ShantanuT01/DACTYL-Pretraining huggingface dataset:
We investigate the estimation technique called quantum state smoothing introduced by Guevara and Wiseman [Phys.~Rev.~Lett.~{\bf 115}, 180407 (2015)], which offers a valid quantum state estimate for a partially monitored system, conditioned on the observed record both prior and posterior to an estimation time. Partial monitoring by an observer implies that there may exist records unobserved by that observer. It was shown that, given only the observed record, the observer can better estimate the underlying true quantum states, by inferring the unobserved record and using quantum state smoothing, rather than the usual quantum filtering approach. However, the improvement in estimation fidelity, originally examined for a resonantly driven qubit coupled to two vacuum baths, was also shown to vary depending on the types of detection used for the qubit's fluorescence. In this work, we analyse this variation in a systematic way for the first time. We first define smoothing power using an average purity recovery and a relative average purity recovery, of smoothing over filtering. Then, we explore the power for various combinations of fluorescence detection for both observed and unobserved channels. We next propose a method to explain the variation of the smoothing power, based on multi-time correlation strength between fluorescence detection records. The method gives a prediction of smoothing power for different combinations, which is remarkably successful in comparison with numerically simulated qubit trajectories.
Sharir and Welzl [1] derived a bound on crossing-free matchings primarily based on solving a recurrence based on the size of the matchings. We show that the recurrence given in Lemma 2.3 in Sharir and Welzl can be improve to $(2n-6s)\textbf{Ma}_{m}(P)\leq\frac{68}{3}(s+2)\textbf{Ma}_{m-1}(P)$ and $(3n-7s)\textbf{Ma}_{m}(P)\leq44.5(s+2)\textbf{Ma}_{m-1}(P)$, thereby improving the upper bound for crossing-free matchings.
We extend the analysis of weak decays of heavy hadrons to the case of doubly charmed baryons, \Xi_{cc}^{++}, \Xi_{cc}^{+} and \Omega_{cc}^{+}. Doubly charmed baryons are modeled as a heavy-light system containing a heavy cc-diquark and a light quark. Such a model leads to preasymptotic effects in semileptonic and nonleptonic decays which are essentially proportional to the meson wave function. Very clear predictions for semileptonic branching ratios and lifetimes of doubly charmed baryons are obtained.
OH 231.8+4.2, a bipolar outflow around a Mira-type variable star, displays a unique molecular richness amongst circumstellar envelopes (CSEs) around O-rich AGB and post-AGB stars. We report line observations of the HCO+ and H13CO+ molecular ions and the first detection of SO+, N2H+, and (tentatively) H3O+ in this source. SO+ and H3O+ have not been detected before in CSEs around evolved stars. These data have been obtained as part of a full mm-wave and far-IR spectral line survey carried out with the IRAM 30 m radio telescope and with Herschel/HIFI. Except for H3O+, all the molecular ions detected in this work display emission lines with broad profiles (FWHM 50-90 km/s), which indicates that these ions are abundant in the fast bipolar outflow of OH 231.8. The narrow profile (FWHM 14 km/s) and high critical densities (>1e6cm-3 ) of the H3O+ transitions observed are consistent with this ion arising from denser, inner (and presumably warmer) layers of the fossil remnant of the slow AGB CSE at the core of the nebula. From rotational diagram analysis, we deduce excitation temperatures of Tex 10-20 K for all ions except for H3O+, which is most consistent with Tex 100 K. Although uncertain, the higher excitation temperature suspected for H3O+ is similar to that recently found for H2O and a few other molecules, which selectively trace a previously unidentified, warm nebular component.The column densities of the molecular ions reported here are in the range Ntot [1-8]x1e13 cm-2, leading to beam-averaged fractional abundances relative to H2 of X(HCO+) 1e-8, X(H13CO+) 2e-9, X(SO+) 4e-9, X(N2H+) 2e-9, and X(H3O+) 7e-9 cm-2. We have performed chemical kinetics models to investigate the formation of these ions in OH 231.8 as the result of standard gas phase reactions initiated by cosmic-ray and UV-photon ionization. (abridged).
It has been experimentally demonstrated only recently that a simultaneous excitation of interfering electric and magnetic resonances can lead to uni-directional scattering of visible light in zero-dimensional dielectric nanoparticles. We show both theoretically and experimentally, that strongly anisotropic scattering also occurs in individual dielectric nanowires. The effect occurs even under either pure transverse electric or pure transverse magnetic polarized normal illumination. This allows for instance to toggle the scattering direction by a simple rotation of the incident polarization. Finally, we demonstrate that directional scattering is not limited to cylindrical cross-sections, but can be further tailored by varying the shape of the nanowires.
We test and improve the numerical schemes in our smoothed particle hydrodynamics (SPH) code for cosmological simulations, including the pressure-entropy formulation (PESPH), a time-dependent artificial viscosity, a refined timestep criterion, and metal-line cooling that accounts for photoionisation in the presence of a recently refined Haardt \& Madau (2012) model of the ionising background. The PESPH algorithm effectively removes the artificial surface tension present in the traditional SPH formulation, and in our test simulations it produces better qualitative agreement with mesh-code results for Kelvin-Helmholtz instability and cold cloud disruption. Using a set of cosmological simulations, we examine many of the quantities we have studied in previous work. Results for galaxy stellar and HI mass functions, star formation histories, galaxy scaling relations, and statistics of the Ly$\alpha$ forest are robust to the changes in numerics and microphysics. As in our previous simulations, cold gas accretion dominates the growth of high-redshift galaxies and of low mass galaxies at low redshift, and recycling of winds dominates the growth of massive galaxies at low redshift. However, the PESPH simulation removes spurious cold clumps seen in our earlier simulations, and the accretion rate of hot gas increases by up to an order of magnitude at some redshifts. The new numerical model also influences the distribution of metals among gas phases, leading to considerable differences in the statistics of some metal absorption lines, most notably NeVIII.
Let $X$ be a 3-dimensional affine variety with a faithful action of a 2-dimensional torus $T$. Then the space of first order infinitesimal deformations $T^1(X)$ is graded by the characters of $T$, and the zeroth graded component $T^1(X)_0$ consists of all equivariant first order (infinitesimal) deformations.   Suppose that using the construction of such varieties from [1], one can obtain $X$ from a proper polyhedral divisor $\mathscr D$ on $\mathbb P^1$ such that the tail cone of (any of) the used polyhedra is pointed and full-dimensional, and all vertices of all polyhedra are lattice points. Then we compute $\dim T^1(X)_0$ and find a formally versal equivariant deformation of $X$. We also establish a connection between our formula for $\dim T^1(X)_0$ and known formulas for the dimensions of the graded components of $T^1$ of toric varieties.
We review photon Bremsstrahlung in extra-dimensional models with massive gravitons. The photon spectrum is harder than in the Standard Model. In the RS scenario, radiative return to gravitons below the c.m. energy can lead to a considerable increase of the cross section.
Medical imaging is the technique used to create images of the human body or parts of it for clinical purposes. Medical images always have large sizes and they are commonly corrupted by single or multiple noise type at the same time, due to various reasons, these two reasons are the triggers for moving toward parallel image processing to find alternatives of image de-noising techniques. This paper presents a parallel hybrid filter implementation for gray scale medical image de-noising. The hybridization is between adaptive median and wiener filters. Parallelization is implemented on the adaptive median filter to overcome the latency of neighborhood operation, parfor implicit parallelism powered by MatLab 2013a is used. The implementation is tested on an image of 2.5 MB size, which is divided into 2, 4 and 8 partitions; a comparison between the proposed implementation and sequential implementation is given, in terms of time. Thus, each case has the best time when assigned to number of threads equal to the number of its partitions. Moreover, Speed up and efficiency are calculated for the algorithm and they show a measured enhancement.
We establish uniform a-priori estimates for solutions of the semilinear Dirichlet problem \begin{equation} \begin{cases} (-\Delta)^m u=h(x,u)\quad&\mbox{in }\Omega,\\ u=\partial_nu=\cdots=\partial_n^{m-1}u=0\quad&\mbox{on }\partial\Omega, \end{cases} \end{equation} where $h$ is a positive superlinear and subcritical nonlinearity in the sense of the Trudinger-Moser-Adams inequality, either when $\Omega$ is a ball or, provided an energy control on solutions is prescribed, when $\Omega$ is a smooth bounded domain. The analogue problem with Navier boundary conditions is also studied. Finally, as a consequence of our results, existence of a positive solution is shown by degree theory.
In this study, cosmological models with perfect fluid and a gravitational framework f(Q) will be examined. In this modified theory of gravity, the gravitational force has the form f(Q), where Q stands for the non-metricity scalar. I create two bouncing cosmological models, one in which the Lagrangian f(Q) is assumed to have a linear dependence on Q and the other in which it has a polynomial functional form. It has been discovered that the parameters of the individual models largely determine how they will behave. The resulting models' equation of state (EoS) parameter captures the universe's ironic behavior. It should be highlighted that the built-in cosmological models go against the energy requirements. The models' kinematical and physical characteristics are discussed.
The first part of this note shows that the odd period polynomial of each Hecke cusp eigenform for full modular group produces via Rodriguez--Villegas transform ([Ro--V]) a polynomial satisfying the functional equation of zeta type and having nontrivial zeros only on the middle line of its critical strip. The second part discusses Chebyshev lambda--structure of the polynomial ring as Borger's descent data to $\bold{F}_1$ and suggests its role in possible relation of $\Gamma_{\bold{R}}$--factor to "real geometry over $\bold{F}_1$" (cf. also [CoCons2]).
There are a countless number of fonts with various shapes and styles. In addition, there are many fonts that only have subtle differences in features. Due to this, font identification is a difficult task. In this paper, we propose a method of determining if any two characters are from the same font or not. This is difficult due to the difference between fonts typically being smaller than the difference between alphabet classes. Additionally, the proposed method can be used with fonts regardless of whether they exist in the training or not. In order to accomplish this, we use a Convolutional Neural Network (CNN) trained with various font image pairs. In the experiment, the network is trained on image pairs of various fonts. We then evaluate the model on a different set of fonts that are unseen by the network. The evaluation is performed with an accuracy of 92.27%. Moreover, we analyzed the relationship between character classes and font identification accuracy.
Kaneko and Tsumura introduced a new kind of multiple zeta functions $\eta(k_1,\ldots,k_r;s_1,\ldots,s_r)$. This is an analytic function of complex variables $s_1,\ldots,s_r$, while $k_1,\ldots,k_r$ are non-positive integer parameters. In this paper, we first extend this function to an analytic function $\eta(s'_1,\ldots,s'_r;s_1,\ldots,s_r)$ of $2r$ complex variables. Then we investigate its special values at positive integers. In particular, we prove some linear relations among these $\eta$-values and the multiple zeta values $\zeta(k_1,\ldots,k_r)$ of Euler-Zagier type.
A general discussion is given for first-kind (FK) and quantum non-demolition (QND) measurements. The general conditions for these measurements are derived, including the most general one (called the weak condition), an intermediate one, and the strongest one. The weak condition indicates that we can realize a FK or QND measuring apparatus of wide classes of observables by allowing the apparatus to have a finite response range. A recently-proposed QND photodetector using an electron interferometer is an example of such apparatus.
We compare the highly clustered populations of very high redshift galaxies with proto-clusters identified numerically in a standard $\Lambda$CDM universe ($\Omega_0=0.3, \lambda_0=0.7$) simulation. We evolve 256^3 dark matter particles in a comoving box of side 150h^{-1}Mpc. By the present day there are 63 cluster sized objects of mass in excess of 10^{14}h^{-1}Mo in this box. We trace these clusters back to higher redshift finding that their progenitors at z=4--5 are extended regions of typically 20--40 Mpc (comoving) in size, with dark halos of mass in excess of 10^{12}h^{-1}Mo and are overdense by typically 1.3--13 times the cosmological mean density. Comparison with the observation of Lyman alpha emitting (LAEs) galaxies at z=4.86 and at z=4.1 indicates that the observed excess clustering is consistent with that expected for a proto-cluster region if LAEs typically correspond to massive dark halos of more than 10^{12}h^{-1}Mo. We give a brief discussion on the relation between high redshift concentration of massive dark halos and present day rich clusters of galaxies.
Let X and Y be an m-dimensional F-semimartingale and an n-dimensional H-semimartingale respectively on the same probability space, both enjoying the strong predictable representation property. We propose a martingale representation result under the probability measure P for the square integrable G-martingales, where G is the union of F and H. As a first application we identify the biggest possible value of the multiplicity in the sense of Davis and Varaiya of the union of F1,..., Fd, where, fixed i in (1,...,d), Fi is the reference filtration of a real martingale Mi, which enjoys the Fi-predictable representation property. A second application falls into the framework of credit risk modeling and in particular into the study of the progressive enlargement of the market filtration by a default time. More precisely, when the risky asset price is a multidimensional semimartingale enjoying the strong predictable representation property and the default time satisfies the density hypothesis, we present a new proof of the analogous of the classical theorem of Kusuoka.
Among all the high-energy environments of our Galaxy, the Galactic Center (GC) region is definitely the richest. It harbors a large amount of non-thermal emitters, including the closest supermassive black hole, dense molecular clouds, regions with strong star forming activity, multiple supernova remnants and pulsar wind nebulae, arc-like radio structures, as well as the base of what may be large-scale Galactic outflows, possibly related to the Fermi Bubbles. It also contains a strong diffuse TeV gamma-ray emission along the Galactic ridge, with a disputed origin, including the presence of a possible Pevatron, unresolved sources, and an increased relevance of the diffuse sea of cosmic rays. This very rich region will be one of the key targets for the next generation ground-based observatory for gamma-ray astronomy, the Cherenkov Telescope Array (CTA). Here we review the CTA science case for the study of the GC region, and present the planned survey strategy. These observations are simulated and we assess CTA's potential to better characterize the origin and nature of a selection of gamma-ray sources in the region.
Using a new approximate analytic parameter-free proxy-SU(3) scheme, we make predictions of shape observables for deformed nuclei, namely beta and gamma deformation variables, and compare these with empirical data and with predictions by relativistic and non-relativistic mean-field theories.
We prove various results on the cohomology of arithmetic lattices arising from quaternion algebras over a number field with at least one complex place, including a strong restriction on the allowable weights of cuspidal cohomological automorphic forms and a conditional power saving for their multiplicities when the associated locally symmetric space is a hyperbolic 3-manifold.
Active stereo systems are used in many robotic applications that require 3D information. These depth sensors, however, suffer from stereo artefacts and do not provide dense depth estimates.In this work, we present the first self-supervised depth completion method for active stereo systems that predicts accurate dense depth maps. Our system leverages a feature-based visual inertial SLAM system to produce motion estimates and accurate (but sparse) 3D landmarks. The 3D landmarks are used both as model input and as supervision during training. The motion estimates are used in our novel reconstruction loss that relies on a combination of passive and active stereo frames, resulting in significant improvements in textureless areas that are common in indoor environments. Due to the nonexistence of publicly available active stereo datasets, we release a real dataset together with additional information for a publicly available synthetic dataset (TartanAir [42]) needed for active depth completion and prediction. Through rigorous evaluations we show that our method outperforms state of the art on both datasets. Additionally we show how our method obtains more complete, and therefore safer, 3D maps when used in a robotic platform.
We study the relationship between chaotic behavior and the Central Limit Theorem (CLT) in the Kuramoto model. We calculate sums of angles at equidistant times along deterministic trajectories of single oscillators and we show that, when chaos is sufficiently strong, the Pdfs of the sums tend to a Gaussian, consistently with the standard CLT. On the other hand, when the system is at the "edge of chaos" (i.e. in a regime with vanishing Lyapunov exponents), robust $q$-Gaussian-like attractors naturally emerge, consistently with recently proved generalizations of the CLT.
We study the Cauchy problem for the $1$-d periodic fractional Schr\"odinger equation with cubic nonlinearity. In particular we prove local well-posedness in Sobolev spaces, for solutions evolving from rough initial data. In addition we show the existence of global-in-time infinite energy solutions. Our tools include a new Strichartz estimate on the torus along with ideas that Bourgain developed in studying the periodic cubic NLS.
The automatic detection of major rail components using railway images is beneficial to ensure the rail transport safety. In this paper, we propose an attention-powered deep convolutional network (AttnConv-net) to detect multiple rail components including the rail, clips, and bolts. The proposed method consists of a deep convolutional neural network (DCNN) as the backbone, cascading attention blocks (CAB), and two feed forward networks (FFN). Two types of positional embedding are applied to enrich information in latent features extracted from the backbone. Based on processed latent features, the CAB aims to learn the local context of rail components including their categories and component boundaries. Final categories and bounding boxes are generated via two FFN implemented in parallel. To enhance the detection of small components, various data augmentation methods are employed in the training process. The effectiveness of the proposed AttnConv-net is validated with one real dataset and another synthesized dataset. Compared with classic convolutional neural network based methods, our proposed method simplifies the detection pipeline by eliminating the need of prior- and post-processing, which offers a new speed-quality solution to enable faster and more accurate image-based rail component detections
Video prediction is an extrapolation task that predicts future frames given past frames, and video frame interpolation is an interpolation task that estimates intermediate frames between two frames. We have witnessed the tremendous advancement of video frame interpolation, but the general video prediction in the wild is still an open question. Inspired by the photo-realistic results of video frame interpolation, we present a new optimization framework for video prediction via video frame interpolation, in which we solve an extrapolation problem based on an interpolation model. Our video prediction framework is based on optimization with a pretrained differentiable video frame interpolation module without the need for a training dataset, and thus there is no domain gap issue between training and test data. Also, our approach does not need any additional information such as semantic or instance maps, which makes our framework applicable to any video. Extensive experiments on the Cityscapes, KITTI, DAVIS, Middlebury, and Vimeo90K datasets show that our video prediction results are robust in general scenarios, and our approach outperforms other video prediction methods that require a large amount of training data or extra semantic information.
We correct some errors and omissions primarily in a paper [Albertson&Hutchinson2004], discovered by R.B. Richter, and also some in a proof of [Thomassen1993] and of [Yu1997]. We give a short proof of Thomassen's theorem that every triangulation of a surface with all noncontractible cycles sufficiently long can be 5-colored; part of the shortness is due to the use of the Four Color Theorem, which is not used in Thomassen's original proof.
In this article, we show that the Brownian motion on the circle constructed in Levy (1959) is a regular Euclidean Brownian motion on the half-circle with its own mirror image on the other half-circle, and is degenerated in the sense of Minlos (1959). This raises the question of what the white noise is on the circle. We then formally define the white noise space and its associated Brownian bridge.
We re-examine excitation of a set of disk oscillations in a deformed disk by a resonant process. We assume that the disk is deformed from an axisymmetric steady state by an oscillatory deformation with frequency $\omega_{\rm D}$ and azimuthal wavenumber $m_{\rm D}$. Then, we consider two normal mode oscillations with a set of frequencies and azimuthal wavenumber being ($\omega_1$, $m_1$) and ($\omega_2$, $m_2$) and satisfying the resonant conditions ($\omega_1+\omega_2+\omega_{\rm D}=0$ and $m_1+m_2+m_{\rm D}=0$). These oscillations are resonantly excited if $(E_1/\omega_1)(E_2/\omega_2)>0$, where $E_1$ and $E_2$ are wave energies of the above two oscillations, when the deformation is maintained by external forces or has a large amplitude compared with the oscillations. This instability condition is rather general as long as unperturbed density and pressure vanish on the surface of the system. Possibility of application to superhump and negative superhump in superoutburst state of dwarf novae are briefly discussed.
Noticeable deviations from the prediction of the fiducial LCDM cosmology are found in the angular power spectrum of the CMB. Besides large-angle anomalies, the WMAP 1st year data revealed a dip in the power spectrum at l \sim 200, which seemed to disappear in the 3rd year and subsequent angular power spectra. Using the WMAP 1st, 3rd, and 5th year data as well as the 5 year coadded data, we study the intensity and spatial distribution of this feature in order to unveil its origin and its implications for the cosmological parameters. We show that in all WMAP data releases there is a substantial suppression of the first Doppler peak in a region near the north ecliptic pole.