On a Lower Bound for the Redundancy of Reliable Networks with Noisy Gates

A proof is provided that a logarithmic redundancy factor is necessary for the reliable computation of the parity function by means of a network with noisy gates. This result was first stated by R.L. Dobrushin and S.I. Ortyukov (1977). However, the authors believe that the analysis given by Dobrushin and Ortyukov is not entirely correct. The authors establish the result by following the same steps and by replacing the questionable part of their analysis with entirely new arguments

Computational paradigm for dynamic logic-gates in neuronal activity

In 1943 McCulloch and Pitts suggested that the brain is composed of reliable logic-gates similar to the logic at the core of today's computers. This framework had a limited impact on neuroscience, since neurons exhibit far richer dynamics. Here we propose a new experimentally corroborated paradigm in which the truth tables of the brain's logic-gates are time dependent, i.e. dynamic logicgates (DLGs). The truth tables of the DLGs depend on the history of their activity and the stimulation frequencies of their input neurons. Our experimental results are based on a procedure where conditioned stimulations were enforced on circuits of neurons embedded within a large-scale network of cortical cells in-vitro. We demonstrate that the underlying biological mechanism is the unavoidable increase of neuronal response latencies to ongoing stimulations, which imposes a nonuniform gradual stretching of network delays. The limited experimental results are confirmed and extended by simulations and theoretical arguments based on identical neurons with a fixed increase of the neuronal response latency per evoked spike. We anticipate our results to lead to better understanding of the suitability of this computational paradigm to account for the brain's functionalities and will require the development of new systematic mathematical methods beyond the methods developed for traditional Boolean algebra.Comment: 32 pages, 14 figures, 1 tabl

Defect tolerance: fundamental limits and examples

This paper addresses the problem of adding redundancy to a collection of physical objects so that the overall system is more robust to failures. In contrast to its information counterpart, which can exploit parity to protect multiple information symbols from a single erasure, physical redundancy can only be realized through duplication and substitution of objects. We propose a bipartite graph model for designing defect-tolerant systems, in which the defective objects are replaced by the judiciously connected redundant objects. The fundamental limits of this model are characterized under various asymptotic settings and both asymptotic and finite-size systems that approach these limits are constructed. Among other results, we show that the simple modular redundancy is in general suboptimal. As we develop, this combinatorial problem of defect tolerant system design has a natural interpretation as one of graph coloring, and the analysis is significantly different from that traditionally used in information redundancy for error-control codes.©201

Efficient fault-tolerant routing in multihop optical WDM networks

This paper addresses the problem of efficient routing in unreliable multihop optical networks supported by Wavelength Division Multiplexing (WDM). We first define a new cost model for routing in (optical) WDM networks that is more general than the existing models. Our model takes into consideration not only the cost of wavelength access and conversion but also the delay for queuing signals arriving at different input channels that share the same output channel at the same node. We then propose a set of efficient algorithms in a reliable WDM network on the new cost model for each of the three most important communication patterns - multiple point-to-point routing, multicast, and multiple multicast. Finally, we show how to obtain a set of efficient algorithms in an unreliable WDM network with up to f faulty optical channels and wavelength conversion gates. Our strategy is to first enhance the physical paths constructed by the algorithms for reliable networks to ensure success of fault-tolerant routing, and then to route among the enhanced paths to establish a set of fault-free physical routes to complete the corresponding routing request for each of the communication patterns.published_or_final_versio

Complexity, action, and black holes

Our earlier paper "Complexity Equals Action" conjectured that the quantum computational complexity of a holographic state is given by the classical action of a region in the bulk (the "Wheeler-DeWitt" patch). We provide calculations for the results quoted in that paper, explain how it fits into a broader (tensor) network of ideas, and elaborate on the hypothesis that black holes are the fastest computers in nature.Comment: 55+14 pages, many figures. v2: (so many) typos fixed, references adde

Applications of minimal path set and dual fault tree approach for piecewise reliability evaluation of large-scale electrical power systems.

Reliability assessment techniques and programs handling is an important issue for both power systems planning and testing in existing power system configurations. The Assessment techniques are suitable for detecting weak points in the reliability assessment. The reliability study of bulk power systems indicates the ability of the composite generation and transmission system to satisfy the load demand at major load points. The major burden of the developed methods used is the computation time required to solve a large number of credible contingencies or outage states. This paper presents a novel approach capable of the reliability evaluation for real large-size networks using normal size computers. It calculates the reliability indices at individual load buses and reliability of the whole system. The effect of the loading factor between loads on reliability is also investigated. The proposed approach is expanded to calculate the reliability of composite generation and transmission system taking the following constraints into consideration: amount of reliability of system generation, amount of reliability of transmission lines, maximum system generation capacity, maximum transmission lines capacity and maximum connected load at each bus. The approach is based on the minimal path set and dual fault tree techniques. A new concept of "constant reliability region", which is utilized in the field of optimum operation of power networks, is introduced. A special program is developed for the proposed technique. The comparison between the proposed and the previous techniques confirms that the proposed method is more accurate and precise

Protein logic: a statistical mechanical study of signal integration at the single-molecule level

Information processing and decision making is based upon logic operations, which in cellular networks has been well characterized at the level of transcription. In recent years however, both experimentalists and theorists have begun to appreciate that cellular decision making can also be performed at the level of a single protein, giving rise to the notion of protein logic. Here we systematically explore protein logic using a well known statistical mechanical model. As an example system, we focus on receptors which bind either one or two ligands, and their associated dimers. Notably, we find that a single heterodimer can realize any of the 16 possible logic gates, including the XOR gate, by variation of biochemical parameters. We then introduce the novel idea that a set of receptors with fixed parameters can encode functionally unique logic gates simply by forming different dimeric combinations. An exhaustive search reveals that the simplest set of receptors (two single-ligand receptors and one double-ligand receptor) can realize several different groups of three unique gates, a result for which the parametric analysis of single receptors and dimers provides a clear interpretation. Both results underscore the surprising functional freedom readily available to cells at the single-protein level.Comment: 19 pages, 4 figures and 9 pages S

About the reliability of logic circuits in all complete bases with three-input elements and failures of zero type on their outputs

Рассматривается реализация булевых функций схемами из ненадёжных функциональных элементов в полном базисе, содержащем функции трёх переменных. Предполагается, что элементы схемы переходят в неисправные состояния независимо друг от друга, подвержены однотипным константным неисправностям типа 0 на выходах. Для каждого полного базиса найдено либо точное значение коэффициента ненадёжности, либо его верхняя оценка