We introduce a new approach for analysis and numerical simulations of asymmetric first-price auctions, which is based on dynamical systems. We apply this approach to asymmetric auctions in which players’ valuations are power-law distributed. We utilize a dynamical-systems formulation to provide a proof of the existence and uniqueness of the equilibrium strategies in the cases of two coalitions ...

A systematic way of extending a general fixed-stepsize multistep formula to a minimum storage variable-stepsize formula has been discovered that encompasses fixed-coefficient (interpolatory), variable-coefficient (variable step), and fixed leading coefficient as special cases. In particular, it is shown that the " interpolatory" stepsize changing technique of Nordsieck leads to a truly variable...

The deformable template method obtains a deformation function that maps a template onto an observed image. The method simulates the deformation function using a penalised least squares method and a Markov Chain Monte Carlo Algorithm. The conventional modelling of the deformation uses a Fourier basis. We propose an approach that expresses the deformation in terms of a wavelet basis, that utilise...

We present a numerical method for solving the indefinite least squares problem. We first normalize the coefficient matrix. Then we compute the hyperbolic QR factorization of the normalized matrix. Finally we compute the solution by solving several triangular systems. We give the first order error analysis to show that the method is backward stable. The method is more efficient than the backward...

Cold rolling of steel is one of the most important metal forming processes so an accurate control of its parameters during the process is necessary. In this paper, the friction coefficient has been proposed as a function of cold rolling parameters such as forward slip, forward and backward tensile stresses ,strip thickness, static deformation, resistance of strip before and after rolling ,strip...

Effective target detection and tracking has always been a research hotspot in the field of radar, multi-target is focus radar at present. In order to effectively deal with issue outlier removal track initiation determination process tracking, this paper proposes an improved backward smoothing method based on label iterative processing. This corrects loophole original method, which can cause est...

<p style='text-indent:20px;'>We develop a backward stochastic differential equation based probabilistic machine learning method, which formulates class of neural networks as optimal control problem. An efficient gradient descent algorithm is introduced with the computed through equation. Convergence analysis for optimization and numerical experiments applications are carried out to valida...