Number Of Possible Signals Research Articles

Transmission of the maximum number of signals through a multiconductor transmission line without crosstalk or return loss: theory and simulation

Multiconductor communication is widely used in electronic applications for fast data transfer between different devices. The most common multiconductor transmission media are Cat 6 Ethernet cables, flat cables, and backplanes. In all applications, the data is transferred differentially between pairs of conductors, so that roughly the number of transmitted signals is half the number of conductors. Physically, between N + 1 conductors it is possible to transmit N signals and the reason for not doing so is the huge crosstalk and return loss that would arise when transmitting so many signals. The current work suggests an algorithm for transmitting the maximum number of possible signals without crosstalk or return loss.

Chemical constraints on the evolution of olfactory communication channels of moths

It is estimated there are over 100,000 moth species (Lepidoptera) that produce sex pheromones comprising communication channels used in specific-mate-recognition systems (SMRS) involved in pre-zygotic mating isolation and speciation. About 1572 moth species have been found to use 377 pheromone components, the majority being alcohols, aldehydes or acetate esters of olefinic chains of 10–22 carbons. Since there are limited numbers of possible unsaturated (double bonded) E- and Z-configured isomers of these chains, there may be constraints on incipient species evolving new pheromone components, especially if they are utilized by existing species. Here I develop algorithms that count and name all possible structures of chains with or without a functional group. The results show that for acetate esters there are only seven or nine monounsaturated isomers of six or seven carbon chains, respectively, suggesting use of these compounds could limit the number of communication channels available for radiation of new species (no moths use these short chains). For commonly used 14-carbon chains with an acetate ester functional group, and 1–3 unsaturations, there are 1039 isomers. A total of 2,096,883 isomers were counted from all multiply unsaturated 10–22-carbon chain acetate esters. The number of possible signals quickly extends into millions when considering pheromone blends of 2–4 components used by most species. There should be little chemical constraint on evolution of new communication channels based on compounds of 10 or more carbons, even for closely related species (e.g. ermine moths, Yponomeuta).

Dissecting JNK signaling, one KKKinase at a time

Specificity in signal transduction is essential to ensure distinct and appropriate cellular responses to extracellular cues. Determining the mechanisms that mediate specificity is key to understanding complex cell behaviors in development, when multiple pathways fire simultaneously and individual pathways are used recurrently. Jun kinase (JNK) signal transduction exemplifies a pathway that is used multiple times in animal development and homeostasis. Indeed, molecular genetic analysis of JNK signaling in Drosophila has shown that a core signaling module consisting of Hep (JNKK), Bsk (JNK), and Jun regulates various processes, including tissue morphogenesis, wound repair, stress response, innate immune response, and others. Six putative JNKK kinase (JNKKK) family members are present in the fly genome, which could activate the core module in response to distinct stimuli. The diversity of kinases at this level of the signaling hierarchy could substantially increase the number of possible signals that feed into activation of the core module. Recent studies have described the distinct phenotypic consequences of mutations in three of the genes, Slpr (dMLK), Tak1, and Mekk1. These data, together with Drosophila cell culture and genomic array analyses support the contention that the choice of JNKKK may contribute to signaling specificity in vivo. Whether this is achieved by individual JNKKKs or by means of a combinatorial mechanism will require a systematic characterization of compound mutants and a toolbox of transcriptional reporters specific for distinct JNK-dependent processes.

Commonp-Belief: The General Case

We develop belief operators for information systems where individuals have an uncountable number of possible signals, and we give a general version of Monderer and Samet's (1989) theorem relating “iterative” and “fixed point” notions of commonp-belief.Journal of Economic LiteratureClassification Numbers: D82.

Robust multiple classification of known signals in additive noise-an asymptotic weak signal approach

The problem of extracting one out of a finite number of possible signals of known form given observations in an additive noise model is considered. Two approaches are studied: either the signal with shortest distance to the observed data or the signal having maximal correlation with some transformation of the observed data is chosen. With a weak signal approach, the limiting error probability is a monotone function of the Pitman efficacy and it is the same for both the distance-based and correlation-based detectors. Using the minimax theory of Huber, it is possible to derive robust choices of distance/correlation when the limiting error probability is used as performance criterion. This generalizes previous work in the area, from two signals to an arbitrary number of signals. Considered are M-type and R-type distances and also one-dimensional and two-dimensional signals. Some Monte Carlo simulations are performed to compare the finite sample size error probabilities with the asymptotic error probabilities.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Hypotheses Testing in a Distributed Environment

The problem of optimum detection with n decentralized sensors selecting among m possible signals is considered from the decision theory point of view. The loss function is defined in terms of the decisions made by each observer and the transmitted signal. Then the average of this loss function is minimized. This leads to sets of coupled inequalities in terms of the likelihood ratio of each observer and the decisions made at the other sensors. This determines the structure of the optimum decentralized detection for an arbitrary number of sensors and an arbitrary number of possible signals. These results are valuable in numerous situations that may arise in large-scale and distributed systems.

Sequential detection versus conventional detection: A comparative study

M-ary sequential detection algorithms are discussed in terms of the advantage measure A, the number of possible signals M, and the signal-to-noise ratio SNR. The advantage measure A is defined as the logarithm of the ratio of the error probability of the optimum conventional detector to that of the optimum sequential detector with the same values of M and SNR. It increases as the SNR increases but decreases when M increases. For M → ∞, the advantage measure A diminishes to zero, so that application of the sequential approach is useless for large values of M. Thus, the sequential approach is most useful for binary detection with high signal-to-noise ratios. These results are demonstrated for detection of equiprobable orthogonal signals received in white Gaussian noise.

Role of collision anisotropy in two-photon processes in a magnetic field. Phenomenological analysis

It is shown that the nonlinear susceptibility tensor of an isotropic medium is axially symmetric because of the anisotropy of collisions characterized by a symmetry axis along the field wave vectors. In the collinear geometry a two-photon process is described by six functions of the frequencies and wave vectors of the fields, whereas in the case of a mirror-symmetric medium it is described by three such functions. A new difference method is proposed for separating just the collision anisotropy contribution to the signal of a two-photon process in a magnetic field. The method makes it possible to obtain several types of difference signal. In a probe field variant the number of possible signals is four and eight for mirror-symmetric and mirror-asymmetric media, respectively. In a variant involving observation of fluorescence at right-angles to the magnetic field and also parallel to the direction of propagation of the exciting light, the number of possible difference signals is eight and sixteen for mirror-symmetric and mirror-asymmetric media, respectively, whereas in the case of observations along a magnetic field there is only one type of signal. An analysis is made of the parity of the difference resonances relative to reversal of the magnetic field direction.

Performance of M-ary feedback communication systems

An M-ary decision feedback communication system with the MAP strategy is investigated. The performance of this system is analytically evaluated as follows. First, an approximate lower performance bound is found by means of the Cauchy inequality. Then an approximate lower performance bound is found by means of the Jensen inequality. Finally, the bounds are compared and found to coincide, yielding an approximate estimate of the system performance. The same estimate may also be obtained by means of mean path approximation. Thus, the mean path approximation tends to underestimate the system average transmission time. For verification purposes, the results are compared with those obtained from computer simulation and are found to be in good agreement. Furthermore, the feedback transmission is compared with one-way transmission. It is shown that feedback systems are better than one-way systems in terms of the signal/noise ratio required to achieve a prescribed error probability. The estimated power advantage of feedback systems is between 5.4 dB and 3 dB, depending on the number of possible signals M; the power advantage decreases as M increases. The results obtained for M→ ∞ imply that the feedback increases the capacity of an infinite-bandwidth Gaussian channel. However, the last result was not proved with the degree of rigour required in mathematics; rather, we have used approximate performance bounds and computer simulation data in our analysis.

More on the Detection of One of M Orthogonal Signals

Receiver operating characteristics (ROC's) for the classic problem of detecting the presence or absence of one of M orthogonal signals is presented. Previous results were valid for low detectability, for which the ROC is approximately normal (i.e., appears as a straight line with unit slope on normal normal probability paper) and the detectability depends on the logarithm of the number of possible signals M. For high detectability, however, the ROC departs from normality. In addition, the rate at which detectability decreases as M increases is more rapid than that predicted by the classical approximation.

Effects of independent variations in stimulus and response probability.

THE time taken by human beings to react to one of a number of possible signals increases with the number of alternatives involved. The effects of jointly varying stimulus and response uncertainty have been long known and adequately discussed1,2. In the present investigation these were varied independently, by using situations where the same response was required for a number of stimuli. The number of responses, and the ratio of response/stimuli were varied.