ShantanuT01/DACTYL-Pretraining huggingface dataset:
Sondow et al have studied Ramanujan primes (RPs) and observed numerically that, while half of all primes are RPs asymptotically, one obtains runs of consecutives RPs (resp. non-RPs) which are statistically significantly longer than one would expect if one was tossing an unbiased coin. In this discussion paper we attempt a heuristic explanation of this phenomenon. Our heuristic follows naturally from the Prime Number Theorem, but seems to be only partly satisfactory. It motivates why one should obtain long runs of both RPs and non-RPs, and also longer runs of non-RPs than of RPs. However, it also suggests that one should obtain longer runs of RPs than have so far been observed in the data, and this issue remains puzzling.
Given a property of representations satisfying a basic stability condition, Ramakrishna developed a variant of Mazur's Galois deformation theory for representations with that property. We introduce an axiomatic definition of pseudorepresentations with such a property. Among other things, we show that pseudorepresentations with a property enjoy a good deformation theory, generalizing Ramakrishna's theory to pseudorepresentations.
The state-of-the-art physics consists of two irreconcilable branches, i.e., the quantum theory and the general relativity, which work well in their own territories, independently. However, what are quantum and spacetime after all? The key question was never addressed, satisfactorily. In this work, we describe a possibility to reformulate the quantum theory in the Minkowski spacetime from the viewpoint of classic physics in the Euclidean spacetime, i.e., classic mechanics and stochastic process theory. We show that quantum theory and Minkowski spacetime may connect with each other and emerge from a single fundamental entity.
After shortly reviewing the fundamentals of approach theory as introduced by R. Lowen in 1989, we show that this theory is intimately related with the well-known Wasserstein metric on the space of probability measures with a finite first moment on a complete and separable metric space. More precisely, we introduce a canonical approach structure, called the contractive approach structure, and prove that it is metrized by the Wasserstein metric. The key ingredients of the proof of this result are Dini's Theorem, Ascoli's Theorem, and the fact that the class of real-valued contractions on a metric space has some nice stability properties. We then combine the obtained result with Prokhorov's Theorem to establish inequalities between the relative Hausdorff measure of non-compactness for the Wasserstein metric and a canonical measure of non-uniform integrability.
Theories of the magnetotransport, based on the quasipartricle of the Fermi-liquid, in the normal state of high-Tc cuprate superconductors, are critically examined and the necessity of the collective transport theory beyond the quasiparticle is discussed.
In this paper, we attempt to find out the `spectro-temporal' characteristics during the jet ejection, of several outbursting Galactic black hole sources based on RXTE-PCA/HEXTE data in the energy band of 2 - 100 keV. We present results of detailed analysis of these sources during the rising phase of their outburst, whenever simultaneous or near-simultaneous X-ray and Radio observations are `available'. We find that before the peak radio flare (transient jet) a few of the sources (in addition to those reported earlier) exhibit `local' softening within the soft intermediate state itself. Except the duration, all the properties of the `local' softening (QPO not observed, reduction in total rms, soft spectra) are observed to be similar to the canonical soft state. We find similar `local' softening for the recent outburst of V404 Cyg also based on SWIFT observations. Fast changes in the `spectro-temporal' properties during the `local' softening implies that it may not be occurring due to change in Keplerian accretion rate. We discuss these results in the framework of the magnetized two component advective flow model.
We introduce the Local Increasing Regularity Method (LIRM) which allows us to get from \emph{local} a priori estimates, on solutions $u$ of a linear equation $\displaystyle Du=\omega ,$ \emph{global} ones.   As an application we shall prove that if $D$ is an elliptic linear differential operator of order $m$ with ${\mathcal{C}}^{\infty }$ coefficients operating on the sections of a complex vector bundle $\displaystyle G:=(H,\pi ,M)$ over a compact Riemannian manifold $M$ without boundary and $\omega \in L^{r}_{G}(M)\cap (\mathrm{k}\mathrm{e}\mathrm{r}D^{*})^{\perp },$ then there is a $u\in W^{m,r}_{G}(M)$ such that $Du=\omega $ on $M.$ \quad Next we investigate the case of a compact manifold with boundary by use of the "riemannian double manifold". In the last sections we study the more delicate case of a complete but non compact Riemannian manifold by use of adapted weights.
This article deals with a cosmological scenario in $ f(R,T) $ gravity for a flat FLRW model of the universe. We consider the $ f(R,T) $ function as $ f(R)+f(T) $ which starts with a quadratic correction of the geometric term $ f(R) $ having structure $ f(R)=R+\alpha R^2 $, and a linear matter term $ f(T)=2\lambda T $. To achieve the solution of the gravitational field equations in the $ f(R,T) $ formalism, we take the form of a geometrical parameter, i.e. scale factor $ a(t)= sinh^{\frac{1}{n}}(\beta t) $ \cite{cha}, where $ \beta $ and $ n $ are model parameters. An eternal acceleration can be predicted by the model for $ 0<n<1 $, while the cosmic transition from the early decelerated phase to the present accelerated epoch can be anticipated for $ n\geq 1 $. The obtained model facilitate the formation of structure in the Universe according to the Jeans instability condition as our model transits from radiation dominated era to matter dominated era. We study the varying role of the equation of state parameter $ \omega $. We analyze our model by studying the behavior of the scalar field and discuss the energy conditions on our achieved solution. We examine the validity of our model via Jerk parameter, Om diagnostic, Velocity of sound and Statefinder diagnostic tools. We investigate the constraints on the model parameter $ n $ and $ H_0 $ (Hubble constant) using some observational datasets: $SNeIa$ dataset, $ H(z)$ (Hubble parameter) dataset, $ BAO $ (Baryon Acoustic Oscillation data) and their combinations as joint observational datasets $ H(z)$ + $ SNeIa $ and $ H(z)$ + $ SNeIa $ + $ BAO $. It is testified that the present study is well consistent with these observations. We also perform some cosmological tests and a detailed discussion of the model.
We consider a functional relation between a given Wilsonian RG flow, which has to be related to a specific coarse-graining procedure, and an infinite family of (UV cutoff) scale dependent field redefinitions. Within this framework one can define a family of Wilsonian proper-time exact RG equations associated to an arbitrary regulator function. New applications of these RG flow schemes to the Ising Universality class in three dimensions in the derivative expansion are shortly illustrated.
We study some phenomenological consequences of having moduli fields with large vacuum expectation values (v.e.v.). The v.e.vs of the moduli are dynamically determined once supersymmetry is broken in 4D string theories. The study constraints the possible Yukawa interactions and modular weights for matter fields.
We present a method for measuring the cosmic expansion history H(z) in uncorrelated redshift bins, and apply it to current and simulated type Ia supernova data assuming spatial flatness. If the matter density parameter Omega_m can be accurately measured from other data, then the dark energy density history X(z)=rho_X(z)/rho_X(0) can trivially be derived from this expansion history H(z). In contrast to customary ``black box'' parameter fitting, our method is transparent and easy to interpret: the measurement of H(z)^{-1} in a redshift bin is simply a linear combination of the measured comoving distances for supernovae in that bin, making it obvious how systematic errors propagate from input to output.   We find the Riess et al. (2004) ``gold'' sample to be consistent with the ``vanilla'' concordance model where the dark energy is a cosmological constant. We compare two mission concepts for the NASA/DOE Joint Dark Energy Mission (JDEM), the Joint Efficient Dark-energy Investigation (JEDI), and the Supernova Accelaration Probe (SNAP), using simulated data including the effect of weak lensing (based on numerical simulations) and a systematic bias from K-corrections. Estimating H(z) in seven uncorrelated redshift bins, we find that both provide dramatic improvements over current data: JEDI can measure H(z) to about 10% accuracy and SNAP to 30-40% accuracy.
We examine the Casimir effect for a perfectly conducting cylinder of elliptical section, taking as reference the known case of circular section. The zero-point energy of this system is evaluated by the mode summation method, using the ellipticity as a perturbation parameter. Mathieu function techniques are applied.
In this work we present a generalized Laplace method for a formal, simple, quasi-classical, determination of the outer and inner horizon radius of Kerr-Newman black hole. We consider classical gravitational interaction between a thin, with homogeneously distributed mass and electric charge, spherical (black) shell and a probe particle. Also, we use relativistic equivalence principle. Finally we suppose that probe particle propagates radially to shell with speed of light while tangentially it rotates in common with shell, so that total energy of a probe particle equals zero.
We present for the first time the complete twist-4 result for the semi-inclusive deeply inelastic scattering $e^- N \to e^-qX$ with polarized electron and proton beams at the tree level of pQCD. The calculations have been carried out using the formulism obtained after collinear expansion where the multiple gluon scattering are taken into account and gauge links are obtained automatically in a systematical way. The results show in particular that there are twist-4 contributions to all the eight twist-2 structure functions for $e^- N \to e^-hX$ that correspond to the eight twist-2 transverse momentum dependent parton distribution functions. Such higher twist effects could be very significant and therefore have important impacts on extracting these three-dimensional parton distribution functions from the asymmetry data on $e^- N \to e^-hX$. We suggest also an approximate way for a rough estimation of such higher twist contributions.
We consider the modified Zakharov-Kuznetsov (mZK) equation in two space dimensions in both focusing and defocusing cases. Using the $I$-method, we prove the global well-posedness of the $H^s$ solutions for $s>\frac{3}{4}$ for any data in the defocusing case and under the assumption that the mass of the initial data is less than the mass of the ground state solution of $\Delta \varphi - \varphi + \varphi^3 = 0$ in the focusing case. This improves the global well-posedness result of Linares and Pastor [20].
Unsupervised domain adaptation (UDA) has been vastly explored to alleviate domain shifts between source and target domains, by applying a well-performed model in an unlabeled target domain via supervision of a labeled source domain. Recent literature, however, has indicated that the performance is still far from satisfactory in the presence of significant domain shifts. Nonetheless, delineating a few target samples is usually manageable and particularly worthwhile, due to the substantial performance gain. Inspired by this, we aim to develop semi-supervised domain adaptation (SSDA) for medical image segmentation, which is largely underexplored. We, thus, propose to exploit both labeled source and target domain data, in addition to unlabeled target data in a unified manner. Specifically, we present a novel asymmetric co-training (ACT) framework to integrate these subsets and avoid the domination of the source domain data. Following a divide-and-conquer strategy, we explicitly decouple the label supervisions in SSDA into two asymmetric sub-tasks, including semi-supervised learning (SSL) and UDA, and leverage different knowledge from two segmentors to take into account the distinction between the source and target label supervisions. The knowledge learned in the two modules is then adaptively integrated with ACT, by iteratively teaching each other, based on the confidence-aware pseudo-label. In addition, pseudo label noise is well-controlled with an exponential MixUp decay scheme for smooth propagation. Experiments on cross-modality brain tumor MRI segmentation tasks using the BraTS18 database showed, even with limited labeled target samples, ACT yielded marked improvements over UDA and state-of-the-art SSDA methods and approached an "upper bound" of supervised joint training.
A hybrid system composed of an isotropic nanoparticle and a semiconductor heterostructure with a quantum well has been considered. The nanoparticle is supposed to be polarizable in an external electric field. A theoretical model of the hybrid system is substantiated and formulated. Exact solutions of the model equations are obtained. The frequencies of charge oscillations in the hybrid system and their damping owing to the dipole--plasmon interaction are found, the damping mechanism being similar to that of Landau damping. The space-time behavior of concentration perturbations in the two-dimensional electron gas is analyzed, and the polarization oscillations of a nanoparticle are studied. The induced polarization of a nanoparticle at nonzero electron drift velocities is found to have a complicated dynamics. In particular, the polarization vector circulates along elliptic trajectories for two of three frequency dispersion branches. If the electric current flows through the quantum well due to an applied electric field, the damping of oscillations in the hybrid system is replaced by their growth in time, which corresponds to the electric instability of the system. New phenomena in hybrid systems can be used to excite the emission of nanoparticles by an electric current and to electrically stimulate the emission in the terahertz spectral range.
Understanding the statistical behavior of the heat in stochastic systems gives us insight about the thermodynamics of such systems. Using the recently proposed Relativistic Stochastic Thermodynamics, we investigate the statistics of the heat of a Relativistic Ornstein-Uhlenbeck particle, comparing with the classical cases. The results are exact through numerical integration of the Fokker-Planck of the joint distribution, and are validated by numerical simulations.
The generating entangled state by using a 50/50 beamsplitter has been discussed in the literature before . In this paper we explore how to use an asymmetric beam-splitter to produce a new kind of entangled state. We construct such kind of states theoretically and then prove that they make up a complete and orthonormal representation in two-mode Fock space. Its application in finding new squeezing operator and new squeezed state is introduced.
A procedure is developed to rigorously decompose experimental loss spectra of medium-energy electrons reflected from solid surfaces into contributions due to surface and volume electronic excitations. This can be achieved by analysis of two spectra acquired under different experimental conditions, e.g. measured at two different energies and/or geometrical configurations. The input parameters of this procedure comprise the elastic scattering cross section and the inelastic mean free path for volume scattering. The (normalized) differential inelastic mean free path as well as the differential surface excitation probability are retrieved by this procedure. Reflection electron energy loss spectroscopy (REELS) data for Si, Cu and Au are subjected to this procedure and the retrieved differential surface and volume excitation probabilities are compared with data from the literature. The results verify the commonly accepted model for medium energy electron transport in solids with unprecedented detail.
We analyze leptogenesis in the context of seesaw models with almost conserved lepton number, focusing on the L-conserving contribution to the flavoured CP asymmetries. We find that, contrary to previous claims, successful leptogenesis is feasible for masses of the lightest heavy neutrino as low as M1 ~ 10^6 GeV, without resorting to the resonant enhancement of the CP asymmetry for strongly degenerate heavy neutrinos. This lower limit renders thermal leptogenesis compatible with the gravitino bound in supersymmetric scenarios.
In this paper, we propose a new approach to singular limits of inviscid fluid flows based on the concept of dissipative measure-valued solutions. We show that dissipative measure-valued solutions of the compressible Euler equations converge to the smooth solution of the incompressible Euler system when the Mach number tends to zero. This holds both for well-prepared and ill-prepared initial data, where in the latter case the presence of acoustic waves causes difficulties. However this effect is eliminated on unbounded domains thanks to dispersion.
Certain smoothing inequalities were proposed in the recent paper posted on arXiv at arxiv:1301.2828 in order to lessen the very large gap between the best correctly established upper and lower bounds on the constant factor in the nonuniform Berry-Esseen bound. As an illustration of the possible uses of those inequalities, a quick proof of Nagaev's classical nonuniform bound was given there. Here we describe another, apparently more effective class of smoothing inequalities, and give a yet quicker and simpler proof of Nagaev's result.
Let $f$ and $g$ be weakly holomorphic modular functions on $\Gamma_0(N)$ with the trivial character. For an integer $d$, let $\Tr_d(f)$ denote the modular trace of $f$ of index $d$. Let $r$ be a rational number equivalent to $i\infty$ under the action of $\Gamma_0(4N)$. In this paper, we prove that, when $z$ goes radially to $r$, the limit $Q_{\hat{H}(f)}(r)$ of the sum $H(f)(z) = \sum_{d>0}\Tr_d(f)e^{2\pi idz}$ is a special value of a regularized twisted $L$-function defined by $\Tr_d(f)$ for $d\leq0$. It is proved that the regularized $L$-function is meromorphic on $\mathbb{C}$ and satisfies a certain functional equation. Finally, under the assumption that $N$ is square free, we prove that if $Q_{\hat{H}(f)}(r)=Q_{\hat{H}(g)}(r)$ for all $r$ equivalent to $i \infty$ under the action of $\Gamma_0(4N)$, then $\Tr_d(f)=\Tr_d(g)$ for all integers $d$.
Let $K$ be a imaginary quadratic field where the prime $p$ splits. Our goal in this article is to prove results towards the Iwasawa main conjectures for $p$-nearly-ordinary families associated to $\mathrm{GL}_2\times \mathrm{Res}_{K/\mathbb{Q}}\mathrm{GL}_1$ with a minimal set of assumptions. The main technical input is an improvement on the locally restricted Euler system machinery that allows the treatment of residually reducible cases, which we apply with the Beilinson--Flach Euler system.
We present a composite light-curve model of the symbiotic nova PU Vul (Nova Vulpeculae 1979) that shows a long-lasted flat optical peak followed by a slow decline. Our model light-curve consists of three components of emission, i.e., an outbursting white dwarf (WD), its M-giant companion, and nebulae. The WD component dominates in the flat peak while the nebulae dominate after the photospheric temperature of the WD rises to log T (K) >~ 4.5, suggesting its WD origin. We analyze the 1980 and 1994 eclipses to be total eclipses of the WD occulted by the pulsating M-giant companion with two sources of the nebular emission; one is an unocculted nebula of the M-giant's cool-wind origin and the other is a partially occulted nebula associated to the WD. We confirmed our theoretical outburst model of PU Vul by new observational estimates, that spanned 32 yr, of the temperature and radius. Also our eclipse analysis confirmed that the WD photosphere decreased by two orders of magnitude between the 1980 and 1994 eclipses. We obtain the reddening E(B-V) ~ 0.3 and distance to PU Vul d ~ 4.7 kpc. We interpret the recent recovery of brightness in terms of eclipse of the hot nebula surrounding the WD, suggesting that hydrogen burning is still going on. To detect supersoft X-rays, we recommend X-ray observations around June 2014 when absorption by neutral hydrogen is minimum.
The scaling behavior over four decades of the ratio of temperature T to magnetic field B observed in the magnetization in beta-YbAlB4 is theoretically examined. By developing a theoretical framework that exhibits the quantum critical phenomena of Yb-valence fluctuations under a magnetic field, we show that the T/B-scaling behavior can appear near the quantum critical point of the valence transition. The emergence of the T/B scaling indicates the presence of the small characteristic energy scale of critical Yb-valence fluctuations. It is argued that the quantum valence criticality offers a unified explanation for the unconventional quantum criticality as well as the T/B scaling in beta-YbAlB4.
To study some characteristics of the interstellar medium, observational data of pulsars with large Faraday rotation values (|RM|> 300 rad / m2) were used. It was suggested and justified that large |RM| values can be due to the contribution of the regions with increased electron concentration, projected on the pulsar. Most likely these are the HII regions, dark nebulae and molecular clouds. In these objects the magnetic field can be oriented in the direction of a large-scale field of the Galaxy, or simply is a deformed extension of the galactic field. It was shown that the Galactic distribution of rotation measures of pulsars with |RM|> 300rad / m2 corresponds to the circular model of the magnetic field of the Galaxy, with the counter-clockwise direction of the magnetic field in the galactocentric circle 5 kpc <R <7 kpc.
A graph $G$ is a $D\!D_2$-graph if it has a pair $(D,D_2)$ of disjoint sets of vertices of $G$ such that $D$ is a dominating set and $D_2$ is a 2-dominating set of $G$. We provide several characterizations and hardness results concerning $D\!D_2$-graphs.
Sharp bounds are obtained, under a variety of assumptions on the eigenvalues of the Einstein tensor, for the ratio of the Hawking mass to the areal radius in static, spherically symmetric space-times.
We explore the electronic and topological properties of single crystal SrAl$_2$Si$_2$ using magnetotransport experiments in conjunction with first-principle calculations. We find that the temperature-dependent resistivity shows a pronounced peak near 50 K. We observe several remarkable features at low temperatures, such as large non-saturating magnetoresistance, Shubnikov-de Haas oscillations and cusp-like magneto-conductivity. The maximum value of magnetoresistance turns out to be 459\% at 2 K and 12 T. The analysis of the cusp-like feature in magneto-conductivity indicates a clear signature of weak anti-localization. Our Hall resistivity measurements confirm the presence of two types of charge carriers in SrAl$_2$Si$_2$, with low carrier density.
Problems of finite-temperature quantum statistical mechanics can be formulated in terms of imaginary (Euclidean) -time Green's functions and self-energies. In the context of realistic Hamiltonians, the large energy scale of the Hamiltonian (as compared to temperature) necessitates a very precise representation of these functions. In this paper, we explore the representation of Green's functions and self-energies in terms of a series of Chebyshev polynomials. We show that many operations, including convolutions, Fourier transforms, and the solution of the Dyson equation, can straightforwardly be expressed in terms of the series expansion coefficients. We then compare the accuracy of the Chebyshev representation for realistic systems with the uniform-power grid representation, which is most commonly used in this context.