ShantanuT01/DACTYL-Pretraining huggingface dataset:
In the conventional ferromagnetic systems, topological magnon bands and thermal Hall effect are due to the Dzyaloshinskii-Moriya interaction (DMI). In principle, however, the DMI is either negligible or it is not allowed by symmetry in some quantum magnets. Therefore, we expect that topological magnon features will not be present in those systems. In addition, quantum magnets on the triangular-lattice are not expected to possess topological features as the DMI or spin-chirality cancels out due to equal and opposite contributions from adjacent triangles. Here, however, we predict that the isomorphic frustrated honeycomb-lattice and bilayer triangular-lattice antiferromagnetic system will exhibit topological magnon bands and topological thermal Hall effect in the absence of an intrinsic DMI. These unconventional topological magnon features are present as a result of magnetic-field-induced non-coplanar spin configurations with nonzero scalar spin chirality. The relevance of the results to realistic bilayer triangular antiferromagnetic materials are discussed.
We introduce the inversion polynomial for Dedekind sums $f_b(x)=\sum x^{\operatorname{inv}(a,b)}$ to study the number of $s(a,b)$ which have the same value for given $b$. We prove several properties of this polynomial and present some conjectures. We also introduce connections between Kloosterman sums and the inversion polynomial evaluated at particular roots of unity. Finally, we improve on previously known bounds for the second highest value of the Dedekind sum and provide a conjecture for a possible generalization. Lastly, we include a new restriction on equal Dedekind sums based on the reciprocity formula.
The pulsar B1620-26 has two companions, one of stellar mass and one of planetary mass. We detected the stellar companion using Hubble Space Telescope observations. The color and magnitude of the stellar companion indicate that it is an undermassive white dwarf ($0.34 \pm 0.04 M_{\odot}$) of age $480\pm 140$ Myr. This places a constraint on the recent history of this triple system and supports a scenario in which the current configuration arose through a dynamical exchange interaction in the cluster core. This implies that planets may be relatively common in low-metallicity globular clusters and that planet formation is more widespread and happened earlier than previously believed.
A unified and consistent phenomenological approach to single transverse spin asymmetries in the framework of perturbative QCD, with the inclusion of a new class of spin and k_T dependent distribution and fragmentation functions, is presented. As an example, results on A_N(p(pol) p --> pion X) and P_Lambda(p p -->Lambda(pol) X) are shown.
Persistence is considered in diffusion--limited cluster--cluster aggregation, in one dimension and when the diffusion coefficient of a cluster depends on its size $s$ as $D(s) \sim s^\gamma$. The empty and filled site persistences are defined as the probabilities, that a site has been either empty or covered by a cluster all the time whereas the cluster persistence gives the probability of a cluster to remain intact. The filled site one is nonuniversal. The empty site and cluster persistences are found to be universal, as supported by analytical arguments and simulations. The empty site case decays algebraically with the exponent $\theta_E = 2/(2 - \gamma)$. The cluster persistence is related to the small $s$ behavior of the cluster size distribution and behaves also algebraically for $0 \le \gamma < 2$ while for $\gamma < 0$ the behavior is stretched exponential. In the scaling limit $t \to \infty$ and $K(t) \to \infty$ with $t/K(t)$ fixed the distribution of intervals of size $k$ between persistent regions scales as $n(k;t) = K^{-2} f(k/K)$, where $K(t) \sim t^\theta$ is the average interval size and $f(y) = e^{-y}$. For finite $t$ the scaling is poor for $k \ll t^z$, due to the insufficient separation of the two length scales: the distances between clusters, $t^z$, and that between persistent regions, $t^\theta$. For the size distribution of persistent regions the time and size dependences separate, the latter being independent of the diffusion exponent $\gamma$ but depending on the initial cluster size distribution.
We consider the 1/2 BPS circular Wilson loop in a generic N=2 SU(N) SYM theory with conformal matter content. We study its vacuum expectation value, both at finite $N$ and in the large-N limit, using the interacting matrix model provided by localization results. We single out some families of theories for which the Wilson loop vacuum expectation values approaches the N=4 result in the large-N limit, in agreement with the fact that they possess a simple holographic dual. At finite N and in the generic case, we explicitly compare the matrix model result with the field-theory perturbative expansion up to order g^8 for the terms proportional to the Riemann value zeta(5), finding perfect agreement. Organizing the Feynman diagrams as suggested by the structure of the matrix model turns out to be very convenient for this computation.
A prescription is given for computing anomalous dimensions of single trace operators in SYM at strong coupling and large $N$ using a reduced model of matrix quantum mechanics. The method involves treating some parts of the operators as "BPS condensates" which, in certain limit, have a dual description as null geodesics on the $S^5$. In the gauge theory, the condensate is similar to a representative of the chiral ring and it is described by a background of commuting matrices. Excitations around these condensates correspond to excitations around this background and take the form of "string bits" which are dual to the "giant magnons" of Hofman and Maldacena. In fact, the matrix model approach gives a {\it quantum} description of these string configurations and explains why the infinite momentum limit suppresses the quantum effects. This method allows, not only to derive part of the classical sigma model Hamiltonian of the dual string (in the infinite momentum limit), but also its quantum canonical structure. Therefore, it provides an alternative method of testing the AdS/CFT correspondence without the need of integrability.
In this paper, we study non-trivial upper bounds for the sum $\sum \limits_{n \in S} |\lambda_f(n)|$ where $f$ is a normalized Maass eigencusp form for the full modular group, $\lambda_f(n)$ is the $n$th normalized Fourier coefficient of $f$ and $S$ is a proper subset of positive integers in $[1,x]$ with certain properties.
Deep convolutional networks (CNNs) have exhibited their potential in image inpainting for producing plausible results. However, in most existing methods, e.g., context encoder, the missing parts are predicted by propagating the surrounding convolutional features through a fully connected layer, which intends to produce semantically plausible but blurry result. In this paper, we introduce a special shift-connection layer to the U-Net architecture, namely Shift-Net, for filling in missing regions of any shape with sharp structures and fine-detailed textures. To this end, the encoder feature of the known region is shifted to serve as an estimation of the missing parts. A guidance loss is introduced on decoder feature to minimize the distance between the decoder feature after fully connected layer and the ground-truth encoder feature of the missing parts. With such constraint, the decoder feature in missing region can be used to guide the shift of encoder feature in known region. An end-to-end learning algorithm is further developed to train the Shift-Net. Experiments on the Paris StreetView and Places datasets demonstrate the efficiency and effectiveness of our Shift-Net in producing sharper, fine-detailed, and visually plausible results. The codes and pre-trained models are available at https://github.com/Zhaoyi-Yan/Shift-Net.
Well-controlled quantum devices with their increasing system size face a new roadblock hindering further development of quantum technologies: The effort of quantum tomography---the characterization of processes and states within a quantum device---scales unfavorably to the point that state-of-the-art systems can no longer be treated. Quantum compressed sensing mitigates this problem by reconstructing the state from an incomplete set of observables. In this work, we present an experimental implementation of compressed tomography of a seven qubit system---the largest-scale realization to date---and we introduce new numerical methods in order to scale the reconstruction to this dimension. Originally, compressed sensing has been advocated for density matrices with few non-zero eigenvalues. Here, we argue that the low-rank estimates provided by compressed sensing can be appropriate even in the general case. The reason is that statistical noise often allows only for the leading eigenvectors to be reliably reconstructed: We find that the remaining eigenvectors behave in a way consistent with a random matrix model that carries no information about the true state. We report a reconstruction of quantum states from a topological color code of seven qubits, prepared in a trapped ion architecture, based on tomographically incomplete data involving 127 Pauli basis measurement settings only, repeated 100 times each.
We suggest that the atmospheric neutrino anomaly observed in the Super-Kamiokande (and other) experiments results from the combined effects of muon-neutrino to tau-neutrino oscillations with a Delta m^2 value of approximately 0.4 eV^2 and oscillations between muon neutrinos and electron neutrinos (and vice-versa) with 0.0001 < Delta m^2 < 0.001 eV^2. With an appropriate choice of a three-neutrino mixing matrix, such a hypothesis is consistent with essentially all neutrino observations.
In classical case there is simplest method of error correction with using three equal bits instead of one. In the paper is shown, how the scheme fails for quantum error correction with complex vector spaces of usual quantum mechanics, but works in real and quaternionic cases. It is discussed also, how to implement the three qubits scheme with using encoding of quaternionic qubit by Majorana spinor. Necessary concepts and formulae from area of quantum error corrections are closely introduced and proved.
We consider a four-terminal Aharonov-Bohm interference setup formed out of two edges of a quantum spin Hall insulator, supporting helical Luttinger liquids (HLLs). We show that the temperature and bias dependence of the interference oscillations are linked to the amount of spin flips in tunneling between two HLLs which is a unique signature of a HLL. We predict that spin dephasing depends on the electron-electron (e-e) interaction but differently from the charge dephasing due to distinct dominant tunneling excitations. In contrast, in a spinful Luttinger liquid with SU(2) invariance, uncharged spin excitations can carry spin current without dephasing in spite of the presence of e-e interactions.
Although there have been many studies of statistical mechanical models of magnetic friction, most of these have focused on the behavior in the steady state. In this study, we prepare a system composed of a chain and a lattice of Ising spins that interact with each other, and investigate the relaxation of the system when the relative velocity $v$ changes suddenly. The situation where $v$ is given is realized by attaching the chain to a spring, the other end of which moves with a constant velocity $v$. Numerical simulation finds that, when the spring constant has a moderate value, the relaxation of the frictional force is divided into two processes, which are a sudden change and a slow relaxation. This behavior is also observed on regular solid surfaces, although caused by different factors than our model. More specifically, the slow relaxation process is caused by relaxation of the magnetic structure in our model, but is caused by creep deformation in regular solid surfaces.
For any genus g > 1 we give an example of a family of smooth complex projective curves of genus g such that the image of the monodromy representation of the Hitchin connection on the sheaf of generalized SL(2)-theta functions of level l different from 1,2,4 and 8 contains an element of infinite order.
With the rise of focus on man made changes to our planet and wildlife therein, more and more emphasis is put on sustainable and responsible gathering of resources. In an effort to preserve maritime wildlife the Norwegian government has decided that it is necessary to create an overview over the presence and abundance of various species of wildlife in the Norwegian fjords and oceans. In this paper we apply and analyze an object detection scheme that detects fish in camera images. The data is sampled from a submerged data station at Fulehuk in Norway. We implement You Only Look Once (YOLO) version 3 and create a dataset consisting of 99,961 images with a mAP of $\sim 0.88$. We also investigate intermediate results within YOLO, gaining insight into how it performs object detection.
In this note we discuss several properties of the Schur index of N=2 superconformal theories in four dimensions. In particular, we study modular properties of this index under SL(2,Z) transformations of its parameters.
We introduce a notion of Homological Projective Duality for smooth algebraic varieties in dual projective spaces, a homological extension of the classical projective duality. If algebraic varieties $X$ and $Y$ in dual projective spaces are Homologically Projectively Dual, then we prove that the orthogonal linear sections of $X$ and $Y$ admit semiorthogonal decompositions with an equivalent nontrivial component. In particular, it follows that triangulated categories of singularities of these sections are equivalent. We also investigate Homological Projective Duality for projectivizations of vector bundles.
We investigate the influence of vacuum polarization of quantum massive fields on the scalar sector of quasinormal modes in spherically symmetric black holes. We consider the evolution of a massless scalar field on the spacetime corresponding to a charged semiclassical black hole, consisting of the quantum corrected geometry of a Reissner-Nordstr\"om black hole dressed by a quantum massive scalar field in the large mass limit. Using a sixth order WKB approach we find the shift in the quasinormal mode frequencies due to vacuum polarization .
We present detailed pedagogical derivation of covariant derivative of fermions and some related expressions, including commutator of covariant derivatives and energy-momentum tensor of a free Dirac field. On top of that, local conformal transformations for a Dirac fermion in curved spacetime are considered and we obtain the expression for the energy-momentum tensor on the cosmological background.
An extended $U(3)_L\bigotimes U(3)_R$ chiral effective field theory which includes pseudoscalar and vector meson nonets as dynamic variables is presented. The theory combines a hidden symmetry approach with a general procedure of including the $\eta'$ meson into chiral theory, and accounts for $direct$ and $indirect$ symmetry breaking effects via a mechanism based on the quark mass matrix. The theory is applied to anomalous radiative decays using particle mixing schemes, corresponding to different symmetry breaking assumptions and uniquely determined by the lagarngian presumed. Radiative decays of light flavor mesons are best explained within the framework of a one mixing angle scheme and provide evidence for $SU(3)_F$ and nonet symmetry breaking.
We report the first detection of multiphase gas within a quiescent galaxy beyond $z\approx0$. The observations use the brighter image of doubly lensed QSO HE 0047$-$1756 to probe the ISM of the massive ($M_{\rm star}\approx 10^{11} \mathrm{M_\odot}$) elliptical lens galaxy at $z_\mathrm{gal}=0.408$. Using Hubble Space Telescope's Cosmic Origins Spectrograph (COS), we obtain a medium-resolution FUV spectrum of the lensed QSO and identify numerous absorption features from $\mathrm{H_2}$ in the lens ISM at projected distance $d=4.6$ kpc. The $\mathrm{H_2}$ column density is $\log N(\mathrm{H_2})/\mathrm{cm^{-2}}=17.8^{+0.1}_{-0.3}$ with a molecular gas fraction of $f_\mathrm{H_2}=2-5\%$, roughly consistent with some local quiescent galaxies. The new COS spectrum also reveals kinematically complex absorption features from highly ionized species O VI and N V with column densities log $N(\mathrm{O VI})/\mathrm{cm^{-2}} =15.2\pm0.1$ and log $N(\mathrm{N V})/\mathrm{cm^{-2}} =14.6\pm0.1$, among the highest known in external galaxies. Assuming the high-ionization absorption features originate in a transient warm ($T\sim10^5\,$K) phase undergoing radiative cooling from a hot halo surrounding the galaxy, we infer a mass accretion rate of $\sim 0.5-1.5\,\mathrm{M_\odot\,yr^{-1}}$. The lack of star formation in the lens suggests the bulk of this flow is returned to the hot halo, implying a heating rate of $\sim10^{48}\,\mathrm{erg\,yr^{-1}}$. Continuous heating from evolved stellar populations (primarily SNe Ia but also winds from AGB stars) may suffice to prevent a large accumulation of cold gas in the ISM, even in the absence of strong feedback from an active nucleus.
This paper revisits the H\"{o}lder regularity of mild solutions of parabolic stochastic Cauchy problems in Lebesgue spaces $L^p(\mathcal{O}),$ with $p\geq 2$ and $\mathcal{O}\subset\mathbb{R}^d$ a bounded domain. We find conditions on $p, \beta$ and $\gamma$ under which the mild solution has almost surely trajectories in $\mathcal{C}^\beta([0,T];\mathcal{C}^\gamma(\bar{\mathcal{O}})).$ These conditions do not depend on the Cameron-Martin Hilbert space associated with the driving cylindrical noise. The main tool of this study is a regularity result for stochastic convolutions in M-type 2 Banach spaces by Z. Brze\'zniak (Stoch. Stoch. Rep. Vol. 61, Iss. 3-4, 1997).
In this paper, we propose a new notion of Forward--Backward Martingale Problem (FBMP), and study its relationship with the weak solution to the forward--backward stochastic differential equations (FBSDEs). The FBMP extends the idea of the well-known (forward) martingale problem of Stroock and Varadhan, but it is structured specifically to fit the nature of an FBSDE. We first prove a general sufficient condition for the existence of the solution to the FBMP. In the Markovian case with uniformly continuous coefficients, we show that the weak solution to the FBSDE (or equivalently, the solution to the FBMP) does exist. Moreover, we prove that the uniqueness of the FBMP (whence the uniqueness of the weak solution) is determined by the uniqueness of the viscosity solution of the corresponding quasilinear PDE.
We report high-cadence photometry of the ultra-fast ($t_2\sim1.2$ d) nova V1674 Her during its rise to maximum light ($V\sim6.3$) and the beginning of its subsequent decline. These observations from Evryscope and the Mount Laguna Observatory All-Sky Camera reveal a plateau in the pre-maximum light curve at $g\sim14$ ($\sim$8 mag below peak) that lasted for at least three hours. Similar features (so-called pre-maximum halts) have been observed in some novae near maximum light, but to our knowledge the detection of a plateau in the light curve $\sim$8 mag below peak is unprecedented.
Using a large sample of galaxies from the SDSS-DR7, we have analysed the alignment of disk galaxies around cosmic voids. We have constructed a complete sample of cosmic voids (devoid of galaxies brighter than M_r-5 log(h) =-20.17) with radii larger than 10 Mpc/h up to redshift 0.12. Disk galaxies in shells around these voids have been used to look for particular alignments between the angular momentum of the galaxies and the radial direction of the voids. We find that disk galaxies around voids larger than >~ 15 Mpc/h within distances not much larger than 5 Mpc/h from the surface of the voids present a significant tendency to have their angular momenta aligned with the void's radial direction with a significance >~ 98.8% against the null hypothesis. The strength of this alignment is dependent on the void's radius and for voids with ~<15 Mpc/h the distribution of the orientation of the galaxies is compatible with a random distribution. Finally, we find that this trend observed in the alignment of galaxies is similar to the one observed for the minor axis of dark matter halos around cosmic voids found in cosmological simulations, suggesting a possible link in the evolution of both components.
X-ray data of the Centaurus cluster, obtained with {\it XMM-Newton} for 45 ksec, were analyzed. Deprojected EPIC spectra from concentric thin shell regions were reproduced equally well by a single-phase plasma emission model, or by a two-phase model developed by {\it ASCA}, both incorporating cool (1.7--2.0 keV) and hot ($\sim 4$ keV) plasma temperatures. However, EPIC spectra with higher statistics, accumulated over 3-dimentional thick shell regions, were reproduced better by the two-phase model than by the singe-phase one. Therefore, hot and cool plasma phases are inferred to co-exist in the cluster core region within $\sim 70$ kpc. The iron and silicon abundances of the plasma were reconfirmed to increase significantly towards the center, while that of oxygen was consistent with being radially constant. The implied non-solar abundance ratios explains away the previously reported excess X-ray absorption from the central region. Although an additional cool ($\sim 0.7$ keV) emission was detected within $\sim 20$ kpc of the center, the RGS data gave tight upper limits on any emission with a tempeartures below $\sim 0.5$ keV. These results are compiled into a magnetosphere model, which interprets the cool phase as confined within closed magnetic loops anchored to the cD galaxy. When combined with so-called Rosner-Tucker-Vaiana mechanism which applies to solar coronae, this model can potentially explain basic properties of the cool phase, including its temperature and thermal stability.
We use $\ell$-adic class field theory to take a new view on cyclotomic norms and Leopoldt or Gross generalized conjectures. By the way we recall and complete some classical results. We illustrate the logarithmic approach by various numerical examples and counter-examples obtained with PARI.
We present a novel parameter-free cosmological void finder (\textsc{dive}, Delaunay TrIangulation Void findEr) based on Delaunay Triangulation (DT), which efficiently computes the empty spheres constrained by a discrete set of tracers. We define the spheres as DT voids, and describe their properties, including an universal density profile together with an intrinsic scatter. We apply this technique on 100 halo catalogues with volumes of 2.5\,$h^{-1}$Gpc side each, with a bias and number density similar to the BOSS CMASS Luminous Red Galaxies, performed with the \textsc{patchy} code. Our results show that there are two main species of DT voids, which can be characterised by the radius: they have different responses to halo redshift space distortions, to number density of tracers, and reside in different dark matter environments. Based on dynamical arguments using the tidal field tensor, we demonstrate that large DT voids are hosted in expanding regions, whereas the haloes used to construct them reside in collapsing ones. Our approach is therefore able to efficiently determine the troughs of the density field from galaxy surveys, and can be used to study their clustering. We further study the power spectra of DT voids, and find that the bias of the two populations are different, demonstrating that the small DT voids are essentially tracers of groups of haloes.
The PS-model treated in this paper is motivated by freelance job websites where multiple freelancers compete for a single job. In the context of such websites, multistage service of a job means collection of applications from multiple freelancers. Under Markovian stochastic assumptions, we develop fluid limit approximations for the PS-model in overload. Based on this approximation, we estimate what proportion of freelancers get the jobs they apply for. In addition, the PS-model studied here is an instant of PS with routing and impatience, for which no Lyapunov function is known, and we suggest some partial solutions.