ShantanuT01/DACTYL-Pretraining huggingface dataset:
Let $\mathcal{E}_d^{(s)}$ denote the set of coefficient vectors $(a_1,\dots,a_d)\in \mathbb{R}^d$ of contractive polynomials $x^d+a_1x^{d-1}+\dots+a_d\in \mathbb{R}[x]$ that have exactly $s$ pairs of complex conjugate roots and let $v_d^{(s)}=\lambda_d(\mathcal{E}_d^{(s)})$ be its ($d$-dimensional) Lebesgue measure. We settle the instance $s=1$ of a conjecture by Akiyama and Peth\H{o}, stating that the ratio $v_d^{(s)}/v_d^{(0)}$ is an integer for all $d\ge 2s.$ Moreover we establish the surprisingly simple formula $v_d^{(1)}/v_d^{(0)} = (P_d(3)-2d-1)/4,$ where $P_d(x)$ are the Legendre polynomials.
We show that every degree $d$ meromorphic function on a smooth connected projective curve $C\subset \mathbb P^2$ of degree $d>4$ is isomorphic to a linear projection from a point $p\in \mathbb {P}^2 \setminus C$ to $\mathbb P^1$. We then pose a Zeuthen-type problem for calculating the plane Hurwitz numbers.
We report on X-ray studies of the gamma-ray pulsar PSR J1418$-$6058 in the Rabbit pulsar wind nebula (PWN) carried out using archival Chandra and XMM-Newton observations. A refined timing analysis performed with the 120-ks XMM-Newton data finds significant ($p\approx10^{-7}$) pulsation at $P\approx110$ ms which is consistent with that measured with the Fermi large area telescope (LAT). In the Chandra image, we find extended emission around the pulsar similar to those seen around other pulsars in young PWNe, which further argues for association between PSR J1418$-$6058 and the Rabbit PWN. The X-ray spectrum of the pulsar is hard and similar to those of soft-gamma pulsars. Hence PSR J1418$-$6058 may add to the list of soft-gamma pulsars.
Considering three-dimensional Chern-Simons theory, either coupled to matter or with a Yang-Mills term, we show the validity of a trace identity, playing the role of a local form of the Callan-Symanzik equation, in all orders of perturbation theory. From this we deduce the vanishing of the $\beta$-function associated to the Chern-Simons coupling constant and the full finiteness in the case of the Yang-Mills Chern-Simons theory. The main ingredient in the proof of the latter property is the noninvariance of the Chern-Simons form under the gauge transformations. Our results hold for the three-dimensional Chern-Simons model in a general Riemannian manifold.
We present the first determination of the 15micron luminosity functio galaxies from the European Large Area ISO survey (ELAIS) southern fields. We have adopted a new criterion to separate the quiescent, non-evolving and the starburst, evolving populations based on the ratio of mid-infrared to optical luminosities. Strong evolution is suggested by our data for the starburst galaxy population, while normal spiral galaxies are consistent with no evolution. The starburst population must evolve both in luminosity and in density with rates of the order L(z) (1+z)^(3.5) and rho(z) (1+z)^3.8 up to z~1. The evolutionary parameters of our model have been tested by comparing the model predictions with other observables, like source counts at all flux density levels (from 0.1 to 300 mJy) and redshift distributions and luminosity functions at high-z (0.7 < z < 1.0 from HDF-N data). The agreement between our model predictions and the observed data is remarkably good. We use our data to estimate the star-formation density of the Universe up to z=0.4 and we use the luminosity function model to predict the trend of the star-formation history up to z=1.
In this paper, we investigate the influence of hyperfine splitting on complex spectral lines, with the aim of evaluating canonical abundances by decomposing their dependence on hyperfine structures. This is achieved from first principles through deconvolution. We present high spectral resolution observations of the rotational ground state transitions of CH near 2 THz seen in absorption toward the strong FIR-continuum sources AGAL010.62$-$00.384, AGAL034.258+00.154, AGAL327.293$-$00.579, AGAL330.954$-$00.182, AGAL332.826$-$00.549, AGAL351.581$-$00.352 and SgrB2(M). These were observed with the GREAT instrument on board SOFIA. The observed line profiles of CH were deconvolved from the imprint left by the lines' hyperfine structures using the Wiener filter deconvolution, an optimised kernel acting on direct deconvolution. The quantitative analysis of the deconvolved spectra first entails the computation of CH column densities. Reliable N(CH) values are of importance owing to the status of CH as a powerful tracer for H$_2$ in the diffuse regions of the interstellar medium. The N(OH)/N(CH) column density ratio is found to vary within an order of magnitude with values ranging from one to 10, for the individual sources that are located outside the Galactic centre. Using CH as a surrogate for H$_2$, we determined the abundance of the OH molecule to be X(OH)=1.09$\times$10$^{-7}$ with respect to H$_2$. The radial distribution of CH column densities along the sightlines probed in this study, excluding SgrB2(M), showcase a dual peaked distribution peaking between 5 and 7 kpc. The similarity between the correspondingly derived column density profile of H$_2$ with that of the CO-dark H$_2$ gas traced by the cold neutral medium component of [CII] 158$~\mu$m emission across the Galactic plane, further emphasises the use of CH as a tracer for H$_2$.
Distance measures are part and parcel of many computer vision algorithms. The underlying assumption in all existing distance measures is that feature elements are independent and identically distributed. However, in real-world settings, data generally originate from heterogeneous sources even if they do possess a common data-generating mechanism. Since these sources are not identically distributed by necessity, the assumption of identical distribution is inappropriate. Here, we use statistical analysis to show that feature elements of local image descriptors are indeed non-identically distributed. To test the effect of omitting the unified distribution assumption, we created a new distance measure called the Poisson-Binomial Radius (PBR). PBR is a bin-to-bin distance which accounts for the dispersion of bin-to-bin information. PBR's performance was evaluated on twelve benchmark data sets covering six different classification and recognition applications: texture, material, leaf, scene, ear biometrics and category-level image classification. Results from these experiments demonstrate that PBR outperforms state-of-the-art distance measures for most of the data sets and achieves comparable performance on the rest, suggesting that accounting for different distributions in distance measures can improve performance in classification and recognition tasks.
Superconducting microwave circuits show great potential for practical quantum technological applications such as quantum information processing. However, fast and on-demand initialization of the quantum degrees of freedom in these devices remains a challenge. Here, we experimentally implement a tunable heat sink that is potentially suitable for the initialization of superconducting qubits. Our device consists of two coupled resonators. The first resonator has a high quality factor and a fixed frequency whereas the second resonator is designed to have a low quality factor and a tunable resonance frequency. We engineer the low quality factor using an on-chip resistor and the frequency tunability using a superconducting quantum interference device. When the two resonators are in resonance, the photons in the high-quality resonator can be efficiently dissipated. We show that the corresponding loaded quality factor can be tuned from above $10^5$ down to a few thousand at 10 GHz in good quantitative agreement with our theoretical model.
In this article, we use Lindstr\"om Gessel Viennot Lemma to give a short, combinatorial, visualizable proof of the identity of Schur polynomials -- the sum of monomials of Young tableaux equals to the quotient of determinants. As a by-product, we have a proof of Vandermonde determinant without words. We also prove the cauchy identity. In the remarks, we discuss factorial Schur polynomials, dual Cauchy identity and the relation beteen Newton interpolation formula.
Diamond field-effect transistors (FETs) have potential applications in power electronics and high-output high-frequency amplifications. In such applications, high charge-carrier mobility is desirable for a reduced loss and high-speed operation. We have recently fabricated diamond FETs with a hexagonal-boron-nitride gate dielectric and observed a high mobility above 300 cm$^{2}$V$^{-1}$s$^{-1}$. In this study, we examine which scattering mechanism limits the mobility of our FETs through theoretical calculations. Our calculations reveal that the dominant carrier scattering is caused by surface charged impurities with the density of $\approx$1$\times10^{12}$ cm$^{-2}$, and suggest a possible increase in mobility over 1000 cm$^{2}$V$^{-1}$s$^{-1}$ by reducing the impurities.
Let $n, u \geq 0$, $M$ be a ($n$+$u$) $\times$ $n$ matrices over $\mathbb{Z}_p$, and $G$ be a finite abelian p-group group. We find that the probability that the cokernel of $M$ is isomorphic to $\mathbb{Z}_p^u \oplus G$ as $n$ goes to infinity is exactly what is expected from Cohen-Lenstra heuristics for the classical case when $u$ is negative.
IC 3418 is a dwarf irregular galaxy falling into the Virgo cluster, and a 17 kpc long trail is seen behind the galaxy, which is considered to have formed due to ram pressure stripping. The trail contains compact knots and diffuse blobs of ultraviolet and blue optical emission and, thus, it is a clear site of recent star formation but in an unusual environment, surrounded by a million degree intra-cluster medium. We report on our optical spectroscopy of a compact source in the trail, SDSS J122952.66+112227.8, and show that the optical spectrum is dominated by emission from a massive blue supergiant star. If confirmed, our report would mark the farthest star with spectroscopic observation. We interpret that a massive O-type star formed in situ in the trail has evolved recently out of the main sequence into this blue supergiant phase, and now lacks any detectable spectral sign of its associated HII region. We argue that turbulence within the ram pressure striped gaseous trail may play a dominant role for the star formation within such trails.
We theoretically investigate the stability of a square skyrmion crystal (SkX) in a centrosymmetric tetragonal lattice structure with the emphasis on the role of the magnetic anisotropy arising from the absence of vertical mirror symmetry. Our analysis is based on an effective bilinear and biquadratic model in momentum space, which is a canonical model for itinerant magnets in a weak-coupling regime. By performing the simulated annealing for the model on the two-dimensional square lattice, we find that the off-diagonal spin component in the interaction, which becomes nonzero when the vertical mirror symmetry is broken, gives rise to the square SkX with a definite helicity in an external magnetic field. We show that the helicity of the centrosymmetric SkXs is determined by the competition between the off-diagonal and diagonal anisotropic interactions, the latter of which appears in the discrete fourfold-rotational lattice structure. Furthermore, we discuss helicity-dependent physical phenomena by introducing odd-parity multipoles, where electric (magnetic) and electric (magnetic) toroidal multipoles are sources of an antisymmetric spin polarization and an Edelstein effect (a magnetoelectric effect). We also discuss the stability of the SkXs with different helicities in a magnetic field rotation. Our results provide a way of engineering the helicity-locked SkXs by the symmetric anisotropic interaction in centrosymmetric magnets, which is distinct from that by the antisymmetric Dzyaloshinskii-Moriya interaction in noncentrosymmetric magnets.
In generative modeling, the Wasserstein distance (WD) has emerged as a useful metric to measure the discrepancy between generated and real data distributions. Unfortunately, it is challenging to approximate the WD of high-dimensional distributions. In contrast, the sliced Wasserstein distance (SWD) factorizes high-dimensional distributions into their multiple one-dimensional marginal distributions and is thus easier to approximate. In this paper, we introduce novel approximations of the primal and dual SWD. Instead of using a large number of random projections, as it is done by conventional SWD approximation methods, we propose to approximate SWDs with a small number of parameterized orthogonal projections in an end-to-end deep learning fashion. As concrete applications of our SWD approximations, we design two types of differentiable SWD blocks to equip modern generative frameworks---Auto-Encoders (AE) and Generative Adversarial Networks (GAN). In the experiments, we not only show the superiority of the proposed generative models on standard image synthesis benchmarks, but also demonstrate the state-of-the-art performance on challenging high resolution image and video generation in an unsupervised manner.
We investigate the occurrence of divergences in maximal supergravity in various dimensions from the point of view of supersymmetry constraints on the U-duality invariant threshold functions defining the higher derivative couplings in the effective action. Our method makes use of tensorial differential equations that constrain these couplings. We study in detail the Fourier modes and wave-front sets of the associated automorphic functions and find that they are always associated to special nilpotent orbits.
Using the finite Fourier transform, we introduce a generalization of Pauli-spin matrices for $d$-dimensional spaces, and the resulting set of unitary matrices $S(d) $ is a basis for $d\times d$ matrices. If $N=d_{1}\times d_{2}\times...\times d_{b}$ and $H^{[ N]}=\bigotimes H^{% [ d_{k}]}$, we give a sufficient condition for separability of a density matrix $\rho $ relative to the $H^{[ d_{k}]}$ in terms of the $L_{1}$ norm of the spin coefficients of $\rho >.$ Since the spin representation depends on the form of the tensor product, the theory applies to both full and partial separability on a given space $H^{[ N]}$% . It follows from this result that for a prescribed form of separability, there is always a neighborhood of the normalized identity in which every density matrix is separable. We also show that for every prime $p$ and $n>1$ the generalized Werner density matrix $W^{[ p^{n}]}(s) $ is fully separable if and only if $s\leq (1+p^{n-1}) ^{-1}$.
State space geometry is obtained for the one dimensional Blume Emery Griffiths model and the associated scalar curvature(s) investigated for various parameter regimes, including the Blume-Capel limit and the Griffiths model limit. For the one-dimensional case two complementary geometries with their associated curvatures $R_m$ and $R_q$ are found which are related to the fluctuations in the two order parameters, namely the magnetic moment and the quadrupole moment. An excellent agreement is obtained in significant regions of the parameter space between the two curvatures and the two corresponding correlation lengths $\xi_1$ and $\xi_2$. The three dimensional scalar curvature $R_g$ is also found to efficiently encode interactions. The scaling function for the free energy near critical points and the tricritical point is obtained by making use of Ruppeiner's conjecture relating the inverse of the singular free energy to the thermodynamic scalar curvature.
In contrast to the canonical case, microcanonical thermodynamic functions can show nonanalyticities also for finite systems. In this paper we contribute to the understanding of these nonanalyticities by working out the relation between nonanalyticities of the microcanonical entropy and its configurational counterpart. If the configurational microcanonical entropy $\omega_N^c(v)$ has a nonanalyticity at $v=v_c$, then the microcanonical entropy $\omega_N(\epsilon)$ has a nonanalyticity at the same value $\epsilon=v_c$ of its argument for any finite value of the number of degrees of freedom $N$. The presence of the kinetic energy weakens the nonanalyticities such that, if the configurational entropy is $p$ times differentiable, the entropy is $p+\lfloor N/2 \rfloor$-times differentiable. In the thermodynamic limit, however, the behaviour is very different: The nonanalyticities do not longer occur at the same values of the arguments, but the nonanalyticity of the microcanonical entropy is shifted to a larger energy. These results give a general explanation of the peculiar behaviour previously observed for the mean-field spherical model. With the hypercubic model we provide a further example illustrating our results.
We discuss the decoupling solution to SUSY flavor problem in the fat brane scenario. We present a simple model to yield the decoupling sfermion spectrum in a five dimensional theory. Sfermion masses are generated by the overlap between the wave functions of the matter fields and the chiral superfields on the SUSY breaking brane. Two explicit examples of the spectrum are given.
We study the existence and multiplicity of periodic weak solutions for a non-local equation involving an odd subcritical nonlinearity which is asymptotically linear at infinity. We investigate such problem by applying the the pseudo-index theory developed by Bartolo, Benci and Fortunato \cite{bbf} after transforming the problem to a degenerate elliptic problem in a half-cylinder with a Neumann boundary condition, via a Caffarelli-Silvestre type extension in periodic setting. The periodic nonlocal case, considered here, presents, respect to the cases studied in literature, some new additional difficulties and a careful analysis of the fractional spaces involved is necessary.
We use Bayesian component estimation methods to examine the prospects for large-scale polarized map and cosmological parameter estimation with simulated Planck data assuming simplified white noise properties. The sky signal is parametrized as the sum of the CMB, synchrotron emission, and thermal dust emission. The synchrotron and dust components are modelled as power-laws, with a spatially varying spectral index for synchrotron and a uniform index for dust. Using the Gibbs sampling technique, we estimate the linear polarisation Q and U posterior amplitudes of the CMB, synchrotron and dust maps as well as the two spectral indices in ~4 degree pixels. We use the recovered CMB map and its covariance in an exact pixel likelihood algorithm to estimate the optical depth to reionization tau, the tensor-to-scalar ratio r, and to construct conditional likelihood slices for the EE and BB spectra. Given our foreground model, we find sigma(tau)~0.004 for tau=0.1, sigma(r)~0.03 for a model with r=0.1, and a 95% upper limit of r<0.02 for r=0.0.
Long-range spatial correlations in the velocity and energy fields of a granular fluid are discussed in the framework of a 1d lattice model. The dynamics of the velocity field occurs through nearest-neighbour inelastic collisions that conserve momentum but dissipate energy. A set of equations for the fluctuating hydrodynamics of the velocity and energy mesoscopic fields give a first approximation for (i) the velocity structure factor and (ii) the finite-size correction to the Haff law, both in the homogeneous cooling regime. At a more refined level, we have derived the equations for the two-site velocity correlations and the total energy fluctuations. First, we seek a perturbative solution thereof, in powers of the inverse of system size. On the one hand, when scaled with the granular temperature, the velocity correlations tend to a stationary value in the long time limit. On the other hand, the scaled standard deviation of the total energy diverges, that is, the system shows multiscaling. Second, we find an exact solution for the velocity correlations in terms of the spectrum of eigenvalues of a certain matrix. The results of numerical simulations of the microscopic model confirm our theoretical results, including the above described multiscaling phenomenon.
We perform a combined analysis of cosmic shear tomography, galaxy-galaxy lensing tomography, and redshift-space multipole power spectra (monopole and quadrupole) using 450 deg$^2$ of imaging data by the Kilo Degree Survey (KiDS) overlapping with two spectroscopic surveys: the 2-degree Field Lensing Survey (2dFLenS) and the Baryon Oscillation Spectroscopic Survey (BOSS). We restrict the galaxy-galaxy lensing and multipole power spectrum measurements to the overlapping regions with KiDS, and self-consistently compute the full covariance between the different observables using a large suite of $N$-body simulations. We methodically analyze different combinations of the observables, finding that galaxy-galaxy lensing measurements are particularly useful in improving the constraint on the intrinsic alignment amplitude (by 30%, positive at $3.5\sigma$ in the fiducial data analysis), while the multipole power spectra are useful in tightening the constraints along the lensing degeneracy direction (e.g. factor of two stronger matter density constraint in the fiducial analysis). The fully combined constraint on $S_8 \equiv \sigma_8 \sqrt{\Omega_{\rm m}/0.3} = 0.742 \pm 0.035$, which is an improvement by 20% compared to KiDS alone, corresponds to a $2.6\sigma$ discordance with Planck, and is not significantly affected by fitting to a more conservative set of scales. Given the tightening of the parameter space, we are unable to resolve the discordance with an extended cosmology that is simultaneously favored in a model selection sense, including the sum of neutrino masses, curvature, evolving dark energy, and modified gravity. The complementarity of our observables allows for constraints on modified gravity degrees of freedom that are not simultaneously bounded with either probe alone, and up to a factor of three improvement in the $S_8$ constraint in the extended cosmology compared to KiDS alone.
We study the warm-tachyon inflationary universe model with viscous pressure in high-dissipation regime. General conditions which are required for this model to be realizable are derived in the slow-roll approximation. We present analytic expressions for density perturbation and amplitude of tensor perturbation in longitudinal gauge. Expressions of tensor-to-scalar ratio, scalar spectral index and its running are obtained. We develop our model by using exponential potential, the characteristics of this model are calculated for two specific cases in great details: 1- Dissipative parameter $\Gamma$ and bulk viscous parameter $\zeta$ are constant parameters. 2- Dissipative parameter is a function of tachyon field $\phi$ and bulk viscous parameter is a function of matter-radiation mixture energy density $\rho$. The parameters of the model are restricted by recent observational data from the nine-year Wilkinson microwave anisotropy probe (WMAP9), Planck and BICEP2 data.
Our main aim in this thesis is to address the results and prospects of boundary logarithmic conformal field theories: theories with boundaries that contain the above Jordan cell structure. We have investigated c_{p,q} boundary theory in search of logarithmic theories and have found logarithmic solutions of two-point functions in the context of the Coulomb gas picture. Other two-point functions have also been studied in the free boson construction of BCFT with SU(2)_k symmetry. In addition, we have analyzed and obtained the boundary Ishibashi state for a rank-2 Jordan cell structure [hep-th/0103064]. We have also examined the (generalised) Ishibashi state construction and the symplectic fermion construction at c=-2 for boundary states in the context of the c=-2 triplet model. The differences between two constructions are interpreted, resolved and extended beyond each case.