Digit Strings Research Articles

Frequencies of digits, divergence points, and Schmidt games

Sets of divergence points, i.e. numbers x (or tuples of numbers) for which the limiting frequency of a given string of N-adic digits of x fails to exist, have recently attracted huge interest in the literature. In this paper we consider sets of simultaneous divergence points, i.e. numbers x (or tuples of numbers) for which the limiting frequencies of all strings of N-adic digits of x fail to exist. We show that many natural sets of simultaneous divergence points are ( α, β)-wining sets in the sense of the Schmidt game. As an application we obtain lower bounds for the Hausdorff dimension of these sets.

Issues with uncertainty decoding for noise robust automatic speech recognition

Interest continues in a class of robustness algorithms for speech recognition that exploit the notion of uncertainty introduced by environmental noise. These techniques share the property that the uncertainty varies with the noise level and is propagated to the decoding stage, resulting in increased model variances. In observation uncertainty forms, the uncertainty variance is simply the variance of the error in enhancement that is added to the model variances. Another form, called uncertainty decoding, refers to a factorisation which results in a linear feature transform and model variance bias that increases with noise; using appropriate approximations, efficient implementations may be obtained, with the goal of achieving near model-based performance without the associated computational cost. Unfortunately, uncertainty decoding forms that compute the uncertainty in the front-end and pass this to the decoder may suffer from a theoretical problem in low signal-to-noise ratio conditions. This report discusses how this fundamental issue arises, and demonstrates it through two schemes: SPLICE with uncertainty and front-end joint uncertainty decoding ( FE-Joint). A method to mitigate this for FE-Joint compensation is presented, as well as how SPLICE implicitly addresses it. However, it is shown that a model-based joint uncertainty decoding approach does not suffer from this limitation, like these front-end forms do, and is more computationally attractive. The issues described and performance of the various schemes are examined on two artificially corrupted corpora: the AURORA 2.0 digit string recognition and 1000-word Resource Management tasks.

Solving Large-Margin Hidden Markov Model Estimation via Semidefinite Programming

In this paper, we propose to use a new optimization method, i.e., semidefinite programming (SDP), to solve the large-margin estimation (LME) problem of continuous-density hidden Markov model (CDHMM) in speech recognition. First, we introduce a new constraint for LME to guarantee the boundedness of the margin of CDHMM. Second, we show that the LME problem subject to this new constraint can be formulated as an SDP problem under some relaxation conditions. Therefore, it can be solved using many efficient optimization algorithms specially designed for SDP. The new LME/SDP method has been evaluated on a speaker independent E-set speech recognition task using the ISOLET database and a connected digit string recognition task using the TIDIGITS database. Experimental results clearly demonstrate that large-margin estimation via semidefinite programing (LME/SDP) can significantly reduce word error rate (WER) over other existing CDHMM training methods, such as MLE and MCE. It has also been shown that the new SDP-based method largely outperforms the previously proposed LME optimization methods using gradient descent search.

Digital forensic text string searching: Improving information retrieval effectiveness by thematically clustering search results

Current digital forensic text string search tools use match and/or indexing algorithms to search digital evidence at the physical level to locate specific text strings. They are designed to achieve 100% query recall (i.e. find all instances of the text strings). Given the nature of the data set, this leads to an extremely high incidence of hits that are not relevant to investigative objectives. Although Internet search engines suffer similarly, they employ ranking algorithms to present the search results in a more effective and efficient manner from the user's perspective. Current digital forensic text string search tools fail to group and/or order search hits in a manner that appreciably improves the investigator's ability to get to the relevant hits first (or at least more quickly). This research proposes and empirically tests the feasibility and utility of post-retrieval clustering of digital forensic text string search results – specifically by using Kohonen Self-Organizing Maps, a self-organizing neural network approach. This paper is presented as a work-in-progress. A working tool has been developed and experimentation has begun. Findings regarding the feasibility and utility of the proposed approach will be presented at DFRWS 2007, as well as suggestions for follow-on research.

Visual word processing and experiential origins of functional selectivity in human extrastriate cortex.

How do category-selective regions arise in human extrastriate cortex? Visually presented words provide an ideal test of the role of experience: Although individuals have extensive experience with visual words, our species has only been reading for a few thousand years, a period not thought to be long enough for natural selection to produce a genetically specified mechanism dedicated to visual word recognition per se. Using relatively high-resolution functional magnetic resonance imaging (1.4 x 1.4 x 2-mm voxels), we identified a small region of extrastriate cortex in most participants that responds selectively to both visually presented words and consonant strings, compared with line drawings, digit strings, and Chinese characters. Critically, we show that this pattern of selectivity is dependent on experience with specific orthographies: The same region responds more strongly to Hebrew words in Hebrew readers than in nonreaders of Hebrew. These results indicate that extensive experience with a given visual category can produce strong selectivity for that category in discrete cortical regions.

Information, Consciousness, and Health

A 16-year empirical assessment of anomalous human/machine interactions provides strong evidence that consciousness can add information to otherwise random digital strings. A parallel program of remote perception studies establishes the inverse process: the anomalous acquisition of information about distant physical targets. Remarkably, neither of these extraordinary capabilities shows any dependence on either the distance or the time separating the participant from the target. The relevance of these consciousness abilities to human health follows from recognition that physiology entails myriad subtle information processes, all of which involve some degree of randomicity in their normal functions, and thus may be similarly influenced by conscious volition.

Using multiple acoustic feature sets for speech recognition

In this paper, the use of multiple acoustic feature sets for speech recognition is investigated. The combination of both auditory as well as articulatory motivated features is considered. In addition to a voicing feature, we introduce a recently developed articulatory motivated feature, the spectrum derivative feature. Features are combined both directly using linear discriminant analysis (LDA) as well as indirectly on model level using discriminative model combination (DMC). Experimental results are presented for both small- and large-vocabulary tasks. The results show that the accuracy of automatic speech recognition systems can be significantly improved by the combination of auditory and articulatory motivated features. The word error rate is reduced from 1.8% to 1.5% on the SieTill task for German digit string recognition. Consistent improvements in word error rate have been obtained on two large-vocabulary corpora. The word error rate is reduced from 19.1% to 18.4% on the VerbMobil II corpus, a German large-vocabulary conversational speech task, and from 14.1% to 13.5% on the British English part of the European parliament plenary sessions (EPPS) task from the 2005 TC-STAR ASR evaluation campaign.

Visually-guided Attention Enhances Target Identification in a Complex Auditory Scene

In auditory scenes containing many similar sound sources, sorting of acoustic information into streams becomes difficult, which can lead to disruptions in the identification of behaviorally relevant targets. This study investigated the benefit of providing simple visual cues for when and/or where a target would occur in a complex acoustic mixture. Importantly, the visual cues provided no information about the target content. In separate experiments, human subjects either identified learned birdsongs in the presence of a chorus of unlearned songs or recalled strings of spoken digits in the presence of speech maskers. A visual cue indicating which loudspeaker (from an array of five) would contain the target improved accuracy for both kinds of stimuli. A cue indicating which time segment (out of a possible five) would contain the target also improved accuracy, but much more for birdsong than for speech. These results suggest that in real world situations, information about where a target of interest is located can enhance its identification, while information about when to listen can also be helpful when targets are unfamiliar or extremely similar to their competitors.

Self-similar and Markov composition structures

The bijection between composition structures and random closed subsets of the unit interval implies that the composition structures associated with S ⋂ [0, 1] for a self-similar random set S ⊂ ℝ+ are those that are consistent with respect to a simple truncation operation. Using the standard coding of compositions by finite strings of binary digits starting with a 1, the random composition of n is defined by the first n terms of a random binary sequence of infinite length. The locations of 1’s in the sequence are the positions visited by an increasing time-homogeneous Markov chain on the positive integers if and only if S = exp(−W) for some stationary regenerative random subset W of the real line. Complementing our study presented in previous papers, we identify self-similar Markov composition structures associated with the two-parameter family of partition structures. Bibliography: 19 titles.

Crack Identification in Beam Using Genetic Algorithm and Three Dimensional p-FEM

In this paper, a method for identification of a crack in a beam is demonstrated by the use of the genetic algorithm (GA) based on changes in natural frequencies. To calculate the natural frequencies of cracked beams, p-FEM code, which is based on a parametric three dimensional finite element, is developed because the accuracy of the forward analysis is important. In the analysis, an edge crack model is considered. To identify the crack location and the depth from frequency measurements, crack parameters of the beam are coded into a fixed-length binary digit string. By using GA, the square sum of residuals between the measured data and the calculated data is minimized in the identification process and thus the crack is identified. To avoid a high calculation cost, a response surface method (RSM) is also adopted in the minimizing process. The combination of GA and RSM have made the identification more effective and robust. The availability of the proposed method is confirmed by the results of numerical simulation.

An automatic speech recognition system based on the scene analysis account of auditory perception

Despite many years of concentrated research, the performance gap between automatic speech recognition (ASR) and human speech recognition (HSR) remains large. The difference between ASR and HSR is particularly evident when considering the response to additive noise. Whereas human performance is remarkably robust, ASR systems are brittle and only operate well within the narrow range of noise conditions for which they were designed. This paper considers how humans may achieve noise robustness. We take the view that robustness is achieved because the human perceptual system treats the problems of speech recognition and sound source separation as being tightly coupled. Taking inspiration from Bregman’s Auditory Scene Analysis account of auditory organisation, we present a speech recognition system which couples these processes by using a combination of primitive and schema-driven processes: first, a set of coherent spectro-temporal fragments is generated by primitive segmentation techniques; then, a decoder based on statistical ASR techniques performs a simultaneous search for the correct background/foreground segmentation and word sequence hypothesis. Mutually supporting solutions to both the source segmentation and speech recognition problems arise as a result. The decoder is tested on a challenging corpus of connected digit strings mixed monaurally at 0 dB and recognition performance is compared with that achieved by listeners using identical data. The results, although preliminary, are encouraging and suggest that techniques which interface ASA and statistical ASR have great potential. The paper concludes with a discussion of future research directions that may further develop this class of perceptually motivated ASR solutions.

Precursors of Insight in Event-related Brain Potentials

Event-related potentials (ERPs) were investigated to find precursors of insightful behavior. Participants had to process successive pairs in strings of digits to obtain a final response in each trial. Within the sequence of five responses required in each trial, the last two responses mirrored the two preceding ones. This hidden regularity, allowing for shortcutting each trial from five to two responses, was discovered by 6 out of 26 participants. Both groups, solvers and nonsolvers, implicitly learned the regularity, reflected by faster responses to the repeated, predictable responses, but this differential effect was larger in solvers, whereas nonsolvers became unspecifically faster with all responses. Several ERP components were larger in solvers than in nonsolvers from the outset: slow positive wave, frontocentral P3a, anterior N1 to those digits that triggered the critical repeating responses, and P3b to the digit that evoked the immediately repeating response. Being already present in the first block, these effects were early precursors of insightful behavior. This early occurrence suggests that participants who will gain insight may be distinguished beforehand by their individual characteristics.

Large margin hidden Markov models for speech recognition

In this paper, motivated by large margin classifiers in machine learning, we propose a novel method to estimate continuous-density hidden Markov model (CDHMM) for speech recognition according to the principle of maximizing the minimum multiclass separation margin. The approach is named large margin HMM. First, we show this type of large margin HMM estimation problem can be formulated as a constrained minimax optimization problem. Second, we propose to solve this constrained minimax optimization problem by using a penalized gradient descent algorithm, where the original objective function, i.e., minimum margin, is approximated by a differentiable function and the constraints are cast as penalty terms in the objective function. The new training method is evaluated in the speaker-independent isolated E-set recognition and the TIDIGITS connected digit string recognition tasks. Experimental results clearly show that the large margin HMMs consistently outperform the conventional HMM training methods. It has been consistently observed that the large margin training method yields significant recognition error rate reduction even on top of some popular discriminative training methods.

An equilibrium network design model with a social cost function for multimodal networks

In this paper, we present a comprehensive investment planning model and its solution approach. The model takes a bilevel programming form and allows a variety of effects of the investments incorporated. The model is characterized by its ability to address the total social costs occurring in transportation networks and to estimate the equilibrium link volumes in multimodal networks. Two solution algorithms were proposed. Both algorithms handle the discrete optimization problem by exploiting the strings of binary digits of integer variables. In an illustrative example, we performed network design analyses for three scenarios in which 25, 50, and 75% of the total required capital is available. By applying the two solution algorithms to the example problem, the optimal network alternative for each scenario was found. If a cost/benefit analysis is coupled with the proposed model, the optimal investments and the optimal network configuration will be determined simultaneously.

Look-and-Say Biochemistry: Exponential RNA and Multistranded DNA

(2006). Look-and-Say Biochemistry: Exponential RNA and Multistranded DNA. The American Mathematical Monthly: Vol. 113, No. 4, pp. 289-307.

A strong hot spot theorem

A real number α \alpha is said to be b b -normal if every m m -long string of digits appears in the base- b b expansion of α \alpha with limiting frequency b − m b^{-m} . We prove that α \alpha is b b -normal if and only if it possesses no base- b b “hot spot”. In other words, α \alpha is b b -normal if and only if there is no real number y y such that smaller and smaller neighborhoods of y y are visited by the successive shifts of the base- b b expansion of α \alpha with larger and larger frequencies, relative to the lengths of these neighborhoods.

Attentional capture triggers an attentional blink

Two experiments examined the possibility that attention directed to a distractor during rapid serial visual presentation (RSVP) can produce an attentional blink (AB). A to-be-ignored distractor (D1) preceded a target word (T2) by a variable lag in RSVP streams of black false-font distractors. D1 was highlighted by color and was a word, a string of consonants, a string of digits, or a string of false-font characters. Recall of T2 was significantly suppressed at short D1-T2 lags (the AB) but only when D1 contained letters; the AB was completely absent when D1 was composed of digits or false-font characters. Thus, the AB can be triggered by a highlighted distractor if the distractor shares features with a target.

The Role of Meaning in Grapheme-Colour Synaesthesia

When the synaesthete, J, is shown black graphemes, in addition to perceiving the black digits or letters she also experiences highly specific colours that overlay the graphemes (e.g., 5 is pink, S is green). We used ambiguous graphemes in a Stroop-type task to show that the exact same forms (e.g., 5) can elicit different synaesthetic colours depending on whether they are interpreted as digits or letters. J was shown strings of black digits (e.g., 3 4 5 6 7) or words (e.g., MUSIC) for 1 sec. All but one of the graphemes then disappeared and the remaining grapheme changed to a colour that J had to name as quickly as possible. The key trials involved coloured graphemes that were ambiguous (e.g., the 5 in the strings above could be interpreted either as a digit or as a letter). On congruent trials, the colour of the ambiguous target grapheme was the same as J's photism for the digit or letter interpretations of the grapheme. On incongruent trials, the colours of the ambiguous target graphemes were different than the colours of J's photisms for the digit or letter interpretations of the graphemes. On digit-context incongruent trials, the ambiguous graphemes were presented in J's colour for the letter-interpretations of the graphemes, whereas on letter-context incongruent trials, the ambiguous graphemes were presented in J's colours for the digit-interpretations of the graphemes. Thus the same ambiguous grapheme (e.g., a pink 5) served as a congruent stimulus in one context and an incongruent stimulus in another context. J's response times showed that ambiguous graphemes elicited different photisms depending on whether they were interpreted as digits or letters. This finding suggests that it is not the form but the meaning of graphemes (whether they are interpreted as digits or letters) that determines the colours of synaesthetic photisms.

Crack Identification of Plates Using Genetic Algorithm

In this paper, a method for identifying of a crack in a plate that uses a genetic algorithm (GA) based on changes in natural frequencies is presented. To calculate the natural frequencies of the cracked plates, a FEM (Finite Element Method) program, which is based on the BFM (Bogner, Fox and Schmidt) model, is developed since the accuracy of the forward solver is important. In the analysis, two types of cracks, i.e., internal and edge cracks are considered. To identify the crack location and the depth from frequency measurements, the width and position of the crack in a plate are coded into a fixed-length binary digit string. Using GA, the square sum of residuals between the measured data and the calculated data is minimized in the identification process and thus the crack is identified. To avoid a high calculation cost, the response surface method (RSM) is also adopted in the minimizing process. The combination of GA and RSM makes the identification more effective and robust. The applicability of the proposed method is confirmed by the results of numerical simulation.

Speech recognition on DSP: issues on computational efficiency and performance analysis

This paper provides a thorough description of the implementation of automatic speech recognition (ASR) algorithms on a fixed-point digital signal processor (DSP). It is intended to serve as a useful self-contained reference for DSP engineers to follow when developing similar applications. The work is based on a detailed analysis of hidden Markov model (HMM) based ASR algorithms. The computationally critical steps are clearly identified, and for each of them, different ways of optimization for real-time computation are suggested and evaluated. The trade-off among computational efficiency, memory requirements and recognition performance is illustrated quantitatively via three example systems, one for the recognition of isolated Chinese words and the other two for the recognition of English and Chinese digit strings, respectively. The paper also discusses about other techniques that can be implemented to further improve the recognition performance in real-world applications.