Sequence Of Symbols Research Articles

Development of a method to recognize punch shapes for progressive dies

A generic method for automatic shape recognition on two-dimensional contours, particularly used for recognizing punch shapes for progressive dies, is presented in this article. In this work, shapes of two-dimensional contours are defined by shape templates using a sequence of symbols, lists, and numbers, and their definitions are stored in a specially designed database for the minimum number of shape definitions to be retrieved during shape recognition for optimal computational efficiency. When a contour is input from a computer-aided design system for shape recognition, the computer-aided design data are translated into shape components and input to the shape recognition device. Upon successful recognition of a shape, the shape code will be composed and its dimensional values will be extracted. Standard or special punch purchase code may be created automatically through this method.

Blind sequence‐length estimation of low‐SNR cyclostationary sequences

Several existing direct-sequence spread spectrum (DSSS) detection and estimation algorithms assume prior knowledge of the symbol period or sequence length, although very few sequence-length estimation techniques are available in the literature. This study presents two techniques to estimate the sequence length of a baseband DSSS signal affected by additive white Gaussian noise. The first technique is based on a known autocorrelation technique which is used as reference, and the second technique is based on principal component analysis. Theoretical analysis and computer simulation show that the second technique can correctly estimate the sequence length at a lower signal-to-noise ratio than the first technique. The techniques presented in this study can estimate the sequence length blindly which can then be fed to semi-blind detection and estimation algorithms.

Exact Test of Independence Using Mutual Information

Using a recently discovered method for producing random symbol sequences with prescribed transition counts, we present an exact null hypothesis significance test (NHST) for mutual information between two random variables, the null hypothesis being that the mutual information is zero (i.e., independence). The exact tests reported in the literature assume that data samples for each variable are sequentially independent and identically distributed (iid). In general, time series data have dependencies (Markov structure) that violate this condition. The algorithm given in this paper is the first exact significance test of mutual information that takes into account the Markov structure. When the Markov order is not known or indefinite, an exact test is used to determine an effective Markov order.

Different Methods of Partitioning the Phase Space of a Dynamic System

In symbolic dynamics, the definition of a symbolic sequence from a continuous times series depends on the use of an appropriate partition of the phase space. In fact, the best way is to estimate a generating partition. However, it is not possible to find generating partitions for most experimental observations because such partitions do not exist when noise is present. In this paper, different partition methods applied to stochastic and chaotic system will be compared in order to choose one which conserves system entropy rate. This partition is called a Markov partition.

Symbolic extensions applied to multiscale structure of genomes.

A genome of a living organism consists of a long string of symbols over a finite alphabet carrying critical information for the organism. This includes its ability to control post natal growth, homeostasis, adaptation to changes in the surrounding environment, or to biochemically respond at the cellular level to various specific regulatory signals. In this sense, a genome represents a symbolic encoding of a highly organized system of information whose functioning may be revealed as a natural multilayer structure in terms of complexity and prominence. In this paper we use the mathematical theory of symbolic extensions as a framework to shed light onto how this multilayer organization is reflected in the symbolic coding of the genome. The distribution of data in an element of a standard symbolic extension of a dynamical system has a specific form: the symbolic sequence is divided into several subsequences (which we call layers) encoding the dynamics on various “scales”. We propose that a similar structure resides within the genomes, building our analogy on some of the most recent findings in the field of regulation of genomic DNA functioning.

Generalization of entropy based divergence measures for symbolic sequence analysis.

Entropy based measures have been frequently used in symbolic sequence analysis. A symmetrized and smoothed form of Kullback-Leibler divergence or relative entropy, the Jensen-Shannon divergence (JSD), is of particular interest because of its sharing properties with families of other divergence measures and its interpretability in different domains including statistical physics, information theory and mathematical statistics. The uniqueness and versatility of this measure arise because of a number of attributes including generalization to any number of probability distributions and association of weights to the distributions. Furthermore, its entropic formulation allows its generalization in different statistical frameworks, such as, non-extensive Tsallis statistics and higher order Markovian statistics. We revisit these generalizations and propose a new generalization of JSD in the integrated Tsallis and Markovian statistical framework. We show that this generalization can be interpreted in terms of mutual information. We also investigate the performance of different JSD generalizations in deconstructing chimeric DNA sequences assembled from bacterial genomes including that of E. coli, S. enterica typhi, Y. pestis and H. influenzae. Our results show that the JSD generalizations bring in more pronounced improvements when the sequences being compared are from phylogenetically proximal organisms, which are often difficult to distinguish because of their compositional similarity. While small but noticeable improvements were observed with the Tsallis statistical JSD generalization, relatively large improvements were observed with the Markovian generalization. In contrast, the proposed Tsallis-Markovian generalization yielded more pronounced improvements relative to the Tsallis and Markovian generalizations, specifically when the sequences being compared arose from phylogenetically proximal organisms.

Analysis of Various Periodicity Detection Algorithms in Time Series Data with Design of New Algorithm

Time series datasets consist of sequence of numeric values obtained over repeated measurements of time. They are Popular in many applications such as stock market analysis, power consumption, economic and sells forecasting, temperature etc. Periodic pattern mining or periodicity detection is process of finding periodic patterns in time series database. It has a number of applications, such as prediction, forecasting, detection of unusual activities, etc. Periodicity mining needs to give more attention as its increased need in real life applications. The types of periodicities are symbol periodicity, sequence periodicity and segment periodicity and they should be identified even in the presence of noise in the time series database. There are number of algorithms exists for periodic pattern mining. Those algorithms have some advantages and disadvantages. In this paper, we have compared different periodicity mining algorithms and given plan for developing efficient periodicity mining algorithm which detect symbol periodicity, sequence periodicity and segment periodicity and noise-resilient .

Foreground extraction based on anomaly detection

A robust method to detect foreground regions in video sequences is presented. For each pixel, the time series of pixel intensity is represented as symbol sequences that are trained and modelled using the Markov model to obtain the anomaly detection threshold. The foreground extraction is performed by comparing the anomaly transition probability of each pixel and its detection threshold. The experimental results demonstrate that the proposed method outperforms the traditional methods.

Human-computer music performance: A brief history and future prospects

Computer accompaniment began in the eighties as a technology to synchronize computers to live musicians by sensing, following, and adapting to expressive musical performances. The technology has progressed from systems where performances were modeled as sequences of discrete symbols, i.e., pitches, to modern systems that use continuous probabilistic models. Although score following techniques have been a common focus, computer accompaniment research has addressed many other interesting topics, including the musical adjustment of tempo, the problem of following an ensemble of musicians, and making systems more robust to unexpected mistakes by performers. Looking toward the future, we find that score following is only one of many ways musicians use to synchronize. Score following is appropriate when scores exist and describe the performance accurately, and where timing deviations are to be followed rather than ignored. In many cases, however, especially in popular music forms, tempo is rather steady, and performers improvise many of their parts. Traditional computer accompaniment techniques do not solve these important music performance scenarios. The term Human-Computer Music Performance (HCMP) has been introduced to cover a broader spectrum of problems and technologies where humans and computers perform music together, adding interesting new problems and directions for future research.

Assessing randomness and complexity in human motion trajectories through analysis of symbolic sequences.

Complexity is a hallmark of intelligent behavior consisting both of regular patterns and random variation. To quantitatively assess the complexity and randomness of human motion, we designed a motor task in which we translated subjects' motion trajectories into strings of symbol sequences. In the first part of the experiment participants were asked to perform self-paced movements to create repetitive patterns, copy pre-specified letter sequences, and generate random movements. To investigate whether the degree of randomness can be manipulated, in the second part of the experiment participants were asked to perform unpredictable movements in the context of a pursuit game, where they received feedback from an online Bayesian predictor guessing their next move. We analyzed symbol sequences representing subjects' motion trajectories with five common complexity measures: predictability, compressibility, approximate entropy, Lempel-Ziv complexity, as well as effective measure complexity. We found that subjects' self-created patterns were the most complex, followed by drawing movements of letters and self-paced random motion. We also found that participants could change the randomness of their behavior depending on context and feedback. Our results suggest that humans can adjust both complexity and regularity in different movement types and contexts and that this can be assessed with information-theoretic measures of the symbolic sequences generated from movement trajectories.

Path sets in one-sided symbolic dynamics

Path sets are spaces of one-sided infinite symbol sequences associated to pointed graphs (G,v0), which are edge-labeled directed graphs with a distinguished vertex v0. Such sets arise naturally as address labels in geometric fractal constructions and in other contexts. The resulting set of symbol sequences need not be closed under the one-sided shift. This paper establishes basic properties of the structure and symbolic dynamics of path sets, and shows that they are a strict generalization of one-sided sofic shifts.

Symbolic sequence learning is associated with cognitive–affective profiles in female FMR1 premutation carriers

This study examines implicit sequence learning impairments that may indicate at-risk cerebellar profiles proposed to underlie some aspects of subtle cognitive and affective dysfunctions found among female fragile X mental retardation 1 (FMR1) premutation (PM)-carriers. A total of 34 female PM-carriers and 33 age- and intelligence-matched controls completed an implicit symbolically primed serial reaction time task (SRTT) previously shown to be sensitive to cerebellar involvement. Implicit learning scores indicated a preservation of learning in both groups; however, PM-carriers demonstrated poorer learning through significantly elevated response latencies overall and at each specific block within the symbolic SRTT. Group comparisons also revealed a core deficit in response inhibition, alongside elevated inattentive symptoms in female PM-carriers. Finally, strong and significant associations were observed between poor symbolic SRTT performance and executive, visuospatial and affective deficits in the PM-carrier group. These associations remained strong even after controlling motor speed, and were not observed in age- and intelligence quotient-matched participants. The findings implicate cerebellar non-motor networks subserving the implicit sequencing of responses in cognitive-affective phenotypes previously observed in female PM-carriers. We contend that symbolic SRTT performance may offer clinical utility in future pharmaceutical interventions in female PM-carriers.

A Novel Circular Mapping Technique for Spectral Classification of Exons and Introns in Human DNA Sequences

Signals that represent information may be classified into two forms: numeric and symbolic. Symbolic signals such as DNA symbolic sequences cannot be directly processed with digital signal processing (DSP) techniques. The only way to apply DSP in genomic field is the mapping of DNA symbolic sequences to numerical sequences. Hence, biological properties are reflected in a numerical domain. This opens a field to present a set of tools for solving genomic problems. In literature many techniques have been developed for numerical representation of DNA sequences. The main drawback of these techniques is that each nucleotide is represented by a numerical value depending on nucleotide type only ignoring its position in codon and DNA sequence. In this paper a new approach for DNA symbolic to numeric representation called Circular Mapping (CM) is introduced. Its based on graphical representation of DNA sequence that maps each nucleotide by a complex numerical value depending not only on nucleotide type but also on its position in codons. The main applications of this method are the gene prediction that aims to locate the protein-coding regions and the classification of exons and introns in DNA sequences. The proposed approach showed significant improvement in exons and introns classification as compared with the existing techniques. The efficiency of this method in classification depends on the right choice of the mapping angle ( ) as indicated by the power spectral analysis results over the sequences of the human genome (GRch37/hg19).

Codimension-2 Border Collision, Bifurcations in One-Dimensional, Discontinuous Piecewise Smooth Maps

We consider a two-parametric family of one-dimensional piecewise smooth maps with one discontinuity point. The bifurcation structures in a parameter plane of the map are investigated, related to codimension-2 bifurcation points defined by the intersections of two border collision bifurcation curves. We describe the case of the collision of two stable cycles of any period and any symbolic sequences. For this case, we prove that the local monotonicity of the functions constituting the first return map defined in a neighborhood of the border point at the parameter values related to the codimension-2 bifurcation point determines, under suitable conditions, the kind of bifurcation structure originating from this point; this can be either a period adding structure, or a period incrementing structure, or simply associated with the coupling of colliding cycles.

A Hierarchical Approach to Makam Classification of Turkish Makam Music, Using Symbolic Data

A method for hierarchical classification of makams from symbolic data is presented. A makam generally implies a miscellany of rules for melodic composition using a given scale. Therefore, makam detection is to some level similar to the key detection problem. The proposed algorithm classifies makams by applying music theoretical knowledge and statistical evidence in a hierarchical manner. The makams using similar scales are first grouped together, and then identified in detail later. The first level of the hierarchical decision is based on statistical information provided by the n-gram likelihood of the symbolic sequences. A cross-entropy based metric, perplexity, is used to calculate similarity between makam models and the input music piece. Later, using statistical features related to the content of the piece, such as the tonic note, the average pitch level for local excerpts and the overall pitch progression, a more detailed identification of the makam is achieved. Different length n-grams and representation paradigms are used, including the Arel theory, the 12 tone equal tempered representation, and interval contour. Results show that the hierarchical approach is better, compared to a straightforward n-gram classification, for the makams which have similar pitch space, such as Hüseyni–Muhayyerand Rast–Mahur. Using the proposed methodology, the system’s recall rate increases from 88.7% to 90.9% where there exists still some confusion between the makams Uşşak and Beyati.

Fault isolation by comparing alarm lists using a symbolic sequence matching algorithm

A fault isolation method using the Needleman and Wunsch algorithm (NWA), a symbolic sequence matching algorithm widely used in bio informatics, is proposed. A fault is represented by the chronologically ordered list of alarms raised by the control system on its occurrence. It is transformed in a symbolic sequence where each alarm forms the letter of a very large alphabet. NWA is used to align the k examples of the same fault stored in the data base and then to automatically extract the minimal sequence of alarms typical of the fault, named the fault sequence template. Any new alarm sequence is then compared to the fault templates by means of the similarity measure provided by NWA. The performances are compared with a pattern matching approach using Hamming distance and evaluated on a set of data obtained from a very realistic simulator of a CERN Large Hadron Collider process.

Continuation and collapse of homoclinic tangles

By a classical theorem transversal homoclinic points of maps lead to shift dynamics on a maximal invariant set, also referred to as a homoclinic tangle. In this paper we study the fate of homoclinic tangles in parameterized systems from the viewpoint of numerical continuation and bifurcation theory. The new bifurcation result shows that the maximal invariant set near a homoclinic tangency, where two homoclinic tangles collide, can be characterized by a system of bifurcation equations that is indexed by a symbolic sequence. These bifurcation equations consist of a finite or infinite set of hilltop normal forms known from singularity theory. For the Henon family we determine numerically the connected components of branches with multi-humped homoclinic orbits that pass through several tangencies. The homoclinic network found by numerical continuation is explained by combining our bifurcation result with graph-theoretical arguments.

Textual Approximation Methods for Time Series Classification: TAX and l-TAX

SUMMARY A lot of work has been conducted on time series classification and similarity search over the past decades. However, the classification of a time series with high accuracy is still insufficient in applications such as ubiquitous or sensor systems. In this paper, a novel textual approximation of a time series, called TAX, is proposed to achieve high accuracy time series classification. l-TAX, an extended version of TAX that shows promising classification accuracy over TAX and other existing methods, is also proposed. We also provide a comprehensive comparison between TAX and l-TAX, and discuss the benefits of both methods. Both TAX and l-TAX transform a time series into a textual structure using existing document retrieval methods and bioinformatics algorithms. In TAX, a time series is represented as a document like structure, whereas l-TAX used a sequence of textual symbols. This paper provides a comprehensive overview of the textual approximation and techniques used by TAX and l-TAX

Representation and Symbolization of Motion Captured Human Action by Locality Preserving Projections

Human motion analysis and assessment are important in determining Parkinsons disease and stroke, or in measuring skill quality in basic motions. Reduced space is useful in representing motion segments and finding basic behavioral patterns for humanoid robot control using the modularized approach. In the current paper, we represent motion-captured data of human action in a reduced space of nonlinear degrees of freedom in which the original motion is characterized. First, we represent high-dimensional data, such as motion sequence of the position of joints in Cartesian space, in a reduced space using the locality preserving projection (LPP) method. Second, we find a similarity measure between the actions. Finally, we assess human motions using a similarity measure to find the most similar one. The LPP is a linear dimensionality reduction algorithm that builds a graph for neighborhood information and maps data points to a reduced space. The reason for using LPP in our study is that it is defined globally, and any new data element can be mapped in the reduced space. Our method includes the generation of symbolic code sequence corresponding to complex, high-dimensional motion. Interdisciplinary synergy combined with information technology and wearable sensor systems can broaden the possible future applications in rehabilitation engineering.

Topography prediction of helical transmembrane proteins by a new modification of the sliding window method.

Protein functions are specified by its three-dimensional structure, which is usually obtained by X-ray crystallography. Due to difficulty of handling membrane proteins experimentally to date the structure has only been determined for a very limited part of membrane proteins (<4%). Nevertheless, investigation of structure and functions of membrane proteins is important for medicine and pharmacology and, therefore, is of significant interest. Methods of computer modeling based on the data on the primary protein structure or the symbolic amino acid sequence have become an actual alternative to the experimental method of X-ray crystallography for investigating the structure of membrane proteins. Here we presented the results of the study of 35 transmembrane proteins, mainly GPCRs, using the novel method of cascade averaging of hydrophobicity function within the limits of a sliding window. The proposed method allowed revealing 139 transmembrane domains out of 140 (or 99.3%) identified by other methods. Also 236 transmembrane domain boundary positions out of 280 (or 84%) were predicted correctly by the proposed method with deviation from the predictions made by other methods that does not exceed the detection error of this method.