ShantanuT01/DACTYL-Pretraining huggingface dataset:
We prove that uniqueness of the stationary chain, or equivalently, of the $g$-measure, compatible with an attractive regular probability kernel is equivalent to either one of the following two assertions for this chain: (1) it is a finitary coding of an i.i.d. process with countable alphabet, (2) the concentration of measure holds at exponential rate. We show in particular that if a stationary chain is uniquely defined by a kernel that is continuous and attractive, then this chain can be sampled using a coupling-from-the-past algorithm. For the original Bramson-Kalikow model we further prove that there exists a unique compatible chain if and only if the chain is a finitary coding of a finite alphabet i.i.d. process. Finally, we obtain some partial results on conditions for phase transition for general chains of infinite order.
In this review given at the Hot and Cool: Bridging Gaps in Massive Star Evolution conference, I present the state of the art in red supergiant star atmosphere modelling. The last generation of hydrostatic 1D LTE MARCS models publicly released in 2008 have allowed great achievements in the past years, like the calibration of effective temperature scales. I rapidly describe this release, and then I discuss in some length the impact of the opacity sampling approximation on the thermal structure of models and on their emergent spectra. I also insist on limitations inherent to these models. Estimates of collisional and radiative time scales for electronic transitions in e.g. TiO suggest that non-LTE effects are important, and should be further investigated. Classical 1D models are not capable either to provide the large and non-gaussian velocity fields we know exist in red supergiants atmospheres. I therefore also present current efforts in 3D radiative hydrodynamical simulation of RSGs. I show that line profiles and shifts are predicted by these simulations, without the need for fudge micro- and macroturbulence velocities. This is a great progress, although line depths and widths are slightly too shallow. This is probably caused by the simplified grey radiative transfer used in these heavy simulations. Future non-grey 3D simulations should provide a better fit to observations in terms of line strengths and widths.
Torsion models constitute a well known class of extended quantum gravity models. In this work, one investigates the phenomenological consequences of a torsion field interacting with top quarks at the LHC. A torsion field could appear as a new heavy state characterized by its mass and couplings to fermions. This new state would form a resonance decaying into a top anti-top pair. The latest ATLAS $t\bar t$ production results from LHC 13 TeV data are used to set limits on torsion parameters. The integrated luminosity needed to observe torsion resonance at the next LHC upgrades are also evaluated, considering different values for the torsion mass and its couplings to Standard Model fermions. Finally, prospects for torsion exclusion at the future LHC phases II and III are obtained using fast detector simulations.
We study infinite systems of particles which undergo coalescence and fragmentation, in a manner determined solely by their masses. A pair of particles having masses $x$ and $y$ coalesces at a given rate $K(x,y)$. A particle of mass $x$ fragments into a collection of particles of masses $\theta\_1 x, \theta\_2 x, \ldots$ at rate $F(x) \beta(d\theta)$. We assume that the kernels $K$ and $F$ satisfy H\"older regularity conditions with indices $\lambda \in (0,1]$ and $\alpha \in [0, \infty)$ respectively. We show existence of such infinite particle systems as strong Markov processes taking values in $\ell\_{\lambda}$, the set of ordered sequences $(m\_i)\_{i \ge 1}$ such that $\sum\_{i \ge 1} m\_i^{\lambda} \textless{} \infty$. We show that these processes possess the Feller property. This work relies on the use of a Wasserstein-type distance, which has proved to be particularly well-adapted to coalescence phenomena.
Event cameras are novel bio-inspired vision sensors that output pixel-level intensity changes in microsecond accuracy with a high dynamic range and low power consumption. Despite these advantages, event cameras cannot be directly applied to computational imaging tasks due to the inability to obtain high-quality intensity and events simultaneously. This paper aims to connect a standalone event camera and a modern intensity camera so that the applications can take advantage of both two sensors. We establish this connection through a multi-modal stereo matching task. We first convert events to a reconstructed image and extend the existing stereo networks to this multi-modality condition. We propose a self-supervised method to train the multi-modal stereo network without using ground truth disparity data. The structure loss calculated on image gradients is used to enable self-supervised learning on such multi-modal data. Exploiting the internal stereo constraint between views with different modalities, we introduce general stereo loss functions, including disparity cross-consistency loss and internal disparity loss, leading to improved performance and robustness compared to existing approaches. The experiments demonstrate the effectiveness of the proposed method, especially the proposed general stereo loss functions, on both synthetic and real datasets. At last, we shed light on employing the aligned events and intensity images in downstream tasks, e.g., video interpolation application.
We study the transformation properties of the electron states in crystals with spin-orbit coupling, focusing primarily on the limitations of the frequently used pseudospin-1/2 description of twofold degenerate Bloch bands. Using the language of corepresentations of magnetic point groups, we construct the Bloch bases across the Brillouin zone in a way which is consistent with all symmetry requirements. This construction is applied to derive the effective spin-orbit Hamiltonians in noncentrosymmetric crystals, known as the generalized Rashba models, in both single-band and multiband cases.
We enumerate all dissections of an equilateral triangle into smaller equilateral triangles up to size 20, where each triangle has integer side lengths. A perfect dissection has no two triangles of the same side, counting up- and down-oriented triangles as different. We computationally prove W. T. Tutte's conjecture that the smallest perfect dissection has size 15 and we find all perfect dissections up to size 20.
We present 44 and 226 GHz observations of the Galactic center within 20$"$ of Sgr A*. Millimeter continuum emission at 226 GHz is detected from eight stars that have previously been identified at near-IR and radio wavelengths. We also detect a 5.8 mJy source at 226 GHz coincident with the magnetar SGR~J1745-29 located 2.39$"$ SE of Sgr A* and identify a new 2.5$"\times1.5"$ halo of mm emission centered on Sgr A*. The X-ray emission from this halo has been detected previously and is interpreted in terms of a radiatively inefficient accretion flow. The mm halo surrounds an EW linear feature which appears to arise from Sgr A* and coincides with the diffuse X-ray emission and a minimum in the near-IR extinction. We argue that the millimeter emission is produced by synchrotron emission from relativistic electrons in equipartition with a $\sim 1.5$mG magnetic field. The origin of these is unclear but its coexistence with hot gas supports scenarios in which the gas is produced by the interaction of winds either from the fast moving S-stars, the photo-evaporation of low-mass YSO disks or by a jet-driven outflow from Sgr A*. The spatial anti-correlation of the X-ray, radio and mm emission from the halo and the low near-IR extinction provides compelling evidence for an outflow sweeping up the interstellar material, creating a dust cavity within 2$"$ of Sgr A*. Finally, the radio and mm counterparts to eight near-IR identified stars within $\sim$10\arcs\ of Sgr A* provide accurate astrometry to determine the positional shift between the peak emission at 44 and 226 GHz.
We sketch a Weyl creation operator approach to the Riemann Hypothesis; i.e.,arithmetic on the Weyl algebras with ergodic theory to transport operators. We prove that finite Hasse-Dirichlet alternating zeta functions or eta functions can be induced from a product of "creation operators". The latter idea is the result of considering complex quantum mechanics with complex time-space related concepts. Then we overview these ideas, with variations, which may provide a pathway that may settle RH; e.g., a Euler Factor analysis to study the quantum behavior of the integers as one pushes up the critical line near a macro zeta function zero.
Simple unsmoothed formulas to compute the Riemann zeta function, and Dirichlet $L$-functions to a power-full modulus, are derived by elementary means (Taylor expansions and the geometric series). The formulas enable square-root of the analytic conductor complexity, up to logarithmic loss, and have an explicit remainder term that is easy to control. The formula for zeta yields a convexity bound of the same strength as that from the Riemann-Siegel formula, up to a constant factor. Practical parameter choices are discussed.
We study Piatetski-Shapiro sequences $(\lfloor n^c\rfloor)_n$ modulo m, for non-integer $c >1$ and positive $m$, and we are particularly interested in subword occurrences in those sequences. We prove that each block $\in\{0,1\}^k$ of length $k < c + 1$ occurs as a subword with the frequency $2^{-k}$, while there are always blocks that do not occur. In particular, those sequences are not normal. For $1<c<2$, we estimate the number of subwords from above and below, yielding the fact that our sequences are deterministic and not morphic. Finally, using the Daboussi-K\'{a}tai criterion, we prove that the sequence $\lfloor n^c\rfloor$ modulo m is asymptotically orthogonal to multiplicative functions bounded by $1$ and with mean value $0$.
This paper presents a novel method that allows to generalise the use of the Adam-Bashforth to Partial Differential Equations with local and non local operator. The Method derives a two step Adam-Bashforth numerical scheme in Laplace space and the solution is taken back into the real space via inverse Laplace transform. The method yields a powerful numerical algorithm for fractional order derivative where the usually very difficult to manage summation in the numerical scheme disappears. Error Analysis of the method is also presented. Applications of the method and numerical simulations are presented on a wave-equation like, and on a fractional order diffusion equation.
This paper investigates the following quasilinear Keller-Segel-Navier-Stokes system $$\left\{ \begin{array}{l} n_t+u\cdot\nabla n=\Delta n^m-\nabla\cdot(n\nabla c),\quad x\in \Omega, t>0, \\ c_t+u\cdot\nabla c=\Delta c-c+n,\quad x\in \Omega, t>0,\\ u_t+\nabla P=\Delta u+n\nabla \phi,\quad x\in \Omega, t>0,\\ \nabla\cdot u=0, \quad x\in \Omega, t>0 \end{array}\right.$$ under homogeneous boundary conditions of Neumann type for $n$ and $c$, and of Dirichlet type for $u$ in a three-dimensional bounded domains $\Omega\subseteq \mathbb{R}^3$ with smooth boundary, where $\phi\in W^{1,\infty}(\Omega),m>0$. It is proved that if $m>\frac{4}{3}$, then for any sufficiently regular nonnegative initial data there exists at least one global boundedness solution for system $(KSF)$, which in view of the known results for the fluid-free system mentioned below (see Introduction) is an optimal restriction on $m$.
The equivalence principle can be tested by precision experiments based on classical and quantum systems, on the ground as well as in space. In many models, these tests are mostly equivalent in their ability to constrain physics beyond the Standard Model. We mention differences that nevertheless exist between spaceborne and quantum mechanical tests and their conventional competitors.
We present a simple and accurate method to constrain galaxy bias based on the distribution of counts in cells. The most unique feature of our technique is that it is applicable to non-linear scales, where both dark matter statistics and the nature of galaxy bias are fairly complex. First, we estimate the underlying continuous distribution function from precise counts-in-cells measurements assuming local Poisson sampling. Then a robust, non-parametric inversion of the bias function is recovered from the comparison of the cumulative distributions in simulated dark matter and galaxy catalogs. Obtaining continuous statistics from the discrete counts is the most delicate novel part of our recipe. It corresponds to a deconvolution of a (Poisson) kernel. For this we present two alternatives: a model independent algorithm based on Richardson-Lucy iteration, and a solution using a parametric skewed lognormal model. We find that the latter is an excellent approximation for the dark matter distribution, but the model independent iterative procedure is more suitable for galaxies. Tests based on high resolution dark matter simulations and corresponding mock galaxy catalogs show that we can reconstruct the non-linear bias function down to highly non-linear scales with high precision in the range of $-1 \le \delta \le 5$. As far as the stochasticity of the bias, we have found a remarkably simple and accurate formula based on Poisson noise, which provides an excellent approximation for the scatter around the mean non-linear bias function. In addition we have found that redshift distortions have a negligible effect on our bias reconstruction, therefore our recipe can be safely applied to redshift surveys.
Electrons with kinetic energies of the order 100 keV are capable of exciting atomic vibrational states from a distance of microns. Despite such a large interaction distance, our detailed calculations show that the scattering physics permits a high-energy electron beam to locate vibrational excitations with atomic-scale spatial resolution. Pursuits to realize this capability experimentally could potentially benefit numerous fields across the physical sciences.
Tidal disruption events (TDEs) occur when a star passes too close to a supermassive black hole and is destroyed by tidal gravitational forces. Radio observations of TDEs trace synchrotron emission from outflowing material that may be ejected from the inner regions of the accretion flow around the SMBH or by the tidal debris stream. Radio detections of tidal disruption events are rare, but provide crucial information about the launching of jets and outflows from supermassive black holes and the circumnuclear environment in galaxies. Here we present the radio detection of the TDE AT2020opy, including three epochs of radio observations taken with the Karl G. Jansky's Very Large Array (VLA), MeerKAT, and upgraded Giant Metrewave Radio telescope. AT2020opy is the most distant thermal TDE with radio emission reported to date, and from modelling the evolving synchrotron spectra we deduce that the host galaxy has a more dense circumnuclear medium than other thermal TDEs detected in the radio band. Based on an equipartition analysis of the synchrotron spectral properties of the event, we conclude that the radio-emitting outflow was likely launched approximately at the time of, or just after, the initial optical flare. We find no evidence for relativistic motion of the outflow. The high luminosity of this event supports that a dense circumnuclear medium of the host galaxy produces brighter radio emission that rises to a peak more quickly than in galaxies with lower central densities.
We prove a large deviation type estimate for the asymptotic behavior of a weighted local time of $\varepsilon W$ as $\varepsilon\to0$.
We propose a new approach to image segmentation, which exploits the advantages of both conditional random fields (CRFs) and decision trees. In the literature, the potential functions of CRFs are mostly defined as a linear combination of some pre-defined parametric models, and then methods like structured support vector machines (SSVMs) are applied to learn those linear coefficients. We instead formulate the unary and pairwise potentials as nonparametric forests---ensembles of decision trees, and learn the ensemble parameters and the trees in a unified optimization problem within the large-margin framework. In this fashion, we easily achieve nonlinear learning of potential functions on both unary and pairwise terms in CRFs. Moreover, we learn class-wise decision trees for each object that appears in the image. Due to the rich structure and flexibility of decision trees, our approach is powerful in modelling complex data likelihoods and label relationships. The resulting optimization problem is very challenging because it can have exponentially many variables and constraints. We show that this challenging optimization can be efficiently solved by combining a modified column generation and cutting-planes techniques. Experimental results on both binary (Graz-02, Weizmann horse, Oxford flower) and multi-class (MSRC-21, PASCAL VOC 2012) segmentation datasets demonstrate the power of the learned nonlinear nonparametric potentials.
A matching $M$ in a graph $G$ is connected if all the edges of $M$ are in the same component of $G$. Following \L uczak,there have been many results using the existence of large connected matchings in cluster graphs with respect to regular partitions of large graphs to show the existence of long paths and other structures in these graphs. We prove exact   Ramsey-type bounds on the sizes of monochromatic connected matchings in $2$-edge-colored multipartite graphs. In addition, we prove a stability theorem for such matchings.
We investigate the microscopic dynamics at the initial stage of photoinduced phase transitions in tetrathiafulvalene-$p$-chloranil by exact diagonalization. We first show that the one-dimensional extended Peierls-Hubbard model exhibits a neutral phase with small ionicity and negligible dimerization and an ionic phase with moderate ionicity and dimerization. Aside from these phases, we find a doubly ionized phase with strong dimerization that we call the "dipole" phase. These ground-state phases are characterized by various order parameters and the Zak phase, which is relevant to electronic polarization. We further explore the microscopic dynamics of the three phases triggered by short monocycle optical pulses. The electronic order parameters and lattice displacement suggest that the neutral-ionic, ionic-neutral, and dipole-ionic transitions are induced. Furthermore, clear spectroscopic changes are observed in the time-dependent spectral density and pump-probe conductivity. A detailed analysis of the spectroscopy demonstrates the generation of coherent charge-transfer strings via multiphoton absorption and the crucial roles of the excited states and the metastable ground state at the new lattice position for the ultrafast dynamics.
We study a notion of derived foliations on schemes and derived schemes of arbitrary characteristics. We introduce the Hodge filtration associated to a derived foliation, which functorialy filters derived de Rham cohomology. We use this filtration to study vanishing results of Chern classes of perfect complexes endowed with connexions along derived foliations. As an application, we prove a positive characteristic version of Bott's vanishing theorem and more generally of existence of residues for foliations with singularities due to Baum-Bott in characteristic zero.
The acoustic Faraday rotation in the 4f paramagnet Tb3Ga5O12 has recently been observed by Sytcheva et al (arXiv:1006.0141). As in earlier examples the rotation angle per unit length of transverse acoustic modes was found to depend linearly on sound frequency. Existing theories for this effect consistently require that it should vary with the square of the frequency. In the present work a solution for this long-standing problem is provided. We propose a model based on magnetoelastic interactions with 4f quadrupole moments that includes both acoustic and optical phonons. The symmetry allows a direct and induced coupling between the latter. This leads to an indirect acoustic Faraday rotation via the field induced splitting of doubly degenerate optical phonon modes. It varies linearly with frequency in accordance with experiment and dominates the rotation angle. It also explains the observed resonance of the rotation angle in the field range between 17-20 T. The mechanism is of general validity for non-Bravais lattices and applies to previous examples of the acoustic Faraday effect.
As V. I. Arnold observed in the 1960s, the Euler equations of incompressible fluid flow correspond formally to geodesic equations in a group of volume-preserving diffeomorphisms. Working in an Eulerian framework, we study incompressible flows of shapes as critical paths for action (kinetic energy) along transport paths constrained to have characteristic-function densities. The formal geodesic equations for this problem are Euler equations for incompressible, inviscid potential flow of fluid with zero pressure and surface tension on the free boundary. The problem of minimizing this action exhibits an instability associated with microdroplet formation, with the following outcomes: Any two shapes of equal volume can be approximately connected by an Euler spray---a countable superposition of ellipsoidal geodesics. The infimum of the action is the Wasserstein distance squared, and is almost never attained except in dimension 1. Every Wasserstein geodesic between bounded densities of compact support provides a solution of the (compressible) pressureless Euler system that is a weak limit of (incompressible) Euler sprays. Each such Wasserstein geodesic is also the unique minimizer of a relaxed least-action principle for a two-fluid mixture theory corresponding to incompressible fluid mixed with vacuum.
We write the Mathisson-Papapetrou equations of motion for a spinning particle in a stationary spacetime using the quasi-Maxwell formalism and give an interpretation of the coupling between spin and curvature. The formalism is then used to compute equilibrium positions for spinning particles in the NUT spacetime.
I discuss the physics of polarization in models with early reionization. For sufficiently high optical depth to recombination the polarization is boosted on large scales while it is suppressed on smaller scales. New peaks appear in the polarization power spectrum, their position is proportional to the square root of the redshift at which the reionization occurs while their amplitude is proportional to the optical depth. For standard scenarios the rms degree of linear polarization as measured with a 7 degree FWHM antenna (like the one of the Brown University experiment) is $1.6\mu K$, $1.2 \mu K$, $4.8\times 10^{-2} \mu K$ for an optical depth of 1, 0.5 or 0 respectively. For a 1 degree FWHM antenna this same models give $2.7 \mu K$ , $1.8 \mu K$ and $0.77 \mu K$. Detailed measurement of polarization on large angular scales could provide an accurate determination of the epoch of reionization, which cannot be obtained from temperature measurements alone.
The Kondo system CeRu$_4$Sn$_6$ shows a strong anisotropy in its electric, optic and magnetic properties. We employ density functional theory plus dynamical mean field theory and show that the predominant Ce-$f$ state has total angular moment $J=5/2$ and $z$-component $m_J=\pm 1/2$ in agreement with recent X-ray absorption experiments. Even though CeRu$_4$Sn$_6$ has the direct gap of a Kondo insulator through most of the Brillouin zone it remains weakly metallic. This is because of (i) a band crossing in the $z$-direction and (ii) a negative indirect gap.