ShantanuT01/DACTYL-Pretraining huggingface dataset:
The paper is concerned with the equilibrium distribution $\Pi_n$ of the $n$-th element in a sequence of continuous-time density dependent Markov processes on the integers. Under a $(2+\a)$-th moment condition on the jump distributions, we establish a bound of order $O(n^{-(\a+1)/2}\sqrt{\log n})$ on the difference between the point probabilities of $\Pi_n$ and those of a translated Poisson distribution with the same variance. Except for the factor $\sqrt{\log n}$, the result is as good as could be obtained in the simpler setting of sums of independent integer-valued random variables. Our arguments are based on the Stein-Chen method and coupling.
A classic result of Erd\H{o}s and, independently, of Bondy and Simonovits says that the maximum number of edges in an $n$-vertex graph not containing $C_{2k}$, the cycle of length $2k$, is $O( n^{1+1/k})$. Simonovits established a corresponding supersaturation result for $C_{2k}$'s, showing that there exist positive constants $C,c$ depending only on $k$ such that every $n$-vertex graph $G$ with $e(G)\geq Cn^{1+1/k}$ contains at least $c\left(\frac{e(G)}{v(G)}\right)^{2k}$ many copies of $C_{2k}$, this number of copies tightly achieved by the random graph (up to a multiplicative constant).   In this paper, we extend Simonovits' result to a supersaturation result of $r$-uniform linear cycles of even length in $r$-uniform linear hypergraphs. Our proof is self-contained and includes the $r=2$ case. As an auxiliary tool, we develop a reduction lemma from general host graphs to almost-regular host graphs that can be used for other supersaturation problems, and may therefore be of independent interest.
Unsupervised domain adaptation methods traditionally assume that all source categories are present in the target domain. In practice, little may be known about the category overlap between the two domains. While some methods address target settings with either partial or open-set categories, they assume that the particular setting is known a priori. We propose a more universally applicable domain adaptation framework that can handle arbitrary category shift, called Domain Adaptative Neighborhood Clustering via Entropy optimization (DANCE). DANCE combines two novel ideas: First, as we cannot fully rely on source categories to learn features discriminative for the target, we propose a novel neighborhood clustering technique to learn the structure of the target domain in a self-supervised way. Second, we use entropy-based feature alignment and rejection to align target features with the source, or reject them as unknown categories based on their entropy. We show through extensive experiments that DANCE outperforms baselines across open-set, open-partial and partial domain adaptation settings. Implementation is available at https://github.com/VisionLearningGroup/DANCE.
We study the properties of voids in two different types of coupled scalar field theories. Due to the fifth force produced by the scalar field coupling, the matter particles feel stronger attraction amongst each other and cluster more quickly than they do in the standard LCDM model. Consequently voids in the coupled scalar field theories start to develop earlier and end up bigger, which is confirmed by our numerical simulations. We find that a significantly larger portion of the whole space is under-densed in the coupled scalar field theories and there are more voids whose sizes exceed given thresholds. This is more prominent in early times because at later times the under-dense regions have already been evacuated in coupled scalar field theories and there is time for the LCDM model to catch up. The coupled scalar field theories also predict a sharper transition between voids and high density regions. All in all, the qualitative behaviour is different not only from the LCDM result, but also amongst specific coupled scalar field models, making voids a potential candidate to test alternative ideas about the cosmic structure formation.
Strongly long-range interacting quantum systems---those with interactions decaying as a power-law $1/r^{\alpha}$ in the distance $r$ on a $D$-dimensional lattice for $\alpha\le D$---have received significant interest in recent years. They are present in leading experimental platforms for quantum computation and simulation, as well as in theoretical models of quantum information scrambling and fast entanglement creation. Since no notion of locality is expected in such systems, a general understanding of their dynamics is lacking. As a first step towards rectifying this problem, we prove two new Lieb-Robinson-type bounds that constrain the time for signaling and scrambling in strongly long-range interacting systems, for which no tight bounds were previously known. Our first bound applies to systems mappable to free-particle Hamiltonians with long-range hopping, and is saturable for $\alpha\le D/2$. Our second bound pertains to generic long-range interacting spin Hamiltonians, and leads to a tight lower bound for the signaling time to extensive subsets of the system for all $\alpha < D$. This result also lower-bounds the scrambling time, and suggests a path towards achieving a tight scrambling bound that can prove the long-standing fast scrambling conjecture.
We present new far-infrared (70-500micron) Herschel PACS and SPIRE imaging observations as well as new mid-IR Gemini/T-ReCS imaging (8.7 and 18.3micron) and spectroscopy of the inner Lindblad resonance (ILR) region (R<2.5kpc) of the spiral galaxy NGC1365. We complemented these observations with archival Spitzer imaging and spectral mapping observations. The ILR region of NGC1365 contains a Seyfert 1.5 nucleus and a ring of star formation with an approximate diameter of 2kpc. The strong star formation activity in the ring is resolved by the Herschel/PACS imaging data, as well as by the Spitzer 24micron continuum emission, [NeII]12.81micron line emission, and 6.2 and 11.3micron PAH emission. The AGN is the brightest source in the central regions up to lambda~24micron, but it becomes increasingly fainter in the far-infrared when compared to the emission originating in the infrared clusters (or groups of them) located in the ring. We modeled the AGN unresolved infrared emission with the CLUMPY torus models and estimated that the AGN contributes only to a small fraction (~5%) of the infrared emission produced in the inner ~5kpc. We fitted the non-AGN 24-500micron spectral energy distribution of the ILR region and found that the dust temperatures and mass are similar to those of other nuclear and circumnuclear starburst regions. Finally we showed that within the ILR region of NGC1365 most of the on-going star formation activity is taking place in dusty regions as probed by the 24micron emission.
Expanding media are typical in many different fields, e.g. in Biology and Cosmology. In general, a medium expansion (contraction) brings about dramatic changes in the behavior of diffusive transport properties. Here, we focus on such effects when the diffusion process is described by the Continuous Time Random Walk (CTRW) model. For the case where the jump length and the waiting time probability density functions (pdfs) are long-tailed, we derive a general bifractional diffusion equation which reduces to a normal diffusion equation in the appropriate limit. We then study some particular cases of interest, including L\'evy flights and subdiffusive CTRWs. In the former case, we find an analytical exact solution for the Green's function (propagator). When the expansion is sufficiently fast, the contribution of the diffusive transport becomes irrelevant at long times and the propagator tends to a stationary profile in the comoving reference frame. In contrast, for a contracting medium a competition between the spreading effect of diffusion and the concentrating effect of contraction arises. For a subdiffusive CTRW in an exponentially contracting medium, the latter effect prevails for sufficiently long times, and all the particles are eventually localized at a single point in physical space. This "Big Crunch" effect stems from inefficient particle spreading due to subdiffusion. We also derive a hierarchy of differential equations for the moments of the transport process described by the subdiffusive CTRW model. In the case of an exponential expansion, exact recurrence relations for the Laplace-transformed moments are obtained. Our results confirm the intuitive expectation that the medium expansion hinders the mixing of diffusive particles occupying separate regions. In the case of L\'evy flights, we quantify this effect by means of the so-called "L\'evy horizon".
Context. Emission lines formed in the transition region and corona show dominantly redshifts and blueshifts, respectively. Aims. We investigate the Doppler shifts in a 3D radiation MHD model of the quiet Sun and compare these to observed properties. We concentrate on Si IV 1394 A originating in the transition region and examine the Doppler shifts of several other spectral lines at different formation temperatures. Methods. We construct a radiation MHD model extending from the upper convection zone to the lower corona using the MURaM code. In this quiet Sun model the magnetic field is self-consistently maintained by the action of a small-scale dynamo. We synthesize the profiles of several optically thin emission lines, formed at temperatures from the transition region into the corona. We investigate the spatial structure and coverage of red- and blueshifts and how this changes with line-formation temperature. Results. The model successfully reproduces the observed change of average net Doppler shifts from red- to blueshifted from the transition region into the corona. In particular, the model shows a clear imbalance of area coverage of red- vs. blueshifts in the transition region of ca. 80% to 20%. We determine that (at least) four processes generate the systematic Doppler shifts in our model, including pressure enhancement in the transition region, transition region brightenings unrelated to coronal emission, boundaries between cold and hot plasma, and siphon-type flows. Conclusions. We show that there is not a single process that is responsible for the observed net Doppler shifts in the transition region and corona. Because current 3D MHD models do not yet fully capture the evolution of spicules, one of the key ingredients of the chromosphere, most probably these have still to be added to the list of processes responsible for the persistent Doppler shifts.
By employing a Boltzmann transport equation and using an energy and size dependent relaxation time ($\tau$) approximation (RTA), we evaluate self-consistently the thermoelectric figure-of-merit $ZT$ of a quantum wire with rectangular cross-section. The inferred $ZT$ shows abrupt enhancement in comparison to its counterparts in bulk systems. Still, the estimated $ZT$ for the representative Bi$_2$Te$_3$ nanowires and its dependence on wire parameters deviate considerably from those predicted by the existing RTA models with a constant $\tau$. In addition, we address contribution of the higher energy subbands to the transport phenomena, the effect of chemical potential tuning on $ZT$, and correlation of $ZT$ with quantum size effects (QSEs). The obtained results are of general validity for a wide class of systems and may prove useful in the ongoing development of the modern thermoelectric applications.
We study the dynamics of a homogeneous granular gas heated by a stochastic thermostat, in the low density limit. It is found that, before reaching the stationary regime, the system quickly "forgets" the initial condition and then evolves through a universal state that does not only depend on the dimensionless velocity, but also on the instantaneous temperature, suitably renormalized by its steady state value. We find excellent agreement between the theoretical predictions at Boltzmann equation level for the one-particle distribution function, and Direct Monte Carlo simulations. We conclude that at variance with the homogeneous cooling phenomenology, the velocity statistics should not be envisioned as a single-parameter, but as a two-parameter scaling form, keeping track of the distance to stationarity.
The mysterious universal line revealing an independence of spin fluctuation contributions to the heat capacity of (Mn,Co)Si on impurity contents and its nature is discovered. This situation probably declares an invariance of the spin subsystem energy that may provide by the response of itinerant electron system on the volume change at doping.
Two classes of X-ray/$\gamma$-ray sources, the Soft Gamma Repeaters and the Anomalous X-ray Pulsars have been identified with isolated, slowly spinning magnetars, neutron stars whose emission draws energy from their extremely strong magnetic field ($\sim 10^{15}-10^{16}$ G). Magnetars are believed to form with millisecond spin period and to represent an important fraction of the whole population of young neutron stars. Newborn magnetars can convert very quickly their rotational energy into electromagnetic and/or gravitational waves, by virtue of their strong magnetic fields and fast spins. This chapter provides a brief summary of astrophysical problems and scenarios in which millisecond magnetars are believed to play a key role: these include Gamma Ray Bursts, Supernovae, Gravitational Wave events and Fast Radio Bursts.
We highlight the importance of transit observations on understanding the physics of planetary atmospheres and interiors. Transmission spectra and emission spectra allow us to characterize this exotic atmospheres, which possess TiO, VO, H2O, CO, Na, and K, as principal absorbers. We calculate mass-radius relations for water-rock-iron and gas giant planets and examine these relations in light of current and future transit observations. A brief review is given of mechanisms that could lead to the large radii observed for some transiting planets.
We study the quantitative characterization of the performance of qubit measurements in this paper. In particular, the back-action evading nature of quantum nondemolition (QND) readout of qubits is fully quantified by quantum trace distance. Only computational basis states are necessary to be taken into consideration. Most importantly, we propose an experimentally efficient method to evaluate the QND fidelity based on the classical trace distance, which uses an experimental scheme with two consecutive measurements. The three key quantifiers of a measurement, i.e., QND fidelity, readout fidelity, and projectivity, can be derived directly from the same experimental scheme. Besides, we present the relationships among these three factors. Theoretical simulation results for the dispersive readout of superconducting qubits show the validity of the proposed QND fidelity. Efficient quantification of measurement performance is of practical significance for the diagnosis, performance improvement, and design of measurement apparatuses.
For relativistic three-body calculations, essentially two different approaches are in use: field theory and relativistic direct interactions. Results for relativistic corrections of the triton binding energy obtained from the two approaches differ even in their sign, which is rather puzzling. In this paper, we discuss the origin of such discrepancy. We show that the use of an invariant two-body amplitude, as done in the field-theoretic approach, increases the triton binding energy by about 0.30 MeV. This may explain a large part of the discrepancy.
I review the properties of a matrix action of relevance for IIB superstrings. This model generalizes the action proposed by Ishibashi, Kawai, Kitazawa, and Tsuchiya by introducing an auxillary field Y, which is the matrix version of the auxillary field g in the Schild action.
We consider the most general form of extended Hubbard Hamiltonian conserving the total spin and number of electrons, and find all the 1-dimensional completely integrable models which can be derived from first degree polynomial solution of the Yang-Baxter equation. It is shown that such models are 96. They are identified with the 16-dimensional representation of a new class of solutions of symmetric group relations, acting as generalized permutators. As particular examples, the EKS and some other known models are obtained.
We investigate the ground-state property and the excitation gap of a one-dimensional spin-orbital model with isotropic spin and anisotropic orbital exchange interactions, which represents the strong-coupling limit of a two-orbital Hubbard model including the Hund's rule coupling ($J$) at quarter filling, by using a density-matrix renormalization group method. At J=0, spin and orbital correlations coincide with each other with a peak at $q=\pi/2$, corresponding to the SU(4) singlet state. On the other hand, spin and orbital states change in a different way due to the Hund's rule coupling. With increasing $J$, the peak position of orbital correlation changes to $q=\pi$, while that of spin correlation remains at $q=\pi/2$. In addition, orbital dimer correlation becomes robust in comparison with spin dimer correlation, suggesting that quantum orbital fluctuation is enhanced by the Hund's rule coupling. Accordingly, a relatively large orbital gap opens in comparison with a spin gap, and the system is described by an effective spin system on the background of the orbital dimer state.
In 2000 Deaconescu raised a question whether there exists a composite $n$ for which $S_2(n)|\phi(n)-1$, where $\phi(n)$ is Euler's function and $S_2(n)$ is Schemmel's totient function. In this paper we prove that any such $n$ is odd, squarefree and has at least seven distinct prime factors. We also prove that any such $n$ with exactly $K$ distinct prime divisors is necessarily less than $2^{2^{K+1}}$.
This is a second paper of a series of two. In this paper, we directly correct the problem pointed out in the first paper of this series, dark energy does not cluster on the scale of galaxy clusters, but the current describing the flowing of dark energies outside the clusters is ignored in almost all the previous papers. We set up and solve a first order differential equation which describes the evolution of the clusters in a back ground universe containing dark energies.   From the solution we extract the key parameters of the model and find them depending on the equation of state coefficients of dark energies rather non-trivially. We then apply the results in Press-Scheter theory and calculate the number density of galaxy clusters and its evolutions, we find the observable quantities are strongly affected by the equation of state coefficients of dark energies.
The evolution of surface morphology during the growth of N-polar (000-1) GaN under N-rich condition is studied by kinetic Monte Carlo (kMC) simulations for two substrates miscuts 2deg and 4deg. The results are compared with experimentally observed surface morphologies of (000-1) GaN layers grown by plasma-assisted molecular beam epitaxy. The proposed kMC two-component model of GaN(000-1) surface where both types of atoms: nitrogen and gallium attach the surface and diffuse independently, explains that at relatively high rates of the step flow (miscut angle <2deg) the low diffusion of gallium adatoms causes surface instabilities and leads to experimentally observed roughening while for low rates of the step flow (miscut 4deg), smooth surface can be obtained. In the presence of almost immobile nitrogen atoms under N-rich conditions, the growth is realized by the process of two-dimensional island nucleation and coalescence. Additionally, we show that higher crystal miscut, lower crystal growth rate or higher temperature results in similar effect of the smoothening of the surface. We show that the surface also smoothens for the growth conditions with very high N-excess. The presence of large number of nitrogen atoms changes locally mobility of gallium atoms thus providing easier coalescence of separated island.
Some merging galaxy clusters host diffuse extended radio emission, so-called radio halos and relics. Here we present observations between 147 MHz and 4.9 GHz of a new radio-selected galaxy cluster 1RXS J0603.3+4214 (z=0.225). The cluster is also detected as an extended X-ray source in the RASS. It hosts a large bright 1.9 Mpc radio relic, an elongated ~2 Mpc radio halo, and two smaller radio relics. The large radio relic has a peculiar linear morphology. For this relic we observe a clear spectral index gradient, in the direction towards the cluster center. We performed Rotation Measure (RM) Synthesis between 1.2 and 1.7 GHz. The results suggest that for the west part of the large relic some of the Faraday rotation is caused by ICM and is not only due to galactic foregrounds. We also carried out a detailed spectral analysis of this radio relic and created radio color-color diagrams. We find (i) an injection spectral index of -0.6 to -0.7, (ii) steepening spectral index and increasing spectral curvature in the post-shock region, and (iii) an overall power-law spectrum between 74 MHz and 4.9 GHz with \alpha=-1.10 \pm 0.02. Mixing of emission in the beam from regions with different spectral ages is probably the dominant factor that determines the shape of the radio spectra. Changes in the magnetic field, total electron content, or adiabatic gains/losses do not play a major role. A model in which particles are (re)accelerated in a first order Fermi process at the front of the relic provides the best match to the observed spectra. We speculate that in the post-shock region particles are re-accelerated by merger induced turbulence to form the radio halo as the relic and halo are connected. The 1RXS J0603.3+4214 merger is probably more complex than the "simple'" binary merger events that are thought to give rise to symmetric double radio relics.
We investigate the effects of the environment on star-formation in a sample of massive luminous and ultra-luminous infrared galaxies (LIRGs and ULIRGs) with S(24 micron)>80 uJy and i+<24 in the COSMOS field. We exploit the accurate photometric redshifts in COSMOS to characterize the galaxy environment and study the evolution of the fraction of LIRGs and ULIRGs in different environments in the redshift range z=0.3-1.2 and in bins of stellar mass. We find that the environment plays a role in the star formation processes and evolution of LIRGs and ULIRGs. We find an overall increase of the ULIRG+LIRG fraction in an optically-selected sample with increasing redshift, as expected from the evolution of the star formation rate density. We find that the ULIRG+LIRG fraction decreases with increasing density up to z~1, and that the dependence on density flattens with increasing redshift. We do not observe the reversal of the star-formation rate density relation up to z=1 in massive LIRGs and ULIRGs, suggesting that such reversal might occur at higher redshift in this infrared luminosity range.
Fingerprint is widely used in a variety of applications. Security measures have to be taken to protect the privacy of fingerprint data. Cancelable biometrics is proposed as an effective mechanism of using and protecting biometrics. In this paper we propose a new method of constructing cancelable fingerprint template by combining real template with synthetic template. Specifically, each user is given one synthetic minutia template generated with random number generator. Every minutia point from the real template is individually thrown into the synthetic template, from which its k-nearest neighbors are found. The verification template is constructed by combining an arbitrary set of the k-nearest neighbors. To prove the validity of the scheme, testing is carried out on three databases. The results show that the constructed templates satisfy the requirements of cancelable biometrics.