ShantanuT01/DACTYL-Pretraining huggingface dataset:
Every 4-connected graph with minimum degree $\delta$ and connectivity $\kappa$ either has a cycle of length at least $4\delta-2\kappa$ or has a dominating cycle.
We construct a deterministic, Lagrangian many-particle approximation to a class of nonlocal transport PDEs with nonlinear mobility arising in many contexts in biology and social sciences. The approximating particle system is a nonlocal version of the follow-the-leader scheme. We rigorously prove that a suitable discrete piece-wise density reconstructed from the particle scheme converges strongly in $L^1_{loc}$ towards the unique entropy solution to the target PDE as the number of particles tends to infinity. The proof is based on uniform BV estimates on the approximating sequence and on the verification of an approximated version of the entropy condition for large number of particles. As part of the proof, we also prove uniqueness of entropy solutions. We also provide a specific example of non-uniqueness of weak solutions and discuss about the interplay of the entropy condition with the steady states. Finally, we produce numerical simulations supporting the need of a concept of entropy solution in order to get a well-posed semigroup in the continuum limit, and showing the behaviour of solutions for large times.
We derive and discuss the constraints induced by Poincare' invariance on the form of the heavy-quark potential up to order 1/m^2. We present two derivations: one uses general arguments directly based on the Poincare' algebra and the other follows from an explicit calculation on the expression of the potential in terms of Wilson loops. We confirm relations from the literature, but also clarify the origin of a long-standing false statement pointed out recently.
We prove a pro-$p$ Hom-form of the birational anabelian conjecture for function fields over sub-$p$-adic fields. Our starting point is the Theorem of Mochizuki in the case of transcendence degree 1.
The approach to equilibrium of a nondegenerate quantum system involves the damping of microscopic population oscillations, and, additionally, the bringing about of detailed balance, i.e. the achievement of the correct Boltzmann factors relating the populations. These two are separate effects of interaction with a reservoir. One stems from the randomization of phases and the other from phase space considerations. Even the meaning of the word `phase' differs drastically in the two instances in which it appears in the previous statement. In the first case it normally refers to quantum phases whereas in the second it describes the multiplicity of reservoir states that corresponds to each system state. The generalized master equation theory for the time evolution of such systems is here developed in a transparent manner and both effects of reservoir interactions are addressed in a unified fashion. The formalism is illustrated in simple cases including in the standard spin-boson situation wherein a quantum dimer is in interaction with a bath consisting of harmonic oscillators. The theory has been constructed for application in energy transfer in molecular aggregates and in photosynthetic reaction centers.
We present a learning model that makes full use of boundary information for salient object segmentation. Specifically, we come up with a novel loss function, i.e., Contour Loss, which leverages object contours to guide models to perceive salient object boundaries. Such a boundary-aware network can learn boundary-wise distinctions between salient objects and background, hence effectively facilitating the saliency detection. Yet the Contour Loss emphasizes on the local saliency. We further propose the hierarchical global attention module (HGAM), which forces the model hierarchically attend to global contexts, thus captures the global visual saliency. Comprehensive experiments on six benchmark datasets show that our method achieves superior performance over state-of-the-art ones. Moreover, our model has a real-time speed of 26 fps on a TITAN X GPU.
In this paper, we investigate the symmetry properties of a variable coefficient nonlinear space-time fractional Burgers' equation. Fractional Lie symmetries and corresponding infinitesimal generators are obtained. With the help of the infinitesimal generators some group invariant solutions are deduced. Further, some exact solutions of fractional Burgers' equation are generated by the invariant subspace method.
High energy ($> 250$ keV) emission has been detected persisting for several tens of seconds after the initial spike of magnetar giant flares. It has been conjectured that this emission might arise via inverse Compton scattering in a highly extended corona generated by super-Eddington outflows high up in the magnetosphere. In this paper we undertake a detailed examination of this model. We investigate the properties of the required scatterers, and whether the mechanism is consistent with the degree of pulsed emission observed in the tail of the giant flare. We conclude that the mechanism is consistent with current data, although the origin of the scattering population remains an open question. We propose an alternative picture in which the emission is closer to that star and is dominated by synchrotron radiation. The $RHESSI$ observations of the December 2004 flare modestly favor this latter picture. We assess the prospects for the Fermi Gamma-Ray Space Telescope to detect and characterize a similar high energy component in a future giant flare. Such a detection should help to resolve some of the outstanding issues.
The Hubbard model on fcc-type lattices is studied in the dynamical mean-field theory of infinite spatial dimensions. At intermediate interaction strength finite temperature Quantum Monte Carlo calculations yield a second order phase transition to a highly polarized, metallic ferromagnetic state. The Curie temperatures are calculated as a function of electronic density and interaction strength. A necessary condition for ferromagnetism is a density of state with large spectral weight near one of the band edges.
Recently the anisotropy of the short gamma-ray bursts detected by BATSE was announced (Vavrek et al. 2008). The impact of this discovery on cosmology is discussed. It is shown that the anisotropy found may cause the breakdown of the cosmological principle.
The recent results on anisotropic flow in ultrarelativistic nuclear collisions along with recent methodical developments and achievements in the understanding of the phenomena, are reviewed. The emphasis is given to the elliptic flow results.
We propose a method for self-supervised image representation learning under the guidance of 3D geometric consistency. Our intuition is that 3D geometric consistency priors such as smooth regions and surface discontinuities may imply consistent semantics or object boundaries, and can act as strong cues to guide the learning of 2D image representations without semantic labels. Specifically, we introduce 3D geometric consistency into a contrastive learning framework to enforce the feature consistency within image views. We propose to use geometric consistency sets as constraints and adapt the InfoNCE loss accordingly. We show that our learned image representations are general. By fine-tuning our pre-trained representations for various 2D image-based downstream tasks, including semantic segmentation, object detection, and instance segmentation on real-world indoor scene datasets, we achieve superior performance compared with state-of-the-art methods.
When making use of tabulations of empirical bolometric corrections for stars (BC_V), a commonly overlooked fact is that while the zero point is arbitrary, the bolometric magnitude of the Sun (Mbol_Sun) that is used in combination with such tables cannot be chosen arbitrarily. It must be consistent with the zero point of BC_V so that the apparent brightness of the Sun is reproduced. The latter is a measured quantity, for which we adopt the value V_Sun = -26.76 +/- 0.03. Inconsistent values of Mbol_Sun are listed in many of the most popular sources of BC_V. We quantify errors that are introduced by not paying attention to this detail. We also take the opportunity to reprint the BC_V coefficients of the often used polynomial fits by Flower (1996), which were misprinted in the original publication.
Recently, a Verwey-type transition in the mixed-valence alkali sesquioxide Cs$_4$O$_6$ was deduced from the charge ordering of molecular peroxide O$_2^{2-}$ and superoxide O$_2^-$ anions accompanied by the structural transformation and a dramatic change in electronic conductivity [Adler et al, Sci. Adv 4, eaap7581 (2018)]. Here, we report that in the sister compound Rb$_4$O$_6$ a similar Verwey-type charge ordering transition is strongly linked to O$_2^-$ orbital and spin dynamics. On cooling, a powder neutron diffraction experiment reveals a charge ordering and a cubic-to-tetragonal transition at $T_{\rm CO}=290$ K, which is followed by a further structural instability at $T_{\rm s}=92$ K that involves an additional reorientation of magnetic O$_2^-$ anions. Magnetic resonance techniques supported by density functional theory computations suggest the emergence of a peculiar type of $\pi^*$-orbital ordering of the magnetically active O$_2^-$ units, which promotes the formation of a quantum spin state composed of weakly coupled spin dimers. These results reveal that similarly as in 3$d$ transition metal compounds, also in in the $\pi^*$ open-shell alkali sesquioxides the interplay between Jahn-Teller-like electron-lattice coupling and Kugel-Khomskii-type superexchange determines the nature of orbital ordering and the magnetic ground state.
(abridged) We present spectroscopy data for a sample of 14 FUors and 2 TTauri stars observed with the Spitzer Space Telescope or with the Infrared Space Observatory (ISO). Based on the appearance of the 10 micron silicate feature we define 2 categories of FUors. Objects showing the silicate feature in absorption (Category 1) are still embedded in a dusty and icy envelope. The shape of the 10 micron silicate absorption bands is compared to typical dust compositions of the interstellar medium and found to be in general agreement. Only one object (RNO 1B) appears to be too rich in amorphous pyroxene dust, but a superposed emission feature can explain the observed shape. We derive optical depths and extinction values from the silicate band and additional ice bands at 6.0, 6.8 and 15.2 micron. In particular the analysis of the CO_2 ice band at 15.2 micron allows us to search for evidence for ice processing and constrains whether the absorbing material is physically linked to the central object or in the foreground. For objects showing the silicate feature in emission (Category 2), we argue that the emission comes from the surface layer of accretion disks. Analyzing the dust composition reveals that significant grain growth has already taken place within the accretion disks, but no clear indications for crystallization are present. We discuss how these observational results can be explained in the picture of a young, and highly active accretion disk. Finally, a framework is proposed as to how the two categories of FUors can be understood in a general paradigm of the evolution of young, low-mass stars. Only one object (Parsamian 21) shows PAH emission features. Their shapes, however, are often seen toward evolved stars and we question the object's status as a FUor and discuss other possible classifications.
Let $\phi:\,X\rightarrow Y$ be a (possibly ramified) cover between two algebraic curves of positive genus. We develop tools that may identify the Prym variety of $\phi$, up to isogeny, as the Jacobian of a quotient curve $C$ in the Galois closure of the composition of $\phi$ with a well-chosen map $Y\rightarrow \mathbb{P}^1$. This method allows us to recover all previously obtained descriptions of a Prym variety in terms of a Jacobian that are known to us, besides yielding new applications. We also find algebraic equations for some of these new cases, including one where $X$ has genus $3$, $Y$ has genus $1$ and $\phi$ is a degree $3$ map totally ramified over $2$ points.
We calculate neutron capture cross sections for r-process nucleosynthesis in the $^{48}$Ca region, namely for the isotopes $^{40-44}$S, $^{46-50}$Ar, $^{56-66}$Ti, $^{62-68}$Cr, and $^{72-76}$Fe. While previously only cross sections resulting from the compound nucleus reaction mechanism (Hauser-Feshbach) have been considered, we recalculate not only that contribution to the cross section but also include direct capture on even-even nuclei. The level schemes, which are of utmost importance in the direct capture calculations, are taken from quasi-particle states obtained with a folded-Yukawa potential and Lipkin-Nogami pairing. Most recent deformation values derived from experimental data on $\beta$-decay half lives are used where available. Due to the consideration of direct capture, the capture rates are enhanced and the "turning points" in the r-process path are shifted to slightly higher mass numbers. We also discuss the sensitivity of the direct capture cross sections on the assumed deformation.
Let $k$ be a perfect field of odd characteristic and $X$ a smooth algebraic variety over $k$ which is $W_2$-liftable. We show that the exponent twisiting of the classical Cartier descent gives an equivalence of categories between the category of nilpotent Higgs sheaves of exponent $\leq p-1$ over $X/k$ and the category of nilpotent flat sheaves of exponent $\leq p-1$ over $X/k$, and it is equivalent up to sign to the inverse Cartier and Cartier transforms for these nilpotent objects constructed in the nonabelian Hodge theory in positive characteristic by Ogus-Vologodsky. In view of the crucial role that Deligne-Illusie's lemma has ever played in their algebraic proof of $E_1$ degeneration and Kodaira vanishing theorem in abelian Hodge theory, it may not be overly surprising that again this lemma plays a significant role via the concept of Higgs-de Rham flow in establishing $p$-adic Simpson correspondence in nonabelian Hodge theory and Langer's algebraic proof of Bogomolov inequality for semistable Higgs bundles and Miyaoka-Yau inequality.
We investigate the effect of measurement on the persistent current density in a lattice ring penetrated by an Aharonov-Bohm flux and coupled to a quantum dot which is continuously monitored by a point contact detector. It is demonstrated by explicit analysis of the time-evolution of current density that the persistent current in the lattice ring is suppressed completely due to dephasing of quantum states induced by an analogous which-way-measurment that whether or not the electron is localized on the quantum dot. Practical experiments to observe the measurment induced dephasing is proposed.
The game of best choice (or "secretary problem") is a model for making an irrevocable decision among a fixed number of candidate choices that are presented sequentially in random order, one at a time. Because the classically optimal solution is known to reject an initial sequence of candidates, a paradox emerges from the fact that candidates have an incentive to position themselves immediately after this cutoff which challenges the assumption that candidates arrive in uniformly random order.   One way to resolve this is to consider games for which every (reasonable) strategy results in the same probability of success. In this work, we classify these "strategy-indifferent" games of best choice. It turns out that the probability of winning such a game is essentially the reciprocal of the expected number of left-to-right maxima in the full collection of candidate rank orderings. We present some examples of these games based on avoiding permutation patterns of size 3, which involves computing the distribution of left-to-right maxima in each of these pattern classes.
Typical heat engines exhibit a kind of homotypy: The heat exchanges between a cyclic heat engine and its two heat reservoirs abide by the same function type; the forward and backward flows of an autonomous heat engine also conform to the same function type. This homotypy mathematically reflects in the existence of hidden symmetries for heat engines. The heat exchanges between the cyclic heat engine and its two reservoirs are dual under the joint transformation of parity inversion and time-reversal operation. Similarly, the forward and backward flows in the autonomous heat engine are also dual under the parity inversion. With the consideration of these hidden symmetries, we derive a generic nonlinear constitutive relation up to the quadratic order for tight-coupling cyclic heat engines and that for tight-coupling autonomous heat engines, respectively.
We explore quantum mechanical theories whose fundamental degrees of freedom are rectangular matrices with Grassmann valued matrix elements. We study particular models where the low energy sector can be described in terms of a bosonic Hermitian matrix quantum mechanics. We describe the classical curved phase space that emerges in the low energy sector. The phase space lives on a compact Kahler manifold parameterized by a complex matrix, of the type discovered some time ago by Berezin. The emergence of a semiclassical bosonic matrix quantum mechanics at low energies requires that the original Grassmann matrices be in the long rectangular limit. We discuss possible holographic interpretations of such matrix models which, by construction, are endowed with a finite dimensional Hilbert space.
We present a time-resolved study of the logical operation of a polariton condensate transistor switch. Creating a polariton condensate (source) in a GaAs ridge-shaped microcavity with a non-resonant pulsed laser beam, the polariton propagation towards a collector, at the ridge edge, is controlled by a second weak pulse (gate), located between the source and the collector. The experimental results are interpreted in the light of simulations based on the generalized Gross-Pitaevskii equation, including incoherent pumping, decay and energy relaxation within the condensate.
Context. The gas kinetic temperature (TK) determines the physical and chemical evolution of the Interestellar Medium (ISM). However, obtaining reliable TK estimates usually requires expensive observations including the combination of multi-line analysis and dedicated radiative transfer calculations. Aims. This work explores the use of HCN and HNC observations, and particularly its I(HCN)/I(HNC) intensity ratio of their J=1-0 lines, as direct probe of the gas kinetic temperature in the molecular ISM. Methods. We obtained a new set of large-scale observations of both HCN and HNC (1-0) lines along the Integral Shape Filament (ISF) in Orion. In combination with ancillary gas and dust temperature measurements, we find a systematic temperature dependence of the observed I(HCN)/I(HNC) intensity ratio across our maps. Additional comparisons with chemical models demonstrate that these observed I(HCN)/I(HNC) variations are driven by the effective destruction and isomerization mechanisms of HNC under low energy barriers. Results. The observed variations of I(HCN)/I(HNC) with TK can be described with a two-part linear function. This empirical calibration is then used to create a temperature map of the entire ISF. Comparisons with similar dust temperature measurements in this cloud, as well as in other regions and galactic surveys, validate this simple technique to obtain direct estimates of the gas kinetic temperature in a wide range of physical conditions and scales with an optimal working range between 15 K and 40 K. Conclusions. Both observations and models demonstrate the strong sensitivity of the I(HCN)/I(HNC) ratio to the gas kinetic temperature. Since these lines are easily obtained in observations of local and extragalactic sources, our results highlight the potential use of this observable as new chemical thermometer for the ISM.
In the framework of the quantum inverse scattering method, we consider a problem of constructing local operators for two-dimensional quantum integrable models, especially for the lattice versions of the nonlinear Schrodinger and sine-Gordon models. We show that a certain class of local operators can be constructed from the matrix elements of the monodromy matrix in a simple way. They are closely related to the quantum projectors and have nice commutation relations with the half of the matrix elements of the elementary monodromy matrix. The form factors of these operators can be calculated by using the standard algebraic Bethe ansatz techniques.
For 4$d^1$ and 5$d^1$ spin-orbit-coupled electron configurations, the notion of nonmagnetic j=3/2 quartet ground state discussed in classical textbooks is at odds with the observed variety of magnetic properties. Here we throw fresh light on the electronic structure of 4$d^1$ and 5$d^1$ ions in molybdenum- and osmium-based double-perovskite systems and reveal different kinds of on-site many-body physics in the two families of compounds: while the sizable magnetic moments and $g$ factors measured experimentally are due to both metal $d$-ligand $p$ hybridization and dynamic Jahn-Teller interactions for 4$d$ electrons, it is essentially $d$-$p$ covalency for the 5$d^1$ configuration. These results highlight the subtle interplay of spin-orbit interactions, covalency and electron-lattice couplings as the major factor in deciding the nature of the magnetic ground states of 4$d$ and 5$d$ quantum materials. Cation charge imbalance in the double-perovskite structure is further shown to allow a fine tuning of the gap between the $t_{2g}$ and $e_g$ levels, an effect of much potential in the context of orbital engineering in oxide electronics.
We use a semiclassical approach to study out of equilibrium dynamics and transport in quantum systems with massive quasiparticle excitations having internal quantum numbers. In the universal limit of low energy quasiparticles, the system is described in terms of a classical gas of colored hard-core particles. Starting from an inhomogeneous initial state, in this limit we give analytic expressions for the space and time dependent spin density and spin current profiles. Depending on the initial state, the spin transport is found to be ballistic or diffusive. In the ballistic case we identify a `second front' that moves more slowly than the maximal quasiparticle velocity. Our analytic results also capture the diffusive broadening of this ballistically propagating front. To go beyond the universal limit, we study the effect of non-trivial scattering processes in the $O(3)$ non-linear sigma model by performing Monte Carlo simulations, and observe local equilibration around the second front in terms of the densities of the particle species.
We study the minimal Weierstrass equations for genus 2 curves defined over a ring of integers $\mathcal O_{\mathbb F}$. This is done via reduction theory and Julia invariant of binary sextics. We show that when the binary sextics has extra automorphisms this is usually easier to compute. Moreover, we show that when the curve is given in the standard form $y^2=f(x^2)$, where $f(x)$ is a monic polynomial, $f(0)=1$ which is defined over $\mathcal O_{\mathbb F}$ then this form is reduced.