Search results for: Combinatorics

Authors: T. Kjosmoen, T. Ryen, T. Eftestøl

Abstract:

In biological and biomedical research motif finding tools are important in locating regulatory elements in DNA sequences. There are many such motif finding tools available, which often yield position weight matrices and significance indicators. These indicators, p-values and E-values, describe the likelihood that a motif alignment is generated by the background process, and the expected number of occurrences of the motif in the data set, respectively. The various tools often estimate these indicators differently, making them not directly comparable. One approach for comparing motifs from different tools, is computing the E-value as the product of the p-value and the number of possible alignments in the data set. In this paper we explore the combinatorics of the motif alignment models OOPS, ZOOPS, and ANR, and propose a generic algorithm for computing the number of possible combinations accurately. We also show that using the wrong alignment model can give E-values that significantly diverge from their true values.

Keywords: Motif alignment, combinatorics, p-value, E-value, OOPS, ZOOPS, ANR.

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Authors: Costas S. Iliopoulos, Spiros Michalakopoulos

Abstract:

A new, combinatorial model for analyzing and inter- preting an electrocardiogram (ECG) is presented. An application of the model is QRS peak detection. This is demonstrated with an online algorithm, which is shown to be space as well as time efficient. Experimental results on the MIT-BIH Arrhythmia database show that this novel approach is promising. Further uses for this approach are discussed, such as taking advantage of its small memory requirements and interpreting large amounts of pre-recorded ECG data.

Keywords: Combinatorics, ECG analysis, MIT-BIH Arrhythmia Database, QRS Detection, String Algorithms

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Authors: Wajdi Mohamed Ratemi

Abstract:

The very well-known stacked sets of numbers referred to as Pascal’s triangle present the coefficients of the binomial expansion of the form (x+y)n. This paper presents an approach (the Staircase Horizontal Vertical, SHV-method) to the generalization of planar Pascal’s triangle for polynomial expansion of the form (x+y+z+w+r+⋯)n. The presented generalization of Pascal’s triangle is different from other generalizations of Pascal’s triangles given in the literature. The coefficients of the generalized Pascal’s triangles, presented in this work, are generated by inspection, using embedded Pascal’s triangles. The coefficients of I-variables expansion are generated by horizontally laying out the Pascal’s elements of (I-1) variables expansion, in a staircase manner, and multiplying them with the relevant columns of vertically laid out classical Pascal’s elements, hence avoiding factorial calculations for generating the coefficients of the polynomial expansion. Furthermore, the classical Pascal’s triangle has some pattern built into it regarding its odd and even numbers. Such pattern is known as the Sierpinski’s triangle. In this study, a presentation of Sierpinski-like patterns of the generalized Pascal’s triangles is given. Applications related to those coefficients of the binomial expansion (Pascal’s triangle), or polynomial expansion (generalized Pascal’s triangles) can be in areas of combinatorics, and probabilities.

Keywords: Generalized Pascal’s triangle, Pascal’s triangle, polynomial expansion, Sierpinski’s triangle, staircase horizontal vertical method.

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Authors: Randy Gomez, Keisuke Nakamura, Kazuhiro Nakadai

Abstract:

Distant-talking voice-based HCI system suffers from performance degradation due to mismatch between the acoustic speech (runtime) and the acoustic model (training). Mismatch is caused by the change in the power of the speech signal as observed at the microphones. This change is greatly influenced by the change in distance, affecting speech dynamics inside the room before reaching the microphones. Moreover, as the speech signal is reflected, its acoustical characteristic is also altered by the room properties. In general, power mismatch due to distance is a complex problem. This paper presents a novel approach in dealing with distance-induced mismatch by intelligently sensing instantaneous voice power variation and compensating model parameters. First, the distant-talking speech signal is processed through microphone array processing, and the corresponding distance information is extracted. Distance-sensitive Gaussian Mixture Models (GMMs), pre-trained to capture both speech power and room property are used to predict the optimal distance of the speech source. Consequently, pre-computed statistic priors corresponding to the optimal distance is selected to correct the statistics of the generic model which was frozen during training. Thus, model combinatorics are post-conditioned to match the power of instantaneous speech acoustics at runtime. This results to an improved likelihood in predicting the correct speech command at farther distances. We experiment using real data recorded inside two rooms. Experimental evaluation shows voice recognition performance using our method is more robust to the change in distance compared to the conventional approach. In our experiment, under the most acoustically challenging environment (i.e., Room 2: 2.5 meters), our method achieved 24.2% improvement in recognition performance against the best-performing conventional method.

Keywords: Human Machine Interaction, Human Computer Interaction, Voice Recognition, Acoustic Model Compensation, Acoustic Speech Enhancement.

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