ShantanuT01/DACTYL-Pretraining huggingface dataset:
We describe the effects of phase coherence on transport and thermodynamic properties of a disordered conducting network. In analogy with weak-localization correction, we calculate the phase coherence contribution to the magnetic response of mesoscopic metallic isolated networks. It is related to the return probability for a diffusive particle on the corresponding network. By solving the diffusion equation on various types of networks, including a ring with arms, an infinite square network or a chain of connected rings, we deduce the magnetic response. As it is the case for transport properties --weak-localization corrections or universal conductance fluctuations-- the magnetic response can be written in term of a single function S called spectral function which is related to the spatial average of the return probability on the network. We have found that the magnetization of an ensemble of CONNECTED rings is of the same order of magnitude as if the rings were disconnected.
This paper has been withdrawn by the author due to a the manuscript error.
The set of all electronic states that can be expressed as a single Slater determinant forms a submanifold, isomorphic to the Grassmannian, of the projective Hilbert space of wave functions. We explored this fact by using tools of Riemannian geometry of Grassmannians as described by Absil et. al [Acta App. Math. 80, 199 (2004)], to propose an algorithm that converges to a Slater determinant that is critical point of the overlap function with a correlated wave function. This algorithm can be applied to quantify the entanglement or correlation of a wave function. We show that this algorithm is equivalent to the Newton method using the standard parametrization of Slater determinants by orbital rotations, but it can be more efficiently implemented because the orbital basis used to express the correlated wave function is kept fixed throughout the iterations. We present the equations of this method for a general configuration interaction wave function and for a wave function with up to double excitations over a reference determinant. Applications of this algorithm to selected electronic systems are also presented and discussed.
A cascade of fully convolutional neural networks is proposed to segment multi-modal Magnetic Resonance (MR) images with brain tumor into background and three hierarchical regions: whole tumor, tumor core and enhancing tumor core. The cascade is designed to decompose the multi-class segmentation problem into a sequence of three binary segmentation problems according to the subregion hierarchy. The whole tumor is segmented in the first step and the bounding box of the result is used for the tumor core segmentation in the second step. The enhancing tumor core is then segmented based on the bounding box of the tumor core segmentation result. Our networks consist of multiple layers of anisotropic and dilated convolution filters, and they are combined with multi-view fusion to reduce false positives. Residual connections and multi-scale predictions are employed in these networks to boost the segmentation performance. Experiments with BraTS 2017 validation set show that the proposed method achieved average Dice scores of 0.7859, 0.9050, 0.8378 for enhancing tumor core, whole tumor and tumor core, respectively. The corresponding values for BraTS 2017 testing set were 0.7831, 0.8739, and 0.7748, respectively.
Supra-arcade downflows (SADs) are dark, teardrop-shaped features descending upon flare arcades. They are thought to be the results of magnetic reconnection, but the detailed formation mechanism of SADs and their relationship to flare energy release are still unclear. In this work, we explore the thermodynamical properties of SADs in the 2011 October 22 limb flare using the observations of the Solar Dynamics Observatory/Atmospheric Imaging Assembly and an improved Differential Emission Measure (DEM) technique. Different heating events around SADs are identified and the propagation speeds of plasma heating are calculated. The first heating event starts with the increase of the emission measure at temperatures higher than 5 MK, about 2.8 minutes before the arrival of the first studied SAD. Its propagation speed is about 140 km/s, a little faster than the speed of the SAD. However, the other two events have fast propagation speeds more than 700 km/s. We suspect that the first heating event can be explained by adiabatic compression, but the others may have different causes. Besides, we observed that SADs can push away their surrounding spikes. The formation of SADs is further explained on the basis of patchy and bursty magnetic reconnection that reconnection outflows may push away surrounding plasma and leave dark lanes behind them. The reliability of the DEM results, heating and cooling mechanisms, and other SAD explanations are discussed.
We extend on ideas from standard thermodynamics to show that temperature can be assigned to a general nonequilibrium quantum system. By choosing a physically motivated complete set of observables and expanding the system state thereupon, one can read a set of relevant, independent thermodynamic variables which include internal energy. This expansion allows us to read a nonequilibrium temperature as the partial derivative of the von Neumann entropy with respect to internal energy. We show that this definition of temperature is one of a set of thermodynamics parameters unambiguously describing the system state. It has appealing features such as positivity for passive states and consistency with the standard temperature for thermal states. By attributing temperature to correlations in a bipartite system, we obtain a universal relation which connects the temperatures of subsystems, total system as a whole, and correlation. All these temperatures can be different even when the composite system is in a well-defined Gibbsian thermal state.
We aim at determining the masses of Cepheids in binary systems, as well as their geometric distances and the flux contribution of the companions. The combination of interferometry with spectroscopy will offer a unique and independent estimate of the Cepheid masses. Using long-baseline interferometry at visible and infrared wavelengths, it is possible to spatially resolve binary systems containing a Cepheid down to milliarcsecond separations. Based on the resulting visual orbit and radial velocities, we can then derive the fundamental parameters of these systems, particularly the masses of the components and the geometric distance. We therefore performed interferometric observations of the first-overtone mode Cepheid V1334 Cyg with the CHARA/MIRC combiner. We report the first detection of a Cepheid companion using long-baseline interferometry. We detect the signature of a companion orbiting V1334 Cyg at two epochs. We measure a flux ratio between the companion and the Cepheid f = 3.10+/-0.08%, giving an apparent magnitude mH = 8.47+/-0.15mag. The combination of interferometric and spectroscopic data have enabled the unique determination of the orbital elements: P = 1938.6+/-1.2 days, Tp = 2 443 616.1+/-7.3, a = 8.54+/-0.51mas, i = 124.7+/-1.8{\deg}, e = 0.190+/-0.013, {\omega} = 228.7+/-1.6{\deg}, and {\Omega} = 206.3+/-9.4{\deg}. We derive a minimal distance d ~ 691 pc, a minimum mass for both stars of 3.6 Msol, with a spectral type earlier than B5.5V for the companion star. Our measured flux ratio suggests that radial velocity detection of the companion using spectroscopy is within reach, and would provide an orbital parallax and model-free masses.
The linked double star $S_c(n,m)$, where $n \geq m \geq 0$, is the graph consisting of the union of two stars $K_{1,n}$ and $K_{1,m}$ with a path on $c$ vertices joining the centers. Its ramsey number $r(S_c(n,m))$ is the smallest integer $r$ such that every $2$-coloring of the edges of a $K_r$ admits a monochromatic $S_c(n,m)$. In this paper, we study the ramsey numbers of linked double stars when $c$ is odd. In particular, we establish bounds on the value of $r(S_c(n,m))$ and determine the exact value of $r(S_c(n,m))$ if $n \geq c$, or if $n \leq \lfloor \frac{c}{2} \rfloor - 2$ and $m = 2$.
The abundance of neutral hydrogen (HI) in satellite galaxies in the Local Group is important for studying the formation history of our Local Group. In this work, we generated mock HI satellite galaxies in the Local Group using the high mass resolution hydrodynamic \textsc{apostle} simulation. The simulated HI mass function agrees with the ALFALFA survey very well above $10^6M_{\odot}$, although there is a discrepancy below this scale because of the observed flux limit. After carefully checking various systematic elements in the observations, including fitting of line width, sky coverage, integration time, and frequency drift due to uncertainty in a galaxy's distance, we predicted the abundance of HI in galaxies in a future survey that will be conducted by FAST. FAST has a larger aperture and higher sensitivity than the Arecibo telescope. We found that the HI mass function could be estimated well around $10^5 M_{\odot}$ if the integration time is 40 minutes. Our results indicate that there are 61 HI satellites in the Local Group, and 36 in the FAST field above $10^5 M_{\odot}$. This estimation is one order of magnitude better than the current data, and will put a strong constraint on the formation history of the Local Group. Also more high resolution simulated samples are needed to achieve this target.
We use an Ornstein--Uhlenbeck (OU) process to approximate the queue length process in a $GI/GI/n+M$ queue. This one-dimensional diffusion model is able to produce accurate performance estimates in two overloaded regimes: In the first regime, the number of servers is large and the mean patience time is comparable to or longer than the mean service time; in the second regime, the number of servers can be arbitrary but the mean patience time is much longer than the mean service time. Using the diffusion model, we obtain Gaussian approximations for the steady-state queue length and the steady-state virtual waiting time. Numerical experiments demonstrate that the approximate distributions are satisfactory for queues in these two regimes.   To mathematically justify the diffusion model, we formulate the two overloaded regimes into an asymptotic framework by considering a sequence of queues. The mean patience time goes to infinity in both asymptotic regimes, whereas the number of servers approaches infinity in the first regime but does not change in the second. The OU process is proved to be the diffusion limit for the queue length processes in both regimes. A crucial tool for proving the diffusion limit is a functional central limit theorem for the superposition of time-scaled renewal processes. We prove that the superposition of $n$ independent, identically distributed stationary renewal processes, after being centered and scaled in both space and time, converges in distribution to a Brownian motion as $n$ goes to infinity.
A new algebraic Bethe ansatz scheme is proposed to diagonalise classes of integrable models relevant to the description of Bose-Einstein condensates in dilute alkali gases. This is achieved by introducing the notion of Z-graded representations of the Yang-Baxter algebra.
We present the analysis of four M dwarf stars -plus one M giant that seeped past our selection criteria- observed in Cycle 3 of Kepler Guest Observer program (GO3) in a search for intrinsic pulsations. Stellar oscillations in M dwarfs were theoretically predicted by Rodr\'iguez-L\'opez et al. (2012) to be in the range ~20-40 min and ~4-8 h, depending on the age and the excitation mechanism. We requested Kepler short cadence observations to have an adequate sampling of the oscillations. The targets were chosen on the basis of detectable rotation in the initial Kepler results, biasing towards youth.The analysis reveals no oscillations attributable to pulsations at a detection limit of several parts per million, showing that either the driving mechanisms are not efficient in developing the oscillations to observable amplitudes, or that if pulsations are driven, the amplitudes are very low. The size of the sample, and the possibility that the instability strip is not pure, allowing the coexistence of pulsators and non-pulsators, prevent us from deriving definite conclusions. Inmediate plans include more M dwarfs photometric observations of similar precision with Kepler K2 mission and spectroscopic searches already underway within the Cool Tiny Beats Project (Anglada-Escud\'e et al. 2014, Berdi\~nas et al. 2014) with the high-resolution spectrographs HARPS and HARPS-N.
Magnetic properties for the one-dimensional multicomponent quantum spin system with the excitation gap are studied based on the integrable spin model introduced by Bariev {\it et al}. By exactly computing the magnetization, we show how the characteristic structure with plateaus and cusps appears in the magnetization process. To study low-energy dynamics of the system, we apply the finite-size scaling analysis to the excitation spectrum, and thereby evaluate the power-law exponent as well as the enhancement factor for the low-temperature NMR relaxation rate $1/T_1$. We discuss the critical properties of $1/T_1$ around plateaus and cusps in the magnetization curve.
We present the results of a program that monitored the near-IR spectroscopic variability of a sample of 19 embedded protostars. Spectra were taken on time intervals from 2 days to 3 years, over a wavelength range from 0.85 {\mu}m to 2.45 {\mu}m, for 4-9 epochs of observations per target. We found that the spectra of all targets are variable, and that every emission feature observed is also variable (although not for all targets). With one exception, there were no drastic changes in the continua of the spectra, nor did any line completely disappear, nor did any line appear that was not previously apparent. This analysis focuses on understanding the connection between accretion (traced by H Br $\gamma$ and CO) and the wind (traced by He I, [FeII], and sometimes H$_2$). For both accretion and wind tracers, the median variability was constant versus time interval between observations, however the maximum variability that we observed increased with time interval between observations. Extinction is observed to vary within the minimum sampling time of 2 days, suggesting extinguishing material within a few stellar radii at high disk latitudes. The variability of [FeII] and H$_2$ were correlated for most (but not all) of the 7 YSOs showing both features, and the amplitude of the variability depends on the veiling. Although the occurrence of CO and Br $\gamma$ emission are connected, their variability is uncorrelated, suggesting that these emissions originate in separate regions near the protostar (e.g., disk and wind).
We surveyed the (1,1), (2,2), and (3,3) lines of NH3 and the H2O maser toward the molecular cloud L935 in the extended HII region NGC 7000 with an angular resolution of 1.6' using the Kashima 34-m telescope. We found five clumps in the NH3 emission with a size of 0.2--1 pc and mass of 9--452 M_sun. The molecular gas in these clumps has a similar gas kinetic temperature of 11--15 K and a line width of 1--2 km/s. However, they have different star formation activities such as the concentration of T-Tauri type stars and the association of H2O maser sources. We found that these star formation activities are related to the geometry of the HII region. The clump associated with the T-Tauri type star cluster has a high star formation efficiency of 36--62%. This clump is located near the boundary of the HII region and molecular cloud. Therefore, we suggest that the star formation efficiency increases because of the triggered star formation.
We present a review of the present state of knowledge regarding the relative ages of Galactic globular clusters. First, we discuss the relevant galaxy formation models and describe the detailed predictions they make with respect to the formation timescale and chemical evolution of the globular clusters. Next, the techniques used to estimate globular cluster ages are described and evaluated with particular emphasis on the advantages and disadvantages of each method. With these techniques as a foundation, we present arguments in favor of the following assertions: 1) The age of a globular cluster is the likeliest candidate to be the global second parameter, which along with metal abundance, controls the morphology of the horizonal branch. 2) A total age range of as much as $\sim$5 Gyr exists among the bulk of the Galactic globulars. 3) There is a significant relation between age and metallicity among the Galactic globular clusters if the slope of the \mvrr-\feh relation is less than $\sim$0.23. These conclusions along with other supporting evidence favor a formation scenario in which the inner regions of the Galactic halo collapsed in a monotonic fashion over a short time period much less than 1 Gyr. In contrast, the outer regions of the halo fragmented and collapsed in a chaotic manner over several Gyrs.
Piperazinium Hexachlorodicuprate (PHCC) is shown to be a frustrated quasi-two-dimensional quantum Heisenberg antiferromagnet with a gapped spectrum. Zero-field inelastic neutron scattering and susceptibility and specific heat measurements as a function of applied magnetic field are presented. At T = 1.5 K, the magnetic excitation spectrum is dominated by a single propagating mode with a gap, Delta = 1 meV, and bandwidth of approximately 1.8 meV in the (h0l) plane. The mode has no dispersion along the b* direction indicating that neighboring a-c planes of the triclinic structure are magnetically decoupled. The heat capacity shows a reduction of the gap as a function of applied magnetic field in agreement with a singlet-triplet excitation spectrum. A field-induced ordered phase is observed in heat capacity and magnetic susceptibility measurements for magnetic fields greater than H_c1 approximately equal to 7.5 Tesla. Analysis of the neutron scattering data reveals the important exchange interactions and indicates that some of these are highly frustrated.
We introduce two natural notions for the occupation measure of a function $V$ with finite variation. The first yields a signed measure, and the second a positive measure. By comparing two versions of the change-of-variables formula, we show that both measures are absolutely continuous with respect to Lebesgue measure. Occupation densities can be thought of as local times of $V$, and are described by a Meyer-Tanaka like formula.
Combining visual and spectroscopic orbits of binary stars leads to a determination of the full 3D orbit, individual masses, and distance to the system. We present a full analysis of the evolved binary system $\delta$ Delphini using astrometric data from the MIRC and PAVO instruments on the CHARA long-baseline interferometer, 97 new spectra from the Fairborn Observatory, and 87 unpublished spectra from Lick Observatory. We determine the full set of orbital elements for $\delta$ Del, along with masses of $1.78 \pm 0.07$ $M_{\odot}$ and $1.62 \pm 0.07$ $M_{\odot}$ for each component, and a distance of $63.61 \pm 0.89$ pc. These results are important in two contexts: for testing stellar evolution models and defining the detection capabilities for future planet searches. We find that the evolutionary state of this system is puzzling, as our measured flux ratios, radii, and masses imply a $\sim$ 200 Myr age difference between the components using standard stellar evolution models. Possible explanations for this age discrepancy include mass transfer scenarios with a now ejected tertiary companion. For individual measurements taken over a span of 2 years we achieve $<10$ $\mu$-arcsecond precision on differential position with 10-minute observations. The high precision of our astrometric orbit suggests that exoplanet detection capabilities are within reach of MIRC at CHARA. We compute exoplanet detection limits around $\delta$ Del, and conclude that if this precision is extended to wider systems we should be able to detect most exoplanets $>2$ M$_{J}$ on orbits $>0.75$ AU around individual components of hot binary stars via differential astrometry.
Within a dynamical transport approach we investigate charged current interactions in neutrino-nucleus reactions for neutrino energies of 0.3 - 1.5 GeV with particular emphasis on resonant pion production channels via the $\Delta_{33}(1232)$ resonance. The final-state-interactions of the resonance as well as of the emitted pions are calculated explicitly for $^{12}C$ and $^{56}Fe$ nuclei and show a dominance of pion suppression at moderate momenta $p_\pi >$ 0.2 GeV/c. A comparison to integrated $\pi^+$ spectra for $\nu_\mu + ^{12}C$ reactions with the available (preliminary) data demonstrates a reasonable agreement.
We develop an algebraic method of studying of Diophantine quadratic equations in three variables over the ring of Gaussian integers.
We consider the stochastic heat equation with multiplicative noise $u_t={1/2}\Delta u+ u \diamond \dot{W}$ in $\bR_{+} \times \bR^d$, where $\diamond$ denotes the Wick product, and the solution is interpreted in the mild sense. The noise $\dot W$ is fractional in time (with Hurst index $H \geq 1/2$), and colored in space (with spatial covariance kernel $f$). We prove that if $f$ is the Riesz kernel of order $\alpha$, or the Bessel kernel of order $\alpha<d$, then the sufficient condition for the existence of the solution is $d \leq 2+\alpha$ (if $H>1/2$), respectively $d<2+\alpha$ (if $H=1/2$), whereas if $f$ is the heat kernel or the Poisson kernel, then the equation has a solution for any $d$. We give a representation of the $k$-th order moment of the solution, in terms of an exponential moment of the "convoluted weighted" intersection local time of $k$ independent $d$-dimensional Brownian motions.
Let $X$ be a toric Del-Pezzo surface and let $Crit(W) \subset (\mathbb{C}^{\ast})^n$ be the solution scheme of the Landau-Ginzburg system of equations. Denote by $X^{\circ}$ the polar variety of $X$. Our aim in this work is to describe a map $L : Crit(W) \rightarrow Fuk_{trop}(X^{\circ})$ whose image under homological mirror symmetry corresponds to a full strongly exceptional collection of line bundles.
In order to clarify a key role of orbital degree of freedom in the spin S=1 Haldane system, we investigate ground-state properties of the t2g-orbital degenerate Hubbard model on the linear chain by using numerical techniques. Increasing the Hund's rule coupling in multi-orbital systems, in general, there occurs a transition from an antiferromagnetic to a ferromagnetic phase. We find that the antiferromagnetic phase is described as the Haldane system with spin gap, while in the ferromagnetic phase, there exists the gapless excitation with respect to orbital degree of freedom. Possible relevance of the present results to actual systems is also discussed.
This paper is an overview of the classical level crossing problem which is studied extensively in the literature and is fundamental in many branches of applied probability. We discuss a number of approximations with an emphasis on their performance, methods of justification and technical conditions which are required in these methods, including a new approximation called "inverse Gaussian". It is derived by a new method, is fruitful for solving related problems, and is valid under mild regularity conditions. We emphasize its novelty and boons.
Based on first-principles calculations, we propose a sandwich structure composed of a G-type anti-ferromagnetic (AFM) Mott insulator LaCrO$_3$ grown along the [001] direction with one atomic layer replaced by an inverse-perovskite material Sr$_3$PbO. We show that the system is in a topologically nontrivial phase characterized by simultaneous nonzero charge and spin Chern numbers, which can support a spin-polarized and dissipationless edge current in a finite system. Since these two materials are stable in bulk and match each other with only small lattice distortions, the composite material is expected easy to synthesize.