ShantanuT01/DACTYL-Pretraining huggingface dataset:
Maximal signal and peak of high-frequency relic gravitational waves (GW's), recently expected by quintessential inflationary models, may be firmly localized in the GHz region, the energy density of the relic gravitons in critical units (i.e., $ h_0^2 \Omega_{GW}$) is of the order $10^{-6}$, roughly eight orders of magnitude larger than in ordinary inflationary models. This is just right best frequency band of the electromagnetic (EM) response to the high-frequency GW's in smaller EM detecting systems. We consider the EM response of a Gaussian beam passing through a static magnetic field to a high-frequency relic GW. It is found that under the synchroresonance condition, the first-order perturbative EM power fluxes will contain "left circular wave" and "right circular wave" around the symmetrical axis of the Gaussian beam, but the perturbative effects produced by the states of + polarization and $\times$ polarization of the relic GW have different properties, and the perturbations on behavior are obviously different from that of the background EM fields in the local regions. For the high-frequency relic GW with the typical parameters $ \nu_g = 10^{10}Hz$, $ h = 10^{- 30} $ in the quintessential inflationary models, the corresponding perturbative photon flux passing through the region $ 10^{- 2} m^{2} $ would be expected to be $ 10^{3}s^{-1} $. This is largest perturbative photon flux we recently analyzed and estimated using the typical laboratory parameters. In addition, we also discuss geometrical phase shift generated by the high-frequency relic GW in the Gaussian beam and estimate possible physical effects.
We use a population synthesis approach to characterise, as a function of cosmic time, the extragalactic close binary population descended from stars of low to intermediate initial mass. The unresolved gravitational wave (GW) background due to these systems is calculated for the 0.1-10 mHz frequency band of the planned Laser Interferometer Space Antenna (LISA). This background is found to be dominated by emission from close white dwarf-white dwarf pairs. The spectral shape can be understood in terms of some simple analytic arguments. To quantify the astrophysical uncertainties, we construct a range of evolutionary models which produce populations consistent with Galactic observations of close WD-WD binaries. The models differ in binary evolution prescriptions as well as initial parameter distributions and cosmic star formation histories. We compare the resulting background spectra, whose shapes are found to be insensitive to the model chosen, and different to those found recently by Schneider et al. (2001). From this set of models, we constrain the amplitude of the extragalactic background to be 1E-12 < Omega(1 mHz) < 6E-12, in terms of Omega(f), the fraction of closure density received in gravitational waves in the logarithmic frequency interval around f.
We formulate the Gamow shell model (GSM) in coupled-channel (CC) representation for the description of proton/neutron radiative capture reactions and present the first application of this new formalism for the calculation of cross-sections in mirror reactions 7Be(p,gamma)8B and 7Li(n,gamma)8Li. The GSM-CC formalism is applied to a translationally-invariant Hamiltonian with an effective finite-range two-body interaction. Reactions channels are built by GSM wave functions for the ground state 3/2- and the first excited state 1/2- of 7Be/7Li and the proton/neutron wave function expanded in different partial waves.
We overview nonequilibrium Green function combined with density functional theory (NEGF-DFT) modeling of independent electron and phonon transport in nanojunctions with applications focused on a new class of thermoelectric devices where a single molecule is attached to two metallic zigzag graphene nanoribbons (ZGNRs) via highly transparent contacts. Such contacts make possible injection of evanescent wavefunctions from ZGNRs, so that their overlap within the molecular region generates a peak in the electronic transmission. Additionally, the spatial symmetry properties of the transverse propagating states in the ZGNR electrodes suppress hole-like contributions to the thermopower. Thus optimized thermopower, together with diminished phonon conductance through a ZGNR/molecule/ZGNR inhomogeneous structure, yields the thermoelectric figure of merit ZT~0.5 at room temperature and 0.5<ZT<2.5 below liquid nitrogen temperature. The reliance on evanescent mode transport and symmetry of propagating states in the electrodes makes the electronic-transport-determined power factor in this class of devices largely insensitive to the type of sufficiently short conjugated organic molecule, which we demonstrate by showing that both 18-annulene and C10 molecule sandwiched by the two ZGNR electrodes yield similar thermopower. Thus, one can search for molecules that will further reduce the phonon thermal conductance (in the denominator of ZT) while keeping the electronic power factor (in the nominator of ZT) optimized. We also show how often employed Brenner empirical interatomic potential for hydrocarbon systems fails to describe phonon transport in our single-molecule nanojunctions when contrasted with first-principles results obtained via NEGF-DFT methodology.
The h^*-polynomial of a lattice polytope is the numerator of the generating function of the Ehrhart polynomial. Let P be a lattice polytope with h^*-polynomial of degree d and with linear coefficient h^*_1. We show that P has to be a lattice pyramid over a lower-dimensional lattice polytope, if the dimension of P is greater or equal to h^*_1 (2d+1) + 4d-1. This result has a purely combinatorial proof and generalizes a recent theorem of Batyrev.
A scheme of single-photon multi-port router is put forward by coupling two optomechanical cavities with waveguides. It is shown that the coupled two optomechanical cavities can exhibit photon blockade effect, which is generated from interference of three mode interaction. A single-photon travel along the system is calculated. The results show that the single photon can be controlled in the multi-port system because of the radiation pressure, which should be useful for constructing quantum network.
Instrumental selection effects can act upon the estimates of the peak energy Ep, the fluence F and the peak flux P of GRBs. If this were the case, then the correlations involving the corresponding rest frame quantities (i.e. Ep, Eiso and the peak luminosity Liso) would be questioned. We estimated, as a function of Ep, the minimum peak flux necessary to trigger a GRB and the minimum fluence a burst must have to determine the value of Ep by considering different instruments (BATSE, Swift, BeppoSAX). We find that the latter dominates over the former. We then study the Ep-fluence (and flux) correlation in the observer plane. GRBs with redshift show well defined Ep-F and Ep-P correlations: in this planes the selection effects are present, but do not determine the found orrelations. This is not true for Swift GRBs with redshift, for which the spectral analysis threshold does affect their distribution in the observer planes. Extending the sample to GRBs without z, we still find a significant Ep-F correlation, although with a larger scatter than that defined by GRBs with redshift. We find that 6% are outliers of the Amati correlation. The Ep-P correlation of GRBs with or without redshift is the same and no outlier is found among bursts without redshift.
In this paper we define the triangulated category of motives over a simplicial scheme. The morphisms between the Tate objects in this category compute the motivic cohomology of the underlying scheme. In the last section we consider the special case of "embedded" simplicial schemes, which correspond to the subsheaves of the constant sheaf and naturally appear in the descent problems for motivic cohomology such as the Bloch-Kato conjecture.
The evolution of galaxies is influenced by the environment in which they reside. This effect should be strongest for the least-mass and -luminosity galaxies. To study dwarf galaxies in extremely low density environments we have compiled a deep catalogue of dwarf galaxies in the nearby Lynx-Cancer void. This void hosts some of the most metal-poor dwarfs known to date. It borders the Local Volume at the negative supergalactic Z (SGZ) coordinates and has the size of more than 16 Mpc. With a distance to its centre of only 18 Mpc it is close enough to allow the search for the faintest dwarfs. Within the void 75 dwarf (-11.9 > M_B > -18.0) and 4 subluminous (-18.0 > M_B > -18.4) galaxies have been identified. We present the parameters of the void galaxies and give a detailed analysis of the completeness of the catalogue as a function of magnitude and surface brightness. The catalogue appears almost complete to M_B < -14 mag, but misses part of the fainter low surface brightness (LSB) face-on galaxies. This sample of void galaxies builds the basis of forthcoming observational studies that will give insight into the main stellar population, HI-mass-to-light ratio, metallicity and age for comparison with dwarfs in higher density regions. We briefly summarize the information on the unusual objects in the void and conclude that their concentration hints that voids are environments that are favourable for finding and studying unevolved dwarf galaxies.
Micro-expressions (MEs) are rapid, involuntary facial expressions which reveal emotions that people do not intend to show. Studying MEs is valuable as recognizing them has many important applications, particularly in forensic science and psychotherapy. However, analyzing spontaneous MEs is very challenging due to their short duration and low intensity. Automatic ME analysis includes two tasks: ME spotting and ME recognition. For ME spotting, previous studies have focused on posed rather than spontaneous videos. For ME recognition, the performance of previous studies is low. To address these challenges, we make the following contributions: (i)We propose the first method for spotting spontaneous MEs in long videos (by exploiting feature difference contrast). This method is training free and works on arbitrary unseen videos. (ii)We present an advanced ME recognition framework, which outperforms previous work by a large margin on two challenging spontaneous ME databases (SMIC and CASMEII). (iii)We propose the first automatic ME analysis system (MESR), which can spot and recognize MEs from spontaneous video data. Finally, we show our method outperforms humans in the ME recognition task by a large margin, and achieves comparable performance to humans at the very challenging task of spotting and then recognizing spontaneous MEs.
In this paper, we study the Tamagawa numbers of a crystalline representation over a tower of cyclotomic extensions under certain technical conditions on the representation. In particular, we show that we may improve the asymptotic bounds given in the thesis of Arthur Laurent in certain cases.
In this paper, we consider a generalization of Horadam sequence fwng which is defined by the recurrence relation wn = x(n)wn-1+ cwn-2; where x(n) = a if n is even, x(n) = b if n is odd with arbitrary initial conditions w0;w1 and nonzero real numbers a, b and c. As a special case, by taking initial conditions 0, 1 and 2, b we define the sequences {un} and {vn}, respectively. The main purpose of this study is to derive some basic properties of the sequences {un}, {vn} and {wn} by using matrix approach.
We study the asymptotics, for small and large values, of the supremum of a product of symmetric stable processes. We show in particular that the persistence exponent remains the same as for only one process, up to some logarithmic terms.
Let $p$ be a prime number such that $p=2$ or $p\equiv 1\pmod 4$. Let $\varepsilon_p$ denote the fundamental unit of $\mathbb{Q}(\sqrt{p})$ and let $a$ be a positive square-free integer. The main aim of this paper is to determine explicitly the Hilbert genus field of the imaginary cyclic quartic fields of the form $\mathbb{Q}(\sqrt{-a\varepsilon_p\sqrt{p}})$.
Suppose that $\theta$ is irrational. Then almost all elements $\nu\in {\mathbb Z}[\theta]$ that may be written as a $k$-fold product of the shifted integers $n+\theta$ $(n\in {\mathbb N})$ are thus represented essentially uniquely.
Two non-harmonic canonical-dissipative limit cycle oscillators are considered that oscillate in one-dimensional Smorodinsky-Winternitz potentials. It is shown that the standard approach of the canonical-dissipative framework to introduce dissipative forces leads naturally to a coupling force between the oscillators that establishes synchronization. The non-harmonic character of the limit cycles in the context of anchoring, the phase difference between the synchronized oscillators, and the degree of synchronization are studied in detail.
We have carried out temperature and pressure-dependent Raman and x-ray measurements on single crystals of Tb$_2$Ti$_2$O$_7$. We attribute the observed anomalous temperature dependence of phonons to phonon-phonon anharmonic interactions. The quasiharmonic and anharmonic contributions to the temperature-dependent changes in phonon frequencies are estimated quantitatively using mode Gr\"{u}neisen parameters derived from pressure-dependent Raman experiments and bulk modulus from high pressure x-ray measurements. Further, our Raman and x-ray data suggest a subtle structural deformation of the pyrochlore lattice at $\sim$ 9 GPa. We discuss possible implications of our results on the spin-liquid behaviour of Tb$_2$Ti$_2$O$_7$.
These notes are a considerably revised and expanded version of expository lectures given at the Fields Institute Workshop on "Nonlinear Dispersive Partial Differential Equations and Inverse Scattering" in August 2017. We give a complete and self-contained treatment of inverse scattering for the defocussing cubic NLS in one-dimension, following the 2003 paper of Deift and Zhou, and the defocussing Davey-Stewartson equation in two space dimensions, following the work of Perry and more recent work of Nachman, Regev, and Tataru.
In this paper we study the automorphisms group of some $K3$ surfaces which are double covers of the projective plane ramified over a smooth sextic plane curve. More precisely, we study the case of a $K3$ surface of Picard rank two such that there is a rational curve of degree $d$ which is tangent to the sextic in $d$ points.
We report on investigations of the applicability of non-relativistic constituent quark models to the low-energy nucleon-nucleon (NN) interaction. The major innovations of a resulting NN potential are the use of the $^3$P$_0$ decay model and quark model wave functions to derive nucleon-nucleon-meson form-factors, and the use of a colored spin-spin contact hyperfine interaction to model the repulsive core rather than the phenomenological treatment common in other NN potentials. We present the results of the model for experimental free NN scattering phase shifts, S-wave scattering lengths and effective ranges and deuteron properties. Plans for future study are discussed.
A variation of low density parity check (LDPC) error correcting codes defined over Galois fields ($GF(q)$) is investigated using statistical physics. A code of this type is characterised by a sparse random parity check matrix composed of $C$ nonzero elements per column. We examine the dependence of the code performance on the value of $q$, for finite and infinite $C$ values, both in terms of the thermodynamical transition point and the practical decoding phase characterised by the existence of a unique (ferromagnetic) solution. We find different $q$-dependencies in the cases of C=2 and $C \ge 3$; the analytical solutions are in agreement with simulation results, providing a quantitative measure to the improvement in performance obtained using non-binary alphabets.
Given finitely many connected polygonal obstacles $O_1,\dots,O_k$ in the plane and a set $P$ of points in general position and not in any obstacle, the {\em visibility graph} of $P$ with obstacles $O_1,\dots,O_k$ is the (geometric) graph with vertex set $P$, where two vertices are adjacent if the straight line segment joining them intersects no obstacle. The obstacle number of a graph $G$ is the smallest integer $k$ such that $G$ is the visibility graph of a set of points with $k$ obstacles. If $G$ is planar, we define the planar obstacle number of $G$ by further requiring that the visibility graph has no crossing edges (hence that it is a planar geometric drawing of $G$). In this paper, we prove that the maximum planar obstacle number of a planar graph of order $n$ is $n-3$, the maximum being attained (in particular) by maximal bipartite planar graphs. This displays a significant difference with the standard obstacle number, as we prove that the obstacle number of every bipartite planar graph (and more generally in the class PURE-2-DIR of intersection graphs of straight line segments in two directions) of order at least $3$ is $1$.
According to the recent proposal by Aharony, Bergman, Jafferis and Maldacena the N=6 supersymmetric Chern-Simons theory in three dimensions has a 't Hooft limit whose holographic dual is described by type IIA superstings on AdS_4 x CP^3 background. We argue that the Green-Schwarz action for type IIA string theory on AdS_4 x CP^3 with kappa-symmetry partially fixed can be understood as a coset sigma-model on the same space supplied with a proper Wess-Zumino term. We construct the corresponding sigma-model Lagrangian and show that it is invariant under a local fermionic symmetry which for generic bosonic string configurations allows one to remove 8 out of 24 fermionic degrees of freedom. The remaining 16 fermions together with their bosonic partners should describe the physical content of AdS_4 x CP^3 superstring. As further evidence, we demonstrate that in the plane-wave limit the quadratic action arising from our model reproduces the one emerging from the type IIA superstring. The coset sigma-model is classically integrable which opens up the possibility to investigate its dynamics in a way very similar to the case of AdS_5 x S^5 superstrings.
When is it possible to interpret a given Markov process as a L\'evy-like process? Since the class of L\'evy processes can be defined by the relation between transition probabilities and convolutions, the answer to this question lies in the existence of a convolution-like operator satisfying the same relation with the transition probabilities of the process. It is known that the so-called Sturm-Liouville convolutions have the desired properties and therefore the question above has a positive answer for a certain class of one-dimensional diffusions. However, more general processes have never been systematically treated in the literature. This study addresses this gap by considering the general problem of constructing a convolution-like operator for a given strong Feller process on a general locally compact metric space. Both necessary and sufficient conditions for the existence of such convolution-like structures are determined, which reveal a connection between the answer to the above question and certain analytical and geometrical properties of the eigenfunctions of the transition semigroup. The case of reflected Brownian motions on bounded domains of R d and compact Riemannian manifolds is considered in greater detail: various special cases are analysed, and a general discussion on the existence of appropriate convolution-like structures is presented.
We have investigated the thermal rectification phenomenon in a single-wall mass graded carbon nanotube by molecular dynamics simulation. Second generation Brenner potential has been used to model the inter atomic carbon interaction. Fixed boundary condition has been taken into account. We compare our findings to a previous study by Alaghemandi et al which has been done with a different potential and boundary condition. The dependence of the rectification factor $R$ on temperature, nanotube diameter and length as well as mass gradient are obtained. It is shown that by increasing the temperature, the rectification decreases whereas by increasing the other parameters namely the mass gradient, diameter and the tube length it increases.
We present observations of OY Car, obtained with the Anglo-Australian Telescope, during a normal outburst in August 1991. Two sinusoidal components are resolved in the H$\beta$ trailed spectra and we determine the location of the narrow component to be on the secondary star with a maximum contributed flux of ~2.5 per cent to the total flux. Imaging of the line distribution reveals that the other emission component is associated with the gas stream. This follows a velocity close to the ballistic one from the red star to a distance of ~0.5 R$_{L_{1}}$ from the white dwarf. This emission penetrates the accretion disc (from 0.5--0.1 R$_{L_{1}}$), with a velocity now closer (but lower) to the keplerian velocities along the path of the gas stream. We finally discuss the implications of having observed simultaneously line emission from the gas stream and the red star during outburst.
Exact solution of the Ising model on the simple cubic lattice is one of the long-standing open problems in rigorous statistical mechanics. Indeed, it is generally believed that settling it would constitute a methodological breakthrough, fomenting great prospects for further application, similarly to what happened when Lars Onsager solved the two dimensional model eighty years ago. Hence, there have been many attempts to find analytic expressions for the exact partition function $Z$, but all such attempts have failed due to unavoidable conceptual or mathematical obstructions. Given the importance of this simple yet paradigmatic model, here we set out clear-cut criteria for any claimed exact expression for $Z$ to be minimally plausible. Specifically, we present six necessary -- but not sufficient -- conditions that $Z$ must satisfy. These criteria will allow very quick plausibility checks of future claims. As illustrative examples, we discuss previous mistaken ``solutions,'' unveiling their shortcomings.
The goal of open-world compositional zero-shot learning (OW-CZSL) is to recognize compositions of state and objects in images, given only a subset of them during training and no prior on the unseen compositions. In this setting, models operate on a huge output space, containing all possible state-object compositions. While previous works tackle the problem by learning embeddings for the compositions jointly, here we revisit a simple CZSL baseline and predict the primitives, i.e. states and objects, independently. To ensure that the model develops primitive-specific features, we equip the state and object classifiers with separate, non-linear feature extractors. Moreover, we estimate the feasibility of each composition through external knowledge, using this prior to remove unfeasible compositions from the output space. Finally, we propose a new setting, i.e. CZSL under partial supervision (pCZSL), where either only objects or state labels are available during training, and we can use our prior to estimate the missing labels. Our model, Knowledge-Guided Simple Primitives (KG-SP), achieves state of the art in both OW-CZSL and pCZSL, surpassing most recent competitors even when coupled with semi-supervised learning techniques. Code available at: https://github.com/ExplainableML/KG-SP.
The Abelian Higgs model forms an essential part of the electroweak standard model: it is the sector containing only Z and Higgs bosons. We present a diagram-based proof of the tree-level unitarity of this model inside the unitary gauge, where only physical degrees of freedom occur. We derive combinatorial recursion relations for off-shell amplitudes in the massless approximation, which allows us to prove the cancellation of the first two orders in energy of unitarity-violating high-energy behaviour for any tree-level amplitude in this model. We describe a deformation of the amplitudes by extending the physical phase space to at least 7 spacetime dimensions, which leads to on-shell recursion relations a la BCFW. These lead to a simple proof that all on-shell tree amplitudes obey partial-wave unitarity.