ShantanuT01/DACTYL-Pretraining huggingface dataset:
The Borcherds lift for indefinite unitary groups, previously constructed by the author, is examined here in greater detail for the special case of the group U(1,1). The inputs for the lifting in this case are weakly holomorphic modular forms of weight zero, which are lifted to meromorphic modular forms on the usual complex upper half plane transforming under an arithmetic subgroup of U(1,1). In this setting, we can completely describe the Weyl-chambers involved and explicitly calculate the attached Weyl-vectors, for a family of input functions with principle part $q^{-n}$. Since these are a basis for the input space, we obtain similarly explicit results for arbitrary input functions. The Heegner divisors in this case consist of CM-points, the CM-order of which is also determined.
Human face recognition is, indeed, a challenging task, especially under the illumination and pose variations. We examine in the present paper effectiveness of two simple algorithms using coiflet packet and Radon transforms to recognize human faces from some databases of still gray level images, under the environment of illumination and pose variations. Both the algorithms convert 2-D gray level training face images into their respective depth maps or physical shape which are subsequently transformed by Coiflet packet and Radon transforms to compute energy for feature extraction. Experiments show that such transformed shape features are robust to illumination and pose variations. With the features extracted, training classes are optimally separated through linear discriminant analysis (LDA), while classification for test face images is made through a k-NN classifier, based on L1 norm and Mahalanobis distance measures. Proposed algorithms are then tested on face images that differ in illumination,expression or pose separately, obtained from three databases,namely, ORL, Yale and Essex-Grimace databases. Results, so obtained, are compared with two different existing algorithms.Performance using Daubechies wavelets is also examined. It is seen that the proposed Coiflet packet and Radon transform based algorithms have significant performance, especially under different illumination conditions and pose variation. Comparison shows the proposed algorithms are superior.
We study N=2 supersymmetric gauge theories on squashed 3-sphere and S^1xS^2. Recent studies have shown that the partition functions in a class of N=2 theories have factorized forms in terms of vortex and anti-vortex partition functions by explicitly evaluating matrix integrals obtained from Coulomb branch localization. We directly derive this structure by performing Higgs branch localization. It turns out that more general N=2 theories have this factorization property. We also discuss the factorization of supersymmetric Wilson loop.
We have investigated shot noise in a 6-nm-diameter, semiconducting multiwalled carbon nanotube FET at 4.2 K over the frequency range 600 - 950 MHz. We find a transconductance of 3 - 3.5 $\mu$S for optimal positive and negative source-drain voltages V. For the gate referred input voltage noise, we obtain 0.2 and 0.3 $\mu{V}/ \sqrt{Hz}$ for V>0 and V<0, respectively. As effective charge noise this corresponds to $2-3 \cdot 10^{-5}$ e/$\sqrt{Hz}$.
The most accurate ages for the oldest stars are those obtained for nearby halo subgiants, because they depend almost entirely on just the measured parallaxes and absolute oxygen abundances. In this study, we have used the Fine Guidance Sensors on the Hubble Space Telescope to determine trigonometric parallaxes, with precisions of 2.1% or better, for the Population II subgiants HD 84937, HD 132475, and HD 140283. High quality spectra have been used to derive their surface abundances of O, Fe, Mg, Si, and Ca, which are assumed to be 0.1-0.15 dex less than their initial abundances due to the effects of diffusion. Comparisons of isochrones with the three subgiants on the $(\log\,T_{\rm eff}, M_V)$-diagram yielded ages of $12.08 \pm 0.14, 12.56 \pm 0.46$, and $14.27 \pm 0.38$ Gyr for HD 84937, HD 132475, and HD 140283, in turn, where each error bar includes only the parallax uncertainty. The total uncertainty is estimated to be $\sim\pm 0.8$ Gyr (larger in the case of the near-turnoff star HD 84937). Although the age of HD 140283 is greater than the age of the universe as inferred from the cosmic microwave background by $\sim$ 0.4-0.5 Gyr, this discrepancy is at a level of $< 1\,\sigma$. Nevertheless, the first Population II stars apparently formed very soon after the Big Bang. (Stellar models that neglect diffusive processes seem to be ruled out as they would predict that HD 140283 is $\sim 1.5$ Gyr older than the universe.) The halo field subgiants appear to be older than globular clusters of similar metallicities: if distances close to those implied by the RR Lyrae standard candle are assumed, M92 and M5 are younger than HD 140283 and HD 132475 by $\sim 1.5$ and $\sim 1.0$ Gyr, respectively.
Let $0<\alpha<2$ be any real number. In this paper, we investigate the following semilinear equations involving the fractional Laplacian \begin{equation}(-\bigtriangleup)^{\alpha/2} u(x)=f(u),\end{equation} on $\mathbb{R}^n$ and $\mathbb{R}^n_+$.   Applying a direct method of moving planes for the fractional Laplacian, we prove symmetry and nonexistence of positive solutions on $\mathbb{R}^n$ and $\mathbb{R}^n_+$ under mild conditions on $f$.
The study of arithmetic properties of coefficients of modular forms $f(\tau) = \sum a(n)q^n$ has a rich history, including deep results regarding congruences in arithmetic progressions. Recently, work of C.-S. Radu, S. Ahlgren, B. Kim, N. Andersen, and S. L\"{o}brich have employed the $q$-expansion principle of P. Deligne and M. Rapoport in order to determine more about where these congruences can occur. Here, we extend the method to give additional results for a large class of modular forms. We also give analogous results for generalized Frobenius partitions and the two mock theta functions $f(q)$ and $\omega(q).$
By using the Zubarev nonequilibrium statistical operator method, and the Liouville equation with fractional derivatives, a generalized diffusion equation with fractional derivatives is obtained within the Renyi statistics. Averaging in generalized diffusion coefficient is performed with a power distribution with the Renyi parameter $q$.
The nucleon-nucleon interaction arising from the exchange of three pions and the excitation of $\Delta(1232)$-isobars in intermediate states is studied. Approximating the $\Delta$-propagator by the inverse $\Delta$N mass-splitting, analytical expressions are derived for the spectral-functions of the isoscalar and isovector central, spin-spin and tensor NN-potentials in momentum-space. A trans- lation of the spectral-functions into coordinate-space potentials reveals that the main effect of these specific exchange and excitation mechanisms is a repulsive isoscalar central NN-potential.
Given an integral hyperplane arrangement, Kamiya-Takemura-Terao (2008 & 2011) introduced the notion of characteristic quasi-polynomial, which enumerates the cardinality of the complement of the arrangement modulo a positive integer. The most popular candidate for period of the characteristic quasi-polynomials is the lcm period. In this paper, we initiate a study of period collapse in characteristic quasi-polynomials stemming from the concept of period collapse in the theory of Ehrhart quasi-polynomials. We say that period collapse occurs in a characteristic quasi-polynomial when the minimum period is strictly less than the lcm period. Our first main result is that in the non-central case, with regard to period collapse anything is possible: period collapse occurs in any dimension $\ge 1$, occurs for any value of the lcm period $\ge 2$, and the minimum period when it is not the lcm period can be any proper divisor of the lcm period. Our second main result states that in the central case, however, no period collapse is possible in any dimension, that is, the lcm period is always the minimum period.
Handwritten text recognition in low resource scenarios, such as manuscripts with rare alphabets, is a challenging problem. The main difficulty comes from the very few annotated data and the limited linguistic information (e.g. dictionaries and language models). Thus, we propose a few-shot learning-based handwriting recognition approach that significantly reduces the human labor annotation process, requiring only few images of each alphabet symbol. The method consists in detecting all the symbols of a given alphabet in a textline image and decoding the obtained similarity scores to the final sequence of transcribed symbols. Our model is first pretrained on synthetic line images generated from any alphabet, even though different from the target domain. A second training step is then applied to diminish the gap between the source and target data. Since this retraining would require annotation of thousands of handwritten symbols together with their bounding boxes, we propose to avoid such human effort through an unsupervised progressive learning approach that automatically assigns pseudo-labels to the non-annotated data. The evaluation on different manuscript datasets show that our model can lead to competitive results with a significant reduction in human effort. The code will be publicly available in this repository: \url{https://github.com/dali92002/HTRbyMatching}
Multi-manifold modeling is increasingly used in segmentation and data representation tasks in computer vision and related fields. While the general problem, modeling data by mixtures of manifolds, is very challenging, several approaches exist for modeling data by mixtures of affine subspaces (which is often referred to as hybrid linear modeling). We translate some important instances of multi-manifold modeling to hybrid linear modeling in embedded spaces, without explicitly performing the embedding but applying the kernel trick. The resulting algorithm, Kernel Spectral Curvature Clustering, uses kernels at two levels - both as an implicit embedding method to linearize nonflat manifolds and as a principled method to convert a multiway affinity problem into a spectral clustering one. We demonstrate the effectiveness of the method by comparing it with other state-of-the-art methods on both synthetic data and a real-world problem of segmenting multiple motions from two perspective camera views.
As noted by Witten, compactifying a $d$-dimensional holographic CFT on an $S^1$ gives a class of $(d-1)$-dimensional confining theories with gravity duals. The prototypical bulk solution dual to the ground state is a double Wick rotation of the AdS$_{d+1}$ Schwarzschild black hole known as the AdS soliton. We generalize such examples by allowing slow variations in the size of the $S^1$, and thus in the confinement scale. Coefficients governing the second order response of the system are computed for $3 \le d \le 8$ using a derivative expansion closely related to the fluid-gravity correspondence. The primary physical results are that i) gauge-theory flux tubes tend to align orthogonal to gradients and along the eigenvector of the Hessian with the lowest eigenvalue, ii) flux tubes aligned orthogonal to gradients are attracted to gradients for $d \le 6$ but repelled by gradients for $d \ge 7$, iii) flux tubes are repelled by regions where the second derivative along the tube is large and positive but are attracted to regions where the eigenvalues of the Hessian are large and positive in directions orthogonal to the tube, and iv) for $d > 3$, inhomogeneities act to raise the total energy of the confining vacuum above its zeroth order value.
While quantum entanglement is known to be monogamous (i.e. shared entanglement is restricted in multi-partite settings), here we show that distributed entanglement (or the potential for entanglement) is by nature polygamous. By establishing the concept of one-way unlocalizable entanglement (UE) and investigating its properties, we provide a polygamy inequality of distributed entanglement in tripartite quantum systems of arbitrary dimension. We also provide a polygamy inequality in multi-qubit systems, and several trade offs between UE and other correlation measures.
We study a generating function for the sum over fatgraphs with specified valences of vertices and faces, inversely weighted by the order of their symmetry group. A compact expression is found for general (i.e. non necessarily connected) fatgraphs. This expression admits a matrix integral representation which enables to perform semi--classical computations, leading in particular to a closed formula corresponding to (genus zero, connected) trees.
Suppose that two players take turns coloring the vertices of a given graph G with k colors. In each move the current player colors a vertex such that neighboring vertices get different colors. The first player wins this game if and only if at the end, all the vertices are colored. The game chromatic number $\chi_g(G)$ is defined as the smallest k for which the first player has a winning strategy.   Recently, Bohman, Frieze and Sudakov [Random Structures and Algorithms 2008] analysed the game chromatic number of random graphs and obtained lower and upper bounds of the same order of magnitude. In this paper we improve existing results and show that with high probability, the game chromatic number $\chi_g(G_{n,p})$ of dense random graphs is asymptotically twice as large as the ordinary chromatic number $\chi(G_{n,p})$.
It has long been regarded as difficult for a cosmological model to account simultaneously for the galaxy luminosity, mass, and velocity distributions. We revisit this issue using a modern compilation of observational data along with the best available large-scale cosmological simulation of dark matter. We find that the standard cosmological model, used in conjunction with halo abundance matching (HAM) and simple dynamical corrections, fits all basic statistics of galaxies with circular velocities Vcirc > 80 km/s. Our observational constraint is the luminosity-velocity relation which allows all types of galaxies to be included. We have compiled data for a variety of galaxies ranging from dwarf irregulars to giant ellipticals. The data present a clear monotonic luminosity-velocity relation from 50 km/s to 500 km/s, with a bend below 80 km/s and a systematic offset between late- and early-type galaxies. For comparison to theory, we employ our LCDM "Bolshoi" simulation of dark matter, which has unprecedented mass and force resolution. We use halo abundance matching to assign rank-ordered galaxy luminosities to the dark matter halos. The resulting predictions for the luminosity-velocity relation are in excellent agreement with the available data on both early-type and late-type galaxies for the luminosity range from Mr = -14-22. We also compare our predictions for the "cold" baryon mass (i.e., stars and cold gas) of galaxies as a function of circular velocity with the available observations, again finding a very good agreement. The predicted circular velocity function is in agreement with the galaxy velocity function for 80-400 km/s. However, we find that the dark matter halos with Vcirc < 80 km/s are much more abundant than observed galaxies with the same Vcirc . We find that the two-point correlation function of galaxies in our model matches very well the results from the SDSS.
Relying on the method developed in [debusscheromito2014], we prove the existence of a density for two different examples of random fields indexed by $(t,x)\in(0,T]\times \Rd$. The first example consists of SPDEs with Lipschitz continuous coefficients driven by a Gaussian noise white in time and with a stationary spatial covariance, in the setting of [dalang1999]. The density exists on the set where the nonlinearity $\sigma$ of the noise does not vanish. This complements the results in [sanzsuess2015] where $\sigma$ is assumed to be bounded away from zero. The second example is an ambit field with a stochastic integral term having as integrator a L\'evy basis of pure-jump, stable-like type.
In an unpublished 2005 paper T. Rivoal proved a formula giving 4/pi as the infinite product of factors (1 + 1/(k+1)) to a power involving the integer part of the logarithm of k in base 2 and a 4-periodic sequence. We show how a lemma in a 1988 paper of J. Shallit and the author allows us to prove that formula, as well as a family of similar formulas involving occurrences of blocks of digits in the base-B expansion of the integer k, where B is an integer larger than 1.
In 1999, Jacobson and Lehel conjectured that for $k \geq 3$, every $k$-regular Hamiltonian graph has cycles of at least linearly many different lengths. This was further strengthened by Verstra\"{e}te, who asked whether the regularity can be replaced with the weaker condition that the minimum degree is at least $3$. Despite attention from various researchers, until now, the best partial result towards both of these conjectures was a $\sqrt{n}$ lower bound on the number of cycle lengths. We resolve these conjectures asymptotically, by showing that the number of cycle lengths is at least $n^{1-o(1)}$.
Continuous photometry with up to three BRITE satellites was obtained for 12 targets and subjected to a period search. Contemporaneous high-resolution optical spectroscopy with STELLA was used to obtain radial velocities through cross correlation with template spectra as well as to determine astrophysical parameters through a comparison with model spectra. The Capella red light curve was found to be constant over 176 days with a root mean square of 1 mmag, but the blue light curve showed a period of 10.1$\pm$0.6 d, which we interpret to be the rotation period of the G0 component. The BRITE light curve of the F0 supergiant $\varepsilon$Aur suggests 152 d as its main pulsation period, while the STELLA radial velocities reveal a clear 68 d period. An ingress of an eclipse of the $\zeta$Aur binary system was covered with BRITE and a precise timing for its eclipse onset derived. $\eta$Aur is identified as a slowly pulsating B (SPB) star with a main period of 1.29 d and is among the brightest SPB stars discovered so far. The rotation period of the magnetic Ap star $\theta$Aur is detected from photometry and spectroscopy with a period of 3.6189 d and 3.6177 d, respectively, likely the same within the errors. Photometric rotation periods are also confirmed for the magnetic Ap star $\tau$Aur of 2.463 d and for the solar-type star $\kappa^1$Cet of 9.065 d, and also for the B7 HgMn giant $\beta$Tau of 2.74 d. Revised orbital solutions are derived for the eclipsing SB2 binary $\beta$Aur, for the 27 year eclipsing SB1 $\varepsilon$Aur, and for the RS CVn binary HR 1099. The two stars $\nu$ Aur and $\iota$Aur are found to be long-term, low-amplitude RV and brightness variables, but provisional orbital elements based on a period of 20 yr and an eccentricity of 0.7 could only be extracted for $\nu$Aur. The variations of $\iota$Aur are due to oscillations with a period of $\approx$4 yr.
The spectrum and the eigenstates of a finite 2D tight-binding electronic system, with Dirichlet boundary conditions, in magnetic field and external linear potential are studied. The eigenstates show an equipotential character and may cross the plaquette in the direction perpendicular to the electric field. When leads are added to the plaquette, the channels carrying the current may be shortcut by equipotentials, resulting in additional plateaus situated inbetween the usual IQHE plateaus. This idea is confirmed by a numerical calculation within the four-terminal Landauer-B\"{u}ttiker approach.
The algebra of biquaternions possess a manifestly Lorentz invariant form and induces an extended space-time geometry. We consider the links between this complex pre-geometry and real geometry of the Minkowski space-time. Twistor structures naturally arise in the framework of biquaternionic analysis. Both together, algebraic and twistor structures impose rigid restriction on the transport of singular points of biquaternion-valued fields identified with particle-like formations.
Quantum networking allows the transmission of information in ways unavailable in the classical world. Single packets of information can now be split and transmitted in a coherent way over different routes. This aggregation allows information to be transmitted in a fault tolerant way between different parts of the quantum network (or the future internet) - even when that is not achievable with a single path approach. It is a quantum phenomenon not available in conventional telecommunication networks either. We show how the multiplexing of independent quantum channels allows a distributed form of quantum error correction to protect the transmission of quantum information between nodes or users of a quantum network. Combined with spatial-temporal single photon multiplexing we observe a significant drop in network resources required to transmit that quantum signal - even when only two channels are involved. This work goes far beyond the concepts of channel capacities and shows how quantum networking may operate in the future. Further it shows that quantum networks are likely to operate differently from their classical counterparts which is an important distinction as we design larger scale ones.
We define the coherence non-generating channel as the completely positive trace-preserving map which does not generate quantum coherence from an incoherent state. The incoherent operations are the strict subset of the coherence non-generating channels. We prove that the relative entropy of coherence is monotonically decreasing under the coherence non-generating channels, while the coherence of formation may increase under such channels. Interestingly, by combining mathematically the coherence of formation to the entanglement of formation, we show that the coherence of formation of a single-qubit is never increased by a coherence non-generating channel. This leads to the superadditivity property for the coherence increasing power of quantum channels, namely, while two channels can not increase coherence individually, they may increase the quantum coherence of a composed system. Further, we derive the general form of the rank-2 coherence non-generating qubit channels. Our results contribute to the resource theory of quantum coherence.
In this paper, we propose a pixel-wise method named TextCohesion for scene text detection, which splits a text instance into five key components: a Text Skeleton and four Directional Pixel Regions. These components are easier to handle than the entire text instance. A confidence scoring mechanism is designed to filter characters that are similar to text. Our method can integrate text contexts intensively when backgrounds are complex. Experiments on two curved challenging benchmarks demonstrate that TextCohesion outperforms state-of-the-art methods, achieving the F-measure of 84.6% on Total-Text and bfseries86.3% on SCUT-CTW1500.