ShantanuT01/DACTYL-Pretraining huggingface dataset:
We explore the N=1* theories compactified on a circle with twisted boundary conditions. The gauge algebra of these theories are the so-called twisted affine Lie algebra. We propose the exact superpotentials by guessing the sum of all monopole-instanton contributions and also by requiring SL(2,Z) modular properties. The latter is inherited from the N=4 theory, which will be justified in the M theory setting. Interestingly all twisted theories possess full SL(2,Z) invariance, even though none of them are simply-laced. We further notice that these superpotentials are associated with certain integrable models widely known as elliptic Calogero-Moser models. Finally, we argue that the glueball superpotential must be independent of the compactification radius, and thus of the twisting, and confirm this by expanding it in terms of glueball superfield in weak coupling expansion.
This paper is a review on the observational Hubble parameter data that have gained increasing attention in recent years for their illuminating power on the dark side of the universe --- the dark matter, dark energy, and the dark age. Currently, there are two major methods of independent observational H(z) measurement, which we summarize as the "differential age method" and the "radial BAO size method". Starting with fundamental cosmological notions such as the spacetime coordinates in an expanding universe, we present the basic principles behind the two methods. We further review the two methods in greater detail, including the source of errors. We show how the observational H(z) data presents itself as a useful tool in the study of cosmological models and parameter constraint, and we also discuss several issues associated with their applications. Finally, we point the reader to a future prospect of upcoming observation programs that will lead to some major improvements in the quality of observational H(z) data.
A simple method has been introduced to derive the all order quantum corrected Bose-Einstein distribution as the solution of the Wigner equation. The process is a perturbative one where the Bose-Einstein distribution has been taken as the unperturbed solution. This solution has been applied to calculate the number density of the bosons at finite temperature. The study may be important to investigate the properties of bosons and bose condensates at finite temperature. This process can also be applied to obtain the quantum corrected Fermi distribution.
We present a composite spectrum of 60 long duration gamma-ray burst (GRB) afterglows with redshifts in the range 0.35<z<6.7 observed with low resolution optical spectra. The composite spectrum covers the wavelength range 700-6600 A in the rest frame and has a mean signal-to-noise ratio of 150 per 1 A pixel and reaches a maximum of ~300 in the range 2500-3500 A. Equivalent widths are measured from metal absorption lines from the Lya line to ~5200 A, and associated metal and hydrogen lines are identified between the Lyman break and Lya line. The average transmission within the Lyman forest is consistent with that found along quasar lines of sight. We find a temporal variation in fine structure lines when dividing the sample into bursts observed within 2 hours from their trigger and those observed later. Other lines in the predominantly neutral gas show variations too, but this is most likely a random effect caused by weighting of individual strong absorption lines and which mimics a temporal variation. Bursts characterized with high or low prompt GRB energy release produce afterglows with similar absorption line strengths, and likewise for bursts with bright or faint optical afterglows. Bursts defined as dark from their optical to X-ray spectral index have stronger absorption lines relative to the optically bright bursts. The composite spectrum has strong CaII and MgII absorption lines as commonly found in dusty galaxies, however, we find no evidence for dust or a significant molecular content based on the non-detection of diffuse interstellar bands. Compared to starburst galaxy spectra, the GRB composite has much stronger fine structure lines, while metal absorption lines are weaker.
The centres of galaxies are powerful laboratories to test the current $\Lambda$CDM model for structure formation and evolution. While these sub-galactic scales can be directly investigated in the local Universe, it is observationally extremely difficult to access them at high redshift. The combination of strong gravitational lensing and VLBI observations allows us to access these scales to study both the baryonic and the dark matter distribution at the largest distances. For example, it becomes possible to unveil complex mass density distribution of lensing galaxies, faint cold molecular gas reservoirs, offset and binary AGN candidates at $z>1$. Currently, these detailed studies are limited by the small number of known radio-loud lensed sources. Wide-field VLBI observations may provide a viable way to search for many more radio-loud systems and test strategies in preparation for the future surveys with the next generation of interferometers.
A hypersurface formed of two null sheets, or "light fronts", swept out by the future null normal geodesics emerging from a common spacelike 2-disk can serve as a Cauchy surface for a region of spacetime. Already in the 1960s free (unconstrained) initial data for general relativity were found for such hypersurfaces. Here an expression is obtained for the symplectic 2-form of vacuum general relativity in terms of such free data. This can be done, even though variations of the geometry do not in general preserve the nullness of the initial hypersurface, because of the diffeomorphism gauge invariance of general relativity. The present expression for the symplectic 2-form has been used previously to calculate the Poisson brackets of the free data.
Two integrable quantum spin ladder systems will be introduced associated with the fundamental su(2|2) solution of the Yang-Baxter equation. The first model is a generalized quantum Ising system with Ising rung interactions. In the second model the addition of extra interactions allows us to impose Heisenberg rung interactions without violating integrability. The existence of a Bethe ansatz solution for both models allows us to investigate the elementary excitations for antiferromagnetic rung couplings. We find that the first model does not show a gap whilst in the second case there is a gap for all positive values of the rung coupling.
Coherent control of bound state processes via the interfering overlapping resonances scenario [Christopher et al., J. Chem. Phys. 123, 064313 (2006)] is developed to control intramolecular vibrational redistribution (IVR). The approach is applied to the flow of population between bonds in a model of chaotic OCS vibrational dynamics, showing the ability to significantly alter the extent and rate of IVR by varying quantum interference contributions.
We investigate statistical properties of vorticity fluctuations in fully developed turbulence, which are known to exhibit a strong intermittent behavior. Taking as the starting point the Navier-Stokes equations with a random force term correlated at large scales, we obtain in the high Reynolds number regime a closed analytical expression for the probability distribution function of an arbitrary component of the vorticity field. The central idea underlying the analysis consists in the phase-space restriction to a particular sector where the rate of strain and the rotation tensors can be locally regarded as slow and fast degrees of freedom, respectively. This prescription is implemented along the Martin-Siggia-Rose functional framework, whereby instantons and perturbations around them are taken into account within a steepest-descent approach.
We present a possible construction of coherent states on the unit circle as configuration space. In our approach the phase space is the product Z x S^1. Because of the duality of canonical coordinates and momenta, i.e. the angular variable and the integers, this formulation can also be interpreted as coherent states over an infinite periodic chain. For the construction we use the analogy with our quantization over a finite periodic chain where the phase space was Z_M x Z_M. Properties of the coherent states constructed in this way are studied and the coherent states are shown to satisfy the resolution of unity.
The Fermi-Watson theorem is generalized to the case of two coupled channels with different masses and applied to final state interaction in $K_{e4}$ decays. The impact of considered effect on the phase of the $\pi\pi$ scattering is estimated and shown that it can be crucial for scattering lengths extraction from experimental data on $K_{e4}$ decays.
We present a theory for the growth dynamics of the World Wide Web that takes into account the wide range of stochastic growth rates in the number of pages per site, as well as the fact that new sites are created at different times. This leads to the prediction of a universal power law in the distribution of the number of pages per site which we confirm experimentally by analyzing data from large crawls made by the search engines Alexa and Infoseek. The existence of this power law not only implies the lack of any length scale for the Web, but also allows one to determine the expected number of sites of any given size without having to exhaustively crawl the Web.
The fraction of star-forming to quiescent dwarf galaxies varies from almost infinity in the field to zero in the centers of rich galaxy clusters. What is causing this pronounced morphology-density relation? What do quiescent dwarf galaxies look like when studied in detail, and what conclusions can be drawn about their formation mechanism? Here we study a nearly magnitude-complete sample (-19 < M_r < -16 mag) of 121 Virgo cluster early types with deep near-infrared images from the SMAKCED project. We fit two-dimensional models with optional inner and outer components, as well as bar and lens components (in ~15% of the galaxies), to the galaxy images. While a single S\'ersic function may approximate the overall galaxy structure, it does not entirely capture the light distribution of two-thirds of our galaxies, for which multi-component models provide a better fit. This fraction of complex galaxies shows a strong dependence on luminosity, being larger for brighter objects. We analyze the global and component-specific photometric scaling relations of early-type dwarf galaxies and discuss similarities with bright early and late types. The dwarfs' global galaxy parameters show scaling relations that are similar to those of bright disk galaxies. The inner components are mostly fitted with S\'ersic n values close to 1. At a given magnitude they are systematically larger than the bulges of spirals, suggesting that they are not ordinary bulges. We argue that the multi-component structures in early-type dwarfs are mostly a phenomenon inherent to the disks, and may indeed stem from environmental processing.
A method for solving few-body scattering equations is proposed and examined. The solution of the scattering equations at complex energies is analytically continued to get scattering T-matrix with real positive energy. Numerical examples document that the method works well for two-nucleon scattering and three-nucleon scattering, if the set of complex energies is properly chosen.
We discuss quantum interference effects in a three-level atom in lambda-configuration, where both transitions from the upper state to the lower states are driven by a single monochromatic laser field. Although the system has two lower states, quantum interference is possible because there are interfering pathways to each of the two lower states. The additional interference terms allow for interesting effects such as the suppression of a dark state which is present without the interference. Finally we examine a narrow spectral feature in the resonance fluorescence of the atom with quantum interference.
We construct the theta function solution to the initial value problem for the generalized periodic discrete Toda equation.
Supervised semantic segmentation normally assumes the test data being in a similar data domain as the training data. However, in practice, the domain mismatch between the training and unseen data could lead to a significant performance drop. Obtaining accurate pixel-wise label for images in different domains is tedious and labor intensive, especially for histopathology images. In this paper, we propose a dual adaptive pyramid network (DAPNet) for histopathological gland segmentation adapting from one stain domain to another. We tackle the domain adaptation problem on two levels: 1) the image-level considers the differences of image color and style; 2) the feature-level addresses the spatial inconsistency between two domains. The two components are implemented as domain classifiers with adversarial training. We evaluate our new approach using two gland segmentation datasets with H&E and DAB-H stains respectively. The extensive experiments and ablation study demonstrate the effectiveness of our approach on the domain adaptive segmentation task. We show that the proposed approach performs favorably against other state-of-the-art methods.
We consider stochastic dynamics for a spin system with mean field interaction, in which the interaction potential is subject to noisy and dissipative stochastic evolution. We show that, in the thermodynamic limit and at sufficiently low temperature, the magnetization of the system has a time periodic behavior, despite of the fact that no periodic force is applied.
We analyze the mathematical model that describes the heat generated by electromagnetic nanoparticles. We use the known optical properties of the nanoparticles to control the support and amount of the heat needed around a nanoparticle. Precisely, we show that the dominant part of the heat around the nanoparticle is the electric field multiplied by a constant dependent, explicitly and only, on the permittivity and quantities related to the eigenvalues and eigenfunctions of the Magnetization (or the Newtonian) operator, defined on the nanoparticle, and inversely proportional to the distance to the nanoparticle.   The nanoparticles are described via the Lorentz model. If the used incident frequency is chosen related to the plasmonic frequency $\omega_p$ (via the Magnetization operator) then the nanoparticle behaves as a plasmonic one while if it is chosen related to the undamped resonance frequency $\omega_0$ (via the Newtonian operator), then it behaves as a dielectric one. The two regimes exhibit different optical behaviors. In both cases, we estimate the generated heat and discuss advantages of each incident frequency regime.   The analysis is based on time-domain integral equation techniques avoiding the use of (formal) Fourier type transformations.
Some simulations of Type Ia supernovae feature self-consistent thermonuclear detonations. However, these detonations are not meaningful if the simulations are not resolved, so it is important to establish the requirements for achieving a numerically converged detonation. In this study we examine a test detonation problem inspired by collisions of white dwarfs. This test problem demonstrates that achieving a converged thermonuclear ignition requires spatial resolution much finer than 1 km in the burning region. Current computational resource constraints place this stringent resolution requirement out of reach for multi-dimensional supernova simulations. Consequently, contemporary simulations that self-consistently demonstrate detonations are possibly not converged and should be treated with caution.
Starting from 6D superconformal field theories (SCFTs) realized via F-theory, we show how reduction on a circle leads to a uniform perspective on the phase structure of the resulting 5D theories, and their possible conformal fixed points. Using the correspondence between F-theory reduced on a circle and M-theory on the corresponding elliptically fibered Calabi--Yau threefold, we show that each 6D SCFT with minimal supersymmetry directly reduces to a collection of between one and four 5D SCFTs. Additionally, we find that in most cases, reduction of the tensor branch of a 6D SCFT yields a 5D generalization of a quiver gauge theory. These two reductions of the theory often correspond to different phases in the 5D theory which are in general connected by a sequence of flop transitions in the extended Kahler cone of the Calabi--Yau threefold. We also elaborate on the structure of the resulting conformal fixed points, and emergent flavor symmetries, as realized by M-theory on a canonical singularity.
We report the discovery of Ge III $\lambda$1088.46 in the planetary nebulae (PNe) SwSt 1, BD+30$^{\rm o}$3639, NGC 3132, and IC 4593, observed with the Far Ultraviolet Spectroscopic Explorer. This is the first astronomical detection of this line and the first measurement of Ge (Z = 32) in PNe. We estimate Ge abundances using S and Fe as reference elements, for a range of assumptions about gas-phase depletions. The results indicate that Ge, which is synthesized in the initial steps of the s-process and therefore can be self-enriched in PNe, is enhanced by factors of > 3-10. The strongest evidence for enrichment is seen for PNe with Wolf-Rayet central stars, which are likely to contain heavily processed material.
We present high statistics simulation data for the average time $\langle T_{\rm cover}(L)\rangle$ that a random walk needs to cover completely a 2-dimensional torus of size $L\times L$. They confirm the mathematical prediction that $\langle T_{\rm cover}(L)\rangle \sim (L \ln L)^2$ for large $L$, but the prefactor {\it seems} to deviate significantly from the supposedly exact result $4/\pi$ derived by A. Dembo {\it et al.}, Ann. Math. {\bf 160}, 433 (2004), if the most straightforward extrapolation is used. On the other hand, we find that this scaling does hold for the time $ T_{\rm N(t)=1}(L)$ at which the average number of yet unvisited sites is 1, as also predicted previously. This might suggest (wrongly) that $\langle T_{\rm cover}(L)\rangle$ and $T_{\rm N(t)=1}(L)$ scale differently, although the distribution of rescaled cover times becomes sharp in the limit $L\to\infty$. But our results can be reconciled with those of Dembo {\it et al.} by a very slow and {\it non-monotonic} convergence of $\langle T_{\rm cover}(L)\rangle/(L \ln L)^2$, as had been indeed proven by Belius {\it et al.} [Prob. Theory \& Related Fields {\bf 167}, 1 (2014)] for Brownian walks, and was conjectured by them to hold also for lattice walks.
We explore the salient features of the `Kitaev ladder', a two-legged ladder version of the spin-1/2 Kitaev model on a honeycomb lattice, by mapping it to a one-dimensional fermionic p-wave superconducting system. We examine the connections between spin phases and topologically non-trivial phases of non-interacting fermionic systems, demonstrating the equivalence between the spontaneous breaking of global Z2 symmetry in spin systems and the existence of isolated Majorana modes. In the Kitaev ladder, we investigate topological properties of the system in different sectors characterized by the presence or absence of a vortex in each plaquette of the ladder. We show that vortex patterns can yield a rich parameter space for tuning into topologically non-trivial phases. We introduce a new topological invariant which explicitly determines the presence of zero energy Majorana modes at the boundaries of such phases. Finally, we discuss dynamic quenching between topologically non-trivial phases in the Kitaev ladder, and in particular, the post-quench dynamics governed by tuning through a quantum critical point.
Neutron scattering measurements have demonstrated that the heavily Cu-doped NaFe$_{1-x}$Cu$_{x}$As compound behaves like a Mott insulator exhibiting both real space Fe-Cu stripes, as well as antiferromagnetism below a N\'eel temperature for $x\lesssim 0.5$. We have investigated evolution of structural and magnetic ordering using $^{23}$Na and $^{75}$As NMR for single crystals ($x$ = 0.39 and 0.48), confirming antiferromagnetism in the form of magnetic stripes. We show that end-chain defects in these stripes are the principal source of magnetic disorder and are responsible for cluster spin-glass transitions in both compounds, in the latter case coexistent with antiferromagnetism. Aided by our numerical simulation of the $^{75}$As spectra, we show that a staggered magnetization at the Fe sites is induced by non-magnetic Cu dopants.
An important constraint for galaxy evolution models is how much gas resides in galaxies, in particular at the peak of star formation z=1-3. We attempt a novel approach by letting long-duration Gamma Ray Bursts (LGRBs) x-ray their host galaxies and deliver column densities to us. This requires a good understanding of the obscurer and biases introduced by incomplete follow-up observations. We analyse the X-ray afterglow of all 844 Swift LGRBs to date for their column density $N_H$. To derive the population properties we propagate all uncertainties in a consistent Bayesian methodology. The $N_H$ distribution covers the $10^{20-23}\mathrm{cm}^{-2}$ range and shows no evolutionary effect. Higher obscurations, e.g. Compton-thick columns, could have been detected but are not observed. The $N_H$ distribution is consistent with sources randomly populating a ellipsoidal gas cloud of major axis $N_H^\text{major}=10^{23}\mathrm{cm}^{-2}$ with 0.22 dex intrinsic scatter between objects. The unbiased SHOALS survey of afterglows and hosts allows us to constrain the relation between Spitzer-derived stellar masses and X-ray derived column densities $N_H$. We find a well-constrained powerlaw relation of $N_H=10^{21.7}\mathrm{cm}^{-2}\times\left(M_{\star}/10^{9.5}M_{\odot}\right)^{1/3}$, with 0.5 dex intrinsic scatter between objects. The Milky Way and the Magellanic clouds also follow this relation. From the geometry of the obscurer, its stellar mass dependence and comparison with local galaxies we conclude that LGRBs are primarily obscured by galaxy-scale gas. Ray tracing of simulated Illustris galaxies reveals a relation of the same normalisation, but a steeper stellar-mass dependence and mild redshift evolution. Our new approach provides valuable insight into the gas residing in high-redshift galaxies.
An explicit solution of a similarity type is obtained for a one-phase Stefan problem in a semi-infinite material using Kummer functions. Motivated by [D.A. Tarzia, Relationship between Neumann solutions for two phase Lam\'e-Clapeyron-Stefan problems with convective and temperature boundary conditions, Thermal Sci.(2016) DOI 10.2298/TSCI 140607003T, In press], and [Y. Zhou, L.J. Xia, Exact solution for Stefan problem with general power-type latent heat using Kummer function, Int. J. Heat Mass Transfer, 84 (2015) 114-118], we consider a phase-change problem with a latent heat defined as a power function of the position with a non-negative real exponent and a convective boundary condition at the fixed face $x=0$. Existence and uniqueness of the solution is proved. Relationship between this problem and the problems already solved by Zhou and Xia with temperature and flux boundary condition is analysed. Furthermore it is studied the limit behaviour of the solution when the coefficient which characterizes the heat transfer at the fixed boundary tends to infinity. Numerical computation of the solution is done over certain examples, with a view to comparing this results with those obtained by general algorithms that solve Stefan problems.