ShantanuT01/DACTYL-Pretraining huggingface dataset:
We construct a quantum algorithm that performs function-dependent phase transform and requires no initialization of an ancillary register. The algorithm recovers the initial state of an ancillary register regardless of whether its state is pure or mixed. Thus we can use any qubits as an ancillary register even though they are entangled with others and are occupied by other computational process. We also show that our algorithm is optimal in the sense of the number of function evaluations.
We consider equivariant solutions for the Schr\"odinger map problem from $\mathbb{R}^{2+1}$ to $\mathbb{S}^2$ with energy less than $4\pi$ and show that they are global in time and scatter.
To obtain 3D annotations, we are restricted to controlled environments or synthetic datasets, leading us to 3D datasets with less generalizability to real-world scenarios. To tackle this issue in the context of semi-supervised 3D hand shape and pose estimation, we propose the Pose Alignment network to propagate 3D annotations from labelled frames to nearby unlabelled frames in sparsely annotated videos. We show that incorporating the alignment supervision on pairs of labelled-unlabelled frames allows us to improve the pose estimation accuracy. Besides, we show that the proposed Pose Alignment network can effectively propagate annotations on unseen sparsely labelled videos without fine-tuning.
We investigate the behavior of energy fluctuations in several models of granular gases maintained in a non-equilibrium steady state. In the case of a gas heated from a boundary, the inhomogeneities of the system play a predominant role. Interpreting the total kinetic energy as a sum of independent but not identically distributed random variables, it is possible to compute the probability density function (pdf) of the total energy. Neglecting correlations and using the analytical expression for the inhomogeneous temperature profile obtained from the granular hydrodynamic equations, we recover results which have been previously observed numerically and which had been attributed to the presence of correlations. In order to separate the effects of spatial inhomogeneities from those ascribable to velocity correlations, we have also considered two models of homogeneously thermostated gases: in this framework it is possible to reveal the presence of non-trivial effects due to velocity correlations between particles. Such correlations stem from the inelasticity of collisions. Moreover, the observation that the pdf of the total energy tends to a Gaussian in the large system limit, suggests that they are also due to the finite size of the system.
In this paper, we study the differential inclusion associated to the minimal surface system for two-dimensional graphs in $\mathbb{R}^{2 + n}$. We prove regularity of $W^{1,2}$ solutions and a compactness result for approximate solutions of this differential inclusion in $W^{1,p}$. Moreover, we make a perturbation argument to infer that for every $R > 0$ there exists $\alpha(R) >0$ such that $R$-Lipschitz stationary points for functionals $\alpha$-close in the $C^2$ norm to the area functional are always regular. We also use a counterexample of \cite{KIRK} to show the existence of irregular critical points to inner variations of the area functional.
We perform a generalization of the geometrical approach to describing extended objects for studying the doubly supersymmetric twistor--like formulation of super--p--branes. Some basic features of embedding world supersurface into target superspace specified by a geometrodynamical condition are considered. It is shown that the main attributes of the geometrical approach, such as the second fundamental form and extrinsic torsion of the embedded surface, and the Codazzi, Gauss and Ricci equations, have their doubly supersymmetric counterparts. At the same time the embedding of supersurface into target superspace has its particular features. For instance, the embedding may cause more rigid restrictions on the geometrical properties of the supersurface. This is demonstrated with the examples of an N=1 twistor--like supermembrane in D=11 and type II superstrings in D=10, where the geometrodynamical condition causes the embedded supersurface to be minimal and puts the theories on the mass shell.
We have identified 17 A-type stars in the Galactic Plane that have mid-IR excesses at 8 micron. From the observed colors in the (r'-H_alpha)-(r'-i') plane, we first identified 23050 early A-type main sequence (MS) star candidates in the Isaac Newton Photometric H-Alpha Survey (IPHAS) point source database that are located in Spitzer GLIMPSE Galactic Plane fields. Imposing the requirement that they be detected in all seven 2MASS and IRAC bands led to a sample of 2692 candidate A-type stars with fully sampled 0.6 to 8 micron SEDs. Optical classification spectra of 18 of the IPHAS candidate A-type MS stars showed that all but one could be well fitted using main sequence A-type templates, with the other being an A-type supergiant. Out of the 2692 A-type candidates 17 (0.6%) were found to have 8-micron excesses above the expected photospheric values. Taking into account non-A-Type contamination estimates, the 8-micron excess fraction is adjusted to ~0.7%. The distances to these sources range from 0.7-2.5 kpc. Only 10 out of the 17 excess stars had been covered by Spitzer MIPSGAL survey fields, of which 5 had detectable excesses at 24 micron. For sources with excesses detected in at least two mid-IR wavelength bands, blackbody fits to the excess SEDs yielded temperatures ranging from 270 to 650 K, and bolometric luminosity ratios L_IR/L* from 2.2x10^{-3}-1.9x10^{-2}, with a mean value of 7.9x10^{-3} (these bolometric luminosities are lower limits as cold dust is not detectable by this survey). Both the presence of mid-IR excesses and the derived bolometric luminosity ratios are consistent with many of these systems being in the planet-building transition phase between the early protoplanetary disk phase and the later debris disk phase.
In this paper we discuss a left-right symmetric model for elementary particles and their connection with the mass spectrum of elementary fermions. The model is based on the group $SU(2)_L\otimes SU(2)_R\otimes U(1)$. New mirror fermions and a minimal set of Higgs particles that breaks the symmetry down to $U(1)_{em}$ are proposed. The model can accommodate a consistent pattern for charged and neutral fermion masses as well as neutrino oscillations. An important consequence of the model is that the connection between the left and right sectors can be done by the neutral vector gauge bosons Z and a new heavy Z'.
The large scale binary black hole effort in numerical relativity has led to an increasing distinction between numerical and mathematical relativity. This note discusses this situation and gives some examples of succesful interactions between numerical and mathematical methods is general relativity.
We report the results of a coherent study of three chemically anomalous metal-poor ([Fe/H] ~ -2) stars. These objects exhibit unusually low abundances of Mg, Si, Ca (alpha-elements) and Sr, Y, and Ba (neutron-capture elements). Our analyses confirm and expand upon earlier reports of atypical abundances in BD+80~245, G4-36, and CS22966-043. We also find that the latter two stars exhibit enhanced abundances of Cr, Mn, Ni, and Zn (iron-peak elements), along with what appears to be large abundances of Ga, with respect to the abundance of iron. Comparing the chemical abundances of these stars to supernova model yields, we derive supernovae ratios of Type Ia versus Type II events in the range of 0.6 <= (N_Ia/N_II) <= 1.3. Whereas, for the Sun, we derive supernovae ratios in good agreement with those found in the literature: 0.18 +/- 0.01 < (N_Ia/N_II)_sun < 0.25 +/- 0.06. Given the relatively low metallicity and high (N_Ia/N_II) ratios of the low-alpha stars studied here, these objects may have witnessed, or been born from material produced in the yields of the earliest supernova Type Ia events.
Photon antibunching, a hallmark of quantum light, has been observed in the correlations of light from isolated atomic and atomic-like solid-state systems. Two-dimensional semiconductor heterostructures offer a unique method to create a quantum light source: a small lattice mismatch or relative twist in a heterobilayer can create moir\'e trapping potentials for excitons which are predicted to create arrays of quantum emitters. While signatures of moir\'e trapped excitons have been observed, their quantum nature has yet to be confirmed. Here we report photon antibunching from single moir\'e trapped interlayer excitons in a heterobilayer. Via polarization resolved magneto-optical spectroscopy, we demonstrate the discrete anharmonic spectra arise from bound band-edge electron-hole pairs trapped in moir\'e potentials. Finally, using an out-of-plane electric field, we exploit the large permanent dipole of interlayer excitons to achieve large DC Stark tuning, up to 40 meV, of the quantum emitters. Our results confirm the quantum nature of moir\'e confined excitons and open opportunities to investigate their inhomogeneity and interactions between the emitters or tune single emitters into resonance with cavity modes or other emitters.
We extend the technique of constructive expansions to compute the connected functions of matrix models in a uniform way as the size of the matrix increases. This provides the main missing ingredient for a non-perturbative construction of the $\phi^{\star 4}_4$ field theory on the Moyal four dimensional space.
Accurately quantifying swelling of alloys that have undergone irradiation is essential for understanding alloy performance in a nuclear reactor and critical for the safe and reliable operation of reactor facilities. However, typical practice is for radiation-induced defects in electron microscopy images of alloys to be manually quantified by domain-expert researchers. Here, we employ an end-to-end deep learning approach using the Mask Regional Convolutional Neural Network (Mask R-CNN) model to detect and quantify nanoscale cavities in irradiated alloys. We have assembled the largest database of labeled cavity images to date, which includes 400 images, >34k discrete cavities, and numerous alloy compositions and irradiation conditions. We have evaluated both statistical (precision, recall, and F1 scores) and materials property-centric (cavity size, density, and swelling) metrics of model performance, and performed in-depth analysis of materials swelling assessments. We find our model gives assessments of material swelling with an average (standard deviation) swelling mean absolute error based on random leave-out cross-validation of 0.30 (0.03) percent swelling. This result demonstrates our approach can accurately provide swelling metrics on a per-image and per-condition basis, which can provide helpful insight into material design (e.g., alloy refinement) and impact of service conditions (e.g., temperature, irradiation dose) on swelling. Finally, we find there are cases of test images with poor statistical metrics, but small errors in swelling, pointing to the need for moving beyond traditional classification-based metrics to evaluate object detection models in the context of materials domain applications.
The class of type Ic supernovae have drawn increasing attention since 1998 owing to their sparse association (only four so far) with long duration gamma-ray bursts. Although both phenomena originate from the core collapse of a massive star, supernovae emit mostly at optical wavelengths, whereas GRBs emit mostly in soft gamma-rays or hard X-rays. Though the GRB central engine generates ultra-relativistic jets, which beam the early emission into a narrow cone, no relativistic outflows have hitherto been found in type Ib/c supernovae explosions, despite theoretical expectations and searches. Here we report radio (interferometric) observations that reveal a mildly relativistic expansion in a nearby type Ic supernova, SN 2007gr. Using two observational epochs 60 days apart, we detect expansion of the source and establish a conservative lower limit for the average apparent expansion velocity of 0.6c. Independently, a second mildly relativistic supernova has been reported. Contrary to the radio data, optical observations of SN 2007gr indicate a typical type Ic supernova with ejecta velocities ~6000 km/s, much lower than in GRB-associated supernovae. We conclude that in SN 2007gr a small fraction of the ejecta produced a low-energy mildly relativistic bipolar radio jet, while the bulk of the ejecta were slower and, as shown by optical spectro-polarimetry, mildly aspherical.
We consider the dyadic model, which is a toy model to test issues of well-posedness and blow-up for the Navier-Stokes and Euler equations. We prove well-posedness of positive solutions of the viscous problem in the relevant scaling range which corresponds to Navier-Stokes. Likewise we prove well-posedness for the inviscid problem (in a suitable regularity class) when the parameter corresponds to the strongest transport effect of the non-linearity.
A systematic theory of the conductance measurements of non-invasive (weak probe) scanning gate microscopy is presented that provides an interpretation of what precisely is being measured. A scattering approach is used to derive explicit expressions for the first and second order conductance changes due to the perturbation by the tip potential in terms of the scattering states of the unperturbed structure. In the case of a quantum point contact, the first order correction dominates at the conductance steps and vanishes on the plateaus where the second order term dominates. Both corrections are non-local for a generic structure. Only in special cases, such as that of a centrally symmetric quantum point contact in the conductance quantization regime, can the second order correction be unambiguously related with the local current density. In the case of an abrupt quantum point contact we are able to obtain analytic expressions for the scattering eigenfunctions and thus evaluate the resulting conductance corrections.
The consequences of a flavor broken SU(3)_f dynamical parton model are studied in the context of the elastic scattering of supersymmetric dark matter off nucleons. It is shown that the predictions of this model differ considerably from those of the commonly applied `standard' parton model. Some notable properties of the dynamical parton model are finally presented and discussed.
One of the most challenging open problems in quantum information theory is to clarify and quantify how entanglement behaves when part of an entangled state is sent through a quantum channel. Of central importance in the description of a quantum channel or completely positive map (CP-map) is the dual state associated to it. The present paper is a collection of well-known, less known and new results on quantum channels, presented in a unified way. We will show how this dual state induces nice characterizations of the extremal maps of the convex set of CP-maps, and how normal forms for states defined on a Hilbert space with a tensor product structure lead to interesting parameterizations of quantum channels.
We give an overview of results on irregular complex surfaces of general type, discussing in particular the distribution of the numerical invariants self-intersection of a canonical divisor and holomorphic Euler characteristic for the minimal ones. This is an expanded version of the talk given by the second author at the workshop "Classical Algebraic Geometry Today", M.S.R.I., January 26--30, 2009.
We present a Monte Carlo numerical investigation of the Hamiltonian Mean Field (HMF) model. We begin by discussing canonical Metropolis Monte Carlo calculations, in order to check the caloric curve of the HMF model and study finite size effects. In the second part of the paper, we present numerical simulations obtained by means of a modified Monte Carlo procedure with the aim to test the stability of those states at minimum temperature and zero magnetization (homogeneous Quasi Stationary States) which exist in the condensed phase of the model just below the critical point. For energy densities smaller than the limiting value $U\sim 0.68$, we find that these states are unstable, confirming a recent result on the Vlasov stability analysis applied to the HMF model.
We employ the Langevin equation and Wigner function to describe the bottom equark dynamical evolutions and their formation into a bound state in the expanding Quark Gluon Plasma (QGP). The additional suppressions from parton inelastic scatterings are supplemented in the regenerated bottomonium. Hot medium modifications on $\Upsilon(1S)$ properties are studied consistently by taking the bottomonium potential to be the color-screened potential from Lattice results, which affects both $\Upsilon(1S)$ regeneration and dissociation rates. Finally, we calculated the $\Upsilon(1S)$ nuclear modification factor $R_{AA}^{\rm rege}$ from bottom quark combination with different diffusion coefficients in Langevin equation, representing different thermalization of bottom quarks. In the central Pb-Pb collisions (b=0) at $\sqrt{s_{NN}}=5.02$ TeV, we find a non-negligible $\Upsilon(1S)$ regeneration, and it is small in the minimum bias centrality. The connections between bottomonium regeneration and bottom quark energy loss in the heavy ion collisions are also discussed.
Let $G$ be a $t$-tough graph of order $n$ and minimum degree $\delta$ with $t>1$. It is proved that if $\delta\ge(n-2)/3$ then each longest cycle in $G$ is a dominating cycle.
A variational Monte Carlo method is used to generate sets of orthogonal trial functions, Psi_T(J^pi,T), for given quantum numbers in various light p-shell nuclei. These Psi_T are then used as input to Green's function Monte Carlo calculations of first, second, and higher excited (J^pi,T) states. Realistic two- and three-nucleon interactions are used. We find that if the physical excited state is reasonably narrow, the GFMC energy converges to a stable result. With the combined Argonne v_18 two-nucleon and Illinois-2 three-nucleon interactions, the results for many second and higher states in A = 6--8 nuclei are close to the experimental values.
The reaction pi N -> pi pi N is studied at tree level up to next-to-leading order in the framework of manifestly covariant baryon chiral perturbation theory with explicit Delta(1232) degrees of freedom. Using total cross section data to determine the relevant low-energy constants, predictions are made for various differential as well as total cross sections at higher energies. A detailed comparison of results based on the heavy-baryon and relativistic formulations of chiral perturbation theory with and without explicit Delta degrees of freedom is given.
Reactions A(\gamma, pi^+p) are considered to proceed through the formation of pion-proton pairs on delta constituents in nuclei. We develop the nonrelativistic operator for \Delta^{++}(\gamma, pi^+)p process in an arbitrary frame. The calculated cross section for C12(\gamma, \pi^+p) reaction is compared to the existing experimental data.
In this work, we investigate the interactions between the charmed-strange meson ($D_s, D_s^{*}$) in $H$-doublet and the (anti-)charmed-strange meson ($D_{s1}, D_{s2}^{*}$) in $T$-doublet, where the one boson exchange model is adopted by considering the $S$-$D$ wave mixing and the coupled-channel effects. By extracting the effective potentials for the discussed $H_s\bar{T}_s$ and $H_s{T}_s$ systems, we try to find the bound state solutions for the corresponding systems. We predict the possible hidden-charm hadronic molecular states with hidden strangeness, i.e., the $D_s^{*}\bar D_{s1}+c.c.$ states with $J^{PC}$=$0^{--}, 0^{-+}$ and the $D_s^{*}\bar D_{s2}^{*}+c.c.$ states with $J^{PC}$=$1^{--}, 1^{-+}$. Applying the same theoretical framework, we also discuss the $H_s T_s$ systems. Unfortunately, the existence of the open-charm and open-strange molecular states corresponding to the $H_s T_s$ systems can be excluded.
In this paper, we proved that a compression space of rank $2$ is equivalent to an irreducible representation over a Lie algebra.
We provide an elementary proof to a conjecture by Robinson that multiples of (powers of) primes in the Somos-4 sequence are equally spaced. We also show, almost as a corollary, for the generalised Somos-4 sequence defined by $\tau_{n+2}\tau_{n-2}=\alpha\tau_{n+1}\tau_{n-1}+\beta\tau_n^2$ and initial values $\tau_1=\tau_2=\tau_3=\tau_4=1$, that the polynomial $\tau_n(\alpha,\beta)$ is a divisor of $\tau_{n+k(2n-5)}(\alpha,\beta)$ for all $n,k\in\mathbb Z$ and establish a similar result for the generalized Somos-5 sequence.
We propose a definition for the P\'olya number of continuous-time quantum walks to characterize their recurrence properties. The definition involves a series of measurements on the system, each carried out on a different member from an ensemble in order to minimize the disturbance caused by it. We examine various graphs, including the ring, the line, higher dimensional integer lattices and a number of other graphs and calculate their P\'olya number. For the timing of the measurements a Poisson process as well as regular timing are discussed. We find that the speed of decay for the probability at the origin is the key for recurrence.
Time-resolved two color pump-probe polarization spectroscopy was performed at room temperature on SrTiO3 films grown directly on Si with film thickness varying from 2 nm to 7.8 nm. The E soft mode with a characteristic frequency of 0.2 THz is impulsively generated and measured in these coherently strained tetragonal phase SrTiO3 thin films. Another over-damped signal observed indicates the possible relaxational hopping of Ti ion between double potential wells. The dependence of the coherent phonon signal on pump and probe laser polarization helps to identify the phonon modes.
A multipole expansion analysis is applied to 1420 MHz radio continuum images of supernova remnants (SNRs) in order to compare Type Ia and core collapse (CC) SNRs. Because the radio synchrotron emission is produced at the outer shock between the SNR and the ISM, we are investigating whether the ISM interaction of SNRs is different between Type Ia and CC SNRs. This is in contrast to previous investigations, which have shown that Type Ia and CC SNRs have different asymmetries in the X-ray emission from their ejecta. The sample consists of 19 SNRs which have been classified as either Type Ia or CC. The quadrupole and octupole moments normalized to their monopole moments (total emission) are used as a measure of asymmetry of the emission. A broad range (by a factor of ~1000) is found for both quadrupole and octupole normalized moments. The strongest correlation we find is that large quadrupole moments are associated with large octupole moments, indicating that both serve as similar indicators of asymmetry. The other correlation we find is that both moments increase with SNR age or radius. This indicates that interstellar medium structure is a strong contributor to asymmetries in the radio emission from SNRs. This does not seem to apply to molecular clouds, because we find that association of a SNR with a molecular cloud is not correlated with larger quadrupole or octupole moments.
We deduce the qualitative phase diagram of a long flexible neutral polymer chain immersed in a poor solvent near an attracting surface using phenomenological arguments. The actual positions of the phase boundaries are estimated numerically from series expansion up to 19 sites of a self-attracting self avoiding walk in three dimensions. In two dimensions, we calculate analytically phase boundaries in some cases for a partially directed model. Both the numerical as well as analytical results corroborate the proposed qualitative phase diagram.