ShantanuT01/DACTYL-Pretraining huggingface dataset:
We classified prime $\mathbb{Q}$-Fano $3$-folds $X$ with only $1/2(1,1,1)$-singularities and with $h^{0}(-K_{X})\geq 4$ a long time ago. The classification was undertaken by blowing up each $X$ at one $1/2(1,1,1)$-singularity and constructing a Sarkisov link. The purpose of this paper is to reveal the geometries behind the Sarkisov links for $X$ in 5 classes. The main result asserts that any $X$ in the 5 classes can be embedded as linear sections into bigger dimensional $\mathbb{Q}$-Fano varieties called key varieties, where the key varieties are constructed by extending partially the Sarkisov link in higher dimensions.
Let U be an open subset of a unirational variety (or more generally of a separably rationally connected variety). We prove that there is rational curve C in U such that the fundamental group of C surjects onto the fundamental group of U. The proof improves the earlier proof (math.AG/0003138) and works in any characteristic. Much improved version, thanks to comments of Colliot-Th\'el\`ene.
We investigate a selection-mutation model for the dynamics of technological innovation,a special case of reaction-diffusion equations. Although mutations are assumed to increase the variety of technologies, not their average success ("fitness"), they are an essential prerequisite for innovation. Together with a selection of above-average technologies due to imitation behavior, they are the "driving force" for the continuous increase in fitness. We will give analytical solutions for the probability distribution of technologies for special cases and in the limit of large times.   The selection dynamics is modelled by a "proportional imitation" of better technologies. However, the assessment of a technology's fitness may be imperfect and, therefore, vary stochastically. We will derive conditions, under which wrong assessment of fitness can accelerate the innovation dynamics, as it has been found in some surprising numerical investigations.
We shall show the existence of 15 automorphic forms of weight 8 on the moduli space of marked Hessian quartic surfaces of cubic surfaces. These automorphic forms can be interpreted in terms of the coefficients of the Sylvester form of a general cubic surface.
String theory tells us that quantum gravity has a dual description as a field theory (without gravity). We use the field theory dual to ask what happens to an object as it falls into the simplest black hole: the 2-charge extremal hole. In the field theory description the wavefunction of a particle is spread over a large number of `loops', and the particle has a well-defined position in space only if it has the same `position' on each loop. For the infalling particle we find one definition of `same position' on each loop, but there is a different definition for outgoing particles and no canonical definition in general in the horizon region. Thus the meaning of `position' becomes ill-defined inside the horizon.
We investigated the dependence of spectral lag on energy band based on 28 bright GRBs detected by the SPI and IBIS/ISGRI instruments on the INTEGRAL observatory. It is found that for simple structured bursts or well separated pulses of multi-pulse bursts the spectral lag can be approximated by the relation t=Alog(E), where A is a positive parameter, which correlates with pulse duration. We have not found any negative lag in simple structured bursts or in well separated pulses. While investigating the time profile of the whole burst negative lag may appear due to different spectral parameters of the pulses.
Fluctuation theorems, which have been developed over the past 15 years, have resulted in fundamental breakthroughs in our understanding of how irreversibility emerges from reversible dynamics, and have provided new statistical mechanical relationships for free energy changes. They describe the statistical fluctuations in time-averaged properties of many-particle systems such as fluids driven to nonequilibrium states, and provide some of the very few analytical expressions that describe nonequilibrium states. Quantitative predictions on fluctuations in small systems that are monitored over short periods can also be made, and therefore the fluctuation theorems allow thermodynamic concepts to be extended to apply to finite systems. For this reason, fluctuation theorems are anticipated to play an important role in the design of nanotechnological devices and in understanding biological processes. These theorems, their physical significance and results for experimental and model systems are discussed.
Let $u_t-a(t)u_{xx}=f(x, t)$ in $0\leq x \leq \pi,\,\,t\geq 0.$ Assume that $u(0,t)=u_1(t)$, $u(\pi,t)=u_2(t)$, $u(x,0)=h(x)$, and the extra data $u_x(0,t)=g(t)$ are known. The inverse problem is: {\it   How does one determine the unknown $a(t)$?}   The function $a(t)>a_0>0$ is assumed continuous and bounded. This question is answered and a method for recovery of $a(t)$ is proposed. There are several papers in which sufficient conditions are given for the uniqueness and existence of $a(t)$, but apparently there was no method proposed for calculating of $a$. The method given in this paper for proving the uniqueness and existence of the solution to inverse problem is new and it allows one to calculate the unknown coefficient $a(t)$.
The classical square well potential is smoothed with a finite range smoothing function in order to get a new simple strictly finite range form for the phenomenological nuclear potential. The smoothed square well form becomes exactly zero smoothly at a finite distance, in contrast to the Woods-Saxon form. If the smoothing range is four times the diffuseness of the Woods-Saxon shape both the central and the spin-orbit terms of the Woods-Saxon shape are reproduced reasonably well. The bound single particle energies in a Woods-Saxon potential can be well reproduced with those in the smoothed square well potential. The same is true for the complex energies of the narrow resonances.
We describe explicit formulas for the product rule in $\kappa^*(\mathcal{M}_{g,n}^{ct})$.
The object of this brief review is to reconcile different points of view on how the spin of proton is made up from its constituents. On the basis of naive quark model with flavour symmetry such as isospin or SU(3) one finds a static description. On the contrary the local SU(3) colour symmetry gives a dynamical view. Both these views are contrasted and the role of U(1) axial anomaly and the ambiguity for the measurable spin content is discussed.
The performance of low temperature detectors utilizing thermal effects is determined by their energy relaxation properties. Usually, heat transport experiments in mesoscopic structures are carried out in the steady-state, where temperature gradients do not change in time. Here, we present an experimental study of dynamic thermal relaxation in a mesoscopic system -- thin metallic film. We find that the thermal relaxation of hot electrons in copper and silver films is characterized by several time constants, and that the annealing of the films changes them. In most cases, two time constants are observed, and we can model the system by introducing an additional thermal reservoir coupled to the film electrons. We determine the specific heat of this reservoir and its coupling to the electrons. The experiments point at the importance of grain structure on the thermal relaxation of electrons in metallic films.
We compute the form factors of exponential operators $e^{kg\varphi(x)}$ in the two-dimensional integrable Bullough-Dodd model ($a_2^{(2)}$ Affine Toda Field Theory). These form factors are selected among the solutions of general nonderivative scalar operators by their asymptotic cluster property. Through analitical continuation to complex values of the coupling constant these solutions permit to compute the form factors of scaling relevant primary fields in the lightest-breather sector of integrable $\phi_{1,2}$ and $\phi_{1,5}$ deformations of conformal minimal models. We also obtain the exact wave-function renormalization constant Z(g) of the model and the properly normalized form factors of the operators $\varphi(x)$ and $:\varphi^2(x):$.
Deep neural networks have achieved state-of-the-art performance in a variety of fields. Recent works observe that a class of widely used neural networks can be viewed as the Euler method of numerical discretization. From the numerical discretization perspective, Strong Stability Preserving (SSP) methods are more advanced techniques than the explicit Euler method that produce both accurate and stable solutions. Motivated by the SSP property and a generalized Runge-Kutta method, we propose Strong Stability Preserving networks (SSP networks) which improve robustness against adversarial attacks. We empirically demonstrate that the proposed networks improve the robustness against adversarial examples without any defensive methods. Further, the SSP networks are complementary with a state-of-the-art adversarial training scheme. Lastly, our experiments show that SSP networks suppress the blow-up of adversarial perturbations. Our results open up a way to study robust architectures of neural networks leveraging rich knowledge from numerical discretization literature.
We give a short proof of the following theorem due to Jon H. Folkman (1969): The chromatic number of any graph is at most $2$ plus the maximum over all subgraphs of the difference between half the number of vertices and the independence number.
We use observations from the ACS study of Galactic globular clusters to investigate the spatial distribution of the inner regions of the disrupting Sagittarius dwarf spheroidal galaxy (Sgr). We combine previously published analyses of four Sgr member clusters located near or in the Sgr core (M54, Arp 2, Terzan 7 and Terzan 8) with a new analysis of diffuse Sgr material identified in the background of five low-latitude Galactic bulge clusters (NGC 6624, 6637, 6652, 6681 and 6809) observed as part of the ACS survey. By comparing the bulge cluster CMDs to our previous analysis of the M54/Sgr core, we estimate distances to these background features. The combined data from four Sgr member clusters and five Sgr background features provides nine independent measures of the Sgr distance and, as a group, provide uniformly measured and calibrated probes of different parts of the inner regions of Sgr spanning twenty degrees over the face of the disrupting dwarf. This allows us, for the first time, to constrain the three dimensional orientation of Sgr's disrupting core and globular cluster system and compare that orientation to the predictions of an N-body model of tidal disruption. The density and distance of Sgr debris is consistent with models that favor a relatively high Sgr core mass and a slightly greater distance (28-30 kpc, with a mean of 29.4 kpc). Our analysis also suggests that M54 is in the foreground of Sgr by ~2 kpc, projected on the center of the Sgr dSph. While this would imply a remarkable alignment of the cluster and the Sgr nucleus along the line of sight, we can not identify any systematic effect in our analysis that would falsely create the measured 2 kpc separation. Finally, we find that the cluster Terzan 7 has the most discrepant distance (25 kpc) among the four Sgr core clusters, which may suggest a different dynamical history than the other Sgr core clusters.
The scaling properties of a phase-ordering system with a conserved order parameter are studied. The theory developed leads to scaling functions satisfying certain general properties including the Tomita sum rule. The theory also gives good agreement with numerical results for the order parameter scaling function in three dimensions. The values of the associated nonequilibrium decay exponents are given by the known lower bounds.
Let $L/K$ be a finite Galois extension of complete discrete valued fields of characteristic $p$. Assume that the induced residue field extension $k_L/k_K$ is separable. For an integer $n\geq 0$, let $W_n(\sO_L)$ denote the ring of Witt vectors of length $n$ with coefficients in $\sO_L$. We show that the proabelian group ${H^1(G,W_n(\sO_L))}_{n\in \N}$ is zero. This is an equicharacteristic analogue of Hesselholt's conjecture.
A mixed graph $G$ can contain both (undirected) edges and arcs (directed edges). Here we derive an improved Moore-like bound for the maximum number of vertices of a mixed graph with diameter at least three. Moreover, a complete enumeration of all optimal $(1,1)$-regular mixed graphs with diameter three is presented, so proving that, in general, the proposed bound cannot be improved.
We report on the radio brightening of the blazar TXS 0506+056 (at $z=0.3365$), supporting its identification as source of the high-energy (HE) neutrino IC-170922A by the IceCube Neutrino Observatory. MOJAVE/VLBA data indicate its radio brightness abruptly increasing since January 2016. When decomposing the total radio flux density curve (January 2008 - July 2018) provided by the Owens Valley Radio Observatory into eight Gaussian flares, the peak time of the largest flare overlaps with the HE neutrino detection, while the total flux density exhibits a threefold increase since January 2016. We reveal the radio structure of TXS 0506+056 by analysing VLBI data from the MOJAVE/VLBA Survey. The jet-components maintain quasi-stationary core separations. The structure of the ridge line is indicative of a jet curve at the region $0.5\div2$ mas ($2.5\div9.9$ pc projected) from the VLBI core. The brightness temperature of the core and the pc-scale radio morphology support a helical jet structure at small inclination angle ($<8.2^{\circ}$). The jet pointing towards the Earth is key property facilitating multimessenger observations (HE neutrinos, $\gamma$- and radio flares). The radio brightening preceding the detection of a HE neutrino is similar to the one reported for the blazar PKS 0723--008 and IceCube event ID5.
Radiative capture of the K-minus by the deuteron as a reaction for measurement of the Lambda-neutron scattering lengths. The use of spin information to separate the singlet and triplet scattering lengths is treated.
The properties of magnetic deluted and strong correlated systems of MnxSi1-x systems are discussed. In frame work of the model of the double defects including manganese ion and silicon vacancy are considered properties of these systems. The role of the Jahn -Teller distortions of different symmetry types in MnSi system magnetic-properties formation is discussed. It has been established that defect {Mns+1 - Vsio} is the center with negative-U properties and Jahn-Teller's full symmetric vibration mode initiates change of a crystal-field value from intermediate (a configuration - {Mns+1 - Vsio}) to strong (a configuration -{Mns-1 - Vsi+2}).
We study the phase diagram of the frustrated $t{-}t^\prime$ Hubbard model on the square lattice by using a novel variational wave function. Taking the clue from the backflow correlations that have been introduced long-time ago by Feynman and Cohen and have been used for describing various interacting systems on the continuum (like liquid $^3$He, the electron jellium, and metallic Hydrogen), we consider many-body correlations to construct a suitable approximation for the ground state of this correlated model on the lattice. In this way, a very accurate {\it ansatz} can be achieved both at weak and strong coupling. We present the evidence that an insulating and non-magnetic phase can be stabilized at strong coupling and sufficiently large frustrating ratio $t^\prime/t$.
The extension of chiral theories to the description of resonances, via the incorporation of unitarity in coupled channels, has provided us with a new theoretical perspective on the nature of some of the observed excited hadrons. In this contribution some of the early achievements in the field of baryonic resonances are reviewed, the recent evidence of the two-pole nature of the Lambda(1405) is discussed and results on charmed baryon resonances are presented.
Eta Carinae (or Eta Car) is a colliding-wind binary that shows non-thermal emission from hard X-rays to high-energy $\gamma$-rays. The $\gamma$-ray spectrum exhibits two spectral components, where the high-energy component extends up to 300 GeV. Previous observations of Eta Carinae with the High Energy Stereoscopic System (H.E.S.S.) resulted in upper limits. With the addition of the large 28-m central telescope to the H.E.S.S. array in 2012 the lower bound on the energy range has significantly been reduced. This lowers the energy threshold of the analysis compared to the published results due to the improved instrument sensitivity at energies below 400 GeV. Eta Carinae has been regularly observed in the following years with H.E.S.S. II. Here we report on the first results of Eta Carinae observations, which also cover the periastron passage in 2014 - the time of maximum $\gamma$-ray emission seen in GeV $\gamma$-rays with Fermi-LAT.
Certain solutions to a gravitational form of Schrodinger's equation can yield stable, macroscopic eigenstate solutions having no classical analogue, with properties resembling those of dark matter. Some more tractable solutions show: (1) radiative lifetimes far exceeding the universe's age, implying negligible emission and inherent stability w.r.t. gravitational collapse, (2) negligible interaction with EMR and visible matter, (3) potential to give rise to flat rotation curves and (4) eigenstate energies and `sizes' consistent with that expected for the galactic halo. Traditional baryonic particles occupying such eigenstates will be invisible and weakly interacting, and may be assimilated into galactic evolution scenarios without significantly disturbing BBN ratios. It is proposed that such structures may explain the nature and origin of dark matter.
The optical conductivities of graphene layers are strongly dependent on their stacking orders. Our first-principle calculations show that while the optical conductivities of single layer graphene (SLG) and bilayer graphene (BLG) with Bernal stacking are almost frequency independent in the visible region, the optical conductivity of twisted bilayer graphene (TBG) is frequency dependent, giving rise to additional absorption features due to the band folding effect. Experimentally, we obtain from contrast spectra the optical conductivity profiles of BLG with different stacking geometries. Some TBG samples show additional features in their conductivity spectra in full agreement with our calculation results, while a few samples give universal conductivity values similar to that of SLG. We propose those variations of optical conductivity spectra of TBG samples originate from the difference between the commensurate and incommensurate stackings. Our results reveal that the optical conductivity measurements of graphene layers indeed provide an efficient way to select graphene films with desirable electronic and optical properties, which would great help the future application of those large scale misoriented graphene films in photonic devices.
Data input modality plays an important role in video action recognition. Normally, there are three types of input: RGB, flow stream and compressed data. In this paper, we proposed a new input modality: gray stream. Specifically, taken the stacked consecutive 3 gray images as input, which is the same size of RGB, can not only skip the conversion process from video decoding data to RGB, but also improve the spatio-temporal modeling ability at zero computation and zero parameters. Meanwhile, we proposed a 1D Identity Channel-wise Spatio-temporal Convolution(1D-ICSC) which captures the temporal relationship at channel-feature level within a controllable computation budget(by parameters G & R). Finally, we confirm its effectiveness and efficiency on several action recognition benchmarks, such as Kinetics, Something-Something, HMDB-51 and UCF-101, and achieve impressive results.
In the context of gravity's rainbow, we study the deformed Starobinsky model in which the deformations take the form $f(R)\sim R^{2(1-\alpha)}$, with $R$ the Ricci scalar and $\alpha$ a positive parameter. We show that the spectral index of curvature perturbation and the tensor-to-scalar ratio can be written in terms of $N,\,\lambda$ and $\alpha$, with $N$ being the number of {\it e}-foldings, $\lambda$ a rainbow parameter. We compare the predictions of our models with Planck data. With the sizeable number of {\it e}-foldings and proper choices of parameters, we discover that the predictions of the model are in excellent agreement with the Planck analysis. Interestingly, we obtain the upper limit and the lower limit of a rainbow parameter $\lambda$ and a positive constant $\alpha$, respectively.
We study the formation of marginally trapped surfaces in the head-on collision of two ultrarelativistic charges in $(A)dS$ space-time. The metric of ultrarelativistic charged particles in $(A)dS$ is obtained by boosting Reissner-Nordstr\"om $(A)dS$ space-time to the speed of light. We show that formation of trapped surfaces on the past light cone is only possible when charge is below certain critical - situation similar to the collision of two ultrarelativistic charges in Minkowski space-time. This critical value depends on the energy of colliding particles and the value of a cosmological constant. There is richer structure of critical domains in $dS$ case. In this case already for chargeless particles there is a critical value of the cosmological constant only below which trapped surfaces formation is possible. Appearance of arbitrary small nonzero charge significantly changes the physical picture. Critical effect which has been observed in the neutral case does not take place more. If the value of the charge is not very large solution to the equation on trapped surface exists for any values of cosmological radius and energy density of shock waves. Increasing of the charge leads to decrease of the trapped surface area, and at some critical point the formation of trapped surfaces of the type mentioned above becomes impossible.
Given a Weil non-integral divisor $D$, it is natural to associate it the line bundle of its integral part $\mathcal{O}_X([D])$. In this work we study which of the classical characterizations of ample and big divisors can be extended to non-integral divisors via the corresponding line bundles.
A proof of the optimality of the eigenfunctions of the Laplace-Beltrami operator (LBO) in representing smooth functions on surfaces is provided and adapted to the field of applied shape and data analysis. It is based on the Courant-Fischer min-max principle adapted to our case. % The theorem we present supports the new trend in geometry processing of treating geometric structures by using their projection onto the leading eigenfunctions of the decomposition of the LBO. Utilisation of this result can be used for constructing numerically efficient algorithms to process shapes in their spectrum. We review a couple of applications as possible practical usage cases of the proposed optimality criteria. % We refer to a scale invariant metric, which is also invariant to bending of the manifold. This novel pseudo-metric allows constructing an LBO by which a scale invariant eigenspace on the surface is defined. We demonstrate the efficiency of an intermediate metric, defined as an interpolation between the scale invariant and the regular one, in representing geometric structures while capturing both coarse and fine details. Next, we review a numerical acceleration technique for classical scaling, a member of a family of flattening methods known as multidimensional scaling (MDS). There, the optimality is exploited to efficiently approximate all geodesic distances between pairs of points on a given surface, and thereby match and compare between almost isometric surfaces. Finally, we revisit the classical principal component analysis (PCA) definition by coupling its variational form with a Dirichlet energy on the data manifold. By pairing the PCA with the LBO we can handle cases that go beyond the scope defined by the observation set that is handled by regular PCA.