ShantanuT01/DACTYL-Pretraining huggingface dataset:
We demonstrate that a Langevin equation that describes the motion of a Brownian particle under non-equilibrium conditions can be exactly transformed to a special equation that explicitly exhibits the response of the velocity to a time dependent perturbation. This transformation is constructed on the basis of an operator formulation originally used in nonlinear perturbation theory for differential equations by extending it to stochastic analysis. We find that the obtained expression is useful for the calculation of fundamental quantities of the system, and that it provides a physical basis for the decomposition of the forces in the Langevin description into effective driving, dissipative, and random forces in a large-scale description.
In this paper, we aim to reduce the computational cost of spatio-temporal deep neural networks, making them run as fast as their 2D counterparts while preserving state-of-the-art accuracy on video recognition benchmarks. To this end, we present the novel Multi-Fiber architecture that slices a complex neural network into an ensemble of lightweight networks or fibers that run through the network. To facilitate information flow between fibers we further incorporate multiplexer modules and end up with an architecture that reduces the computational cost of 3D networks by an order of magnitude, while increasing recognition performance at the same time. Extensive experimental results show that our multi-fiber architecture significantly boosts the efficiency of existing convolution networks for both image and video recognition tasks, achieving state-of-the-art performance on UCF-101, HMDB-51 and Kinetics datasets. Our proposed model requires over 9x and 13x less computations than the I3D and R(2+1)D models, respectively, yet providing higher accuracy.
We present new VLBI observations of a complete sample of Brigthest Cluster Galaxies (BCGs) in nearby Abell Clusters. These data show a possible difference between BCGs in cool core clusters (two-sided parsec scale jets) and in non cool core clusters (one-sided parsec scale jet). We suggest that this difference could be due to the jet interaction with the surrounding medium. More data are necessary to discuss whether parsec-scale properties of BCGs are influenced by their peculiar morphology and position at the center of rich galaxy clusters.
We study the probability distribution $\mathcal{P}(H,t,L)$ of the surface height $h(x=0,t)=H$ in the Kardar-Parisi-Zhang (KPZ) equation in $1+1$ dimension when starting from a parabolic interface, $h(x,t=0)=x^2/L$. The limits of $L\to\infty$ and $L\to 0$ have been recently solved exactly for any $t>0$. Here we address the early-time behavior of $\mathcal{P}(H,t,L)$ for general $L$. We employ the weak-noise theory - a variant of WKB approximation -- which yields the optimal history of the interface, conditioned on reaching the given height $H$ at the origin at time $t$. We find that at small $H$ $\mathcal{P}(H,t,L)$ is Gaussian, but its tails are non-Gaussian and highly asymmetric. In the leading order and in a proper moving frame, the tails behave as $-\ln \mathcal{P}= f_{+}|H|^{5/2}/t^{1/2}$ and $f_{-}|H|^{3/2}/t^{1/2}$. The factor $f_{+}(L,t)$ monotonically increases as a function of $L$, interpolating between time-independent values at $L=0$ and $L=\infty$ that were previously known. The factor $f_{-}$ is independent of $L$ and $t$, signalling universality of this tail for a whole class of deterministic initial conditions.
A generalized Langevin equation with fluctuating diffusivity (GLEFD) is proposed, and it is shown that the GLEFD satisfies a generalized fluctuation-dissipation relation. If the memory kernel is a power law, the GLEFD exhibits anomalous subdiffusion, non-Gaussianity, and stretched-exponential relaxation. The case in which the memory kernel is given by a single exponential function is also investigated as an analytically tractable example. In particular, the mean-square displacement and the self-intermediate-scattering function of this system show plateau structures. A numerical scheme to integrate the GLEFD is also presented.
Based on a prior model on double pion photoproduction on the proton, successfully tested in total cross sections and invariant mass distributions, we make a theoretical study of the angular dependence of helicity asymmetries from the interaction of circularly polarized photons with unpolarized protons. We show that this observable is sensitive to details of the internal mechanisms and, thus, represents a complementary test of the theoretical model.
We present a closed form expression for the semiclassical OPE coefficients that are universal for all 2D CFTs with a "weak" light spectrum, by taking the semiclassical limit of the fusion kernel. We match this with a properly regularized and normalized bulk action evaluated on a geometry with three conical defects, analytically continued in the deficit angles beyond the range for which a metric with positive signature exists. The analytically continued geometry has a codimension-one coordinate singularity surrounding the heaviest conical defect. This singularity becomes a horizon after Wick rotating to Lorentzian signature, suggesting a connection between universality and the existence of a horizon.
We study supersymmetric vacua of the N=1 cascading SU(M+p)xSU(p) gauge theory with flavor - the theory on p D3-branes and M wrapped D5-branes at the tip of the conifold, and N_f flavor D7-branes wrapping a holomorphic four-cycle inside the conifold. The Coulomb branch of the moduli space is inherited from the pure gauge theory without flavor and was thoroughly studied in the past. Besides, there is a Higgs branch where some D3 and/or D5-branes dissolve in the D7-branes forming the worldvolume gauge instantons. We study the Higgs branch both from the field theory and the bulk point of view. On the classical level the moduli space is closely related to the one of the N=2 C^2/Z_2 orbifold theory, in particular certain vacua of the N=1 theory are related to noncommutative instantons on the resolved C^2/Z_2. On the quantum level the Higgs branch acquires corrections due to renormalization of the Kahler potential and non-perturbative effects in field theory. In the bulk this is encoded in the classical D7-brane geometry. We compute the VEVs of the protected operators and the field theory RG flow and find an agreement with the parallel computations in the bulk.
Fringe tracking in interferometers is typically analyzed with the implicit assumption that there is a single phase associated with each telescope in the array. If the telescopes have apertures significantly larger than r0 and only partial adaptive optics correction, then the phase measured by a fringe sensor may differ significantly from the "piston" component of the aperture phase. In some cases, speckle noise will cause "branch points" in the measured phase as a function of time, causing large and sudden jumps in the phase. We present simulations showing these effects in order to understand their implications for the design of fringe tracking algorithms.
When constructing general relativity (GR), Einstein required 4D general covariance. In contrast, we derive GR (in the compact, without boundary case) as a theory of evolving 3-dimensional conformal Riemannian geometries obtained by imposing two general principles: 1) time is derived from change; 2) motion and size are relative. We write down an explicit action based on them. We obtain not only GR in the CMC gauge, in its Hamiltonian 3 + 1 reformulation but also all the equations used in York's conformal technique for solving the initial-value problem. This shows that the independent gravitational degrees of freedom obtained by York do not arise from a gauge fixing but from hitherto unrecognized fundamental symmetry principles. They can therefore be identified as the long-sought Hamiltonian physical gravitational degrees of freedom.
The relation between force and stretch in the worm-like chain model of entropic elasticity is examined. Although no closed-form expression is valid for all values of forcing, solutions in the form of asymptotic series can be obtained under conditions of small and large applied force. The small and large stretch limits correspond to regular and boundary layer perturbation problems, respectively. The perturbation problems are solved and series solutions obtained for force as a function of stretch. The form of the asymptotic series suggest a uniform approximation valid for all stretch that is an improvement on existing approximations.
We examine the recoil velocity induced by the superposition of the magnetic dipole and quadrupole radiation from a pulsar/magnetar born with rapid rotation. The resultant velocity depends on not the magnitude, but rather the ratio of the two moments and their geometrical configuration. The model does not necessarily lead to high spatial velocity for a magnetar with a strong magnetic field, which is consistent with the recent observational upper bound. The maximum velocity predicted with this model is slightly smaller than that of observed fast-moving pulsars.
The glasses in the system (100-x)TeO2-xCaCu3Ti4O12, (x=0.25 to 3 mol %) were fabricated. The color varied from olive green to brown as the CaCu3Ti4O12 (CCTO) content increased in TeO2 matrix. The X-ray powder diffraction and differential scanning calorimetric analyses that were carried out on the as-quenched samples confirmed their amorphous and glassy nature respectively. The dielectric constant and loss in the 100 Hz-1MHz frequency range were monitored as a function of temperature (50-400oC). The dielectric constant and the loss (D) increased as the CCTO content increased in TeO2 at all the frequencies and temperatures under investigation. Further, the effective dielectric constant and D were found to be frequency independent in the 50-200oC temperature range. The value obtained for the loss at 1MHz was 0.0019 which was typical of low loss materials, and exhibited near constant loss (NCL) in the 100Hz-1MHz frequency range. The electrical relaxation was rationalized using the electric modulus formalism. These glasses may be of considerable interest as substrates for high frequency circuit elements in conventional semiconductor industries owing to their high thermal stability.
An evolving Riemannian manifold $(M,g_t)_{t\in I}$ consists of a smooth $d$-dimensional manifold $M$, equipped with a geometric flow $g_t$ of complete Riemannian metrics, parametrized by $I=(-\infty,T)$. Given an additional $C^{1,1}$ family of vector fields $(Z_t)_{t\in I}$ on $M$. We study the family of operators $L_t=\Delta_t +Z_t $ where $\Delta_t$ denotes the Laplacian with respect to the metric $g_t$. We first give sufficient conditions, in terms of space-time Lyapunov functions, for non-explosion of the diffusion generated by $L_t$, and for existence of evolution systems of probability measures associated to it. Coupling methods are used to establish uniqueness of the evolution systems under suitable curvature conditions. Adopting such a unique system of probability measures as reference measures, we characterize supercontractivity, hypercontractivity and ultraboundedness of the corresponding time-inhomogeneous semigroup. To this end, gradient estimates and a family of (super-)logarithmic Sobolev inequalities are established.
We consider a GI/GI/1 queue with the shortest remaining processing time discipline (SRPT) and light-tailed service times. Our interest is focused on the tail behavior of the sojourn-time distribution. We obtain a general expression for its large-deviations decay rate. The value of this decay rate critically depends on whether there is mass in the endpoint of the service-time distribution or not. An auxiliary priority queue, for which we obtain some new results, plays an important role in our analysis. We apply our SRPT-results to compare SRPT with FIFO from a large-deviations point of view.
We use the weighted moduli height as defined in \cite{sh-h} to investigate the distribution of fine moduli points in the moduli space of genus two curves.   We show that for any genus two curve with equation $y^2=f(x)$, its weighted moduli height $\mathfrak h (\mathfrak{p}) \leq 2^3 \sqrt{3 \cdot 5 \cdot 7} \, \cdot H(f)$, where $H(f)$ is the minimal naive height of the curve as defined in \cite{height}. Based on the weighted moduli height $\mathfrak h$ we create a database of genus two curves defined over $\mathbb Q$ with small $\mathfrak h$ and show that for small such height ($\mathfrak h < 5$) about 30% of points are fine moduli points.
Cohesive powders form agglomerates that can be very porous. Hence they are also very fragile. Consider a process of complete fragmentation on a characteristic length scale $\ell$, where the fragments are subsequently allowed to settle under gravity. If this fragmentation-reagglomeration cycle is repeated sufficiently often, the powder develops a fractal substructure with robust statistical properties. The structural evolution is discussed for two different models: The first one is an off-lattice model, in which a fragment does not stick to the surface of other fragments that have already settled, but rolls down until it finds a locally stable position. The second one is a simpler lattice model, in which a fragment sticks at first contact with the agglomerate of fragments that have already settled. Results for the fragment size distribution are shown as well. One can distinguish scale invariant dust and fragments of a characteristic size. Their role in the process of structure formation will be addressed.
We present Very Long Baseline Interferometry (VLBI) observations of 22 GHz H$_2$O masers in the high-mass star-forming region of \objectname{W75N}, carried out with VLBI Exploration of Radio Astrometry (VERA) for three-epochs in 2007 with an angular resolution of $\sim$ 1 mas. We detected H$_2$O maser emission toward the radio jet in VLA 1 and the expanding shell-like structure in VLA 2. We have made elliptical fits to the VLA 2 H$_2$O maser shell-like structure observed in the different epochs (1999, 2005, and 2007), and found that the shell is still expanding eight years after its discovery. From the difference in the size of the semi-major axes of the fitted ellipses in the epochs 1999 ($\simeq$ 71$\pm$1 mas), 2005 ($\simeq$ 97$\pm$3 mas), and 2007 ($\simeq$ 111$\pm$1 mas), we estimate an average expanding velocity of $\sim$ 5 mas yr$^{-1}$, similar to the proper motions measured in the individual H$_2$O maser features. A kinematic age of $\sim$ 20 yr is derived for this structure. In addition, our VERA observations indicate an increase in the ellipticity of the expanding shell around VLA 2 from epochs 1999 to 2007. In fact, the elliptical fit of the VERA data shows a ratio between the minor and major axes of $\sim$ 0.6, in contrast with a most circular shape for the shell detected in 1999 and 2005 (b/a $\sim$ 0.9). This suggests that we are probably observing the formation of a jet-driven H$_2$O maser structure in VLA2, evolving from a non-collimated pulsed-outflow event during the first stages of evolution of a massive young stellar object (YSO). This may support predictions made earlier by other authors on this issue, consistent with recent magnetohydrodynamical simulations. We discuss possible implications of our results in the study of the first stages of evolution of massive YSOs.
In this paper we present some results concerning the study of the development of galactic winds in blue compact galaxies. In particular, we model a situation very similar to that of the galaxy IZw18, the most metal poor and unevolved galaxy known locally. To do that we compute the chemo-dynamical evolution of a galaxy in the case of one istantaneous isolated starburst as well as in the case of two successive instantaneous starbursts. We show that in both cases a metal enriched wind develops and that the metals produced by the type Ia SNe are lost more efficiently than those produced by type II SNe. We also find that one single burst is able to enrich chemically the surrounding region in few Myr. Both these results are the effect of the assumed efficiency of energy transfer from SNe to ISM and to the consideration of type Ia SNe in this kind of problem. The comparison with observed abundances of IZw18 suggests that this galaxy is likely to have suffered two bursts in its life, with the previous being less intense than the last one.
A numerical evidence for the dependence of the substructure abundance of cluster halos on the orientation coherence of the surrounding tidal fields is presented. Applying the adapted minimal spanning tree (MST) algorithm to the cluster halos with $M\ge 10^{14}\,h^{-1}\,M_{\odot}$ from the Big MultiDark-Planck Simulations, we identify primary MST stems composed of multiple nodes as the filaments and measure their specific sizes (spatial extents per node), which quantify the orientation coherence of the tidal field on the cluster scales. Classifying the cluster halos into five samples by the specific sizes of their host filaments and tallying the mass distributions of the five samples, we investigate if and how the substructure abundance of the cluster halos differs among the five samples. It is found that the cluster halos embedded in the filaments with larger specific sizes tend to possess less substructures. This anti-correlation is also shown robust against narrowing down the formation epochs of the cluster halos as well as against fixing the node number of the filaments. Given that the filaments with larger specific sizes form at the regions where the surrounding tidal fields are coherent over large scales in the orientations of their principal axes, we suggest that in the filaments with larger specific sizes the satellite infall and matter accretion onto the cluster halos should be obstructed due to the development of the tangential velocities in the plane perpendicular to the elongated axes of the filaments.
In the present work we report comprehensive set of shell model calculations for arsenic isotopes. We performed shell model calculations with two recent effective interactions JUN45 and jj44b. The overall results for the energy levels and magnetic moments are in rather good agreement with the available experimental data. We have also reported competition of proton- and neutron-pair breakings analysis to identify which nucleon pairs are broken to obtain the total angular momentum of the calculated states. Further theoretical development is needed by enlarging model space by including $\pi 0f_{7/2}$ and $\nu 1d_{5/2}$ orbitals.
Accurate detection of fingertips in depth image is critical for human-computer interaction. In this paper, we present a novel two-stream convolutional neural network (CNN) for RGB-D fingertip detection. Firstly edge image is extracted from raw depth image using random forest. Then the edge information is combined with depth information in our CNN structure. We study several fusion approaches and suggest a slow fusion strategy as a promising way of fingertip detection. As shown in our experiments, our real-time algorithm outperforms state-of-the-art fingertip detection methods on the public dataset HandNet with an average 3D error of 9.9mm, and shows comparable accuracy of fingertip estimation on NYU hand dataset.
The Fredrickson-Andersen one spin facilitated model (FA-1f) on Z belongs to the class of kinetically constrained spin models (KCM). Each site refreshes with rate one its occupation variable to empty (respectively occupied) with probability q (respectively $p = 1 - q$), provided at least one nearest neighbor is empty. Here, we study the non equilibrium dynamics of FA-1f started from a configuration entirely occupied on the left half-line and focus on the evolution of the front, namely the position of the leftmost zero. We prove, for q larger than a threshold $\bar{q} < 1$, a law of large numbers and a central limit theorem for the front, as well as the convergence to an invariant measure of the law of the process seen from the front.
We introduce a class extending the notion of Chern-Mather class to possibly nonreduced schemes, and use it to express the difference between Schwartz-MacPherson's Chern class and the class of the virtual tangent bundle of a singular hypersurface of a nonsingular variety. Applications include constraints on the possible singularities of a hypersurface and on contacts of nonsingular hypersurfaces, and multiplicity computations.
The discovery of a binary comprising a black hole (BH) and a millisecond pulsar (MSP) would yield insights into stellar evolution and facilitate exquisitely sensitive tests of general relativity. Globular clusters (GCs) are known to harbor large MSP populations and recent studies suggest that GCs may also retain a substantial population of stellar mass BHs. We modeled the formation of BH+MSP binaries in GCs through exchange interactions between binary and single stars. We found that in dense, massive clusters most of the dynamically formed BH+MSP binaries will have orbital periods of 2 to 10 days, regardless of the mass of the BH, the number of BHs retained by the cluster, and the nature of the GC's binary population. The size of the BH+MSP population is sensitive to several uncertain parameters, including the BH mass function, the BH retention fraction, and the binary fraction in GCs. Based on our models, we estimate that there are $0.6\pm0.2$ dynamically formed BH+MSP binaries in the Milky Way GC system, and place an upper limit on the size of this population of $\sim 10$. Interestingly, we find that BH+MSP binaries will be rare even if GCs retain large BH populations.
We consider the origin of new phases in supersymmetric grand unification model, and show how significant new contributions arise from the gluino mediated diagram. We then present a more general model independent analysis of various modes of B-decays suggested previously for measurement of the CKM phases and point out what they really measure. It is in principle possible to separate out all the phases.
We expand on a previous study of fronts in finite particle number reaction-diffusion systems in the presence of a reaction rate gradient in the direction of the front motion. We study the system via reaction-diffusion equations, using the expedient of a cutoff in the reaction rate below some critical density to capture the essential role of fl uctuations in the system. For large density, the velocity is large, which allows for an approximate analytic treatment. We derive an analytic approximation for the front velocity depe ndence on bulk particle density, showing that the velocity indeed diverge s in the infinite density limit. The form in which diffusion is impleme nted, namely nearest-neighbor hopping on a lattice, is seen to have an essential impact on the nature of the divergence.
We perform one-dimensional radiation-hydrodynamic simulations of energetic supernova ejecta colliding with a massive circumstellar medium (CSM) aiming at explaining SN 2016aps, likely the brightest supernova observed to date. SN 2016aps was a superluminous Type-IIn SN, which released as much as $\gtrsim 5\times 10^{51}$ erg of thermal radiation. Our results suggest that the multi-band light curve of SN 2016aps is well explained by the collision of a $30\ M_\odot$ SN ejecta with the explosion energy of $10^{52}$ erg and a $\simeq 8\ M_\odot$ wind-like CSM with the outer radius of $10^{16}$ cm, i.e., a hypernova explosion embedded in a massive CSM. This finding indicates that very massive stars with initial masses larger than $40\ M_\odot$, which supposedly produce highly energetic SNe, occasionally eject their hydrogen-rich envelopes shortly before the core-collapse. We suggest that the pulsational pair-instability SNe may provide a natural explanation for the massive CSM and the energetic explosion. We also provide the relations between the peak luminosity, the radiated energy, and the rise time for interacting SNe with the kinetic energy of $10^{52}$ erg, which can be used for interpreting SN 2016aps-like objects in future surveys.