ShantanuT01/DACTYL-Pretraining huggingface dataset:
In this paper, we consider the fully coupled forward-backward stochastic functional differential equations (FBSFDEs) with stochastic functional differential equations as the forward equations and the generalized anticipated backward stochastic differential equations as the backward equations. We will prove the existence and uniqueness theorem for FBSFDEs. As an application, we deal with a quadratic optimal control problem for functional stochastic systems, and get the explicit form of the optimal control by virtue of FBSFDEs.
A tight-binding model with randomly fluctuating atomic positions is studied to discuss the effect of strong disorder in graphene. We employ a strong-disorder expansion for the transport quantities and find a diffusive behavior, where the conductivity is decreasing with increasing disorder. Surprisingly, the magnetic field drops out of the transport quantities in leading order of this expansion. This signals a strong suppression of magnetotransport effects for sufficiently strong disorder. This result is consistent with recent experimental observations by Morozov {\it et al.}
In this paper we consider the Suzuki curve $y^q + y = x^{q_0}(x^q + x)$ over the field with $q = 2^{2m+1}$ elements. The automorphism group of this curve is known to be the Suzuki group $Sz(q)$ with $q^2(q-1)(q^2+1)$ elements. We construct AG codes over $\mathbb{F}_{q^4}$ from a $Sz(q)$-invariant divisor $D$, giving an explicit basis for the Riemann-Roch space $L(\ell D)$ for $0 < \ell \leq q^2-1$. These codes then have the full Suzuki group $Sz(q)$ as their automorphism group. These families of codes have very good parameters and are explicitly constructed with information rate close to one. The dual codes of these families are of the same kind if $2g-1 \leq \ell \leq q^2-1$.
We study the asymptotic behaviour of a $d$-dimensional self-interacting random walk $X_n$ ($n = 1,2,...$) which is repelled or attracted by the centre of mass $G_n = n^{-1} \sum_{i=1}^n X_i$ of its previous trajectory. The walk's trajectory $(X_1,...,X_n)$ models a random polymer chain in either poor or good solvent. In addition to some natural regularity conditions, we assume that the walk has one-step mean drift directed either towards or away from its current centre of mass $G_n$ and of magnitude $\| X_n - G_n \|^{-\beta}$ for $\beta \geq 0$. When $\beta <1$ and the radial drift is outwards, we show that $X_n$ is transient with a limiting (random) direction and satisfies a super-diffusive law of large numbers: $n^{-1/(1+\beta)} X_n$ converges almost surely to some random vector. When $\beta \in (0,1)$ there is sub-ballistic rate of escape. For $\beta \geq 0$ we give almost-sure bounds on the norms $\|X_n\|$, which in the context of the polymer model reveal extended and collapsed phases. Analysis of the random walk, and in particular of $X_n - G_n$, leads to the study of real-valued time-inhomogeneous non-Markov processes $Z_n$ on $[0,\infty)$ with mean drifts at $x$ given approximately by $\rho x^{-\beta} - (x/n)$, where $\beta \geq 0$ and $\rho \in \R$. The study of such processes is a time-dependent variation on a classical problem of Lamperti; moreover, they arise naturally in the context of the distance of simple random walk on $\Z^d$ from its centre of mass, for which we also give an apparently new result. We give a recurrence classification and asymptotic theory for processes $Z_n$ just described, which enables us to deduce the complete recurrence classification (for any $\beta \geq 0$) of $X_n - G_n$ for our self-interacting walk.
Continuous Time Random Walk models (CTRW) of anomalous diffusion are studied, where the anomalous exponent $\beta(x) \in (0,1)$ varies in space. This type of situation occurs e.g. in biophysics, where the density of the intracellular matrix varies throughout a cell. Scaling limits of CTRWs are known to have probability distributions which solve fractional Fokker-Planck type equations (FFPE). This correspondence between stochastic processes and FFPE solutions has many useful extensions e.g. to nonlinear particle interactions and reactions, but has not yet been sufficiently developed for FFPEs of the"variable order" type with non-constant $\beta(x)$.   In this article, variable order FFPEs (VOFFPE) are derived from scaling limits of CTRWs. The key mathematical tool is the 1-1 correspondence of a CTRW scaling limit to a bivariate Langevin process, which tracks the cumulative sum of jumps in one component and the cumulative sum of waiting times in the other. The spatially varying anomalous exponent is modelled by spatially varying $\beta(x)$-stable L\'evy noise in the waiting time component. The VOFFPE displays a spatially heterogeneous temporal scaling behaviour, with generalized diffusivity and drift coefficients whose units are length$^2$/time$^{\beta(x)}$ resp. length/time$^{\beta(x)}$. A global change of the time scale results in a spatially varying change in diffusivity and drift.   A consequence of the mathematical derivation of a VOFFPE from CTRW limits in this article is that a solution of a VOFFPE can be approximated via Monte Carlo simulations. Based on such simulations, we are able to confirm that the VOFFPE is consistent under a change of the global time scale.
We derive global analytic representations of fundamental solutions for a class of linear parabolic systems with full coupling of first order derivative terms where coefficient may depend on space and time. Pointwise convergence of the global analytic expansion is proved. This leads to analytic representations of solutions of initial-boundary problems of first and second type in terms of convolution integrals or convolution integrals and linear integral equations. The results have both analytical and numerical impact. Analytically, our representations of fundamental solutions of coupled parabolic systems may be used to define generalized stochastic processes. Moreover, some classical analytical results based on a priori estimates of elliptic equations are a simple corollary of our main result. Numerically, accurate, stable and efficient schemes for computation and error estimates in strong norms can be obtained for a considerable class of Cauchy- and initial-boundary problems of parabolic type. Furthermore, there are obvious and less obvious applications to finance and physics. Warning: The argument given in the current version is only valid in special cases (essentially the scalar case). A more involved argument is needed for systems and will be communicated soon in a replacement,
A ribbon is a first-order thickening of a non-singular curve. Motivated by a question of Eisenbud and Green, we show that a compactification of the moduli space of line bundles on a ribbon is given by the moduli space of semi-stable sheaves. We then describe the geometry of this space, determining the irreducible components, the connected components, and the smooth locus.
We investigate the renormalization group flow of the Yukawa model with a fixed momentum cutoff at the leading order in 1/N, where N is the number of the fermion species. We demonstrate the scale invariance of coupling constants of the Nambu-Jona-Lasinio model.
We present an X-ray spectral analysis of a sample of 8 bona-fide Seyfert 2 galaxies, selected on the basis of their high $[OIII]\lambda5007$ flux, from the Ho et al. (1997) spectroscopic sample of nearby galaxies. We find that, in general, the X-ray spectra of our Seyfert 2 galaxies are complex, with some our objects having spectra different from the 'typical' spectrum of X-ray selected Seyfert 2 galaxies. Two (NGC3147 and NGC4698) show no evidence for intrinsic absorption. We suggest this is due to the fact that when the torus suppresses the intrinsic medium and hard energy flux, underlying emission from the host galaxy, originating in circumnuclear starbursts, and scattering from warm absorbers contributes in these energy bands more significantly. Our asca data alone cannot discriminate whether low absorption objects are Compton-thick AGN with a strong scattered component or lack an obscuring torus. The most striking example of our low absorption Seyfert 2 is NGC4698. Its spectrum could be explained by either a dusty warm absorber or a lack of broad line clouds so that its appearance as a Seyfert 2 is intrinsic and not due to absorption.
We present a complete quantum mechanical description of a flat FRW universe with equation of state p=\rho. We find a detailed correspondence with our heuristic picture of such a universe as a dense black hole fluid. Features of the geometry are derived from purely quantum input.
We study degree 2 and 4 elliptic subcovers of hyperelliptic curves of genus 3 defined over $\mathbb C$. The family of genus 3 hyperelliptic curves which have a degree 2 cover to an elliptic curve $E$ and degree 4 covers to elliptic curves $E_1$ and $E_2$ is a 2-dimensional subvariety of the hyperelliptic moduli $\mathcal H_3$. We determine this subvariety explicitly. For any given moduli point $\mathfrak p \in \mathcal H_3$ we determine explicitly if the corresponding genus 3 curve $\mathcal X$ belongs or not to such family. When it does, we can determine elliptic subcovers $E$, $E_1$, and $E_2$ in terms of the absolute invariants $t_1, \dots, t_6$ as in \cite{hyp_mod_3}. This variety provides a new family of hyperelliptic curves of genus 3 for which the Jacobians completely split. The sublocus of such family when $E_1$ is isomorphic to $E_2$ is a 1-dimensional variety which we determine explicitly. We can also determine $\mathcal X$ and $E$ starting form the $j$-invariant of $E_1$.
We report on a discovery of an X-ray emitting circumstellar material knot inside the synchrotron dominant supernova remnant (SNR) RX J1713.7-3946. This knot was previously thought to be a Wolf-Rayet star (WR 85), but we realized that it is in fact $\sim$40$^{\prime\prime}$ away from WR 85, indicating no relation to WR 85. We performed high-resolution X-ray spectroscopy with the Reflection Grating Spectrometer (RGS) on board XMM-Newton. The RGS spectrum clearly resolves a number of emission lines, such as N Ly$\alpha$, O Ly$\alpha$, Fe XVIII, Ne X, Mg XI, and Si XIII. The spectrum can be well represented by an absorbed thermal emission model with a temperature of $k_{\rm B}T_{\rm e} = 0.65\pm 0.02$ keV. The elemental abundances are obtained to be ${\rm N/H} = 3.5\pm 0.8{\rm \left(N/H\right)_{\odot}}$, ${\rm O/H} = 0.5\pm0.1{\rm \left(O/H\right)_{\odot}}$, ${\rm Ne/H} = 0.9\pm0.1{\rm \left(Ne/H\right)_{\odot}}$, ${\rm Mg/H} = 1.0\pm0.1{\rm \left(Mg/H\right)_{\odot}}$, ${\rm Si/H} = 1.0\pm0.2{\rm \left(Si/H\right)_{\odot}}$, and ${\rm Fe/H} = 1.3\pm0.1{\rm \left(Fe/H\right)_{\odot}}$. The enhanced N abundance with others being about the solar values allows us to infer that this knot is circumstellar material ejected when the progenitor star evolved into a red supergiant. The abundance ratio of N to O is obtained to be $\rm N/O = 6.8_{-2.1}^{+2.5}\left(N/O\right)_{\odot}$. By comparing this to those in outer layers of red supergiant stars expected from stellar evolution simulations, we estimate the initial mass of the progenitor star to be $15\, \rm M_{\odot} \lesssim \rm M \lesssim 20\, \rm M_{\odot}$.
We present ALMA observations of the $^{12}$CO (2--1) line of the newly born ($t_\mathrm{radio}\sim10^2$ years) active galactic nucleus (AGN), PKS B1718-649. These observations reveal that the carbon monoxide in the innermost 15 kpc of the galaxy is distributed in a complex warped disk. In the outer parts of this disk, the CO gas follows the rotation of the dust lane and of the stellar body of the galaxy hosting the radio source. In the innermost kiloparsec, the gas abruptly changes orientation and forms a circumnuclear disk ($r\lesssim700$ pc) with its major axis perpendicular to that of the outer disk. Against the compact radio emission of PKS B1718-649 ($r\sim 2$ pc), we detect an absorption line at red-shifted velocities with respect to the systemic velocity ($\Delta v = +365\pm22$\kms). This absorbing CO gas could trace molecular clouds falling onto the central super-massive black hole. A comparison with the near-infra red H$_{\,2}$ 1-0 S(1) observations shows that the clouds must be close to the black hole ($r\lesssim 75$ pc). The physical conditions of these clouds are different from the gas at larger radii, and are in good agreement with the predictions for the conditions of the gas when cold chaotic accretion triggers an active galactic nucleus. These observations on the centre of PKS B1718-649 provide one of the best indications that a population of cold clouds is falling towards a radio AGN, likely fuelling its activity.
The effects of atomic diffusion on internal and surface abundances of A and F pre-main-sequence stars with mass loss are studied in order to determine at what age the effects materialize, as well as to further understand the processes at play in HAeBe and young ApBp stars. Self-consistent stellar evolution models of 1.5 to 2.8Msun with atomic diffusion (including radiative accelerations) for all species within the OPAL opacity database were computed and compared to observations of HAeBe stars. Atomic diffusion in the presence of weak mass loss can explain the observed abundance anomalies of pre-main-sequence stars, as well as the presence of binary systems with metal rich primaries and chemically normal secondaries such as V380 Ori and HD72106. This is in contrast to turbulence models which do not allow for abundance anomalies to develop on the pre-main-sequence. The age at which anomalies can appear depends on stellar mass. For A and F stars, the effects of atomic diffusion can modify both the internal and surface abundances before the onset of the MS. The appearance of important surface abundance anomalies on the pre-main-sequence does not require mass loss, though the mass loss rate affects their amplitude. Observational tests are suggested to decipher the effects of mass loss from those of turbulent mixing. If abundance anomalies are confirmed in pre-main-sequence stars they would severely limit the role of turbulence in these stars.
Recent works demonstrated that remote sensing observations of shock waves propagating into the corona and associated with major solar eruptions can be used to derive the strength of coronal magnetic fields met by the shock over a very large interval of heliocentric distances and latitudes. This opinion article will summarize most recent results obtained on this topic and will discuss the weaknesses and strengths of these techniques to open a constructive discussion with the scientific community.
The theoretical treatment of alpha decay by Gamow is revisited by investigating the quantum time scales in tunneling. The time spent by an alpha particle in front of the barrier and traversing it before escape is evaluated using microscopic alpha nucleus potentials. The half-life of a nucleus is shown to correspond to the time spent by the alpha knocking in front of the barrier. Calculations for medium and super heavy nuclei show that from a multitude of available tunneling time definitions, the transmission dwell time gives the bulk of the lifetime of the decaying state, in most cases.
The renormalization of the NN interaction with the Chiral Two Pion Exchange Potential computed using relativistic baryon chiral perturbation theory is considered. The short distance singularity reduces the number of counter-terms to about a half as those in the heavy-baryon expansion. Phase shifts and deuteron properties are evaluated and a general overall agreement is observed.
We present the first constraints on cosmology from the Dark Energy Survey (DES), using weak lensing measurements from the preliminary Science Verification (SV) data. We use 139 square degrees of SV data, which is less than 3\% of the full DES survey area. Using cosmic shear 2-point measurements over three redshift bins we find $\sigma_8 (\Omega_{\rm m}/0.3)^{0.5} = 0.81 \pm 0.06$ (68\% confidence), after marginalising over 7 systematics parameters and 3 other cosmological parameters. We examine the robustness of our results to the choice of data vector and systematics assumed, and find them to be stable. About $20$\% of our error bar comes from marginalising over shear and photometric redshift calibration uncertainties. The current state-of-the-art cosmic shear measurements from CFHTLenS are mildly discrepant with the cosmological constraints from Planck CMB data; our results are consistent with both datasets. Our uncertainties are $\sim$30\% larger than those from CFHTLenS when we carry out a comparable analysis of the two datasets, which we attribute largely to the lower number density of our shear catalogue. We investigate constraints on dark energy and find that, with this small fraction of the full survey, the DES SV constraints make negligible impact on the Planck constraints. The moderate disagreement between the CFHTLenS and Planck values of $\sigma_8 (\Omega_{\rm m}/0.3)^{0.5}$ is present regardless of the value of $w$.
We examine the advantages that quantum strategies afford in communication-limited games. Inspired by the card game blackjack, we focus on cooperative, two-party sequential games in which a single classical bit of communication is allowed from the player who moves first to the player who moves second. Within this setting, we explore the usage of quantum entanglement between the players and find analytic and numerical conditions for quantum advantage over classical strategies. Using these conditions, we study a family of blackjack-type games with varying numbers of card types, and find a range of parameters where quantum advantage is achieved. Furthermore, we give an explicit quantum circuit for the strategy achieving quantum advantage.
We develop a Split Reactive Brownian Dynamics (SRBD) algorithm for particle simulations of reaction-diffusion systems based on the Doi or volume reactivity model, in which pairs of particles react with a specified Poisson rate if they are closer than a chosen reactive distance. In our Doi model, we ensure that the microscopic reaction rules for various association and disassociation reactions are consistent with detailed balance (time reversibility) at thermodynamic equilibrium. The SRBD algorithm uses Strang splitting in time to separate reaction and diffusion, and solves both the diffusion-only and reaction-only subproblems exactly, even at high packing densities. To efficiently process reactions without uncontrolled approximations, SRBD employs an event-driven algorithm that processes reactions in a time-ordered sequence over the duration of the time step. A grid of cells with size larger than all of the reactive distances is used to schedule and process the reactions, but unlike traditional grid-based methods such as Reaction-Diffusion Master Equation (RDME) algorithms, the results of SRBD are statistically independent of the size of the grid used to accelerate the processing of reactions. We use the SRBD algorithm to compute the effective macroscopic reaction rate for both reaction- and diffusion-limited irreversible association in three dimensions. We also study long-time tails in the time correlation functions for reversible association at thermodynamic equilibrium. Finally, we compare different particle and continuum methods on a model exhibiting a Turing-like instability and pattern formation. We find that for models in which particles diffuse off lattice, such as the Doi model, reactions lead to a spurious enhancement of the effective diffusion coefficients.
Recently, Lee et al. used Gaussian mixture models (GMM) to study the radio pulsar population. In the distribution of normal pulsars in the P-dotP plane, they found four clusters. We develop this approach further and apply it to different synthetic pulsar populations in order to determine whether the method can effectively select groups of sources that are physically different. We check several combinations of initial conditions as well as the models of pulsar evolution and the selection effects. We find that in the case of rapidly evolving objects, the GMM is oversensitive to parameter variations and does not produce stable results. We conclude that the method does not help much to identify the sub-populations with different initial parameters or/and evolutionary paths. For the same reason, the GMM does not discriminate effectively between theoretical population synthesis models of normal radio pulsars.
We propose a simple test to demonstrate and detect the presence of vacuum inducde coherence in a $\Lambda$-system. We show that the probe field absorption is modulated due to the presence of such a coherence which is unobservable in fluorescence. We present analytical and numerical results for the modulated absorption, the cosine and sine components of which display different types of behavior.
It is shown that the amplitude of elastic ed scattering beyond Born approximation contains six generalized form factors, but only three linearly independent combinations of them (generalized charge, quadrupole and magnetic form factors) contribute to the reaction cross section in the second order perturbation theory. We examine two-photon exchange and find that it includes two types of diagrams, when two virtual photons interact with the same nucleon and when the photons interact with different nucleons.We discuss contribution of the two-photon exchange in reaction observables, generalized \mathcal A and \mathcal B structure functions and tensor polarization of the deuteron.
We present estimates of intrinsic scatter in the Star Formation Rate (SFR) - Stellar Mass (M*) correlation in the redshift range 0.5 < z < 3.0 and in the mass range 10^7 < M* < 10^11 Msun. We utilize photometry in the Hubble Ultradeep Field (HUDF12), Ultraviolet Ultra Deep Field (UVUDF) campaigns and CANDELS/GOODS-S. We estimate SFR, M* from broadband Spectral Energy Distributions (SEDs) and the best available redshifts. The maximum depth of the HUDF photometry (F160W 29.9 AB, 5 sigma depth) probes the SFR-M* correlation down to M* ~ 10 ^7 Msun, a factor of 10-100X lower in M* than previous studies, and comparable to dwarf galaxies in the local universe. We find the slope of the SFR-M* relationship to be near unity at all redshifts and the normalization to decrease with cosmic time. We find a moderate increase in intrinsic scatter with cosmic time from 0.2 to 0.4 dex across the epoch of peak cosmic star formation. None of our redshift bins show a statistically significant increase in intrinsic scatter at low mass. However, it remains possible that intrinsic scatter increases at low mass on timescales shorter than ~ 100 Myr. Our results are consistent with a picture of gradual and self-similar assembly of galaxies across more than three orders of magnitude in stellar mass from as low as 10^7 Msun.
HSTphot, a photometry package designed to handle the undersampled PSFs found in WFPC2 images, is introduced and described, as well as some of the considerations that have to be made in order to obtain accurate PSF-fitting stellar photometry with WFPC2 data. Tests of HSTphot's internal reliability are made using multiple observations of the same field, and tests of external reliability are made by comparing with DoPHOT reductions of the same data.
We revisit staircases for words and prove several exact as well as asymptotic results for longest left-most staircase subsequences and subwords and staircase separation number, the latter being defined as the number of consecutive maximal staircase subwords packed in a word. We study asymptotic properties of the sequence $h_{r,k}(n),$ the number of $n$-array words with $r$ separations over alphabet $[k]$ and show that for any $r\geq 0,$ the growth sequence $\big(h_{r,k}(n)\big)^{1/n}$ converges to a characterized limit, independent of $r.$ In addition, we study the asymptotic behavior of the random variable $\mathcal{S}_k(n),$ the number of staircase separations in a random word in $[k]^n$ and obtain several limit theorems for the distribution of $\mathcal{S}_k(n),$ including a law of large numbers, a central limit theorem, and the exact growth rate of the entropy of $\mathcal{S}_k(n).$ Finally, we obtain similar results, including growth limits, for longest $L$-staircase subwords and subsequences.