ShantanuT01/DACTYL-Pretraining huggingface dataset:
For $\alpha >0$, the $\alpha$-Lipschitz minorant of a function $f : \mathbb{R} \rightarrow \mathbb{R}$ is the greatest function $m : \mathbb{R} \rightarrow \mathbb{R}$ such that $m \leq f$ and $\vert m(s) - m(t) \vert \leq \alpha \vert s-t \vert$ for all $s,t \in \mathbb{R}$, should such a function exist. If $X=(X_t)_{t \in \mathbb{R}}$ is a real-valued L\'evy process that is not a pure linear drift with slope $\pm \alpha$, then the sample paths of $X$ have an $\alpha$-Lipschitz minorant almost surely if and only if $\mathbb{E}[\vert X_1 \vert]< \infty$ and $\vert \mathbb{E}[X_1]\vert < \alpha$. Denoting the minorant by $M$, we consider the contact set $\mathcal{Z}:=\{ t \in \mathbb{R} : M_t = X_t \wedge X_{t-}\}$, which, since it is regenerative and stationary, has the distribution of the closed range of some subordinator "made stationary" in a suitable sense. We provide a description of the excursions of the L\'evy process away from its contact set similar to the one presented in It\^o excursion theory. We study the distribution of the excursion on the special interval straddling zero. We also give an explicit path decomposition of the other "generic" excursions in the case of Brownian motion with drift $\beta$ with $\vert \beta \vert < \alpha$. Finally, we investigate the progressive enlargement of the Brownian filtration by the random time that is the first point of the contact set after zero.
We analyze a mechanism of coupling of high- and low-$K$ bands in terms of a dynamical treatment for nuclear rotations, i.e.,wobbling motion. The wobbling states are produced through the generator coordinate method after angular momentum projection ({\it GCM-after-AMP}), in which the intrinsic states are constructed through fully self-consistent calculations by the 2d-cranked (or tilted-axis-cranked) HFB method . In particular, the phenomena of ``signature inversion'' and ``signature splitting'' in the t-band (tilted rotational band) are explained in terms of the wobbling model. % Our calculations will be compared with new data for in-band E2 transition rates in $^{182}$Os, which may shed light on the mechanism of the anomalous K=25 isomer decay, directly to the yrast band.
Let $X$ be a complex quasi-projective algebraic variety. In this paper we study the mixed Hodge structures of the symmetric products $Sym^{n}X$ when the cohomology of $X$ is given by exterior products of cohomology classes with odd degree. We obtain an expression for the equivariant mixed Hodge polynomials $\mu_{X^{n}}^{S_{n}}\left(t,u,v\right)$, codifying the permutation action of $S_{n}$ as well as its subgroups. This allows us to deduce formulas for the mixed Hodge polynomials of its symmetric products $\mu_{Sym^{n}X}\left(t,u,v\right)$. These formulas are then applied to the case of linear algebraic groups.
Within the low-energy effective Minimal Supersymmetric extension of Standard Model (effMSSM) we calculated the neutralino relic density taking into account slepton-neutralino and neutralino-chargino/neutralino coannihilation channels. We performed comparative study of these channels and obtained that both of them give sizable contributions to the reduction of the relic density. Due to these coannihilation processes some models (mostly with large neutralino masses) enter into the cosmologically interesting region for relic density, but other models leave this region. Nevertheless, in general, the predictions for direct and indirect dark matter detection rates are not strongly affected by these coannihilation channels in the effMSSM.
We present a short review on the electric and magnetic black strings in 5D spacetime with one compact dimension. Linear static perturbations of these objects indicate presence of the threshold unstable mode. Analysis of the mode shows that the electric black string is less stable than a neutral one. The situation is opposite for the magnetic black string.
Observations of the yellow hypergiant Rho Cas obtained in 2007-2011 in a wide wavelength region with spectral resolution about 60000 have enabled studies of features of its optical spectrum in detail and brought to light previously unknown characteristics of the extended atmosphere of the star. The radial velocity measured from symmetric absorptions of metals varies with an amplitude of about +/-7 km/s around the systemic velocity Vsys=-47 km/s, due to low-amplitude pulsations of the atmospheric layers near the photosphere. At some times, a velocity gradient was found in deep atmospheric layers of the star. A slight velocity stratification in the stellar atmosphere was detected for the first time, manifested as a difference of 3-4 km/s in the velocities measured from absorption lines of neutral metals and of ions. The long-wavelength components of split absorptions of BaII, SrII, TiII, and other strong lines with low excitation potentials for their lower levels are distorted by nearby emission lines. It is suggested that the short-wavelength components, whose locations correspond to the narrow velocity range Vr(blue) from approximately -60 to -70 km/s, are formed in a circumstellar envelope; one component of the D~NaI doublet and the emission components of the FeII 6369.46 and 6432.68 ions are also formed there.
We report on a database of field extensions of the rationals, its properties and the methods used to compute it. At the moment the database encompasses roughly 100,000 polynomials generating distinct number fields over the rationals, of degrees up to 15. It contains polynomials for all transitive permutation groups up to that degree, and even for most of the possible combinations of signature and Galois group in that range. Moreover, whenever these are known, the fields of minimal discriminant with given group and signature have been included.   The database can be downloaded from www.iwr.uni-heidelberg.de/iwr/compalg/minimum/minimum.html or from www.mathematik.uni-kassel.de~malle/minimum/minimum.html and accessed via the computer algebra system Kant. One of the aims of the compilation of this database was to test the limitations of current methods for the realization of groups as Galois groups. It turned out that these methods have limitations if the signature of the resulting Galois extension is also prescribed.
Fibonacci cubes are induced subgraphs of hypercube graphs obtained by restricting the vertex set to those binary strings which do not contain consecutive 1s. This class of graphs has been studied extensively and generalized in many different directions. Induced subgraphs of the hypercube on binary strings with restricted runlengths as vertices define Fibonacci-run graphs. These graphs have the same number of vertices as Fibonacci cubes, but fewer edges and different graph theoretical properties.   Basic properties of Fibonacci-run graphs are presented in a companion paper, while in this paper we consider the nature of the degree sequences of Fibonacci-run graphs. The generating function we obtain is a refinement of the generating function of the degree sequences, and has a number of corollaries, obtained as specializations. We also obtain several properties of Fibonacci-run graphs viewed as a partially ordered set, and discuss its embedding properties.
Micro- and nano-scale systems driven by rapid changes in control parameters (control protocols) dissipate significant energy. In the fast-protocol limit, we find that protocols that minimize dissipation at fixed duration are universally given by a two-step process, jumping to and from a point that balances jump size with fast relaxation. Jump protocols could be exploited by molecular machines or thermodynamic computing to improve energetic efficiency, and implemented in nonequilibrium free-energy estimation to improve accuracy.
In the Left-Right Symmetric Model (LRSM), box diagrams involving the charged right-handed gauge boson W_R may affect B-Bbar mixing as well as CP asymmetries in neutral B decays. The smallness of the epsilon_K parameter in the neutral K-meson system places severe constraints on the right-handed quark mixing matrix V^R, and reduces the number of its effective phases to one. W_R exchange gives a large contribution to B-Bbar mixing when the mass of the W_R boson is up to or higher than 8 TeV, depending on the V^R case, the B_d,s meson, and the asymmetry. The allowed regions of the CP violating asymmetries sin(2beta), sin(gamma), sin(2alpha), and sin(2phi_s), as well as x_s, are calculated as a function of the W_R mass. The results of the LRSM other than for the well measured sin(2beta) show allowable regions that are much broader than that for the Standard Model, showing that new experiments can indicate a presence of new physics, or significantly push up the limits on the W_R mass.
The primary component of the multiple star phi Dra is one of the brightest magnetic chemically peculiar stars in the northern sky. Here we report results of a comprehensive study of the rotational photometric variability, binarity, magnetic field geometry, and surface chemical spot structure for this star. We derived a precise photometric rotational period of 1.71650213(21) d based on one year of TESS nearly continuous space observations and discovered modulation of the stellar light curve with the phase of the 127.9-d binary orbit due to the light time travel effect. We revised parameters of the binary orbit and detected spectroscopic contribution of the secondary. A tomographic mapping technique was applied to the average intensity and circular polarisation profiles derived from Narval high-resolution spectropolarimetric observations. This analysis yielded a detailed map of the global magnetic field topology together with the surface distributions of Si, Cr, and Fe abundances. Magnetic mapping demonstrates that the surface field structure of phi Dra is dominated by a distorted dipolar component with a peak field strength of 1.4 kG and a large asymmetry between the poles. Chemical maps show an enhancement of Cr, Fe and, to a lesser extent, Si in a series of spots encircling intersections of the magnetic and rotational equators. These chemical spot geometries do not directly correlate with either the local field strength or the field inclination.
We study statistical scale invariance and dynamic scaling in a simple solid-on-solid 2+1 - dimensional limited mobility discrete model of nonequilibrium surface growth, which we believe should describe the low temperature kinetic roughening properties of molecular beam epitaxy. The model exhibits long-lived ``transient'' anomalous and multiaffine dynamic scaling properties similar to that found in the corresponding 1+1 - dimensional problem. Using large-scale simulations we obtain the relevant scaling exponents, and compare with continuum theories.
This is a note constructing a certain weight 4 automorphic form on the moduli space of cubic surfaces, posted here because it is referred to in math.AG/0002066
We consider the problem of finding the isolated common roots of a set of polynomial functions defining a zero-dimensional ideal I in a ring R of polynomials over C. We propose a general algebraic framework to find the solutions and to compute the structure of the quotient ring R/I from the null space of a Macaulay-type matrix. The affine dense, affine sparse, homogeneous and multi-homogeneous cases are treated. In the presented framework, the concept of a border basis is generalized by relaxing the conditions on the set of basis elements. This allows for algorithms to adapt the choice of basis in order to enhance the numerical stability. We present such an algorithm and show numerical results.
We investigate the relationships between Mg ii {\lambda}2798 emission line properties, as well as between these properties and inclination angle and Fe ii strength, in a lobe-dominated quasar sample. We find no correlation between Mg ii line width and inclination, unlike previous studies of the general quasar population. This suggests that the Mg ii emission region in these objects is not of a thin disk geometry, however the average equivalent width of the line negates a spherical alternative. A positive correlation between Mg ii equivalent width and inclination cannot be ruled out, meaning there is no strong evidence that Mg ii emission is anisotropic. Since thin disk emission would be highly directional, the geometric implications of these two findings are compatible. The lack of line width correlation with inclination may also indicate that Mg ii is useful for estimating black hole masses in lobe-dominated quasar samples, since it is unbiased by orientation. Some quasars in our sample have almost edge-on viewing angles and therefore cannot have a smooth toroidal obscurer co-planar with the accretion disk. Alternatives may be a distorted dusty disk or a clumpy obscurer. This could result from the sample selection bias towards high inclination objects, rather than intrinsic differences between lobe-dominated and typical quasars. Five objects have visible [O iii] allowing equivalent width calculation, revealing it to be higher than in typical quasars. Since these objects are of high inclination, this finding supports the positive correlation between [O iii] equivalent width and inclination found in a previous study.
Person Search is a relevant task that aims to jointly solve Person Detection and Person Re-identification(re-ID). Though most previous methods focus on learning robust individual features for retrieval, it's still hard to distinguish confusing persons because of illumination, large pose variance, and occlusion. Contextual information is practically available in person search task which benefits searching in terms of reducing confusion. To this end, we present a novel contextual feature head named Attention Context-Aware Embedding(ACAE) which enhances contextual information. ACAE repeatedly reviews the person features within and across images to find similar pedestrian patterns, allowing it to implicitly learn to find possible co-travelers and efficiently model contextual relevant instances' relations. Moreover, we propose Image Memory Bank to improve the training efficiency. Experimentally, ACAE shows extensive promotion when built on different one-step methods. Our overall methods achieve state-of-the-art results compared with previous one-step methods.
Typical weighted random simplices $Z_{\mu}$, $\mu\in(-2,\infty)$, in a Poisson-Delaunay tessellation in $\mathbb{R}^n$ are considered, where the weight is given by the $(\mu+1)$st power of the volume. As special cases this includes the typical ($\mu=-1$) and the usual volume-weighted ($\mu=0$) Poisson-Delaunay simplex. By proving sharp bounds on cumulants it is shown that the logarithmic volume of $Z_{\mu}$ satisfies a central limit theorem in high dimensions, that is, as $n\to\infty$. In addition, rates of convergence are provided. In parallel, concentration inequalities as well as moderate deviations are studied. The set-up allows the weight $\mu=\mu(n)$ to depend on the dimension $n$ as well. A number of special cases are discussed separately. For fixed $\mu$ also mod-$\phi$ convergence and the large deviations behaviour of the logarithmic volume of $Z_{\mu}$ are investigated.
In 1975 Ogg offered a bottle of Jack Daniels for an explanation of the fact that the prime divisors of the order of the monster are the primes p for which the characteristic p supersingular j-invariants are all defined over the field with p elements. This coincidence is often suggested to be the first hint of monstrous moonshine, the deep unexpected interplay between the monster and modular functions. We revisit Ogg's problem, and we point out (using existing tools) that the moonshine functions for order p elements give the set of characteristic p supersingular j-invariants (apart from 0 and 1728). Furthermore, we discuss this coincidence of the two seemingly unrelated sets of primes using the first principles of moonshine.
We calculate the electrostatic potential generated by a point charge in the space-time of Reissner-Nordstrom with a conical defect. An expression for the self-energy is also presented.
RX J1856.5-3754, a bright soft X-ray source believed to be the nearest thermally emitting neutron star, has commanded and continues to command intense interest from X-ray missions. One of the main goals is to determine the radius of this neutron star. An integral part of the determination is an accurate parallax. Walter (2001) analyzed Hubble Space Telescope (HST) data and derived a parallax, pi=16.5+/-2.3 mas. Combining this distance with the angular radius derived from blackbody fits to observations of RX J1856.5-3754 with ROSAT, EUVE, HST, Pons et al. (2001) derived an observed radius ("radiation radius"), R_{infty}= 7 km. This value is smaller than the radii calculated from all proposed equations-of-state (EOS) of dense baryonic matter (Haensel 2001). Here, we have analyzed the same HST data and find pi=7+/-2 mas. We have verified our result using a number of different, independent techniques, and find the result to be robust. Adopting our parallax, the radius of RX J1856.5-3754 is R_{infty}=15+/-6 km. This radius falls squarely in the range of radii, 12--16 km, expected from calculations of neutron star structure for different equations of state. With additional HST observations, the parallax estimate can be improved to the point by which the inferred radius can constrain the choice of EOS.
The Coma supercluster (100 Mpc) offers an unprecedented contiguous range of environments in the nearby Universe. In this paper we present a catalogue of spectroscopically confirmed galaxies in the Coma supercluster detected in the ultraviolet (UV) wavebands. We use the arsenal of UV and optical data for galaxies in the Coma supercluster covering ~ 500 square degrees on the sky to study their photometric and spectroscopic properties as a function of environment at various scales. We identify the different components of the cosmic-web: large-scale filaments and voids using Discrete Persistent Structures Extractor, and groups and clusters using Hierarchical Density-based spatial clustering of applications with noise, respectively. We find that in the Coma supercluster the median emission in Halpha inclines, while the g-r and FUV-NUV colours of galaxies become bluer moving further away from the spine of the filaments out to a radius of around 1 Mpc. On the other hand, an opposite trend is observed as the distance between the galaxy and centre of the nearest cluster or group decreases. Our analysis supports the hypothesis that properties of galaxies are not just defined by its stellar mass and large-scale density, but also by the environmental processes resulting due to the intrafilament medium whose role in accelerating galaxy transformations needs to be investigated thoroughly using multi-wavelength data.
The collective excitations of electrons in the bulk or at the surface, namely plasmons, play an important role in the properties of materials, and have generated the field of plasmonics. We report the observation of a highly unusual plasmon mode on the surface of Van der Waals heterostructures of graphene monolayer on 2D transition metal dichalcogenide substrate. Since the exponentially decaying fields of surface plasmon wave propagating along interface is highly sensitive to the ambient refractive index variations, such heterostructures are useful for ultra-sensitive bio-sensing.
We consider an active run-and-tumble particle (RTP) in $d$ dimensions, starting from the origin and evolving over a time interval $[0,t]$. We examine three different models for the dynamics of the RTP: the standard RTP model with instantaneous tumblings, a variant with instantaneous runs and a general model in which both the tumblings and the runs are non-instantaneous. For each of these models, we use the Sparre Andersen theorem for discrete-time random walks to compute exactly the probability that the $x$ component does not change sign up to time $t$, showing that it does not depend on $d$. As a consequence of this result, we compute exactly other $x$-component properties, namely the distribution of the time of the maximum and the record statistics, showing that they are universal, i.e. they do not depend on $d$. Moreover, we show that these universal results hold also if the speed $v$ of the particle after each tumbling is random, drawn from a generic probability distribution. Our findings are confirmed by numerical simulations. Some of these results have been announced in a recent Letter [Phys. Rev. Lett. 124, 090603 (2020)].
To understand the dynamical origin of the measurement in quantum mechanics, several models have been put forward which have a quantum system coupled to an apparatus. The system and the apparatus evolve in time and the Born rule for the system to be in various eigenstates of the observable is naturally obtained. In this work, we show that the effect of the drive-induced dissipation in such a system can lead to the Born rule, even if there is no separate apparatus. The applied drive needs to be much stronger than the system-environment coupling. In this condition, we show that the dynamics of a driven-dissipative system could be reduced to a Milburn-like form, using a recently-proposed fluctuation-regulated quantum master equation [A. Chakrabarti and R. Bhattacharyya, Phys. Rev. A 97, 063837 (2018)]. The system evolves irreversibly under the action of the first-order effect of the drive and the drive-induced dissipation. The resulting mixed state is identical to that obtained by using the Born rule.
The stratified vector bundles on a smooth variety defined over an algebraically closed field $k$ form a neutral Tannakian category over $k$. We investigate the affine group--scheme corresponding to this neutral Tannakian category.
The proto-planetary nebula Hen 3-1475 shows a remarkable highly collimated optical jet with an S-shaped string of three pairs of knots and extremely high velocities. We present here a detailed analysis of the overall morphology, kinematic structure and the excitation conditions of these knots based on deep ground-based high dispersion spectroscopy complemented with high spatial resolution spectroscopy obtained with STIS onboard HST, and WFPC2 [N II] images. The spectra obtained show double-peaked, extremely wide emission line profiles, and a decrease of the radial velocities with distance to the source in a step-like fashion. We find that the emission line ratios observed in the intermediate knots are consistent with a spectrum arising from the recombination region of a shock wave with shock velocities ranging from 100 to 150 km/s. We propose that the ejection velocity is varying as a function of time with a quasi-periodic variability (with timescale of the order of 100 years) and the direction of ejection is also varying with a precession period of the order of 1500 years.
By numerical simulations and analytical studies, we show that the phenomenon of microwave-induced resistance oscillations can be understood as a classical memory effect caused by re-collisions of electrons with scattering centers after a cyclotron period. We develop a Drude-like approach to magneto-transport in presence of a microwave field, taking account of memory effects, and find an excellent agreement between numerical and analytical results, as well as a qualitative agreement with experiment.