ShantanuT01/DACTYL-Pretraining huggingface dataset:
Let A be a finite subset of $\nat$. Then NIM(A;n) is the following 2-player game: initially there are $n$ stones on the board and the players alternate removing $a\in A$ stones. The first player who cannot move loses. This game has been well studied.   We investigate an extension of the game where Player I starts out with d dollars, Player II starts out with e dollars, and when a player removes a\in A he loses a dollars. The first player who cannot move loses; however, note this can happen for two different reasons: (1) the number of stones is less than min(A), (2) the player has less than $\min(A)$ dollars. This game leads to more complex win conditions then standard NIM.   We prove some general theorems from which we can obtain win conditions for a large variety of finite sets A. We then apply them to the sets A={1,L}, and A={1,L,L+1}.
We introduce new refinements of the Bell, factorial, and unsigned Stirling numbers of the first and second kind that unite the derangement, involution, associated factorial, associated Bell, incomplete Stirling, restricted factorial, restricted Bell, and $r$-derangement numbers (and probably more!). By combining methods from analytic combinatorics, umbral calculus, and probability theory, we derive several recurrence relations and closed form expressions for these numbers. By specializing our results to the classical case, we recover explicit formulae for the Bell and Stirling numbers as sums over compositions.
Active galactic nuclei (AGNs) are characterized by a clear correlation between luminosity and metallicity (L_AGN-Z_AGN relation). The origin of this correlation is not clear. It may result from a relation between the black hole mass (M_BH) and metallicity, or from a relation between the accretion rate (L/L_Edd) and metallicity. To investigate the origin of the L_AGN-Z_AGN relation, we use optical spectra of 2383 quasars at 2.3 < z < 3.0 from the Sloan Digital Sky Survey. By using this data set, we have constructed composite spectra of 33 subsamples in intervals of both M_BH and L/L_Edd. From these composite spectra we measure emission-line flux ratios that are sensitive to the metallicity of the broad line region (BLR); specifically, NV/CIV, NV/HeII, (SiIV+OIV])/CIV, and AlIII/CIV. We find that there is a significant correlation between M_BH and Z_BLR as inferred from all four metallicity-sensitive emission-line flux ratios. This result strongly suggests that the observed L_AGN-Z_AGN relation is mostly a consequence of the M_BH-Z_AGN relation. The relation between M_BH and Z_BLR is likely a consequence of both the M_BH-M_bul relation and of the mass-metallicity relation in the host galaxy. We also find that L/L_Edd correlates with the emission line flux ratios involving NV (more specifically, NV/CIV and NV/HeII), while it does not correlate with the other two metallicity sensitive emission line flux ratios, i.e., (SiIV+OIV])/CIV and AlIII/CIV. These correlations indicate that the emission-line flux ratios involving NV depend on both metallicity and relative abundance of nitrogen. We suggest that the relation between L/L_Edd and those line ratios involving nitrogen, is caused by a delay of the black hole accretion rate relative to the onset of nuclear star formation of about 10^8 years, which is the timescale required for the nitrogen enrichment.
The open cluster M67 offers the unique opportunity to measure rotation periods for solar-age stars across a range of masses, potentially filling a critical gap in the understanding of angular momentum loss in older main sequence stars. The observation of M67 by NASA K2 Campaign 5 provided light curves with high enough precision to make this task possible, albeit challenging, as the pointing instability, 75d observation window, crowded field, and typically low-amplitude signals mean determining accurate rotation periods on the order of 25 - 30d is inherently difficult. Lingering, non-astrophysical signals with power at >25d found in a set of Campaign 5 A and F stars compounds the problem. To achieve a quantitative understanding of the best-case scenario limits for reliable period detection imposed by these inconveniences, we embarked on a comprehensive set of injection tests, injecting 120,000 sinusoidal signals with periods ranging from 5 to 35d and amplitudes from 0.05% to 3.0% into real Campaign 5 M67 light curves processed using two different pipelines. We attempted to recover the signals using a normalized version of the Lomb-Scargle periodogram and setting a detection threshold. We find that while the reliability of detected periods is high, the completeness (sensitivity) drops rapidly with increasing period and decreasing amplitude, maxing at 15% recovery rate for the solar case (i.e. 25d period, 0.1% amplitude). This study highlights the need for caution in determining M67 rotation periods from Campaign 5 data, but this can be extended to other clusters observed by K2 and, soon, TESS.
The performance of still-to-video FR systems can decline significantly because faces captured in unconstrained operational domain (OD) over multiple video cameras have a different underlying data distribution compared to faces captured under controlled conditions in the enrollment domain (ED) with a still camera. This is particularly true when individuals are enrolled to the system using a single reference still. To improve the robustness of these systems, it is possible to augment the reference set by generating synthetic faces based on the original still. However, without knowledge of the OD, many synthetic images must be generated to account for all possible capture conditions. FR systems may, therefore, require complex implementations and yield lower accuracy when training on many less relevant images. This paper introduces an algorithm for domain-specific face synthesis (DSFS) that exploits the representative intra-class variation information available from the OD. Prior to operation, a compact set of faces from unknown persons appearing in the OD is selected through clustering in the captured condition space. The domain-specific variations of these face images are projected onto the reference stills by integrating an image-based face relighting technique inside the 3D reconstruction framework. A compact set of synthetic faces is generated that resemble individuals of interest under the capture conditions relevant to the OD. In a particular implementation based on sparse representation classification, the synthetic faces generated with the DSFS are employed to form a cross-domain dictionary that account for structured sparsity. Experimental results reveal that augmenting the reference gallery set of FR systems using the proposed DSFS approach can provide a higher level of accuracy compared to state-of-the-art approaches, with only a moderate increase in its computational complexity.
Through resistivity measurements of an organic crystal hosting massless Dirac fermions with a charge-ordering instability, we reveal the effect of interactions among Dirac fermions on the charge transport. A low-temperature resistivity upturn appears robustly irrespectively of pressure and is enhanced while approaching the critical pressure of charge ordering, indicating that the insulating behavior originates from short-range Coulomb interactions. Observation of apparently vanishing gap in the charge-ordered phase accords with the theoretical prediction of the non-topological edge states.
We present the spectral/timing properties of the bare Seyfert galaxy Ark 120 through a deep ~420ks XMM-Newton campaign plus recent NuSTAR observations and a ~6-month Swift monitoring campaign. We investigate the spectral decomposition through fractional rms, covariance and difference spectra, finding the mid- to long-timescale (~day-year) variability to be dominated by a relatively smooth, steep component, peaking in the soft X-ray band. Additionally, we find evidence for variable FeK emission red-ward of the FeK-alpha core on long timescales, consistent with previous findings. We detect a clearly-defined power spectrum which we model with a power law with a slope of alpha ~ 1.9. By extending the power spectrum to lower frequencies through the inclusion of Swift and RXTE data, we find tentative evidence of a high-frequency break, consistent with existing scaling relations. We also explore frequency-dependent Fourier time lags, detecting a negative ('soft') lag for the first time in this source with the 0.3-1 keV band lagging behind the 1-4 keV band with a time delay of ~900s. Finally, we analyze the variability in the optical and UV bands using the Optical/UV Monitor on-board XMM-Newton and the UVOT on-board Swift and search for time-dependent correlations between the optical/UV/X-ray bands. We find tentative evidence for the U-band emission lagging behind the X-rays with a time delay of 2.4 +/- 1.8 days, which we discuss in the context of disc reprocessing.
We perform an analytic calculation of thermoelectric transport coefficients for massless Dirac electrons using the approach based on the Kubo--St\v{r}eda formula and generalized Mott's relation. The main focus of the letter is made on the properties of the Nernst coefficient in the vicinity of the Dirac point in quantum limit. We calculate magnetic field and temperature dependencies of the Nernst coefficient and compare our results with recent experiments in $\alpha$-(BEDT-TTF)$_{2}$I$_{3}$ organic conductor. We argue that the Zeeman splitting is important to understand the experimental data at high magnetic fields.
In this paper, we formulate ideas for visual media for trunk quantum networks with lines over 100 km. We investigate the local trends analysis of performance parameters for experimental demonstration of long-distance quantum communication and discuss the prospects of commercialization of quantum-classical cloud security services.
We theoretically demonstrate that a dipole layer on the electrode can modulate the transmission properties of nanoscale devices by influencing the contact properties, through first principles simulations on carbon nanotube based field effect transistors. The dipole layer is realized by potassium adsorption on Au electrodes, which shifts the electrostatic potential at the near contact region significantly. The dipoles parallel to the direction of the bias voltage may act as a supplement to the effect of gate voltages, while the perpendicular dipoles may modify the interface barrier of the contacts.
With the first metal enrichment by Population (Pop) III supernovae (SNe), the formation of the first metal-enriched, Pop II stars becomes possible. In turn, Pop III star formation and early metal enrichment are slowed by the high energy radiation emitted by Pop II stars. Thus, through the SNe and radiation they produce, Populations II and III coevolve in the early Universe, one regulated by the other. We present large (4 Mpc)^3, high resolution cosmological simulations in which we self-consistently model early metal enrichment and the stellar radiation responsible for the destruction of the coolants (H2 and HD) required for Pop III star formation. We find that the molecule-dissociating stellar radiation produced both locally and over cosmological distances reduces the Pop III star formation rate at z > 10 by up to an order of magnitude compared to the case in which this radiation is not included. However, we find that the effect of LW feedback is to enhance the amount of Pop II star formation. We attribute this to the reduced rate at which gas is blown out of dark matter haloes by SNe in the simulation with LW feedback, which results in larger reservoirs for metal-enriched star formation. Even accounting for metal enrichment, molecule-dissociating radiation and the strong suppression of low-mass galaxy formation due to reionization at z < 10, we find that Pop III stars are still formed at a rate of ~ 10^-5 M_sun yr^-1 Mpc^-3 down to z ~ 6. This suggests that the majority of primordial pair-instability SNe that may be uncovered in future surveys will be found at z < 10. We also find that the molecule-dissociating radiation emitted from Pop II stars may destroy H2 molecules at a high enough rate to suppress gas cooling and allow for the formation of supermassive primordial stars which collapse to form ~ 100,000 solar mass black holes.
We construct a low-energy effective field theory which allows the full treatment of isospin-breaking effects in semileptonic weak interactions. To this end, we enlarge the particle spectrum of chiral perturbation theory with virtual photons by including also the light leptons as dynamical degrees of freedom. Using super-heat-kernel techniques, we determine the additional one-loop divergences generated by the presence of virtual leptons and give the full list of associated local counterterms. We illustrate the use of our effective theory by applying it to the decays pi -> l nu_{l} and K -> l nu_{l}.
We discuss geodesic motion in the vacuum C metric using Bondi-like spherical coordinates, with special attention to the role played by the "equatorial plane." We show that the spatial trajectory of photons on such a hypersurface is formally the same of photons on the equatorial plane of the Schwarzschild spacetime, apart from an energy shift involving the spacetime acceleration parameter. Furthermore, we show that photons starting their motion from this hypersurface with vanishing component of the momentum along $\theta$, remain confined on it, differently from the case of massive particles. This effect is shown to have a counterpart also in the massless limit of the C metric, i.e. in Minkowski spacetime. Finally, we give the explict map between Bondi-like spherical coordinates and Fermi coordinates (up to the second order) for the world line of an observer at rest at a fixed spatial point of the equatorial plane of the C metric, a result which may be eventually useful to estimate both the mass and the acceleration parameter of accelerated sources.
The puzzles of black hole evaporation can be studied in the simplified context of 1+1 dimensional gravity. The semi-classical equations of Callan, Giddings, Harvey and Strominger provide a consistent description of the evaporation process which we describe in detail. We consider the possibility that black hole evolution leads to massive stable remnants. We show that such zero temperature remnant solutions exist but we also prove that a decaying black hole cannot evolve into one of them. Finally we consider the issue of loss of quantum information behind the global event horizon which develops in these geometries. An analogy with a well known solvable system shows that there may be less to information than meets the eye.
The multiscale flow structure in the solar convection zone - the coexistence of such features as the granules, mesogranules, supergranules and giant cells - has not yet been properly understood. Here, the possible role of one physical factor - variations in the thermal diffusivity - in the formation of a multiscale convection structure is investigated. Thermal convection in a plane horizontal fluid layer is numerically simulated. The temperature dependence of thermal diffusivity is chosen so as to produce a sharp kink in the static temperature profile near the upper layer boundary. As a result, the magnitude of the (negative) static temperature gradient dTs/dz, being small over the most part of the layer thickness, reaches large values in a thin boundary sublayer. To identify the structures on different scales, we apply a smoothing procedure, computational-homology techniques and spectral processing to the temperature field. The flow is found to be a superposition of three cellular structures with three different characteristic scales. The largest (first-scale) convection cells, with central upflows, fill the whole layer thickness; most of these cells are divided by bridges, or isthmuses, into a few smaller (second-scale) ones, which are localised in the upper portion of the layer; finally, there are numerous tiny (third-scale) features that dot the horizontal sections of the layer located near its upper boundary and exhibit a tendency of gathering in the intercellular lanes of the first-scale cells. The third-scale cellular structures are advected by the first-scale and second-scale convective flows. The spatial spectrum of the flow does not directly indicate the presence of the second-scale and third-scale structures; however, they can be selected by using our processing techniques. On the whole, the simulated flow pattern qualitatively resembles that observed on the Sun.
We introduce a stochastic sandpile model where finite drive and dissipation are coupled to the activity field. The absorbing phase transition here, as expected, belongs to the directed percolation (DP) universality class. We focus on the small drive and dissipation limit, i.e. the so-called self-organised critical (SOC) regime and show that the system exhibits a crossover from ordinary DP scaling to a dissipation-controlled scaling which is independent of the underlying dynamics or spatial dimension. The new scaling regime continues all the way to the zero bulk drive limit suggesting that the corresponding SOC behaviour is only DP, modified by the dissipation-controlled scaling. We demonstrate this for the continuous and discrete Manna model driven by noise and bulk dissipation.
The $k$-deck of a graph is the multiset of its subgraphs induced by $k$ vertices. A graph or graph property is $l$-reconstructible if it is determined by the deck of subgraphs obtained by deleting $l$ vertices. We show that the degree list of an $n$-vertex graph is $3$-reconstructible when $n\ge7$, and the threshold on $n$ is sharp. Using this result, we show that when $n\ge7$ the $(n-3)$-deck also determines whether an $n$-vertex graph is connected; this is also sharp. These results extend the results of Chernyak and Manvel, respectively, that the degree list and connectedness are $2$-reconstructible when $n\ge6$, which are also sharp.
We present a hard X-ray NuSTAR observation of PSR J0437-4715, the nearest millisecond pulsar. The known pulsations at the apparent pulse period ~5.76 ms are detected at energies up to 20 keV. We measure a photon index $\Gamma= 1.65\pm0.24$ (90% confidence) for the power law fit to the non-thermal emission. It had been shown that spectral models with two or three thermal components fit the XMM-Newton spectrum of PSR J0437-4715, depending on the slope of the power-law component, and the amount of absorption of soft X-rays. The new constraint on the high-energy emission provided by NuSTAR removes ambiguities regarding the thermal components of the emission below 3 keV. We performed a simultaneous spectral analysis of the XMM-Newton and NuSTAR data to confirm that three thermal components and a power law are required to fit the 0.3-20 keV emission of PSR J0437-4715. Adding a ROSAT-PSPC spectrum further confirmed this result and allowed us to better constrain the temperatures of the three thermal components. A phase-resolved analysis of the NuSTAR data revealed no significant change in the photon index of the high-energy emission. This NuSTAR observation provides further impetus for future observations with the NICER mission (Neutron Star Interior Composition Explorer) whose sensitivity will provide much stricter constraints on the equation of state of nuclear matter by combining model fits to the pulsar's phase-folded lightcurve with the pulsar's well-defined mass and distance from radio timing observations.
This paper considers a Cram\'er-Lundberg risk setting, where the components of the underlying model change over time. These components could be thought of as the claim arrival rate, the claim-size distribution, and the premium rate, but we allow the more general setting of the cumulative claim process being modelled as a spectrally positive L\'evy process. We provide an intuitively appealing mechanism to create such parameter uncertainty: at Poisson epochs we resample the model components from a finite number of $d$ settings. It results in a setup that is particularly suited to describe situations in which the risk reserve dynamics are affected by external processes (such as the state of the economy, political developments, weather or climate conditions, and policy regulations). We extend the classical Cram\'er-Lundberg approximation (asymptotically characterizing the all-time ruin probability in a light-tailed setting) to this more general setup. In addition, for the situation that the driving L\'evy processes are sums of Brownian motions and compound Poisson processes, we find an explicit uniform bound on the ruin probability, which can be viewed as an extension of Lundberg's inequality; importantly, here it is not required that the L\'evy processes be spectrally one-sided. In passing we propose an importance-sampling algorithm facilitating efficient estimation, and prove it has bounded relative error. In a series of numerical experiments we assess the accuracy of the asymptotics and bounds, and illustrate that neglecting the resampling can lead to substantial underestimation of the risk.
It is well known that the complete multipartite graphs can not be determined by their adjacency spectra. But in this paper, we prove that they can be determined by their distance spectra, which confirms the conjecture proposed by Lin, Hong, Wang and Shu.
A population of obscured supergiant High Mass X-ray Binaries (sgHMXBs) has been discovered by INTEGRAL. X-ray wind tomography of IGR J17252-3616 inferred a slow wind velocity to account for the enhanced obscuration. The main goal of this study is to understand under which conditions high obscuration could occur. We have used an hydrodynamical code to simulate the flow of the stellar wind around the neutron star. A grid of simulations was used to study the dependency of the absorbing column density and of the X-ray light-curves on the model parameters. A comparison between the simulation results and the observations of IGR J17252-3616 provides an estimate on these parameters. We have constrained the wind terminal velocity to 500-600 km/s and the neutron star mass to 1.75-2.15 solar masses. We have confirmed that the initial hypothesis of a slow wind velocity with a moderate mass loss rate is valid. The mass of the neutron star can be constrained by studying its impact on the accretion flow.
The method of screening and renormalization is used to include the Coulomb interaction between the charged particles in the description of few-body nuclear reactions. Calculations are done in the framework of Faddeev-type equations in momentum-space. The reliability of the method is demonstrated. The Coulomb effect on observables is discussed.
We consider the elliptic system of linear elasticity with bounded measurable coefficients in a domain where the second Korn inequality holds. We construct heat kernel of the system subject to Dirichlet, Neumann, or mixed boundary condition under the assumption that weak solutions of the elliptic system are H\"older continuous in the interior. Moreover, we show that if weak solutions of the mixed problem are H\"older continuous up to the boundary, then the corresponding heat kernel has a Gaussian bound. In particular, if the domain is a two dimensional Lipschitz domain satisfying a corkscrew or non-tangential accessibility condition on the set where we specify Dirichlet boundary condition, then we show that the heat kernel has a Gaussian bound. As an application, we construct Green's function for elliptic mixed problem in such a domain.