solutions.   In this work we review the construction of globally defined radial similarity shock and cavity flows, and give a detailed description of their behavior following collapse. We then prove that similarity shock solutions provide genuine weak solutions, of unbounded amplitude, to the multi-dimensional Euler system. However, both types of similarity flows involve regions of vanishing pressure prior to collapse (due to vanishing temperature and vacuum, respectively) - raising the possibility that Euler flows may remain bounded in the absence of such regions.
We study the equilibration of a parton plasma in terms of its parton compositions and its state of thermalization. In studying the evolution of the plasma, one has to assume a small value of the strong coupling constant. This value is by no means fixed. By varying this only parameter in our calculation, we show the dependence of equilibration on its magnitude. It is shown that both kinetic and parton equilibration are faster with increasing coupling but the plasma cools much more rapidly resulting in shortened lifetime. The degree of equilibration improves significantly for quarks and antiquarks but not so for gluons and the total generated entropy is reduced. With a coupling depending on the average parton energy, there is additional acceleration in the equilibration during the evolution.
We analyse LEP and PETRA data on single inclusive charged hadron cross-sections to establish new sets of Next-to-Leading order Fragmentation Functions. Data on hadro-production of large-$p_{\bot}$ hadrons are also used to constrain the gluon Fragmentation Function. We carry out a critical comparison with other NLO parametrizations.
We have updated our previous study on the possibility to observe the rare B0_s -> 2mu decay with detailed simulation of the TDR version of the CMS detector. The full simulation and reconstruction procedure has been done both for the signal and background. We improved our previous results on expected sensitivity using more sophisticated algorithms for the track and vertex reconstruction and tighter selection criteria.
We study the spin Hall effect (SHE) in graphene using a realistic multi-orbital tight-binding model that includes the atomic spin-orbit interaction. The SHE is found to be induced by the spin-dependent Aharonov-Bohm phase. In the metallic case, the calculated values for the spin Hall conductivity (SHC) are much smaller than the quantized Hall conductivity for realistic parameter values of metallic graphene. In the insulating case, quantization of the SHC is violated due to the multi-orbital effect. The present study suggests that the SHE in a honeycomb lattice is enhanced by chemical doping, such as the substitution of carbon atoms with boron atoms.
Understanding and controlling heat transport in molecular junctions would provide new routes to design nanoscale coupled electronic and phononic devices. Using first principles full quantum calculations, we tune thermal conductance of a molecular junction by mechanically compressing and extending a short alkane chain connected to graphene leads. We find that the thermal conductance of the compressed junction drops by half in comparison to the extended junction, making it possible to turn on and off the heat current. The low conductance of the off state does not vary by further approaching the leads and stems from the suppression of the transmission of the in--plane transverse and longitudinal channels. Furthermore, we show that misalignment of the leads does not reduce the conductance ratio. These results also contribute to the general understanding of thermal transport in molecular junctions.
The class of closed graphs by a linear ordering on their sets of vertices is investigated. A recent characterization of such a class of graphs is analyzed by using tools from the proper interval graph theory.
In this paper we used the theory of adiabatic radial oscillations developed by Chandrasekhar to study the conditions for dynamical stability of constant energy-density stars, or Schwarzschild stars, in the unstudied ultra compact regime beyond the Buchdahl limit, that is, for configurations with radius $R$ in the range $R_{\rm S}<R<(9/8)R_{\rm S}$, where $R_{\rm S}$ is the Schwarzschild radius of the star. These recently found analytical solutions exhibit a negative pressure region in their centre and, in the limit when $R\to R_{\rm S}$, the full interior region of the star becomes filled with negative pressure. Here we present a systematic analysis of the stability of these configurations against radial perturbations. We found that, contrary to the usual expectation found in many classical works, the ultra compact Schwarzschild star is stable against radial oscillations. We computed values of the critical adiabatic index $\gamma_{c}$ for several stellar models with varying radius $R/R_{\rm S}$ and found that it also approaches a finite value as $R/R_{\rm S} \to 1$
We propose a new version of SU(N) Yang-Mills theory reformulated in terms of new field variables which are obtained by a nonlinear change of variables from the original Yang-Mills gauge field. The reformulated Yang-Mills theory enables us to study the low-energy dynamics by explicitly extracting the topological degrees of freedom such as magnetic monopoles and vortices to clarify the mechanism for quark confinement.   The dual superconductivity in Yang-Mills theory is understood in a gauge-invariant manner, as demonstrated recently by a non-Abelian Stokes theorem for the Wilson loop operator, although the basic idea of this reformulation is based on the Cho-Faddeev-Niemi decomposition of the gauge potential.
We present rotation curves of 19 galaxies from THINGS, The HI Nearby Galaxy Survey. The high spatial and velocity resolution of THINGS make these the highest quality HI rotation curves available to date for a large sample of nearby galaxies, spanning a wide range of HI masses and luminosities. The high quality of the data allows us to derive the geometrical and dynamical parameters using HI data alone. We do not find any declining rotation curves unambiguously associated with a cut-off in the mass distribution out to the last measured point. The rotation curves are combined with 3.6 um data from SINGS (Spitzer Infrared Nearby Galaxies Survey) to construct mass models. Our best-fit, dynamical disk masses, derived from the rotation curves, are in good agreement with photometric disk masses derived from the 3.6 um images in combination with stellar population synthesis arguments and two different assumptions for the stellar Initial Mass Function (IMF). We test the Cold Dark Matter-motivated cusp model, and the observationally motivated central density core model and find that (independent of IMF) for massive, disk-dominated galaxies, all halo models fit apparently equally well; for low-mass galaxies, however, a core-dominated halo is clearly preferred over a cuspy halo. The empirically derived densities of the dark matter halos of the late-type galaxies in our sample are half of what is predicted by CDM simulations, again independent of the assumed IMF.
We present deep XMM-Newton EPIC observations of the Wolf-Rayet (WR) bubble NGC6888 around the star WR136. The complete X-ray mapping of the nebula confirms the distribution of the hot gas in three maxima spatially associated with the caps and northwest blowout hinted at by previous Chandra observations. The global X-ray emission is well described by a two-temperature optically thin plasma model $T_1$=1.4$\times$10$^{6}$ K, $T_{2}$=8.2$\times$10$^{6}$ K) with a luminosity of $L_{\mathrm{X}}$=7.8$\times$10$^{33}$ erg s$^{-1}$ in the 0.3--1.5 keV energy range. The rms electron density of the X-ray-emitting gas is estimated to be $n_\mathrm{e}$=0.4 cm$^{-3}$. The high-quality observations presented here reveal spectral variations within different regions in NGC6888, which allowed us for the first time to detect temperature and/or nitrogen abundance inhomogeneities in the hot gas inside a WR nebula. One possible explanation for such spectral variations is that the mixing of material from the outer nebula into the hot bubble is less efficient around the caps than in other nebular regions.
We present a minimal viable Gauge-Higgs Grand Unification scenario in warped space based on a $SU(6)$ bulk symmetry - unifying the gauge symmetries of the SM and their breaking sector. We show how the issue of light exotic new states is eliminated by appropriately breaking the gauge symmetry on the UV and IR boundaries by either brane scalars or gauge boundary conditions. The SM fermion spectrum is naturally reproduced including Dirac neutrinos and we compute the Higgs potential at one-loop, finding easily solutions with a realistic $m_h \sim 125$ GeV. The problem of proton decay is addressed by showing that baryon number is a hidden symmetry of the model. Among the phenomenological consequences, we highlight the presence of a scalar leptoquark and a scalar singlet. The usual $X,Y$ gauge bosons from $SU(5)$ GUTs are found at collider accessible masses.