NashAE: Disentangling Representations through Adversarial Covariance Minimization
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Here, we show that in SO(10) models, a Yukawa sector consisting of a real 10H, a real 120 H and a complex 126 H of Higgs fields can provide a realistic fit to all fermion masses and mixings, including the neutrino sector. Although the group theory of SO(10) demands that the 10 H and 120 H be real, most constructions complexify these fields and impose symmetries exterior to SO(10) to achieve predictivity. The proposed new framework with real 10H and real 120 H relies only on SO(10) gauge symmetry, and yet has a limited number of Yukawa parameters. Our analysis shows that while there are restrictions on the observables, a good fit to the entire fermion spectrum can be realized. Unification of gauge couplings is achieved with an intermediate scale Pati-Salam gauge symmetry. Proton decay branching ratios are calculable, with the leading decay modes being p→ $\bar{v}$π + and p→ e + π 0 .
We study dynamics of two-dimensional N = (0, 1) supersymmetric gauge theories. In particular, we propose that there is an infrared triality between certain triples of theories with orthogonal and symplectic gauge groups. The proposal is supported by matching of anomalies and elliptic genera. This triality can be viewed as a (0, 1) counterpart of the (0, 2) triality proposed earlier by two of the authors and A. Gadde. We also describe the relation between global anomalies in gauge theoretic and sigma-model descriptions, filling in a gap in the present literature.
We study four-derivative corrections to pure N = 2, D = 5 gauged supergravity. In particular, we find that, up to field redefinitions, there is a single four-derivative superinvariant that one can add to the action, up to factors of the two-derivative action. Consequently, this selects out a unique set of coefficients for the four-derivative corrections. We confirm these coefficients (in the ungauged limit) on the BMPV solution.
We consider composite Higgs models where the Higgs is a pseudo-Nambu Goldstone boson arising from the spontaneous breaking of an approximate global symmetry by some underlying strong dynamics. We focus on the SO(5) → SO(4) symmetry breaking pattern, assuming the “partial compositeness” paradigm. We study the consequences on Higgs physics of the fermionic representations produced by the strong dynamics, that mix with the Standard Model (SM) degrees of freedom. We consider models based on the lowest-dimensional representations of SO(5) that allow for the custodial protection of the Z b ¯ b coupling, i.e. the 5, 10 and 14. We find a generic suppression of the gluon fusion process, while the Higgs branching fractions can be enhanced or suppressed compared to the SM. Interestingly, a precise measurement of the Higgs boson couplings can distinguish between different realizations in the fermionic sector, thus providing crucial information about the nature of the UV dynamics.
Time optimal control problems for systems with impulsive controls are investigated. Sufficient conditions for the existence of time optimal controls are given. A dynamical programming principle is derived and Lipschitz continuity of an appropriately defined value functional is established. The value functional satisfies a Hamilton–Jacobi–Bellman equation in the viscosity sense. A numerical example for a rider-swing system is presented and it is shown that the reachable set is enlargered by allowing for impulsive controls, when compared to nonimpulsive controls.
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The spleen is a rare site of abdominal ectopic pregnancy. In a review of the literature, we found 16 published cases of primary splenic pregnancies. Of the cases identified, all received surgical intervention, with one case successfully treated with laparoscopic methotrexate injection, and the rest underwent splenectomy. We would like to present a case of primary splenic pregnancy in a 35-year-old woman successfully treated with percutaneous image-guided injection of methotrexate and KCl.
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In this paper, we develop an algorithm to efficiently solve risk-averse optimization problems posed in reflexive Banach space. Such problems often arise in many practical applications as, e.g., optimization problems constrained by partial differential equations with uncertain inputs. Unfortunately, for many popular risk models including the coherent risk measures, the resulting risk-averse objective function is nonsmooth. Here, this lack of differentiability complicates the numerical approximation of the objective function as well as the numerical solution of the optimization problem. To address these challenges, we propose a primal–dual algorithm for solving large-scale nonsmooth risk-averse optimization problems. This algorithm is motivated by the classical method of multipliers and by epigraphical regularization of risk measures. As a result, the algorithm solves a sequence of smooth optimization problems using derivative-based methods. We prove convergence of the algorithm even when the subproblems are solved inexactly and conclude with numerical examples demonstrating the efficiency of our method.
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X-ray inspection of ball grid arrays (BGAs) is typically performed at one or more viewing angles to examine adhesion sites for errors such as voids, joint cracking, or head-in-pillow. During this inspection process, the cir cuit board assembly is subject to ionizing radiation exposure, which can cause trapped charge within oxide layers of semiconductor devices. Some x-ray machines allow for programmable inspection routines, which could be used to optimize radiation exposure to semiconductor components. Using Monte Carlo methods, x-ray inspection of a BGA was simulated to determine a range of acceptable viewing angles. Dose rates to circuit board components were estimated at each inspection angle to determine the view resulting in optimized radiation exposure. Results showed that for each BGA, the maximum unobstructed viewing times without exceeding a 5 Gy dose limit to a single part ranged from 82 to 94 minutes. Using a radiation cost function method, optimized viewing across all components was found. Here, it was observed that for a consistent dose limit applied to silicon-based components, performing inspection with BGAs facing the x-ray source was optimal. A third method was applied, assigning individual dose limits based on empirical data from the NASA Goddard Space Flight Center radiation database. This method showed that optimized viewing maximizes the distance between the radiation source and highly sensitive components. It was also observed that cumulative effects from viewing two BGAs will influence viewing angles, causing the optimal view of one BGA to exist nearly 180° from the other.
For any nonsplit p > 2-extension of finite groups with a cyclic kernel and a quotient group with two generators all the accompanying extensions of which split, there exists a realization of the quotient group as a Galois group of number fields such that the corresponding embedding problem is ultrasolvable (i.e., this embedding problem is solvable and has only fields as solutions).
In modern steelmaking, the decarburization of hot metal is converted into steel primarily in converter processes, such as the basic oxygen furnace. The objective of this work was to develop a new mathematical model for top blown steel converter, which accounts for the complex reaction equilibria in the impact zone, also known as the hot spot, as well as the associated mass and heat transport. An in-house computer code of the model has been developed in Matlab. The main assumption of the model is that all reactions take place in a specified reaction zone. The mass transfer between the reaction volume, bulk slag, and metal determine the reaction rates for the species. The thermodynamic equilibrium is calculated using the partitioning of Gibbs energy (PGE) method. The activity model for the liquid metal is the unified interaction parameter model and for the liquid slag the modified quasichemical model (MQM). The MQM was validated by calculating iso-activity lines for the liquid slag components. The PGE method together with the MQM was validated by calculating liquidus lines for solid components. The results were compared with measurements from literature. The full chemical reaction model was validated by comparing the metal and slag compositions to measurements from industrial scale converter. The predictions were found to be in good agreement with the measured values. Furthermore, the accuracy of the model was found to compare favorably with the models proposed in the literature. The real-time capability of the proposed model was confirmed in test calculations.