Index of Symbols

Symbol retrieval is important for content-based search in digital libraries and for automatic interpretation of line drawings. In this work, we present a complete symbol retrieval system. The proposed system has an off-line content-analysis stage, where the contents of a database of line drawings are represented as a symbol index, which is a compact indexable representation of the database. Such representation allows efficient on-line query retrieval. Within the retrieval system, three methods are presented. First, a feature grouping method for identifying local regions of interest (ROIs) in the drawings. The found ROIs represent symbols' parts. Second, a clustering method based on geometric matching, is used to cluster the similar parts from all the drawings together. A symbol index is then constructed from the clusters' representatives. Finally, the ROIs of a query symbol are matched to the clusters' representatives. The matching symbols' parts are retrieved from the clusters, and spatial verification is performed on the matching parts. By using the symbol index we are able to achieve a query look-up time that is independent of the database size, and dependent on the size of the symbol index. The retrieval system achieves higher recall and precision than state-of-the-art methods.

The autonomic regulation is non-invasively estimated from heart rate variability (HRV). Many methods utilized to assess autonomic regulation require stationarity of HRV recordings. However, non-stationarities are frequently present even during well-controlled experiments, thus potentially biasing HRV indices. The aim of our study is to quantify the potential bias of spectral, symbolic and entropy HRV indices due to non-stationarities. We analyzed HRV series recorded in healthy subjects during uncontrolled daily life activities typical of 24 h Holter recordings and during predetermined levels of robotic-assisted treadmill-based physical exercise. A stationarity test checking the stability of the mean and variance over short HRV series (about 300 cardiac beats) was utilized to distinguish stationary periods from non-stationary ones. Spectral, symbolic and entropy indices evaluated solely over stationary periods were contrasted with those derived from all the HRV segments. When indices were calculated solely over stationary series, we found that (i) during both uncontrolled daily life activities and controlled physical exercise, the entropy-based complexity indices were significantly larger; (ii) during uncontrolled daily life activities, the spectral and symbolic indices linked to sympathetic modulation were significantly smaller and those associated with vagal modulation were significantly larger; (iii) while during uncontrolled daily life activities, the variance of spectral, symbolic and entropy rate indices was significantly larger, during controlled physical exercise, it was smaller. The study suggests that non-stationarities increase the likelihood to overestimate the contribution of sympathetic control and affect the power of statistical tests utilized to discriminate conditions and/or groups.

Symbolic indexing is a data abstraction technique that exploits the partially-ordered state space of symbolic trajectory evaluation (STE). Use of this technique has been somewhat limited in practice because of its complexity. We present logical machinery and efficient algorithms that provide a much simpler interface to symbolic indexing for the STE user. Our logical machinery also allows correctness assertions proved by symbolic indexing to be composed into larger properties, something previously not possible.KeywordsModel CheckTarget VariableBoolean VariableIndexing RelationSide ConditionThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

1. Introduction: Examples of Optimization Problems, Historical Overview.- 2. Optimality Conditions: Convex Sets, Inequalities, Local First- and Second-Order Optimality Conditions, Duality.- 3. Unconstrained Optimization Problems: Elementary Search and Localization Methods, Descent Methods with Line Search, Trust Region Methods, Conjugate Gradient Methods, Quasi-Newton Methods.- 4. Linearly Constrained Optimization Problems: Linear and Quadratic Optimization, Projection Methods.- 5. Nonlinearly Constrained Optimization Methods: Penalty Methods, SQP Methods.- 6. Interior-Point Methods for Linear Optimization: The Central Path, Newton's Method for the Primal-Dual System, Path-Following Algorithms, Predictor-Corrector Methods.- 7. Semidefinite Optimization: Selected Special Cases, The S-Procedure, The Function log det, Path-Following Methods, How to Solve SDO Problems?, Icing on the Cake: Pattern Separation via Ellipsoids.- 8. Global Optimization: Branch and Bound Methods, Cutting Plane Methods.- Appendices: A Second Look at the Constraint Qualifications, The Fritz John Condition, Optimization Software Tools for Teaching and Learning.- Bibliography.- Index of Symbols.- Subject Index.

Preface.- Introduction. The Krein-Milman theorem as an integral representation theorem.- Application of the Krein-Milman theorem to completely monotonic functions.- Choquet's theorem: The metrizable case.- The Choquet-Bishop-de Leeuw existence theorem.- Applications to Rainwater's and Haydon's theorems.- A new setting: The Choquet boundary.- Applications of the Choquet boundary to resolvents.- The Choquet boundary for uniform algebras.- The Choquet boundary and approximation theory.- Uniqueness of representing measures.- Properties of the resultant map.- Application to invariant and ergodic measures.- A method for extending the representation theorems: Caps.- A different method for extending the representation theorems.- Orderings and dilations of measures.- Additional Topics.- References.- Index of symbols.- Index.

In this article, we introduce a new spatial modulation (SM) transmission scheme using turbo trellis coding (TTC) for both antenna and symbol indexes. In spatial modulation scheme with trellis coding (SM-TC) the transmitter encodes the information bits before selecting the transmit antenna and transmitted symbol indexes. The SM-TC scheme is a generalization of the turbo trellis coded SM (TTCSM) scheme, which encodes just the information bits used to select the transmit antenna index. The performances of the SM-TC scheme can be considerably enhanced by using parallel concatenated turbo coding. The new SM-TTC scheme combines the SM-TC transmission with conventional parallel turbo trellis-coded modulation (TTCM). The bit error rate (BER) performances are evaluated using simulations for PSK-SM-TTC transmissions over stationary Rayleigh, Rician, and spatially correlated (SC) fading channels with additive white Gaussian noise (AWGN). Simulation results reveal that the SM-TTC scheme performs better than the previous TTCSM scheme when transmitting over a SC fading channel, especially for a large number of receive antennas.

Vocabulary mismatch is a central problem in information retrieval (IR), i.e., the relevant documents may not contain the same (symbolic) terms of the query. Recently, neural representations have shown great success in capturing semantic relatedness, leading to new possibilities to alleviate the vocabulary mismatch problem in IR. However, most existing efforts in this direction have been devoted to the re-ranking stage. That is to leverage neural representations to help re-rank a set of candidate documents, which are typically obtained from an initial retrieval stage based on some symbolic index and search scheme (e.g., BM25 over the inverted index). This naturally raises a question: if the relevant documents have not been found in the initial retrieval stage due to vocabulary mismatch, there would be no chance to re-rank them to the top positions later. Therefore, in this paper, we study the problem how to employ neural representations to improve the recall of relevant documents in the initial retrieval stage. Specifically, to meet the efficiency requirement of the initial stage, we introduce a neural index for the neural representations of documents, and propose two hybrid search schemes based on both neural and symbolic indices, namely the parallel search scheme and the sequential search scheme. Our experiments show that both hybrid index and search schemes can improve the recall of the initial retrieval stage with small overhead.KeywordsIndexingNeural representationInitial retrieval

This study aimed to evaluate the autonomic modulation of heart rate in sedentary paraplegics and paraplegic wheelchair basketball players with thoracic spinal cord injury below T6. Seven paraplegic wheelchair basketball players (active paraplegic group), five paraplegics who were not involved in regular exercise (sedentary paraplegic group) and 10 able-bodied participants (control group) took part in the study. The heart rate variability was evaluated by linear (low frequency and high frequency band in normalised units and low frequency/high frequency ratio) and nonlinear methods (Shannon entropy, corrected conditional entropy, and symbolic analysis). The sedentary group presented significantly higher values for low frequency, low frequency/high frequency ratio and symbolic index with no significant variations (0V%), and also lower values for the high frequency and symbolic index with two significant unlike variation (2ULV%) compared to active paraplegic group. Shannon entropy and corrected conditional entropy analyses revealed significantly lower values in the sedentary group than in the control or active paraplegic groups. Paraplegic individuals who regularly undertake physical exercise have higher complexity of R-R interval time series, lower sympathetic modulation, and higher parasympathetic modulation than sedentary paraplegic participants.

Advanced Torque Estimation and Control Algorithm of Diesel Engines

Two symbolic indexes, the percentage of sequences characterized by three heart periods with no significant variations (0V%) and that with two significant unlike variations (2UV%), have been found to reflect changes in sympathetic and vagal modulations, respectively. We tested the hypothesis that symbolic indexes may track the gradual shift of the cardiac autonomic modulation during an incremental head-up tilt test. Symbolic analysis was carried out over heart period variability series (250 cardiac beats) derived from ECG recordings during a graded head-up tilt test (0, 15, 30, 45, 60, 75, and 90 degrees ) in 17 healthy subjects. The percentage of subjects showing a significant linear correlation (Spearman rank-order correlation) with tilt angles was utilized to evaluate the performance of symbolic analysis. Spectral analysis was carried out for comparison over the same series. 0V% progressively increased with tilt angles, whereas 2UV% gradually decreased. The decline of 2UV% was greater than the increase of 0V% at low tilt angles. Linear correlation with tilt angles was exhibited in a greater percentage of subjects for 0V% and 2UV% than for any spectral index. Our findings suggest that symbolic analysis performed better than spectral analysis and, thus, is a suitable methodology for assessment of the subtle changes of cardiac autonomic modulation induced by a graded head-up tilt test. Moreover, symbolic analysis indicates that the changes of cardiac sympathetic and vagal modulations observed during this protocol were reciprocal but characterized by different absolute magnitudes.

The topic of the paper is information processing using representations of spatial relations, called symbolic spatial indexes. The paper describes how symbolic spatial indexes can be used in several problems including information retrieval, composition of spatial relations, route planning and update operations.KeywordsSpatial RelationComposition OperatorSpatial KnowledgeTopological RelationSpatial IndexThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Various relation-based systems, concerned with the qualitative representation and processing of spatial knowledge, have been developed in numerous application domains. In this article, we identify the common concepts underlying qualitative spatial knowledge representation, we compare the representational properties of the different systems, and we outline the computational tasks involved in relation-based spatial information processing. We also describe symbolic spatial indexes, relation-based structures that combine several ideas in spatial knowledge representation. A symbolic spatial index is an array that preserves only a set of spatial relations among distinct objects in an image, called the modeling space; the index array discards information, such as shape and size of objects, and irrelevant spatial relations. The construction of a symbolic spatial index from an input image can be thought of as a transformation that keeps only a set of representative points needed to define the relations of the modeling space. By keeping the relative arrangements of the representative points in symbolic spatial indexes and discarding all other points, we maintain enough information to answer queries regarding the spatial relations of the modeling space without the need to access the initial image or an object database. Symbolic spatial indexes can be used to solve problems involving route planning, composition of spatial relations, and update operations.

In this paper, we examine an orthogonal frequency division multiplexing (OFDM) system under imperfect channel conditions and pilot-insertion- based channel estimation. However, unlike conventional pilot-insertion-based channel estimation, some inserted pilot symbols are set to zero where the index of the zero-pilot symbols is employed to transmit extra data bits. In this paper, we employ a minimum mean squared error (MMSE) to detect transmitted pilot symbols; these symbols are then used to estimate channel coefficients. Furthermore, the impact of zero-pilot symbols on the mean-squared error of channel estimation and on system error performance is examined. Our findings show that the index of zero-pilot symbols can be used to improve system throughput by carrying extra information bits without harming channel estimation accuracy or degrading system error performance. Simulation results show that, at a high signal-to-noise ratio, the bit error rate for data bits transmitted via zero-pilot symbols index selection is lower than that of data bits transmitted over data subcarriers.

Index of Symbols

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