ShantanuT01/DACTYL-Pretraining huggingface dataset:
When making simultaneous decisions, our preference for the outcomes on one subset can depend on the outcomes on a disjoint subset. In referendum elections, this gives rise to the separability problem, where a voter must predict the outcome of one proposal when casting their vote on another. A set $S \subset [n]$ is separable for preference order $\succeq$ when our ranking of outcomes on $S$ is independent of outcomes on its complement $[n]-S$. The admissibility problem asks which characters $\mathcal{C} \subset \mathcal{P}([n])$ can arise as the collection of separable subsets for some preference order. We introduce a linear algebraic technique to construct preference orders with desired characters. Each vector in our $2^n$-dimensional voter basis induces a simple preference ordering with nice separability properties. Given any collection $\mathcal{C} \subset \mathcal{P}([n])$ whose subset lattice has a tree structure, we use the voter basis to construct a preference order with character $\mathcal{C}$.
he equation $-\Delta u = \lambda e^u$ posed in the unit ball $B \subseteq \R^N$, with homogeneous Dirichlet condition $u|_{\partial B} = 0$, has the singular solution $U=\log\frac1{|x|^2}$ when $\lambda = 2(N-2)$. If $N\ge 4$ we show that under small deformations of the ball there is a singular solution $(u,\lambda)$ close to $(U,2(N-2))$. In dimension $N\ge 11$ it corresponds to the extremal solution -- the one associated to the largest $\lambda$ for which existence holds. In contrast, we prove that if the deformation is sufficiently large then even when $N\ge 10$, the extremal solution remains bounded in many cases.
Quantum internet will enable a number of revolutionary applications. It relies on entanglement of remote quantum memories over long distances. Despite enormous progresses so far, the maximal physical separation achieved between two nodes is 1.3 km, and challenges for long distance remain. Here we make a significant step forward by entangling two atomic ensembles in one lab via photon transmission through metropolitan-scale fibers. We use cavity enhancement to create bright atom-photon entanglement, and harness quantum frequency conversion to shift the atomic wavelength to telecom. We realize entanglement over 22 km field-deployed fibers via two-photon interference, and entanglement over 50 km coiled fibers via single-photon interference. Our experiment can be extended to physically separated nodes with similar distance as a functional segment for atomic quantum networks, thus paving the way towards establishing atomic entanglement over many nodes and over much longer distance.
The charge ordering transition in the layer compound NaV2O5 is studied by means of exact diagonalization methods for finite systems. The 2-leg ladders of the V-Trellis lattice are associated with one spin variable of the vanadium 3d-electron in the rung and a pseudospin variable that describes its positional degree of freedom. The charge ordering (CO) due to intersite Coulomb interactions is described by an effective Ising-like Hamiltonian for the pseudo-spins that are coupled to the spin fluctuations along the ladder. We employ a Lanczos algortihm on 2D lattice to compute charge (pseudo-spin) and spin-correlation functions and the energies of the low lying excited states. A CO-phase diagram is constructed and the effect of intra-ladder exchange on the CO transition is studied. It is shown that a phase with no-longe range order (no-LRO) exists between the in-line and zig-zag ordered structures. We provide a finite-size scaling analysis for the spin excitation gap and also discuss the type of excitations. In addition we studied the effect of bond-alternation of spin exchange and derived a scaling form for the spin gap in terms of the dimerization parameter.
Low-luminosity active galactic nuclei (LLAGNs) represent the bulk of the AGN population in the present-day universe and they trace the low-level accreting supermassive black holes. In order to probe the accretion and jet physical properties in LLAGNs as a class, we model the broadband radio to X-rays spectral energy distributions (SEDs) of 21 LLAGNs in low-ionization nuclear emission-line regions (LINERs) with a coupled accretion-jet model. The accretion flow is modeled as an inner ADAF outside of which there is a truncated standard thin disk. We find that the radio emission is severely underpredicted by ADAF models and is explained by the relativistic jet. The origin of the X-ray radiation in most sources can be explained by three distinct scenarios: the X-rays can be dominated by emission from the ADAF, or the jet, or the X-rays can arise from a jet-ADAF combination in which both components contribute to the emission with similar importance. For 3 objects both the jet and ADAF fit equally well the X-ray spectrum and can be the dominant source of X-rays whereas for 11 LLAGNs a jet-dominated model accounts better than the ADAF-dominated model for the data. The individual and average SED models that we computed can be useful for different studies of the nuclear emission of LLAGNs. From the model fits, we estimate important parameters of the central engine powering LLAGNs in LINERs, such as the mass accretion rate and the mass-loss rate in the jet and the jet power - relevant for studies of the kinetic feedback from jets.
We consider the renormalisation of the Fayet-Iliopoulos D-term in a softly-broken supersymmetric gauge theory with a non-simple gauge group containing an abelian factor, and present the associated beta-function through three loops. We also include in an appendix the result for several abelian factors. We specialise to the case of the minimal supersymmetric standard model (MSSM), and investigate the behaviour of the Fayet-Iliopoulos coupling for various boundary conditions at the unification scale. We focus particularly on the case of non-standard soft supersymmetry breaking couplings, for which the Fayet-Iliopoulos coupling evolves significantly between the unification scale and the weak scale.
It is shown that potential barriers in bilayer graphene (BLG) and monolayer transition metal dichalcogenides (TMDs) can split a valley unpolarized incident current into reflected and transmitted currents with opposite valley polarization. Valley asymmetric transmission inevitably occurs because of the low symmetry of the total Hamiltonian and when total external reflection occurs the transmission is 100% valley polarized in BLG and 100% spin and valley polarized in TMDs, except for exponentially small corrections. By adjusting the potential, 100% polarization can be obtained regardless of the crystallographic orientation of the barrier. A valley polarizer can be realized by arranging for a collimated beam of carriers to be incident on a barrier within the range of angles for total external reflection. The transmission coefficients of barriers with a relative rotation of $\pm\pi/3$ are related by symmetry. This allows two barriers to be used to demonstrate that the current is valley polarized. A soft-walled potential is used to model the barrier and the method used to find the transmission coefficients is explained. In the case of monolayer TMDs, a 4-band k.p Hamiltonian is used and the k.p parameters are obtained by fitting to ab-initio band structures.
The cosmological Robertson-Walker metric of general relativity is often said to have the consequences that (1) the recessional velocity $v$ of a galaxy at proper distance $\ell$ obeys the Hubble law $v=H\ell$, and therefore galaxies at sufficiently great distance $\ell$ are receding faster than the speed of light $c$; (2) faster than light recession does not violate special relativity theory because the latter is not applicable to the cosmological problem, and because ``space itself is receding'' faster than $c$ at great distance, and it is velocity relative to local space that is limited by $c$, not the velocity of distant objects relative to nearby ones; (3) we can see galaxies receding faster than the speed of light; and (4) the cosmological redshift is not a Doppler shift, but is due to a stretching of photon wavelength during propagation in an expanding universe. We present a particular Robertson-Walker metric (an empty universe metric) for which a coordinate transformation shows that none of these interpretation necessarily holds. The resulting paradoxes of interpretation lead to a deeper understanding of the meaning of the cosmological metric.
A short pedagogical overview of cosmological perturbation theory, following the lectures given during the brazilian school of cosmology held in August 2012. Topics treated are:   I. The background   II. SVT decomposition and the gauge issue.   III. The example of the tensor modes.   IV. Density fluctuations, transfer function and power spectrum.   V. Initial condition theory: quantum vacuum fluctuations.
We present an improved algorithm for tabulating class groups of imaginary quadratic fields of bounded discriminant. Our method uses classical class number formulas involving theta-series to compute the group orders unconditionally for all $\Delta \not \equiv 1 \pmod{8}.$ The group structure is resolved using the factorization of the group order. The $1 \bmod 8$ case was handled using the methods of \cite{jacobson}, including the batch verification method based on the Eichler-Selberg trace formula to remove dependence on the Extended Riemann Hypothesis. Our new method enabled us to extend the previous bound of $|\Delta| < 2 \cdot 10^{11}$ to $2^{40}$. Statistical data in support of a variety conjectures is presented, along with new examples of class groups with exotic structures.
We suggest a new model for the dynamics of a suspension bridge through a system of nonlinear nonlocal hyperbolic differential equations. The equations are of second and fourth order in space and describe the behavior of the main components of the bridge: the deck, the sustaining cables and the connecting hangers. We perform a careful energy balance and we derive the equations from a variational principle. We then prove existence and uniqueness for the resulting problem.
An intrinsic-state formalism for IBM-4 is presented. A basis of deformed bosons is introduced which allows the construction of a general trial wave function which has Wigner's spin-isospin SU(4) symmetry as a particular limit. Intrinsic-state calculations are compared with exact ones showing good agreement.
The notion of $(a,b)$-cores is closely related to rational $(a,b)$ Dyck paths due to Anderson's bijection, and thus the number of $(a,a+1)$-cores is given by the Catalan number $C_a$. Recent research shows that $(a,a+1)$ cores with distinct parts are enumerated by another important sequence- Fibonacci numbers $F_a$. In this paper, we consider the abacus description of $(a,b)$-cores to introduce the natural grading and generalize this result to $(a,as+1)$-cores. We also use the bijection with Dyck paths to count the number of $(2k-1,2k+1)$-cores with distinct parts. We give a second grading to Fibonacci numbers, induced by bigraded Catalan sequence $C_{a,b} (q,t)$.
The behaviour of the lower order moments of the velocity distribution function for a system of inelastic granular disks driven by vertical vibrations is studied using a kinetic theory. A perturbative kinetic theory for vibro-fluidised beds was proposed by Kumaran (JFM, v. 364, 163). A scheme to generalise this theory to higher orders in the moments is presented here. With such a method it is possible to obtain an analytical solution to the moments of the distribution function up to third order.
For two graph H and G, the Ramsey number r(H, G) is the smallest positive integer n such that every red-blue edge coloring of the complete graph K_n on n vertices contains either a red copy of H or a blue copy of G. Motivated by questions of Erdos and Harary, in this note we study how the Ramsey number r(K_s, G) depends on the size of the graph G. For s \geq 3, we prove that for every G with m edges, r(K_s,G) \geq c (m/\log m)^{\frac{s+1}{s+3}} for some positive constant c depending only on s. This lower bound improves an earlier result of Erdos, Faudree, Rousseau, and Schelp, and is tight up to a polylogarithmic factor when s=3. We also study the maximum value of r(K_s,G) as a function of m.
Some experiments have found multi-core events in cosmic rays extensive air showers which should be interpreted by hadronic interaction theory. In this paper, the multi-core events are reproduced by Monte Carlo simulation with CORSIKA. The origin of each sub-cores is tracked back from the observation level. The interaction mechanism and original particles of sub-core are studied in this paper.
Piezoresistance of n-Si is considered with due regard for inter-valley drag. It is shown that inter-valley drag gains the piezocoefficient and diminishes the mobility. In the region of nondegenerate carriers the effect of drag increases when carrier concentration rises and temperature falls.
We study contributions to the cosmic microwave background (CMB) bispectrum from non-Gaussianity induced by secondary anisotropies during reionization. Large-scale structure in the reionized epoch both gravitational lenses CMB photons and produces Doppler shifts in their temperature from scattering off electrons in infall. The resulting correlation is potentially observable through the CMB bispectrum. The second-order Ostriker-Vishniac also couples to a variety of linear secondary effects to produce a bispectrum. For the currently favored flat cosmological model with a low matter content and small optical depth in the reionized epoch $\tau \la 0.3$, however, these bispectrum contributions are well below the detection threshold of MAP and at or below that of Planck, given their cosmic and noise variance limitations. At the upper end of this range, they can serve as an extra source of noise for measurements with Planck of either primordial nongaussianity or that induced by the correlation of gravitational lensing with the integrated Sachs-Wolfe and the thermal Sunyaev-Zel'dovich effects. We include a discussion of the general properties of the CMB bispectrum, its configuration dependence for the various effects, and its computation in the Limber approximation and beyond.
The influence of atomic vacancy defects at different concentrations on electronic properties of MoS$_2$ and WS$_2$ monolayers is studied by means of Slater-Koster tight-binding model with non-orthogonal $sp^3d^5$ orbitals and including the spin-orbit coupling. The presence of vacancy defects induces localized states in the bandgap of pristine MoS$_2$ and WS$_2$, which have potential to modify the electronic structure of the systems, depending on the type and concentration of the defects. It is shown that although the contribution of metal (Mo or W) $d$ orbitals is dominant in the formation of midgap states, the sulphur $p$ and $d$ orbitals have also considerable contribution in the localized states, when metal defects are introduced. Our results suggest that Mo and W defects can turn the monolayers into p-type semiconductors, while the sulphur defects make the system a n-type semiconductor, in agreement with ab initio results and experimental observations.
Diophantine quadruples are sets of four distinct positive integers such that the product of any two is one less than a square. All known examples belong to an infinite set which can be constructed recursively. Some observations on these regular solutions are presented. In particular we see how factors of the four numbers satisfy relations which generalise the Stern-Brocot Tree. There is also an update on the search for rational Diophantine sextuples with five new examples.
In this paper we address the problem of view synthesis from large baseline light fields, by turning a sparse set of input views into a Multi-plane Image (MPI). Because available datasets are scarce, we propose a lightweight network that does not require extensive training. Unlike latest approaches, our model does not learn to estimate RGB layers but only encodes the scene geometry within MPI alpha layers, which comes down to a segmentation task. A Learned Gradient Descent (LGD) framework is used to cascade the same convolutional network in a recurrent fashion in order to refine the volumetric representation obtained. Thanks to its low number of parameters, our model trains successfully on a small light field video dataset and provides visually appealing results. It also exhibits convenient generalization properties regarding both the number of input views, the number of depth planes in the MPI, and the number of refinement iterations.
We present the first part of a new catalog of variable stars (OIII-CVS) compiled from the data collected in the course of the third phase of the Optical Gravitational Lensing Experiment (OGLE-III). In this paper we describe the catalog of 3361 classical Cepheids detected in the ~40 square degrees area in the Large Magellanic Cloud. The sample consists of 1848 fundamental-mode (F), 1228 first-overtone (1O), 14 second-overtone (2O), 61 double-mode F/1O, 203 double-mode 1O/2O, 2 double-mode 1O/3O, and 5 triple-mode classical Cepheids. This sample is supplemented by the list of 23 ultra-low amplitude variable stars which may be Cepheids entering or exiting instability strip.   The catalog data include VI high-quality photometry collected since 2001, and for some stars supplemented by the OGLE-II photometry obtained between 1997 and 2000. We provide basic parameters of the stars: coordinates, periods, mean magnitudes, amplitudes and parameters of the Fourier light curve decompositions. Individual objects of particular interest are discussed, including single-mode second-overtone Cepheids, multiperiodic pulsators with unusual period ratios or Cepheids in eclipsing binary systems.   We discuss the variations of the Fourier coefficients with periods and point out on the sharp feature for periods around 0.35 days of first-overtone Cepheids, which can be explained by the occurrence of 2:1 resonance between the first and fifth overtones. Similar behavior at P=3 days for 1O Cepheids and P=10 days for F Cepheids are also interpreted as an effect of resonances between two radial modes. We fit the period-luminosity relations to our sample of Cepheids and compare these functions with previous determinations.
Ferroelectric domain imaging with piezoresponse force microscopy (PFM) relies on the converse piezoelectric effect: a voltage applied to the sample leads to mechanical deformations. In case of PFM one electrode is realized by the tip, therefore generating a strongly inhomogeneous electric field distribution inside the sample which reaches values up to $10^8 $V/m directly underneath the apex of the tip. Although often assumed, this high electric field does not lead to an enhancement of the piezoelectric deformation of the sample. On the contrary, internal clamping of the material reduces the observed deformation compared to the theoretically expected value which depends only on the voltage thus being independent of the exact field distribution.
It is proved that accelerating nondiffracting gravitational Airy wave--packets are solutions of linearized gravity. It is also showed that Airy functions are exact solutions to Einstein equations for non--accelerating nondiffracting gravitational wave--packets.
We study fiber functors on Tannakian categories which are equipped with a grading or a filtration. Our goal is to give a comprehensive set of foundational results about such functors. A main result is that each filtration on a fiber functor can be split by a grading fpqc-locally on the base scheme.
Tungsten trioxide (WO$_3$) is a paradigmatic electrochromic material, whose peculiar optical properties in the presence of oxygen vacancies or intercalated alkali atoms have been observed and investigated for a long time. In this paper we propose a rationalization of experiments based on first-principles calculations of optical and electrical properties of oxygen deficient (reduced) WO$_3$. Our approach is based on a parameter-free dielectric-dependent hybrid density functional methodology, used in combination with the charge transition levels formalism, for studying excitation mechanisms in the presence of defects. Our results indicate that oxygen vacancies lead to a different physics in $\gamma$-monoclinic WO$_3$, depending on the orientation of the W-O-W chain where the vacancy is created, thus evidencing strong anisotropic effects rooted in the peculiar structural properties of the original nondefective monoclinic cell. Different types of oxygen vacancies can hence be classified on the basis of the calculated ground state properties, electronic structure, and excitation/emission energies, giving a satisfactory explanation to a range of experimental observations made on oxygen deficient WO$_3$.
Binary systems anchor many of the fundamental relations relied upon in asteroseismology. Masses and radii are rarely constrained better than when measured via orbital dynamics and eclipse depths. Pulsating binaries have much to offer. They are clocks, moving in space, that encode orbital motion in the Doppler-shifted pulsation frequencies. They offer twice the opportunity to obtain an asteroseismic age, which is then applicable to both stars. They enable comparative asteroseismology -- the study of two stars by their pulsation properties, whose only fundamental differences are the mass and rotation rates with which they were born. In eccentric binaries, oscillations can be excited tidally, informing our knowledge of tidal dissipation and resonant frequency locking. Eclipsing binaries offer benchmarks against which the asteroseismic scaling relations can be tested. We review these themes in light of both observational and theoretical developments recently made possible by space-based photometry.
The recently measured experimental data of $^{79,81,83}$Se isotopes have been interpreted in terms of shell model calculations. The calculations have been performed in ${f_{5/2}pg_{9/2}}$ space with the recently derived interactions, namely with JUN45 and jj44b. To study the importance of the proton excitations across the $Z=28$ shell in this region. We have also performed calculation in ${fpg_{9/2}}$ valence space using an ${fpg}$ effective interaction with $^{48}$Ca core and imposing a truncation. Excitation energies, $B(2)$ values, quadrupole moments and magnetic moments are compared with experimental data when available. Present study reveals the importance of proton excitations across the $Z=28$ shell for predicting quadrupole and magnetic moments.
We present the systematic study of the resonant tunneling spectroscopy on a series of ferromagnetic-semiconductor Ga1-xMnxAs with the Mn content x from ~0.01 to 3.2%. The Fermi level of Ga1-xMnxAs exists in the band gap in the whole x region. The Fermi level is closest to the valence band (VB) at x=1.0% corresponding to the onset of ferromagnetism near the metal-insulator transition (MIT), but it moves away from the VB as x increasing or decreasing from 1.0%. This anomalous behavior of the Fermi level indicates that the ferromagnetism and MIT emerge in the Mn-derived impurity band.