ShantanuT01/DACTYL-Pretraining huggingface dataset:
We study entanglement-assisted quantum and classical communication over a single use of a quantum channel, which itself can correspond to a finite number of uses of a channel with arbitrarily correlated noise. We obtain characterizations of the corresponding one-shot capacities by establishing upper and lower bounds on them in terms of the difference of two smoothed entropic quantities. In the case of a memoryless channel, the upper and lower bounds converge to the known single-letter formulas for the corresponding capacities, in the limit of asymptotically many uses of it. Our results imply that the difference of two smoothed entropic quantities characterizing the one-shot entanglement-assisted capacities serves as a one-shot analogue of the mutual information, since it reduces to the mutual information, between the output of the channel and a system purifying its input, in the asymptotic, memoryless scenario.
Supernova remnants (SNRs) are prime candidates for efficient particle acceleration up to the knee in the cosmic ray particle spectrum. In this work we present a new method for a systematic search for new TeV-emitting SNR shells in 2864 hours of H.E.S.S. phase I data used for the H.E.S.S. Galactic Plane Survey. This new method, which correctly identifies the known shell morphologies of the TeV SNRs covered by the survey, HESS J1731-347, RX 1713.7-3946, RCW 86, and Vela Junior, reveals also the existence of three new SNR candidates. All three candidates were extensively studied regarding their morphological, spectral, and multi-wavelength (MWL) properties. HESS J1534-571 was associated with the radio SNR candidate G323.7-1.0, and thus is classified as an SNR. HESS J1912+101 and HESS J1614-518, on the other hand, do not have radio or X-ray counterparts that would permit to identify them firmly as SNRs, and therefore they remain SNR candidates, discovered first at TeV energies as such. Further MWL follow up observations are needed to confirm that these newly discovered SNR candidates are indeed SNRs.
In this paper we study the Hilbert scheme of smooth, linearly normal, special scrolls under suitable assumptions on degree, genus and speciality.
We prove that there are infinitely often pairs of primes much closer than the average spacing between primes - almost within the square root of the average spacing. We actually prove a more general result concerning the set of values taken on by the differences between primes.
After reviewing some basic concepts of the theory of strongly interacting matter above nuclear energy density and reviewing some salient results of the experimental program at the Relativistic Heavy Ion Collider (RHIC), these lectures explain why the quark-gluon plasma observed in the RHIC experiments has been called a ``perfect liquid.'' They then give an introduction to some recent ideas concerning the possible origin of the nearly inviscid nature of the quark-gluon plasma and discuss the connection between low viscosity and strong parton energy loss of hot QCD matter.
Controlling the shape and structure of metallic colloids is an important topic. Here, different morphology-structures of colloidal gold particles are investigated with different process parameters in a pulse-based electron-photon and solution interface process. Different tiny-shaped particles of gold developed for different packets of supplied nano-energy as per set pulse OFF to ON time. Depending on the set ratios of pulse OFF to ON times and pulse polarity, packets of nano-energy bind transitional state gold atoms resting at electronically-flat solution surface that is controlled in their own shapes. Tiny particles of joined triangular shape in each case developed under set tuned ratio of bipolar pulses OFF to ON time. At unipolar pulse, tiny particles in triangular shape developed directly. When the ratio of bipolar pulse OFF to ON time was large, distorted shapes of the particles developed. Geometrical shapes of particles developed under significant ratios of pulse OFF to ON times. When the ratio of bipolar pulse OFF to ON time was 3, particles developed in low aspect ratio. But under the fraction of this ratio, particles tend to develop in high aspect ratio. For longer pulse ON time, structures of smooth elements get developed in width less than inter-spacing distance and forcing energy of travelling photons along the interface to flatten them further. Morphology and structure of tiny particles, nanoparticles and particles are discussed for different process parameters opening multiple routes for materials research and their counterparts. This is the overall attained orientation of electrons in elongated atoms forming colloidal particles of different size and shape maintaining the certain color of their solution under sunlight.
This article is concerned with a stochastic multi-patch model in which each local population is subject to a strong Allee effect. The model is obtained by using the framework of interacting particle systems to extend a stochastic two-patch model that has been recently introduced by Kang and the author. The main objective is to understand the effect of the geometry of the network of interactions, which represents potential migrations between patches, on the long-term behavior of the metapopulation. In the limit as the number of patches tends to infinity, there is a critical value for the Allee threshold below which the metapopulation expands and above which the metapopulation goes extinct. Spatial simulations on large regular graphs suggest that this critical value strongly depends on the initial distribution when the degree of the network is large whereas the critical value does not depend on the initial distribution when the degree is small. Looking at the system starting with a single occupied patch on the complete graph and on the ring, we prove analytical results that support this conjecture. From an ecological perspective, these results indicate that, upon arrival of an alien species subject to a strong Allee effect to a new area, though dispersal is necessary for its expansion, strong long range dispersal drives the population toward extinction.
In one of his papers, the author introduces the class of Farkas-related vectors for which a version of Farkas' lemma over integers is derived. In this paper, two similar classes are introduced and studied.
We consider a model of semi-flexible interacting self-avoiding trails (sISAT's) on a lattice, where the walks are constrained to visit each lattice edge at most once. Such models have been studied as an alternative to the self-attracting self-avoiding walks (SASAW) to investigate the collapse transition of polymers, with the attractive interactions being on site, as opposed to nearest-neighbor interactions in SASAW. The grand-canonical version of the sISAT model is solved on a four-coordinated Bethe lattice, and four phases appear: non-polymerized (NP), regular polymerized (P), dense polymerized (DP) and anisotropic nematic (AN), the last one present in the phase diagram only for sufficiently stiff chains. The last two phases are dense, in the sense that all lattice sites are visited once in AN phase and twice in DP phase. In general, critical NP-P and DP-P transition surfaces meet with a NP-DP coexistence surface at a line of bicritical points. The region in which the AN phase is stable is limited by a discontinuous critical transition to the P phase, and we study this somewhat unusual transition in some detail. In the limit of rods, where the chains are totally rigid, the P phase is absent and the three coexistence lines (NP-AN, AN-DP, and NP-DP) meet at a triple point, which is the endpoint of the bicritical line.
We provide a complete classification of Fano threefolds X having canonical Gorenstein singularities and the anticanonical degree (-KX)^3 equal 64.
The SDSS-IV Apache Point Observatory Galactic Evolution Experiment (APOGEE) survey has obtained high-resolution spectra for thousands of red giant stars distributed among the massive satellite galaxies of the Milky Way (MW): the Large and Small Magellanic Clouds (LMC/SMC), the Sagittarius Dwarf (Sgr), Fornax (Fnx), and the now fully disrupted \emph{Gaia} Sausage/Enceladus (GSE) system. We present and analyze the APOGEE chemical abundance patterns of each galaxy to draw robust conclusions about their star formation histories, by quantifying the relative abundance trends of multiple elements (C, N, O, Mg, Al, Si, Ca, Fe, Ni, and Ce), as well as by fitting chemical evolution models to the [$\alpha$/Fe]-[Fe/H] abundance plane for each galaxy. Results show that the chemical signatures of the starburst in the MCs observed by Nidever et al. in the $\alpha$-element abundances extend to C+N, Al, and Ni, with the major burst in the SMC occurring some 3-4 Gyr before the burst in the LMC. We find that Sgr and Fnx also exhibit chemical abundance patterns suggestive of secondary star formation epochs, but these events were weaker and earlier ($\sim$~5-7 Gyr ago) than those observed in the MCs. There is no chemical evidence of a second starburst in GSE, but this galaxy shows the strongest initial star formation as compared to the other four galaxies. All dwarf galaxies had greater relative contributions of AGB stars to their enrichment than the MW. Comparing and contrasting these chemical patterns highlight the importance of galaxy environment on its chemical evolution.
We utilize a suite of multiwavelength data, of 9 nearby spirals, to analyze the shock-induced star formation sequence, that may result from a constant spiral pattern speed. The sequence involves tracers as the HI, CO, 24um, and FUV, where the spiral arms were analyzed with Fourier techniques in order to obtain their azimuthal phases as a function of radius. It was found that only two of the objects, NGC 628 and NGC 5194, present coherent phases resembling the theoretical expectations, as indicated by the phase shifts of CO-24um. The evidence is more clear for NGC 5194, and moderate for NGC 628. It was also found that the phase shifts are different for the two spiral arms. With the exception on NGC 3627, a two-dimensional Fourier analysis showed that the rest of the objects do not exhibit bi-symmetric spiral structures of stellar mass, i.e., grand design spirals. A phase order inversion indicates a corotation radius of ~ 89" for NGC 628, and ~ 202" for NGC 5194. For these two objects, the CO-Halpha phase shifts corroborate the CO-24um azimuthal offsets. Also for NGC 5194, the CO-70um, CO-140um, and CO-250um phase shifts indicate a corotation region.
In samples used to maintain the US resistance standard the breakdown of the dissipationless integer quantum Hall effect occurs as a series of dissipative voltage steps. A mechanism for this type of breakdown is proposed, based on the generation of magneto-excitons when the quantum Hall fluid flows past an ionised impurity above a critical velocity. The calculated generation rate gives a voltage step height in good agreement with measurements. We also compare this model to a hydrodynamic description of breakdown.
Our tightest upper limit on the sum of neutrino mass eigenvalues $M_\nu$ comes from cosmological observations that will improve substantially in the near future, enabling a detection. The combination of the Baryon Acoustic Oscillation feature measured from the Dark Energy Spectroscopic Instrument and a Stage-IV Cosmic Microwave Background experiment has been forecasted to achieve $\sigma(M_\nu) < 1/3$ of the lower limit on $M_\nu$ from atmospheric and solar neutrino oscillations \citep{2013arXiv1309.5383A,2012PhRvD..86a3012F}. Here we examine in detail the physical effects of neutrino mass on cosmological observables that make these constraints possible. We also consider how these constraints would be improved to ensure at least a $5\sigma$ detection.
Inspired by the work of Wang and Yu [21] on wave maps, we show that for all positive numbers T_{0} > 0 and E_{0} > 0, a large kind of semi-linear wave equation on R \times R^{3} has a solution whose life-span is [0; T_{0}], and the energy of the initial Cauchy data is at least E_{0}.
Monte Carlo simulations of the field substellar mass function (MF) are presented. Starting from various representations of the MF below 0.1 M$_{\sun}$ and the stellar birth rate, luminosity functions (LFs) and T$_{eff}$ distributions are produced for comparison with observed samples. These distributions exhibit distinct minima in the mid-type L dwarf regime followed by a rise in number density for fainter/cooler brown dwarfs, predicting many more T-type and cooler brown dwarfs in the field even for relatively shallow mass functions. Deuterium-burning brown dwarfs dominate field objects with 400 $\leq$ T$_{eff}$ $\leq$ 2000 K, while non-fusing brown dwarfs make up a substantial proportion of field dwarfs with T$_{eff}$ $\leq$ 500 K. The shape of the substellar LF is fairly consistent for various assumptions of the Galactic birth rate, choice of evolutionary model, and adopted age and mass ranges, particularly for field T dwarfs, which as a population provide the best constraints for the field substellar MF. Exceptions include a depletion of objects with 1200 $\leq$ T$_{eff}$ $\leq$ 2000 K in ``halo'' systems. Unresolved multiple systems tend to enhance features in the observed LF and may contribute significantly to the space density of very cool brown dwarfs. However, these effects are small ($<$ 10% for T$_{eff} \lesssim 300$ K) for binary fractions typical for brown dwarf systems (10--20%). An analytic approximation to correct the observed space density for unresolved multiple systems in a magnitude-limited survey is derived. [ABRIDGED]
We present the spin and orbitally resolved local density of states (LDOS) for a single Mn impurity and for two nearby Mn impurities in GaAs. The GaAs host is described by a sp^3 tight-binding Hamiltonian, and the Mn impurity is described by a local p-d hybridization and on-site potential. Local spin-polarized resonances within the valence bands significantly enhance the LDOS near the band edge. For two nearby parallel Mn moments the acceptor states hybridize and split in energy. Thus scanning tunneling spectroscopy can directly measure the Mn-Mn interaction as a function of distance.
Always, some individuals in images are more important/attractive than others in some events such as presentation, basketball game or speech. However, it is challenging to find important people among all individuals in images directly based on their spatial or appearance information due to the existence of diverse variations of pose, action, appearance of persons and various changes of occasions. We overcome this difficulty by constructing a multiple Hyper-Interaction Graph to treat each individual in an image as a node and inferring the most active node referring to interactions estimated by various types of clews. We model pairwise interactions between persons as the edge message communicated between nodes, resulting in a bidirectional pairwise-interaction graph. To enrich the personperson interaction estimation, we further introduce a unidirectional hyper-interaction graph that models the consensus of interaction between a focal person and any person in a local region around. Finally, we modify the PageRank algorithm to infer the activeness of persons on the multiple Hybrid-Interaction Graph (HIG), the union of the pairwise-interaction and hyperinteraction graphs, and we call our algorithm the PersonRank. In order to provide publicable datasets for evaluation, we have contributed a new dataset called Multi-scene Important People Image Dataset and gathered a NCAA Basketball Image Dataset from sports game sequences. We have demonstrated that the proposed PersonRank outperforms related methods clearly and substantially.
We investigate correlations of current at contacts and voltage fluctuations at voltage probes coupled to interferometers. The results are compared with correlations of current and occupation number fluctuations at dephasing probes. We use a quantum Langevin approach for the average quantities and their fluctuations. For higher order correlations we develop a stochastic path integral approach and find the generating functions of voltage or occupation number fluctuations. We also derive a generating function for the joint distribution of voltage or occupation number at the probe and current fluctuations at a terminal of a conductor. For energy independent scattering we found earlier that the generating function of current cumulants in interferometers with a one-channel dephasing or voltage probe are identical. Nevertheless, the distribution function for voltage and the distribution function for occupation number fluctuations differ, the latter being broader than that of former in all examples considered here.
We proof a limit theorem for moments in space of the increments of Brownian local time. As special cases for the second and third moments, previous results by Chen et al. (Ann. Prob. 38, 2010, no. 1) and Rosen (Stoch. Dyn. 11, 2011, no. 1), which were later reproven by Hu and Nualart (Electron. Commun. Probab. 14, 2009; Electron. Commun. Probab. 15, 2010) and Rosen (S\'eminaire de Probabilit\'es XLIII, Springer, 2011) are included. Furthermore, a conjecture of Rosen for the fourth moment is settled. In comparison to the previous methods of proof, we follow a fundamentally different approach by exclusively working in the space variable of the Brownian local time, which allows to give a unified argument for arbitrary orders. The main ingredients are Perkins' semimartingale decomposition, the Kailath-Segall identity and an asymptotic Ray-Knight Theorem by Pitman and Yor.
A weighted bicolored plane tree is a bicolored plane tree whose edges are endowed with positive integral weights. The degree of a vertex is defined as the sum of the weights of the edges incident to this vertex. Using the theory of dessins d'enfants, which studies the action of the absolute Galois group on graphs embedded into Riemann surfaces, we show that a weighted plane tree is a graphical representation of a pair of coprime complex polynomials A,B such that: (a) deg A = deg B, and A and B have the same leading coefficient; (b) the multiplicities of the roots of A (respectively, of B) are equal to the degrees of the black (respectively, white) vertices of the corresponding tree; (c) the degree of the difference A-B attains the minimum which is possible for the given multiplicities of the roots of A and B. Moreover, if a tree in question is uniquely determined by the set of its black and white vertex degrees (we call such trees unitrees), then the corresponding polynomials are defined over Q.   The pairs of polynomials A,B such that the degree of the difference A-B attains the minimum, and especially those defined over Q, are related to some important questions of number theory. Dozens of papers were dedicated to their study. The main result of this paper is a complete classification of the unitrees which provides us with the most massive class of such pairs defined over Q. We also study combinatorial invariants of the Galois action on trees, as well as on the corresponding polynomial pairs, which permit us to find yet more examples defined over Q. In a subsequent paper we compute the polynomials A,B corresponding to all the unitrees.
Photoexcited states are relaxed by transferring energy to the environments. In order to study which coupling allows fast energy transfer to lattice vibrations in correlated electron systems, we calculate the time evolutions of the kinetic energies of different types and frequencies of lattice vibrations. The one-dimensional half-filled Hubbard model is augmented with electron-lattice couplings that modulate transfer integrals, site energies, and Coulomb repulsion strengths. The time-dependent Schr\"odinger equation is solved for exact many-electron wave functions, and the classical equation of motion for the lattice displacements. In order to transfer energy to classical lattice vibrations that modulate transfer integrals or site energies, the translational invariance must be broken to give optical activity to an electronic excitation with wave number $ \pi $ and to these lattice vibrations. On the other hand, a certain amount of energy is always transferred to lattice vibrations that modulate Coulomb repulsion strengths, irrespective of the symmetry of the ground state, as long as the corresponding electron-lattice couplings are present. In strongly correlated electron systems, these couplings can be strong, although they are usually insignificant because their effects on the equilibrium properties can be absorbed into redefinition of Coulomb repulsion strengths. We will discuss competition or collaboration between energy transfer pathways through different types of electron-lattice couplings.
Weakly Interacting Massive Particle (WIMP) direct detection experiments are just reaching the sensitivity required to detect Galactic dark matter in the form of neutralinos (or indeed any stable weakly interacting particle). Detection strategies and data analyses are often based on the simplifying assumption of a standard spherical, isothermal halo model, but observations and numerical simulations indicate that galaxy halos are in fact triaxial and anisotropic, and contain substructure. The annual modulation and direction dependence of the event rate (due to the motion of the Earth) provide the best prospects of distinguishing WIMP scattering from background events, however these signals depend sensitively on the local WIMP velocity distribution. I briefly review the status of WIMP direct detection experiments before discussing the dependence of the annual modulation signal on astrophysical input, in particular the structure of the Milky Way halo, and the possibility that the local WIMP distribution is not smooth.
A perfect matroid design (PMD) is a matroid whose flats of the same rank all have the same size. In this paper we introduce the q-analogue of a PMD and its properties. In order to do so, we first establish a new cryptomorphic definition for q-matroids. We show that q-Steiner systems are examples of q-PMD's and we use this q-matroid structure to construct subspace designs from q-Steiner systems. We apply this construction to the only known q-Steiner system, which has parameters S(2,3,13;2), and hence establish the existence of a new subspace design with parameters 2-(13,4,5115;2).
Motivated by the computation of the BPS-invariants on a local Calabi-Yau threefold suggested by S. Katz, we compute the Chow ring and the cohomology ring of the moduli space of stable sheaves of Hilbert polynomial $4m+1$ on the projective plane. As a byproduct, we obtain the total Chern class and Euler characteristics of all line bundles, which provide a numerical data for the strange duality on the plane.
We present three sets of results for the stationary distribution of a two-dimensional semimartingale reflecting Brownian motion (SRBM) that lives in the nonnegative quadrant. The SRBM data can equivalently be specified by three geometric objects, an ellipse and two lines, in the two-dimensional Euclidean space. First, we revisit the variational problem (VP) associated with the SRBM. Building on Avram, Dai and Hasenbein (2001), we show that the value of the VP at a point in the quadrant is equal to the optimal value of a linear function over a convex domain. Depending on the location of the point, the convex domain is either D(1) or D(2) or D(1) cap D(2), where each D(i), i = 1, 2, can easily be described by the three geometric objects. Our results provide a geometric interpretation for the value function of the VP and allow one to see geometrically when one edge of the quadrant has influence on the optimal path traveling from the origin to a destination point. Second, we provide a geometric condition that characterizes the existence of a product form stationary distribution. Third, we establish exact tail asymptotics of two boundary measures that are associated with the stationary distribution; a key step in our proof is to sharpen two asymptotic inversion lemmas in Dai and Miyazawa (2011) that allow one to infer the exact tail asymptotic of a boundary measure from the singularity of its moment generating function.