Auxiliary function-based algorithm for blind extraction of a moving speaker

In this paper, we propose a novel algorithm for blind source extraction (BSE) of a moving acoustic source recorded by multiple microphones. The algorithm is based on independent vector extraction (IVE) where the contrast function is optimized using the auxiliary function-based technique and where the recently proposed constant separating vector (CSV) mixing model is assumed. CSV allows for movements of the extracted source within the analyzed batch of recordings. We provide a practical explanation of how the CSV model works when extracting a moving acoustic source. Then, the proposed algorithm is experimentally verified on the task of blind extraction of a moving speaker. The algorithm is compared with state-of-the-art blind methods and with an adaptive BSE algorithm which processes data in a sequential manner. The results confirm that the proposed algorithm can extract the moving speaker better than the BSE methods based on the conventional mixing model and that it achieves improved extraction accuracy than the adaptive method.

Existence of fixed point and best proximity point of p-cyclic orbital phi-contraction map

In this manuscript, p-cyclic orbital ϕ-contraction map over closed, nonempty, convex subsets of a uniformly convex Banach space X possesses a unique best proximity point if the auxiliary function ϕ is strictly increasing. The given result unifies and extend some existing results in the related literature. We provide an illustrative example to indicate the validity of the observed result.

Accelerated Reduced Gradient Algorithm with Constraint Relaxation in Differential Inverse Kinematics

The Moore-Penrose pseudoinverse-based solution of the differential inverse kinematic task of redundant robots corresponds to the result of a particular optimization underconstraints in which the implementation of Lagrange’s ReducedGradient Algorithm can be evaded simply by considering the zero partial derivatives of the ”Auxiliary Function” associated with this problem. This possibility arises because of the fact that the cost term is built up of quadratic functions of the variable of optimization while the constraint term is linear function of the same variables. Any modification in the cost and/or constraint structure makes it necessary the use of the numerical algorithm. Anyway, the penalty effect of the cost terms is always overridden by the hard constraints that makes practical problems in the vicinity of kinematic singularities where the possible solution stillexists but needs huge joint coordinate time-derivatives. While in the special case the pseudoinverse simply can be deformed, inthe more general one more sophisticated constraint relaxation can be applied. In this paper a formerly proposed acceleratedtreatment of the constraint terms is further developed by the introduction of a simple constraint relaxation. Furthermore, thenumerical results of the algorithm are smoothed by a third order tracking strategy to obtain dynamically implementable solution.The improved method’s operation is exemplified by computation results for a 7 degree of freedom open kinematic chain

Asymptotics for Bailey-type mock theta functions

We compute asymptotic estimates for the Fourier coefficients of two mock theta functions, which come from Bailey pairs derived by Lovejoy and Osburn. To do so, we employ the circle method due to Wright and a modified Tauberian theorem. We encounter cancelation in our estimates for one of the mock theta functions due to the auxiliary function $$\theta _{n,p}$$ θ n , p arising from the splitting of Hickerson and Mortenson. We deal with this by using higher-order asymptotic expansions for the Jacobi theta functions.

Boussinesq's Equations for (2+1)-Dimensional Surface Gravity Waves in an Ideal Fluid Model

We study the problem of gravity surface wa\-ves for the ideal fluid model in (2+1)-dimensional case. We apply a systematic procedure for deriving the Boussinesq equations for a prescribed relationship between the orders of four expansion parameters, the amplitude parameter $\alpha$, the long-wavelength parameter $\beta$, the transverse wavelength parameter $\gamma$, and the bottom variation parameter $\delta$. We also take into account surface tension effects when relevant. For all considered cases, the (2+1)-dimensional Boussinesq equations can not be reduced to a single nonlinear wave equation for surface elevation function. On the other hand, they can be reduced to a single, highly nonlinear partial differential equation for an auxiliary function $f(x,y,t)$ which determines the velocity potential but is not directly observed quantity. The solution $f$ of this equation, if known, determines the surface elevation function. We also show that limiting the obtained the Boussinesq equations to (1+1)-dimensions one recovers well-known cases of the KdV, extended KdV, fifth-order KdV, and Gardner equations.PACS 02.30.Jr · 05.45.-a · 47.35.Bb · 47.35.Fg

Algorithm for adaptive correction of the ship's movement along the trajectory in the presence of a sea current

В статье предложен алгоритм адаптивной коррекции движения судна по траектории при наличии морского течения. В основе предлагаемого подхода лежит алгоритм градиента вспомогательных функций. Показаны преимущества предложенного алгоритма адаптивной коррекции движения судна по траектории. Сущность предлагаемого подхода заключается в замене прямолинейного участка маршрута судна, новой виртуальной траекторией и использовании ее во вспомогательной функции и при вычислении соответствующего вектора градиента. Компьютерное моделирование подтвердило эффективность предложенного алгоритма адаптивной коррекции. Адаптивные свойства разработанного алгоритма выражаются в том, что он обеспечивает асимптотически точное движение по участкам запланированной траектории, не используя информации о скорости и направлении морского течения. Предполагается использование предложенного адаптивного алгоритма при разработке систем автоматического управления движением судна по маршруту. The article proposes an algorithm for adaptive correction of the ship's movement along the trajectory in the presence of a sea current. The proposed approach is based on the gradient algorithm of auxiliary functions. The advantages of the proposed algorithm for adaptive correction of the ship's motion along the trajectory are shown. The essence of the proposed approach is to replace the straight-line section of the ship's route with a new virtual trajectory and use it in an auxiliary function and in calculating the corresponding gradient vector. Computer simulation has confirmed the effectiveness of the proposed adaptive correction algorithm. The adaptive properties of the developed algorithm are expressed in the fact that it provides asymptotically accurate movement along sections of the planned trajectory, without using information about the speed and direction of the sea current. It is supposed to use the proposed adaptive algorithm in the development of systems for automatic control of the ship's movement along the route.

Synchronization of chaotic delayed systems via intermittent control and its adaptive strategy

In this paper the problem of synchronization for delayed chaotic systems is considered based on aperiodic intermittent control. First, delayed chaotic systems are proposed via aperiodic adaptive intermittent control. Next, to cut down the control gain, a new generalized intermittent control and its adaptive strategy is introduced. Then, by constructing a piecewise Lyapunov auxiliary function and making use of piecewise analysis technique, some effective and novel criteria are obtained to ensure the global synchronization of delayed chaotic systems by means of the designed control protocols. At the end, two examples with numerical simulations are provided to verify the effectiveness of the theoretical results proposed scheme.