ShantanuT01/DACTYL-Pretraining huggingface dataset:
This work concerns controlled Markov chains with finite state and action spaces. The transition law satisfies the simultaneous Doeblin condition, and the performance of a control policy is measured by the (long-run) risk-sensitive average cost criterion associated to a positive, but otherwise arbitrary, risk sensitivity coefficient. Within this context, the optimal risk-sensitive average cost is characterized via a minimization problem in a finite-dimensional Euclidean space.
Based upon the Bonn meson-exchange model for the nucleon-nucleon ($NN$) interaction, we study systematically the charge-symmetry-breaking (CSB) of the $NN$ interaction due to nucleon mass splitting. Particular attention is payed to CSB generated by the $2\pi$-exchange contribution to the $NN$ interaction, $\pi\rho$ diagrams, and other multi-meson-exchanges. We calculate the CSB differences in the $^1S_0$ effective range parameters as well as phase shift differences in $S$, $P$ and higher partial waves up to 300 MeV lab. energy. We find a total CSB difference in the singlet scattering length of 1.6 fm which explains the empirical value accurately. The corresponding CSB phase-shift differences are appreciable at low energy in the $^1S_0$ state. In the other partial waves, the CSB splitting of the phase shifts is small and increases with energy, with typical values in the order of 0.1 deg at 300 MeV in $P$ and $D$ waves.
The artificial neural networks (ANNs) have emerged with successful applications in nuclear physics as well as in many fields of science in recent years. In this paper, by using (ANNs), we have constructed a formula for the nuclear charge radii. Statistical modeling of nuclear charge radii by using ANNs has been seen as to be successful. Also, the charge radii, binding energies and two-neutron separation energies of Sn isotopes have been calculated by implementing of the new formula in Hartree-Fock-Bogoliubov (HFB) calculations. The results of the study shows that the new formula is useful for describing nuclear charge radii.
In this paper we extend the boundary string field theory action for a non-BPS D-brane to the one including the target space fermions and the nonlinear supersymmetry with 32 supercharges up to some order. This is based on the idea that the vacuum with a non-BPS D-brane belongs to the spontaneously broken phase of the supersymmetry. As a result, we find that the action is almost uniquely determined up to the field redefinition ambiguities.
We show that every separable Gaussian process with integrable variance function admits a Fredholm representation with respect to a Brownian motion. We extend the Fredholm representation to a transfer principle and develop stochastic analysis by using it. We show the convenience of the Fredholm representation by giving applications to equivalence in law, bridges, series expansions, stochastic differential equations and maximum likelihood estimations.
Consider a branch of unstable solitons of NLS whose linearized operators have one pair of simple real eigenvalues in addition to the zero eigenvalue. Under radial symmetry and standard assumptions, solutions to initial data from a neighbourhood of the branch either converge to a soliton, or exit a larger neighbourhood of the branch transversally. The qualitative dynamic near a branch of unstable solitons is irrespective of whether blowup eventually occurs, which has practical implications for the description of blowup of NLS with supercritical nonlinearity.
Recent advances in time-domain astronomy have uncovered a new class of optical transients with timescales shorter than typical supernovae and a wide range of peak luminosities. Several subtypes have been identified within this broad class, including Ca-rich transients, .Ia supernovae, and fast/bright transients. We examine the predic- tions from a state-of-the-art grid of three-dimensional simulations of dynamical white dwarf interactions in the context of these fast optical transients. We find that for colli- sions involving carbon-oxygen or oxygen-neon white dwarfs the peak luminosities and durations of the light curves in our models are in good agreement with the properties of fast/bright transients. When one of the colliding white dwarfs is made of helium the properties of the light curves are similar to those of Ca-rich gap transients. The model lightcurves from our white dwarf collisions are too slow to reproduce those of .Ia SNe, and too fast to match any normal or peculiar Type Ia supernova.
We define a regularized Shintani theta lift which maps weight $2k+2$ ($k \in \Z, k \geq 0$) harmonic Maass forms for congruence subgroups to (sesqui-)harmonic Maass forms of weight $3/2+k$ for the Weil representation of an even lattice of signature $(1,2)$. We show that its Fourier coefficients are given by traces of CM values and regularized cycle integrals of the input harmonic Maass form. Further, the Shintani theta lift is related via the $\xi$-operator to the Millson theta lift studied in our earlier work. We use this connection to construct $\xi$-preimages of Zagier's weight $1/2$ generating series of singular moduli and of some of Ramanujan's mock theta functions.
Using simultaneous measurements of the attenuation and velocity of surface acoustic waves propagating along GaAs/Al$_{0.3}$Ga$_{0.7}$As heterostructures, complex ac conductance of the latters has been determined. In the magnetic fields corresponding to the middles of the Hall plateaus both the ac conductance, $\sigma (\omega)$, and the sheet electron density, $n_s$, in the two-dimensional conducting layer turn out to be dependent on the samples' cooling rate. As a result, the sample ``remembers'' the cooling conditions. The complex conductance is strongly dependent on an infrared illumination which also changes both $\sigma (\omega)$ and $n_s$. Remarkably, the correlation between $\sigma (\omega)$ and $n_s$ is \emph{universal}, i.e. it is independent of the way to change these quantities. The results are attributed to two-electron defects (so-called $DX^-$ centers) located in the Si doped layer.
The variation in the intensity of cosmic rays at small angular scales is attributed to the interstellar turbulence in the vicinity of the Solar system. We show that {a turbulent origin of the small-scale structures implies that} the morphology of the observed cosmic-ray intensity skymap varies with our location in the interstellar turbulence. The gyroradius of cosmic rays is shown to be the length scale associated with an observable change in the skymap over a radian angular scale. The extent to which the intensity \mpo{at a certain} angular scale varies is proportional to the change in our location with a maximum change of about the amplitude of intensity variation at that scale in the existing skymap.} We suggest that for TeV cosmic rays a measurable variation could occur over a time scale of a decade due to the Earth's motion through the interstellar medium, if interstellar turbulence persists down to the gyroradius, \mpo{about $00\ \mu\mathrm{pc}$ for TeV-ish cosmic rays}. Observational evidence of the variability, or an absence of it, could provide a useful insight into the physical origin of the small-scale anisotropy.
In this paper we study the homogenization of a class of energies concentrated on lines. In dimension $2$ (i.e., in codimension $1$) the problem reduces to the homogenization of partition energies studied by \cite{AB}. There, the key tool is the representation of partitions in terms of $BV$ functions with values in a discrete set. In our general case the key ingredient is the representation of closed loops with discrete multiplicity either as divergence-free matrix-valued measures supported on curves or with $1$-currents with multiplicity in a lattice. In the $3$ dimensional case the main motivation for the analysis of this class of energies is the study of line defects in crystals, the so called dislocations.
The structure of neutrino masses and mixing resulting from trilinear $R$ violating interactions is studied in the presence of the gauge mediated supersymmetry breaking. Neutrino masses arise in this model at tree level through the RG-induced vacuum expectation values of the sneutrinos and also through direct contribution at 1-loop. The relative importance of these contributions is determined by the values of the strong and weak coupling constants. In case of purely $\lambda'$ couplings, the tree contribution dominates over the 1-loop diagram. In this case, one simultaneously obtains atmospheric neutrino oscillations and quasi-vacuum oscillations of the solar neutrinos if all the $\l'$ couplings are assumed to be of similar magnitudes. If R parity violation arises from the trilinear $\l$ couplings, then the loop induced contribution dominates over the tree level. One cannot simultaneously explain the solar and atmospheric deficit in this case if all the $\l$ couplings are of similar magnitude. This however becomes possible with hierarchical $\l$ and we give a specific example of this.
Recently, Castellano and Pastor-Satorras [1] utilized the finite size scaling (FSS) theory to analyze simulation data for the contact process (CP) on scale-free networks (SFNs) and claimed that its absorbing critical behavior is not consistent with the mean-field (MF) prediction. Furthermore, they pointed out large density fluctuations at highly connected vertices as a possible origin for non-MF critical behavior. In this Comment, we propose a scaling theory for relative density fluctuations in the spirit of the MF theory, which turns out to explain simulation data perfectly well. We also measure the value of the critical density decay exponent, which agrees well with the MF prediction. Our results strongly support that the CP on SFNs still exhibits a MF-type critical behavior.
We prove the uniqueness of weak solutions to the critical defocusing wave equation in 3D under a local energy inequality condition. More precisely, we prove the uniqueness of $ u \in L^\infty\_t(\dot{H}^{1})\cap \dot{W}^{1,\infty}\_t(L^2)$, under the condition that $u$ verifies some local energy inequalities.
In this paper we simulate the cyclic circularly-polarised pulses of the ultra-cool dwarf TVLM513-46546, observed with the VLA at 4.88 and 8.44 GHz on May 2006, by using a 3D model of the auroral radio emission from the stellar magnetosphere. During this epoch, the radio light curves are characterised by two pulses left-hand polarised at 4.88 GHz, and one doubly-peaked (of opposite polarisations) pulse at 8.44 GHz. To take into account the possible deviation from the dipolar symmetry of the stellar magnetic field topology, the model described in this paper is also able to simulate the auroral radio emission from a magnetosphere shaped like an offset-dipole. To reproduce the timing and pattern of the observed pulses, we explored the space of parameters controlling the auroral beaming pattern and the geometry of the magnetosphere. Through the analysis of the TVLM513-46546 auroral radio emission, we derive some indications on the magnetospheric field topology that is able to simultaneously reproduce the timing and patterns of the auroral pulses measured at 4.88 and 8.44 GHz. Each set of model solutions simulates two auroral pulses (singly or doubly peaked) per period. To explain the presence of only one 8.44 GHz pulse per period, we analyse the case of auroral radio emission limited only to a magnetospheric sector activated by an external body, like the case of the interaction of Jupiter with its moons.
We construct the ambitwistor pure spinor string in a general type II supergravity background in the semi-classical regime. Almost all supergravity constraints are obtained from nilpotency of the BRST charge and further consistency conditions from additional world-sheet symmetries. We also discuss the case of $AdS_5\times S^5$ background.
We present a theoretical investigation of shot-noise suppression due to long-range Coulomb interaction in nondegenerate diffusive conductors. Calculations make use of an ensemble Monte Carlo simulator self-consistently coupled with a one-dimensional Poisson solver. We analyze the noise in a lightly doped active region surrounded by two contacts acting as thermal reservoirs. By taking the doping of the injecting contacts and the applied voltage as variable parameters, the influence of elastic and inelastic scattering in the active region is investigated. The transition from ballistic to diffusive transport regimes under different contact injecting statistics is analyzed and discussed. Provided significant space-charge effects take place inside the active region, long-range Coulomb interaction is found to play an essential role in suppressing the shot noise at $qU \gg k_BT$. In the elastic diffusive regime, momentum space dimensionality is found to modify the suppression factor $\gamma$, which within numerical uncertainty takes values respectively of about 1/3, 1/2 and 0.7 in the 3D, 2D and 1D cases. In the inelastic diffusive regime, shot noise is suppressed to the thermal value.
The shell model in the complex k-plane (the so-called Gamow Shell Model) has recently been formulated and applied to structure of weakly bound, neutron-rich nuclei. The completeness relations of Newton and Berggren, which apply to the neutron case, are strictly valid for finite-range potentials. However, for long-range potentials, such as the Coulomb potential for protons, for which the arguments based on the Mittag-Leffler theory do not hold, the completeness still needs to be demonstrated. This has been done in this paper, both analytically and numerically. The generalized Berggren relations are then used in the first Gamow Shell Model study of nuclei having both valence neutrons and protons, namely the lithium chain. The single-particle basis used is that of the Hartree-Fock-inspired potential generated by a finite-range residual interaction. The effect of isospin mixing in excited unbound states is discussed.
Aqueous zinc (Zn)-ion batteries (AZIB) are promising candidates for the next-generation energy store systems due to their high capacity and low cost. Despite their nominal performance, Zn anodes tend to rapidly develop dendrite and fracture, leading to substantial capacity loss and cycling stability failure. Well-controlled coating using organic-inorganic hybrid molecules is highly promising to substantially improve their chemo-mechanical stability without compromising their performance. We herein present a critical assessment of the chemical and mechanical stability of alucone-coated Zn surfaces using first-principles simulations. Negative adsorption energies indicate strong cohesive strengths between alucone and the selected Zn surfaces. Energetically favorable alucone coatings are further verified by charge transfer at interfaces as seen through Bader charge analysis. Negative surface stress profiles at alucone coated interface are mostly responsible for surface reconstruction. The contributions of surface elastic constants are dependent on the selection of slip planes and the thickness of the thin film. By considering plane stress conditions, we calculate the mechanical properties which indicate the ductility of the alucone-coated basal thin film.
Giant molecular clouds (GMCs) are well-studied in the local Universe, however, exactly how their properties vary during galaxy evolution is poorly understood due to challenging resolution requirements, both observational and computational. We present the first time-dependent analysis of giant molecular clouds in a Milky Way-like galaxy and an LMC-like dwarf galaxy of the FIRE-2 (Feedback In Realistic Environments) simulation suite, which have sufficient resolution to predict the bulk properties of GMCs in cosmological galaxy formation self-consistently. We show explicitly that the majority of star formation outside the galactic center occurs within self-gravitating gas structures that have properties consistent with observed bound GMCs. We find that the typical cloud bulk properties such as mass and surface density do not vary more than a factor of 2 in any systematic way after the first Gyr of cosmic evolution within a given galaxy from its progenitor. While the median properties are constant, the tails of the distributions can briefly undergo drastic changes, which can produce very massive and dense self-gravitating gas clouds. Once the galaxy forms, we identify only two systematic trends in bulk properties over cosmic time: a steady increase in metallicity produced by previous stellar populations and a weak decrease in bulk cloud temperatures. With the exception of metallicity we find no significant differences in cloud properties between the Milky Way-like and dwarf galaxies. These results have important implications for cosmological star and star cluster formation and put especially strong constraints on theories relating the stellar initial mass function to cloud properties.
In this paper, a scheme is put forward to design pulses which drive a three-level system based on the reverse engineering with Lewis-Riesenfeld invariant theory. The scheme can be applied to a three-level system even when the rotating-wave approximation (RWA) can not be used. The amplitudes of pulses and the maximal values of detunings in the system could be easily controlled by adjusting control parameters. We analyze the dynamics of the system by an invariant operator, so additional couplings are unnecessary. Moreover, the approaches to avoid singularity of pulses are studied and several useful results are obtained. We hope the scheme could contribute to fast quantum information processing without RWA.
Using the Yebes 40m radio telescope, we report the detection of a series of seven lines harmonically related with a rotational constant B0=1295.81581 +/- 0.00026 MHz and a distortion constant D0=27.3 +/- 0.5 Hz towards the cold dense cloud TMC-1. Ab initio calculations indicate that the best possible candidates are the cations HC5NH+ and NC4NH+. From a comparison between calculated and observed rotational constants and other arguments based on proton affinities and dipole moments, we conclude that the best candidate for a carrier of the observed lines is the protonated cyanodiacetylene cation, HC5NH+. The HC5N/HC5NH+ ratio derived in TMC-1 is 240, which is very similar to the HC3N/HC3NH+ ratio. Results are discussed in the framework of a chemical model for protonated molecules in cold dense clouds.
We study the maps induced on cohomology by a Nikulin (i.e. a symplectic) involution on a K3 surface. We parametrize the eleven dimensional irreducible components of the moduli space of algebraic K3 surfaces with a Nikulin involution and we give examples of the general K3 surface in various components. We conclude with some remarks on Morrison-Nikulin involutions, these are Nikulin involutions which interchange two copies of E_8(-1) in the Neron Severi group.
We present the first detection of polarization around the Class 0 low-mass protostar L1157-mm at two different wavelengths. We show polarimetric maps at large scales (10" resolution at 350 um) from the SHARC-II Polarimeter and at smaller scales (1.2"-4.5" at 1.3 mm) from the Combined Array for Research in Millimeter-wave Astronomy (CARMA). The observations are consistent with each other and show inferred magnetic field lines aligned with the outflow. The CARMA observations suggest a full hourglass magnetic field morphology centered about the core; this is only the second well-defined hourglass detected around a low-mass protostar to date. We apply two different methods to CARMA polarimetric observations to estimate the plane-of-sky magnetic field magnitude, finding values of 1.4 and 3.4 mG.
We calculate the excitation frequencies of the low-lying modes of a trapped Bose-condensed gas at nonzero temperatures. We include in our calculation the dynamics of the noncondensed cloud, and find agreement with experimental results if we assume that in the experiment both the in-phase and out-of-phase monopole modes are excited simultaneously. In order to explore whether this is indeed the correct explanation, we also calculate how strongly the modes couple to a perturbation of the external trapping potential.
We combine the Dark Energy Camera Legacy Survey (DECaLS) DR8 photometry with Gaia photometry to study the 3-D structure of Bootes I, Draco, Ursa Minor, Sextans and Sculptor dwarf galaxies using blue horizontal branch (BHB) stars as distance indicators. We construct a new colour-absolute magnitude of BHB stars that we use to measure the distance gradients within the body of the dwarf galaxies. We detect a statistically significant non-zero gradient only in Sextans and Sculptor. Through modeling of the gradient and 2-D density of the systems by triaxial Plummer models we find that the distance gradients in both dwarf galaxies are inconsistent with prolate shape, but compatible with oblate or triaxial shapes. In order to explain the observed gradients, oblate models of Sextans and Sculptor need to have a significant intrinsic ellipticity larger than $0.47$ for Sextans and $0.46$ for Sculptor. The flattened oblate shape may imply a significant anisotropy in velocity distribution in order to be consistent with the lack of significant velocity gradients in these systems.
We introduce a combinatorial enumeration problem that is solved using generalized Catalan numbers. We also study generalizations of the Cycle Lemma beyond the computation of the generalized Catalan numbers.
We calculate an achievable secret key rate for quantum key distribution with a finite number of signals, by evaluating the min-entropy explicitly. The min-entropy can be expressed in terms of the guessing probability, which we calculate for d-dimensional systems. We compare these key rates to previous approaches using the von Neumann entropy and find non-zero key rates for a smaller number of signals. Furthermore, we improve the secret key rates by modifying the parameter estimation step. Both improvements taken together lead to non-zero key rates for only 10^4-10^5 signals. An interesting conclusion can also be drawn from the additivity of the min-entropy and its relation to the guessing probability: for a set of symmetric tensor product states the optimal minimum-error discrimination (MED) measurement is the optimal MED measurement on each subsystem.
We make a critical, next-to-leading order, study of the relationship between the longitudinal structure function FL and the gluon distribution proposed in Cooper- Sarkar et al. (Z. Phys. C 39:281, 1988; Acta Phys. Pol. B 34:2911 2003), which is frequently used to extract the gluon distribution from the proton longitudinal structure function at small x. The gluon density is obtained by expanding at particular choices of the point of expansion and compared with the hard Pomeron behavior for the gluon density. Comparisons with H1 data are made and predictions for the proposed best approach are also provided.