ShantanuT01/DACTYL-Pretraining huggingface dataset:
The optimization of finite-time thermodynamic heat engines was intensively explored recently, yet limited to few cycles, e.g. finite-time Carnot-like cycle. In this paper, we supplement a new type of finite-time engine with quantum Otto cycle and show the better performance. The current model can be widely utilized benefited from the general \mathcal{C}/\tau^{2} scaling of extra work for finite-time adiabatic process with long control time \tau. Such scaling allows analytical optimization of the generic finite-time quantum Otto cycle to surpass the efficiency at maximum power for the Carnot-like engine. We apply the current perturbation method to the quantum piston model and calculate the efficiency at maximum power, which is validated with exact solution.
A real polynomial $P(X_1,..., X_n)$ sign represents $f: A^n \to \{0,1\}$ if for every $(a_1, ..., a_n) \in A^n$, the sign of $P(a_1,...,a_n)$ equals $(-1)^{f(a_1,...,a_n)}$. Such sign representations are well-studied in computer science and have applications to computational complexity and computational learning theory. In this work, we present a systematic study of tradeoffs between degree and sparsity of sign representations through the lens of the parity function. We attempt to prove bounds that hold for any choice of set $A$. We show that sign representing parity over $\{0,...,m-1\}^n$ with the degree in each variable at most $m-1$ requires sparsity at least $m^n$. We show that a tradeoff exists between sparsity and degree, by exhibiting a sign representation that has higher degree but lower sparsity. We show a lower bound of $n(m -2) + 1$ on the sparsity of polynomials of any degree representing parity over $\{0,..., m-1\}^n$. We prove exact bounds on the sparsity of such polynomials for any two element subset $A$. The main tool used is Descartes' Rule of Signs, a classical result in algebra, relating the sparsity of a polynomial to its number of real roots. As an application, we use bounds on sparsity to derive circuit lower bounds for depth-two AND-OR-NOT circuits with a Threshold Gate at the top. We use this to give a simple proof that such circuits need size $1.5^n$ to compute parity, which improves the previous bound of ${4/3}^{n/2}$ due to Goldmann (1997). We show a tight lower bound of $2^n$ for the inner product function over $\{0,1\}^n \times \{0, 1\}^n$.
The aim of this paper is to provide new results and insights for a screw dislocation in functionally graded media within the gauge theory of dislocations. We present the equations of motion for dislocations in inhomogeneous media. We specify the equations of motion for a screw dislocation in a functionally graded material. The material properties are assumed to vary exponentially along the x and y-directions. In the present work we give the analytical gauge field theoretic solution to the problem of a screw dislocation in inhomogeneous media. Using the dislocation gauge approach, rigorous analytical expressions for the elastic distortions, the force stresses, the dislocation density and the pseudomoment stresses are obtained depending on the moduli of gradation and an effective intrinsic length scale characteristic for the functionally graded material under consideration.
We propose two Quantum Direct Communication (QDC) protocols with user authentication. Users can identify each other by checking the correlation of Greenberger-Horne-Zeilinger (GHZ) states. Alice can directly send a secret message to Bob using the remaining GHZ states after authentication. Our second QDC protocol can be used even though there is no quantum link between Alice and Bob. The security of the transmitted message is guaranteed by properties of entanglement of GHZ states.
Be stars have generally been characterized by the emission lines in their spectra, and especially the time variability of those spectroscopic features. They are known to also exhibit photometric variability at multiple timescales, but have not been broadly compared and analyzed by that behavior. We have taken advantage of the advent of wide-field, long-baseline, and high-cadence photometric surveys that search for transiting exoplanets to perform a comprehensive analysis of brightness variations among a large number of known Be stars. The photometric data comes from the KELT transit survey, with a typical cadence of 30 minutes, baseline of up to ten years, photometric precision of about 1%, and coverage of about 60% of the sky. We analyze KELT light curves of 610 known Be stars in both the Northern and Southern hemispheres in an effort to study their variability. Consistent with other studies of Be star variability, we find most of the stars to be photometrically variable. We derive lower limits on the fraction of stars in our sample that exhibit features consistent with non-radial pulsations (25%), outbursts (36%), and long term trends in the circumstellar disk (37%), and show how these are correlated with spectral sub-type. Other types of variability, such as those owing to binarity, are also explored. Simultaneous spectroscopy for some of these systems from the Be Star Spectral Database (BeSS) allow us to better understand the physical causes for the observed variability, especially in cases of outbursts and changes in the disk.
Scalar fields with a "chameleon" property, in which the effective particle mass is a function of its local environment, are common to many theories beyond the standard model and could be responsible for dark energy. If these fields couple weakly to the photon, they could be detectable through the "afterglow" effect of photon-chameleon-photon transitions. The ADMX experiment was used in the first chameleon search with a microwave cavity to set a new limit on scalar chameleon-photon coupling excluding values between 2*10^9 and 5*10^14 for effective chameleon masses between 1.9510 and 1.9525 micro-eV.
We have conducted a study of debris disks around F stars in order to explore correlations between rotation, stellar winds, and circumstellar disks. We obtained new 24 micron photometry from Spitzer's Multiband Imaging Photometer for Spitzer (MIPS) camera for a sample of 188 relatively nearby F dwarfs with various rotation rates and optical colors, and combined it with archival MIPS data for 66 more F stars, as well as Wide-field Infrared Survey Explorer (WISE) data for the entire sample, plus 9 more F stars. Based on the objects' K_s-[24] and [3.4]-[22] colors, we identify 22 stars in our sample as having 22 and/or 24 micron excesses above our detection limit, 13 of which are new discoveries. Our overall disk detection rate is 22/263, or 8%, consistent with previous determinations of disk fractions in the Solar neighborhood. While fast rotating stars are expected to have strong winds capable of efficiently removing dust, we find no correlation between rotational velocity and infrared excess. Similarly, we find no significant difference in excess detection rate between late-type F stars, which have convective surfaces, and early-type F stars, which have fully radiative envelopes. However, the essentially unknown range of ages in this sample may be washing out any effects relating rotation, winds, and disks.
All p-mode parameters vary with time as a response to the changes induced by the cyclic behavior of solar magnetic activity. After the unusual long solar-activity minimum between cycles 23 and 24, where the p-mode parameters have shown a different behavior than the surface magnetic proxies, we analyze the temporal variation of low-degree p-mode parameters measured by GOLF (in velocity) and VIRGO (in intensity) Sun-as-a-star instruments on board SoHO. We then compared our results with other activity proxies.
Let X be a projective variety over an algebraically closed base field, possibly singular. The aim of this paper is to show that the generalized Albanese variety of Esnault-Srinivas-Viehweg can be computed from one general curve C in X, if the base field is of characteristic 0. We illustrate this by an example, which we also use to unravel some mysterious properties of the Albanese of Esnault-Srinivas-Viehweg.
Cu2OSeO3 is known as a unique example of insulating multiferroic compounds with skyrmion spin texture, which is characterized by the chiral cubic crystal structure at ambient pressure. Recently, it has been reported that this compound shows pressure-induced structural transition with large enhancement of magnetic ordering temperature Tc. In the present study, we have investigated the detailed crystal structure in the high pressure phase, by combining the synchrotron X-ray diffraction experiment with the diamond anvil cell and the analysis based on the genetic algorithm. Our results suggest that the original pyrochlore Cu network is sustained even after the structural transition, while the orientation of SeO3 molecule as well as the position of oxygen in the middle of Cu tetrahedra are significantly modified. The latter features may be the key for the reported enhancement of Tc and associated stabilization of skyrmion phase at room temperature.
We present new cooling models for carbon-oxygen white dwarfs with both H- and He-atmospheres, covering the whole relevant mass range, to extend our updated BaSTI (a Bag of Stellar Tracks and Isochrones) stellar evolution archive. They have been computed using core chemical stratifications obtained from new progenitor calculations, adopting a semiempirical initial-final mass relation. The physics inputs have been updated compared to our previous BaSTI calculations: ^{22}Ne diffusion in the core is now included, together with an updated CO phase diagram, and updated electron conduction opacities. We have calculated models with various different neon abundances in the core, suitable to study white dwarfs in populations with metallicities ranging from super-solar to metal poor, and have performed various tests/comparisons of the chemical stratification and cooling times of our models. Two complete sets of calculations are provided, for two different choices of the electron conduction opacities, to reflect the current uncertainty in the evaluation of the electron thermal conductivity in the transition regime between moderate and strong degeneracy, crucial for the H and He envelopes. We have also made a first, preliminary estimate of the effect -- that turns out to be generally small -- of Fe sedimentation on the cooling times of white dwarf models, following recent calculations of the phase diagrams of carbon-oxygen-iron mixtures.   We make publicly available the evolutionary tracks from both sets of calculations, including cooling times and magnitudes in the Johnson-Cousins, Sloan, Pan-STARSS, Galex, Gaia-DR2, Gaia-eDR3, HST-ACS, HST-WFC3, and JWST photometric systems.
We study the Muskat problem for one fluid or two fluids, with or without viscosity jump, with or without rigid boundaries, and in arbitrary space dimension $d$ of the interface. The Muskat problem is scaling invariant in the Sobolev space $H^{s_c}(\mathbb{R}^d)$ where $s_c=1+\frac{d}{2}$. Employing a paradifferential approach, we prove local well-posedness for large data in any subcritical Sobolev spaces $H^s(\mathbb{R}^d)$, $s>s_c$. Moreover, the rigid boundaries are only required to be Lipschitz and can have arbitrarily large variation. The Rayleigh-Taylor stability condition is assumed for the case of two fluids with viscosity jump but is proved to be automatically satisfied for the case of one fluid. The starting point of this work is a reformulation solely in terms of the Drichlet-Neumann operator. The key elements of proofs are new paralinearization and contraction results for the Drichlet-Neumann operator in rough domains.
Dataset creation is typically one of the first steps when applying Artificial Intelligence methods to a new task; and the real world performance of models hinges on the quality and quantity of data available. Producing an image dataset for semantic segmentation is resource intensive, particularly for specialist subjects where class segmentation is not able to be effectively farmed out. The benefit of producing a large, but poorly labelled, dataset versus a small, expertly segmented dataset for semantic segmentation is an open question. Here we show that a large, noisy dataset outperforms a small, expertly segmented dataset for training a Fully Convolutional Network model for semantic segmentation of corrosion in images. A large dataset of 250 images with segmentations labelled by undergraduates and a second dataset of just 10 images, with segmentations labelled by subject matter experts were produced. The mean Intersection over Union and micro F-score metrics were compared after training for 50,000 epochs. This work is illustrative for researchers setting out to develop deep learning models for detection and location of specialist features.
The Tremaine-Weinberg equations are solved for a pattern speed that is allowed to vary with radius. The solution method transforms an integral equation for the pattern speed to a least squares problem with well established procedures for statistical analysis. The method applied to the HI spiral pattern of the barred, grand-design galaxy NGC 1365 produced convincing evidence for a radial dependence in the pattern speed. The pattern speed behaves approximately as 1/r, and is very similar to the material speed. There are no clear indications of corotation or Lindblad resonances. Tests show that the results are not selection biased, and that the method is not measuring the material speed. Other methods of solving the Tremaine-Weinberg equations for shearing patterns were found to produce results in agreement with those obtained using the current method. Previous estimates that relied on the assumptions of the density-wave interpretation of spiral structure are inconsistent with the results obtained using the current method. The results are consistent with spiral structure theories that allow for shearing patterns, and contradict fundamental assumptions in the density-wave interpretation that are often used for finding spiral arm pattern speeds. The spiral pattern is winding on a characteristic timescale of ~ 500 Myrs.
Much of the published work regarding the Isotropic Singularity is performed under the assumption that the matter source for the cosmological model is a barotropic perfect fluid, or even a perfect fluid with a $\gamma$-law equation of state. There are, however, some general properties of cosmological models which admit an Isotropic Singularity, irrespective of the matter source. In particular, we show that the Isotropic Singularity is a point-like singularity and that vacuum space-times cannot admit an Isotropic Singularity. The relationships between the Isotropic Singularity, and the energy conditions, and the Hubble parameter is explored. A review of work by the authors, regarding the Isotropic Singularity, is presented.
Topological indices are scientific details of graphs which represents its topology and of the most part graph invariant. In QSAR/QSPR, physico-chemical characteristics and topological indices, for example, atom bond connectivity (ABC) and geometric-arithmetic (GA) indices are apply to foresee the bioactivity of concoction mixes. Graph theory discovered a significant practice in the region of investigation. In this paper, we are taking Planar Octahedron networks, produced by honeycomb structure of dimension n and obtain analytical closed results of Multiplicative topological indices for firstly and presents closed formulas of degree based indices.
We present a measurement of the quasar luminosity function in the range 0.68<z<4 down to extinction corrected magnitude g_dered=22.5, using a simple and well understood target selection technique based on the time-variability of quasars. The completeness of our sample was derived directly from a control sample of quasars, without requiring complex simulations of quasar light-curves or colors. A total of 1877 quasar spectra were obtained from dedicated programs on the Sloan telescope (as part of the SDSS-III/BOSS survey) and on the Multiple Mirror Telescope. They allowed us to derive the quasar luminosity function. It agrees well with previously published results in the redshift range 0.68<z<2.6. Our deeper data allow us to extend the measurement to z=4. We measured quasar densities to g_dered<22.5, obtaining 30 QSO per deg^2 at z<1, 99 QSO per deg^2 for 1<z<2.15, and 47 QSO per deg^2 at z>2.15. Using pure luminosity evolution models, we fitted our LF measurements, and predicted quasar number counts as a function of redshift and observed magnitude. These predictions are useful inputs for future cosmology surveys such as those relying on the observation of quasars to measure baryon acoustic oscillations.
The Balitsky-Kovchegov QCD equation for rapidity evolution describing saturation effects at high energy admits universal asymptotic traveling-wave solutions when the nonlinear damping becomes effective. The asymptotic solutions fall in universality classes depending only on some specific properties of the solution of the associated linear equation. We derive these solutions for the recent QCD formulations of the Balitsky-Kovchegov equation with running coupling constant obtained from quark-loop calculation. While the associated linear solutions depend in different ways with observables and higher-order effects, we show that the asymptotic traveling-wave solutions all belong to the same universality class whose solutions are given. Hence the influence of saturation stabilizes the QCD evolution with respect to higher order effects and leads to universal features at high enough rapidity, such as the form of the traveling waves, the intercept of the saturation scale and geometric scaling in square-root of the rapidity.
In the present paper we continue the investigation of solutions to higher-order heat-type equations with random initial conditions, which play the important role in many applied areas. We consider the random initial conditions given by harmonizable $\varphi$-sub-Gaussian processes. The main results are the bounds for the distributions of the suprema over bounded and unbounded domains for solutions of such equations. The results obtained in the paper hold, in particular, for the case of Gaussian initial condition.
We present two novel methods for the estimation of the angular power spectrum of cosmic microwave background (CMB) anisotropies. We assume an absolute CMB experiment with arbitrary asymmetric beams and arbitrary sky coverage. The methods differ from earlier ones in that the power spectrum is estimated directly from time-ordered data, without first compressing the data into a sky map, and they take into account the effect of asymmetric beams. In particular, they correct the beam-induced leakage from temperature to polarization. The methods are applicable to a case where part of the sky has been masked out to remove foreground contamination, leaving a pure CMB signal, but incomplete sky coverage. The first method (DQML) is derived as the optimal quadratic estimator, which simultaneously yields an unbiased spectrum estimate and minimizes its variance. We successfully apply it to multipoles up to $\ell$=200. The second method is derived as a weak-signal approximation from the first one. It yields an unbiased estimate for the full multipole range, but relaxes the requirement of minimal variance. We validate the methods with simulations for the 70 GHz channel of {\tt Planck} surveyor, and demonstrate that we are able to correct the beam effects in the $TT$, $EE$, $BB$, and $TE$ spectra up to multipole $\ell$=1500. Together the two methods cover the complete multipole range with no gap in between.
We describe high resolution observations of a GOES B-class flare characterized by a circular ribbon at chromospheric level, corresponding to the network at photospheric level. We interpret the flare as a consequence of a magnetic reconnection event occurred at a three-dimensional (3D) coronal null point located above the supergranular cell. The potential field extrapolation of the photospheric magnetic field indicates that the circular chromospheric ribbon is cospatial with the fan footpoints, while the ribbons of the inner and outer spines look like compact kernels. We found new interesting observational aspects that need to be explained by models: 1) a loop corresponding to the outer spine became brighter a few minutes before the onset of the flare; 2) the circular ribbon was formed by several adjacent compact kernels characterized by a size of 1"-2"; 3) the kernels with stronger intensity emission were located at the outer footpoint of the darker filaments departing radially from the center of the supergranular cell; 4) these kernels start to brighten sequentially in clockwise direction; 5) the site of the 3D null point and the shape of the outer spine were detected by RHESSI in the low energy channel between 6.0 and 12.0 keV. Taking into account all these features and the length scales of the magnetic systems involved by the event we argued that the low intensity of the flare may be ascribed to the low amount of magnetic flux and to its symmetric configuration.
Dynamical processes on networks are currently being considered in different domains of cross-disciplinary interest. Reaction-diffusion systems hosted on directed graphs are in particular relevant for their widespread applications, from neuroscience, to computer networks and traffic systems. Due to the peculiar spectrum of the discrete Laplacian operator, homogeneous fixed points can turn unstable, on a directed support, because of the topology of the network, a phenomenon which cannot be induced on undirected graphs. A linear analysis can be performed to single out the conditions that underly the instability. The complete characterization of the patterns, which are eventually attained beyond the linear regime of exponential growth, calls instead for a full non linear treatment. By performing a multiple time scale perturbative calculation, we here derive an effective equation for the non linear evolution of the amplitude of the most unstable mode, close to the threshold of criticality. This is a Stuart-Landau equation whose complex coefficients appear to depend on the topological features of the embedding directed graph. The theory proves adequate versus simulations, as confirmed by operating with a paradigmatic reaction-diffusion model.
We present an accretion cycle which can explain state transitions and other observed phenomena in black hole X-ray binaries. This model is based on the process of disc tearing, where individual rings of gas break off the disc and precess effectively independently. This occurs when the Lense-Thirring effect is stronger than the local disc viscosity. We discuss implications of this model for quasi-periodic oscillations and the disc-jet-corona coupling. We also speculate on applying this model to active galactic nuclei and other accreting systems.
We present an analytical solution of the Ginzburg's $\Psi$-theory for the behavior of the Casimir force in a film of $^4$He in equilibrium with its vapor near the superfluid transition point, and we revisit the corresponding experiments in light of our findings. We find reasonably good agreement between the $\Psi$-theory predictions and the experimental data. Our calculated force is attractive, and the largest absolute value of the scaling function is $1.848$, while experiment yields $1.30$. The position of the extremum is predicted to be at $x=(L/\xi_0)(T/T_\lambda-1)^{1/\nu}=\pi$, while experiment is consistent with $x=3.8$. Here $L$ is the thickness of the film, $T_\lambda$ is the bulk critical temperature and $\xi_0$ is the correlation length amplitude of the system for $T>T_\lambda$.
This paper is concerned with various aspects of the Slepian process $(B_{t+1} - B_t, t \ge 0)$ derived from a one-dimensional Brownian motion $(B_t, t \ge 0 )$. In particular, we offer an analysis of the local structure of the Slepian zero set $\{t : B_{t+1} = B_t \}$, including a path decomposition of the Slepian process for $0 \le t \le 1$. We also establish the existence of a random time $T$ such that $T$ falls in the the Slepian zero set almost surely and the process $(B_{T+u} - B_T, 0 \le u \le 1)$ is standard Brownian bridge.