On two variations of identifying codes

Identifying codes have been introduced in 1998 to model fault-detection in multiprocessor systems. In this paper, we introduce two variations of identifying codes: weak codes and light codes. They correspond to fault-detection by successive rounds. We give exact bounds for those two definitions for the family of cycles

Detector dead-time effects and paralyzability in high-speed quantum key distribution

Recent advances in quantum key distribution (QKD) have given rise to systems that operate at transmission periods significantly shorter than the dead times of their component single-photon detectors. As systems continue to increase in transmission rate, security concerns associated with detector dead times can limit the production rate of sifted bits. We present a model of high-speed QKD in this limit that identifies an optimum transmission rate for a system with given link loss and detector response characteristics

On implicational bases of closure systems with unique critical sets

We show that every optimum basis of a finite closure system, in D.Maier's sense, is also right-side optimum, which is a parameter of a minimum CNF representation of a Horn Boolean function. New parameters for the size of the binary part are also established. We introduce a K-basis of a general closure system, which is a refinement of the canonical basis of Duquenne and Guigues, and discuss a polynomial algorithm to obtain it. We study closure systems with the unique criticals and some of its subclasses, where the K-basis is unique. A further refinement in the form of the E-basis is possible for closure systems without D-cycles. There is a polynomial algorithm to recognize the D-relation from a K-basis. Thus, closure systems without D-cycles can be effectively recognized. While E-basis achieves an optimum in one of its parts, the optimization of the others is an NP-complete problem.Comment: Presented on International Symposium of Artificial Intelligence and Mathematics (ISAIM-2012), Ft. Lauderdale, FL, USA Results are included into plenary talk on conference Universal Algebra and Lattice Theory, June 2012, Szeged, Hungary 29 pages and 2 figure

Optimal placement of a limited number of observations for period searches

Robotic telescopes present the opportunity for the sparse temporal placement of observations when period searching. We address the best way to place a limited number of observations to cover the dynamic range of frequencies required by an observer. We show that an observation distribution geometrically spaced in time can minimise aliasing effects arising from sparse sampling, substantially improving signal detection quality. The base of the geometric series is however a critical factor in the overall success of this strategy. Further, we show that for such an optimal distribution observations may be reordered, as long as the distribution of spacings is preserved, with almost no loss of quality. This implies that optimal observing strategies can retain significant flexibility in the face of scheduling constraints, by providing scope for on-the-fly adaptation. Finally, we present optimal geometric samplings for a wide range of common observing scenarios, with an emphasis on practical application by the observer at the telescope. Such a sampling represents the best practical empirical solution to the undersampling problem that we are aware of. The technique has applications to robotic telescope and satellite observing strategies, where target acquisition overheads mean that a greater total target exposure time (and hence signal-to-noise) can often in practice be achieved by limiting the number of observations.Comment: 8 pages with 16 figure

Management of the technical training process of athletes in cycling sports

In cyclic sports, the main indicator that characterizes adversarial activity is the average speed of passing distances. The presence of functional dependencies of speed factors on various indicators of sports activity can determine its dynamics. It allows to simulate the process of competitive activity, and according to the dynamics of speed, to determine the nature of a particular indicator. Cyclists and swimmers defined law of motion, the dependence of the athlete's instantaneous speed and its acceleration ontime, applied forces, resistance forces and forces of inertia, as well as on specific physical and morphological data. The presence of a mathematical model allows us to create an adaptive system for controlling the technical preparedness of athletes in cyclic sports

Financial Impact of Fines in the Unbound Pavement Layers

INE/AUTC 14.1