ShantanuT01/DACTYL-Pretraining huggingface dataset:
State-of-the-art face recognition algorithms are able to achieve good performance when sufficient training images are provided. Unfortunately, the number of facial images is limited in some real face recognition applications. In this paper, we propose ComplexFace, a novel and effective algorithm for face recognition with limited samples using complex number based data augmentation. The algorithm first generates new representations from original samples and then fuse both into complex numbers, which avoids the difficulty of weight setting in other fusion approaches. A test sample can then be expressed by the linear combination of all the training samples, which mapped the sample to the new representation space for classification by the kernel function. The collaborative representation based classifier is then built to make predictions. Extensive experiments on the Georgia Tech (GT) face database and the ORL face database show that our algorithm significantly outperforms existing methods: the average errors of previous approaches ranging from 31.66% to 41.75% are reduced to 14.54% over the GT database; the average errors of previous approaches ranging from 5.21% to 10.99% are reduced to 1.67% over the ORL database. In other words, our algorithm has decreased the average errors by up to 84.80% on the ORL database.
We prove that there exists a norm in the plane under which no n-point set determines more than O(n log n log log n) unit distances. Actually, most norms have this property, in the sense that their complement is a meager set in the metric space of all norms (with the metric given by the Hausdorff distance of the unit balls).
We show how to use the combinatorial notion of jump sets to parametrize the possible structures of the group of principal units of local fields, viewed as filtered modules. We establish a natural bijection between the set of jump sets and the orbit space of a $p$-adic group of filtered automorphisms acting on a free filtered module. This, together with a Markov process on Eisenstein polynomials, culminates into a mass-formula for unit filtrations. As a bonus the proof leads in many cases to explicit invariants of Eisenstein polynomials, yielding a link between the filtered structure of the unit group and ramification theory. Finally, with the basic theory of filtered modules developed here, we recover, with a more conceptual proof, a classification, due to Miki, of the possible sets of upper jumps of a wild character: these are all jump sets, with a set of exceptions explicitly prescribed by the jump set of the local field and the size of its residue field.
Nonlinear sigma models compatible with the aratyn-Ferreira-Zimerman ansatz are discussed, the latter ansatz automatically leading to configurations with definite values of the Hopf index. These models are allowed to involve a weight factor which is a function of one of the toroidal coordinates. Depending on the choice of the weight factor, the field equation takes various forms. In one model with a special weight factor, the field equation turns out to be the fifth Painleve equation. This model suggests the existence of a knot soliton strictly confined in a finite spatial volume. Some other interesting cases are also discussed.
The root-mean square radius of the deuteron magnetic moment distribution, $ r_{Md}$, is calculated for several realistic models of the $NN$--interaction. For the Paris potential the result is $r_{Md} = 2.312 \pm 0.010 $ fm. The dependence of $r_{Md} $ on the choice of $NN$ model, relativistic effects and meson exchange currents is investigated. The experimental value of $r_{Md}$ is also considered. The necessity of new precise measurements of the deuteron magnetic form factor at low values of $Q^2$ is stressed.
We find an exact solution for the problem of electron spin relaxation in a 2D circle with Rashba spin-orbit interaction. Our analysis shows that the spin relaxation in finite-size regions involves three stages and is described by multiple spin relaxation times. It is important that the longest spin relaxation time increases with decrease in system radius but always remains finite. Therefore, at long times, the spin polarization in small 2D systems decays exponentially with a size-dependent rate. This prediction is supported by results of Monte Carlo simulations.
Stellar shells around galaxies could provide precious insights into their assembly history. However, their formation mechanism remains poorly empirically constrained, in particular the type of galaxy collisions at their origin. We present MUSE@VLT data of the most prominent outer shell of NGC 474, to constrain its formation history. The stellar shell spectrum is clearly detected, with a signal-to-noise ratio of around 65 pix$^{-1}$. We use a full spectral fitting method to determine the line-of-sight velocity and the age and metallicity of the shell and associated point-like sources within the MUSE field of view. We detect six GC candidates and eight PN candidates which are all kinematically associated to the stellar shell. We show that the shell has an intermediate metallicity, [M/H] = $-0.83^{+0.12}_{-0.12}$ and a possible $\alpha$-enrichment, [$\alpha$/Fe] ~ 0.3. Assuming the material of the shell comes from a lower mass companion, and that the latter had no initial metallicity gradient, such a stellar metallicity would constrain the mass of the progenitor to be around 7.4 x 10^8 M$_\odot$, implying a merger mass ratio of about 1:100. However our census of PNs and earlier photometry of the shell would suggest a much higher ratio, around 1:20. Given the uncertainties, this difference is significant only at the ~1sigma level. We discuss the characteristics of the progenitor, in particular whether the progenitor could also be composed of stars from the low metallicity outskirts from a more massive galaxy. Ultimately, the presented data does not allow us to put a firm constraint on the progenitor mass. We show that at least two globular cluster candidates possibly associated with the shell are quite young, with ages below 1.5~Gyr. We also note the presence of a young (~1Gyr) stellar population in the center of NGC 474. The two may have resulted from the same event.
Galactic magnetic field (GMF) and secondary cosmic rays (CRs) (e.g. $^{10}$beryllium, boron, antiproton) are important components to understand the propagation of CRs in the Milky Way Galaxy. Realistic modeling of GMF is based on the Faraday rotation measurements of various Galactic and extragalactic radio sources and synchrotron emission from CR leptons in the radio frequency range, thereby providing information of halo height. On the other hand, diffusion coefficient and halo height are also estimated from the $^{10}$Be/$^{9}$Be and B/C ratios. Moreover, density distribution of gaseous components of interstellar medium (ISM) also plays an important role as secondary CRs are produced due to interaction of primary CRs with the gaseous components of ISM. We consider mainly molecular, atomic, and ionized components of hydrogen gas for our study. Recent observations and hydrodynamical simulations provide new forms of density profiles of hydrogen gas in Milky Way Galaxy. In the \texttt{DRAGON} code, we have implemented our chosen density profiles, based on realistic observations in radio, X-ray and $\gamma$-ray wavebands, and hydrodynamical simulations of interstellar hydrogen gas to study the variation in the height of the halo required to fit the observed CR spectra. Our results show the halo height ($z_{t}$) varies in the range of 2 to 6 kpc for the density profiles considered in our work.
We consider the problem of birationally modifying a morphism of complete varieties to make it a morphism from a nonsingular variety to a normal variety. Our main result is to give a counterexample to this problem. This example also is a counterexample to the related conjecture of Abhyankar on ``weak simultaneous global resolution''.   We also give some positive results. Forinstance, a positive result of this kind is possible if we remove the separatedness condition.
We present three epochs of early-time ultraviolet (UV) and optical HST/STIS spectroscopy of the young, nearby Type IIP supernova (SN) 2021yja. We complement the HST data with two earlier epochs of Swift UVOT spectroscopy. The HST and Swift UVOT spectra are consistent with those of other well-studied Type IIP supernovae (SNe). The UV spectra exhibit rapid cooling at early times, while less dramatic changes are seen in the optical. We also present Lick/KAIT optical photometry up to the late-time-tail phase, showing a very long plateau and shallow decline compared with other SNe IIP. Our modeling of the UV spectrum with the TARDIS radiative-transfer code produces a good fit for a high-velocity explosion, a low total extinction $E(B-V) = 0.07$ mag, and a subsolar metallicity. We do not find a significant contribution to the UV flux from an additional heating source, such as interaction with the circumstellar medium, consistent with the observed flat plateau. Furthermore, the velocity width of the Mg II $\lambda$2798 line is comparable to that of the hydrogen Balmer lines, suggesting that the UV emission is confined to a region close to the photosphere.
Quantum mechanics and classical statistical mechanics are two physical theories that share several analogies in their mathematical apparatus and physical foundations. In particular, classical statistical mechanics is hallmarked by the complementarity between two descriptions that are unified in thermodynamics: (i) the parametrization of the system macrostate in terms of mechanical macroscopic observables $I=\{I^{i}\}$; and (ii) the dynamical description that explains the evolution of a system towards the thermodynamic equilibrium. As expected, such a complementarity is related to the uncertainty relations of classical statistical mechanics $\Delta I^{i}\Delta \eta_{i}\geq k$. Here, $k$ is the Boltzmann's constant, $\eta_{i}=\partial \mathcal{S}(I|\theta)/\partial I^{i}$ are the restituting generalized forces derived from the entropy $\mathcal{S}(I|\theta)$ of a closed system, which is found in an equilibrium situation driven by certain control parameters $\theta=\{\theta^{\alpha}\}$. These arguments constitute the central ingredients of a reformulation of classical statistical mechanics from the notion of complementarity. In this new framework, Einstein postulate of classical fluctuation theory $dp(I|\theta)\sim\exp[\mathcal{S}(I|\theta)/k]dI$ appears as the correspondence principle between classical statistical mechanics and thermodynamics in the limit $k\rightarrow0$, while the existence of uncertainty relations can be associated with the non-commuting character of certain operators.
The conjecture that M-theory has the rank eleven Kac-Moody symmetry e11 implies that Type IIA and Type IIB string theories in ten dimensions possess certain infinite dimensional perturbative symmetry algebras that we determine. This prediction is compared with the symmetry algebras that can be constructed in perturbative string theory, using the closed string analogues of the DDF operators. Within the limitations of this construction close agreement is found. We also perform the analogous analysis for the case of the closed bosonic string.
The coherence resource theory needs to study the operational value and efficiency which can be broadly formulated as the question: when can one coherent state be converted into another under incoherent operations. We answer this question completely for one-mode continuous-variable systems by characterizing conversion of coherent Gaussian states under incoherent Gaussian operations in terms of their first and second moments. The no-go theorem of purification of coherent Gaussian states is also built. The structure of incoherent Gaussian operations of two-mode continuous-variable systems is discussed further and is applied to coherent conversion for pure Gaussian states with standard second moments. The standard second moments are images of all second moments under local linear unitary Bogoliubov operations. As concrete applications, we obtain some peculiarities of a Gaussian system: (1) There does not exist a maximally coherent Gaussian state which can generate all coherent Gaussian states; (2) The conversion between pure Gaussian states is reversible; (3) The coherence of input pure state and the coherence of output pure state are equal.
We find that the best RVB state of the spin-$\frac{1}{2}$ Kagome antiferromagnetic Heisenberg model(spin-$\frac{1}{2}$ KAFH) is described by a $Z_{2}$ gapped mean field ansatz, which hosts a mean field spinon dispersion very different from that of the widely studied $U(1)$ Dirac spin liquid state. However, we find that the physical spin fluctuation spectrum calculated from the Gutzwiller projected RPA(GRPA) theory above such an RVB state is actually gapless and is almost identical to that above the $U(1)$ Dirac spin liquid state. We find that such a peculiar behavior can be attributed to the unique flat band physics on the Kagome lattice, which makes the mapping between the mean field ansatz and the RVB state non-injective. We find that the spin fluctuation spectrum of the spin-$\frac{1}{2}$ KAFH is not at all featureless, but is characterized by a prominent spectral peak at about $0.25J$ around the $\mathbf{M}$ point, which is immersed in a broad continuum extending to $2.7J$. Based on these results, we argue that the spectral peak below 2 meV in the inelastic neutron scattering(INS) spectrum of Hebertsmithite ZnCu$_{3}$(OH)$_{6}$Cl$_{2}$, which has been attributed to the contribution of Cu$^{2+}$ impurity spins occupying the Zn$^{2+}$ site, should rather be understood as the intrinsic contribution from the Kagome layer. We propose to verify such a picture by measuring the Knight shift on the Cu site, rather than the O site, which is almost blind to the spin fluctuation at the $\mathbf{M}$ point as a result of the strong antiferromagnetic correlation between nearest neighboring spins on the Kagome lattice.
Mechanisms have been proposed that might rotate the linear polarization of the cosmic microwave background (CMB) as it propagates from the surface of last scatter. In the simplest scenario, the rotation will be uniform across the sky, but the rotation angle may also vary across the sky. We develop in detail the complete set of full-sky quadratic estimators for the rotation of the CMB polarization that can be constructed from the CMB temperature and polarization. We derive the variance with which these estimators can be measured and show that these variances reduce to the simpler flat-sky expressions in the appropriate limit. We evaluate the variances numerically. While the flat-sky formalism may be suitable if the rotation angle arises as a realization of a random field, the full-sky formalism will be required to search for rotations that vary slowly across the sky as well as for models in which the angular power spectrum for the rotation angle peaks at large angles.
The {\it Sierpi\'nski fractal} or {\it Sierpi\'nski gasket} $\Sigma$ is a familiar object studied by specialists in dynamical systems and probability. In this paper, we consider a graph $S_n$ derived from the first $n$ iterations of the process that leads to $\Sigma$, and study some of its properties, including its cycle structure, domination number and pebbling number. Various open questions are posed.
We study the dynamical appearance of scaling solutions in relativistic hydrodynamics. The phase transition effects are included through the temperature dependent sound velocity. If a pre-equilibrium transverse flow is included in the initial conditions, then it may reach the form of the asymptotic Hubble flow, r/t, in short evolution times, 7-15 fm. The numerical solutions are found to support to the freeze-out models (Blast-Wave, Buda-Lund, Cracow).
We compute upper limits on CMB cross-polarization by cross-correlating the PIQUE and Saskatoon experiments. We also discuss theoretical and practical issues relevant to measuring cross-polarization and illustrate them with simulations of the upcoming BOOMERanG 2002 experiment. We present a method that separates all six polarization power spectra (TT, EE, BB, TE, TB, EB) without any other "leakage" than the familiar EE-BB mixing caused by incomplete sky coverage. Since E and B get mixed, one might expect leakage between TE and TB, between EE and EB and between BB and EB - our method eliminates this by preserving the parity symmetry under which TB and EB are odd and the other four power spectra are even.
Minor totals of natural sequence were shown to possess some properties in respect to their units digits. Depending on numeral system applied the units digits may take any digit of the system or there may be exclusions. i.e. some system digits can never appear in the units digits of the minor totals. Natural sequence arithmetics may be applied to model multicellular organism growth. It can be shown that growth of an idealized organism may follow a power law in the form of the minor totals.
The variational principle of quantum mechanics is the backbone of hybrid quantum computing for a range of applications. However, as the problem size grows, quantum logic errors and the effect of barren plateaus overwhelm the quality of the results. There is now a clear focus on strategies that require fewer quantum circuit steps and are robust to device errors. Here we present an approach in which problem complexity is transferred to dynamic quantities computed on the quantum processor - Hamiltonian moments, $\langle H^n\rangle$. From these quantum computed moments, estimates of the ground-state energy are obtained using the "infinum" theorem from Lanczos cumulant expansions which manifestly correct the associated variational calculation. With system dynamics encoded in the moments the burden on the trial-state quantum circuit depth is eased. The method is introduced and demonstrated on 2D quantum magnetism models on lattices up to 5 $\times$ 5 (25 qubits) implemented on IBM Quantum superconducting qubit devices. Moments were quantum computed to fourth order with respect to a parameterised antiferromagnetic trial-state. A comprehensive comparison with benchmark variational calculations was performed, including over an ensemble of random coupling instances. The results showed that the infinum estimate consistently outperformed the benchmark variational approach for the same trial-state. These initial investigations suggest that the quantum computed moments approach has a high degree of stability against trial-state variation, quantum gate errors and shot noise, all of which bodes well for further investigation and applications of the approach.
In this study, a new method is presented to classify flares derived from the photoelectric photometry of UV Ceti type stars. This method is based on statistical analyses using an independent samples t-test. The data used in analyses were obtained from four flare stars observed between 2004 and 2007. The total number of flares obtained in the observations of AD Leo, EV Lac, EQ Peg, and V1054 Oph is 321 in the standard Johnson U band. As a result flares can be separated into two types, slow and fast, depending on the ratio of flare decay time to flare rise time. The ratio is below 3.5 for all slow flares, while it is above 3.5 for all fast flares. Also, according to the independent samples t-test, there is a difference of about 157 s between equivalent durations of slow and fast flares. In addition, there are significant differences between amplitudes and rise times of slow and fast flares.
We explore the possibility that the hotspot of ultrahigh energy cosmic rays (UHECR) detected by the Telescope Array (TA) from the approximate direction of M82 and the M81 group of galaxies might be the echo of UHECR emitted by Centaurus A in an earlier more powerful phase. Echoes from other starburst galaxies or groups of galaxies may contribute to the UHECR flux at the Earth. We use an illustrative Monte Carlo model of mono-energetic UHECR transport by small angle scattering to generate synthetic sky maps. The model informs a discussion of overall energetics and time and distance scales. We find a viable echo model for the observed UHECR hotspots if the UHECR luminosity of Centaurus A 20 Myr ago was 200 times its present luminosity and if the ordered magnetic field exceeds 10-20nG out to a distance of 400-800kpc in the circumgalactic medium of M82 and other starburst galaxies.
We propose a theoretical/computational protocol based on the use of the Ground State (GS) Path Integral (PI) Quantum Monte Carlo (QMC) for the calculation of the kinetic and Coulomb energy density for a system of $N$ interacting electrons in an external potential. The idea is based on the derivation of the energy densities via the $N-1$-conditional probability density within the framework of the Levy-Lieb constrained search principle. The consequences for the development of energy functionals within the context of Density Functional Theory (DFT) are discussed. We propose also the possibility of going beyond the energy densities and extend this idea to a computational procedure where the $N-1$-conditional probability is an implicit functional of the electron density, independently from the external potential. In principle, such a procedure paves the way for an {\it on-the-fly} determination of the energy functional for any system.
The VERITAS array of 12-m atmospheric-Cherenkov telescopes in southern Arizona began full-scale operations in 2007, and it is one of the world's most sensitive detectors of astrophysical VHE (E > 100 GeV) gamma rays. Forty-one blazars are known to emit VHE photons, and observations of blazars are one of the VERITAS Collaboration's Key Science Projects (KSPs). More than 400 hours per year are devoted to this program, and ~100 blazars have already been observed with the array, in most cases with the deepest-ever VHE exposure. These observations have resulted in 20 detections, including 10 new VHE blazars. Highlights of the VERITAS blazar observation program, and the collaboration's long-term blazar observation strategy, are presented.
This paper delineates the first steps in a systematic quantitative study of the spacetime fluctuations induced by quantum fields in an evaporating black hole under the stochastic gravity program. The central object of interest is the noise kernel, which is the symmetrized two-point quantum correlation function of the stress tensor operator. As a concrete example we apply it to the study of the spherically-symmetric sector of metric perturbations around an evaporating black hole background geometry. For macroscopic black holes we find that those fluctuations grow and eventually become important when considering sufficiently long periods of time (of the order of the evaporation time), but well before the Planckian regime is reached. In addition, the assumption of a simple correlation between the fluctuations of the energy flux crossing the horizon and far from it, which was made in earlier work on spherically-symmetric induced fluctuations, is carefully scrutinized and found to be invalid. Our analysis suggests the existence of an infinite amplitude for the fluctuations when trying to localize the horizon as a three-dimensional hypersurface, as in the classical case, and, as a consequence, a more accurate picture of the horizon as possessing a finite effective width due to quantum fluctuations. This is supported by a systematic analysis of the noise kernel in curved spacetime smeared with different functions under different conditions, the details are collected in the appendices. This case study shows a pathway for probing quantum metric fluctuations near the horizon and understanding their physical meaning.