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.
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.
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.
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.