From Intrusion Detection to an Intrusion Response System: Fundamentals, Requirements, and Future Directions*Algorithms* **2017**, *10*(2), 39; doi:10.3390/a10020039 - 27 March 2017**Abstract **

In the past few decades, the rise in attacks on communication devices in networks has resulted in a reduction of network functionality, throughput, and performance. To detect and mitigate these network attacks, researchers, academicians, and practitioners developed Intrusion Detection Systems (IDSs) with automatic

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In the past few decades, the rise in attacks on communication devices in networks has resulted in a reduction of network functionality, throughput, and performance. To detect and mitigate these network attacks, researchers, academicians, and practitioners developed Intrusion Detection Systems (IDSs) with automatic response systems. The response system is considered an important component of IDS, since without a timely response IDSs may not function properly in countering various attacks, especially on a real-time basis. To respond appropriately, IDSs should select the optimal response option according to the type of network attack. This research study provides a complete survey of IDSs and Intrusion Response Systems (IRSs) on the basis of our in-depth understanding of the response option for different types of network attacks. Knowledge of the path from IDS to IRS can assist network administrators and network staffs in understanding how to tackle different attacks with state-of-the-art technologies.
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DNA Paired Fragment Assembly Using Graph Theory*Algorithms* **2017**, *10*(2), 36; doi:10.3390/a10020036 - 24 March 2017**Abstract **

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DNA fragment assembly requirements have generated an important computational problem created by their structure and the volume of data. Therefore, it is important to develop algorithms able to produce high-quality information that use computer resources efficiently. Such an algorithm, using graph theory, is

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DNA fragment assembly requirements have generated an important computational problem created by their structure and the volume of data. Therefore, it is important to develop algorithms able to produce high-quality information that use computer resources efficiently. Such an algorithm, using graph theory, is introduced in the present article. We first determine the overlaps between DNA fragments, obtaining the edges of a directed graph; with this information, the next step is to construct an adjacency list with some particularities. Using the adjacency list, it is possible to obtain the DNA *contigs* (group of assembled fragments building a contiguous element) using graph theory. We performed a set of experiments on real DNA data and compared our results to those obtained with common assemblers (*Edena* and *Velvet*). Finally, we searched the *contigs* in the original genome, in our results and in those of *Edena* and *Velvet*.
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An Asynchronous Message-Passing Distributed Algorithm for the Generalized Local Critical Section Problem*Algorithms* **2017**, *10*(2), 38; doi:10.3390/a10020038 - 24 March 2017**Abstract **

This paper discusses the generalized local version of critical section problems including mutual exclusion, mutual inclusion, *k*-mutual exclusion and *l*-mutual inclusion. When a pair of numbers (*l*_{i}, *k*_{i}) is given for each process *P*_{i},

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This paper discusses the generalized local version of critical section problems including mutual exclusion, mutual inclusion, *k*-mutual exclusion and *l*-mutual inclusion. When a pair of numbers (*l*_{i}, *k*_{i}) is given for each process *P*_{i}, it is the problem of controlling the system in such a way that the number of processes that can execute their critical sections at a time is at least *l*_{i} and at most *k*_{i} among its neighboring processes and *P*_{i} itself. We propose the first solution for the generalized local (*l*_{i}, |*N*_{i}| + 1)-critical section problem (i.e., the generalized local *l*_{i}-mutual inclusion problem). Additionally, we show the relationship between the generalized local (*l*_{i}, *k*_{i})-critical section problem and the generalized local (|*N*_{i}| + 1 − *k*_{i}, |*N*_{i}| + 1 − *l*_{i})-critical section problem. Finally, we propose the first solution for the generalized local (*l*_{i}, *k*_{i})-critical section problem for arbitrary (*l*_{i}, *k*_{i}), where 0 ≤ *l*_{i} < *k*_{i} + |*N*_{i}_{}| + 1 for each process *P*_{i}_{}.
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A Spatial-Temporal-Semantic Neural Network Algorithm for Location Prediction on Moving Objects*Algorithms* **2017**, *10*(2), 37; doi:10.3390/a10020037 - 24 March 2017**Abstract **

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Location prediction has attracted much attention due to its important role in many location-based services, such as food delivery, taxi-service, real-time bus system, and advertisement posting. Traditional prediction methods often cluster track points into regions and mine movement patterns within the regions. Such

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Location prediction has attracted much attention due to its important role in many location-based services, such as food delivery, taxi-service, real-time bus system, and advertisement posting. Traditional prediction methods often cluster track points into regions and mine movement patterns within the regions. Such methods lose information of points along the road and cannot meet the demand of specific services. Moreover, traditional methods utilizing classic models may not perform well with long location sequences. In this paper, a spatial-temporal-semantic neural network algorithm (STS-LSTM) has been proposed, which includes two steps. First, the spatial-temporal-semantic feature extraction algorithm (STS) is used to convert the trajectory to location sequences with fixed and discrete points in the road networks. The method can take advantage of points along the road and can transform trajectory into model-friendly sequences. Then, a long short-term memory (LSTM)-based model is constructed to make further predictions, which can better deal with long location sequences. Experimental results on two real-world datasets show that STS-LSTM has stable and higher prediction accuracy over traditional feature extraction and model building methods, and the application scenarios of the algorithm are illustrated.
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A Geo-Clustering Approach for the Detection of Areas-of-Interest and Their Underlying Semantics*Algorithms* **2017**, *10*(1), 35; doi:10.3390/a10010035 - 18 March 2017**Abstract **

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Living in the “era of social networking”, we are experiencing a data revolution, generating an astonishing amount of digital information every single day. Due to this proliferation of data volume, there has been an explosion of new application domains for information mined from

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Living in the “era of social networking”, we are experiencing a data revolution, generating an astonishing amount of digital information every single day. Due to this proliferation of data volume, there has been an explosion of new application domains for information mined from social networks. In this paper, we leverage this “socially-generated knowledge” (i.e., user-generated content derived from social networks) towards the detection of areas-of-interest within an urban region. These large and homogeneous areas contain multiple points-of-interest which are of special interest to particular groups of people (e.g., tourists and/or consumers). In order to identify them, we exploit two types of metadata, namely *location-based information* included within geo-tagged photos that we collect from Flickr, along with plain *simple textual information* from user-generated tags. We propose an algorithm that divides a predefined geographical area (i.e., the center of Athens, Greece) into “tile”-shaped sub-regions and based on an iterative merging procedure, it aims to detect larger, cohesive areas. We examine the performance of the algorithm both in a qualitative and quantitative manner. Our experiments demonstrate that the proposed geo-clustering algorithm is able to correctly detect regions that contain popular tourist attractions within them with very promising results.
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A Novel, Gradient Boosting Framework for Sentiment Analysis in Languages where NLP Resources Are Not Plentiful: A Case Study for Modern Greek*Algorithms* **2017**, *10*(1), 34; doi:10.3390/a10010034 - 6 March 2017**Abstract **

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Sentiment analysis has played a primary role in text classification. It is an undoubted fact that some years ago, textual information was spreading in manageable rates; however, nowadays, such information has overcome even the most ambiguous expectations and constantly grows within seconds. It

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Sentiment analysis has played a primary role in text classification. It is an undoubted fact that some years ago, textual information was spreading in manageable rates; however, nowadays, such information has overcome even the most ambiguous expectations and constantly grows within seconds. It is therefore quite complex to cope with the vast amount of textual data particularly if we also take the incremental production speed into account. Social media, e-commerce, news articles, comments and opinions are broadcasted on a daily basis. A rational solution, in order to handle the abundance of data, would be to build automated information processing systems, for analyzing and extracting meaningful patterns from text. The present paper focuses on sentiment analysis applied in Greek texts. Thus far, there is no wide availability of natural language processing tools for Modern Greek. Hence, a thorough analysis of Greek, from the lexical to the syntactical level, is difficult to perform. This paper attempts a different approach, based on the proven capabilities of gradient boosting, a well-known technique for dealing with high-dimensional data. The main rationale is that since English has dominated the area of preprocessing tools and there are also quite reliable translation services, we could exploit them to transform Greek tokens into English, thus assuring the precision of the translation, since the translation of large texts is not always reliable and meaningful. The new feature set of English tokens is augmented with the original set of Greek, consequently producing a high dimensional dataset that poses certain difficulties for any traditional classifier. Accordingly, we apply gradient boosting machines, an ensemble algorithm that can learn with different loss functions providing the ability to work efficiently with high dimensional data. Moreover, for the task at hand, we deal with a class imbalance issues since the distribution of sentiments in real-world applications often displays issues of inequality. For example, in political forums or electronic discussions about immigration or religion, negative comments overwhelm the positive ones. The class imbalance problem was confronted using a hybrid technique that performs a variation of under-sampling the majority class and over-sampling the minority class, respectively. Experimental results, considering different settings, such as translation of tokens against translation of sentences, consideration of limited Greek text preprocessing and omission of the translation phase, demonstrated that the proposed gradient boosting framework can effectively cope with both high-dimensional and imbalanced datasets and performs significantly better than a plethora of traditional machine learning classification approaches in terms of precision and recall measures.
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Large Scale Implementations for Twitter Sentiment Classification*Algorithms* **2017**, *10*(1), 33; doi:10.3390/a10010033 - 4 March 2017**Abstract **

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Sentiment Analysis on Twitter Data is indeed a challenging problem due to the nature, diversity and volume of the data. People tend to express their feelings freely, which makes Twitter an ideal source for accumulating a vast amount of opinions towards a wide

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Sentiment Analysis on Twitter Data is indeed a challenging problem due to the nature, diversity and volume of the data. People tend to express their feelings freely, which makes Twitter an ideal source for accumulating a vast amount of opinions towards a wide spectrum of topics. This amount of information offers huge potential and can be harnessed to receive the sentiment tendency towards these topics. However, since no one can invest an infinite amount of time to read through these tweets, an automated decision making approach is necessary. Nevertheless, most existing solutions are limited in centralized environments only. Thus, they can only process at most a few thousand tweets. Such a sample is not representative in order to define the sentiment polarity towards a topic due to the massive number of tweets published daily. In this work, we develop two systems: the first in the MapReduce and the second in the Apache Spark framework for programming with Big Data. The algorithm exploits all hashtags and emoticons inside a tweet, as sentiment labels, and proceeds to a classification method of diverse sentiment types in a parallel and distributed manner. Moreover, the sentiment analysis tool is based on Machine Learning methodologies alongside Natural Language Processing techniques and utilizes Apache Spark’s Machine learning library, MLlib. In order to address the nature of Big Data, we introduce some pre-processing steps for achieving better results in Sentiment Analysis as well as Bloom filters to compact the storage size of intermediate data and boost the performance of our algorithm. Finally, the proposed system was trained and validated with real data crawled by Twitter, and, through an extensive experimental evaluation, we prove that our solution is efficient, robust and scalable while confirming the quality of our sentiment identification.
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A New Quintic Spline Method for Integro Interpolation and Its Error Analysis*Algorithms* **2017**, *10*(1), 32; doi:10.3390/a10010032 - 3 March 2017**Abstract **

In this paper, to overcome the innate drawbacks of some old methods, we present a new quintic spline method for integro interpolation. The method is free of any exact end conditions, and it can reconstruct a function and its first order to fifth

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In this paper, to overcome the innate drawbacks of some old methods, we present a new quintic spline method for integro interpolation. The method is free of any exact end conditions, and it can reconstruct a function and its first order to fifth order derivatives with high accuracy by only using the given integral values of the original function. The approximation properties of the obtained integro quintic spline are well studied and examined. The theoretical analysis and the numerical tests show that the new method is very effective for integro interpolation.
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Towards Efficient Positional Inverted Index †*Algorithms* **2017**, *10*(1), 30; doi:10.3390/a10010030 - 22 February 2017**Abstract **

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We address the problem of positional indexing in the natural language domain. The positional inverted index contains the information of the word positions. Thus, it is able to recover the original text file, which implies that it is not necessary to store the

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We address the problem of positional indexing in the natural language domain. The positional inverted index contains the information of the word positions. Thus, it is able to recover the original text file, which implies that it is not necessary to store the original file. Our *Positional Inverted Self-Index* (`PISI`) stores the word position gaps encoded by variable byte code. Inverted lists of single terms are combined into one inverted list that represents the backbone of the text file since it stores the sequence of the indexed words of the original file. The inverted list is synchronized with a presentation layer that stores separators, *stop words*, as well as variants of the indexed words. The Huffman coding is used to encode the presentation layer. The space complexity of the `PISI` inverted list is $\mathcal{O}((N-n)\lceil {log}_{{2}^{b}}N\rceil +(\lfloor \frac{N-n}{\alpha}\rfloor +n)\times (\lceil {log}_{{2}^{b}}n\rceil +1))$ where *N* is a number of stems, *n* is a number of unique stems, *α* is a step/period of the *back pointers* in the inverted list and *b* is the size of the word of computer memory given in bits. The space complexity of the presentation layer is $\mathcal{O}(-{\sum}_{i=1}^{N}\lceil {log}_{2}{p}_{i}^{n(i)}\rceil -{\sum}_{j=1}^{{N}^{\prime}}\lceil {log}_{2}{p}_{j}^{\prime}\rceil +N)$ with respect to ${p}_{i}^{n(i)}$ as a probability of a stem variant at position *i*, ${p}_{j}^{\prime}$ as the probability of separator or stop word at position *j* and ${N}^{\prime}$ as the number of separators and stop words.
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Optimization-Based Approaches to Control of Probabilistic Boolean Networks*Algorithms* **2017**, *10*(1), 31; doi:10.3390/a10010031 - 22 February 2017**Abstract **

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Control of gene regulatory networks is one of the fundamental topics in systems biology. In the last decade, control theory of Boolean networks (BNs), which is well known as a model of gene regulatory networks, has been widely studied. In this review paper,

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Control of gene regulatory networks is one of the fundamental topics in systems biology. In the last decade, control theory of Boolean networks (BNs), which is well known as a model of gene regulatory networks, has been widely studied. In this review paper, our previously proposed methods on optimal control of probabilistic Boolean networks (PBNs) are introduced. First, the outline of PBNs is explained. Next, an optimal control method using polynomial optimization is explained. The finite-time optimal control problem is reduced to a polynomial optimization problem. Furthermore, another finite-time optimal control problem, which can be reduced to an integer programming problem, is also explained.
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Mining Domain-Specific Design Patterns: A Case Study †*Algorithms* **2017**, *10*(1), 28; doi:10.3390/a10010028 - 21 February 2017**Abstract **

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Domain-specific design patterns provide developers with proven solutions to common design problems that arise, particularly in a target application domain, facilitating them to produce quality designs in the domain contexts. However, research in this area is not mature and there are no techniques

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Domain-specific design patterns provide developers with proven solutions to common design problems that arise, particularly in a target application domain, facilitating them to produce quality designs in the domain contexts. However, research in this area is not mature and there are no techniques to support their detection. Towards this end, we propose a methodology which, when applied on a collection of websites in a specific domain, facilitates the automated identification of domain-specific design patterns. The methodology automatically extracts the conceptual models of the websites, which are subsequently analyzed in terms of all of the reusable design fragments used in them for supporting common domain functionalities. At the conceptual level, we consider these fragments as recurrent patterns consisting of a configuration of front-end interface components that interrelate each other and interact with end-users to support certain functionality. By performing a pattern-based analysis of the models, we locate the occurrences of all the recurrent patterns in the various website designs which are then evaluated towards their consistent use. The detected patterns can be used as building blocks in future designs, assisting developers to produce consistent and quality designs in the target domain. To support our case, we present a case study for the educational domain.
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Stable Analysis of Compressive Principal Component Pursuit*Algorithms* **2017**, *10*(1), 29; doi:10.3390/a10010029 - 21 February 2017**Abstract **

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Compressive principal component pursuit (CPCP) recovers a target matrix that is a superposition of low-complexity structures from a small set of linear measurements. Pervious works mainly focus on the analysis of the existence and uniqueness. In this paper, we address its stability. We

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Compressive principal component pursuit (CPCP) recovers a target matrix that is a superposition of low-complexity structures from a small set of linear measurements. Pervious works mainly focus on the analysis of the existence and uniqueness. In this paper, we address its stability. We prove that the solution to the related convex programming of CPCP gives an estimate that is stable to small entry-wise noise. We also provide numerical simulation results to support our result. Numerical results show that the solution to the related convex program is stable to small entry-wise noise under board condition.
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Analysis and Improvement of Fireworks Algorithm*Algorithms* **2017**, *10*(1), 26; doi:10.3390/a10010026 - 17 February 2017**Abstract **

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The Fireworks Algorithm is a recently developed swarm intelligence algorithm to simulate the explosion process of fireworks. Based on the analysis of each operator of Fireworks Algorithm (FWA), this paper improves the FWA and proves that the improved algorithm converges to the global

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The Fireworks Algorithm is a recently developed swarm intelligence algorithm to simulate the explosion process of fireworks. Based on the analysis of each operator of Fireworks Algorithm (FWA), this paper improves the FWA and proves that the improved algorithm converges to the global optimal solution with probability 1. The proposed algorithm improves the goal of further boosting performance and achieving global optimization where mainly include the following strategies. Firstly using the opposition-based learning initialization population. Secondly a new explosion amplitude mechanism for the optimal firework is proposed. In addition, the adaptive t-distribution mutation for non-optimal individuals and elite opposition-based learning for the optimal individual are used. Finally, a new selection strategy, namely Disruptive Selection, is proposed to reduce the running time of the algorithm compared with FWA. In our simulation, we apply the CEC2013 standard functions and compare the proposed algorithm (IFWA) with SPSO2011, FWA, EFWA and dynFWA. The results show that the proposed algorithm has better overall performance on the test functions.
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Fragile Watermarking for Image Authentication Using the Characteristic of SVD*Algorithms* **2017**, *10*(1), 27; doi:10.3390/a10010027 - 17 February 2017**Abstract **

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Digital image authentication has become a hot topic in the last few years. In this paper, a pixel-based fragile watermarking method is presented for image tamper identification and localization. By analyzing the left and right singular matrices of SVD, it is found that

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Digital image authentication has become a hot topic in the last few years. In this paper, a pixel-based fragile watermarking method is presented for image tamper identification and localization. By analyzing the left and right singular matrices of SVD, it is found that the matrix product between the first column of the left singular matrix and the transposition of the first column in the right singular matrix is closely related to the image texture features. Based on this characteristic, a binary watermark consisting of image texture information is generated and inserted into the least significant bit (LSB) of the original host image. To improve the security of the presented algorithm, the Arnold transform is applied twice in the watermark embedding process. Experimental results indicate that the proposed watermarking algorithm has high security and perceptual invisibility. Moreover, it can detect and locate the tampered region effectively for various malicious attacks.
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An On-Line Tracker for a Stochastic Chaotic System Using Observer/Kalman Filter Identification Combined with Digital Redesign Method*Algorithms* **2017**, *10*(1), 25; doi:10.3390/a10010025 - 15 February 2017**Abstract **

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This is the first paper to present such a digital redesign method for the (conventional) OKID system and apply this novel technique for nonlinear system identification. First, the Observer/Kalman filter Identification (OKID) method is used to obtain the lower-order state-space model for a

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This is the first paper to present such a digital redesign method for the (conventional) OKID system and apply this novel technique for nonlinear system identification. First, the Observer/Kalman filter Identification (OKID) method is used to obtain the lower-order state-space model for a stochastic chaos system. Then, a digital redesign approach with the high-gain property is applied to improve and replace the observer identified by OKID. Therefore, the proposed OKID combined with an observer-based digital redesign novel tracker not only suppresses the uncertainties and the nonlinear perturbations, but also improves more accurate observation parameters of OKID for complex Multi-Input Multi-Output systems. In this research, Chen’s stochastic chaotic system is used as an illustrative example to demonstrate the effectiveness and excellence of the proposed methodology.
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Problems on Finite Automata and the Exponential Time Hypothesis*Algorithms* **2017**, *10*(1), 24; doi:10.3390/a10010024 - 5 February 2017**Abstract **

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We study several classical decision problems on finite automata under the (Strong) Exponential Time Hypothesis. We focus on three types of problems: universality, equivalence, and emptiness of intersection. All these problems are known to be CoNP-hard for nondeterministic finite automata, even when restricted

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We study several classical decision problems on finite automata under the (Strong) Exponential Time Hypothesis. We focus on three types of problems: universality, equivalence, and emptiness of intersection. All these problems are known to be CoNP-hard for nondeterministic finite automata, even when restricted to unary input alphabets. A different type of problems on finite automata relates to aperiodicity and to synchronizing words. We also consider finite automata that work on commutative alphabets and those working on two-dimensional words.
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An Architectural Based Framework for the Distributed Collection, Analysis and Query from Inhomogeneous Time Series Data Sets and Wearables for Biofeedback Applications*Algorithms* **2017**, *10*(1), 23; doi:10.3390/a10010023 - 1 February 2017**Abstract **

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The increasing professionalism of sports persons and desire of consumers to imitate this has led to an increased metrification of sport. This has been driven in no small part by the widespread availability of comparatively cheap assessment technologies and, more recently, wearable technologies.

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The increasing professionalism of sports persons and desire of consumers to imitate this has led to an increased metrification of sport. This has been driven in no small part by the widespread availability of comparatively cheap assessment technologies and, more recently, wearable technologies. Historically, whilst these have produced large data sets, often only the most rudimentary analysis has taken place (Wisbey et al in: “Quantifying movement demands of AFL football using GPS tracking”). This paucity of analysis is due in no small part to the challenges of analysing large sets of data that are often from disparate data sources to glean useful key performance indicators, which has been a largely a labour intensive process. This paper presents a framework that can be cloud based for the gathering, storing and algorithmic interpretation of large and inhomogeneous time series data sets. The framework is architecture based and technology agnostic in the data sources it can gather, and presents a model for multi set analysis for inter- and intra- devices and individual subject matter. A sample implementation demonstrates the utility of the framework for sports performance data collected from distributed inertial sensors in the sport of swimming.
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Evaluation of Diversification Techniques for Legal Information Retrieval*Algorithms* **2017**, *10*(1), 22; doi:10.3390/a10010022 - 29 January 2017**Abstract **

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“Public legal information from all countries and international institutions is part of the common heritage of humanity. Maximizing access to this information promotes justice and the rule of law”. In accordance with the aforementioned declaration on free access to law by legal information

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“Public legal information from all countries and international institutions is part of the common heritage of humanity. Maximizing access to this information promotes justice and the rule of law”. In accordance with the aforementioned declaration on free access to law by legal information institutes of the world, a plethora of legal information is available through the Internet, while the provision of legal information has never before been easier. Given that law is accessed by a much wider group of people, the majority of whom are not legally trained or qualified, diversification techniques should be employed in the context of legal information retrieval, as to increase user satisfaction. We address the diversification of results in legal search by adopting several state of the art methods from the web search, network analysis and text summarization domains. We provide an exhaustive evaluation of the methods, using a standard dataset from the common law domain that we objectively annotated with relevance judgments for this purpose. Our results: (i) reveal that users receive broader insights across the results they get from a legal information retrieval system; (ii) demonstrate that web search diversification techniques outperform other approaches (e.g., summarization-based, graph-based methods) in the context of legal diversification; and (iii) offer balance boundaries between reinforcing relevant documents or sampling the information space around the legal query.
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Concurrent vs. Exclusive Reading in Parallel Decoding of LZ-Compressed Files*Algorithms* **2017**, *10*(1), 21; doi:10.3390/a10010021 - 28 January 2017**Abstract **

Broadcasting a message from one to many processors in a network corresponds to concurrent reading on a random access shared memory parallel machine. Computing the trees of a forest, the level of each node in its tree and the path between two nodes

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Broadcasting a message from one to many processors in a network corresponds to concurrent reading on a random access shared memory parallel machine. Computing the trees of a forest, the level of each node in its tree and the path between two nodes are problems that can easily be solved with concurrent reading in a time logarithmic in the maximum height of a tree. Solving such problems with exclusive reading requires a time logarithmic in the number of nodes, implying message passing between disjoint pairs of processors on a distributed system. Allowing concurrent reading in parallel algorithm design for distributed computing might be advantageous in practice if these problems are faced on shallow trees with some specific constraints. We show an application to LZC (Lempel-Ziv-Compress)-compressed file decoding, whose parallelization employs these computations on such trees for realistic data. On the other hand, zipped files do not have this advantage, since they are compressed by the Lempel–Ziv sliding window technique.
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Computing a Clique Tree with the Algorithm Maximal Label Search*Algorithms* **2017**, *10*(1), 20; doi:10.3390/a10010020 - 25 January 2017**Abstract **

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The algorithm MLS (Maximal Label Search) is a graph search algorithm that generalizes the algorithms Maximum Cardinality Search (MCS), Lexicographic Breadth-First Search (LexBFS), Lexicographic Depth-First Search (LexDFS) and Maximal Neighborhood Search (MNS). On a chordal graph, MLS computes a PEO (perfect elimination ordering)

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The algorithm MLS (Maximal Label Search) is a graph search algorithm that generalizes the algorithms Maximum Cardinality Search (MCS), Lexicographic Breadth-First Search (LexBFS), Lexicographic Depth-First Search (LexDFS) and Maximal Neighborhood Search (MNS). On a chordal graph, MLS computes a PEO (perfect elimination ordering) of the graph. We show how the algorithm MLS can be modified to compute a PMO (perfect moplex ordering), as well as a clique tree and the minimal separators of a chordal graph. We give a necessary and sufficient condition on the labeling structure of MLS for the beginning of a new clique in the clique tree to be detected by a condition on labels. MLS is also used to compute a clique tree of the complement graph, and new cliques in the complement graph can be detected by a condition on labels for any labeling structure. We provide a linear time algorithm computing a PMO and the corresponding generators of the maximal cliques and minimal separators of the complement graph. On a non-chordal graph, the algorithm MLSM, a graph search algorithm computing an MEO and a minimal triangulation of the graph, is used to compute an atom tree of the clique minimal separator decomposition of any graph.
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