ShantanuT01/DACTYL-Pretraining huggingface dataset:
We construct a combinatorial model that is described by the cube recurrence, a nonlinear recurrence relation introduced by Propp, which generates families of Laurent polynomials indexed by points in $\mathbb{Z}^3$. In the process, we prove several conjectures of Propp and of Fomin and Zelevinsky, and we obtain a combinatorial interpretation for the terms of Gale-Robinson sequences. We also indicate how the model might be used to obtain some interesting results about perfect matchings of certain bipartite planar graphs.
We study localized plasma configurations in 3+1 dimensional massive field theories obtained by Scherk-Schwarz compactification of 4+1 dimensional CFT to predict the thermodynamic properties of localized blackholes and blackrings in Scherk-Schwarz compactified $AdS_6$ using the AdS/CFT correspondence. We present an exact solution to the relativistic Navier-Stokes equation in the thin ring limit of the fluid configuration. We also perform a thorough numerical analysis to obtain the thermodynamic properties of the most general solution. Finally we compare our results with the recent proposal for the phase diagram of blackholes in six flat dimensions and find some similarities but other differences.
Recent simulations and observations have shown large scale filaments in the cosmic web connecting nodes, with accreting materials (baryonic and dark matter) flowing through them. Current high sensitivity observations also show that the propagation of shocks through filaments can heat them up, and make filaments visible between two or more galaxy clusters or around massive clusters, based on optical and/or X-ray observations. We are reporting here the special case of the cluster A3017 associated with a hot filament. The temperature of the filament is 3.4$^{-0.77}_{+1.30}$ ~keV and its length is $\sim$ 1 Mpc. We have analysed its archival {\it Chandra} data and report various properties. We also analysed GMRT 235/610 MHz radio data. Radio observations have revealed symmetric two-sided lobes which fill cavities in the A3017 cluster core region, associated with central AGN. In the radio map, we also noticed a peculiar linear vertical radio structure in the X-ray filament region which might be associated with a cosmic filament shock. This radio structure could be a radio phoenix or old plasma where an old relativistic population is re-accelerated by shock propagation. Finally we put an upper limit on the radio luminosity of the filament region.
Simultaneous Localization and Mapping (SLAM) have made the real-time dense reconstruction possible increasing the prospects of navigation, tracking, and augmented reality problems. Some breakthroughs have been achieved in this regard during past few decades and more remarkable works are still going on. This paper presents an overview of SLAM approaches that have been developed till now. Kinect Fusion algorithm, its variants, and further developed approaches are discussed in detailed. The algorithms and approaches are compared for their effectiveness in tracking and mapping based on Root Mean Square error over online available datasets.
Using a synthesis of the functional integral and operator approaches we discuss the fermion-boson mapping and the role played by the Bose field algebra in the Hilbert space of two-dimensional gauge and anomalous gauge field theories with massive fermions. In the $QED_2$ with quartic self-interaction among massive fermions, the use of an auxiliary vector field introduces a redundant Bose field algebra that should not be considered as an element of the intrinsic algebraic structure defining the model. In the anomalous chiral $QED_2$ with massive fermions the effect of the chiral anomaly leads to the appearance in the mass operator of a spurious Bose field combination. This phase factor carries no fermion selection rule and the expected absence of $\theta$-vacuum in the anomalous model is displayed from the operator solution. Even in the anomalous model with massive Fermi fields, the introduction of the Wess-Zumino field replicates the theory, changing neither its algebraic content nor its physical content.
We have investigated magnetocaloric effect in double perovskite Gd2NiMnO6 (GNMO) and Gd2CoMnO6 (GCMO) samples by magnetic and heat capacity measurements. Ferromagnetic ordering is observed at ~130 K (~112 K) in GNMO (GCMO), while the Gd exchange interactions seem to dominate for T < 20 K. In GCMO, below 50 K, an antiferromagnetic behaviour due to 3d-4f exchnage interaction is observed. A maximum entropy (-{\Delta}SM) and adiabatic temperature change of ~35.5 J Kg-1 K-1 (~24 J Kg-1 K-1) and 10.5 K (6.5 K) is observed in GNMO (GCMO) for a magnetic field change of 7 T at low temperatures. Absence of magnetic and thermal hysteresis and their insulating nature make them promising for low temperature magnetic refrigeration.
We apply the machinery of projection lattices and von Neumann algebras to analyze the question of how modal interpretations can (and do) circumvent von Neumann's infamous 'no-hidden-variables' theorem.
In \cite{2012a}, Abdo and Dimitov defined the total irregularity of a graph $G=(V,E)$ as   \hskip3.3cm $\rm irr_{t}$$(G) = \frac{1}{2}\sum_{u,v\in V}|d_{G}(u)-d_{G}(v)|, $   \noindent where $d_{G}(u)$ denotes the vertex degree of a vertex $u\in V$. In this paper, we investigate the minimal total irregularity of the connected graphs, determine the minimal, the second minimal, the third minimal total irregularity of trees, unicyclic graphs, bicyclic graphs on $n$ vertices, and propose an open problem for further research.
This paper is concerned with the critical conditions of nonlinear elliptic equations with weights and the corresponding integral equations with Riesz potentials and Bessel potentials. We show that the equations and some energy functionals are invariant under the scaling transformation if and only if the critical conditions hold. In addition, the Pohozaev identity shows that those critical conditions are the necessary and sufficient conditions for existence of the finite energy positive solutions or weak solutions. Finally, we discuss respectively the existence of the negative solutions of the $k$-Hessian equations in the subcritical case, critical case and supercritical case. Here the Serrin exponent and the critical exponent play key roles.
Nowadays, random telegraph signals play an important role in integrated circuit performance variability, leading for instance to failures in memory circuits. This problem is related to the successive captures and emissions of electrons at the many traps stochastically distributed at the silicon-oxide (Si-SiO2) interface of MOS transistors. In this paper we propose a novel analytical and numerical approach to statistically describe the fluctuations of current due to random telegraph signal in time domain. Our results include two distinct situations: when the density of interface trap density is uniform in energy, and when it is an u-shape curve as prescribed in literature, here described as simple quadratic function. We establish formulas for relative error as function of the parameters related to capture and emission probabilities. For a complete analysis experimental u-shape curves are used and compared with the theoretical aproach.
The quantum mechanical position operators, and their products, are not well-defined in systems obeying periodic boundary conditions. Here we extend the work of Resta who developed a formalism to calculate the electronic polarization as an expectation value of a many-body operator, to include higher multipole moments, e.g., quadrupole and octupole. We define $n$-th order multipole operators whose expectation values can be used to calculate the $n$-th multipole moment when all of the lower moments are vanishing (modulo a quantum). We show that changes in our operators are tied to flows of $n-1$-st multipole currents, and encode the adiabatic evolution of the system in the presence of an $n-1$-st gradient of the electric field. Finally, we test our operators on a set of tightbinding models to show that they correctly determine the phase diagrams of topological quadrupole and octupole models, capture an adiabatic quadrupole pump, and distinguish a bulk quadrupole moment from other mechanisms that generate corner charges.
B037 is of interest because it is both the most luminous and the most highly reddened cluster known in M31. Images of deep observations and of highly spatial resolutions with the Advanced Camera for Surveys on the {\sl HST} firstly show that this cluster is crossed by a dust lane. Photometric data in the F606W and F814W filters obtained in this paper provide that, colors of ($\rm {F606W-F814W}$) in the dust lane are redder $\sim 0.4$ mags than ones in the other regions of B037. The {\sl HST} images show that, this dust lane seems to be contained in B037, not from the M31 disk or the Milky Way. As we know, the formation of dust requires gas with a rather high metallicity. However, B037 has a low metallicity to be $\rm [Fe/H]=-1.07\pm 0.20$. So, it seems improbable that the observed dust lane is physically associated with B037. It is clear that the origin of this dust lane is worthy of future study. In addition, based on these images, we present the precise variation of ellipticity and position angle, and of surface brightness profile, and determine the structural parameters of B037 by fitting a single-mass isotropic King model. In the F606W filter, we derive the best-fitting scale radius, $r_0=0.56\pm0.02\arcsec~(=2.16\pm0.08~\rm{pc})$, a tidal radius, $r_t=8.6\pm0.4\arcsec~(=33.1\pm1.5~\rm{pc})$, and a concentration index $c=\log (r_t/r_0)=1.19\pm0.02$. In the F814W filter, we derive $r_0=0.56\pm0.01\arcsec~(=2.16\pm0.04~\rm{pc})$, $r_t=8.9\pm0.3\arcsec~(=34.3\pm1.2~\rm{pc})$, and $c=\log (r_t/r_0)=1.20\pm0.01$. The extinction-corrected central surface brightness is $\mu_0=13.53\pm 0.03~{\rm mag~arcsec^{-2}}$ in the F606W filter, and $12.85\pm 0.03~{\rm mag~arcsec^{-2}}$ in the F814W filter, respectively.
The well-studied M9 dwarf TVLM 513-46546 is a rapid rotator (P_rot ~ 2 hr) hosting a stable, dipolar magnetic field of ~3 kG surface strength. Here we report its detection with ALMA at 95 GHz at a mean flux density of $56 \pm 12$ uJy, making it the first ultracool dwarf detected in the millimeter band, excluding young, disk-bearing objects. We also report flux density measurements from unpublished archival VLA data and new optical monitoring data from the Liverpool Telescope. The ALMA data are consistent with a power-law radio spectrum that extends continuously between centimeter and millimeter wavelengths. We argue that the emission is due to the synchrotron process, excluding thermal, free-free, and electron cyclotron maser emission as possible sources. During the interval of the ALMA observation that phases with the maximum of the object's optical variability, the flux density is higher at a ~1.8 sigma significance level. These early results show how ALMA opens a new window for studying the magnetic activity of ultracool dwarfs, particularly shedding light on the particle acceleration mechanism operating in their immediate surroundings.
The Kepler Input Catalog (KIC) provides reddening estimates for its stars, based on the assumption of a simple exponential dusty screen. This project focuses on evaluating and improving these reddening estimates for the KIC's giant stars, for which extinction is a much more significant concern than for the nearby dwarf stars. We aim to improve the calibration (and thus consistency) amongst various photometric and spectroscopic temperatures of stars in the Kepler field by removing systematics due to incorrect extinction assumptions. The revised extinction estimates may then be used to derive improved stellar and planetary properties. We plan to eventually use the large number of KIC stars as probes into the structure and properties of the Galactic ISM.
We define a hierarchy of dynamic relaxed gas spheres as solutions of the Poisson equation coupled to a hierarchy of approximations of the Liouville equation leading, when this equation is satisfied, to the well-known isothermal gas spheres in the static case, but also to a new form of dynamic maximum relaxation. The two previous steps of the hierarchy correspond to an increasing degree of local relaxation at the center of the configuration.
We propose a systematic approach to the systems of correlated electrons, the so-called $\mathbf{k}$-DE-GWF method, based on reciprocal-space ($\mathbf{k}$-resolved) diagrammatic expansion of the variational Gutzwiller-type wave function for parametrized models of correlated fermions. The present approach, in contrast to either variational Monte-Carlo (VMC), or the recently developed real-space diagrammatic expansion of the Gutzwiller-type wave function (direct-space DE-GWF technique), is applicable directly in the thermodynamic limit and thus is suitable for describing selected singular features of the wave-vector-dependent quantities. We employ the $\mathbf{k}$-DE-GWF method to extract the non-analytic part of the two leading moments of the fermion spectral-density function across the (two-dimensional) Brillouin zone for the Hubbard model and away from the half-filling. Those moments are used to evaluate the nodal quasiparticle velocities and their spectral weights in the correlated superconducting state. The two velocities determined in that manner exhibit scaling with the electron concentration qualitatively different from that obtained earlier for the excited states of the high-$T_c$ cuprates within the projected quasi-particle ansatz, and the results are in a very good quantitative agreement with experimental data if interpreted as those characterizing the spectrum below and above the observed kink. We provide a detailed discussion of the two gaps and two excitation branches (two velocities) appearing naturally within our DE-GWF approach. The two separate sets of characteristics distinguish the renormalized quasiparticle states very close to the Fermi surface from the deeper correlated-state properties. Also, an enhancement of the $\mathbf{k}$-dependent magnetic susceptibility is shown to contain a spin-fluctuation contribution within our language.
It has been suggested that optically thin and geometrically thick accretion flows are responsible for the observed radio/X-ray luminosity relation of the X-ray bright galactic nuclei. If this is the case then central supermassive black hole masses can be estimated directly from measurements of the core radio luminosity and the X-ray luminosity, provided that properties of such accretion flows are known. Calculated ratios of the luminosities are presented in cases of the standard ADAF model and modified ADAF models, in which a truncation of inner parts of the flows and winds causing a reduction of the infalling matter are included. We compare the observed ratio of the luminosities with predictions from models of optically thin accretion flows. We also discuss the possible effects of the convection in ADAFs. We confirm that the supermassive black hole (SMBH) mass estimate is possible with the radio/X-ray luminosity relation due to ADAF models in the absence of a radio jet. We find that observational data are insufficient to distinguish the standard ADAF model from its modified models. However, the ADAF model with convection is inconsistent with observations, unless microphysics parameters are to be substantially changed. High resolution radio observations are required to avoid the contamination of other components, such as, a jet component. Otherwise, the SMBH mass is inclined to be over-estimated.
We present phase-resolved spectroscopies based on Hilbert-Huang transform (HHT) for millihertz quasi-periodic oscillations (mHz QPOs) in 4U 1636-536. This ~8 mHz QPO can be detected approximately several thousand seconds before a type-I X-ray burst. It was interpreted as marginally stable burning on the neutron-star surface. In this study, we used HHT to analyze the data collected by XMM-Newton between 2007 and 2009. HHT is a powerful tool that enables us to obtain instantaneous frequency, amplitude and phase of non-stationary periodicity phenomena, such as QPOs. With well-defined phases, the oscillation profile of the ~8 mHz QPO for 4U 1636-53 can be precisely revealed. In addition to the oscillation profile, phase-resolved spectra for the complete cycle are constructed. From the correlation between spectral parameters and fluxes, we find that the oscillation is mainly attributed to the variations of emitting area of blackbody radiation in three out of four observations with mHz QPO detections whereas the other one shows concurrent variation of temperature and flux with a constant emitting area. Although the cause of the difference is not clear, it might be related to the spectral state of the source that can be observed from hard color difference in color-color diagram.
Let $S$ be a smooth projective surface on a smooth threefold $X$ such that $X$ has Picard rank 1 and NS$(S)$ is generated by the restriction of divisors from X. We show that if $X$ satisfies the Bogomolov-Gieseker type inequality for tilt semistable objects conjectured by Bayer-Macr\`i-Stellari, then the minimum degree of a dominant rational map $S\dashrightarrow\mathbb{P}^2$ is either relatively large or determined by a net of curves of low degree on $S$. As one application, we prove that the complete intersection of three very general quadrics in $\mathbb{P}^5$ has degree of irrationality 4.
It has recently been shown that light can be stored in Bose-Einstein condensates for over a second. Here we propose a method for realizing a controlled phase gate between two stored photons. The photons are both stored in the ground state of the effective trapping potential inside the condensate. The collision-induced interaction is enhanced by adiabatically increasing the trapping frequency and by using a Feshbach resonance. A controlled phase shift of $\pi$ can be achieved in one second.
Single-layer transition metal dichalcogenide (TMD) WSe2 has recently attracted a lot of attention because it is a 2D semiconductor with a direct band-gap. Due to low doping levels it is intrinsic and shows ambipolar transport. This opens up the possibility to realize devices with the Fermi level located in valence band, where the spin/valley coupling is strong and leads to new and interesting physics. As a consequence of its intrinsically low doping, large Schottky barriers form between WSe2 and metal contacts, which impede the injection of charges at low temperatures. Here, we report on the study of single-layer WSe2 transistors with a polymer electrolyte gate (PEO:LiClO4). Polymer electrolytes allow the charge carrier densities to be modulated to very high values, allowing the observation of both the electron- and the hole-doped regimes. Moreover, our ohmic contacts formed at low temperatures allow us to study the temperature dependence of electron and hole mobilities. At high electron densities, a re-entrant insulating regime is also observed, a feature which is absent at high hole densities.
An infinite family of axisymmetric charged dust disks of finite extension is presented. The disks are obtained by solving the vacuum Einstein-Maxwell equations for conformastatic spacetimes, which are characterized by only one metric function. In order to obtain the solutions, it is assumed that the metric function and the electric potential are functionally related and that the metric function is functionally dependent of another auxiliary function, which is taken as a solution of Laplace equation. The solutions for the auxiliary function are then taken as given by the infinite family of generalized Kalnajs disks recently obtained by Gonz\'alez and Reina (MNRAS 371, 1873, 2006), which is expressed in terms of the oblate spheroidal coordinates and represents a well behaved family of finite axisymmetric flat galaxy models. The so obtained relativistic thin disks have then a charge density that is equal, except maybe by a sign, to their mass density, in such a way that the electric and gravitational forces are in exact balance. The energy density of the disks is everywhere positive and well behaved, vanishing at the edge. Accordingly, as the disks are made of dust, their energy-momentum tensor it agrees with all the energy conditions.
The Nernst-Planck-Navier-Stokes system models electrodiffusion of ions in a fluid. We prove global existence of solutions in bounded domains in three dimensions with either blocking (no-flux) or uniform selective (special Dirichlet) boundary conditions for ion concentrations. The global existence of strong solutions is established for initial conditions that are sufficiently small perturbations of steady state solutions. The solutions remain close to equilibrium in strong norms. The main two steps of the proof are (1) the decay of the sum of relative entropies (Kullback-Leibler divergences) and (2) the control of $L^2$ norms of deviations by the sum of relative entropies.
Lepton-flavor-violating decays of the type L->l gamma gamma (mu->e gamma gamma, tau->e gamma gamma, and tau->mu gamma gamma) are proposed as new probes of R-parity-violating supersymmetry. Non-penguin diagrams with a sneutrino that decays into two photons via a triangle graph might trigger such decays even in the absence of the corresponding radiative decays into one photon only, e.g. mu->e gamma. Thus, processes of the type L->l gamma gamma may provide an independent probe of new flavor physics.
Molecular beam epitaxy technique has been used to deposit a single layer and a bilayer of MoSe 2 on sapphire. Extensive characterizations including in-situ and ex-situ measurements show that the layered MoSe 2 grows in a scalable manner on the substrate and reveals characteristics of a stoichiometric 2H-phase. The layered MoSe 2 exhibits polycrystalline features with domains separated by defects and boundaries. Temperature and magnetic field dependent resistivity measurements unveil a carrier hopping character described within two-dimensional variable range hopping mechanism. Moreover, a negative magnetoresistance was observed, stressing a fascinating feature of the charge transport under the application of a magnetic field in the layered MoSe 2 system. This negative magnetoresistance observed at millimeter-scale is similar to that observed recently at room temperature inWS2 flakes at a micrometer scale [Zhang et al., Appl. Phys. Lett. 108, 153114 (2016)]. This scalability highlights the fact that the underlying physical mechanism is intrinsic to these two-dimensional materials and occurs at very short scale.
Motivated by Popescu's example of hidden nonlocality, we elaborate on the conjecture that quantum states that are intuitively nonlocal, i.e., entangled, do not admit a local causal hidden variables model. We exhibit quantum states which either (i) are nontrivial counterexamples to this conjecture or (ii) possess a new kind of more deeply hidden irreducible nonlocality. Moreover, we propose a nonlocality complexity classification scheme suggested by the latter possibility. Furthermore, we show that Werner's (and similar) hidden variables models can be extended to an important class of generalized observables. Finally a result of Fine on the equivalence of stochastic and deterministic hidden variables is generalized to causal models.
The basic ideas and some recent developments of the chiral perturbation theory approach to hadron dynamics at low-energies are reviewed. (Invited talk at the HADRON'93 Conference Como, Italy June 1993.)
Quantum canonical transformations are defined in analogy to classical canonical transformations as changes of the phase space variables which preserve the Dirac bracket structure. In themselves, they are neither unitary nor non-unitary. A definition of quantum integrability in terms of canonical transformations is proposed which includes systems which have fewer commuting integrals of motion than degrees of freedom. The important role of non-unitary transformations in integrability is discussed.