ShantanuT01/DACTYL-Pretraining huggingface dataset:
We study matrix factorizations of a section W of a line bundle on an algebraic stack. We relate the corresponding derived category (the category of D-branes of type B in the Landau-Ginzburg model with potential W) with the singularity category of the zero locus of W generalizing a theorem of Orlov. We use this result to construct push-forward functors for matrix factorizations with relatively proper support.
Physical configurations corresponding to topological excitations present in the XY limit of a quantum spin 1/2 Heisenberg ferromagnet, are investigated on a two dimensional square lattice. Quantum vortices(anti-vortices) are constructed in terms of terms of coherent spin field components and the crucial role of the associated Wess-Zumino term is highlighted. It is shown that this term can identify a large class of vortices(anti-vortices). In particular the excitations with odd topological charge belonging to this class, are found to exhibit a self-similar pattern regarding the internal charge distribution. Our formalism is distinctly different from the coventional approach for the construction of quantum vortices(anti-vortices).
We propose and study an SU(3) trimer resonating-valence-bond (tRVB) state with $C_{4v}$ point-group symmetry on the square lattice. By devising a projected entangled-pair state representation, we show that all (connected) correlation functions between local operators in this SU(3) tRVB state decay exponentially, indicating its gapped nature. We further calculate the modular $S$ and $T$ matrices by constructing all nine topological sectors on a torus and establish the existence of $\mathbb{Z}_3$ topological order in this SU(3) tRVB state.
The lack of experimental evidence for supersymmetry motivates R-parity violating realizations of the MSSM. Dropping R-parity, alternative symmetries have to be imposed in order to stabilize the proton. We determine the possible discrete R and non-R symmetries, which allow for renormalizable R-parity violating terms in the superpotential and which, at the effective level, are consistent with the constraints from nucleon decay. Assuming a gauge origin, we require the symmetry to be discrete gauge anomaly-free, allowing also for cancellation via the Green Schwarz mechanism. Furthermore, we demand lepton number violating neutrino mass terms either at the renormalizable or non-renormalizable level. In order to solve the mu problem, the discrete Z_N or Z_N^R symmetries have to forbid any bilinear superpotential operator at tree level. In the case of renormalizable baryon number violation the smallest possible symmetry satisfying all conditions is a unique hexality Z_6^R. In the case of renormalizable lepton number violation the smallest symmetries are two hexalities, one Z_6 and one Z_6^R.
We propose an adaptive, two steps strategy, for the estimation of mixed qubit states. We show that the strategy is optimal in a local minimax sense for the trace norm distance as well as other locally quadratic figures of merit. Local minimax optimality means that given $n$ identical qubits, there exists no estimator which can perform better than the proposed estimator on a neighborhood of size $n^{-1/2}$ of an arbitrary state. In particular, it is asymptotically Bayesian optimal for a large class of prior distributions.   We present a physical implementation of the optimal estimation strategy based on continuous time measurements in a field that couples with the qubits.   The crucial ingredient of the result is the concept of local asymptotic normality (or LAN) for qubits. This means that, for large $n$, the statistical model described by $n$ identically prepared qubits is locally equivalent to a model with only a classical Gaussian distribution and a Gaussian state of a quantum harmonic oscillator.   The term `local' refers to a shrinking neighborhood around a fixed state $\rho_{0}$. An essential result is that the neighborhood radius can be chosen arbitrarily close to $n^{-1/4}$. This allows us to use a two steps procedure by which we first localize the state within a smaller neighborhood of radius $n^{-1/2+\epsilon}$, and then use LAN to perform optimal estimation.
We discuss some aspects of heterotic-Type I duality. We focus on toroidal compactification, with special attention for the topology of the gauge group, and the topology of the bundle. We review the arguments leading to a classification of Spin(32)/Z_2-bundles over tori, suitable for string compactifications. A central role is played by n-gerbes with connection, a generalization of bundles with connection.
We report on a search for high-energy counterparts to fast radio bursts (FRBs) with the Fermi Gamma-ray Burst Monitor (GBM), Fermi Large Area Telescope (LAT), and the Neil Gehrels Swift Observatory Burst Alert Telescope (BAT). We find no significant associations for any of the 23 FRBs in our sample, but report upper limits to the high-energy fluence for each on timescales of 0.1, 1, 10, and 100 s. We report lower limits on the ratio of the radio to high-energy fluence, $\frac{f_{r}}{f_{\gamma}}$, for timescales of 0.1 and 100 s. We discuss the implications of our non-detections on various proposed progenitor models for FRBs, including analogs of giant pulses from the Crab pulsar and hyperflares from magnetars. This work demonstrates the utility of analyses of high-energy data for FRBs in tracking down the nature of these elusive sources.
We consider the behavior of the nonlocal minimal surfaces in the vicinity of the boundary. By a series of detailed examples, we show that nonlocal minimal surfaces may stick at the boundary of the domain, even when the domain is smooth and convex. This is a purely nonlocal phenomenon, and it is in sharp contrast with the boundary properties of the classical minimal surfaces.   In particular, we show stickiness phenomena to half-balls when the datum outside the ball is a small half-ring and to the side of a two-dimensional box when the oscillation between the datum on the right and on the left is large enough.   When the fractional parameter is small, the sticking effects may become more and more evident. Moreover, we show that lines in the plane are unstable at the boundary: namely, small compactly supported perturbations of lines cause the minimizers in a slab to stick at the boundary, by a quantity that is proportional to a power of the perturbation.   In all the examples, we present concrete estimates on the stickiness phenomena. Also, we construct a family of compactly supported barriers which can have independent interest.
We discuss the higher-order topological field theory and response of topological crystalline insulators with no other symmetries. We show how the topology and geometry of the system is organised in terms of the elasticity tetrads which are ground state degrees of freedom labelling lattice topological charges, higher-form conservation laws and responses on sub-dimensional manifolds of the bulk system. In a crystalline insulator, they classify higher-order global symmetries in a transparent fashion. This coincides with the dimensional hierarchy of topological terms, the multipole expansion, and anomaly inflow, related to a mixed number of elasticity tetrads and electromagnetic gauge fields. In the continuum limit of the elasticity tetrads, the semi-classical expansion can be used to derive the higher-order or embedded topological responses to global U(1) symmetries, such as electromagnetic gauge fields with explicit formulas for the higher-order quasi-topological invariants in terms of the elasticity tetrads and Green's functions. The topological responses and readily generalized in parameter space to allow for e.g. multipole pumping. Our simple results further bridge the recently appreciated connections between topological field theory, higher form symmetries and gauge fields, fractonic excitations and topological defects with restricted mobility elasticity in crystalline insulators.
SLE($\kappa,\rho$) is a variant of the Schramm-Loewner Evolution which describes the curves which are not conformal invariant, but are self-similar due to the presence of some other preferred points on the boundary. In this paper we study the left passage probability (LPP) for SLE($\kappa,\rho$) through field theoretical framework and find the differential equation which govern this probability. This equation is solved (up to two undetermined constants) for the special case $\kappa= 2$ and $h_\rho = 0$ for large x0 at which the boundary condition changes. This case may be referred to the Abelian sandpile model with a sink on the boundary. As an example, we apply this formalism to SLE($\kappa,\kappa-6$) which governs the curves that start from and end on the real axis.
A 1-parameter variation of Hodge structures corresponds to a holomorphic, horizontal, locally liftable map into a classifying space of Hodge structures. In this paper it is shown that such a map has a limit in the reductive Borel-Serre compactification of the classifying space. The boundary component in which the limit lies is a union over possible polarizations of classifying spaces of Hodge structures on the primitive parts. It is discussed which boundary components can contain such limit points.
Spectral computed tomography (CT) has a great potential in material identification and decomposition. To achieve high-quality material composition images and further suppress the x-ray beam hardening artifacts, we first propose a one-step material reconstruction model based on Taylor first-order expansion. Then, we develop a basic material reconstruction method named material simultaneous algebraic reconstruction technique (MSART). Considering the local similarity of each material image, we incorporate a powerful block matching frame (BMF) into the material reconstruction (MR) model and generate a BMF based MR (BMFMR) method. Because the BMFMR model contains the L0-norm problem, we adopt a split-Bregman method for optimization. The numerical simulation and physical phantom experiment results validate the correctness of the material reconstruction algorithms and demonstrate that the BMF regularization outperforms the total variation and no-local mean regularizations.
We present a stability analysis of an interacting two-species Bose-Einstein condensate driven by a quantized field in the semi-classical limit. Transitions from Rabi to Josephson dynamics are identified depending on both the inter-atomic interaction to field-condensate coupling ratio and the ratio between the total excitation number and the condensate size. The quantized field is found to produce asymmetric dynamics for symmetric initial conditions for both Rabi and Josephson oscillations.
In this paper, we proved that a log smooth family of log general type klt pairs with a special (in the sense of Campana) quasi-projective base is isotrivial. As a consequence, we proved the generalized Kebekus-Kov\'acs conjecture \cite[Conjecture 1.1]{WW19}, for smooth families of general type varieties as well as log smooth families of log canonical pairs of log general type, assuming the existence of relative good minimal models.
Face image quality is an important factor in facial recognition systems as its verification and recognition accuracy is highly dependent on the quality of image presented. Rejecting low quality images can significantly increase the accuracy of any facial recognition system. In this project, a simple approach is presented to train a deep convolutional neural network to perform end-to-end face image quality assessment. The work is done in 2 stages : First, generation of quality score label and secondly, training a deep convolutional neural network in a supervised manner to predict quality score between 0 and 1. The generation of quality labels is done by comparing the face image with a template of best quality images and then evaluating the normalized score based on the similarity.
We describe the serendipitous discovery in the spectroscopic data of the Sloan Digital Sky Survey of a star-like object, SDSSJ103913.70+533029.7, at a heliocentric radial velocity of +1012 km/s. Its proximity in position and velocity to the spiral galaxy NGC 3310 suggests an association with the galaxy. At this distance, SDSSJ103913.70+533029.7 has the luminosity of a super star cluster and a projected distance of 17 kpc from NGC 3310. Its spectroscopic and photometric properties imply a mass of > 10^6 solar masses and an age close to that of the tidal shells seen around NGC 3310, suggesting that it formed in the event which formed the shells.
We propose a probabilistic construction for the solution of a general class of fractional high order heat-type equations in the one-dimensional case, by using a sequence of random walks in the complex plane with a suitable scaling. A time change governed by a class of subordinated processes allows to handle the fractional part of the derivative in space. We first consider evolution equations with space fractional derivatives of any order, and later we show the extension to equations with time fractional derivative (in the sense of Caputo derivative) of order $\alpha \in (0,1)$.
We investigate the distribution of field theories that arise from the low energy limit of flux vacua built on type IIB string theory compactified on the mirror quintic. For a large collection of these models, we numerically determine the distribution of Taylor coefficients in a polynomial expansion of each model's scalar potential to fourth order, and show that they differ significantly from potentials generated by random choices of such coefficients over a flat measure.
Aims. We constrain a hypothetical variation in the fundamental physical constants over the course of cosmic time. Methods. We use unique observations of the CO(7-6) rotational line and the [CI] 3P_2 - 3P_1 fine-structure line towards a lensed galaxy at redshift z = 5.2 to constrain temporal variations in the constant F = alpha^2/mu, where mu is the electron-to-proton mass ratio and alpha is the fine-structure constant. The relative change in F between z = 0 and z = 5.2, dFF = (F_obs - F_lab)/F_lab, is estimated from the radial velocity offset, dV = V_rot - V_fs, between the rotational transitions in carbon monoxide and the fine-structure transition in atomic carbon. Results. We find a conservative value dV = 1 +/- 5 km/s (1sigma C.L.), which when interpreted in terms of dFF gives dFF < 2x10^-5. Independent methods restrict the mu-variations at the level of dmm < 1x10^-7 at z = 0.7 (look-back time t_z0.7 = 6.4 Gyr). Assuming that temporal variations in mu, if any, are linear, this leads to an upper limit on dmm < 2x10^-7 at z = 5.2 (t_z5.2 = 12.9 Gyr). From both constraints on dFF and dmm, one obtains for the relative change in alpha the estimate daa < 8x10^-6, which is at present the tightest limit on daa at early cosmological epochs.
Based on maximally entangled states in the full- and sub-spaces of two qutrits, we present an alternative decomposition of two-qutrit pure states in a form $|\Psi>=\frac{p_{1}}{\sqrt{3}}(|00>+|11>+|22>) +\frac{p_{2}}{\sqrt{2}}(|01>+|12>)+ p_{3}e^{i\theta}|02>$. Similar to the Schmidt decomposition, all two-qutrit pure states can be transformed into the alternative decomposition under local unitary transformations, and the parameter $p_1$ is shown to be an entanglement invariant.
We explore the predictions of Milgromian gravity (MOND) in the Local Universe by considering the distribution of the `phantom' dark matter (PDM) that would source the MOND gravitational field in Newtonian gravity, allowing an easy comparison with the dark matter framework. For this, we specifically deal with the quasi-linear version of MOND (QUMOND). We compute the `stellar-to-(phantom)halo-mass relation' (SHMR), a monotonically increasing power-law resembling the SHMR observationally deduced from spiral galaxy rotation curves in the Newtonian context. We show that the gas-to-(phantom)halo-mass relation is flat. We generate a map of the Local Volume in QUMOND, highlighting the important influence of distant galaxy clusters, in particular Virgo. This allows us to explore the scatter of the SHMR and the average density of PDM around galaxies in the Local Volume, $\Omega_{\rm pdm} \approx 0.1$, below the average cold dark matter density in a $\Lambda$CDM Universe. We provide a model of the Milky Way in its external field in the MOND context, which we compare to an observational estimate of the escape velocity curve. Finally, we highlight the peculiar features related to the external field effect in the form of negative PDM density zones in the outskirts of each galaxy, and test a new analytic formula for computing galaxy rotation curves in the presence of an external field in QUMOND. While we show that the negative PDM density zones would be difficult to detect dynamically, we quantify the weak lensing signal they could produce for lenses at $z \sim 0.3$.
Solar flares are sudden and violent releases of magnetic energy in the solar atmosphere that can be divided in eruptive flares, when plasma is ejected from the solar atmosphere, resulting in a coronal mass ejection (CME), and confined flares when no CME is associated with the flare. We present a case-study showing the evolution of key topological structures, such as spines and fans which may determine the eruptive versus non-eruptive behavior of the series of eruptive flares, followed by confined flares, which are all originating from the same site. To study the connectivity of the different flux domains and their evolution, we compute a potential magnetic field model of the active region. Quasi-separatrix layers are retrieved from the magnetic field extrapolation. The change of behavior of the flares from one day to the next -eruptive to confined- can be attributed to the change of orientation of the magnetic field below the fan with respect to the orientation of the overlaying spine, rather than an overall change in the stability of the large scale field. Flares tend to be more-and-more confined when the field that supports the filament and the overlying field gradually become less-and-less anti-parallel, as a direct result of changes in the photospheric flux distribution, being themselves driven by continuous shearing motions of the different magnetic flux concentrations.
In this article we investigate exact cylindrically symmetric solutions to the modified Einstein field equations in the brane world gravity scenarios. It is shown that for the special choice of the equation of state $2U+P=0$ for the dark energy and dark pressure, the solutions found could be considered formally as solutions of the Einstein-Maxwell equations in 4-D general relativity.
2MASSI J1315309-264951 is an L3 dwarf with strong H-alpha emission discovered in the course of a color-selected survey for active galactic nuclei using the Two-Micron All-Sky Survey (2MASS). The strength of its H-alpha emission decreased by about a factor of two between two epochs separated by 137 days. This is the first time that variable H-alpha emission has been reported in an L dwarf, and is probably the first observation of an H-alpha flare in an L dwarf. The value of log(L_Halpha/L_bol)>-4.17 observed at the discovery epoch is larger than that of any other L dwarf but comparable to that of 2MASSI J1237392+652615, the only reported T dwarf with H-alpha emission. The observed variability indicates that the H-alpha emission of 2MASSI J1315309-264951 is powered either by magnetic fields or by accretion in a binary system. Spectroscopic or narrow-band H-alpha monitoring of L and T dwarfs on timescales of hours to days would be the most useful step toward a better understanding of their H-alpha emission mechanism(s).
Extreme sources in the Transient Universe show evidence of relativistic outflows from intermittent inner engines, such as cosmological gamma-ray bursts. They probably derive from rotating back holes interacting with surrounding matter. We show that these interactions are enhanced inversely proportional to the duty cycle in advection of magnetic flux, as may apply at high accretion rates. We demonstrate the morphology and ballistic propagation of relativistic ejecta from burst outflows by numerical simulations in relativistic magnetohydrodynamics. Applied to stellar mass black holes in core-collapse of massive stars, it provides a robust explosion mechanism as a function of total energy output. At breakout, these ejecta may produce a low-luminosity GRB. A long GRB may ensue from an additional ultra-relativistic baryon-poor inner jet from a sufficiently long-lived intermittent inner engine. The simulations demonstrate a complex geometry in mergers of successive ejecta, whose mixing and shocks provide a pathway to broadband high energy emission from magnetic reconnection and shocks.
Earlier the authors considered and, in some cases, computed Poincare series of two sorts of multi-index filtrations on the ring of germs of functions on a complex (normal) surface singularity (in particular on the complex plane). A filtration from the first class was defined by a curve (with several branches) on the surface singularity. The other one (so called divisorial filtration) was defined by a set of components of the exceptional divisor of a modification of the surface singularity. Here we define a filtration corresponding to an ideal or to a set of ideals in the ring of germs of functions on a surface singularity and compute the corresponding Poincare series in some cases. For the complex plane this notion unites the two classes of filtrations described above.
We consider the one-armed bandit problem of Woodroofe [J. Amer. Statist. Assoc. 74 (1979) 799--806], which involves sequential sampling from two populations: one whose characteristics are known, and one which depends on an unknown parameter and incorporates a covariate. The goal is to maximize cumulative expected reward. We study this problem in a minimax setting, and develop rate-optimal polices that involve suitable modifications of the myopic rule. It is shown that the regret, as well as the rate of sampling from the inferior population, can be finite or grow at various rates with the time horizon of the problem, depending on "local" properties of the covariate distribution. Proofs rely on martingale methods and information theoretic arguments.
One attractive scenario for the excess of sub-PeV/PeV neutrinos recently reported by IceCube is that they are produced by cosmic rays in starburst galaxies colliding with the dense interstellar medium. These proton-proton ($pp$) collisions also produce high-energy gamma-rays, which finally contribute to the diffuse high-energy gamma-ray background. We calculate the diffuse gamma-ray flux with a semi-analytic approach and consider that the very high energy gamma-rays will be absorbed in the galaxies and converted into electron-position pairs, which then lose almost all their energy through synchrotron radiation in the strong magnetic fields in the starburst region. Since the synchrotron emission goes into energies below GeV, this synchrotron loss reduces the diffuse high-energy gamma-ray flux by a factor of about two, thus leaving more room for other sources to contribute to the gamma-ray background. For a $E_\nu^{-2}$ neutrino spectrum, we find that the diffuse gamma-ray flux contributes about 20% of the observed diffuse gamma-ray background in the 100 GeV range. However, for a steeper neutrino spectrum, this synchrotron loss effect is less important, since the energy fraction in absorbed gamma-rays becomes lower.