Three-Loop Anomalous Dimension of the Heavy Quark Pair Production Current in Non-Relativistic QCD

The three-loop non-mixing contributions to the anomalous dimension of the leading order quark pair production current in non-relativistic QCD are computed. It is demonstrated that the renormalization procedure can only be carried out consistently if the dynamics of both soft and the ultrasoft degrees of freedom is present for all scales below the heavy quark mass, and if the soft and ultrasoft renormalization scales are always correlated.Comment: 19 pages, revtex, 5 postscript figures include

Partially obscured human detection based on component detectors using multiple feature descriptors

This paper presents a human detection system based on component detector using multiple feature descriptors. The contribution presents two issues for dealing with the problem of partially obscured human. First, it presents the extension of feature descriptors using multiple scales based Histograms of Oriented Gradients (HOG) and parallelogram based Haar-like feature (PHF) for improving the accuracy of the system. By using multiple scales based HOG, an extensive feature space allows obtaining high-discriminated features. Otherwise, the PHF is adaptive limb shapes of human in fast computing feature. Second, learning system using boosting classifications based approach is used for training and detecting the partially obscured human. The advantage of boosting is constructing a strong classification by combining a set of weak classifiers. However, the performance of boosting depends on the kernel of weak classifier. Therefore, the hybrid algorithms based on AdaBoost and SVM using the proposed feature descriptors is one of solutions for robust human detection.This paper presents a human detection system based on component detector using multiple feature descriptors. The contribution presents two issues for dealing with the problem of partially obscured human. First, it presents the extension of feature descriptors using multiple scales based Histograms of Oriented Gradients (HOG) and parallelogram based Haar-like feature (PHF) for improving the accuracy of the system. By using multiple scales based HOG, an extensive feature space allows obtaining high-discriminated features. Otherwise, the PHF is adaptive limb shapes of human in fast computing feature. Second, learning system using boosting classifications based approach is used for training and detecting the partially obscured human. The advantage of boosting is constructing a strong classification by combining a set of weak classifiers. However, the performance of boosting depends on the kernel of weak classifier. Therefore, the hybrid algorithms based on AdaBoost and SVM using the proposed feature descriptors is one of solutions for robust human detection

EnSolver: Uncertainty-Aware CAPTCHA Solver Using Deep Ensembles

The popularity of text-based CAPTCHA as a security mechanism to protect websites from automated bots has prompted researches in CAPTCHA solvers, with the aim of understanding its failure cases and subsequently making CAPTCHAs more secure. Recently proposed solvers, built on advances in deep learning, are able to crack even the very challenging CAPTCHAs with high accuracy. However, these solvers often perform poorly on out-of-distribution samples that contain visual features different from those in the training set. Furthermore, they lack the ability to detect and avoid such samples, making them susceptible to being locked out by defense systems after a certain number of failed attempts. In this paper, we propose EnSolver, a novel CAPTCHA solver that utilizes deep ensemble uncertainty estimation to detect and skip out-of-distribution CAPTCHAs, making it harder to be detected. We demonstrate the use of our solver with object detection models and show empirically that it performs well on both in-distribution and out-of-distribution data, achieving up to 98.1% accuracy when detecting out-of-distribution data and up to 93% success rate when solving in-distribution CAPTCHAs.Comment: Epistemic Uncertainty - E-pi UAI 2023 Worksho

On the solutions of universal differential equation by noncommutative Picard-Vessiot theory

Basing on Picard-Vessiot theory of noncommutative differential equations and algebraic combinatorics on noncommutative formal series with holomorphic coefficients, various recursive constructions of sequences of grouplike series converging to solutions of universal differential equation are proposed. Basing on monoidal factorizations, these constructions intensively use diagonal series and various pairs of bases in duality, in concatenation-shuffle bialgebra and in a Loday's generalized bialgebra. As applications, the unique solution, satisfying asymptotic conditions, of Knizhnik-Zamolodchikov equations is provided by d\'evissage

Soft-Collinear Factorization and Zero-Bin Subtractions

We study the Sudakov form factor for a spontaneously broken gauge theory using a (new) Delta -regulator. To be well-defined, the effective theory requires zero-bin subtractions for the collinear sectors. The zero-bin subtractions depend on the gauge boson mass M and are not scaleless. They have both finite and 1/epsilon contributions, and are needed to give the correct anomalous dimension and low-scale matching contributions. We also demonstrate the necessity of zero-bin subtractions for soft-collinear factorization. We find that after zero-bin subtractions the form factor is the sum of the collinear contributions 'minus' a soft mass-mode contribution, in agreement with a previous result of Idilbi and Mehen in QCD. This appears to conflict with the method-of-regions approach, where one gets the sum of contributions from different regions.Comment: 9 pages, 5 figures. V2:ref adde

Families of eulerian functions involved in regularization of divergent polyzetas

Extending the Eulerian functions, we study their relationship with zeta function of several variables. In particular, starting with Weierstrass factorization theorem (and Newton-Girard identity) for the complex Gamma function, we are interested in the ratios of $\zeta(2k)/\pi^{2k}$ and their multiindexed generalization, we will obtain an analogue situation and draw some consequences about a structure of the algebra of polyzetas values, by means of some combinatorics of noncommutative rational series. The same combinatorial frameworks also allow to study the independence of a family of eulerian functions.Comment: preprin

On The Global Renormalization and Regularization of Several Complex Variable Zeta Functions by Computer

This review concerns the resolution of a special case of Knizhnik-Zamolodchikov equations ($KZ_3$) using our recent results on combinatorial aspects of zeta functions on several variables and software on noncommutative symbolic computations. In particular, we describe the actual solution of $(KZ_3)$ leading to the unique noncommutative series, $\Phi_{KZ}$, so-called Drinfel'd associator (or Drinfel'd series). Non-trivial expressions for series with rational coefficients, satisfying the same properties with $\Phi_{KZ}$, are also explicitly provided due to the algebraic structure and the singularity analysis of the polylogarithms and harmonic sums

Top quark mass definition and top quark pair production near threshold at the NLC

We suggest an infrared-insensitive quark mass, defined by subtracting the soft part of the quark self energy from the pole mass. We demonstrate the deep relation of this definition with the static quark-antiquark potential. At leading order in 1/m this mass coincides with the PS mass which is defined in a completely different manner. Going beyond static limit, the small normalization point introduces recoil corrections which are calculated here as well. Using this mass concept and other concepts for the quark mass we calculate the cross section of e+ e- -> t t-bar near threshold at NNLO accuracy adopting three alternative approaches, namely (1) fixing the pole mass, (2) fixing the PS mass, and (3) fixing the new mass which we call the PS-bar mass. We demonstrate that perturbative predictions for the cross section become much more stable if we use the PS or the PS-bar mass for the calculations. A careful analysis suggests that the top quark mass can be extracted from a threshold scan at NLC with an accuracy of about 100-200 MeV.Comment: published version, 21 pages in LaTeX including 11 PostScript figure

The Threshold t-tbar Cross Section at NNLL Order

The total cross section for top quark pair production close to threshold in e+e- annihilation is investigated. Details are given about the calculation at next-to-next-to-leading logarithmic order. The summation of logarithms leads to a convergent expansion for the normalization of the cross section, and small residual dependence on the subtraction parameter nu. A detailed analysis of the residual nu dependence is carried out. A conservative estimate for the remaining uncertainty in the normalization of the total cross section from QCD effects is $\lesssim \pm 3$. This makes precise extractions of the strong coupling and top width feasible, and further studies of electroweak effects mandatory.Comment: 33 pages, 11 figs, a program to produce the cross section will be available soo

Top Quark Pair Production close to Threshold: Top Mass, Width and Momentum Distribution

The complete NNLO QCD corrections to the total cross section $\sigma(e^+e^- \to Z*,\gamma*\to t\bar t)$ in the kinematic region close to the top-antitop threshold are calculated by solving the corresponding Schroedinger equations exactly in momentum space in a consistent momentum cutoff regularization scheme. The corrections coming from the same NNLO QCD effects to the top quark three-momentum distribution $d\sigma/d |\vec k_t|$ are determined. We discuss the origin of the large NNLO corrections to the peak position and the normalization of the total cross section observed in previous works and propose a new top mass definition, the 1S mass M_1S, which stabilizes the peak in the total cross section. If the influence of beamstrahlung and initial state radiation on the mass determination is small, a theoretical uncertainty on the 1S top mass measurement of 200 MeV from the total cross section at the linear collider seems possible. We discuss how well the 1S mass can be related to the $\bar{MS}$ mass. We propose a consistent way to implement the top quark width at NNLO by including electroweak effects into the NRQCD matching coefficients, which then can become complex.Comment: 53 pages, latex; minor changes, a number of typos correcte