ShantanuT01/DACTYL-Pretraining huggingface dataset:
Wormhole solutions corresponding to space-time geometries $R^1\times S^1\times S^2$ and $R^1\times S^3$ are obtained from reduced string effective action and the action is written in a manifestly $O(d,d)$ invariant form. A general treatment is given for obtaining wormhole solutions of different topologies from dimensional reduction. For specific ansatz of internal metric and antisymmetric field the reduced action is shown to have a global $SL(2,C)$ symmetry. The $SL(2,C)$ and duality symmetries have been exploited to generate new configurations of internal fields which produce wormhole solutions in four space-time dimensions. The $SL(2,C)$ symmetry discussed in this paper arises due to specific form of the moduli and these transformations belong to a subgroup of $O(d,d)$ global symmetry.
An alternative quantum algorithm for the discrete logarithm problem is presented. The algorithm uses two quantum registers and two Fourier transforms whereas Shor's algorithm requires three registers and four Fourier transforms. A crucial ingredient of the algorithm is a quantum state that needs to be constructed before we can perform the computation. After one copy of this state is created, the algorithm can be executed arbitrarily many times.
With references to recent observational results on the nebula IC59, we applied our previously developed Smoothed Particle Hydrodynamics (SPH) code which is based on Radiative Driven Implosion (RDI) model, to investigate the possible formation mechanism for the observed morphological structures of differently shaped BRCs. The simulation results confirmed the existence of the 4th type morphology of BRCs -- type M BRC. We are able to find the necessary condition for the appearance of the type M BRC based on the fact that the simulated physical properties of the cloud are consistent with observations on IC59. More importantly, the prospect of RDI triggered star formation by RDI model in all of the observed type M BRCs is ruthlessly eliminated.
We study the correspondence between the non-trivial topological properties associated with the individual valleys of gapped bilayer graphene (BLG), as a prototypical multi-valley system, and the gapless modes at its edges and other interfaces. We find that the exact connection between the valley-specific Hall conductivity and the number of gapless edge modes does not hold in general, but is dependent on the boundary conditions, even in the absence of intervalley coupling. This non-universality is attributed to the absence of a well-defined topological invariant within a given valley of BLG; yet, a more general topological invariant may be defined in certain cases, which explains the distinction between the BLG-vacuum and BLG-BLG interfaces.
Depth data provide geometric information that can bring progress in RGB-D scene parsing tasks. Several recent works propose RGB-D convolution operators that construct receptive fields along the depth-axis to handle 3D neighborhood relations between pixels. However, these methods pre-define depth receptive fields by hyperparameters, making them rely on parameter selection. In this paper, we propose a novel operator called malleable 2.5D convolution to learn the receptive field along the depth-axis. A malleable 2.5D convolution has one or more 2D convolution kernels. Our method assigns each pixel to one of the kernels or none of them according to their relative depth differences, and the assigning process is formulated as a differentiable form so that it can be learnt by gradient descent. The proposed operator runs on standard 2D feature maps and can be seamlessly incorporated into pre-trained CNNs. We conduct extensive experiments on two challenging RGB-D semantic segmentation dataset NYUDv2 and Cityscapes to validate the effectiveness and the generalization ability of our method.
According to the Alday-Maldacena program the strong coupling limit of Super Yang-Mills scattering amplitudes is given by minimal area surfaces in AdS spacetime with a boundary consisting of a momentum space polygon. The string equations in AdS systematically reduce to coupled Toda type equations whose Euclidean classical solutions are then of direct relevance. While in the simplest case of AdS_3 exact solutions were known from earlier studies of the sinh-Gordon equation, there exist at present no similar exact forms for the generalized Toda equations related to AdS_d with d>=4. In this paper we develop a series method for the solution to those equations and evaluate their contribution to the finite piece of the worldsheet area. For the known sinh-Gordon case the method is seen to give results in excellent agreement with the exact answer.
It is now widely accepted that globular cluster red giant branch stars owe their strange abundance patterns to a combination of pollution from progenitor stars and in situ extra mixing. In this hybrid theory a first generation of stars imprint abundance patterns into the gas from which a second generation forms. The hybrid theory suggests that extra mixing is operating in both populations and we use the variation of [C/Fe] with luminosity to examine how efficient this mixing is. We investigate the observed red giant branches of M3, M13, M92, M15 and NGC 5466 as a means to test a theory of thermohaline mixing. The second parameter pair M3 and M13 are of intermediate metallicity and our models are able to account for the evolution of carbon along the RGB in both clusters. Although, in order to fit the most carbon-depleted main-sequence stars in M13 we require a model whose initial [C/Fe] abundance leads to a carbon abundance lower than is observed. Furthermore our results suggest that stars in M13 formed with some primary nitrogen (higher C+N+O than stars in M3). In the metal-poor regime only NGC 5466 can be tentatively explained by thermohaline mixing operating in multiple populations. We find thermohaline mixing unable to model the depletion of [C/Fe] with magnitude in M92 and M15. It appears as if extra mixing is occurring before the luminosity function bump in these clusters. To reconcile the data with the models would require first dredge-up to be deeper than found in extant models.
We consider a random walk with a negative drift and with a jump distribution which under Cram\'er's change of measure belongs to the domain of attraction of a spectrally positive stable law. If conditioned to reach a high level and suitably scaled, this random walk converges in law to a nondecreasing Markov process which can be interpreted as a spectrally-positive L\'evy %-Khinchin process conditioned not to overshoot level one.
In this paper, we consider the task of space-time video super-resolution (ST-VSR), which can increase the spatial resolution and frame rate for a given video simultaneously. Despite the remarkable progress of recent methods, most of them still suffer from high computational costs and inefficient long-range information usage. To alleviate these problems, we propose a Bidirectional Recurrence Network (BRN) with the optical-flow-reuse strategy to better use temporal knowledge from long-range neighboring frames for high-efficiency reconstruction. Specifically, an efficient and memory-saving multi-frame motion utilization strategy is proposed by reusing the intermediate flow of adjacent frames, which considerably reduces the computation burden of frame alignment compared with traditional LSTM-based designs. In addition, the proposed hidden state in BRN is updated by the reused optical flow and refined by the Feature Refinement Module (FRM) for further optimization. Moreover, by utilizing intermediate flow estimation, the proposed method can inference non-linear motion and restore details better. Extensive experiments demonstrate that our optical-flow-reuse-based bidirectional recurrent network (OFR-BRN) is superior to state-of-the-art methods in accuracy and efficiency.
The authors investigate quantum transport in a narrow constriction fabricated by narrow band gap semiconductor materials with spin-orbit (SO) couplings. We consider the Rashba-Dresselhaus (RD) spin-orbit interactions (SOIs) and the Zeeman effect induced by an in-plane magnetic field along the transport direction. The interplay of the RD-SOI and the Zeeman effect may induce a SOI-Zeeman gap and influence the transport properties. We demonstrate that an attractive scattering potential may induce electron-like quasi-bound-state feature and manifest the RD-SOI-Zeeman induced Fano line-shape in conductance. Furthermore, a repulsive scattering potential may induce hole-like quasi-bound-state feature on the subband top of the lower spin branch.
High resolution spectropolarimetric observations of 3 sunspots taken with Hinode demonstrate the existence of supersonic downflows at or close to the umbra-penumbra boundary which have not been reported before. These downflows are confined to large patches, usually encompassing bright penumbral filaments, and have lifetimes of more than 14 hr. The presence of strong downflows in the center-side penumbra near the umbra rules out an association with the Evershed flow. Chromospheric filtergrams acquired close to the time of the spectropolarimetric measurements show large, strong, and long-lived brightenings in the neighborhood of the downflows. The photospheric intensity also exhibit persistent brightenings comparable to the quiet Sun. Interestingly, the orientation of the penumbral filaments at the site of the downflows is similar to that resulting from the reconnection process described by Ryutova et al. The existence of such downflows in the inner penumbra represents a challenge for numerical models of sunspots because they have to explain them in terms of physical processes likely affecting the chromosphere.
A worm algorithm is proposed for the two-dimensional spin glasses. The method is based on a low-temperature expansion of the partition function. The low-temperature configurations of the spin glass on square lattice can be viewed as strings connecting pairs of frustrated plaquettes. The worm algorithm directly manipulates these strings. It is shown that the worm algorithm is as efficient as any other types of cluster or replica-exchange algorithms. The worm algorithm is even more efficient if free boundary conditions are used. We obtain accurate low-temperature specific heat data consistent with a form c = T^{-2} exp(-2J/(k_BT)), where T is temperature and J is coupling constant, for the +/-J two-dimensional spin glass.
V350 Sgr is a classical Cepheid suitable for mass determination. It has a hot companion which is prominent in the ultraviolet and which is not itself a binary. We have obtained two high resolution echelle spectra of the companion at orbital velocity maximum and minimum with the Hubble Space Telescope (HST) Space Telescope Imaging Spectrograph (STIS) in the 1320 to 1510 \AA\/ region. By cross-correlating these spectra we obtained the orbital velocity amplitude of the companion with an uncertainty in the companion amplitude of 1.9 km sec$^{-1}$. This provides a mass ratio of the Cepheid to the companion of 2.1. The ultraviolet energy distribution of the companion provides the mass of the companion, yielding a Cepheid mass of 5.2 $\pm$ 0.3 M$_\odot$. This mass requires some combination of moderate main sequence core convective overshoot and rotation to match evolutionary tracks.
In this article, we introduce the parametrix technique in order to construct fundamental solutions as a general method based on semigroups and their generators. This leads to a probabilistic interpretation of the parametrix method that is amenable to Monte Carlo simulation. We consider the explicit examples of continuous diffusions and jump driven stochastic differential equations with H\"{o}lder continuous coefficients.
It is well known that the charged scalar perturbations of the Reissner-Nordstrom metric will decay slower at very late times than the neutral ones, thereby dominating in the late time signal. We show that at the stage of quasinormal ringing, on the contrary, the neutral perturbations will decay slower for RN, RNAdS and dilaton black holes. The QN frequencies of the nearly extreme RN black hole have the same imaginary parts (damping times) for charged and neutral perturbations. An explanation of this fact is not clear but, possibly, is connected with the Choptuik scaling.
Recent progress on qubit manipulation allows application of periodic driving signals on qubits. In this study, a harmonic driving field is added to a Rabi dimer to engineer photon and qubit dynamics in a circuit quantum electrodynamics device. To model environmental effects, qubits in the Rabi dimer are coupled to a phonon bath with a sub-Ohmic spectral density. A non-perturbative treatment, the Dirac-Frenkel time-dependent variational principle together with the multiple Davydov D$_2$ {\it Ansatz} is employed to explore the dynamical behavior of the tunable Rabi dimer. In the absence of the phonon bath, the amplitude damping of the photon number oscillation is greatly suppressed by the driving field, and photons can be created thanks to resonances between the periodic driving field and the photon frequency. In the presence of the phonon bath, one still can change the photon numbers in two resonators, and indirectly alter the photon imbalance in the Rabi dimer by directly varying the driving signal in one qubit. It is shown that qubit states can be manipulated directly by the harmonic driving. The environment is found to strengthen the interqubit asymmetry induced by the external driving, opening up a new venue to engineer the qubit states.
Kepler allows the measurement of starspot variability in a large sample of field red giants for the first time. With a new method that combines autocorrelation and wavelet decomposition, we measure 361 rotation periods from the full set of 17,377 oscillating red giants in our sample. This represents 2.08% of the stars, consistent with the fraction of spectroscopically detected rapidly rotating giants in the field. The remaining stars do not show enough variability to allow us to measure a reliable surface rotation period. Because the stars with detected rotation periods have measured oscillations, we can infer their global properties, e.g. mass and radius, and quantitatively evaluate the predictions of standard stellar evolution models as a function of mass. Consistent with results for cluster giants when we consider only the 4881 intermediate-mass stars, M>2.0 M$_\odot$ from our full red giant sample, we do not find the enhanced rates of rapid rotation expected from angular momentum conservation. We therefore suggest that either enhanced angular momentum loss or radial differential rotation must be occurring in these stars. Finally, when we examine the 575 low-mass (M<1.1 M$_\odot$) red clump stars in our sample, which were expected to exhibit slow (non-detectable) rotation, 15% of them actually have detectable rotation. This suggests a high rate of interactions and stellar mergers on the red giant branch.
When looking for analytical approaches to treat frustrated quantum magnets, it is often very useful to start from a limit where the ground state is highly degenerate. This chapter discusses several ways of deriving {effective Hamiltonians} around such limits, starting from standard {degenerate perturbation theory} and proceeding to modern approaches more appropriate for the derivation of high-order effective Hamiltonians, such as the perturbative continuous unitary transformations or contractor renormalization. In the course of this exposition, a number of examples taken from the recent literature are discussed, including frustrated ladders and other dimer-based Heisenberg models in a field, as well as the mapping between frustrated Ising models in a transverse field and quantum dimer models.
A diagram for Bianchi spaces with vanishing vector of structure constants (type A in the Ellis-MacCallum classification) illustrates the relations among their different types under similarity transformations. The Ricci coefficients and the Ricci tensor are related by a Cremona transformation.
A generic explanation for the recently observed anomalous crossing frequencies in odd proton rare earth nuclei is given. As an example, the proton ${1\over 2} [541]$ band in $^{175}$Ta is discussed in detail by using the angular momentum projection theory. It is shown that the quadrupole pairing interaction is decisive in delaying the crossing point and the changes in crossing frequency along the isotope chain are due to the different neutron shell fillings.
A Friedman-Robertson-Walker cosmology arising from a five-dimensional Chern-Simons (CS) theory for the group S0(1,5) coupled to matter is considered as an alternative model for dark energy and matter. The four-dimensional reduction describes an accelerating universe having a time dependent Newton's coupling G and a positive cosmological constant. Five dimensional matter gives rise to what we interprete as four dimensional ordinary plus dark matter and a dark energy is provided by a cosmological constant term plus a fluid arising from the CS coupling. The case of five dust is studied in detail, leading to acceptable limits for most of the cosmological parameters considered, in the context of an open non-flat universe. Nevertheless, a value for ${\dot G}/G $ which is two orders of magnitude higher than recent bounds is predicted.
In these proceedings, we summarise the results of the recent calculation of the NNLO QCD corrections for the production of a top-quark pair in association with a bottom-flavoured hadron. The results consist of differential distributions of observables involving the identified hadron.
In this work, we consider a diffusive two-species d-dimensional model and study it in great details. Two types of particles, with hard-core, diffuse symmetrically and cross each other. For arbitrary dimensions, we obtain the exact density, the instantaneous, as well as non-instantaneous, two-point correlation functions for various initial conditions.   We study the impact of correlations in the initial state on the dynamics.   Finally, we map the one-dimensional version of the model under consideration onto a growth model of RSOS type with three states and solve its dynamics.
We prove an implicit function theorem for non-commutative functions. We use this to show that if $p(X,Y)$ is a generic non-commuting polynomial in two variables, and $X$ is a generic matrix, then all solutions $Y$ of $p(X,Y)=0$ will commute with $X$.
Let $(S,H)$ be a generalized Fermat pair of the type $(k,n)$. If $F\subset S$ is the set of fixed points of the non-trivial elements of the group $H$, then $F$ is exactly the set of hyperoscualting points of the standard embedding $S\hookrightarrow {\mathbb{P}}^{n}$. We provide an optimal lower bound (this being sharp in a dense open set of the moduli space of the generalized Fermat curves) for the Weierstrass weight of these points.
It is proved that the special fibre of the Nash transform of an irreducible isolated singularity has maximal dimension.
Starting from the microscopic description of a normal fluid in terms of any kind of local interacting many-particle theory we present a well defined step by step procedure to derive the hydrodynamic equations for the macroscopic phenomena. We specify the densities of the conserved quantities as the relevant hydrodynamic variables and apply the methods of non-equilibrium statistical mechanics with projection operator techniques. As a result we obtain time-evolution equations for the hydrodynamic variables with three kinds of terms on the right-hand sides: reversible, dissipative and fluctuating terms. In their original form these equations are completely exact and contain nonlocal terms in space and time which describe nonlocal memory effects. Applying a few approximations the nonlocal properties and the memory effects are removed. As a result we find the well known hydrodynamic equations of a normal fluid with Gaussian fluctuating forces. In the following we investigate if and how the time-inversion invariance is broken and how the second law of thermodynamics comes about. Furthermore, we show that the hydrodynamic equations with fluctuating forces are equivalent to stochastic Langevin equations and the related Fokker-Planck equation. Finally, we investigate the fluctuation theorem and find a modification by an additional term.
In this paper, we study transition density functions for pure jump unimodal L\'evy processes killed upon leaving an open set $D$. Under some mild assumptions on the L\'evy density, we establish two-sided Dirichlet heat kernel estimates when the open set $D$ is $C^{1, 1}$. Our result covers the case that the L\'evy densities of unimodal L\'evy processes are regularly varying functions whose indices are equal to the Euclidean dimension. This is the first results on two-sided Dirichlet heat kernel estimates for L\'evy processes such that the weak lower scaling index of the L\'evy densities is not necessarily strictly bigger than the Euclidean dimension.
Let $\mathbb{F}_q$ be a finite field with $q$ elements, $n\geq2$ a positive integer, $\mathbb{V}_0$ a $n$-dimensional vector space over $\mathbb{F}_q$ and $\mathbb{T}_0$ the set of all linear functionals from $\mathbb{V}_0$ to $\mathbb{F}_q$. Let $\mathbb{V}=\mathbb{V}_0\setminus\{0\}$ and $\mathbb{T}=\mathbb{T}_0\setminus\{0\}$. The \emph{linear functional graph} of $\mathbb{V}_0$ dented by $\digamma(\mathbb{V})$, is an undirected bipartite graph, whose vertex set $V$ is partitioned into two sets as $V=\mathbb{V}\cup \mathbb{T}$ and two vertices $v\in \mathbb{V}$ and $f\in \mathbb{T}$ are adjacent if and only if $f$ sends $v$ to the zero element of $\mathbb{F}_q$ (i.e. $f(v)=0$). In this paper, the structure of all automorphisms of this graph is characterized and formolized. Also the cardinal number of automorphisms group   for this graph is determined.
The internal thermal noise in LIGO's test masses is analyzed by a new technique, a direct application of the Fluctuation-Dissipation Theorem to LIGO's readout observable, $x(t)=$(longitudinal position of test-mass face, weighted by laser beam's Gaussian profile). Previous analyses, which relied on a normal-mode decomposition of the test-mass motion, were valid only if the dissipation is uniformally distributed over the test-mass interior, and they converged reliably to a final answer only when the beam size was a non-negligible fraction of the test-mass cross section. This paper's direct analysis, by contrast, can handle inhomogeneous dissipation and arbitrary beam sizes. In the domain of validity of the previous analysis, the two methods give the same answer for $S_x(f)$, the spectral density of thermal noise, to within expected accuracy. The new analysis predicts that thermal noise due to dissipation concentrated in the test mass's front face (e.g. due to mirror coating) scales as $1/r_0^2$, by contrast with homogeneous dissipation, which scales as $1/r_0$ ($r_0$ is the beam radius); so surface dissipation could become significant for small beam sizes.
We propose a hybrid quantum computing scheme where qubit degrees of freedom for computation are combined with quantum continuous variables for communication. In particular, universal two-qubit gates can be implemented deterministically through qubit-qubit communication, mediated by a continuous-variable bus mode ("qubus"), without direct interaction between the qubits and without any measurement of the qubus. The key ingredients are controlled rotations of the qubus and unconditional qubus displacements. The controlled rotations are realizable through typical atom-light interactions in quantum optics. For such interactions, our scheme is universal and works in any regime, including the limits of weak and strong nonlinearities.