ShantanuT01/DACTYL-Pretraining huggingface dataset:
A generalized strong external difference family (briefly $(v, m; k_1,\dots,k_m; \lambda_1,\dots,\lambda_m)$-GSEDF) was introduced by Paterson and Stinson in 2016. In this paper, we construct some new GSEDFs for $m=2$ and use them to obtain some results on graph decomposition. We also give some nonexistence results for GSEDFs. Especially, we prove that a $(v, 3;k_1,k_2,k_3; \lambda_1,\lambda_2,\lambda_3)$-GSEDF does not exist when $k_1+k_2+k_3< v$.
Let $\{V_q\}_{q}$ be a complex one-parameter family of smooth hypersurfaces in a toric variety. In this paper, we give a concrete description of the monodromy transformation of $\{V_q\}_q$ around $q=\infty$ in terms of tropical geometry. The main tool is the tropical localization introduced by Mikhalkin.
We present preliminary results of observations made, during the spring of 1996, with the 3-m liquid mirror telescope of the NASA Orbital Debris Observatory. A 20-arcmin-wide strip of sky was observed at latitude of 32deg56 N using 10 narrow-band filters. Although the detector and the optical corrector were not optimized for astronomical observations, valuable information could be extracted down to magnitude 19 in R. From these observations we are generating a catalog of positions and AB magnitudes of objects in the strip. In this present work, we show images, maps and counts representative of the dataset.
We discuss the laser theory for a single-mode laser with nonlinear gain. We focus in particular on a micromaser which is pumped with a dilute beam of excited atoms crossing the laser cavity. In the weak-coupling regime, an expansion in the coupling strength is developed that preserves the Lindblad form of the master equation, securing the positivity of the density matrix. This expansion breaks rapidly down above threshold. This can be improved with an alternative approach, not restricted to weak coupling: the Lindblad operators are expanded in orthogonal polynomials adapted to the probability distribution for the atom-laser interaction time. Results for the photon statistics and the laser linewidth illustrate the theory.
In this paper, we consider the Schr\"odinger equation in one space-dimension with potential and we aim at exhibiting dynamic interaction phenomena produced by the potential. To this end, we focus our attention on the time-asymptotic behaviour of the two first terms of the Dyson-Phillips series, which gives a representation of the solution of the equation according to semigroup theory. The first term is actually the free wave packet while the second term corresponds to the wave packet resulting from a first interaction between the free solution and the potential. In order to follow a method developed in a series of papers and aiming at describing propagation features of wave packets, we suppose that both the potential and the initial datum are in bounded Fourier-frequency bands; in particular a family of potentials satisfying this hypothesis is constructed for illustration. We show then that the two terms are time-asymptotically localised in space-time cones which depend explicitly on the frequency bands. Since the inclination and the width of these cones indicate the time-asymptotic motion and dispersion of the two terms, our approach permits to highlight interaction phenomena produced by the potential.
We perform a phase space analysis of a non-minimally coupled modified gravity theory with the Lagrangian density of the form $\frac{1}{2} f_{1}(R)+[1+\lambda f_{2}(R)]{{\cal{L}}_{m}}$, where $f_1(R)$ and $f_2(R)$ are arbitrary functions of the curvature scalar $R$ and ${{\cal{L}}_{m}}$ is the matter Lagrangian density. We apply the dynamical system approach to this scenario in two particular models. In the first model we assume $f_1(R)=2R$ with a general form for $f_2(R)$ and set favorable values for effective equation of state parameter which is related to the several epochs of the cosmic evolution and study the critical points and their stability in each cosmic eras. In the second case, we allow the $f_1(R)$ to be an arbitrary function of $R$ and set $f_2(R)=2R$. We find the late time attractor solution for the model and show that this model has a late time accelerating epoch and an acceptable matter era.
To further reduce the lattice thermal conductivity of thermoelectric materials, the technique of embedding nano-inclusions into bulk matrix materials, in addition to point defect scattering via alloying, was widely applied. Differential Effective Medium (DEM) method was employed to calculate two-phase heterogeneous systems. However, in most effective medium treatment, the interface scattering of matrix phonons by embedded nanoparticle was underestimated by adopting particle's projected area as scattering cross-section. Herein, modified cross-section calculations, as well as grain sizes dispersions, are applied in DEM, with the calculations then validated by comparing with Monte-Carlo simulations and existing experimental data. Predictions of lattice thermal conductivity reduction on in-situ formed Full Heusler(FH)/Half Heusler(HH) nano/matrix system are discussed.
Continuous-time quantum error correction (CTQEC) is a technique for protecting quantum information against decoherence, where both the decoherence and error correction processes are considered continuous in time. Given any [[n,k,d]] quantum stabilizer code, we formulate a class of protocols to implement CTQEC, involving weak coherent measurements and weak unitary corrections. Under this formalism, we show that the minimal required size of the ancillary system is n-k+1 qubits, and we propose one scheme that meets this minimal requirement. Furthermore, we compare our method with other known schemes, and show that a particular measure of performance described in this paper is better when using our method.
We study the asymptotics of a Markovian system of $N \geq 3$ particles in $[0,1]^d$ in which, at each step in discrete time, the particle farthest from the current centre of mass is removed and replaced by an independent $U [0,1]^d$ random particle. We show that the limiting configuration contains $N-1$ coincident particles at a random location $\xi_N \in [0,1]^d$. A key tool in the analysis is a Lyapunov function based on the squared radius of gyration (sum of squared distances) of the points. For d=1 we give additional results on the distribution of the limit $\xi_N$, showing, among other things, that it gives positive probability to any nonempty interval subset of $[0,1]$, and giving a reasonably explicit description in the smallest nontrivial case, N=3.
We carried out Heyd-Scuseria-Ernzerhof hybrid density functional theory plane wave supercell calculations in wurtzite aluminum nitride in order to characterize the geometry, formation energies, transition levels and hyperfine tensors of the nitrogen split interstitial defect. The calculated hyperfine tensors may provide useful fingerprint of this defect for electron paramagnetic resonance measurement.
We present a method to compute the geometric Picard rank of a $K3$ surface over $\bbQ$. Contrary to a widely held belief, we show it is possible to verify Picard rank $1$ using reduction only at a single prime. Our method is based on deformation theory for invertible sheaves.
Lev A. Borisov has shown that the class of the affine line is a zero divisor in the Grothendieck ring of algebraic varieties over complex numbers. We improve the final formula by removing a factor.
For the Bd meson system, CP, T and CPT indirect violation can be described using two physical parameters, epsilon and delta. The traditional observables based on flavour tag and used in the kaon system, are not helpful in the Bd case, and new asymmetries have to be introduced. Here such alternative observables, based on CP tag, are presented, together with the first estimation on the sensitivity that current asymmetric B-factories can achieve on their measurement.
We show that hydrodynamical and field approaches in theory of cosmological scalar perturbations are equivalent for a single medium. We also give relations between notations introduced by V. Lukash, J. Bardeen, J. Bardeen et al. and G. Chibisov and V. Mukhanov.
We study some structural aspects of the evolution equations with Pomeron loops recently derived in QCD at high energy and for a large number of colors, with the purpose of clarifying their probabilistic interpretation. We show that, in spite of their appealing dipolar structure and of the self-duality of the underlying Hamiltonian, these equations cannot be given a meaningful interpretation in terms of a system of dipoles which evolves through dissociation (one dipole splitting into two) and recombination (two dipoles merging into one). The problem comes from the saturation effects, which cannot be described as dipole recombination, not even effectively. We establish this by showing that a (probabilistically meaningful) dipolar evolution in either the target or the projectile wavefunction cannot reproduce the actual evolution equations in QCD.
In this note we develop tools to study the Cauchy problem for the system of thermo-elasticity in higher dimensions. The theory is developed for general homogeneous anisotropic media under non-degeneracy conditions.   For degenerate cases a method of treatment is sketched and for the cases of cubic media and hexagonal media detailed studies are provided.
The exact diagonalization and the variational cluster approximation (VCA) are used to study the nature of a novel Mott insulator induced by a strong spin-orbit coupling for a two-dimensional three-band Hubbard model consisting of the $t_{2g}$ manifold of $5d$ orbitals. To characterize the ground state, we introduce a local Kramer's doublet which can represent a state with effective angular momentum $J_{\rm eff}=|{\bm S}-{\bm L}|=1/2$ as well as spin $S=1/2$. Our systematic study of the pseudo-spin structure factor defined by the Kramer's doublet shows that the $J_{\rm eff}=1/2$ Mott insulator is smoothly connected to the $S=1/2$ Mott insulator. Using the Kramer's doublet as a variational state for the VCA, we examine the one-particle excitations for the Mott insulating phase. These results are compared with recent experiments on Sr$_2$IrO$_4$.
This paper proposes a method for video smoke detection using synthetic smoke samples. The virtual data can automatically offer precise and rich annotated samples. However, the learning of smoke representations will be hurt by the appearance gap between real and synthetic smoke samples. The existed researches mainly work on the adaptation to samples extracted from original annotated samples. These methods take the object detection and domain adaptation as two independent parts. To train a strong detector with rich synthetic samples, we construct the adaptation to the detection layer of state-of-the-art single-model detectors (SSD and MS-CNN). The training procedure is an end-to-end stage. The classification, location and adaptation are combined in the learning. The performance of the proposed model surpasses the original baseline in our experiments. Meanwhile, our results show that the detectors based on the adversarial adaptation are superior to the detectors based on the discrepancy adaptation. Code will be made publicly available on http://smoke.ustc.edu.cn. Moreover, the domain adaptation for two-stage detector is described in Appendix A.
The paper demonstrates that a two-dimensional ballistic nanodevice in which the electron gas satisfies either the Schroodinger equation (as in quantum wells in common semiconductor heterostructures) or the Dirac equation (as in graphene) is able to rectify an electric signal if the device has a non-uniform cross section, for instance a taper configuration. No p-n junctions or dissimilar electrodes are necessary for rectification.
We apply simple analyses techniques developed for the study of complex networks to the study of the cosmic web, the large scale galaxy distribution. In this paper, we measure three network centralities (ranks of topological importance), Degree Centrality (DC), Closeness Centrality (CL), and Betweenness Centrality (BC) from a network built from the Cosmological Evolution Survey (COSMOS) catalog. We define 8 galaxy populations according to the centrality measures; Void, Wall, and Cluster by DC, Main Branch and Dangling Leaf by BC, and Kernel, Backbone, and Fracture by CL. We also define three populations by voronoi tessellation density to compare these with the DC selection. We apply the topological selections to galaxies in the (photometric) redshift range $0.91<z<0.94$ from the COSMOS survey, and explore whether the red and blue galaxy populations show differences in color, star-formation rate (SFR) and stellar mass in the different topological regions. Despite the limitations and uncertainties associated with using photometric redshift and indirect measurements of galactic parameters, the preliminary results illustrate the potential of network analysis. The coming future surveys will provide better statistical samples to test and improve this "network cosmology".
A partial lattice P is ideal-projective, with respect to a class C of lattices, if for every K $\in$ C and every homomorphism $\phi$ of partial lattices from P to the ideal lattice of K, there are arbitrarily large choice functions f : P $\rightarrow$ K for $\phi$ that are also homomorphisms of partial lattices. This extends the traditional concept of (sharp) transferability of a lattice with respect to C. We prove the following: (1) A finite lattice P, belonging to a variety V, is sharply transferable with respect to V iff it is projective with respect to V and weakly distributive lattice homomorphisms, iff it is ideal-projective with respect to V. (2) Every finite distributive lattice is sharply transferable with respect to the class R mod of all relatively complemented modular lattices. (3) The gluing D 4 of two squares, the top of one being identified with the bottom of the other one, is sharply transferable with respect to a variety V iff V is contained in the variety M$\omega$ generated by all lattices of length 2. (4) D 4 is projective, but not ideal-projective, with respect to R mod. (5) D 4 is transferable, but not sharply transferable, with respect to the variety M of all modular lattices. This solves a 1978 problem of G. Gr\"atzer. (6) We construct a modular lattice whose canonical embedding into its ideal lattice is not pure. This solves a 1974 problem of E. Nelson.
Among the interfacial transport modulations to the LaAlO3/SrTiO3 (LAO/STO) heterostructure, mechanical strain has been proven to be an effective approach by growing the LAO/STO films on different substrates with varying lattice mismatches to STO. However, this lattice-mismatch-induced strain effect is static and biaxial, hindering the study of the strain effect in a dynamic way. In this work we realize dynamic and uniaxial strain to the LAO/STO oxide heterostructure at low temperature, through mechanical coupling from a magnetostrictive template. This anisotropic strain results in symmetry breaking at the interface and induces further splitting of the electronic band structure and therefore produces different conductivities along the x and y in-plane directions. In particular, we observe that along the strained direction the interface conductivity decreases by up to 70% under a tensile strain, while it increases by 6.8% under a compressive strain at 2 K. Also, it is revealed that the modulation on the interfacial transport property can be anisotropic, i.e., the resistance changes differently when an excitation current is parallel or perpendicular to the strain direction. This approach of strain engineering provides another degree of freedom for control of transport properties of oxide heterostructures and opens an additional way to investigate strain effects in materials science.
One-shot NAS method has attracted much interest from the research community due to its remarkable training efficiency and capacity to discover high performance models. However, the search spaces of previous one-shot based works usually relied on hand-craft design and were short for flexibility on the network topology. In this work, we try to enhance the one-shot NAS by exploring high-performing network architectures in our large-scale Topology Augmented Search Space (i.e., over 3.4*10^10 different topological structures). Specifically, the difficulties for architecture searching in such a complex space has been eliminated by the proposed stabilized share-parameter proxy, which employs Stochastic Gradient Langevin Dynamics to enable fast shared parameter sampling, so as to achieve stabilized measurement of architecture performance even in search space with complex topological structures. The proposed method, namely Stablized Topological Neural Architecture Search (ST-NAS), achieves state-of-the-art performance under Multiply-Adds (MAdds) constraint on ImageNet. Our lite model ST-NAS-A achieves 76.4% top-1 accuracy with only 326M MAdds. Our moderate model ST-NAS-B achieves 77.9% top-1 accuracy just required 503M MAdds. Both of our models offer superior performances in comparison to other concurrent works on one-shot NAS.
We analyse the evolution of the Intergalactic Medium (IGM) by means of an extended set of large box size hydrodynamical simulations which include pre-heating. We focus on the properties of the z~2 Lyman-alpha forest and on the population of clusters and groups of galaxies at z=0. We investigate the distribution of voids in the Lyman-alpha flux and the entropy-temperature relation of galaxy groups, comparing the simulation results to recent data from high-resolution quasar spectra and from X-ray observations. Pre-heating is included through a simple phenomenological prescription, in which at z=4 the entropy of all gas particles, whose overdensity exceeds a threshold value delta_h is increased to a minimum value K_fl. While the entropy level observed in the central regions of galaxy groups requires a fairly strong pre-heating, with K_fl>100 keV cm^2, the void statistics of the Lyman-alpha forest impose that this pre-heating should take place only in relatively high-density regions, in order not to destroy the cold filaments that give rise to the forest. We conclude that any injection of non-gravitational energy in the diffuse baryons should avoid low-density regions at high redshift and/or take place at relatively low redshift.
In this letter, we have assumed that the Universe is filled in tachyonic field with potential, which gives the acceleration of the Universe. For certain choice of potential, we have found the exact solutions of the field equations. We have shown the decaying nature of potential. From recently developed statefinder parameters, we have investigated the role of tachyonic field in different stages of the evolution of the Universe.
Path-dependent PDEs (PPDEs) are natural objects to study when one deals with non Markovian models. Recently, after the introduction of the so-called pathwise (or functional or Dupire) calculus (see [15]), in the case of finite-dimensional underlying space various papers have been devoted to studying the well-posedness of such kind of equations, both from the point of view of regular solutions (see e.g. [15, 9]) and viscosity solutions (see e.g. [16]). In this paper, motivated by the study of models driven by path-dependent stochastic PDEs, we give a first well-posedness result for viscosity solutions of PPDEs when the underlying space is a separable Hilbert space. We also observe that, in contrast with the finite-dimensional case, our well-posedness result, even in the Markovian case, applies to equations which cannot be treated, up to now, with the known theory of viscosity solutions.
We present a sub-grid model that emulates the magnetic dynamo operating in magnetized accretion disks. We have implemented this model in the general relativisic radiation magnetohydrodynamic (GRRMHD) code \koral, using results from local shearing sheet simulations of the magnetorotational instability to fix the parameters of the dynamo. With the inclusion of this dynamo, we are able to run 2D axisymmetric GRRMHD simulations of accretion disks for arbitrarily long times. The simulated disks exhibit sustained turbulence, with the poloidal and toroidal magnetic field components driven towards a state similar to that seen in 3D studies. Using this dynamo code, we present a set of long-duration global simulations of super-Eddington, optically-thick disks around non-spinning and spinning black holes. Super-Eddington disks around non-rotating black holes exhibit a surprisingly large efficiency, $\eta\approx0.04$, independent of the accretion rate, where we measure efficiency in terms of the total energy output, both radiation and mechanical, flowing out to infinity. Super-Eddington disks around spinning black holes are even more efficient, and appear to extract black hole rotational energy through a process similar to the Blandford-Znajek mechanism. All the simulated models are characterized by highly super-Eddington radiative fluxes collimated along the rotation axis. We also present a set of simulations that were designed to have Eddington or slightly sub-Eddington accretion rates ($\dot{M} \lesssim 2\dot M_{\rm Edd}$). None of these models reached a steady state. Instead, the disks collapsed as a result of runaway cooling, presumably because of a thermal instability.
The combination of the local-density approximation (LDA) with the rotationally invariant slave-boson theory (RISB) is used to investigate the realistic correlated electronic structure of Sr$_3$Ru$_2$O$_7$. From Wannier-downfolding the low-energy band structure to a three-band model for the Ru($t_{2g}$) states, the interacting problem is solved including intra- and inter-orbital Hubbard terms as well as spin-flip and pair-hopping interactions. Therewith it is possible to obtain valuable insight into the orbital occupations, relevant local spin multiplets and the fermiology with increasing correlation strength. Besides generic correlation-induced band-narrowing and -shifting, an intriguing quasiparticle structure close to the Fermi level is found in the neigborhood of the notorious $\gamma_2$ pocket in the Brillouin zone. Along the $\Gamma$$-$$X$ direction in {\bf k}-space, that structure appears very sensitive to electronic self-energy effects. The subtle sensitivity, connected also its manifest multi-orbital character, may put this very low-energy structure in context with the puzzling metamagnetic properties of the compound.
We have analyzed a large sample of clean blazars detected by Fermi Large Area Telescope (LAT). Using literature and calculation, we obtained intrinsic $\gamma$-ray luminosity excluding beaming effect, black hole mass, broad-line luminosity (used as a proxy for disk luminosity), jet kinetic power from "cavity" power and bulk Lorentz factor for parsec-scale radio emission, and studied the distributions of these parameters and relations between them. Our main results are as follows. (i) After excluding beaming effect and redshift effect, intrinsic $\gamma$-ray luminosity with broad line luminosity, black hole mass and Eddington ratio have significant correlations. Our results confirm the physical distinction between BL Lacs and FSRQs. (ii) The correlation between broad line luminosity and jet power is significant which supports that jet power has a close link with accretion. Jet power depends on both the Eddington ratio and black hole mass. We also obtain $LogL_{\rm BLR}\sim(0.98\pm0.07)Log P_{\rm jet}$ for all blazars, which is consistent with the theoretical predicted coefficient. These results support that jets are powered by energy extraction from both accretion and black hole spin (i.e., not by accretion only). (iii) For almost all BL Lacs, $P_{\rm jet}>L_{\rm disk}$; for most of FSRQs, $P_{\rm jet}<L_{\rm disk}$. The "jet-dominance" (parameterized as $\frac{P_{\rm jet}}{L_{\rm disk}}$) is mainly controlled by the bolometric luminosity. Finally, the radiative efficiency of $\gamma$-ray and properties of TeV blazars detected by Fermi LAT were discussed.