The number of edges on generalizations of Paley graphs

Evans, Pulham, and Sheenan computed the number of complete 4-subgraphs of Paley graphs by counting the number of edges of the subgraph containing only those nodes x for which x and x−1 are quadratic residues. Here we obtain formulae for the number of edges of generalizations of these subgraphs using Gaussian hypergeometric series and elliptic curves. Such formulae are simple in several infinite families, including those studied by Evans, Pulham, and Sheenan

The Expected Variation of Random Bounded Integer Sequences of Finite Length

From the enumerative generating function of an abstract adjacency statistic, we deduce the mean and variance of the variation on random permutations, rearrangements, compositions, and bounded integer sequences of finite length

Development of a Wideband PLC Channel Emulator with Random Noise Scenarios

Channel emulators are an integral part of the test equipment that offers a more practical approach to testing new communication devices. It is imperative though to develop the emulator such that it best represents the channel. For PLC channel emulator, the channel representation can be either topdown or bottom-up. In this paper, the top-down characterisation and reference channels are used. In this approach, statistical measurements of the characteristics of the power line were conducted, and the closest mathematical representation is presented. The emulator operates in the frequency domain utilising 4096 transform points for the FFT process and 14 fractional bits for fixed point presentation. This number of bits allowed the emulator to sufficiently generate an average of 0.4% error between the software simulation results and the hardware test results. The input signal is converted to an LVDS signal by the FMC151 which serves as the AFE of the emulator. Two linear regulators block are used to convert both the negative and positive values of the input signal. The random generation of noise reduced the taxing efforts of adding different combinations of noise thus providing ease in focusing on the analysis of the resulting waveform

A particle swarm optimization-based algorithm for finding gapped motifs

<p>Abstract</p> <p>Background</p> <p>Identifying approximately repeated patterns, or motifs, in DNA sequences from a set of co-regulated genes is an important step towards deciphering the complex gene regulatory networks and understanding gene functions.</p> <p>Results</p> <p>In this work, we develop a novel motif finding algorithm (PSO+) using a population-based stochastic optimization technique called Particle Swarm Optimization (PSO), which has been shown to be effective in optimizing difficult multidimensional problems in continuous domains. We propose a modification of the standard PSO algorithm to handle discrete values, such as characters in DNA sequences. The algorithm provides several features. First, we use both consensus and position-specific weight matrix representations in our algorithm, taking advantage of the efficiency of the former and the accuracy of the latter. Furthermore, many real motifs contain gaps, but the existing methods usually ignore them or assume a user know their exact locations and lengths, which is usually impractical for real applications. In comparison, our method models gaps explicitly, and provides an easy solution to find gapped motifs without any detailed knowledge of gaps. Our method allows the presence of input sequences containing zero or multiple binding sites.</p> <p>Conclusion</p> <p>Experimental results on synthetic challenge problems as well as real biological sequences show that our method is both more efficient and more accurate than several existing algorithms, especially when gaps are present in the motifs.</p

Discrepancies between dimensions of interoception in autism: implications for emotion and anxiety

Emotions and affective feelings are influenced by one's internal state of bodily arousal via interoception. Autism Spectrum Conditions (ASC) are associated with difficulties in recognising others' emotions, and in regulating own emotions. We tested the hypothesis that, in people with ASC, such affective differences may arise from abnormalities in interoceptive processing. We demonstrated that individuals with ASC have reduced interoceptive accuracy (quantified using heartbeat detection tests) and exaggerated interoceptive sensibility (subjective sensitivity to internal sensations on self-report questionnaires), reflecting an impaired ability to objectively detect bodily signals alongside an over-inflated subjective perception of bodily sensations. The divergence of these two interoceptive axes can be computed as a trait prediction error. This error correlated with deficits in emotion sensitivity and occurrence of anxiety symptoms. Our results indicate an origin of emotion deficits and affective symptoms in ASC at the interface between body and mind, specifically in expectancy-driven interpretation of interoceptive information