ShantanuT01/DACTYL-Pretraining huggingface dataset:
We consider the problem of estimating the intersection multiplicity between an algebraic variety and a Pfaffian foliation, at every point of the variety. We show that this multiplicity can be majorized at every point $p$ by the local algebraic multiplicity at $p$ of a suitably constructed algebraic cycle. The construction is based on Gabrielov's complex analog of the Rolle-Khovanskii lemma.   We illustrate the main result by deriving similar uniform estimates for the complexity of the Milnor fiber of a deformation (under a smoothness assumption) and for the order of contact between an algebraic hypersurface and an arbitrary non-singular one-dimensional foliation. We also use the main result to give an alternative geometric proof for a classical multiplicity estimate in the context of commutative group varieties.
We investigate the dynamical nature of the collapse process of a spherically symmetric star in quasi-static hydrodynamical equilibrium. The star collapses from an initial static configuration by dissipating energy in the form of a radial heat flux. The dissipation ensures that the singularity is never formed and the stellar mass completely evaporates over a finite time.
Since 2014, a new detector (New-Tupi) consisting of four plastic scintillators ($150 \times 75 \times 5 cm^3$) placed in pairs and located in Niteroi, Rio de Janeiro, Brazil, has been used for the search of transient solar events and photomuons from gamma-ray bursts (GRBs). On September 15, 2015, at 21:18:24 UT, the Swift Burst Alert Telescope (BAT) triggered and located GRB 150915A (trigger 655721). The GRB light curve shows a weak complex structure of long duration $T_{90}=164.7 \pm 49.7 $ s, and a fluence in the 15-150 keV band of $8.0 \pm 1.8 \times 10^{-7}erg/cm^2$. GRB 150915A was fortuitously located in the field of view of the New-Tupi detector, and a search for prompt emission in the GeV energy range is presented here. The analysis was made using the "scaler" or "single-particle" technique. The New-Tupi detector registered a counting rate excess peak of duration $T_{90}=(6.1\pm 0.6)$ s with a signal significance $(4.4\pm 0.5)\sigma$, (and not $6.9\sigma$ as reported in the previous version). The signal is within the T90 duration of the Swift BAT GRB, with an estimated "excess" fluence of $F_S(E>0.1 GeV)=1.3 \pm 0.3 \times 10^{-6} erg/cm^2$. This value can be considered the lower limit of the gamma ray fluence in the GeV energy region. However, the Poisson probability of the event to be a background fluctuation is $5.0 \times 10^{-6}$ and it appears in the counting rate of the New-Tupi detector with an annual rate $\sim 76$. In addition, the signal has a significance of only $2\sigma$ in the time profiles with a bin above 2 seconds. Thus we conclude that the event has a high probability to be background fluctuation.
This paper concerns the long term behaviour of a growth model describing a random sequential allocation of particles on a finite cycle graph. The model can be regarded as a reinforced urn model with graph-based interactions. It is motivated by cooperative sequential adsorption, where adsorption rates at a site depend on the configuration of existing particles in the neighbourhood of that site. Our main result is that, with probability one, the growth process will eventually localise either at a single site, or at a pair of neighbouring sites.
We study both the classical and the quantum target space of (p,q) minimal string theory, using the FZZT brane as a probe. By thinking of the target space as the moduli space of FZZT branes, parametrized by the boundary cosmological constant x, we see that classically it consists of a Riemann surface \CM_{p,q} which is a p-sheeted cover of the complex x plane. However, we show using the dual matrix model that the exact quantum FZZT observables exhibit Stokes' phenomenon and are entire functions of x. Along the way we clarify some points about the semiclassical limit of D-brane correlation functions. The upshot is that nonperturbative effects modify the target space drastically, changing it from \CM_{p,q} to the complex x plane. To illustrate these ideas, we study in detail the example of (p,q)=(2,1), which is dual to the Gaussian matrix model. Here we learn that the other sheets of the classical Riemann surface describe instantons in the effective theory on the brane. Finally, we discuss possible applications to black holes and the topological string.
We derive the contribution of $\Delta$-h excitations to quasielastic charged-current neutrino-nucleus scattering in the framework of relativistic mean-field theory. We discuss the effect of $\Delta$ production on the determination of the axial mass $M_A$ in neutrino scattering experiments.
Detection of gravitational waves(GW) involves using the network of GW telescopes to observe a large sky region. However, owing to the arrangement of the GW telescopes, even with aLIGO- aVirgo-KAGRA network,parameter estimation accuracy deteriorates depending on the sky region of the GW source due to the ill-posed nature of the inverse operator. A regularization-based method is proposed herein to improve parameter estimation accuracy. Although conventional regularization methods cannot optimize all regulator parameters completely, the proposed method archives full optimization by applying an a-posteriori parameter choice rule to determine regulator parameters. We demonstrate that the proposed method can shrink the credible regions of inclination vs lumi- nosity distance and polarization vs initial phase significantly in the sky wherein the accuracy of the amplitude parameters of a GW has been deteriorated. The proposed method suppresses the systematic error of a GW depending on the sky region and allows us investigating the cosmological information more precisely.
We present a full classification of the short-time behaviour of the interfaces and local solutions to the nonlinear parabolic $p$-Laplacian type reaction-diffusion equation of non-Newtonian elastic filtration \[ u_t-\Big(|u_x|^{p-2}u_x\Big)_x+bu^{\beta}=0, \ p>2, \beta >0 \] The interface may expand, shrink, or remain stationary as a result of the competition of the diffusion and reaction terms near the interface, expressed in terms of the parameters $p,\beta, sign~b$, and asymptotics of the initial function near its support. In all cases, we prove the explicit formula for the interface and the local solution with accuracy up to constant coefficients. The methods of the proof are based on nonlinear scaling laws, and a barrier technique using special comparison theorems in irregular domains with characteristic boundary curves.
This paper analyzes the reconstruction of diffusion and absorption parameters in an elliptic equation from knowledge of internal data. In the application of photo-acoustics, the internal data are the amount of thermal energy deposited by high frequency radiation propagating inside a domain of interest. These data are obtained by solving an inverse wave equation, which is well-studied in the literature. We show that knowledge of two internal data based on well-chosen boundary conditions uniquely determines two constitutive parameters in diffusion and Schroedinger equations. Stability of the reconstruction is guaranteed under additional geometric constraints of strict convexity. No geometric constraints are necessary when $2n$ internal data for well-chosen boundary conditions are available, where $n$ is spatial dimension. The set of well-chosen boundary conditions is characterized in terms of appropriate complex geometrical optics (CGO) solutions.
The measurement of resistivity across a wide temperature range - from 15 to 1473 K - in rare-earth manganite series of compounds reveals a very interesting feature : normally observed insulating pattern beyond Tc (Curie Point) gives way to a reentrant metallic pattern around a characteristic temperature T*. The transport activation barrier Ea collapses to zero around T*. T* is found to be dependent on the carrier concentration or the concentration of the Jahn-Teller-active Mn(3+) ions as well as on the average A-site radius <rA> for a fixed carrier concentration. These factors govern the effective lattice distortion and hence lead to the variation in the conduction bandwidth. Our data cover a wide range - from T*>>Tc for smaller bandwidth to T* tending towards Tc for larger bandwidth. These results seem to provide evidence of the onset of lattice distortion at high temperature (around T*) and its variation. Since lattice distortion governs the magnetic, transport and other important behaviors significantly, our data assume importance as they offer a new measure of the effective distortion and its tunability.
With computer vision reaching an inflection point in the past decade, face recognition technology has become pervasive in policing, intelligence gathering, and consumer applications. Recently, face recognition technology has been deployed on bodyworn cameras to keep officers safe, enabling situational awareness and providing evidence for trial. However, limited academic research has been conducted on this topic using traditional techniques on datasets with small sample size. This paper aims to bridge the gap in the state-of-the-art face recognition using bodyworn cameras (BWC). To this aim, the contribution of this work is two-fold: (1) collection of a dataset called BWCFace consisting of a total of 178K facial images of 132 subjects captured using the body-worn camera in in-door and daylight conditions, and (2) open-set evaluation of the latest deep-learning-based Convolutional Neural Network (CNN) architectures combined with five different loss functions for face identification, on the collected dataset. Experimental results on our BWCFace dataset suggest a maximum of 33.89% Rank-1 accuracy obtained when facial features are extracted using SENet-50 trained on a large scale VGGFace2 facial image dataset. However, performance improved up to a maximum of 99.00% Rank-1 accuracy when pretrained CNN models are fine-tuned on a subset of identities in our BWCFace dataset. Equivalent performances were obtained across body-worn camera sensor models used in existing face datasets. The collected BWCFace dataset and the pretrained/ fine-tuned algorithms are publicly available to promote further research and development in this area. A downloadable link of this dataset and the algorithms is available by contacting the authors.
Padmanabhan in his paper [arxiv: 1206.4916] put forth an intriguing idea arguing that the accelerated expansion of the universse can be viewed as the emergence of cosmic space as cosmic time progresses, with the expansion triggered due to the difference in the degrees of freedom on a holographic surface and the one in its emerged bulk. We show that the modified expansion law of the universe proposed by Sheykhi in a non-flat Friedmann- Robertson-Walker (FRW) universe and by Cai in a flat FRW universe could be derived starting from the first law of thermodynamics, in (n+1) dimensional Einstein gravity, Gauss-Bonnet and more general Lovelock gravity theories. We have also derived the modified versions of the expansion law for a flat universe due to Yang et al, in the case of Gauss-Bonnet and Lovelock gravities, from the first law of thermodynamics. This approach is unique in the sense that all these modified versions of the expansion law is derived from a thermodynamic identity that has the same form regardless of the gravity theory and irrespective of whether the universe is flat or non-flat
Anharmonic guest atom oscillation has direct connection to the thermal transport and thermo- electric behavior of type-I Ba8Ga16Sn30 clathrates. This behavior can be observed through several physical properties, with for example the heat capacity providing a measure of the overall excita- tion level structure. Localized anharmonic excitations also influence the low-temperature resistivity, as we show in this paper. By combining heat capacity, transport measurements and our previous NMR relaxation results, we address the distribution of local oscillators in this material, as well as the shape of the confining potential and the excitation energies for Ba(2) ions in the cages. We also compare to the soft-potential model and other models used for similar systems. The results show good agreement between the previously deduced anharmonic rattler potential and experimental data.
In this paper, we investigate models where a scalar field driving inflation is minimally coupled with gravity and it is subjected to a scalar potential. We present several examples of coupling between the field and gravity, and we furnish realistic models for inflation in agreement with the last Planck results.
We construct spinning black hole solutions in five dimensions that take into account the mixed gauge-gravitational Chern-Simons term and its supersymmetric completion. The resulting entropy formula is discussed from several points of view. We include a Taub-NUT base space in order to test recent conjectures relating 5D black holes to 4D black holes and the topological string. Our explicit results show that certain charge shifts have to be taken into account for these relations to hold. We also compute corrections to the entropy of black rings in terms of near horizon data.
We derive the fragmentation function (FF), which describes the probability for a charm quark to emit a $D$ meson with a certain momentum fraction, in the Nambu-Jona-Lasinio (NJL) model. The corresponding elementary FF is calculated with the quark-meson coupling determined in the NJL model involving charm quarks. The FF in the infinite momentum frame is constructed through the jet process governed by the elementary FF, and then evolved to the charm scale, at which it is defined. To prepare the FF suitable for an analysis of $D$ meson production at CLEO, we further match the above FF to that in the finite momentum frame at one loop in QCD. It is shown that the charm quark FF including the finite momentum effects leads to theoretical results in agreement with the CLEO data.
Shor's and Grover's famous quantum algorithms for factoring and searching show that quantum computers can solve certain computational problems significantly faster than any classical computer. We discuss here what quantum computers_cannot_ do, and specifically how to prove limits on their computational power. We cover the main known techniques for proving lower bounds, and exemplify and compare the methods.
We present mass and radius derivations for a sample of very young, mid- to late M, low-mass stellar and substellar objects in Upper Sco and Taurus. In a previous paper, we determined effective temperatures and surface gravities for these targets, from an analysis of their high-resolution optical spectra and comparisons to the latest synthetic spectra. We now derive extinctions, radii, masses and luminosities by combining our previous results with observed photometry, surface fluxes from the synthetic spectra and the known cluster distances. These are the first mass and radius estimates for young, very low mass bodies that are independent of theoretical evolutionary models (though our estimates do depend on spectral modeling). We find that for most of our sample, our derived mass-radius and mass-luminosity relationships are in very good agreement with the theoretical predictions. However, our results diverge from the evolutionary model values for the coolest, lowest-mass targets: our inferred radii and luminosities are significantly larger than predicted for these objects at the likely cluster ages, causing them to appear much younger than expected. We suggest that uncertainties in the evolutionary models - e.g., in the choice of initial conditions and/or treatment of interior convection - may be responsible for this discrepancy. Finally, two of our late-M objects (USco 128 and 130) appear to have masses close to the deuterium-fusion boundary (9--14 Jupiters, within a factor of 2). This conclusion is primarily a consequence of their considerable faintness compared to other targets with similar extinction, spectral type and temperature (difference of 1 mag). Our result suggests that the faintest young late-M or cooler objects may be significantly lower in mass than the current theoretical tracks indicate.
We describe the effects of both magnetic buoyancy and differential rotation on a disc of isothermal gas embedded in a purely azimuthal magnetic field, in order to study the evolution and interplay of Parker and shearing instabilities. Both instabilities occur on the slow MHD branch of the dispersion relation, and can affect the same waves. We put a stress on the natural polarization properties of the slow MHD waves to get a better understanding of the physics involved. The mechanism of the shearing instability is described in details. Waves with a vertical wavelength shorter than the scale height of the disc are subject to both the Parker and the transient shearing instabilities. They occur in different ranges of radial wavenumbers, \ie at different times in the shearing evolution ; these ranges can overlap or, on the contrary, be separated by a phase of wave-like oscillations, depending on the strength of differential rotation. Our results can be applied to both galactic and accretion discs.
We study the formation of a black hole and its subsequent evaporation in a model employing a minisuperspace approach to loop quantum gravity. In previous work the static solution was obtained and shown to be singularity-free. Here, we examine the more realistic dynamical case by generalizing the static case with help of the Vaidya metric. We track the formation and evolution of trapped surfaces during collapse and evaporation and examine the buildup of quantum gravitationally caused stress-energy preventing the formation of a singularity.
We study energy flow between two resistors coupled by an arbitrary linear and lossless electric circuit. We show that the fluctuations of energy transferred between the resistors are determined by random scattering of photons on an effective barrier with frequency dependent transmission probability $\tau(\omega)$. We express the latter in terms of the circuit parameters. Our results are valid in both quantum and classical regimes and for non-equilibrium electron distribution functions in the resistors.
Conductivity and Hall coefficient for various types of t-J ladders are calculated as a function of temperature and frequency by numerical diagonalization. A crossover from an incoherent to a coherent charge dynamics is found at a temperature T_{coh}. There exists another crossover at T_{PG} below which a pseudogap opens in the optical spectra, induced by the opening of a spin gap. In the absence of the spin gap, T_{coh} and the coherent weight are suppressed especially with increasing dimensionality. On the contrary, T_{coh} is strongly enhanced by the pseudogap formation below T_{PG}, where the coherent Drude weight decreases with increasing dimensionality. The Hall coefficient shows a strong crossover at T_{PG} below which it has large amplitude for small doping concentration.
The scaling behaviors of anisotropic flows of light charged particles are studied for 25 \,MeV/nucleon $^{40}$Ca+$^{40}$Ca collisions at different impact parameters by the isospin-dependent quantum molecular dynamics model. The number of nucleons scaling of elliptic flow is existed and the scaling of the ratios of $v_{4}/v_{2}^{2}$ and $v_{3}/(v_{1}v_{2})$ are applicable for collisions at almost all impact parameters except for peripheral collisions.
We give formulas for the image Milnor number of a weighted-homogeneous map-germ $(\mathbb{C}^n,0)\to(\mathbb{C}^{n+1},0)$, for $n=4$ and $5$, in terms of weights and degrees. Our expressions are obtained by a purely interpolative method, applied to a result by Ohmoto. We use our approach to recover the formulas for $n=2$ and $3$ due to Mond and Ohmoto, respectively. For $n\geq 6$, the method is valid as long as certain multi-singularity conjecture holds.
The ratio of the number of muons with a threshold of 1 GeV and charged particles at a distance of 600 m from the axis is analyzed. Air showers with energies above 5 EeV and zenith angles with less than 60 degrees are considered. Comparison of experimental data with calculations by the QGSJETII-04 model for various primary nuclei, including a gamma ray, showed that the mass composition of cosmic rays up to energies of $\sim$ 10 EeV mainly consists of protons and helium nuclei, with a small number of heavy nuclei. Data include air showers with a very low muon content, which are assumed to be produced by primary gamma rays.
Mn ions' doping site and valence were studied in PbTiO$_{3}$ (PT) with the native vacancy defects by the first-principles calculations. Firstly, the native vacancy defects of Pb, O and Ti in PT were investigated and it was found that Pb vacancy is preferred to others. And then the growth of Mn doped PT should be preferred to Mn ion substituting for an A-site Pb ion with +3 valence when Pb is deficient under equilibrium conditions driven solely by minimization of the formation energy, and this could result in a larger lattice distortion of PT. In addition, when Mn enters the Pb site, the electronegativity of O becomes weaker which makes the domain movement easier in PT to improve the performance of PT, while Mn ion substitution for a B-site Ti ion is the opposite.
The Gamma kernel is a projection kernel of the form (A(x)B(y)-B(x)A(y))/(x-y), where A and B are certain functions on the one-dimensional lattice expressed through Euler's Gamma function. The Gamma kernel depends on two continuous parameters; its principal minors serve as the correlation functions of a determinantal probability measure P defined on the space of infinite point configurations on the lattice. As was shown earlier (Borodin and Olshanski, Advances in Math. 194 (2005), 141-202; arXiv:math-ph/0305043), P describes the asymptotics of certain ensembles of random partitions in a limit regime.   Theorem: The determinantal measure P is quasi-invariant with respect to finitary permutations of the nodes of the lattice.   This result is motivated by an application to a model of infinite particle stochastic dynamics.
The TDA and RPA many-body methods are applied to a QCD motivated Hamiltonian in the Coulomb gauge. The gluon effects in the low energy domain are accounted for by the Instantaneous color-Coulomb Interaction between color-charge densities, approximated by the sum of a Coulomb and a confining linear potentials. We use the eigenfunctions of the harmonic oscillator as a basis for the quantization of the quark fields, and discuss how suitable this basis is in various steps of the calculation. We show that the TDA results already reproduce the gross-structure of the light flavored meson states. The pion-like state in the RPA description, which is a highly collective state, is in a better agreement with the experimental value. The results are related to other nonperturbative treatments and compared to experimental data. We discuss the advantages of the present approach.
Although the mechanisms responsible for heating the Sun's corona and accelerating the solar wind are still being actively investigated, it is largely accepted that photospheric motions provide the energy source and that the magnetic field must play a key role in the process. \citet{2010ApJ...708L.116V} presented a model for heating and accelerating the solar wind based on the turbulent dissipation of Alfv\'en waves. We first use a time-dependent model of the solar wind to reproduce one of \citeauthor{2010ApJ...708L.116V}'s solutions; then we extend its application to the case when the energy equation includes thermal conduction and radiation losses, and the upper chromosphere is part of the computational domain. Using this model, we explore parameter space and describe the characteristics of a fast-solar-wind solution. We discuss how this formulation may be applied to a 3D MHD model of the coron a and solar wind \citep{2009ApJ...690..902L}.