ShantanuT01/DACTYL-Pretraining huggingface dataset:
Assume that the link of a complex normal surface singularity is a rational homology sphere. Then its Seiberg-Witten invariant can be computed as the `periodic constant' of the topological multivariable Poincar\'e series (zeta function). This involves a complicated regularization procedure (via quasipolynomials measuring the asymptotic behaviour of the coefficients).   We show that the (a Gorenstein type) symmetry of the zeta function combined with Ehrhart-Macdonald-Stanley reciprocity (of Ehrhart theory of polytopes) provide a simple expression for the periodic constant. Using these dualities we also find a multivariable polynomial generalization of the Seiberg-Witten invariant, and we compute it in terms of lattice points of certain polytopes. All these invariants are also determined via lattice point counting, in this way we establish a completely general topological analogue of formulae of Khovanskii and Morales valid for singularities with non-degenerate Newton principal part.
We present the results of a multiwavelength campaign searching for young objects in the intragroup medium of seven compact groups of galaxies: HCG 2, 7, 22, 23, 92, 100 and NGC 92. We used Fabry-Perot velocity fields and rotation curves together with GALEX NUV and FUV images, optical R-band and HI maps to evaluate the stage of interaction of each group. We conclude that groups (i) HCG 7 and HCG 23 are in an early stage of interaction, (ii) HCG 2 and HCG 22 are mildly interacting, and (iii) HCG 92, HCG 100 and NGC 92 are in a late stage of evolution. Evolved groups have a population of young objects in their intragroup medium while no such population is found within the less evolved groups. We also report the discovery of a tidal dwarf galaxy candidate in the tail of NGC 92. These three groups, besides containing galaxies which have peculiar velocity fields, also show extended HI tails. Our results indicate that the advanced stage of evolution of a group together with the presence of intragroup HI clouds may lead to star formation in the intragroup medium.
In Vasiliev's unfolded formulation of higher-spin dynamics the standard fields are embedded on-shell into covariantly constant master fields valued in Lorentz-covariant slices of the star-product algebra A of functions on the singleton phase space. Correspondingly, the harmonic expansion is taken over compact slices of A that are unitarizable in a rescaled trace-norm rather than the standard Killing norm. Motivated by the higher-derivative nature of the theory, we examine indecomposable unitarizable Harish-Chandra modules consisting of standard massless particles plus linearized runaway solutions. This extension arises naturally in the above fiber approach upon realizing compact-weight states as non-polynomial analytic functions in A.
We explore the benefits of using a passively evolving population of galaxies to measure the evolution of the rate of structure growth between z=0.25 and z=0.65 by combining data from the SDSS-I/II and SDSS-III surveys. The large-scale linear bias of a population of dynamically passive galaxies, which we select from both surveys, is easily modeled. Knowing the bias evolution breaks degeneracies inherent to other methodologies, and decreases the uncertainty in measurements of the rate of structure growth and the normalization of the galaxy power-spectrum by up to a factor of two. If we translate our measurements into a constraint on sigma_8(z=0) assuming a concordance cosmological model and General Relativity (GR), we find that using a bias model improves our uncertainty by a factor of nearly 1.5. Our results are consistent with a flat Lambda Cold Dark Matter model and with GR.
We consider the distance to the nearest integer of f(p), where f is a quadratic polynomial with irrational leading coefficient. This distance is very small as a function of p, for infinitely many primes p. We give a 14% improvement in the exponent that measures the distance, compared with the most recent result in the literature.
Interacting double white dwarf binaries can give rise to a wide variety of astrophysical outcomes ranging from faint thermonuclear and Type Ia supernovae to the formation of neutron stars and stably accreting AM Canum Venaticorum systems. One key factor affecting the final outcome is whether mass transfer remains dynamically stable or instead diverges, leading to the tidal disruption of the donor and the merger of the binary. It is typically thought that for low ratios of the donor mass to the accretor mass, mass transfer remains stable, especially if accretion occurs via a disk. In this Letter, we examine low mass ratio double white dwarf binaries and find that the initial phase of hydrogen-rich mass transfer leads to a classical nova-like outburst on the accretor. Dynamical friction within the expanding nova shell shrinks the orbit and causes the mass transfer rate to increase dramatically above the accretor's Eddington limit, possibly resulting in a binary merger. If the binary survives the first hydrogen-rich nova outbursts, dynamical friction within the subsequent helium-powered nova shells pushes the system even more strongly towards merger. While further calculations are necessary to confirm this outcome for the entire range of binaries previously thought to be dynamically stable, it appears likely that most, if not all, interacting double white dwarf binaries will merge during the course of their evolution.
We apply Bridgeland stability conditions machinery to describe the geometry of some classical moduli spaces associated with canonical genus four curves in $\mathbb{P}^3$ via an effective control over its wall-crossing. These moduli spaces with several irreducible components include the moduli space of Pandharipande-Thomas stable pairs, and the Hilbert scheme, which are not previously studied. We give a full list of irreducible components of the space of stable pairs, along with a birational description of each component, and a partial list for the Hilbert scheme.
We discuss the concept of characteristic squeezing modes applied to a travelling-wave optical parametric amplifier pumped by an ultrashort pulse. The characteristic modes undergo decoupled single-mode squeezing transformations, and therefore they form a useful basis to describe the evolution of the entire multimode system. This provides an elegant and intuitive picture of quantum statistical properties of parametric fluorescence. We analyse the efficiency of detecting quadrature squeezing, and present results of numerical calculations for a realistic nonlinear medium.
For a set of nonnegative integers $c_1, \ldots, c_k$, a $(c_1, c_2,\ldots, c_k)$-coloring of a graph $G$ is a partition of $V(G)$ into $V_1, \ldots, V_k$ such that for every $i$, $1\le i\le k, G[V_i]$ has maximum degree at most $c_i$. We prove that all planar graphs without 4-cycles and no less than two edges between triangles are $(2,0,0)$-colorable.
Detecting traversable road areas ahead a moving vehicle is a key process for modern autonomous driving systems. A common approach to road detection consists of exploiting color features to classify pixels as road or background. These algorithms reduce the effect of lighting variations and weather conditions by exploiting the discriminant/invariant properties of different color representations. Furthermore, the lack of labeled datasets has motivated the development of algorithms performing on single images based on the assumption that the bottom part of the image belongs to the road surface.   In this paper, we first introduce a dataset of road images taken at different times and in different scenarios using an onboard camera. Then, we devise a simple online algorithm and conduct an exhaustive evaluation of different classifiers and the effect of using different color representation to characterize pixels.
In this paper, we investigate some interesting properties of q-Berstein polynomials realted to q-Euler numbers by using the fermionic q-integral on Zp.
We report on the electrical and thermal transport properties of nickel nanoparticles with crystallite size from 23.1 to 1.3 nm. These nanoparticles show a systematic metal to insulator transition with the change in the conduction type from n to p type, colossal Seebeck coefficient, and ultralow thermal conductivity at 300 K as the crystallite size drops. The electrical resistivity analysis reveals a dramatic change in the electronic excitation spectrum indicating the opening of an energy gap, and cotunneling and Coulomb blockade of the charge carriers. Seebeck coefficient shows transport energy degradation of charge carriers as transport level moves away from the Fermi level with decrease in crystallite size. The Lorenz number rising to about four orders of magnitude in the metallic regimes with decrease in crystallite size, showing a large violation of the Wiedemann Franz law in these compacted nickel nanoparticles. Such an observation provides the compelling confirmation for unconventional quasiparticle dynamics where the transport of charge and heat is independent of each other. Therefore, such nanoparticles provide an intriguing platform to tune the charge and heat transport, which may be useful for thermoelectrics and heat dissipation in nanocrystal array-based electronics.
HST/NICMOS images of the class I protostar TMR-1 (IRAS04361+2547) reveal a faint companion with 10.0" = 1400 AU projected separation. The central protostar is itself resolved as a close binary with 0.31" = 42 AU separation, surrounded by circumstellar reflection nebulosity. A long narrow filament seems to connect the protobinary to the faint companion TMR-1C, suggesting a physical association. If the sources are physically related then we hypothesize that TMR-1C has been ejected by the protobinary. If TMR-1C has the same age and distance as the protobinary then current models indicate its flux is consistent with a young giant planet of several Jovian masses.
The optical, elastic anisotropic and thermodynamic properties of TiN in the NaCl (B1) structure are analyzed in detail in the temperature range from 0 to 2000 K and the pressure range from 0 to 20 GPa. From the calculated dielectric constants, a first order isostructural phase transition between 29 and 30 GPa is found for TiN. The absorption spectra exhibit high values ranging from the far infrared region to the ultra-violet one. The anisotropy value of Young's modulus of TiN is smaller than that of c-BN at 0 GPa and the anisotropy of TiN clearly increases with an increase of pressure. The effects of pressure and temperature on the bulk modulus, Gr\"uneisen parameter, Gibbs free energy, and Debye temperature are significant. The Gr\"uneisen parameter of TiN is much larger than that of c-BN. At temperatures below 1000 K, TiN's heat capacity is much larger than that of c-BN.
The formalism of state estimation and hidden Markov models (HMMs) can simplify and clarify the discussion of stochastic thermodynamics in the presence of feedback and measurement errors. After reviewing the basic formalism, we use it to shed light on a recent discussion of phase transitions in the optimized response of an information engine, for which measurement noise serves as a control parameter. The HMM formalism also shows that the value of additional information shows a maximum at intermediate signal-to-noise ratios. Finally, we discuss how systems open to information flow can apparently violate causality; the HMM formalism can quantify the performance gains due to such violations.
In driving scenarios with poor visibility or occlusions, it is important that the autonomous vehicle would take into account all the uncertainties when making driving decisions, including choice of a safe speed. The grid-based perception outputs, such as occupancy grids, and object-based outputs, such as lists of detected objects, must then be accompanied by well-calibrated uncertainty estimates. We highlight limitations in the state-of-the-art and propose a more complete set of uncertainties to be reported, particularly including undetected-object-ahead probabilities. We suggest a novel way to get these probabilistic outputs from bird's-eye-view probabilistic semantic segmentation, in the example of the FIERY model. We demonstrate that the obtained probabilities are not calibrated out-of-the-box and propose methods to achieve well-calibrated uncertainties.
With a simple transformation of the three exponents the generalized Fermat equation can be put into the same form as the Fermat equation. When it is rewritten into this new altered form any real solutions to the altered equation equal a subset of real solutions to the Fermat equation. This result, along with a paradigm previously established by G. Frey and Y. Hellegouarch, can be used to show that the generalized Fermat equation has no solutions in coprime integers. In fact we prove one can derive an elliptic curve over $\mathbb{Q}$ for primes (p \geq 3), from the assumption that (x_{0}^{k} + y_{0}^{l} = z_{0}^{m}), (k, l, m \geq 3), has coprime solutions in integers. The curve then can be used to show the unsolvability of this equation. Our aim is not to arrive at very deep results. Rather the goal in this paper is to apply prior results obtained by G. Frey, K. Ribet and A. Wiles, to show the lack of solutions to the generalized Fermat equation.
We have developed a frequentist approach for model selection which determines the consistency between any cosmological model and the data using the distribution of likelihoods from the iterative smoothing method. Using this approach, we have shown how confidently we can conclude whether the data support any given model without comparison to a different one. In this current work, we compare our approach with the conventional Bayesian approach based on the estimation of the Bayesian evidence using nested sampling. We use simulated future Roman (formerly WFIRST)-like type Ia supernovae data in our analysis. We discuss the limits of the Bayesian approach for model selection and show how our proposed frequentist approach can perform better in the falsification of individual models. Namely, if the true model is among the candidates being tested in the Bayesian approach, that approach can select the correct model. If all of the options are false, then the Bayesian approach will select merely the least incorrect one. Our approach is designed for such a case and we can conclude that all of the models are false.
Throttling addresses the question of minimizing the sum or the product of the resources used to accomplish a task and the time needed to complete that task for various graph searching processes. Graph parameters of interest include various types of zero forcing, power domination, and Cops and Robbers. We provide a survey of product throttling for these parameters.
The expected gamma-ray flux coming from dark matter annihilation in dwarf spheroidal (dSph) galaxies depends on the so-called `J-factor', the integral of the squared dark matter density along the line-of-sight. We examine the degree to which estimates of J are sensitive to contamination (by foreground Milky Way stars and stellar streams) of the stellar-kinematic samples that are used to infer dark matter densities in `ultrafaint' dSphs. Applying standard kinematic analyses to hundreds of mock data sets that include varying levels of contamination, we find that mis-classified contaminants can cause J-factors to be overestimated by orders of magnitude. Stellar-kinematic data sets for which we obtain such biased estimates tend 1) to include relatively large fractions of stars with ambiguous membership status, and 2) to give estimates for J that are sensitive to specific choices about how to weight and/or to exclude stars with ambiguous status. Comparing publicly-available stellar-kinematic samples for the nearby dSphs Reticulum~II and Segue~I, we find that only the latter displays both of these characteristics. Estimates of Segue~I's J-factor should therefore be regarded with a larger degree of caution when planning and interpreting gamma-ray observations. Moreover, robust interpretations regarding dark matter annihilation in dSph galaxies in general will require explicit examination of how interlopers might affect the inferred dark matter density profile.
We investigate the possibilities of searching for a self-conjugate polarizable particle in the self-interactions of light. We first observe that polarizability can arise either from the exchange of mediator states or as a consequence of the inner structure of the particle. To exemplify this second possibility we calculate the polarizability of a neutral bosonic open string, and find it is described only by dimension-8 operators. Focussing on the spin-0 case, we calculate the light-by-light scattering amplitudes induced by the dimension-6 and 8 polarizability operators. Performing a simulation of exclusive diphoton production with proton tagging at the LHC, we find that the imprint of the polarizable dark particle can be potentially detected at 5$\sigma$ significance for mass and cutoff reaching values above the TeV scale, for $\sqrt{s}=$13~TeV and 300 fb$^{-1}$ of integrated luminosity. If the polarizable dark particle is stable, it can be a dark matter candidate, in which case we argue this exclusive diphoton search may complement the existing LHC searches for polarizable dark matter.
In this work, electronic structure of several doped TiO$_2$ anatase systems is computed using DFT+$U$. Effective masses of charge carriers are also computed to quantify how the dopant atoms perturb the bands of the host anatase material. $U$ is computed systematically for all the dopants using the linear response method rather than using fitting procedures to physically known quantities. A combination of $d$ and $f$ block elements (Nb, Ta, V, Mo, W, Cr, La, Cu, Co and Ce) are considered as dopants. Depending upon the energies of their outer $d$ or $f$ electrons, the dopants are found to form defect states at various positions in the band structure of host anatase system. Some dopants like Cr, Mo etc. form mid-gap states, which could reduce transparency. Other dopants like Nb, Ta and W are found to have the Fermi levels positioned near the conduction band edge, indicating these systems to exhibit $n$-type conductivity. From the effective mass analysis, dopants are found to increase the effective mass of charge carriers and the non-parabolic nature of bands. Based on electronic structure and effective mass analysis, Nb, Ta and W are identified to exhibit higher transparency and conductivity as compared to the other dopants considered here. The theoretical results presented here, increase our understanding and show the potential of dopants to alter the properties in anatase TiO$_2$.
We analyze the effect of twists on the electronic structure of configurations of infinite stacks of graphene layers. We focus on three different cases: an infinite stack where each layer is rotated with respect to the previous one by a fixed angle, two pieces of semi-infinite graphite rotated with respect to each other, and finally a single layer of graphene rotated with respect to a graphite surface. In all three cases we find a rich structure, with sharp resonances and flat bands for small twist angles. The method used can be easily generalized to more complex arrangements and stacking sequences.
Primitively polarized genus $g$ Nikulin surfaces $(S,M,H)$ are of two types, that we call standard and non-standard depending on whether the lattice embedding $\mathbb{Z}[H] \oplus_{\perp} \mathbf{N} \subset \rm{Pic}(S)$ is primitive. Here $H$ is the genus $g$ polarization and $\mathbf{N}$ is the Nikulin lattice. We concentrate on the non-standard case, which only occurs in odd genus. In particular, we study the birational geometry of the moduli space of non-standard Nikulin surfaces of genus $g$ and prove its rationality for $g=7,11$ and the existence of a rational double cover of it when $g=9$. Furthermore, if $(S,M,H)$ is general in the above moduli space and $(C,M|_C)$ is a general Prym curve in $|H|$, we determine the dimension of the family of non-standard Nikulin surfaces of genus $g$ containing $(C, M|_C)$ for $3\leq g\leq 11$; this completes the study of the Prym-Nikulin map initiated in our previous work.
The paper is devoted to a systematic study of the duality of processes in the sense that $E f(X_t^x,y)=E f (x, Y_t^y)$ for a certain $f$.   This classical topic has well known applications in interacting particles, intertwining, superprocesses, stochastic monotonicity, exit - entrance laws, ruin probabilities in finances, etc. Aiming mostly at the case of $f$ depending on the difference of its arguments, we shall give a systematic study of duality via the analysis of the generators of dual Markov processes leading to various results and insights.
We introduce a multispecies exclusion model where length-conserving probabilistic fusion and fission of the hard rods are allowed. Although all rods enter the system with the same initial length ${\ell}=1$, their length can keep changing, because of fusion and fission, as they move in a step-by-step manner towards the exit. Two neighboring hard rods of lengths ${\ell}_{1}$ and ${\ell}_{2}$ can fuse into a single rod of longer length ${\ell}={\ell}_{1}+{\ell}_{2}$ provided ${\ell} \leq N$. Similarly, length-conserving fission of a rod of length ${\ell}' \leq N$ results in two shorter daughter rods. Based on the extremum current hypothesis, we plot the phase diagram of the model under open boundary conditions utilizing the results derived for the same model under periodic boundary condition using mean-field approximation. The density profile and the flux profile of rods are in excellent agreement with computer simulations. Although the fusion and fission of the rods are motivated by similar phenomena observed in Intraflagellar Transport (IFT) in eukaryotic flagella, this exclusion model is too simple to account for the quantitative experimental data for any specific organism. Nevertheless, the concepts of `flux profile' and `transition zone' that emerge from the interplay of fusion and fission in this model are likely to have important implications for IFT and for other similar transport phenomena in long cell protrusions.
We report on initial results from a Spitzer program to search for very low-mass brown dwarfs in Ophiuchus. This program is an extension of an earlier study by Allers et al. which had resulted in an extraordinary success rate, 18 confirmed out of 19 candidates. Their program combined near-infrared and Spitzer photom- etry to identify objects with very cool photospheres together with circumstellar disk emission to indicate youth. Our new program has obtained deep IRAC pho- tometry of a 0.5 deg2 field that was part of the original Allers et al. study. We report 18 new candidates whose luminosities extend down to 10-4 L\cdot which sug- gests masses down to ~ 2 MJ if confirmed. We describe our selection techniques, likely contamination issues, and follow-on photometry and spectroscopy that are in progress.
The rho - omega interference in the exclusive reaction pi N \to N' e+ e- is studied within a schematic model including the established baryon resonances up to 1720 MeV. Near threshold the interference can be used to separate the isoscalar part of the electromagnetic current. The role of various baryon resonances is highlighted.
We consider a generic framework where the Standard Model (SM) coexists with a hidden sector endowed with some additional gauge symmetry. When this symmetry is broken by a scalar field charged under the hidden gauge group, the corresponding scalar boson generally mixes with the SM Higgs boson. In addition, massive hidden gauge bosons emerge and via the mixing, the observed Higgs-like mass eigenstate is the only known particle that couples to these hidden gauge bosons directly.   We study the LHC monojet signatures of this scenario and the corresponding constraints on the gauge coupling of the hidden gauge group as well as the mixing of the Higgs scalars.