ShantanuT01/DACTYL-Pretraining huggingface dataset:
A method of random integral representation, that is, a method of representing a given probability measure as the probability distribution of some random integral, was quite successful in the past few decades. In this note we show that a composition of two random integral mappings $\J^\be$ is again a random integral mapping. We illustrate our results on some examples.
The Initial-Boundary Value Problem for the heat equation is solved by using a new algorithm based on a random walk on heat balls. Even if it represents a sophisticated generalization of the Walk on Spheres (WOS) algorithm introduced to solve the Dirich-let problem for Laplace's equation, its implementation is rather easy. The definition of the random walk is based on a new mean value formula for the heat equation. The convergence results and numerical examples permit to emphasize the efficiency and accuracy of the algorithm.
Let $X\subset\mathbb{P}^{N}$ be an irreducible, non-degenerate variety. The generalized variety of sums of powers $VSP_H^X(h)$ of $X$ is the closure in the Hilbert scheme $Hilb_{h}(X)$ of the locus parametrizing collections of points $\{x_{1},...,x_{h}\}$ such that the $(h-1)$-plane $\left\langle x_{1},...,x_{h}\right\rangle$ passes trough a fixed general point $p\in\mathbb{P}^{N}$. When $X = V_{d}^{n}$ is a Veronese variety we recover the classical variety of sums of powers $VSP(F,h)$ parametrizing additive decompositions of a homogeneous polynomial as powers of linear forms. In this paper we study the birational behavior of $VSP_H^X(h)$. In particular we will show how some birational properties, such as rationality, unirationality and rational connectedness, of $VSP_H^X(h)$ are inherited from the birational geometry of variety $X$ itself.
We represent fractional conditional expectations of a functional of fractional Brownian motion as a convergent series in L^2 space. When the target random variable is some function of a discrete trajectory of fractional Brownian motion, we obtain a backward Taylor series representation; when the target functional is generated by a continuous fractional filtration, the series representation is obtained by applying a "frozen path" operator and an exponential operator to the functional. Three examples are provided to show that our representation gives useful series expansions of ordinary expectations of target random variables.
Erosion of rocky coasts spontaneously creates irregular seashores. But the geometrical irregularity, in turn, damps the sea-waves, decreasing the average wave amplitude. There may then exist a mutual self-stabilisation of the waves amplitude together with the irregular morphology of the coast. A simple model of such stabilisation is studied. It leads, through a complex dynamics of the earth-sea interface, to the appearance of a stationary fractal seacoast with dimension close to 4/3. Fractal geometry plays here the role of a morphological attractor directly related to percolation geometry.
We review recent theoretical and experimental developments concerning collective spin excitations in two-dimensional electron liquid (2DEL) systems, with particular emphasis on the interplay between many-body and spin-orbit effects, as well as the intrinsic dissipation due to the spin-Coulomb drag. Historically, the experimental realization of 2DELs in silicon inversion layers in the 60s and 70s created unprecedented opportunities to probe subtle quantum effects, culminating in the discovery of the quantum Hall effect. In the following years, high quality 2DELs were obtained in doped quantum wells made in typical semiconductors like GaAs or CdTe. These systems became important test beds for quantum many-body effects due to Coulomb interaction, spin dynamics, spin-orbit coupling, effects of applied magnetic fields, as well as dissipation mechanisms. Here we focus on the recent results involving chiral effects and intrinsic dissipation of collective spin modes: these are not only of fundamental interest but also important towards demonstrating new concepts in spintronics. Moreover, new realizations of 2DELs are emerging beyond traditional semiconductors, for instance in multilayer graphene, oxide interfaces, dichalcogenide monolayers, and many more. The concepts discussed in this review will be relevant also for these emerging systems.
External fields in Migromian dynamics (MD or MOND, Milgrom 1983) break the Strong Equivalence Principle (SEP) and change the dynamics of self-bound stellar systems moving in space-varying background gravitational fields. We study two kinds of re-virialisation of the stellar systems: the violent phase transition and the adiabatic phase transition for systems moving on radial orbits, where the external field evolves from strong to weak and whose corresponding dynamics changes from Newtonian to Milgromian. We find that the time scale for the phase tranformation from Newtonian to Milgromian gravity lies only within one to a few crossing times for low density globular clusters with masses ranging from $10^4\msun$ to $10^6\msun$. Thus a globular cluster can appear frozen in the Newtonian regime despite being in the Milgromian regime for not longer than a few crossing times. We also study the kinematics and anisotropy profiles of the systems. The velocity dispersions of the systems are larger after the phase transitions, especially for the outer regions of the stellar systems. Moreover, the isotropic systems become radially anisotropic, especially for the outer parts, after the process caused by the dynamical phase transition. Deeper Milgromian systems have more radially anisotropic velocity dispersion functions. We also find that the final profiles of density, velocity dispersion and anisotropy do not depend on the details of the phase transition. I.e., the mass distribution and kinematics of the end-states of the globular clusters do not depend on the rapidity of the transition from Newtonian to Milgromian gravity. Thus, the transition from the Newtonian to the Milgromian regime naturally induces a significant radially anisotropic velocity distribution in a globular cluster.
After picking out what may seem more realistic minimal gravitational deformation of quantum mechanics, we study its back reaction on gravity. The large distance behaviour of Newtonian potential coincides with the result obtained by using of effective field theory approach to general relativity (the correction proves to be of repulsive nature). The short distance corrections result in Planck mass black hole remnants with zero temperature. The deformation of position-momentum uncertainty relations leads to the superluminal motion that can be avoided by making similar deformation of time-energy uncertainty relation. Such deformation also avoids UV divergences in QFT.
In connection with the space-time uncertainty principle which gives a simple qualitative characterization of non-local or non-commutative nature of short-distance space-time structure in string theory, author's recent approaches toward field theories for D-branes are briefly outlined, putting emphasis on some key ideas lying in the background. The final section of the present report is devoted partially to a tribute to Yukawa on the occasion of the centennial of his birth.
We use hexagonalization to compute four-point correlation functions of long BPS operators with special R-charge polarizations. We perform the computation at weak coupling and show that at any loop order our correlators can be expressed in terms of single-valued polylogarithms with uniform maximal transcendentality. As a check of our results we extract nine-loop OPE data and compare it against sum rules of (squared) structures constants of non-protected exchanged operators described by hundreds of Bethe solutions.
Extended calculations of the deuteron's static properties, based on the numerical solution of the Bethe-Salpeter equation, are presented. A formalism is developed, which provides a comparative analysis of the covariant amplitudes in various representations and nonrelativistic wave functions. The magnetic and quadrupole moments of the deuteron are calculated in the Bethe-Salpeter formalism and the role of relativistic corrections is discussed.
The coherent charge transport through an illuminated graphene ribbon is studied as function of electronic doping, frequency and strength of the electromagnetic driving, for monochromatic circularly polarized light. We focus on the DC current carried by 2D bulk carriers which is dominant (over edge transport) for short and wide enough samples. Broad dips in conductance are predicted for one-photon and multi-photon resonances between the valence and conductance bands. The residual conductance can be associated with evanescent states and related to dynamical gaps in the Floquet quasi-energy spectrum.
Saliency maps that identify the most informative regions of an image for a classifier are valuable for model interpretability. A common approach to creating saliency maps involves generating input masks that mask out portions of an image to maximally deteriorate classification performance, or mask in an image to preserve classification performance. Many variants of this approach have been proposed in the literature, such as counterfactual generation and optimizing over a Gumbel-Softmax distribution. Using a general formulation of masking-based saliency methods, we conduct an extensive evaluation study of a number of recently proposed variants to understand which elements of these methods meaningfully improve performance. Surprisingly, we find that a well-tuned, relatively simple formulation of a masking-based saliency model outperforms many more complex approaches. We find that the most important ingredients for high quality saliency map generation are (1) using both masked-in and masked-out objectives and (2) training the classifier alongside the masking model. Strikingly, we show that a masking model can be trained with as few as 10 examples per class and still generate saliency maps with only a 0.7-point increase in localization error.
If a complex analytic function, $f$, has a stratified isolated critical point, then it is known that the cohomology of the Milnor fibre of $f$ has a direct sum decomposition in terms of the normal Morse data to the strata. We use microlocal Morse theory to obtain the same result under the weakened hypothesis that the vanishing cycles along $f$ have isolated support. We also investigate an index-theoretic proof of this fact.
We report results of theoretical studies of thermoelectric efficiency of single-molecule junctions with long molecular linkers. The linker is simulated by a chain of identical sites described using a tight-binding model. It is shown that thermoelectric figure of merit ZT strongly depends on the bridge length, being controlled by the lineshape of electron transmission function within the tunnel energy range corresponding to HOMO/LUMO transport channel. Using the adopted model we demonstrate that ZT may significantly increase as the linker lengthens, and that gateway states on the bridge (if any) may noticeably affect the length-dependent ZT. Temperature dependences of ZT for various bridge lengths are analyzed. It is shown that broad minima emerge in ZT versus temperature curves whose positions are controlled by the bridge lengths.
We report the discovery of 19 hot, evolved, massive stars near the Galactic center region (GCR). These objects were selected for spectroscopy owing to their detection as strong sources of Paschen-alpha emission-line excess, following a narrowband imaging survey of the central 0.65 x 0.25 degress (l, b) around Sgr A* with the Hubble Space Telescope. Discoveries include 5 carbon-type (WC) and 6 nitrogen-type (WN) Wolf-Rayet stars, 6 O supergiants, and 2 B supergiants. Two of the O supergiants have X-ray counterparts, the properties of which are broadly consistent with colliding-wind binaries and solitary O stars. The infrared photometry of 17 stars is consistent with the Galactic center distance, but 2 of them are located in the foreground. Several WC stars exhibit a relatively large infrared excesses, which is possibly the signature of thermal emission from hot dust. Most of the stars appear scattered throughout the GCR, with no relation to the three known massive young clusters; several others lie near the Arches and Quintuplet clusters and may have originated within one of these systems. The results of this work bring the total sample of Wolf-Rayet stars in the GCR to 92. All sources of strong P-alpha excess have been identified in the area surveyed with HST, which implies that the sample of WN stars in this region is near completion, and is dominated by late (WNL) types. The current WC sample, although probably not complete, is almost exclusively dominated by late (WCL) types. The observed Wolf-Rayet subtype distribution in the GCR is a reflection of the intrinsic rarity of early subtypes (WNE and WCE) in the inner Galaxy, an effect that is driven by metallicity.
Lifetime limited optical excitation lines of single nitrogen vacancy (NV) defect centers in diamond have been observed at liquid helium temperature. They display unprecedented spectral stability over many seconds and excitation cycles. Spectral tuning of the spin selective optical resonances was performed via the application of an external electric field (i.e. the Stark shift). A rich variety of Stark shifts were observed including linear as well as quadratic components. The ability to tune the excitation lines of single NV centers has potential applications in quantum information processing.
We introduce a new continuous cellular automaton that presents self-organized criticality. It is one-dimensional, totally deterministic, without any kind of embedded randomness, not even in the initial conditions. This system is in the same universality class as the Oslo rice pile system, boundary driven interface depinning and the train model for earthquakes. Although the system is chaotic, in the thermodynamic limit chaos occurs only in a microscopic level.
Calculations in Ising model can be cumbersome and non-intuitive. Here we provide a formulation that addresses these issues for 1-D scenario. We represent the microstates of spin interactions as a diagonal matrix. This is done using two operations: Kronecker sum and Kronecker product. The calculations thus become simple matter of manipulating diagonal matrices. We address the following problems in this work: spins in the magnetic field, open-chain 1-D Ising model, closed-chain 1-D Ising model, 1-D Ising model in an external magnetic field. We believe that this representation will help provide students as well as experts with a simple yet powerful technique to carry out calculations in this model.
We present a new method for incorporating nonthermal pressure from bulk motions of gas into an analytic model of the intracluster medium in clusters of galaxies, which is based on a polytropic equation of state and hydrostatic equilibrium inside gravitational potential wells drawn from cosmological dark matter simulations. The pressure is allowed to have thermal and nonthermal components with different radial distributions; the overall level of nonthermal support is based on the dynamical state of the halo, such that it is lower in more relaxed clusters. This level is normalized by comparison to pressure profiles derived from X-ray observations, and to a high resolution hydrodynamical simulation. The nonthermal pressure fraction measured at r_500 is typically in the range 10-20%, increasing with cluster mass and with redshift. The resulting model cluster properties are in accord with Sunyaev-Zel'dovich (SZ) effect observations of clusters. Inclusion of nonthermal pressure reduces the expected angular power spectrum of SZ fluctuations in the microwave sky by 24%.
In order to investigate relativistic effects we compare the transverse flow calculated by using the four versions of the QMD approaches with that of the full covariant RQMD approach. From the comparison we conclude that the simplified RQMD (RQMD/S), which uses the common time coordinate to all particles, can be used instead of RQMD up to 6 GeV/u.
The doubly charged Higgs bosons $H^{\pm\pm}$ searches at the Large Hadron Collider (LHC) have been studied extensively and strong bound is available for $H^{\pm\pm}$ dominantly decaying into a pair of same-sign di-leptons. In this paper we point out that there is a large cavity in the light $H^{\pm\pm}$ mass region left unexcluded. In particular, $H^{\pm\pm}$ can dominantly decay into $WW$ or $WW^*$ (For instance, in the type-II seesaw mechanism the triplet acquires a vacuum expectation value around 1 GeV.), and then it is found that $H^{\pm\pm}$ with mass even below $2m_W$ remains untouched by the current collider searches. Searching for such a $H^{\pm\pm}$ at the LHC is the topic of this paper. We perform detailed signal and background simulation, especially including the non-prompt $t\bar{t}$ background which is the dominant one nevertheless ignored before. We show that such $H^{\pm\pm}$ should be observable at the 14 TeV LHC with 10-30 fb$^{-1}$ integrated luminosity.
N-type doping in Si by shallow impurities, such as P, As and Sb, exhibits an intrinsic limit due to the Fermi-level pinning via defect complexes at high doping concentrations. Here we demonstrate that doping Si with the chalcogen Te by non-equilibrium processing, a deep double donor, can exceed this limit and yield higher electron concentrations. In contrast to shallow impurities, both the interstitial Te fraction decreases with increasing doping concentration and substitutional Te dimers become the dominant configuration as effective donors, leading to a non-saturating carrier concentration as well as to an insulator-to-metal transition. First-principle calculations reveal that the Te dimers possess the lowest formation energy and donate two electrons per dimer to the conduction band. These results provide novel insight into physics of deep impurities and lead to a possible solution for the ultra-high electron concentration needed in today's Si-based nanoelectronics.
Here we develop a microscopic approach aimed at the description of a suite of physical effects related to carrier transport in, and the optical properties of, halide perovskites. Our theory is based on the description of the nuclear dynamics to all orders and goes beyond the common assumption of linear electron-phonon coupling in describing the carrier dynamics and band gap characteristics. When combined with first-principles calculations and applied to the prototypical MAPbI$_{3}$ system, our theory explains seemingly disparate experimental findings associated with both the charge-carrier mobility and optical absorption properties, including their temperature dependencies. Our findings demonstrate that orbital overlap fluctuations in the lead-halide structure plays a significant role in determining the optoelectronic features of halide perovskites.
Let $f(\mathbb{z},\bar{\mathbb{z}})$ be a convenient Newton non-degenerate mixed polynomial with strongly polar non-negative mixed weighted homogeneous face functions. We consider a convenient regular simplicial cone subdivision $\Sigma^*$ which is admissible for $f$ and take the toric modification $\hat{\pi} : X \to \mathbb{C}^n$ associated with $\Sigma^*$. We show that the toric modification resolves topologically the singularity of the mixed hypersurface germ defined by $f(\mathbb{z},\bar{\mathbb{z}})$ under the Assumption (*) (Theorem 32). This result is an extension of the first part of Theorem 11 ([4]) by Mutsuo Oka. We also consider some typical examples (\S 9).
The combinatorial theory of rotor-routers has connections with problems of statistical mechanics, graph theory, chaos theory, and computer science. A rotor-router network defines a deterministic walk on a digraph G in which a particle walks from a source vertex until it reaches one of several target vertices. Motivated by recent results due to Giacaglia et al., we study rotor-router networks in which all non-target vertices have the same type. A rotor type r is universal if every hitting sequence can be achieved by a homogeneous rotor-router network consisting entirely of rotors of type r. We give a conjecture that completely classifies universal rotor types. Then, this problem is simplified by a theorem we call the Reduction Theorem that allows us to consider only two-state rotors. A rotor-router network called the compressor, because it tends to shorten rotor periods, is introduced along with an associated algorithm that determines the universality of almost all rotors. New rotor classes, including boppy rotors, balanced rotors, and BURD rotors, are defined to study this algorithm rigorously. Using the compressor the universality of new rotor classes is proved, and empirical computer results are presented to support our conclusions. Prior to these results, less than 100 of the roughly 260,000 possible two-state rotor types of length up to 17 were known to be universal, while the compressor algorithm proves the universality of all but 272 of these rotor types.
We present a study of the tunnel magneto-Seebeck (TMS) effect in MgO based magnetic tunnel junctions (MTJs). The electrodes consist of CoFeB with in-plane magnetic anisotropy. The temperature gradients which generate a voltage across the MTJs layer stack are created using laser heating. Using this method, the temperature can be controlled on the micrometer length scale: here, we investigate, how both, the TMS voltage and the TMS effect, depend on the size, position and intensity of the applied laser spot. For this study, a large variety of different temperature distributions was created across the junction. We recorded two-dimensional maps of voltages generated by heating in dependence of the laser spot position and the corresponding calculated TMS values. The voltages change in value and sign, from large positive values when heating the MTJ directly in the centre to small values when heating the junction on the edges and even small negative values when heating the sample away from the junction. Those zero crossings lead to very high calculated TMS ratios. Our systematic analysis shows, that the distribution of the temperature gradient is essential, to achieve high voltage signals and reasonable resulting TMS ratios. Furthermore, artefacts on the edges produce misleading results, but also open up further possibilities of more complex heating scenarios for spincaloritronics in spintronic devices.
The in-medium properties of a hyperon-nucleon potential, derived within chiral effective field theory and fitted to Lambda-N and Sigma-N scattering data, are investigated. Results for the single-particle potentials of the Lambda and Sigma hyperons in nuclear matter are reported, based on a conventional first-order Brueckner calculation. The Sigma-nucleus potential is found to be repulsive, in agreement with phenomenological information. A weak Lambda-nucleus spin-orbit interaction can be achieved by an appropriate adjustment of a low-energy constant corresponding to an antisymmetric Lambda-N -- Sigma-N spin-orbit interaction that arises at next-to-leading order in the effective field theory approach.
Let $k$ be a perfect field of characteristic $p > 2$, and let $K$ be a finite totally ramified extension of $W(k)[\frac{1}{p}]$. We prove that the locus of potentially semi-stable $\mathrm{Gal}(\bar{K}/K)$-representations of a given Hodge-Tate type and Galois type is a closed subspace of the universal deformation ring, generalizing the result of Kisin (2007) where $k$ is assumed to be finite.
We use a dynamic programming algorithm to establish a new lower bound on the domination number of complete cylindrical grid graphs of the form $C_n\square P_m$, that is, the Cartesian product of a path and a cycle, when $n\equiv 2\pmod{5}$, and we establish a new upper bound equal to the lower bound, thus computing the exact domination number for these graphs.