A Maximal Correlation Framework for Fair Machine Learning

As machine learning algorithms grow in popularity and diversify to many industries, ethical and legal concerns regarding their fairness have become increasingly relevant. We explore the problem of algorithmic fairness, taking an information–theoretic view. The maximal correlation framework is introduced for expressing fairness constraints and is shown to be capable of being used to derive regularizers that enforce independence and separation-based fairness criteria, which admit optimization algorithms for both discrete and continuous variables that are more computationally efficient than existing algorithms. We show that these algorithms provide smooth performance–fairness tradeoff curves and perform competitively with state-of-the-art methods on both discrete datasets (COMPAS, Adult) and continuous datasets (Communities and Crimes).     

Safety margin criterion of nonlinear unbalance elastic axle system

IntroductionAtpresentanewanddevelopingsubject—chaoticdynamicsstartsabroadprospectforanalysisofnonlinearsystem[1～ 5 ].Largerotatingmachineryisatypicalnonlinearnon_autonomoussystem .Thesaferunofrotorsystemisofgreatsignificancetosociallifeandeconomicdevelopment.Thestabilityisthekeytosafeoperation .Thesafestabilityanalysisandcontrolforlargesystemisnotonlyamajorbasicresearchbutalsoisveryimportanttosolvethesafeproblemsinlifeandproduction[6 ,7].Soar,althoughmanymathematicians,mechanistsandengineer…     

Two-parameter failure criterion for elastoplastic bodies with mode I cracks

The generalized Dugdale crack model is used to formulate two-parameter failure criteria for the cases of quasibrittle state and developed plastic zones at a mode I crack tip. The failure criteria relate the fracture strength characteristics and the stress mode at the crack tip through the plastic constraint factor. The critical state of bodies with cracks under uni-and biaxial loading is analyzed in the cases of plane stress and plane strain using the Tresca and von Mises yield criteria. A small-scale yield criterion, which is an analytic relation between the critical stress intensity factor and T-stresses, is established __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 7, pp. 47–57, July 2007.     

Adiabatic dynamics of one-dimensional classical Hamiltonian dissipative systems

A linearized plane pendulum with the slowly varying mass and length of string and the suspension point moving at a slowly varying speed is presented as an example of a simple 1D mechanical system described by the generalized harmonic oscillator equation, which is a basic model in discussion of the adiabatic dynamics and geometric phase. The expression for the pendulum geometric phase is obtained by three different methods. The pendulum is shown to be canonically equivalent to the damped harmonic oscillator. This supports the mathematical conclusion, not widely accepted in physical community, of no difference between the dissipative and Hamiltonian 1D systems.     

Improving weighted information criterion by using optimization

Although artificial neural networks (ANN) have been widely used in forecasting time series, the determination of the best model is still a problem that has been studied a lot. Various approaches available in the literature have been proposed in order to select the best model for forecasting in ANN in recent years. One of these approaches is to use a model selection strategy based on the weighted information criterion (WIC). WIC is calculated by summing weighted different selection criteria which measure the forecasting accuracy of an ANN model in different ways. In the calculation of WIC, the weights of different selection criteria are determined heuristically. In this study, these weights are calculated by using optimization in order to obtain a more consistent criterion. Four real time series are analyzed in order to show the efficiency of the improved WIC. When the weights are determined based on the optimization, it is obviously seen that the improved WIC produces better results.     

LMI Approach to Robust Delay-Dependent Mixed H 2/H ∞ Controller of Uncertain Neutral Systems with Discrete and Distributed Time-Varying Delays

The design of a robust mixed H ₂/H _∞ controller for a class of uncertain neutral systems with discrete, distributed, and input time-varying delays is considered. More precisely, the proposed robust mixed H ₂/H _∞ controller minimizes an upper bound of the H ₂ performance measure, while guaranteeing an H _∞ norm bound constraint. Based on the Lyapunov-Krasovskii functional theory, a delay-dependent criterion is derived for the existence of a desired mixed H ₂/H _∞ controller, which can be constructed easily via feasible linear matrix inequalities (LMIs). Furthermore, a convex optimization problem satisfying some LMI constraints is formulated to obtain a suboptimal robust mixed H ₂/H _∞ controller achieving the minimization of an upper bound of the closed-loop H ₂ performance measure. Finally, a numerical example is illustrated to show the usefulness of the obtained design method.The research reported here was supported by the National Science Council of Taiwan, ROC under Grant NSC 94-2213-E-507-002.     

New construction of special Lagrangian submanifolds in T^＊R^n equipped with the standard metric

A class of twisted special Lagrangian submanifolds in T~*R~n and a kind of austere submanifold from conormal bundle of minimal surface of R~3 are constructed.     

Non-commutative Chiral QCD2 Model

The effective action of chiral QCD₂ was studied in two-dimensional non-commutative space-time by using path integral approach. It is shown that vector boson has a mass generation and the effective Lagrangian contains a term corresponding to a Wess-Zumino-Witten-like term.