ShantanuT01/DACTYL-Pretraining huggingface dataset:
We study the equivariant Gromov-Witten and Donaldson-Thomas theories of $\mathbf{P}^2$-bundles over curves. We show the equivariant GW/DT correspondence holds to first order for certain curve classes
Necking or cold drawing is a smoothed jump in cross-sectional area of long and thin bars (filaments orfilms) propagating with a constant speed. The necks in polymers, first observed about seventy years ago, arenow commonly used in modern processing of polymer films and fibers. Yet till recently there was a lack infundamental understanding of necking mechanism(s). For semi-crystalline polymers with co-existingamorphous and crystalline phases, recent experiments revealed that such a mechanism is related tounfolding crystalline blocks. Using this idea, this paper develops a theoretical model and includes it in ageneral continuum framework. Additionally, the paper explains the forced (reversible) elasticity observedin slowly propagating polymeric necks, and also briefly analyses the viscoelastic effects and dissipative heatgeneration when polymer necks propagate fast enough.
In this paper, we propose a novel algorithm to rectify illumination of the digitized documents by eliminating shading artifacts. Firstly, a topographic surface of an input digitized document is created using luminance value of each pixel. Then the shading artifact on the document is estimated by simulating an immersion process. The simulation of the immersion process is modeled using a novel diffusion equation with an iterative update rule. After estimating the shading artifacts, the digitized document is reconstructed using the Lambertian surface model. In order to evaluate the performance of the proposed algorithm, we conduct rigorous experiments on a set of digitized documents which is generated using smartphones under challenging lighting conditions. According to the experimental results, it is found that the proposed method produces promising illumination correction results and outperforms the results of the state-of-the-art methods.
This paper presents a computational model to recover the most likely interpretation of the 3D scene structure from a planar image, where some objects may occlude others. The estimated scene interpretation is obtained by integrating some global and local cues and provides both the complete disoccluded objects that form the scene and their ordering according to depth. Our method first computes several distal scenes which are compatible with the proximal planar image. To compute these different hypothesized scenes, we propose a perceptually inspired object disocclusion method, which works by minimizing the Euler's elastica as well as by incorporating the relatability of partially occluded contours and the convexity of the disoccluded objects. Then, to estimate the preferred scene we rely on a Bayesian model and define probabilities taking into account the global complexity of the objects in the hypothesized scenes as well as the effort of bringing these objects in their relative position in the planar image, which is also measured by an Euler's elastica-based quantity. The model is illustrated with numerical experiments on, both, synthetic and real images showing the ability of our model to reconstruct the occluded objects and the preferred perceptual order among them. We also present results on images of the Berkeley dataset with provided figure-ground ground-truth labeling.
Paralleling our recent computationally-intensive (quasi-Monte Carlo) work for the case N=4 (quant-ph/0308037), we undertake the task for N=6 of computing to high numerical accuracy, the formulas of Sommers and Zyczkowski (quant-ph/0304041) for the (N^2-1)-dimensional volume and (N^2-2)-dimensional hyperarea of the (separable and nonseparable) N x N density matrices, based on the Bures (minimal monotone) metric -- and also their analogous formulas (quant-ph/0302197) for the (non-monotone) Hilbert-Schmidt metric. With the same seven billion well-distributed (``low-discrepancy'') sample points, we estimate the unknown volumes and hyperareas based on five additional (monotone) metrics of interest, including the Kubo-Mori and Wigner-Yanase. Further, we estimate all of these seven volume and seven hyperarea (unknown) quantities when restricted to the separable density matrices. The ratios of separable volumes (hyperareas) to separable plus nonseparable volumes (hyperareas) yield estimates of the separability probabilities of generically rank-six (rank-five) density matrices. The (rank-six) separability probabilities obtained based on the 35-dimensional volumes appear to be -- independently of the metric (each of the seven inducing Haar measure) employed -- twice as large as those (rank-five ones) based on the 34-dimensional hyperareas. Accepting such a relationship, we fit exact formulas to the estimates of the Bures and Hilbert-Schmidt separable volumes and hyperareas.(An additional estimate -- 33.9982 -- of the ratio of the rank-6 Hilbert-Schmidt separability probability to the rank-4 one is quite clearly close to integral too.) The doubling relationship also appears to hold for the N=4 case for the Hilbert-Schmidt metric, but not the others. We fit exact formulas for the Hilbert-Schmidt separable volumes and hyperareas.
Spectra for 2D stars in the 1.5D approximation are created from synthetic spectra of 1D non-local thermodynamic equilibrium (NLTE) spherical model atmospheres produced by the PHOENIX code. The 1.5D stars have the spatially averaged Rayleigh-Jeans flux of a K3-4 III star, while varying the temperature difference between the two 1D component models ($\Delta T_{\mathrm{1.5D}}$), and the relative surface area covered. Synthetic observable quantities from the 1.5D stars are fitted with quantities from NLTE and local thermodynamic equilibrium (LTE) 1D models to assess the errors in inferred $T_{\mathrm{eff}}$ values from assuming horizontal homogeneity and LTE. Five different quantities are fit to determine the $T_{\mathrm{eff}}$ of the 1.5D stars: UBVRI photometric colors, absolute surface flux SEDs, relative SEDs, continuum normalized spectra, and TiO band profiles. In all cases except the TiO band profiles, the inferred $T_{\mathrm{eff}}$ value increases with increasing $\Delta T_{\mathrm{1.5D}}$. In all cases, the inferred $T_{\mathrm{eff}}$ value from fitting 1D LTE quantities is higher than from fitting 1D NLTE quantities and is approximately constant as a function of $\Delta T_{\mathrm{1.5D}}$ within each case. The difference between LTE and NLTE for the TiO bands is caused indirectly by the NLTE temperature structure of the upper atmosphere, as the bands are computed in LTE. We conclude that the difference between $T_{\mathrm{eff}}$ values derived from NLTE and LTE modelling is relatively insensitive to the degree of the horizontal inhomogeneity of the star being modeled, and largely depends on the observable quantity being fit.
The dynamic stability of the Boolean networks representing a model for the gene transcriptional regulation (Kauffman model) is studied by calculating analytically and numerically the Hamming distance between two evolving configurations. This turns out to behave in a universal way close to the phase boundary only for in-degree distributions with a finite second moment. In-degree distributions of the form $P_d(k)\sim k^{-\gamma}$ with $2<\gamma<3$, thus having a diverging second moment, lead to a slower increase of the Hamming distance when moving towards the unstable phase and to a broadening of the phase boundary for finite $N$ with decreasing $\gamma$. We conclude that the heterogeneous regulatory network connectivity facilitates the balancing between robustness and evolvability in living organisms.
We consider various forms of a process, which we call {\em gluing}, for combining two or more complementary quantum channel pairs $(\mathcal{B},\mathcal{C})$ to form a composite. One type of gluing combines a perfect channel with a second channel to produce a \emph{generalized erasure channel} pair $(\mathcal{B}_g,\mathcal{C}_g)$. We consider two cases in which the second channel is (i) an amplitude-damping, or (ii) a phase-damping qubit channel; (ii) is the \emph{dephrasure channel} of Leditzky et al. For both (i) and (ii), $(\mathcal{B}_g,\mathcal{C}_g)$ depends on the damping parameter $0\leq p\leq 1$ and a parameter $0 \leq \lambda \leq 1$ that characterizes the gluing process. In both cases we study $Q^{(1)}(\mathcal{B}_g)$ and $Q^{(1)}(\mathcal{C}_g)$, where $Q^{(1)}$ is the channel coherent information, and determine the regions in the $(p,\lambda)$ plane where each is zero or positive, confirming previous results for (ii). A somewhat surprising result for which we lack any intuitive explanation is that $Q^{(1)}(\mathcal{C}_g)$ is zero for $\lambda \leq 1/2$ when $p=0$, but is strictly positive (though perhaps extremely small) for all values of $\lambda> 0$ when $p$ is positive by even the smallest amount. In addition we study the nonadditivity of $Q^{(1)}(\mathcal{B}_g)$ for two identical channels in parallel. It occurs in a well-defined region of the $(p,\lambda)$ plane in case (i). In case (ii) we have extended previous results for the dephrasure channel without, however, identifying the full range of $(p,\lambda)$ values where nonadditivity occurs. Again, an intuitive explanation is lacking.
In this study we show how to represent a continuous time autoregressive moving average (CARMA) as a higher order stochastic delay differential equation, which may be thought of as a continuous-time equivalent of the AR($\infty$) representation. Furthermore, we show how this representation gives rise to a prediction formula for CARMA processes. To be used in the above mentioned results we develop a general theory for multivariate stochastic delay differential equations, which will be of independent interest, and which will have particular focus on existence, uniqueness and representations.
The discriminant of a trinomial of the form $x^n \pm x^m \pm 1$ has the form $\pm n^n \pm (n-m)^{n-m} m^m$ if $n$ and $m$ are relatively prime. We investigate when these discriminants have nontrivial square factors. We explain various unlikely-seeming parametric families of square factors of these discriminant values: for example, when $n$ is congruent to 2 (mod 6) we have that $((n^2-n+1)/3)^2$ always divides $n^n - (n-1)^{n-1}$. In addition, we discover many other square factors of these discriminants that do not fit into these parametric families. The set of primes whose squares can divide these sporadic values as $n$ varies seems to be independent of $m$, and this set can be seen as a generalization of the Wieferich primes, those primes $p$ such that $2^{p-1}$ is congruent to 1 (mod $p^2$). We provide heuristics for the density of squarefree values of these discriminants and the density of these "sporadic" primes.
In order to analyze stability of a two-queue model, we consider a two-dimensional quasi-birth-and-death process (2d-QBD process), denoted by $\{\boldsymbol{Y}(t)\}=\{((L_1(t),L_2(t)),J(t))\}$. The two-dimensional process $\{(L_1(t),L_2(t))\}$ on $\mathbb{Z}_+^2$ is called a level process, where the individual processes $\{L_1(t)\}$ and $\{L_2(t)\}$ are assumed to be skip free. The supplemental process $\{J(t)\}$ is called a phase process and it takes values in a finite set. The 2d-QBD process is a CTMC, in which the transition rates of the level process vary according to the state of the phase process like an ordinary (one-dimensional) QBD process. In this paper, we first state the conditions ensuring a 2d-QBD process is positive recurrent or transient and then demonstrate that the efficiency of a two-queue model can be estimated by using the conditions we obtain.
Complexity of geometric symmetry for differential operators with mixed homogeniety is examined here. Sharp Sobolev estimates are calculated for the Grushin operator in low dimensions using hyperbolic symmetry and conformal geometry.
Let $S$ be a smooth complex connected analytic surface which admits a holomorphic symplectic structure. Let $S^{(n)}$ be its $n$th symmetric product. We prove that every projective symplectic resolution of $S^{(n)}$ is isomorphic to the Douady-Barlet resolution $S^{[n]} \to S^{(n)}$.
We discuss the three-body decay mechanisms of many-body resonances. Sequential decays proceed via two-body configurations after emission of the third particle. In direct decay all three particles leave simultaneously their interaction regions. The intermediate paths within the interaction regions are not observables and only accessible through models. The momentum distributions carry, apart from polarization, all possible information about decay modes and resonance structure. In this context we discuss detailed results for the decay of the $^{9}$Be($5/2^-$) resonance.
An electron-phonon cavity consisting of a quantum dot embedded in a free-standing GaAs/AlGaAs membrane is characterized in Coulomb blockade measurements at low temperatures. We find a complete suppression of single electron tunneling around zero bias leading to the formation of an energy gap in the transport spectrum. The observed effect is induced by the excitation of a localized phonon mode confined in the cavity. This phonon blockade of transport is lifted at magnetic fields where higher electronic states with nonzero angular momentum are brought into resonance with the phonon energy.
Compression and reconstruction of visual data have been widely studied in the computer vision community, even before the popularization of deep learning. More recently, some have used deep learning to improve or refine existing pipelines, while others have proposed end-to-end approaches, including autoencoders and implicit neural representations, such as SIREN and NeRV. In this work, we propose Neural Visual Representation with Content-adaptive Embedding (CNeRV), which combines the generalizability of autoencoders with the simplicity and compactness of implicit representation. We introduce a novel content-adaptive embedding that is unified, concise, and internally (within-video) generalizable, that compliments a powerful decoder with a single-layer encoder. We match the performance of NeRV, a state-of-the-art implicit neural representation, on the reconstruction task for frames seen during training while far surpassing for frames that are skipped during training (unseen images). To achieve similar reconstruction quality on unseen images, NeRV needs 120x more time to overfit per-frame due to its lack of internal generalization. With the same latent code length and similar model size, CNeRV outperforms autoencoders on reconstruction of both seen and unseen images. We also show promising results for visual data compression. More details can be found in the project pagehttps://haochen-rye.github.io/CNeRV/
At FRM-II the installation of a user office software is under consideration, supporting tasks like proposal handling, beam time allocation, data handling and report creation. Although there are several software systems in use at major facilities, most of them are not portable to other institutes. In this paper the requirements for a modular and extendable user office software are discussed with focus on security related aspects like how to prevent a denial of service attack on fully automated systems. A suitable way seems to be the creation of a web based application using Apache as webserver, MySQL as database system and PHP as scripting language.
We consider renewal shot noise processes with response functions which are eventually nondecreasing and regularly varying at infinity. We prove weak convergence of renewal shot noise processes, properly normalized and centered, in the space $D[0,\infty)$ under the $J_1$ or $M_1$ topology. The limiting processes are either spectrally nonpositive stable L\'{e}vy processes, including the Brownian motion, or inverse stable subordinators (when the response function is slowly varying), or fractionally integrated stable processes or fractionally integrated inverse stable subordinators (when the index of regular variation is positive). The proof exploits fine properties of renewal processes, distributional properties of stable L\'{e}vy processes and the continuous mapping theorem.
Improving the understanding of the processes governing small-scale nonlinear clustering is a necessary task for interpreting upcoming high-quality cosmological data, as it will allow one to break degeneracies and obtain tight neutrino mass and warm dark matter constraints from large-scale structure probes. The Sejong Suite, an extensive collection of state-of-the-art high-resolution cosmological hydrodynamical simulations, has been intended with this primary goal in mind. Spanning a large number of cosmological and astrophysical parameters (especially suitable for the dark sector), and organized into three main categories (Grid Suite, Supporting Suite, and Systematics Suite), the release may be useful for a broader variety of cosmological and astrophysical purposes - while primarily developed for Lyman-Alpha (LyA) forest studies. In particular, the overall architecture of the Grid Suite has been designed to achieve an equivalent resolution up to 3x3328^3=110 billion particles in a 100 Mpc/h box, corresponding to a 30 kpc/h mean grid resolution, which ensures convergence on LyA flux statistics closer to the desired 1.0% level that data from surveys such as the Dark Energy Spectroscopic Instrument (DESI) will provide. Here, we briefly highlight the main characteristics, improvements, and novelties of the Sejong Suite, as well as ongoing and future applications.
The non-potentiality (NP) of the solar magnetic fields is measured traditionally in terms of magnetic shear angle i.e., the angle between observed and potential field azimuth. Here, we introduce another measure of shear that has not been studied earlier in solar active regions, i.e. the one that is associated with the inclination angle of the magnetic field. This form of shear, which we call as the "dip-shear", can be calculated by taking the difference between the observed and potential field inclination. In this Letter, we study the evolution of dip-shear as well as the conventional twist-shear in a $\delta$-sunspot using high-resolution vector magnetograms from {\it Hinode} space mission. We monitor these shears in a penumbral region located close to flare site during 12 and 13 December 2006. It is found that: (i) the penumbral area close to the flaring site shows high value of twist-shear and dip-shear as compared to other parts of penumbra, (ii) after the flare the value of dip-shear drops in this region while the twist-shear in this region tends to increase after the flare, (iii) the dip-shear and twist-shear are correlated such that pixels with large twist-shear also tend to exhibit large dip-shear, and (iv) the correlation between the twist-shear and dip-shear is tighter after the flare. The present study suggests that monitoring twist-shear during the flare alone is not sufficient but we need to monitor it together with dip-shear.
We found that the integral of four Hermite polynomials integrated with squared weight over the real line generates symmetric polynomials with a beautiful recursive property. We pose a question whether that integral admit an explicit formula or not. The question has a certain interpretation in terms of Hermitian matrices.
The intermetallic semiconductor FeGa$_{3}$ acquires itinerant ferromagnetism upon electron doping by a partial replacement of Ga with Ge. We studied the electron spin resonance (ESR) of high-quality single crystals of FeGa$_{3-x}$Ge$_x$ for $x$ from 0 up to 0.162 where ferromagnetic order is observed. For $x = 0$ we observed a well-defined ESR signal, indicating the presence of pre-formed magnetic moments in the semiconducting phase. Upon Ge doping the occurrence of itinerant magnetism clearly affects the ESR properties below $\approx 40$~K whereas at higher temperatures an ESR signal as seen in FeGa$_{3}$ prevails independent on the Ge-content. The present results show that the ESR of FeGa$_{3-x}$Ge$_x$ is an appropriate and direct tool to investigate the evolution of 3d-based itinerant magnetism.
We consider the holographic dual of a general class of N=1* flows in which all three chiral multiplets have independent masses, and in which the corresponding Yang-Mills scalars can develop particular supersymmetry-preserving vevs. We also allow the gaugino to develop a vev. This leads to a six parameter subspace of the supergravity scalar action, and we show that this is a consistent truncation, and obtain a superpotential that governs the N=1* flows on this subspace. We analyse some of the structure of the superpotential, and check consistency with the asymptotic behaviour near the UV fixed point. We show that the dimensions of the six couplings obey a sum rule all along the N=1* flows. We also show how our superpotential describes part of the Coulomb branch of the non-trivial N=1 fixed point theory.
Here we discuss the interaction of massive stars with their parental molecular clouds. A summary of the dynamical evolution of HII regions and wind-driven bubbles in high-pressure cloud cores is given. Both ultracompact HII regions and ultracompact wind-driven bubbles can reach pressure equilibrium with their surrounding medium. The structures stall their expansion and become static and, as long as the ionization sources and the ambient densities remain about constant, the resulting regions are stable and long lived. For cases with negative density gradients, and depending on the density distribution, some regions never reach the static equilibrium condition. For power-law density stratifications, $\rho \propto r^{-w}$, the properties of the evolution depend on a critical exponent, $w_{crit}$, above which the ionization front cannot be slowed down by recombinations or new ionizations, and the cloud becomes fully ionized. This critical exponent is $w_{crit}=3/2$ during the expansion phase. For $w>3/2 $ the gas expands supersonically into the surrounding ionized medium, and there are two regimes separated by $w=3$. For $3/2<w\leq 3$, the slow regime, the inner region drives a weak shock moving with almost constant velocity through the cloud. For $w>3$, the fast regime, the shock becomes strong and accelerates with time. Finally, the evolution of slow winds in highly pressurized region is described briefly.
[Abridged] Type-I X-ray bursts are thermonuclear flashes that take place on the surface of accreting neutron stars. The wait time between consecutive bursts is set by the time required to accumulate the fuel needed to trigger a new burst; this is at least one hour. Sometimes secondary bursts are observed, approximately 10 min after the main burst. These short wait-time bursts are not yet understood. We observed the low-mass X-ray binary and X-ray burster EXO 0748-676 with XMM-Newton for 158 h, during 7 uninterrupted observations lasting up to 30 h each. We detect 76 X-ray bursts. Most remarkably, 15 of these bursts occur in burst triplets, with wait times of 12 min between the three components of the triplet. We also detect 14 doublets with similar wait times between the two components of the doublet. The characteristics of the bursts indicate that possibly all bursts in this system are hydrogen-ignited, in contrast with most other frequent X-ray bursters in which bursts are helium-ignited, but consistent with the low mass accretion rate in EXO 0748-676. Possibly the hydrogen ignition is the determining factor for the occurrence of short wait-time bursts.
We study the nonequilibrium critical point of the zero temperature random field Ising model on a triangular lattice and compare it with known results on honeycomb, square, and simple cubic lattices. We suggest that the coordination number of the lattice rather than its dimension plays the key role in determining the universality class of the nonequilibrium critical behavior. This is discussed in the context of numerical evidence that equilibrium and nonequilibrium critical points of the zero-temperature random field Ising model belong to the same universality class. The physics of this curious result is not fully understood.