ShantanuT01/DACTYL-Pretraining huggingface dataset:
Let $p\geq 5$ be a prime number, $\mathbb{F}$ a finite field of characteristic $p$ and let $\bar{\chi}$ be the mod-$p$ cyclotomic character. Let $\bar{\rho}:\operatorname{G}_{\mathbb{Q}}\rightarrow \operatorname{GL}_2(\mathbb{F})$ be a Galois representation such that the local representation $\bar{\rho}_{\restriction \operatorname{G}_{\mathbb{Q}_p}}$ is flat and irreducible. Further, assume that $\operatorname{det}\bar{\rho}=\bar{\chi}$. The celebrated theorem of Khare and Wintenberger asserts that if $\bar{\rho}$ satisfies some natural conditions, there exists a normalized Hecke-eigencuspform $f=\sum_{n\geq 1} a_n q^n$ and a prime $\mathfrak{p}|p$ in its field of Fourier coefficients such that the associated $\mathfrak{p}$-adic representation ${\rho}_{f,\mathfrak{p}}$ lifts $\bar{\rho}$. In this manuscript we prove a refined version of this theorem, namely, that one may control the valuation of the $p$-th Fourier coefficient of $f$. The main result is of interest from the perspective of the $p$-adic Langlands program.
We investigate how rotationally-constrained, deep convection might give rise to supergranulation, the largest distinct spatial scale of convection observed in the solar photosphere. While supergranulation is only weakly influenced by rotation, larger spatial scales of convection sample the deep convection zone and are presumably rotationally influenced. We present numerical results from a series of nonlinear, 3-D simulations of rotating convection and examine the velocity power distribution realized under a range of Rossby numbers. When rotation is present, the convective power distribution possesses a pronounced peak, at characteristic wavenumber $\ell_\mathrm{peak}$, whose value increases as the Rossby number is decreased. This distribution of power contrasts with that realized in non-rotating convection, where power increases monotonically from high to low wavenumbers. We find that spatial scales smaller than $\ell_\mathrm{peak}$ behave in analogy to non-rotating convection. Spatial scales larger than $\ell_\mathrm{peak}$ are rotationally-constrained and possess substantially reduced power relative to the non-rotating system. We argue that the supergranular scale emerges due to a suppression of power on spatial scales larger than $\ell\approx100$ owing to the presence of deep, rotationally-constrained convection. Supergranulation thus represents the largest non-rotationally-constrained mode of solar convection. We conclude that the characteristic spatial scale of supergranulation bounds that of the deep convective motions from above, making supergranulation an indirect measure of the deep-seated dynamics at work in the solar dynamo. Using the spatial scale of supergranulation in conjunction with our numerical results, we estimate an upper bound of 10 m s$^{-1}$ for the Sun's bulk rms convective velocity.
Classical solutions of equations of motion in low energy effective field theory, describing fundamental charged heterotic string, are found. These solutions automatically carry an electric current equal to the charge per unit length, and hence are accompanied by both, electric and magnetic fields. Force between two parallel strings vanish due to cancellation between electric and magnetic forces, and also between graviton, dilaton, and antisymmetric tensor field induced forces. Multi-string solutions describing configuration of parallel strings are also found. Finally, the solutions are shown to possess partially broken space-time supersymmetry.
Monoaxial chiral magnets can form a peculiar noncollinear spin structure called the chiral soliton lattice in an applied magnetic field perpendicular to the helical axis. We study magnetic properties and electrical transport in the chiral soliton lattice by a Monte Carlo simulation for a one-dimensional Kondo lattice model including the Dzyaloshinskii-Moriya interaction between classical localized spins. We show that the model exhibits a helical spin structure at a zero magnetic field, which turns into the chiral soliton lattice, and finally, to a forced ferromagnetic state with increasing the external magnetic field. In the chiral soliton lattice state, we find negative magnetoresistance proportional to the number of solitons at low temperature, which corroborates the spin scattering of electrons by chiral solitons. We also discuss the temperature and magnetic field dependence of the spin structure factor and electrical resistivity, in comparison with experiments for CrNb$_{3}$S$_{6}$.
We consider the non-analytic terms in the spin susceptibility arising as a result of rescaterring of pairs of quasiparticles. We emphasize the importance of rescattering in the Cooper channel for the analysis of the temperature dependences in the two-dimensional electron systems in the ballistic regime. In the calculation of the linear in $T$ term we use angular harmonics in the Cooper channel, because for each harmonic the interaction amplitude is renormalized independently. We observe, that as a consequence of strong renormalizations in the Cooper ladder, the temperature derivative of the spin susceptibility may change its sign at low temperatures.
We analyse recently proposed physical implementations of a quantum computer based on polar molecules. A set of general requirements for a molecular system is presented, which would provide an optimal combination of quantum gate times, coherence times, number of operations, high gate accuracy and experimental feasibility. We proceed with a detailed analysis of a scheme utilizing switchable dipole-dipole interactions between polar molecules. Switchable dipole-dipole interaction is an efficient tool for realization of two-qubit quantum gates, necessary to construct a universal set of gates. We consider three possible realizations of a phase gate using specific molecules, such as CO, NF, alkali dimers and alkaline-earth monohalides. We suggest suitable electronic states and ransitions and investigate requirements for the pulses driving them. Finally, we analyse possible sources of decoherence.
Various works performed by the present authors in the 1990s are reviewed. The topics discussed in this paper are mainly related to the time-evolution of the coherent and the squeezed states of the systems obeying the su(2)- and the su(1,1)-algebra. The formulations are based on the basic idea of the boson mapping and the TDHF theory in canonical form. Under the time-dependent variational procedure for trial states appropriately chosen, the time-evolution of the systems under investigation is described. Further, it is shown that this method enables us to obtain the classical counterparts of the original quantal systems.
In leading fault-tolerant quantum computing schemes, accurate transformation are obtained by a two-stage process. In a first stage, a discrete, universal set of fault-tolerant operations is obtained by error-correcting noisy transformations and distilling resource states. In a second stage, arbitrary transformations are synthesized to desired accuracy by combining elements of this set into a circuit. Here, we present a scheme which merges these two stages into a single one, directly distilling complex transformations. We find that our scheme can reduce the total overhead to realize certain gates by up to a few orders of magnitude. In contrast to other schemes, this efficient gate synthesis does not require computationally intensive compilation algorithms, and a straightforward generalization of our scheme circumvents compilation and synthesis altogether.
(Abridged) Some supernovae (SNe) may be powered by the interaction of the SN ejecta with a large amount of circumstellar matter (CSM). Here we outline a method to measure the mass of the optically thick CSM around such SNe. We present observations of SN2010jl, including the first detection of a SN using NuSTAR. The total radiated luminosity of SN2010jl is extreme, at least 9e50 erg. By modeling the visible-light data, we robustly show that the mass of the circumstellar material within ~1e16 cm of the progenitor was in excess of 10 solar masses, likely ejected tens of years prior to the SN explosion. Our modeling suggests that the shock velocity during shock breakout was ~6000 km/s, decelerating to ~2600 km/s about two years after maximum light. Our late-time NuSTAR+XMM spectra of the SN presumably provide the first direct measurement of SN shock velocity two years after the SN maximum light -- measured to be in the range of 2000 to 4500 km/s if the ions and electrons are in equilibrium, and >~2000 km/s if they are not in equilibrium. This measurement is in agreement with the shock velocity predicted by our modeling of the optical data. We also show that the mean radial density distribution of the CSM roughly follows an r^-2 law. A possible explanation for the massive CSM with a wind-like profile is that they are the result of multiple pulsational pair instability events prior to the SN explosion, separated from each other by years.
We describe the resonance fluorescence spectrum of an atomic three-level system where two of the states are coupled by a single monochromatic laser field. The influence of the third energy level, which interacts with the two laser-coupled states only via radiative decays, is studied in detail. For a suitable choice of parameters, this system gives rise to a very narrow structure at the laser frequency in the fluorescence spectrum which is not present in the spectrum of a two-level atom. We find those parameter ranges by a numerical analysis and use the results to derive analytical expressions for the additional narrow peak. We also derive an exact expression for the peak intensity under the assumption that a random telegraph model is applicable to the system. This model and a simple spring model are then used to describe the physical origins of the additional peak. Using these results, we explain the connection between our system, a three-level system in V-configuration where both transitions are laser driven, and a related experiment which was recently reported.
In the theory of radiative heat exchanges between two closely-spaced bodies introduced by Polder and van Hove, no interplay between the heat carriers inside the materials and the photons crossing the separation gap is assumed. Here we release this constraint by developing a general theory to describe the conduction-radiation coupling between two solids of arbitrary size separated by a subwavelength separation gap. We show that, as a result of the temperature profile induced by the coupling with conduction, the radiative heat flux exchanged between two parallel slabs at nanometric distances can be several orders of magnitude smaller than the one predicted by the conventional theory. These results could have important implications in the fields of nanoscale thermal management, near-field solid-state cooling and nanoscale energy conversion.
This paper focuses on limit theorems for linear Hawkes processes with random marks. We prove a large deviation principle, which answers the question raised by Bordenave and Torrisi. A central limit theorem is also obtained. We conclude with an example of application in finance.
Let $X$ be a Calabi-Yau 4-fold and $D$ a smooth connected divisor on it. We consider tautological bundles of $L=\mathcal{O}_X(D)$ on Hilbert schemes of points on $X$ and their counting invariants defined by integrating the Euler classes against the virtual classes. We relate these invariants to Maulik-Nekrasov-Okounkov-Pandharipande's invariants of Hilbert schemes of points on $D$ by virtual pullback technique and confirm a conjecture of Cao-Kool. The same strategy is also applied to obtain a virtual pullback formula for tautological invariants of one dimensional stable sheaves. This in turn gives a nontrivial identity on primary and descendent invariants as studied in the works of Cao, Maulik and Toda.
An $[a,b]$-factor of a graph $G$ is a spanning subgraph $H$ such that $a\leq d_{H}(v)\leq b$ for each $v\in V(G)$. In this paper, we provide spectral conditions for the existence of an odd $[1,b]$-factor in a connected graph with minimum degree $\delta$ and the existence of an $[a,b]$-factor in a graph, respectively. Our results generalize and improve some previous results on perfect matchings of graphs. For $a=1$, we extend the result of O\cite{S.O} to obtain an odd $[1,b]$-factor and further improve the result of Liu, Liu and Feng\cite{W.L} for $a=b=1$. For $n\geq 3a+b-1$, we confirm the conjecture of Cho, Hyun, O and Park\cite{E.C}. We conclude some open problems in the end.
Since the discovery of $z\sim 6$ quasars two decades ago, studies of their Ly$\alpha$-transparent proximity zones have largely focused on their utility as a probe of cosmic reionization. But even when in a highly ionized intergalactic medium, these zones provide a rich laboratory for determining the timescales that govern quasar activity and the concomitant growth of their supermassive black holes. In this work, we use a suite of 1D radiative transfer simulations of quasar proximity zones to explore their time-dependent behaviour for activity timescales from $\sim10^3$ to $10^8$ years. The sizes of the simulated proximity zones, as quantified by the distance at which the smoothed Ly$\alpha$ transmission drops below 10% (denoted $R_p$), are in excellent agreement with observations, with the exception of a handful of particularly small zones that have been attributed to extremely short $\lesssim 10^4$ year lifetimes. We develop a physically motivated semi-analytic model of proximity zones which captures the bulk of their equilibrium and non-equilibrium behaviour, and use this model to investigate how quasar variability on $\lesssim10^5$ year timescales is imprinted on the distribution of observed proximity zone sizes. We show that large variations in the ionizing luminosity of quasars on timescales of $\lesssim10^4$ years are disfavored based on the good agreement between the observed distribution of $R_p$ and our model prediction based on "lightbulb" (i.e. steady constant emission) light curves.
In this paper, we study the stability of skyrmions (SKYs) caused by the geometric confinement (GC) effect observed in nano-domains in recent experiments, where SKYs appear only inside the boundary and is stable at the low magnetic field region. However, the mechanism of the GC effect is unclear for skyrmions. We numerically find that this effect is not observed in the standard model, in which the Dzyaloshinskii-Moriya interaction (DMI) energy is discretized on lattice edges, while the effect is observed in a discrete model where the DMI energy is defined on lattice volume elements. In the latter model, the DMI energy on the surfaces effectively becomes very small compared with that of the inside. From this observation, we study a model with zero DMI energy on the surfaces parallel to the external magnetic field and find that SKY is significantly stabilized in the sample in the low magnetic field region.
We compare the bulk flow of the SMAC sample to the predictions of popular cosmological models and to other recent large-scale peculiar velocity surveys. Both analyses account for aliasing of small-scale power due to the sparse and non-uniform sampling of the surveys. We conclude that the SMAC bulk flow is in marginal conflict with flat COBE-normalized Lambda-CDM models which fit the cluster abundance constraint. However, power spectra which are steeper shortward of the peak are consistent with all of the above constraints. When recent large-scale peculiar velocity surveys are compared, we conclude that all measured bulk flows (with the possible exception of that of Lauer & Postman) are consistent with each other given the errors, provided the latter allow for `cosmic covariance'. A rough estimate of the mean bulk flow of all surveys (except Lauer & Postman) is ~400 km/s towards l=270, b=0.
It is shown that Hilb^{4n}(P^3)has exactly two irreducible components.
An updated and improved version of the effective interaction based on the Argonne\textendash Urbana nuclear Hamiltonian\textemdash derived using the formalism of Correlated Basis Functions (CBF) and the cluster expansion technique\textemdash is employed to obtain a number of properties of cold nuclear matter at arbitrary neutron excess within the formalism of many-body perturbation theory. The numerical results\textemdash including the ground-state energy per nucleon, the symmetry energy, the pressure, the compressibility, and the single-particle spectrum\textemdash are discussed in the context of the available empirical information, obtained from measured nuclear properties and heavy-ion collisions.
We investigate the cold fission of 252Cf within the two center shell model to compute the potential energy surface. The fission yields are estimated by using the semiclassical penetration approach. It turns out that the inner cold valley of the total potential energy is strongly connected with Z=50 magic number. The agreement with experimental values is very much improved only by considering mass and charge asymmetry degrees of freedom. Thus, indeed cold fission of 252Cf is a Sn-like radioactivity, related the other two "magic radioactivities", namely alpha-decay and heavy-cluster decay, called also Pb-like radioactivity. This calculation provides the necessary theoretical confidence to estimate the penetration cross section in producing superheavy nuclei, by using the inverse fusion process.
We show evidence that the competition between the antiferromagetic metallic phase and the charge- and orbital-ordered insulating phase at the reentrant phase boundary of a layered manganite, LaSr2Mn2O7, can be manipulated using ultrafast optical excitation. The time-dependent evolution of the Jahn-Teller superlattice reflection, which indicates the formation of the charge and orbital order, was measured at different laser fluences. The laser-induced enhancement and reduction the Jahn-Teller reflection intensity shows a reversal of sign between earlier (~10 ns) and later (~150 ns) time delays during the relaxation after photo excitation. This effect is consistent with a scenario whereby the laser excitation modulates the local competition between the metallic and the insulating phases.
We present the first Herschel PACS and SPIRE photometric observations in a portion of the outer Galaxy ($216.5^{\circ} \lesssim \ell \lesssim 225.5^{\circ}$ and $-2^{\circ} \lesssim b \lesssim 0^{\circ}$) as a part of the Hi-GAL survey. The maps between 70 and 500 $\mu$m, the derived column density and temperature maps, and the compact source catalog are presented. NANTEN CO(1-0) line observations are used to derive cloud kinematics and distances, so that we can estimate distance-dependent physical parameters of the compact sources (cores and clumps) having a reliable spectral energy distribution, that we separate in 255 proto-stellar and 688 starless. Both typologies are found in association with all the distance components observed in the field, up to $\sim 5.8$ kpc, testifying the presence of star formation beyond the Perseus arm at these longitudes. Selecting the starless gravitationally bound sources we identify 590 pre-stellar candidates. Several sources of both proto- and pre-stellar nature are found to exceed the minimum requirement for being compatible with massive star formation, based on the mass-radius relation. For the pre-stellar sources belonging to the Local arm ($d\lesssim1.5$ kpc) we study the mass function, whose high-mass end shows a power-law $N(\log M) \propto M^{-1.0 \pm 0.2}$. Finally, we use a luminosity vs mass diagram to infer the evolutionary status of the sources, finding that most of the proto-stellar are in the early accretion phase (with some cases compatible with a Class I stage), while for pre-stellar sources, in general, accretion has not started yet.
Given a large sample covariance matrix $S_N=\frac 1n\Gamma_N^{1/2}Z_N Z_N^*\Gamma_N^{1/2}\, ,$ where $Z_N$ is a $N\times n$ matrix with i.i.d. centered entries, and $\Gamma_N$ is a $N\times N$ deterministic Hermitian positive semidefinite matrix, we study the location and fluctuations of $\lambda_{\max}(S_N)$, the largest eigenvalue of $S_N$ as $N,n\to\infty$ and $Nn^{-1} \to r\in(0,\infty)$ in the case where the empirical distribution $\mu^{\Gamma_N}$ of eigenvalues of $\Gamma_N$ is tight (in $N$) and $\lambda_{\max}(\Gamma_N)$ goes to $+\infty$. These conditions are in particular met when $\mu^{\Gamma_N}$ weakly converges to a probability measure with unbounded support on $\mathbb{R}^+$. We prove that asymptotically $\lambda_{\max}(S_N)\sim \lambda_{\max}(\Gamma_N)$. Moreover when the $\Gamma_N$'s are block-diagonal, and the following {\em spectral gap condition} is assumed:$$\limsup_{N\to\infty} \frac{\lambda_2(\Gamma_N)}{\lambda_{\max}(\Gamma_N)}<1,$$where $\lambda_2(\Gamma_N)$ is the second largest eigenvalue of $\Gamma_N$, we prove Gaussian fluctuations for $\lambda_{\max}(S_N)/\lambda_{\max}(\Gamma_N)$ at the scale $\sqrt{n}$.In the particular case where $Z_N$ has i.i.d. Gaussian entries and $\Gamma_N$ is the $N\times N$ autocovariance matrix of a long memory Gaussian stationary process $({\mathcal X}_t)_{t\in\mathbb{Z}}$, the columns of $\Gamma_N^{1/2} Z_N$ can be considered as $n$ i.i.d. samples of the random vector $({\mathcal X}_1,\dots,{\mathcal X}_N)^T$. We then prove that $\Gamma_N$ is similar to a diagonal matrix which satisfies all the required assumptions of our theorems, hence our results apply to this case.
The past decade has witnessed significant progress on detecting objects in aerial images that are often distributed with large scale variations and arbitrary orientations. However most of existing methods rely on heuristically defined anchors with different scales, angles and aspect ratios and usually suffer from severe misalignment between anchor boxes and axis-aligned convolutional features, which leads to the common inconsistency between the classification score and localization accuracy. To address this issue, we propose a Single-shot Alignment Network (S$^2$A-Net) consisting of two modules: a Feature Alignment Module (FAM) and an Oriented Detection Module (ODM). The FAM can generate high-quality anchors with an Anchor Refinement Network and adaptively align the convolutional features according to the anchor boxes with a novel Alignment Convolution. The ODM first adopts active rotating filters to encode the orientation information and then produces orientation-sensitive and orientation-invariant features to alleviate the inconsistency between classification score and localization accuracy. Besides, we further explore the approach to detect objects in large-size images, which leads to a better trade-off between speed and accuracy. Extensive experiments demonstrate that our method can achieve state-of-the-art performance on two commonly used aerial objects datasets (i.e., DOTA and HRSC2016) while keeping high efficiency. The code is available at https://github.com/csuhan/s2anet.
A Bus Route Model (BRM) can be defined on a one-dimensional lattice, where buses are represented by "particles" that are driven forward from one site to the next with each site representing a bus stop. We replace the random sequential updating rules in an earlier BRM by parallel updating rules. In order to elucidate the connection between the BRM with parallel updating (BRMPU) and the Nagel-Schreckenberg (NaSch) model, we propose two alternative extensions of the NaSch model with space-/time-dependent hopping rates. Approximating the BRMPU as a generalization of the NaSch model, we calculate analytically the steady-state distribution of the {\it time headways} (TH) which are defined as the time intervals between the departures (or arrivals) of two successive particles (i.e., buses) recorded by a detector placed at a fixed site (i.e., bus stop) on the model route. We compare these TH distributions with the corresponding results of our computer simulations of the BRMPU, as well as with the data from the simulation of the two extended NaSch models. We also investigate interesting kinetic properties exhibited by the BRMPU during its time evolution from random initial states towards its steady-states.