ShantanuT01/DACTYL-Pretraining huggingface dataset:
We construct a quantum-inspired classical algorithm for computing the permanent of Hermitian positive semidefinite matrices, by exploiting a connection between these mathematical structures and the boson sampling model. Specifically, the permanent of a Hermitian positive semidefinite matrix can be expressed in terms of the expected value of a random variable, which stands for a specific photon-counting probability when measuring a linear-optically evolved random multimode coherent state. Our algorithm then approximates the matrix permanent from the corresponding sample mean and is shown to run in polynomial time for various sets of Hermitian positive semidefinite matrices, achieving a precision that improves over known techniques. This work illustrates how quantum optics may benefit algorithms development.
Many Few-Shot Learning research works have two stages: pre-training base model and adapting to novel model. In this paper, we propose to use closed-form base learner, which constrains the adapting stage with pre-trained base model to get better generalized novel model. Following theoretical analysis proves its rationality as well as indication of how to train a well-generalized base model. We then conduct experiments on four benchmarks and achieve state-of-the-art performance in all cases. Notably, we achieve the accuracy of 87.75% on 5-shot miniImageNet which approximately outperforms existing methods by 10%.
To answer questions on the start and duration of the epoch of reionisation, periods of galaxy mergers and properties of other cosmological encounters, the cosmic star formation history (CSFH), is of fundamental importance. Using the association of long gamma-ray bursts (LGRBs) with the death of massive stars and their ultra-luminous nature, the CSFH can be probed to higher redshifts than current conventional methods. Unfortunately, no consensus has been reached on the manner in which the LGRB rate (LGRBR) traces the CSFH, leaving many of the questions mentioned mostly unexplored by this method. Observations by the GRB NIR detector (GROND) over the past 4 years have, for the first time, acquired highly complete LGRB samples. Driven by these completeness levels and new evidence of LGRBs also occurring in more massive and metal rich galaxies than previously thought, the possible biases of the LGRBR-CSFH connection are investigated over a large range of galaxy properties. The CSFH is modelled using empirical fits to the galaxy mass function and galaxy star formation rates. Biasing the CSFH by metallicity cuts, mass range boundaries, and other unknown redshift dependencies, a LGRBR is generated and compared to the highly complete GROND sample. It is found that there is no strong preference for a metallicity cut or fixed galaxy mass boundaries and that there are no unknown redshift effects, in contrast to previous work which suggest values of Z/Z_sun~0.1-0.3. From the best-fit models, we predict that ~1.2% of the LGRB burst sample exists above z=6. The linear relationship between the LGRBR and the CSFH suggested by our results implies that redshift biases present in previous LGRB samples significantly affect the inferred dependencies of LGRBs on their host galaxy properties. Such biases can lead to, e.g., an interpretation of metallicity limitations and evolving LGRB luminosity functions.
Next-to-leading order approximation of the quark helicity distributions are used in the frame work of polarized valon model. The flavor-asymmetry in the light-quark sea of the nucleon can be obtained from the contributions of unbroken sea quark distributions. We employ the polarized valon model and extract the flavor-broken light sea distributions which are modeled with the help of a Pauli-blocking ansatz. Using this ansatz, we can obtain broken polarized valon distributions. From there and by employing convolution integral, broken sea quark distributions are obtainable in this frame work. 0ur results for $\delta u$, $\delta d$, $\delta \bar u$, $\delta \bar d$ and $\delta \bar s$ are in good agreement with recent experimental data for polarized parton distribution from HERMES experimental group and also with GRSV model. Some information on orbital angular momentum as a main ingredient of total nucleon spin are given. The $Q^2$ evolution of this quantity, using the polarized valon model is investigated.
Evidence for an extraterrestrial flux of high-energy neutrinos has now been found in multiple searches with the IceCube detector. The first solid evidence was provided by a search for neutrino events with deposited energies $\gtrsim30$ TeV and interaction vertices inside the instrumented volume. Recent analyses suggest that the extraterrestrial flux extends to lower energies and is also visible with throughgoing, $\nu_\mu$-induced tracks from the Northern hemisphere. Here, we combine the results from six different IceCube searches for astrophysical neutrinos in a maximum-likelihood analysis. The combined event sample features high-statistics samples of shower-like and track-like events. The data are fit in up to three observables: energy, zenith angle and event topology. Assuming the astrophysical neutrino flux to be isotropic and to consist of equal flavors at Earth, the all-flavor spectrum with neutrino energies between 25 TeV and 2.8 PeV is well described by an unbroken power law with best-fit spectral index $-2.50\pm0.09$ and a flux at 100 TeV of $\left(6.7_{-1.2}^{+1.1}\right)\cdot10^{-18}\,\mathrm{GeV}^{-1}\mathrm{s}^{-1}\mathrm{sr}^{-1}\mathrm{cm}^{-2}$. Under the same assumptions, an unbroken power law with index $-2$ is disfavored with a significance of 3.8 $\sigma$ ($p=0.0066\%$) with respect to the best fit. This significance is reduced to 2.1 $\sigma$ ($p=1.7\%$) if instead we compare the best fit to a spectrum with index $-2$ that has an exponential cut-off at high energies. Allowing the electron neutrino flux to deviate from the other two flavors, we find a $\nu_e$ fraction of $0.18\pm0.11$ at Earth. The sole production of electron neutrinos, which would be characteristic of neutron-decay dominated sources, is rejected with a significance of 3.6 $\sigma$ ($p=0.014\%$).
We present a second-order perturbative analysis of the model describing a two-level trapped ion interacting with a traveling laser field, in the Lamb-Dicke regime. Unlike the customary approach, based on the interaction picture and the rotating wave approximation, we reduce the original Hamiltonian to a time-independent model, unitarily equivalent to a spin-boson model, which features a form well suited to apply the perturbation theory. We determine the first and second-order corrections of eigenstates and eigenvalues. By varying the interaction parameters we identify four regimes characterized by different eigenvalue distributions (possibly including level doublets) and suggest the presence of an intermediate regime where the spectrum undergoes macroscopic changes. In this regime, where the perturbation approach does not hold, our reduced Hamiltonian is shown to reproduce the Jaynes-Cummings model.
To test alternative hypotheses for the behavior of KIC 8462852, we obtained measurements of the star over a wide wavelength range from the UV to the mid-infrared from October 2015 through December 2016, using Swift, Spitzer and at AstroLAB IRIS. The star faded in a manner similar to the long-term fading seen in Kepler data about 1400 days previously. The dimming rate for the entire period reported is 22.1 +\- 9.7 milli-mag/yr in the Swift wavebands, with amounts of 21.0 +\- 4.5 mmag in the groundbased B measurements, 14.0 +\- 4.5 mmag in V, and 13.0 +\- 4.5 in R, and a rate of 5.0 +\- 1.2 mmag/yr averaged over the two warm Spitzer bands. Although the dimming is small, it is seen at >= 3 sigma by three different observatories operating from the UV to the IR. The presence of long-term secular dimming means that previous SED models of the star based on photometric measurements taken years apart may not be accurate. We find that stellar models with T_{eff} = 7000 - 7100 K and A_V ~ 0.73 best fit the Swift data from UV to optical. These models also show no excess in the near-simultaneous Spitzer photometry at 3.6 and 4.5 microns, although a longer wavelength excess from a substantial debris disk is still possible (e.g., as around Fomalhaut). The wavelength dependence of the fading favors a relatively neutral color (i.e., R_V >= 5, but not flat across all the bands) compared with the extinction law for the general ISM (R_V = 3.1), suggesting that the dimming arises from circumstellar material.
A $K3$ surface with an ample divisor of self-intersection 2 is a double cover of the plane branched over a sextic curve. We conjecture that a similar statement holds for the generic couple $(X,H)$ with $X$ a deformation of $(K3)^{[n]}$ and $H$ an ample divisor of square 2 for Beauville's quadratic form. If $n=2$ then according to the conjecture $X$ is a double cover of a (singular) sextic 4-fold in $\PP^5$. It follows from the conjecture that a deformation of $(K3)^{[n]}$ carrying a divisor (not necessarily ample) of degree 2 has an anti-symplectic birational involution. We test the conjecture. In doing so we bump into some interesting geometry: examples of two anti-symplectic involutions generating an interesting dynamical system, a case of Strange duality and what is probably an involution on the moduli space of degree-2 quasi-polarized $(X,H)$ where $X$ is a deformation of $(K3)^{[2]}$.
Using typical experimental techniques it is difficult to separate the effects of carrier density and disorder on the superconducting transition in two dimensions. Using a simple fabrication procedure based on metal layer dewetting, we have produced graphene sheets decorated with a non-percolating network of nanoscale tin clusters. These metal clusters both efficiently dope the graphene substrate and induce long-range superconducting correlations. This allows us to study the superconducting transition at fixed disorder and variable carrier concentration. We find that despite structural inhomogeneity on mesoscopic length scales (10-100 nm), this material behaves electronically as a homogenous dirty superconductor. Our simple self-assembly method establishes graphene as an ideal tunable substrate for studying induced two-dimensional electronic systems at fixed disorder and our technique can readily be extended to other order parameters such as magnetism.
The Marcus-Lushnikov process is a simple mean field model of coagulating particles that converges to the homogeneous Smoluchowski equation in the large mass limit. If the coagulation rates grow sufficiently fast as the size of particles get large, giant particles emerge in finite time. This is known as gelation, and such particles are known as gels. Gelation comes in different flavors: simple, instantaneous and complete. In the case of an instantaneous gelation, giant particles are formed in a very short time. If all particles coagulate to form a single particle in a time interval that stays bounded as total mass gets large, then we have a complete gelation. In this article, we describe conditions which guarantee any of the three possible gelations with explicit bounds on the size of gels and the time of their creations.
Let s and t be variables. Define polynomials {n} in s, t by {0}=0, {1}=1, and {n}=s{n-1}+t{n-2} for n >= 2. If s, t are integers then the corresponding sequence of integers is called a Lucas sequence. Define an analogue of the binomial coefficients by   C{n,k}={n}!/({k}!{n-k}!) where {n}!={1}{2}...{n}. It is easy to see that C{n,k} is a polynomial in s and t. The purpose of this note is to give two combinatorial interpretations for this polynomial in terms of statistics on integer partitions inside a k by n-k rectangle. When s=t=1 we obtain combinatorial interpretations of the fibonomial coefficients which are simpler than any that have previously appeared in the literature.
We propose an action of a certain motivic cohomology group on the coherent cohomology of Hilbert modular varieties, extending conjectures of Venkatesh, Prasanna, and Harris. The action is described in two ways: on cohomology modulo $p$ and over $\mathbb C$, and we conjecture that they both lift to an action on cohomology with integral coefficients. The conjecture is supported by theoretical evidence based on Stark's conjecture on special values of Artin $L$-functions, and by numerical evidence in base change cases.
We theoretically investigate a scattering configuration in Compton scattering, in which the orientation of the electron spin is reversed and simultaneously, the photon polarization changes from linear polarization into circular polarization. The intrinsic angular momentum of electron and photon are computed along the coincident propagation direction of the incoming and outgoing photon. We find that this intrinsic angular momentum is not conserved in the considered scattering process. We also discuss the generation of entanglement for the considered scattering setup and present an angle dependent investigation of the corresponding differential cross section, Stokes parameters and spin expectation.
We present the results of spectral investigations of the cataclysmic variable IP Peg in quiescence. Optical spectra obtained on the 6-m telescope at the Special Astrophysical Observatory (Russia), and on the 3.5-m telescope at the German-Spanish Astronomical Center (Calar Alto, Spain), have been analysed by means of Doppler tomography and Phase Modelling Technique. From this analysis we conclude that the quiescent accretion disk of IP Peg has a complex structure. There are also explicit indications of spiral shocks. The Doppler maps and the variations of the peak separation of the emission lines confirm this interpretation. We have detected that all the emission lines show a rather considerable asymmetry of their wings varying with time. The wing asymmetry shows quasi-periodic modulations with a period much shorter than the orbital one. This indicates the presence of an emission source in the binary rotating asynchronously with the binary system. We also have found that the brightness of the bright spot changes considerably during one orbital period. The spot becomes brightest at an inferior conjunction, whereas it is almost invisible when it is located on the distant half of the accretion disk. Probably, this phenomenon is due to an anisotropic radiation of the bright spot and an eclipse of the bright spot by the outer edge of the accretion disk.
In this paper we study the locus of singular tuples of a complex valued multisymmetric tensor. The main problem that we focus on is: given the set of singular tuples of some general tensor, which are all the tensors that admit those same singular tuples. Assume that the triangular inequality holds, that is exactly the condition such that the dual variety to the Segre-Veronese variety is an hypersurface, or equivalently, the hyperdeterminant exists. We show in such case that, when at least one component has degree odd, this tensor is projectively unique. On the other hand, if all the degrees are even, the fiber is an $1$-dimensional space.
We solve the problem of fermionic pairing mediated by a massless boson in the limit of large coupling constant. At weak coupling, the transition temperature is exponentially small and superconductivity is robust against phase fluctuation. In the strong coupling limit, the pair formation occurs at a temperature of the order of the Fermi energy, however, the actual transition temperature is much smaller due to phase and amplitude fluctuations of the pairing gap.   Our model calculations describe superconductivity due to color magnetic interactions in quark matter and in systems close to a ferromagnetic quantum critical point with Ising symmetry. Our strong coupling results are, however, more general and can be applied to other systems as well, including the antiferromagnetic exchange in 2D used for description of the cuprates.
The optical light profiles of nearby early type galaxies are known to exhibit a smooth transition from nuclear light deficits to nuclear light excesses with decreasing galaxy mass, with as much as 80 per cent of the galaxies with stellar masses below 10^10 Msun hosting a massive nuclear star cluster. At the same time, while all massive galaxies are thought to harbor nuclear super-massive black holes (SMBHs), observational evidence for SMBHs is slim at the low end of the mass function. Here, we explore the environmental dependence of the nucleation fraction by comparing two homogeneous samples of nearby field vs. cluster early type galaxies with uniform Hubble Space Telescope (HST) coverage. Existing Chandra X-ray Telescope data for both samples yield complementary information on low-level accretion onto nuclear SMBHs. Specifically, we report on dual-band (F475W & F850LP) Advanced Camera for Surveys (ACS) imaging data for 28 out of the 103 field early type galaxies that compose the AMUSE-Field Chandra survey, and compare our results against the companion HST and Chandra surveys for a sample of 100 Virgo cluster early types (ACS Virgo Cluster and AMUSE-Virgo surveys, respectively). We model the two-dimensional light profiles of the field targets to identify and characterize NSCs, and find a field nucleation fraction of 26% (+17%, -11%; at the 1-sigma level), consistent with the measured Virgo nucleation fraction of 30% (+17%, -12%), across a comparable mass distribution. Coupled with the Chandra result that SMBH activity is higher for the field, our findings indicate that, since the last epoch of star formation, the funneling of gas to the nuclear regions has been inhibited more effectively for Virgo galaxies, arguably via ram pressure stripping.
A systematic analysis of data on strangeness and pion production in nucleon-nucleon and central nucleus-nucleus collisions is presented. It is shown that at all collision energies the pion/baryon and strangeness/pion ratios indicate saturation with the size of the colliding nuclei. The energy dependence of the saturation level suggests that the transition to the Quark Gluon Plasma occurs between 15 AGeV/c (BNL AGS) and 160 AGeV/c (CERN SPS) collision energies. The experimental results interpreted in the framework of a statistical approach show that the effective number of degrees of freedom increases in the course of the phase transition and that the plasma created at CERN SPS energies may have a temperature of about 280 MeV (energy density 10 GeV/fm-3). The presence of the phase transition can lead to the non-monotonic collision energy dependence of the strangeness/pion ratio. After an initial increase the ratio should drop to the characteristic value for the QGP. Above the transition region the ratio is expected to be collision energy independent. Experimental studies of central Pb+Pb collisions in the energy range 20--160 AGeV/c are urgently needed in order to localize the threshold energy, and study the properties of the QCD phase transition.
Magnetic properties of a single vacancy in graphene is a relevant and still unsolved problem. The experimental results point to a clearly detectable magnetic defect state at the Fermi energy, while several calculations based on density functional theory (DFT) yield widely varying results for the magnetic moment, in the range of $\mu=1.04-2.0$ $\mu_{B}$. We present a multi-tool \textit{ab initio} theoretical study of the same defect, using two simulation protocols for a defect in a crystal (cluster and periodic boundary conditions) and different DFT functionals - bare and hybrid DFT, mixing a fraction of exact Hartree-Fock exchange (XC). Our main conclusions are two-fold: First, we find that due to the $\pi$-character of the Fermi-energy states of graphene, inclusion of XC is crucial and for a single isolated vacancy we can predict an integer magnetic moment $\mu=2\mu_{B}$. Second, we find that due to the specific symmetry of the graphene lattice, periodic arrays of single vacancies may provide interesting diffuse spin-spin interactions.
Telescope Array (TA) has recently published results of nearly nine years of $X_{\mathrm{max}}$ observations providing its highest statistics measurement of ultra high energy cosmic ray (UHECR) mass composition to date for energies exceeding $10^{18.2}$ eV. This analysis measured agreement of observed data with results expected for four different single elements. Instead of relying only on the first and second moments of $X_{\mathrm{max}}$ distributions, we employ a morphological test of agreement between data and Monte Carlo to allow for systematic uncertainties in data and in current UHECR hadronic models. Results of this latest analysis and implications of UHECR composition observed by TA are presented. TA can utilize different analysis methods to understand composition as both a crosscheck on results and as a tool to understand systematics affecting $X_{\mathrm{max}}$ measurements. The different analysis efforts underway at TA to understand composition are also discussed.
We find the maximal number of regions that a straight line embedding of a N-cycle graph can enclose.
This article is concerned with the long time behavior of neutral genetic population models, with fixed population size. We design an explicit, finite, exact, genealogical tree based representation of stationary populations that holds both for finite and infinite types (or alleles) models. We then analyze the decays to the equilibrium of finite populations in terms of the convergence to stationarity of their first common ancestor. We estimate the Lyapunov exponent of the distribution flows with respect to the total variation norm. We give bounds on these exponents only depending on the stability with respect to mutation of a single individual; they are inversely proportional to the population size parameter.
Scene understanding for autonomous vehicles is a challenging computer vision task, with recent advances in convolutional neural networks (CNNs) achieving results that notably surpass prior traditional feature driven approaches. However, limited work investigates the application of such methods either within the highly unstructured off-road environment or to RGBD input data. In this work, we take an existing CNN architecture designed to perform semantic segmentation of RGB images of urban road scenes, then adapt and retrain it to perform the same task with multichannel RGBD images obtained under a range of challenging off-road conditions. We compare two different stereo matching algorithms and five different methods of encoding depth information, including disparity, local normal orientation and HHA (horizontal disparity, height above ground plane, angle with gravity), to create a total of ten experimental variations of our dataset, each of which is used to train and test a CNN so that classification performance can be evaluated against a CNN trained using standard RGB input.