Reducing Resource Usage Based on User Hints and Policies

Multimedia applications often have performance requirements that make these applications computing resource intense; e.g., the number of video frames displayed to the user must be about 25 frames per second. A user hint is an indication of the interest that a user has in an application. Examples of user hints include a screen saver being invoked or covering a window with another window. In the case that the user is running video, the occurrence of these hints imply that the user is no longer viewing the video. However, the resource usage of the application has not changed. This paper describes an architecture that make use of user hints to reduce the resource consumption of an application. The emphasis is on network traffic and CPU usage. Experimental results are presented.

Nexus VII: Relationships Between Architecture and Mathematics

Sylvie Duvernoy reports on the seventh international, interdisciplinary Nexus conference for architecture and mathematics. Point Loma Nazarene University, San Diego, USA 23-25 June 2008     

Optimization of boundary control at one end of a string in the presence of a model nonlocal condition

The paper is devoted to problems of optimal boundary control of string vibrations under nonlocal conditions that relate values of string displacement or its derivative at the boundary point with their values at the interior point. The solutions for all problems of boundary control are obtained in explicit analytic form.     

Two classes of extreme motion trajectories of a point with varying specific impulse

The variational problem to determine the optimal trajectories of the center of mass of a spacecraft moving in the central Newtonian field with limited power and specific momentum was considered. The extremal trajectory was shown to contain elements of zero, intermediate, and maximal power with a constant or variable specific momentum. For the circular and spiral trajectories, extremal analytical solutions were established. These elements can find use in the problems of departure and transfer to the parking orbit, as well as in the problems of orbital transfers. The problem of transfer to the given elliptical orbit was considered as an example.     

About a class of systems preserving the stability property at negative feedbacks

For linear and nonlinear systems are obtained tests for conserving the property of asymptotic stability at switching arbitrary coordinatewise negative feedbacks.     

Two strong equilibria for game problems

The paper presents two new definitions of equilibrium for arbitrary game problems. The new definitions allow finding a unique solution for a significantly wider class of problems.     

Mathematical Interpretation of a Thirteen Hundred Year Old Stone Masonry Observatory

The present paper discusses various implications suggested by a thirteen hundred year old stone masonry structure, built by Queen Sun-Duk of the Silla Dynasty, regarding astronomy, religion, symbol, mathematics in architectural form and construction. The name of the 9.1 m tall stone tower, Chum-Sung-Dae, implies its use as celestial observatory and it is claimed to be the oldest one existing in Asia. Although there have been some disagreements about its function as an observatory, this claim is generally accepted in the absence of any evidence to the contrary. No matter what the original function was, Chum-Sung-Dae has been unanimously acknowledged as the product of then state-of-the-art technology. What makes Chum-Sung-Dae so unique and particular among coeval buildings in stone masonry is in its elegant, multiple curvatures. Furthermore, the geometry of Chum-Sung-Dae is reported to embody a notable numerical significance. The absence of mortar between stone layers and sides indicates that the load transfer mechanism of the tower is dependent upon the frictional resistance due to gravity. All these features will be discussed, with an emphasis on the mathematical analysis and interpretation.     

Control of motion of the autonomous underwater vehicle at trajectory survey of the oceanic physical fields

Consideration was given to the control of motion of the autonomous underwater vehicle performing automatic measurements and mapping of the oceanic physical fields. In the general case, it is required to set up a control maintaining motion along the field isolines relying on the trajectory measurements of the level and field gradient components and identification and contouring of the anomalies by the characteristic points and generalized reference points. A practical example based on the experience of bathymetrical and hydrophysical measurements in the Arctic region using an autonomous underwater vehicle was discussed.     

A stochastic estimation problem at aeromagnetometer deviation compensation

A formulation of the problem of magnitometer deviation compensation occurring at aeromagnetic survey is considered in the form of a standard stochastic estimation problem. A specific feature of this approach is the introduction of the model of a geomagnetic field anomaly. The parameters of the stochastic model are selected basing on spectral and variance analysis of the aeromagnetic survey data. Normalization of the problem parameters is made; this makes it possible to estimate the accuracy of compensation and conduct a necessary decomposition. The posed stochastic estimation problem is solved by the method of Kalman filtering.     

Control of the hop height of a one-legged resonance robot

Vertical motions of a resonance leg specially developed for running and hopping robots are considered. The nonstandard drive used that has dual properties and a variable transfer ratio makes it possible to reduce significantly energy expenses. The solution to the problem of control of the hop height for this leg includes the analysis of a physical model and the analytical solutions for the control optimal in time and optimal in energy. The data of experimental investigations are pointed up, which confirm the efficiency of suggested controllers and show the effectiveness of the developed resonance leg.     

Stabilization of oscillations from a monoparametric family of the autonomous system

The problem of oscillation stabilization is solved for the autonomous system in the case when the oscillations form a monoparametric family. For each possible point type of the family the explicit formulae that solve the problem are obtained. It follows from those formulae that the dissipation is a necessary condition of the stabilization. The obtained sufficient conditions of the stabilizations coinside with the appropriate necessary conditions to within the sign of unstrict inequality.     

Construction of invariant ellipsoids in the stabilization problem for a wheeled robot following a curvilinear path

The synthesis control problem for the plane motion of a wheeled robot is studied. The goal of the control is to bring the robot to an assigned curvilinear trajectory and to stabilize its motion along it in the presence of phase and control constraints. For a synthesized control law, invariant ellipsoids—quadratic approximations of the attraction domains of the target trajectory—are constructed, which allow one to check in the course of the robot motion whether the control law can stabilize motion along the current trajectory segment. To take into account constraints on the control, methods of absolute stability theory are applied. The construction of the invariant ellipsoids reduces to solving a system of linear matrix inequalities.     

Studying the stability boundaries of the gyro-stabilized satellite on a circular orbit

Consideration was given to all parts of the stability boundaries of stationary motion of the gyro-stabilized manyaxis satellite. For each of the necessary stability conditions, conversion to zero or equality was analyzed using the second Lyapunov method. Terms of orders higher than two were used to check sign-definiteness of the Lyapunov function on the stability boundaries. Using the terms up to the sixth order, analysis established asymptotic stability on some parts of the boundaries. Terms of the order at most four enabled us to prove instability on other parts of the boundary.     

Operating ratio of the technical systems,subjected to failures

The original way of definition of operating ratio in view of reliability of the equipment of the control, time of the control over periodic checks and time of restoration is offered. The received results allow to define the best value of operating ratio of system both in view of, and without taking into account operational expenses.     

Organization of self-diagnosis of the discrete multicomponent systems a structure like bipartite quasicomplete graphs

Organization of an efficient self-diagnosis of the multicomponent computer and communication systems of diverse structures always attracted attention of the researchers and engineers. A method to solve these problems is presented in the paper by way of the example of a system whose structure is modeled by a uniform ordinary bipartite graph of diameter d = 3, any degree s > 1, and any number n of vertices, where n = s(s ? 1) + 1. The method requires checking of (s ? 1)³ graph loops of length eight each, which is smaller than the number s ²(s ? 1) + s of checks of single graph edges.     

A note on application of the method of supplementary variables to the analysis of a processor sharing system

We present a new proof of Theorem of 1989 about non-stationary (transient) distribution of the number of jobs in the M/G/1 queue with egalitarian processor sharing. To get this goal, we use the well-known method of supplementary variables. The complete proof of that non-trivial Theorem of 1989 (see Theorem 2.1) was first given in the author’s monograph [12, §2.8] (1989) by means of essentially novel analytic method. Before appearing author’s work, this problem had been considered from analytic viewpoint as insoluble one. In essence, Theorem 2.2 almost repeats Theorem 2.1, but with other proof. In Section 3, Theorem 2.2 is extended to the case of an M/G/1-EPS queue with catastrophes which appear according to a Poisson process.     

Organization of the remote access to tomographic data through a slow communications link

Consideration is given to the problem of organization of the remote access to tomographic data obtained as a result of the investigation on the computerized tomograph through a slow communications link. The proposed access strategy together with the developed and realized method of tomographic data compression makes it possible to help users (physicians, scientists, and etc.) work with remote tomographic data, e.g., using the Internet. This, in its turn, opens up vast possibilities for using the data of tomographic investigations for conducting medical consultations “at a distance,” videoconferences, organizing network seminars for medical staff training, and etc.