ShantanuT01/DACTYL-Pretraining huggingface dataset:
We introduce and study tetrahedron instantons, which can be realized in string theory by D$1$-branes probing a configuration of intersecting D$7$-branes in flat spacetime with a proper constant $B$-field. Physically they capture instantons on $\mathbb{C}^{3}$ in the presence of the most general intersecting real codimension-two supersymmetric defects. Moreover, we construct the tetrahedron instantons as particular solutions of general instanton equations in noncommutative field theory. We analyze the moduli space of tetrahedron instantons and discuss the geometric interpretations. We compute the instanton partition function both via the equivariant localization on the moduli space of tetrahedron instantons and via the elliptic genus of the worldvolume theory on the D$1$-branes probing the intersecting D$7$-branes, obtaining the same result. The instanton partition function of the tetrahedron instantons lies between the higher-rank Donaldson-Thomas invariants on $\mathbb{C}^{3}$ and the partition function of the magnificent four model, which is conjectured to be the mother of all instanton partition functions. Finally, we show that the instanton partition function admits a free field representation, suggesting the existence of a novel kind of symmetry which acts on the cohomology of the moduli spaces of tetrahedron instantons.
Estimating pose of the head is an important preprocessing step in many pattern recognition and computer vision systems such as face recognition. Since the performance of the face recognition systems is greatly affected by the poses of the face, how to estimate the accurate pose of the face in human face image is still a challenging problem. In this paper, we represent a novel method for head pose estimation. To enhance the efficiency of the estimation we use contourlet transform for feature extraction. Contourlet transform is multi-resolution, multi-direction transform. In order to reduce the feature space dimension and obtain appropriate features we use LDA (Linear Discriminant Analysis) and PCA (Principal Component Analysis) to remove ineffcient features. Then, we apply different classifiers such as k-nearest neighborhood (knn) and minimum distance. We use the public available FERET database to evaluate the performance of proposed method. Simulation results indicate the superior robustness of the proposed method.
This paper investigates a numerical probabilistic method for the solution of some semilinear stochastic partial differential equations (SPDEs in short). The numerical scheme is based on discrete time approximation for solutions of systems of decoupled forward-backward doubly stochastic differential equations. Under standard assumptions on the parameters, the convergence and the rate of convergence of the numerical scheme is proven. The proof is based on a generalization of the result on the path regularity of the backward equation.
We explore a new definition of the persistence exponent, measuring the probability that a spin never flips after a quench of an Ising-like model at a temperature 0<T<Tc, while the usual definition only makes sense at T=0. This probability is now defined for spin blocks, and a general scaling for it, involving time and block linear size is introduced and illustrated by extensive simulations.
We derive observational consequences of the hypothesis that cosmic rays (CR's) of energy $>10^{19}eV$ originate in the same cosmological objects producing gamma-ray bursts (GRB's). Inter-galactic magnetic fields $\gtrsim 10^{-12} G$ are required in this model to allow CR's to be observed continuously in time by producing energy dependent delays in the CR arrival times. This results in individual CR sources having very narrow observed spectra, since at any given time only those CR's having a fixed time delay are observed. Thus, the brightest CR sources should be different at different energies. The average number of sources contributing to the total CR flux decreases with energy much more rapidly than in a model of steady CR sources, dropping to one at $E_{crit} \simeq2\times10^{20}$~eV with very weak sensitivity to the inter-galactic magnetic field strength. Below $E_{crit}$, a very large number of sources is expected, consistent with observations. Above $E_{crit}$, a source may be observed with a flux considerably higher than the time-averaged CR flux from all sources, if a nearby GRB occurred recently. If such a source is present, its narrow spectrum may produce a ``gap'' in the total spectrum. These signatures should be detectable by the planned ``Auger'' CR experiment.
We extend the results of Pareschi on the constancy of the gonality and Clifford index of smooth curves in a complete linear system on Del Pezzo surfaces of degrees $\geq 2$ to the case of Del Pezzo surfaces of degree 1, where we explicitly classify the cases where the gonality and Clifford index are not constant. We also classify all cases of exceptional curves on Del Pezzo surfaces, which turn out to be the smooth plane curves and some other cases with Clifford dimension 3. Moreover, the property of being exceptional holds for all curves in the complete linear system.   Furthermore, we relate the Clifford index and gonality of smooth curves in $|L|$ to the higher order embedding properties of $|L+K_S|$. More precisely, we show that for a nef line bundle $L$ on a Del Pezzo surface, $L+K_S$ is birationally $k$-very ample if and only if all the smooth curves in $|L|$ have gonality $\geq k+2$, and we also find numerical criteria for birational $k$-very ampleness.
All estimators of the two-point correlation function are based on a random catalogue, a set of points with no intrinsic clustering following the selection function of a survey. High-accuracy estimates require the use of large random catalogues, which imply a high computational cost. We propose to replace the standard random catalogues by glass-like point distributions or glass catalogues, which are characterized by a power spectrum $P(k)\propto k^4$ and exhibit significantly less power than a Poisson distribution with the same number of points on scales larger than the mean inter-particle separation. We show that these distributions can be obtained by iteratively applying the technique of Zeldovich reconstruction commonly used in studies of baryon acoustic oscillations (BAO). We provide a modified version of the widely used Landy-Szalay estimator of the correlation function adapted to the use of glass catalogues and compare its performance with the results obtained using random samples. Our results show that glass-like samples do not add any bias with respect to the results obtained using Poisson distributions. On scales larger than the mean inter-particle separation of the glass catalogues, the modified estimator leads to a significant reduction of the variance of the Legendre multipoles $\xi_\ell(s)$ with respect to the standard Landy-Szalay results with the same number of points. The size of the glass catalogue required to achieve a given accuracy in the correlation function is significantly smaller than when using random samples. Even considering the small additional cost of constructing the glass catalogues, their use could help to drastically reduce the computational cost of configuration-space clustering analysis of future surveys while maintaining high-accuracy requirements.
The Ward identities of the $W_{\infty}$ symmetry in 2D string theory in the tachyon background are studied in the continuum approach. Comparing the solutions with the matrix model results, it is verified that 2D string amplitudes are different from the matrix model amplitudes only by the external leg factors even in higher genus. This talk is based on the recent work [1] and also [2] for the $c_M <1$ model. (Talk given at the workshop on ``Frontiers in Quantum Field Theory'', Osaka, Japan, December 1995.)
We review the results from our studies, and previous published work, on the spatially resolved physical properties of a sample of HII/BCD galaxies, as obtained mainly from integral-field unit spectroscopy with Gemini/GMOS and VLT/VIMOS. We confirm that, within observational uncertainties, our sample galaxies show nearly spatially constant chemical abundances, similar to other low-mass starburst galaxies. They also show He II 4686 emission with properties being suggestive of a mix of excitation sources, with Wolf-Rayet stars being excluded as the primary one. Finally, in this contribution we include a list of all HII/BCD galaxies studied thus far with integral-field unit spectroscopy.
The GAUDI database (Ground-based Asteroseismology Uniform Database Interface, http://sdc.laeff.esa.es/gaudi/) is a preparatory archive for the COROT (COnvection, ROtation and planetary Transits, http://www.astrsp-mrs.fr/projets/corot/) mission developed at LAEFF (Laboratory for Space Astrophysics and Theoretical Physics, http://www.laeff.esa.es). Its intention is to make the ground-based observations obtained in the preparation of the asteroseismology programme available in a simple and efficient way. It contains spectroscopic and photometric data together with inferred physical parameters for more than 1500 objects gathered since January 1998 in 6 years of observational campaigns. In this paper, the main functionalities and characteristics of the system are described. The observations have been collected at ESO-La Silla, Telescopio Nazionale Galileo, Observatoire de Haute-Provence, South African Astronomical Observatory, Tautenberg Observatory and Sierra Nevada Observatory.
New optical spectra of 28 H II regions in the M101 disk have been obtained, yielding 10 new detections of the [O III]{\lambda}4363 auroral line. The oxygen abundance gradient measured from these data, combined with previous observations, displays a local scatter of 0.15+/-0.03 dex along an arc in the west side of the galaxy, compared with a smaller scatter of 0.08+/-0.01 dex in the rest of the disk. One of the H I I regions in our sample (H27) has a significantly lower oxygen abundance than surrounding nebulae at a similar galactocentric distance, while an additional, relatively nearby one (H128) was already known to have a high oxygen abundance for its position in the galaxy. These results represent marginal evidence for the existence of moderate deviations from chemical abundance homogeneity in the interstellar medium of M101. Using a variety of strong-line abundance indicators, we find no evidence for significant large-scale azimuthal variations of the oxygen abundance across the whole disk of the galaxy.
A b-coloring of a graph $G$ is a coloring of its vertices such that every color class contains a vertex that has neighbors in all other classes. The b-chromatic number of $G$ is the largest integer $k$ such that $G$ has a b-coloring with $k$ colors. Javadi and Omoomi ("On b-coloring of cartesian product of graphs", Ars Combinatoria 107 (2012) 521-536) proved that the b-chromatic number of $K_n \times K_n$ (the Cartesian product of two complete graphs on $n$ vertices) is in the set $\{2n-3, 2n-2\}$ and conjectured that the exact value is $2n-3$ for all $n \ge 5$. We give counterexamples to this conjecture for $n=5$, $n=6$ and $n=7$.
A unified first law of black-hole dynamics and relativistic thermodynamics is derived in spherically symmetric general relativity. This equation expresses the gradient of the active gravitational energy E according to the Einstein equation, divided into energy-supply and work terms. Projecting the equation along the flow of thermodynamic matter and along the trapping horizon of a blackhole yield, respectively, first laws of relativistic thermodynamics and black-hole dynamics. In the black-hole case, this first law has the same form as the first law of black-hole statics, with static perturbations replaced by the derivative along the horizon. There is the expected term involving the area and surface gravity, where the dynamic surface gravity is defined as in the static case but using the Kodama vector and trapping horizon. This surface gravity vanishes for degenerate trapping horizons and satisfies certain expected inequalities involving the area and energy. In the thermodynamic case, the quasi-local first law has the same form, apart from a relativistic factor, as the classical first law of thermodynamics, involving heat supply and hydrodynamic work, but with E replacing the internal energy. Expanding E in the Newtonian limit shows that it incorporates the Newtonian mass, kinetic energy, gravitational potential energy and thermal energy. There is also a weak type of unified zeroth law: a Gibbs-like definition of thermal equilibrium requires constancy of an effective temperature, generalising the Tolman condition and the particular case of Hawking radiation, while gravithermal equilibrium further requires constancy of surface gravity. Finally, it is suggested that the energy operator of spherically symmetric quantum gravity is determined by the Kodama vector, which encodes a dynamic time related to E.
For $6D$, ${\cal N}=(1,1)$ SYM theory formulated in ${\cal N}=(1,0)$ harmonic superspace as a theory of interacting gauge multiplet and hypermultiplet we construct the ${\cal N}=(1,1)$ supersymmetric Heisenberg-Euler-type superfield effective action. The effective action is computed for the slowly varying on-shell background fields and involves, in the bosonic sector, all powers of a constant abelian strength.
In this paper we continue the investigations about unlike powers in arithmetic progression. We provide sharp upper bounds for the length of primitive non-constant arithmetic progressions consisting of squares/cubes and $n$-th powers.
We consider a Hilbertian and a charges approach to fractional gradient constraint problems of the type $|D^\sigma u|\leq g$, involving the distributional fractional Riesz gradient $D^\sigma$, $0<\sigma <1$, extending previous results on the existence of solutions and Lagrange multipliers of these nonlocal problems.   We also prove their convergence as $\sigma\nearrow1$ towards their local counterparts with the gradient constraint $|D u|\leq g$.
First introduced in the study of the Sturmian words, the iterated palindromic closure was recently generalized to pseudopalindromes. This operator allows one to construct words with an infinity of pseudopalindromic prefixes, called pseudostandard words. We provide here several combinatorial properties of the fixed points under the iterated pseudopalindromic closure.
Perovskite SrTiO3 (STO) is an attractive photocatalyst for solar water splitting, but suffers from a limited photoresponse in the ultraviolet spectral range due to its wide band gap. By means of hybrid density functional theory calculations, we systematically study engineering its band gap via doping 4d and 5d transition metals M (M=Zr, Nb, Mo, Tc, Ru, Rh, Pd, Hf, Ta, W, Re, Os, Ir and Pt) and chalcogen elements Y (Y=S and Se). We find that transition metal dopant M either has no effect on STO band gap or introduces detrimental mid-gap states, except for Pd and Pt that are able to reduce the STO band gap. In contrast, doping S and Se significantly reduces STO's direct band gap, thus leading to appreciable optical absorption transitions in the visible spectral range. Our findings provide that Pd, S and Se doped STO are potential promising photocatalysts for water splitting under visible light irradiation, thereby providing insightful theoretical guides for experiments to improve the photocatalytic activity of STO.
The structure of exotic nuclei sheds new light on the linkage of the nuclear structure to the nucleonic interaction. The self-consistent mean-field (SCMF) theories are useful to investigate this linkage, which are applicable to many nuclei covering almost the whole range of the nuclear chart without artificial truncation of model space. For this purpose, it is desired to develop effective interaction for the SCMF calculations well connected to the bare nucleonic interaction. Focusing on ground-state properties, I show results of the SCMF calculations primarily with the M3Y-type semi-realistic interaction, M3Y-P6 and M3Y-P6a to be precise, and discuss in detail how the nucleonic interaction affects structure of nuclei including those far off the $\beta$-stability.
The transition from the Asymptotic Giant Branch (AGB) to the planetary nebula (PN) phase is critical in the shaping of PNe. It is suggested that the most asymmetric PNe are the descendant of massive AGB stars. Since these AGB stars are believed to evolve into heavily obscured post-AGB stars and PNe, the compilation of a sample of bona fide obscured post-AGB stars and PNe is important to help understand the formation of asymmetric PNe. We have used 2MASS, Spitzer GLIMPSE, MSX, and IRAS data in search of the near-IR counterparts of a sample of 165 presumably obscured IRAS post-AGB and PN candidates, and DSS red images to identify the optical counterparts among the objects detected in the near-IR. The IR spectral energy distributions (SEDs) in the wavelength range from 1 to 100 microns of the sources with unambiguous near-IR counterparts have been analyzed using appropriate colour-colour diagrams. We have identified the near-IR counterparts of 119 sources out of the 165 IRAS post-AGB and PN candidates in our sample. The improved astrometric coordinates of these sources have allowed us to find optical counterparts for 59 of them, yielding a reduced sample of 60 optically obscured post-AGB star and PN candidates. Among the 119 sources with near-IR counterparts, only 80 have unambiguous identifications in the 2MASS Point Source Catalogue.
We present a compact and general derivation of the generalized Bloch-Wangsness-Redfield kinetic equations for systems with the static spin Hamiltonian utilizing the concept of the Liouville space. We show that the assumptions of short correlation times and large heat capacity of the lattice are sufficient to derive the kinetic equations without the use of perturbation theory for the spin-lattice interaction operator. The perturbation theory is only applied for calculation of the kinetic coefficients, for which we obtain general and compact expressions. We argue that kinetic equations for the density matrix elements are not essential for derivation of the generalized Bloch-Wangsness-Redfield equations for the expectation values of any set of physical quantities, and the latter may be obtained directly under the weak assumptions of mutual orthogonality and completeness. We show that existence of a unity operator in the algebra of spin operators is a necessary condition for convergence of the spin subsystem to thermodynamic equilibrium with the temperature equal to that of the lattice. Finally, as an application of the general theory, we discuss some features of spin relaxation in heterogeneous systems for I=1/2.
A path system $\mathcal{P}$ in a graph $G=(V,E)$ is said to be irreducible if there does not exist a partition $V= A\sqcup B$ such that $\mathcal{P}$ restricts to a path system on both $G[A]$ and $G[B]$. In this paper, we construct an infinite family of non-metrizable irreducible path systems defined on certain Paley graphs.
We study how tidal streams from globular clusters may be used to constrain the mass of ultra-light dark matter particles, called `fuzzy' dark matter (FDM). A general feature of FDM models is the presence of ubiquitous density fluctuations in bound, virialized dark matter structures, on the scale of the de Broglie wavelength, arising from wave interference in the evolving dark matter distribution. These time-varying fluctuations can disturb the motions of stars, leading to potentially observable signatures in cold thin tidal streams in our own Galaxy. The study of this effect has been hindered by the difficulty in simulating the FDM wavefunction in Milky Way-sized systems. We present a simple method to evolve realistic wavefunctions in nearly static potentials, that should provide an accurate estimate of this granulation effect. We quantify the impact of FDM perturbations on tidal streams, and show that initially, while stream perturbations are small in amplitude, their power spectra exhibit a sharp cutoff corresponding to the de Broglie wavelength of the FDM potential fluctuations. Eventually, when stream perturbations become nonlinear, fold caustics generically arise that lead to density fluctuations with universal behavior. This erases the signature of the de Broglie wavelength in the stream density power spectrum, but we show that it will still be possible to determine the FDM mass in this regime, by considering the fluctuations in quantities like angular momenta or actions.
The aim of this work is to solve the dispersion relations near the first excitation threshold of photon propagating along the magnetic field in the strong field limit. We have calculated the time damping of the photon in two particular cases: the degenerate gas as well as the diluted gas limit being both important from the Astrophysical point of view. In particular the diluted gas limit could describe the magnethosphere of neutron stars. The solutions have been used to obtain a finite Quantum Faraday angle in both limits. A resonant behavior for the Faraday angle is also obtained. To reproduce the semi-classical result for the Faraday rotation angle the weak field limit is considered.
In 1916, MacMahon showed that permutations in $S_n$ with a fixed descent set $I$ are enumerated by a polynomial $d_I(n)$. Diaz-Lopez, Harris, Insko, Omar, and Sagan recently revived interest in this descent polynomial, and suggested the direction of studying such enumerative questions for other consecutive patterns (descents being the consecutive pattern $21$). Zhu studied this question for the consecutive pattern $321$. We continue this line of work by studying the case of any consecutive pattern of the form $k,k-1,\ldots,1$, which we call a $k$-descent. In this paper, we reduce the problem of determining the asymptotic number of permutations with a certain $k$-descent set to computing an explicit integral. We also prove an equidistribution theorem, showing that any two sparse $k$-descent sets are equally likely.   Counting the number of $k$-descent-avoiding permutations while conditioning on the length $n$ and first element $m$ simultaneously, one obtains a number triangle $f_k(m,n)$ with some useful properties. For $k=3$, the $m=1$ and $m=n$ diagonals are OEIS sequences A049774 and A080635. We prove a $k$th difference recurrence relation for entries of this number triangle. This also leads to an $O(n^2)$ algorithm for computing $k$-descent functions.   Along the way to these results, we prove an explicit formula for the distribution of first elements of $k$-descent-avoiding permutations, as well as for the joint distribution of first and last elements. We also develop an understanding of discrete order statistics. In our approach, we combine algebraic, analytic, and probabilistic tools. A number of open problems are stated at the end.
Stationary, asymptotically flat black holes in scalar-tensor theories of gravity are studied. It is shown that such black holes have no scalar hair and are the same as in General Relativity.