ShantanuT01/DACTYL-Pretraining huggingface dataset:
Consider the smooth projective models C of curves y^2=f(x) with f(x) in Z[x] monic and separable of degree 2g+1. We prove that for g >= 3, a positive fraction of these have only one rational point, the point at infinity. We prove a lower bound on this fraction that tends to 1 as g tends to infinity. Finally, we show that C(Q) can be algorithmically computed for such a fraction of the curves. The method can be summarized as follows: using p-adic analysis and an idea of McCallum, we develop a reformulation of Chabauty's method that shows that certain computable conditions imply #C(Q)=1; on the other hand, using further p-adic analysis, the theory of arithmetic surfaces, a new result on torsion points on hyperelliptic curves, and crucially the Bhargava-Gross equidistribution theorem for nonzero 2-Selmer group elements, we prove that these conditions are often satisfied for p=2.
In this paper we prove a sharp quantitative version of the Kendall's Theorem. The Kendal Theorem states that under some mild conditions imposed on a probability distribution on positive integers (i.e. probabilistic sequence) one can prove convergence of its renewal sequence. Due to the well-known property - the first entrance last exit decomposition - such results are of interest in the stability theory of time homogeneous Markov chains. In particular the approach may be used to measure rates of convergence of geometrically ergodic Markov chains and consequently implies estimates on convergence of MCMC estimators.
In the current framework, the standard parametrization of our Universe is the so-called Lambda Cold Dark Matter ({\Lambda}CDM) model. Recently, Risaliti & Lusso (2019) have shown a ~4{\sigma} tension with the {\Lambda}CDM model through a model-independent parametrization of a Hubble Diagram of supernovae Ia (SNe Ia) from the JLA survey and quasars. Model-independent approaches and independent samples over a wide redshift range are key to testing this tension and any possible systematics. Here we present an analysis of a combined Hubble Diagram of SNe Ia, quasars, and gamma-ray bursts (GRBs) to check the agreement of the quasar and GRB cosmological parameters at high redshifts (z>2) and to test the concordance flat {\Lambda}CDM model with improved statistical accuracy. We build a Hubble diagram with SNe Ia from the Pantheon sample (Scolnic et al. 2018), quasars from the Risaliti & Lusso (2019) sample, and GRBs from the Demianski et al. (2017a) sample, where quasars are standardised through the observed non-linear relation between their ultraviolet and X-ray emission and GRBs through the correlation between the spectral peak energy and the isotropic-equivalent radiated energy (the so-called "Amati relation"). We fit the data with cosmographic models consisting of a fourth-order logarithmic polynomial and a fifth-order linear polynomial, and compare the results with the expectations from a flat {\Lambda}CDM model. We confirm the tension between the best fit cosmographic parameters and the {\Lambda}CDM model at ~4{\sigma} with SNe Ia and quasars, at ~2{\sigma} with SNe Ia and GRBs, and at >4{\sigma} with the whole SNe Ia+quasars+GRB data set. The completely independent high-redshift Hubble diagrams of quasars and GRBs are fully consistent with each other, strongly suggesting that the deviation from the standard model is not due to unknown systematic effects but to new physics.
In the world without an axion the smallness of $\bar\theta$ may be achieved due to a spontaneously broken discrete left-right symmetry. We analyze the radiatively induced \bar\theta in the context of generic left-right symmetric SUSY models without assuming flavor degeneracy in the squark sector. Left-right symmetry allows to keep \bar\theta within its present bound only if the inter-generational mass splitting in the squark sector at the scale of the left-right symmetry breaking is smaller than 0.5%. We also consider the naturalness of m_u=0 solution to the strong CP problem in the context of horizontal flavor symmetries. A strong bound on the combination of the horizontal charges in the Up quark sector is found in this case.
We consider the moduli space of rank 2 Higgs bundles with fixed determinant over a smooth projective curve X of genus 2 over the complex numbers, and study involutions defined by tensoring the vector bundle with an element $\alpha$ of order 2 in the Jacobian of the curve, combined with multiplication of the Higgs field by $\pm 1$. We describe the fixed points of these involutions in terms of the Prym variety of the covering of $X$ defined by $\alpha$, and give an interpretation in terms of the moduli space of representations of the fundamental group.
Exclusive electroproduction of a K or K^* meson on the nucleon can give a Theta^+ pentaquark in the final state. This reaction offers an opportunity to investigate the structure of pentaquark baryons at parton level. We discuss the generalized parton distributions for the N -> Theta^+ transition and give the leading order amplitude for electroproduction in the Bjorken regime.
We aimed to evaluate computer-aided diagnosis (CADx) system for lung nodule classification focusing on (i) usefulness of gradient tree boosting (XGBoost) and (ii) effectiveness of parameter optimization using Bayesian optimization (Tree Parzen Estimator, TPE) and random search. 99 lung nodules (62 lung cancers and 37 benign lung nodules) were included from public databases of CT images. A variant of local binary pattern was used for calculating feature vectors. Support vector machine (SVM) or XGBoost was trained using the feature vectors and their labels. TPE or random search was used for parameter optimization of SVM and XGBoost. Leave-one-out cross-validation was used for optimizing and evaluating the performance of our CADx system. Performance was evaluated using area under the curve (AUC) of receiver operating characteristic analysis. AUC was calculated 10 times, and its average was obtained. The best averaged AUC of SVM and XGBoost were 0.850 and 0.896, respectively; both were obtained using TPE. XGBoost was generally superior to SVM. Optimal parameters for achieving high AUC were obtained with fewer numbers of trials when using TPE, compared with random search. In conclusion, XGBoost was better than SVM for classifying lung nodules. TPE was more efficient than random search for parameter optimization.
Magnetically gated accretion has emerged as a proposed mechanism for producing extremely short, repetitive bursts of accretion onto magnetized white dwarfs in intermediate polars (IPs), but this phenomenon has not been detected previously in a confirmed IP. We report the 27-day TESS light curve of V1025 Cen, an IP that shows a remarkable series of twelve bursts of accretion, each lasting for less than six hours. The extreme brevity of the bursts and their short recurrence times (~1-3 days) are incompatible with the dwarf-nova instability, but they are natural consequences of the magnetic gating mechanism developed by Spruit & Taam to explain the Type II bursts of the accreting neutron star known as the Rapid Burster. In this model, the accretion flow piles up at the magnetospheric boundary and presses inward until it couples with the star's magnetic field, producing an abrupt burst of accretion. After each burst, the reservoir of matter at the edge of the magnetosphere is replenished, leading to cyclical bursts of accretion. A pair of recent studies applied this instability to the suspected IPs MV Lyr and TW Pic, but the magnetic nature of these two systems has not been independently confirmed. In contrast, previous studies have unambiguously established the white dwarf in V1025 Cen to be significantly magnetized. The detection of magnetically gated bursts in a confirmed IP therefore validates the extension of the Spruit & Taam instability to magnetized white dwarfs.
An explicit equation of the propagational angle of microwave emission between the line-of-sight and the local magnetic field is newly derived. The existence of the solution of propagational angle is clearly shown under a series of typical parameters in solar microwave observations. It could be used to determine the intrinsic mode and linear mode coupling in solar microwave bursts. However, a 180-degree ambiguity still exists in the direction of longitudinal magnetic field, to produce an uncertainty of the intrinsic mode. One example is selected to check the feasibility of the method in the 2001 September 25 event with a loop-like structure nearby the central meridian passage observed by Nobeyama Radio Heliograph and Polarimeters. The calculated angle in one footpoint (FP) varied around 90 degree in two time intervals of the maximum phase, which gives a direct evidence of the emission propagating through a quasi-transverse region where the linear mode coupling took place, while, the angle in another FP was always smaller than 90 degrees where the mode coupling did not happen. Moreover, the right-circular sense at 17 GHz was always observed in both two FPs during the event, which supports that the transition frequency should be larger than 17 GHz in the first FP together with strong magnetic field of over 2000 Gauses in photosphere, where the weakly coupled case should happen. Moreover, there are two possibilities of the intrinsic mode in the two FPs due to the 180-degree ambiguity.
It was checked in paper [1] by comparing the moduli spaces and superconformal indices that two of the BLG theories $(SU(2)_{1}\times SU(2)_{-1})/{\mathbb Z}_2$ and $SU(2)_2\times SU(2)_{-2}$ are dual to $U(2)_1\times U(2)_{-1}$ and $U(2)_{2}\times U(2)_{-2}$ ABJM theories, correspondingly. In this paper we consider the BLG theories $SU(2)_1\times SU(2)_{-1}$ and $(SU(2)_2\times SU(2)_{-2})/{\mathbb Z}_2$. These theories were noted in [1] to be a tensor product of two interacting ${\mathcal N}=8$ SCFT's. In this paper we identify the SCFT's that occur in the product. For both theories one of the sectors is the IR limit of ${\mathcal N}=8$ SU(2) SYM.
Model-predicted and observed properties of the brightness distribution on M-type Mira disks are discussed. Fundamental issues of limb-darkening and diameter definition, of assigning observational data to diameter-type quantities and of interpreting such quantities in terms of model diameters are outlined. The influence of model properties upon interpretation of measured data is clarified. The dependence of the centre-to-limb variation (CLV) of intensity on wavelength, on stellar parameters and on variablity phase and cycle may be used for analyzing the geometrical and physical structure of the Mira atmosphere, for determining fundamental stellar parameters, and for investigating the quality of models. Desirable future observations include simultaneous observations in different spectral features at different phases and cycles, observation of the position of the shock front and observation of the time- and wavelength-dependence of deviations from spherical symmetry.
We describe several explicit examples of simple abelian surfaces over real quadratic fields with real multiplication and everywhere good reduction. These examples provide evidence for the Eichler-Shimura conjecture for Hilbert modular forms over a real quadratic field. Several of the examples also support a conjecture of Brumer and Kramer on abelian varieties associated to Siegel modular forms with paramodular level structures.
It is demonstrated that several series of conformal field theories, while satisfying braid group statistics, can still be described in the conventional setting of the DHR theory, i.e. their superselection structure can be understood in terms of a compact DHR gauge group. Besides theories with only simple sectors, these include (the untwisted part of) c=1 orbifold theories and level two so(N) WZW theories. We also analyze the relation between these models and theories of complex free fermions.
We make an adaptation of laser modelling equations to describe the behavior of a phonon laser (saser). Our saser consists of an AlGaAs/GaAs double barrier heterostructure designed to generate an intense beam of transversal acoustic (TA) phonons. To study our system, we begin with a Hamiltonian that describes the decay of primary longitudinal optical phonons (LO_1) into secondary (LO_2) and TA (LO_1 -> LO_2 + TA) and its inverse process (recombination). Using this Hamiltonian, a set of coupled equations of motion for the phonons is obtained. We also consider the interaction between the phonons and its reservoirs. These interactions are introduced in the equations of motion leading to a set of coupled Langevin equations. In order to obtain an expression to describe our saser we apply, in the Langevin equations, an adiabatic elimination of some variables of the subsystem. Following the method above we obtain the value of the injection threshold for the operation of our phonon laser. At this threshold occurs a phase transition from a disordered to a coherent state. It is shown that it is not necessary a big "optical" pumping to get a sasing region.
This paper aims to improve the accuracy of texture classification based on extracting texture features using five different texture methods and classifying the patterns using a naive Bayesian classifier. Three statistical-based and two model-based methods are used to extract texture features from eight different texture images, then their accuracy is ranked after using each method individually and in pairs. The accuracy improved up to 97.01% when model based -Gaussian Markov random field (GMRF) and fractional Brownian motion (fBm) - were used together for classification as compared to the highest achieved using each of the five different methods alone; and proved to be better in classifying as compared to statistical methods. Also, using GMRF with statistical based methods, such as Gray level co-occurrence (GLCM) and run-length (RLM) matrices, improved the overall accuracy to 96.94% and 96.55%; respectively.
Recent works have discussed the violation of factorization and universality in hadronic hard scattering processes aimed at measurements of T-odd distributions. We use simple arguments to show that it is possible to restore an approximate factorization involving T-odd contributions if the factorization breaking interactions present a frequency spectrum dominated by by a narrow and regular peak whose maximum value corresponds to a respected factorization.
We study the branching of twins appearing in shape memory alloys at the interface between austenite and martensite. In the framework of three-dimensional non-linear elasticity theory, we propose an explicit, low-energy construction of the branched microstructure, generally applicable to any shape memory material without restrictions on the symmetry class of martensite or on the geometric parameters of the interface. We show that the suggested construction follows the expected energy scaling law, i.e., that (for the surface energy of the twins being sufficiently small) the branching leads to energy reduction. Furthermore, the construction can be modified to capture different features of experimentally observed microstructures without violating this scaling law. By using a numerical procedure, we demonstrate that the proposed construction is able to predict realistically the twin width and the number of branching generations in a Cu-Al-Ni single crystal.
We extend the construction of the category of 1-motivic sheaves (introduced by Barbieri-Viale and Kahn) allowing quotients of connected algebraic k-groups by formal k-groups. We show that its bounded derived category is equivalent to the bounded derived category of the category of generalized 1-motives with torsion introduced in a previous paper by Barbieri-Viale and the author.
An induced matching $M$ in a graph $G$ is a matching in $G$ that is also the edge set of an induced subgraph of $G$. That is, any edge not in $M$ must have no more than one incident vertex saturated by $M$. The maximum size $|M|$ of an induced matching $M$ of $G$ is maximum induced matching number of $G$, which is denoted by $\textrm{Max}(G)$. In this article, we obtain upper bounds for $\textrm{Max}(G)$, for $G=G_{n,m}$, grids with $n,m \geq 9$, $m\equiv 1 \mod 4$ and $nm$ odd.
We calculate the efficiency of infrared optical spin injection in single-layer graphene with Rashba spin-orbit coupling and for in-plane magnetic field. The injection rate in the photon frequency range corresponding to the Rashba splitting is shown to be proportional to the ratio of the Zeeman and Rashba splittings. As a result, large spin polarization can be controllably achieved for experimentally available values of the spin-orbit coupling and in magnetic fields below 10 Tesla.
Convective flows are known as the prime means of transporting magnetic fields on the solar surface. Thus, small magnetic structures are good tracers of the turbulent flows. We study the migration and dispersal of magnetic bright features (MBFs) in intergranular areas observed at high spatial resolution with Sunrise/IMaX. We describe the flux dispersal of individual MBFs as a diffusion process whose parameters are computed for various areas in the quiet Sun and the vicinity of active regions from seeing-free data. We find that magnetic concentrations are best described as random walkers close to network areas (diffusion index, gamma=1.0), travelers with constant speeds over a supergranule (gamma=1.9-2.0), and decelerating movers in the vicinity of flux emergence and/or within active regions (gamma=1.4-1.5). The three types of regions host MBFs with mean diffusion coefficients of 130 km^2/s, 80-90 km^2/s, and 25-70 km^2/s, respectively. The MBFs in these three types of regions are found to display a distinct kinematic behavior at a confidence level in excess of 95%.
In the present paper we discuss a generation of large antimatter regions with sizes exceeding the critical surviving size. In the modern epoch domains with high antimatter density evolve to single galaxies with a peculiar content of anti-helium and anti-deuterium.
A geometrical construction of superconformal transformations in six dimensional (2,0) superspace is proposed. Superconformal Killing vectors are determined. It is shown that the transformation of the tensor multiplet involves a zero curvature non-trivial cochain.
In this letter we show that for certain infinite families of modular forms of growing level it is possible to have a control result for the exceptional primes of the attached Galois representations. As an application, a uniform version of a result of Wiese on Galois realizations of linear groups over finite fields of arbitrarily large exponent is proved.
We reconstruct the Equation of State of Dark Energy (EoS) from current data using a non-parametric approach where, rather than assuming a specific time evolution of this function, we bin it in time. We treat the transition between the bins with two different methods, i.e. a smoothed step function and a Gaussian Process reconstruction, investigating whether or not the two approaches lead to compatible results. Additionally, we include in the reconstruction procedure a correlation between the values of the EoS at different times in the form of a theoretical prior that takes into account a set of viability and stability requirements that one can impose on models alternative to $\Lambda$CDM. In such case, we necessarily specialize to broad, but specific classes of alternative models, i.e. Quintessence and Horndeski gravity. We use data coming from CMB, Supernovae and BAO surveys. We find an overall agreement between the different reconstruction methods used; with both approaches, we find a time dependence of the mean of the reconstruction, with different trends depending on the class of model studied. The constant EoS predicted by the $\Lambda$CDM model falls anyway within the $1\sigma$ bounds of our analysis.
Inspired by the 750 GeV diphoton state recently reported by ATLAS and CMS, we propose a U(1)_{B-L} extension of the MSSM which predicts the existence of four spin zero resonance states that are degenerate in mass in the supersymmetric limit. Vector-like fields, a gauge singlet field, as well as the MSSM Higgsinos are prevented from acquiring arbitrary large masses by a U(1) R-symmetry. Indeed, these masses can be considerably lighter than the Z' gauge boson mass. Depending on kinematics the resonance states could decay into right handed neutrinos and sneutrinos, and/or MSSM Higgs fields and Higgsinos with total decay widths in the multi-GeV range.
We present maps, source lists, and number counts from the largest, unbiassed, extragalactic sub-mm survey so far undertaken with the SCUBA camera on the JCMT. Our maps cover 260 sq. arcmin, to a noise level S(850)=2.5 mJy/beam. We have reduced the data using both SURF, and our own pipeline which produces zero-footprint maps and noise images. The uncorrelated noise maps produced by the latter approach have allowed application of a maximum-likelihood method to measure the statistical significance of each peak, leading to properly quantified flux-density errors for all potential sources. We detect 19 sources with S/N > 4, 38 with S/N > 3.5, and 72 with S/N > 3. To assess completeness and the impact of source confusion we have applied our source extraction algorithm to a series of simulated images. The result is a new estimate of the sub-mm source counts in the flux-density range S(850)=5-15mJy, which we compare with other estimates, and with model predictions. Our estimate of the cumulative source count at S(850) > 8 mJy is 320 (+80,-100) per square degree. Assuming that the majority of sources have z > 1.5, the co-moving number density of high-z galaxies forming stars at a rate >1000 solar masses per year is 10^-5 per Mpc^3, with only a weak dependence on the precise redshift distribution. This number density corresponds to that of massive ellipticals with L > 3-4 L* at low redshift and is also the same as the co-moving number density of comparably massive, passively-evolving objects in the redshift band 1<z<2 inferred from recent surveys of extremely red objects. Thus the bright sub-mm sources can plausibly account for the formation of all present-day massive ellipticals. Improved z constraints, and a proper measurement of sub-mm clustering can refine or refute this picture.
We construct a simple but self-consistent collapsar model for gamma-ray bursts (GRBs) and SNe associated with GRBs (GRB-SNe).Our model includes a black hole, an accretion disk, and the envelope surrounding the central system.The evolutions of the different components are connected by the transfer of the mass and angular momentum.To address properties of the jet and the wind-driven SNe, we consider competition of the ram pressure from the infalling envelope and those from the jet and wind.The expected properties of the GRB jet and the wind-driven SN are investigated as a function of the progenitor mass and angular momentum.We find two conditions which should be satisfied if the wind-driven explosion is to explain the properties of the observed GRB-SNe. (1) The wind should be collimated at its base, and (2) it should not prevent further accretion even after the launch of the SN explosion. Under these conditions, some relations seen in the properties of the GRB-SNe could be reproduced by a sequence of different angular momentum in the progenitors.Only the model with the largest angular momentum could explain the observed (energetic) GRB-SNe, and we expect that the collapsar model can result in a wide variety of observational counterparts mainly depending on the angular momentum of the progenitor star.
Measurements have been made of pi+ absorption on He3 at T_pi+ = 118, 162, and 239 MeV using the Large Acceptance Detector System (LADS). The nearly 4pi solid angle coverage of this detector minimizes uncertainties associated with extrapolations over unmeasured regions of phase space. The total absorption cross section is reported. In addition, the total cross section is divided into components in which only two or all three nucleons play a significant role in the process. These are the first direct measurements of the total and three nucleon absorption cross sections.