ShantanuT01/DACTYL-Pretraining huggingface dataset:
We give a detailed path integral derivation of the elliptic genus of a supersymmetric coset conformal field theory, further twisted by a global U(1) symmetry. It gives rise to a Jacobi form in three variables, which is the modular completion of a mock modular form. The derivation provides a physical interpretation to the non-holomorphic part as arising from a difference in spectral densities for the continuous part of the right-moving bosonic and fermionic spectrum. The spectral asymmetry can also be read off directly from the reflection amplitudes of the theory. By performing an orbifold, we show how our twisted elliptic genus generalizes an existing example.
Let K be an algebraic function field of characteristic 2 with constant field C_K. Let C be the algebraic closure of a finite field in K. Assume that C has an extension of degree 2. Assume that there are elements u,x of K with u transcendental over C_K and x algebraic over C(u) and such that K=C_K(u,x). Then Hilbert's Tenth Problem over K is undecidable. Together with Shlapentokh's result for odd characteristic this implies that Hilbert's Tenth Problem for any such field K of finite characteristic is undecidable. In particular, Hilbert's Tenth Problem for any algebraic function field with finite constant field is undecidable.
Narrowband bursts (spikes) appear on dynamic spectra from microwave to decametric frequencies. They are believed to be manifestations of small-scale energy release through magnetic reconnection. We study the position of the spike-like structures relative to the front of type-II bursts and their role in the burst emission. We used high-sensitivity, low-noise dynamic spectra obtained with the acousto-optic analyzer (SAO) of the ARTEMIS-JLS radiospectrograph, in conjunction with images from the Nan\c{c}ay Radioheliograph (NRH) in order to study spike-like bursts near the front of a type-II radio burst during the November 3, 2003 extreme solar event. The spike-like emission in the dynamic spectrum was enhanced by means of high-pass-time filtering. We identified a number of spikes in the NRH images. Due to the lower temporal resolution of the NRH, multiple spikes detected in the dynamic spectrum appeared as single structures in the images. These spikes had an average size of ~200" and their observed brightness temperature was 1.4-5.6x10^9K, providing a significant contribution to the emission of the type-II burst front. At variance with a previous study on the type-IV associated spikes, we found no systematic displacement between the spike emission and the emission between spikes. At 327.0 MHz, the type II emission was located about 0.3 RSUN above the pre-existing continuum emission, which, was located 0.1 RSUN above the western limb. This study indicates that the spike-like chains aligned along the type II burst MHD shock front are not a perturbation of the type II emission, as in the case of type IV spikes, but a manifestation of the type II emission itself. The preponderance of these chains, together with the lack of isolated structures or irregular clusters, points towards some form of small-scale magnetic reconnection, organized along the type-II propagating front.
Coherence, treated as a resource in quantum information theory, is a basis-dependent quantity. Looking for states that have constant coherence under canonical changes of basis yields highly symmetric structures in state space. For the case of a qubit, we find an easy construction of qubit SICs (Symmetric Informationally Complete POVMs). SICs in dimension 3 and 8 are also shown to be equicoherent.
A tidal disruption event (TDE) occurs when a star passes too close to a supermassive black hole and gets torn apart by its gravitational tidal field. After the disruption, the stellar debris form an expanding gaseous stream. The morphology and evolution of this stream is particularly interesting as it ultimately determines the observational properties of the event itself. In this work we perform 3D hydrodynamical simulations of the TDE of a star modelled as a polytropic sphere of index {\gamma} = 5/3, and study the gravitational stability of the resulting gas stream. We provide an analytical solution for the evolution of the stream in the bound, unbound and marginally bound case, that allows us to describe the stream properties and analyse the time-scales of the physical processes involved, applying a formalism developed in star formation context. Our results are that, when fragmentation occurs, it is fueled by the failure of pressure in supporting the gas against its self-gravity. We also show that a stability criterion that includes also the stream gas pressure proves to be far more accurate than one that only considers the black hole tidal forces, giving analytical predictions of the time evolution of the various forces associated to the stream. Our results point out that fragmentation occurs on timescales longer compared with the observational windows of these events and is thus not expected to give rise to significant observational features.
Gravitational waves from a binary with a single dynamically significant spin, notably including precessing black hole-neutron star (BH-NS) binaries, let us constrain that binary's properties: the two masses and the dominant black hole spin. Based on a straightforward fourier transform of $h(t)$ enabled by the corotating frame, we show the Fisher matrix for precessing binaries can be well-approximated by an extremely simple semianalytic approximation. This approximation can be easily understood as a weighted average of independent information channels, each associated with one gravitational wave harmonic. Generalizing previous studies of nonprecessing binaries to include critical symmetry-breaking precession effects required to understand plausible astrophysical sources, our ansatz can be applied to address how well gravitational wave measurements can address a wide range of astrophysical and fundamental questions. Our approach provides a simple method to assess what parameters gravitational wave detectors can measure, how well, and why.
We introduce the formal extension of the Whitney functor and the polynomial extension of the tempered cohomology functor, and prove a natural topological duality between them.
We report the X-ray spectral and timing analysis of the high mass X-ray binary EXO 2030+375 during the 2021 type II outburst. We have incorporated NuSTAR, NICER, \textit{Swift}/BAT \& \textit{Fermi}/GBM observations to carry out a comprehensive analysis of the source. Pulse profiles in different energy ranges and time intervals have been generated and analyzed. We have performed a brief comparison of the observations amidst the peak outburst condition and also during the decaying state of the outburst. Pulse profiles are found to evolve with time and energy. An iron emission line at (6-7) keV is observed in the X-ray continuum. Distinct absorption features were observed in the spectra corresponding to the peak outburst state while such features were not detected during the later decaying phase of the outburst. We have estimated the characteristic spin-up time scale to be $\backsim$ 60 years. The continuum flux of the system and the varying luminosities covering the entire outburst period have been used to interpret the characteristics of the source. We have summarized the variability of various parameters along with their underlying physical implications.
The Desale-Ramanan Theorem is an isomorphism between the moduli space of rank two vector bundles over complex hyperelliptic curve and the variety of linear subspaces in an intersection of two quadrics. We prove a real version of this theorem for the moduli space of real vector bundles over a real hyperelliptic curve. We then apply this result to study the topology of the moduli space, proving that it is relatively spin and identifying the diffeomorphism type for genus two curves. Our results lay the groundwork for future study of the quantum homology of these moduli spaces.
Introducing hierarchical pore structure to microporous materials such as metal-organic frameworks (MOFs) can be beneficial for reactions where the rate of reaction is limited by low rates of diffusion or high pressure drop. This advantageous pore structure can be obtained by defect formation, mostly via post-synthetic acid etching, which has been studied extensively on water-stable MOFs. Here we show that a water-unstable HKUST-1 MOF can also be modified in a corresponding manner by using phosphoric acid as a size-selective etching agent and a mixture of dimethyl sulfoxide and methanol as a dilute solvent. Interestingly, we demonstrate that the etching process which is time- and acidity- dependent, can result in formation of defective HKUST-1 with extra interconnected hexagonal macropores without compromising on the bulk crystallinity. These findings suggest an intelligent scalable synthetic method for formation of hierarchical porosity in MOFs that are prone to hydrolysis, for improved molecular accessibility and diffusion for catalysis.
The stiff problem is concerned with a thermal conduction model with a singular barrier of zero volume. In this paper, we shall build the phase transitions for the stiff problems in one-dimensional space. It turns out that every phase transition definitely depends on the total thermal resistance of the barrier, and the three phases correspond to the so-called impermeable pattern, semi-permeable pattern and permeable pattern of thermal conduction respectively. For each pattern, the related boundary condition of the flux at the barrier is also derived. Mathematically, we shall introduce and explore the so-called snapping out Markov process, which is the probabilistic counterpart of semi-permeable pattern in the stiff problem.
We calculate Tits buildings for certain arithmetic subgroups of Sp(4). These give information about the boundary of the corresponding moduli spaces of abelian surfaces. More pictures (in colour) and a summary of the results (in English) can be found at http://www.bath.ac.uk/~masgks/Buildings/
In the modern content-based image retrieval systems, there is an increasingly interest in constructing a computationally effective model to predict the interestingness of images since the measure of image interestingness could improve the human-centered search satisfaction and the user experience in different applications. In this paper, we propose a unified framework to predict the binary interestingness of images based on discriminant correlation analysis (DCA) and multiple kernel learning (MKL) techniques. More specially, on the one hand, to reduce feature redundancy in describing the interestingness cues of images, the DCA or multi-set discriminant correlation analysis (MDCA) technique is adopted to fuse multiple feature sets of the same type for individual cues by taking into account the class structure among the samples involved to describe the three classical interestingness cues, unusualness,aesthetics as well as general preferences, with three sets of compact and representative features; on the other hand, to make good use of the heterogeneity from the three sets of high-level features for describing the interestingness cues, the SimpleMKL method is employed to enhance the generalization ability of the built model for the task of the binary interestingness classification. Experimental results on the publicly-released interestingness prediction data set have demonstrated the rationality and effectiveness of the proposed framework in the binary prediction of image interestingness where we have conducted several groups of comparative studies across different interestingness feature combinations, different interestingness cues, as well as different feature types for the three interestingness cues.
We investigate the critical temperature of Bose-Einstein condensation of $K^-$ mesons in neutron star matter. This is studied within the framework of relativistic field theoretical models at finite temperature where nucleon-nucleon and (anti)kaon-nucleon interactions are mediated by the exchange of mesons. The melting of the antikaon condensate is studied for different values of antikaon optical potential depths. We find that the critical temperature of antikaon condensation increases with baryon number density. Further it is noted that the critical temperature is lowered as antikaon optical potential becomes less attractive. We also construct the phase diagram of neutron star matter with $K^-$ condensate.
A non-abelian spin liquid in triangular lattice spin-1 systems was recently formulated in the form of continuum field theory [T. Grover, and T. Senthil, Phys. Rev. Lett. 107, 077203 (2011); Cenke Xu, A.W.W. Ludwig, arXiv:1012.5671]. It has spin-1/2 bosonic spinons coupled to emergent quaternion gauge fields, and can be obtained by quantum disordering a non-collinear spin nematic order hypothesized to describe NiGa_2S_4 [H. Tsunetsugu, and M. Arikawa, J. Phys. Soc. Jpn. 75, 083701 (2006)], However a microscopic lattice description, e.g. the lattice spinon (mean-field) Hamiltonian and the spin wavefunction, has been missing, and it has been noted that the standard Schwinger boson or bosonic triplon representations of spin-1 cannot describe this spin liquid. In this paper a two-orbital Schwinger boson representation for spin-1 systems is developed and used to construct a mean-field description of this quaternion spin liquid. Projecting the mean-field state produces a prototype wavefunction, which is a superposition of close-packed AKLT loop configurations with nontrivial amplitudes. This new formalism and related wavefunctions may be generalized to higher spin systems and can possibly produce spin liquid states with even richer emergent gauge structures.
Hyperbolic-parabolic systems have spatially homogenous stationary states. When the dissipation is weak, one can derive weakly nonlinear-dissipative approximations that govern perturbations of these constant states. These approximations are quadratically nonlinear. When the original system has an entropy, the approximation is formally dissipative in a natural Hilbert space. We show that when the approximation is strictly dissipative it has global weak solutions for all initial data in that Hilbert space. We also prove a weak-strong uniqueness theorem for it. In addition, we give a Kawashima type criterion for this approximation to be strictly dissipative. We apply the theory to the compressible Navier-Stokes system.
In this paper we study the non-holomorphic strict endoscopic parts of inner cohomology spaces of a modular Siegel threefold respect to local systems. First we show that there is a non-zero subspace of the strict endoscopic part such that it is constructed by global theta lift of automorphic froms of $(GL(2)\times GL(2))/G_{m}$. Secondly, we present an explicit analytic calculation of levels of lifted forms into GSp(4), based on the paramodular representations theory for $GSp(4; F)$. Finally, we prove the conjecture, by C. Faber and G. van der Geer, that gives a description of the strict endoscopic part for Betti cohomology and (real) Hodge structures in the category of mixed Hodge structures, in which the modular Siegel threefold has level structure one.
Various equivalent conditions for a semigroup or a resolvent generated by a Markov process to be of Feller type are given.
We investigate the general conditions to achieve the adiabatic charge and spin polarizations and quantized pumping in 2D magnetic insulators possessing inhomogeneous spin structures. In particular, we focus on the chiral ferrimagnetic insulators which are generated via spontaneous symmetry breaking from correlated two dimensional topological insulators. Adiabatic deformation of the inhomogeneous spin structure generates the spin gauge flux, which induces adiabatic charge and spin polarization currents. The unit pumped charge/spin are determined by the product of two topological invariants which are defined in momentum and real spaces, respectively. The same topological invariants determine the charge and spin quantum numbers of skyrmion textures. It is found that in noncentrosymmetric systems, a new topological phase, dubbed the topological chiral magnetic insulator, exists in which a skyrmion defect is a spin-1/2 fermion with electric charge $e$. Considering the adiabatic current responses of generic inhomogeneous systems, it is shown that the quantized topological response of chiral magnetic insulators is endowed with the second Chern number.
The star R Corona Borealis (R CrB) shows forbidden lines of [O II], [N II], and [S II] during the deep minimum when the star is fainter by about 8 to 9 magnitudes from normal brightness, suggesting the presence of nebular material around it. We present low and high spectral resolution observations of these lines during the ongoing deep minimum of R CrB, which started in July 2007. These emission lines show double peaks with a separation of about 170 km/s. The line ratios of [S II] and [O II] suggest an electron density of about 100 cm$^{-3}$. We discuss the physical conditions and possible origins of this low density gas. These forbidden lines have also been seen in other R Coronae Borealis stars during their deep light minima and this is a general characteristic of these stars, which might have some relevance to their origins.
Eruptions of classical novae are possible sources of lithium formation and gamma-ray emission. Nova remnants can also become Type Ia supernovae (SNe Ia). The contribution of novae to these phenomena depends on nova rates, which are not well established for the Galaxy. Here, we directly measure a Galactic bulge nova rate of $13.8 \pm 2.6$ per year. This measurement is much more accurate than any previous measurement of this kind thanks to many years' monitoring of the bulge by the Optical Gravitational Lensing Experiment (OGLE) survey. Our sample consists of 39 novae eruptions, $\sim$1/3 of which are OGLE-based discoveries. This long-term monitoring allows us to not only measure the nova rate but also to study in detail the light curves of 39 eruptions and more than 80 post-nova candidates. We measured orbital periods for 9 post-novae and 9 novae, and in 14 cases we procured the first estimates. The OGLE survey is very sensitive to the frequently erupting recurrent novae. We did not find any object similar to M31 2008-12a, which erupts once a year. The lack of detection indicates that there is only a small number of them in the Galactic bulge.
The d=10 type II string theories, d=11 M-theory and d=12 F-theory have the same symmetry group. It can be viewed either as a subgroup of a conformal group OSp(1|64) or as a contraction of OSp(1|32). The theories are related by different identifications of their symmetry operators as generators of OSp(1|32). T- and S-dualities are recognized as redefinitions of generators. Some (s,t) signatures of spacetime allow reality conditions on the generators. All those that allow a real structure are related again by redefinitions within the algebra, due to the fact that the algebra OSp(1|32) has only one real realization. The redefinitions include space/space, time/time and space/time dualities. A further distinction between the theories is made by the identification of the translation generator. This distinguishes various versions of type II string theories, in particular the so-called *-theories, characterized by the fact that the P_0 generator is not the (unique) positive-definite energy operator in the algebra.
We describe a method for calculating the counting statistics of electronic transport through nanoscale devices with both sequential and cotunneling contributions. The method is based upon a perturbative expansion of the von Neumann equation in Liouvillian space, with current cumulants calculated from the resulting nonMarkovian master equation without further approximation. As application, we consider transport through a single quantum dot and discuss the effects of cotunneling on noise and skewness, as well as the properties of various approximation schemes.
Using new ultradeep Spitzer/IRAC photometry from the IRAC Ultradeep Field program (IUDF), we investigate the stellar populations of a sample of 63 Y-dropout galaxy candidates at z~8, only 650Myr after the Big Bang. The sources are selected from HST/ACS+WFC3/IR data over the Hubble Ultra Deep Field (HUDF), two HUDF parallel fields, and wide area data over the CANDELS/GOODS-South. The new Spitzer/IRAC data increase the coverage at 3.6 micron and 4.5 micron to ~120h over the HUDF reaching depths of ~28 (AB,1 sigma). The improved depth and inclusion of brighter candidates result in direct >3 sigma IRAC detections of 20/63 sources, of which 11/63 are detected at > 5 sigma. The average [3.6]-[4.5] colors of IRAC detected galaxies at z~8 are markedly redder than those at z~7, observed only 130Myr later. The simplest explanation is that we witness strong rest-frame optical emission lines (in particular [OIII]4959,5007+Hbeta) moving through the IRAC bandpasses with redshift. Assuming that the average rest-frame spectrum is the same at both z~7 and z~8 we estimate a rest-frame equivalent width of W([OIII]4959,5007+Hbeta) = 670 (+260,-170) Angstrom contributing 0.56 (+0.16,-0.11) mag to the 4.5 micron filter at z~8. The corresponding W(Halpha) = 430 (+160,-110) Angstrom implies an average specific star formation rate of sSFR = 11 (+11,-5) Gyr^-1 and a stellar population age of 100 (+100,-50) Myr. Correcting the spectral energy distribution for the contribution of emission lines lowers the average best-fit stellar masses and mass-to-light ratios by x3, decreasing the integrated stellar mass density to rho*(z=8,MUV<-18)=0.6 (+0.4,-0.3) x 10^6 Msun Mpc^-3.
Convolutional networks are at the core of most state-of-the-art computer vision solutions for a wide variety of tasks. Since 2014 very deep convolutional networks started to become mainstream, yielding substantial gains in various benchmarks. Although increased model size and computational cost tend to translate to immediate quality gains for most tasks (as long as enough labeled data is provided for training), computational efficiency and low parameter count are still enabling factors for various use cases such as mobile vision and big-data scenarios. Here we explore ways to scale up networks in ways that aim at utilizing the added computation as efficiently as possible by suitably factorized convolutions and aggressive regularization. We benchmark our methods on the ILSVRC 2012 classification challenge validation set demonstrate substantial gains over the state of the art: 21.2% top-1 and 5.6% top-5 error for single frame evaluation using a network with a computational cost of 5 billion multiply-adds per inference and with using less than 25 million parameters. With an ensemble of 4 models and multi-crop evaluation, we report 3.5% top-5 error on the validation set (3.6% error on the test set) and 17.3% top-1 error on the validation set.
Injection of spins into semiconductors is essential for the integration of the spin functionality into conventional electronics. Insulating layers are often inserted between ferromagnetic metals and semiconductors for obtaining an efficient spin injection, and it is therefore crucial to distinguish between signatures of electrical spin injection and impurity-driven effects in the tunnel barrier. Here we demonstrate an impurity-assisted tunneling magnetoresistance effect in nonmagnetic-insulator-nonmagnetic and ferromagnetic-insulator-nonmagnetic tunnel barriers. In both cases, the effect reflects on/off switching of the tunneling current through impurity channels by the external magnetic field. The reported effect, which is universal for any impurity-assisted tunneling process, finally clarifies the controversy of a widely used technique that employs the same ferromagnetic electrode to inject and detect spin accumulation.