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Des procédures de classement sont largement utilisées pour décrire les phénomènes observés dans de nombreux domaines des sciences sociales et naturelles, par exemple la sociologie, l’économie, la linguistique, la démographie, la physique, la biologie, etc.Dans cette thèse, nous nous sommes attachés à l’étude des propriétés de classement et des dynamiques sous-jacentes intégrées dans les systèmes complexes. En particulier,nous nous sommes concentrés sur les classements par score ou par prix dans les systèmes sportifs et les classements d’utilisation des mots ou caractères dans les langues humaines. Le but est de comprendre les mécanismes sous-jacents à ces questions en utilisant les méthodes de la physique statistique, de la statistique bayésienne et de la modélisation multi-agents. Les résultats concrets concernent les aspects suivants.Nous avons tout d’abord traité une étude sur les classements par score/prix dans les systèmes sportifs et analysé 40 échantillons de données dans 12 disciplines sportives différentes. Nous avons trouvé des similitudes frappantes dans différents sports, à savoir le fait que la répartition des résultats/prix suit les lois puissance universelles.Nous avons également montré que le principe de Pareto est largement respecté dans de nombreux systèmes sociaux: ainsi 20% des joueurs accumulent 80% des scores et de l’argent. Les données concernant les matchs de tennis en individuels nous ont révélé que lorsque deux joueurs s’affrontent, la probabilité que le joueur de rang supérieur gagne est liée à la différence de rang des deux adversaires. Afin de comprendre les origines de la mise à l’échelle universelle, nous avons proposé un modèle multi-agents,qui peut simuler les matchs de joueurs à travers différentes compétitions. Les résultats de nos simulations sont cohérents avec les résultats empiriques. L’extension du domaine d’étude de la simulation indique que le modèle est assez robuste par rapport aux modifications de certains paramètres. La loi de Zipf est le comportement le plus régulièrement observé dans la linguistique statistique. Elle a dès lors servi de prototype pour les relations entre rang d’apparitions et fréquence d’apparitions (relations rang-fréquence dans la suite du texte) et les lois d’échelle dans les sciences naturelles. Nous avons étudié plusieurs textes, précisé le domaine de validité de la loi de Zipf, et trouvé que la plage de validité augmente lors du mélange de différents textes. Basé sur l’analyse sémantique latente, nous avons proposé un modèle probabiliste, dans lequel nous avons supposé que les mots sont ajoutés au texte avec des probabilités aléatoires, tandis que leur densité a priori est liée, via la statistique bayésienne, aux caractéristiques générales du lexique mental de l’auteur de ce même texte. Notre modèle explique la loi de Zipf ainsi que ses limites de validité, et la généralise aux hautes et basses fréquences et au hapax legomena.Dans une autre étude, nous avons précisé les relations rang-fréquence pour les caractères chinois. Nous avons choisi d’étudier des textes courts en premier, car pour le bien de l’analyse rang fréquence, les longs textes ne sont que des mélanges de textes plus courts, thématiquement homogènes. Nos résultats ont montré que la loi de Zipf appliqués aux caractères chinois tient parfaitement pour des textes assez courts (quelques milliers de caractères différents). Le même domaine de validité est observé pour les textes courts anglais. Nous avons soutenu que les longs textes chinois montrent une structure hiérarchique à deux couches: des caractères dont la fréquence d’apparition suit une loi puissance (première couche) et des caractères dont l’apparition suit une loi exponentielle (deuxième couche)... / Ranking procedures are widely used to describe the phenomena in many differentfields of social and natural sciences, e.g., sociology, economics, linguistics, demography,physics, biology, etc. In this dissertation, we dedicated to study the ranking propertiesand underlying dynamics embedded in complex systems. In particular, we focused onthe scores/prizes ranking in sports systems and the words/characters usage ranking inhuman languages. The aim is to understand the mechanisms behind these issues byusing the methods of statistical physics, Bayesian statistics and agent-based modeling.The concrete results concern the following aspects.We took up an interesting topic on the scores/prizes ranking in sports systems, andanalyzed 40 data samples in 12 different sports fields. We found the striking similaritiesin different sports, i.e., the distributions of scores/prizes follow the universal powerlaws. We also showed that the data yielded the Pareto principle extensively observedin many social systems: 20% of the players accumulate 80% of the scores and money.For the tennis head-to-head data, we revealed that when two players compete, theprobability that the higher-ranked player will win is related to the rank difference ofthe two opponents. In order to understand the origins of the universal scaling, weproposed an agent-based model, which can simulate the competitions of players indifferent matches, and results from our simulations are consistent with the empiricalfindings. Extensive simulation studies indicate that the model is quite robust withrespect to the modifications of some parameters.Zipf’s law is the major regularity of statistical linguistics that served as a prototypefor the rank-frequency relations and scaling laws in natural sciences. We investigatedseveral English texts, clarified the valid range of Zipf’s law, and found this valid rangeincreases upon mixing different texts. Based on the latent semantic analysis, we proposeda probabilistic model, in which we assumed that the words are drawn into thetext with random probabilities, while their apriori density relates, via Bayesian statistics,to the general features of mental lexicon of the author who produced the text. Ourmodel explained the Zipf’s law together with the limits of its validity, its generalizationto high and low frequencies and hapax legomena. In another work, we specified the rank-frequency relations for Chinese characters. We chose to study the short texts first, since for the sake of the rank-frequency analysis,long texts are just mixtures of shorter, thematically homogenous pieces. Our resultsshowed that the Zipf’s law for Chinese characters perfectly holds for sufficiently shorttexts (few thousand different characters), and the scenario of its validity is similar tothat for short English texts. We argued long Chinese texts display a two-layer, hierarchicstructure: power-law rank-frequency characters (first layer) and the exponentialones (second layer). The previous results on the invalidity of the Zipf’s law for longtexts are accounted for by showing that in between of the Zipfian range and the regionof very rare characters (hapax legomena) there emerges a range of ranks, wherethe rank-frequency relation is approximately exponential. From comparative analysisof rank-frequency relations for Chinese and English, we suggested the characters playfor Chinese writers the same role as the words for those writing within alphabeticalsystems.

Um eine Entscheidung zu treffen, muss Information interpretiert und in eine Handlung übersetzt werden. Dafür wird die a priori Wahrscheinlichkeit bezüglich der Entscheidungsalternativen in den Prozess der Entscheidungsfindung integriert und löst Mechanismen der Handlungsvorbereitung aus. In der vorliegenden Dissertation habe ich untersucht, welche Vorbereitungsprozesse aufgrund von wahrscheinlichkeitsbasierter Vorinformation stattfinden und welche Gehirnareale mit der Integration dieser Information assoziiert sind. Um diese Fragen zu beantworten, habe ich eine Verhaltensstudie, eine Studie mit Ableitung des Elektroenzephalogramms (EEG) und eine Studie mittels der funktionellen Magnetresonanztomographie (fMRT) mit simultaner Ableitung des EEGs durchgeführt. Die Versuchspersonen bearbeiteten währenddessen eine Zahlenvergleichsaufgabe mit einem Hinweisreiz, der Wahrscheinlichkeitsinformation bezüglich der erforderlichen Antwort enthielt. Die Reaktionszeit wurde durch die wahrscheinlichkeitsbasierte Vorinformation des Hinweisreizes parametrisch moduliert (Studie 1). Daraus lässt sich schlussfolgern, dass Vorbereitungsprozesse in Abhängigkeit der Wahrscheinlichkeitsinformation stattfinden. Die EEG Studie (Studie 2) ergab einen parametrischen Effekt von Wahrscheinlichkeitsinformation auf die Amplitude der Contingent Negative Variation (CNV), einer EEG-Komponente, die Vorbereitungsprozesse auf prämotorischer Ebene reflektiert. Darüber hinaus fand sich mittels einer Dipolquellenanalyse ein Dipol im anterioren Cingulum (ACC), dessen Aktivität ebenfalls durch die Wahrscheinlichkeitsinformation parametrisch moduliert war. Diese Ergebnisse lassen auf prämotorische Vorbereitungsprozesse aufgrund von Wahrscheinlichkeitsinformation schließen. In den fMRT-Ergebnissen zeigte sich eine parametrisch modulierte neuronale Aktivierung im posterioren Teil des medial-frontalen Kortex (pMFC), die auf eine Kontrollfunktion zur Handlungsanpassung dieses Areals zurückgeführt werden kann (Studie 3a). Um dynamische Fluktuationen der Wahrscheinlichkeitsverarbeitung zu untersuchen, wurde die CNV Amplitude der Einzeltrials in das Modell der fMRT-Analyse integriert (Studie 3b). Die CNV Amplitude korrelierte mit der neuronalen Aktivität in einem Netzwerk, bestehend aus frontalen, parietalen und striatalen Arealen, das mit allgemeiner wahrscheinlichkeitsunabhängiger Handlungsvorbereitung im Zusammenhang steht. Dagegen zeigten sich im dorsolateralen Präfrontalkortex (DLPFC), im inferioren frontalen Gyrus (IPG) und im inferioren Parietallappen (IPL) Aktivierungen, die sich auf die dynamische Integration von Wahrscheinlichkeitsinformation zurückführen lassen. / To prepare actions in advance, prior information about the probability of decision alternatives is integrated into the decision-making process. In the present dissertation, I investigated preparatory processes elicited by prior probability (PP) and the neural basis of PP processing. In three studies, I collected behavioral data and, furthermore, recorded electroencephalographic (EEG) data separately as well as simultaneously with functional magnetic resonance imaging (fMRI). While applying these methods, participants had to perform a number comparison task with a precue delivering PP about a subsequent response-demanding stimulus. The probability precue elicited the preparation of the response, as shown by the parametrical modulation of response time (RT) depending on PP (Study 1). The EEG study (Study 2) revealed a parametrical effect of PP on the contingent negative variation (CNV) during the foreperiod, which is an indicator for premotor response preparation. Furthermore, a dipole was located in the anterior cingulate cortex (ACC) with its activity parametrically modulated by PP. These EEG results suggest that PP influences premotor response preparation in a parametrical fashion. An analysis of fMRI data showed that neural activity in the posterior medial frontal cortex (pMFC) increased with increasing PP (Study 3a), which is attributed to a monitoring function of this region with respect to behavioral adjustment and initiation of response preparation depending on the PP. By applying an EEG-informed fMRI analysis (Study 3b), I focused on trial-to-trial fluctuations in PP processing and general response preparation as represented by the single-trial CNV amplitude. I found that the CNV amplitude was correlated with neural activity in a network consisting of frontal, parietal, and striatal regions reflecting general preparatory processes independently of PP. Parts of the network, namely, the dorsolateral prefrontal cortex (DLPFC), the inferior frontal gyrus (IFG), and the inferior parietal lobule (IPL), showed activations, which exclusively represented the contributions of PP to the CNV amplitude fluctuations. These results suggest that PP elicits premotor response preparation and activates the pMFC parametrically signaling the need for behavioral adjustment. In contrast, DLPFC, IFG, and IPL are involved in dynamically fluctuating PP processing mechanisms.

This thesis deals with an autonomous single-channel deinterleaving. An autonomous single-channel deinterleaving is a separation of the received sequence of impulses from more than one emitter to sequences of impulses from one emitter without a human assistance. Methods used for deinterleaving could be divided into single-parameter and multiple-parameter methods according to the number of parameters used for separation. This thesis primarily deals with multi-parameter methods. As appropriate methods for an autonomous single-channel deinterleaving DBSCAN and variational bayes methods were chosen. Selected methods were adjusted for deinterleaving and implemented in programming language Python. Their efficiency is examined on simulated and real data.

Smokeless powders are a set of energetic materials, known as low explosives, which are typically utilized for reloading ammunition. There are three types which differ in their primary energetic materials; where single base powders contain nitrocellulose as their primary energetic material, double and triple base powders contain nitroglycerin in addition to nitrocellulose, and triple base powders also contain nitroguanidine. Additional organic compounds, while not proprietary to specific manufacturers, are added to the powders in varied ratios during the manufacturing process to optimize the ballistic performance of the powders. The additional compounds function as stabilizers, plasticizers, flash suppressants, deterrents, and opacifiers. Of the three smokeless powder types, single and double base powders are commercially available, and have been heavily utilized in the manufacture of improvised explosive devices. Forensic smokeless powder samples are currently analyzed using multiple analytical techniques. Combined microscopic, macroscopic, and instrumental techniques are used to evaluate the sample, and the information obtained is used to generate a list of potential distributors. Gas chromatography – mass spectrometry (GC-MS) is arguably the most useful of the instrumental techniques since it distinguishes single and double base powders, and provides additional information about the relative ratios of all the analytes present in the sample. However, forensic smokeless powder samples are still limited to being classified as either single or double base powders, based on the absence or presence of nitroglycerin, respectively. In this work, the goal was to develop statistically valid classes, beyond the single and double base designations, based on multiple organic compounds which are commonly encountered in commercial smokeless powders. Several chemometric techniques were applied to smokeless powder GC-MS data for determination of the classes, and for assignment of test samples to these novel classes. The total ion spectrum (TIS), which is calculated from the GC-MS data for each sample, is obtained by summing the intensities for each mass-to-charge (m/z) ratio across the entire chromatographic profile. A TIS matrix comprising data for 726 smokeless powder samples was subject to agglomerative hierarchical cluster (AHC) analysis, and six distinct classes were identified. Within each class, a single m/z ratio had the highest intensity for the majority of samples, though the m/z ratio was not always unique to the specific class. Based on these observations, a new classification method known as the Intense Ion Rule (IIR) was developed and used for the assignment of test samples to the AHC designated classes. Discriminant models were developed for assignment of test samples to the AHC designated classes using k-Nearest Neighbors (kNN) and linear and quadratic discriminant analyses (LDA and QDA, respectively). Each of the models were optimized using leave-one-out (LOO) and leave-group-out (LGO) cross-validation, and the performance of the models was evaluated by calculating correct classification rates for assignment of the cross-validation (CV) samples to the AHC designated classes. The optimized models were utilized to assign test samples to the AHC designated classes. Overall, the QDA LGO model achieved the highest correct classification rates for assignment of both the CV samples and the test samples to the AHC designated classes. In forensic application, the goal of an explosives analyst is to ascertain the manufacturer of a smokeless powder sample. In addition, knowledge about the probability of a forensic sample being produced by a specific manufacturer could potentially decrease the time invested by an analyst during investigation by providing a shorter list of potential manufacturers. In this work, Bayes* Theorem and Bayesian Networks were investigated as an additional tool to be utilized in forensic casework. Bayesian Networks were generated and used to calculate posterior probabilities of a test sample belonging to specific manufacturers. The networks were designed to include manufacturer controlled powder characteristics such as shape, color, and dimension; as well as, the relative intensities of the class associated ions determined from cluster analysis. Samples were predicted to belong to a manufacturer based on the highest posterior probability. Overall percent correct rates were determined by calculating the percentage of correct predictions; that is, where the known and predicted manufacturer were the same. The initial overall percent correct rate was 66%. The dimensions of the smokeless powders were added to the network as average diameter and average length nodes. Addition of average diameter and length resulted in an overall prediction rate of 70%.

Behavioral operations management (BOM) has gained popularity in the last two decades. The main theme in this new stream of research is to include the human behavior in Operations Management (OM) models to increase the effectiveness of such models. BOM is classified into 4 areas: cognitive psychology, social psychology, group dynamics and system dynamics (Bendoly et al. 2010). This dissertation will focus on the first class, namely cognitive psychology. Cognitive psychology is further classified into heuristics and biases. Tversky and Kahneman (1974) discussed 3 heuristics and 13 cognitive biases that usually face decision makers. This dissertation is going to study 6 cognitive biases under the representativeness heuristic. The model in this dissertation states that cognitive reflection of the individual (Frederick 2005) and training about cognitive biases in the form of warning (Kaufmann and Michel 2009) will help decisions’ makers make less biased decisions. The 6 cognitive biases investigated in this dissertation are insensitivity to prior probability, insensitivity to sample size, misconception of chance, insensitivity to predictability, the illusion of validity and misconception of regression. 6 scenarios in OM contexts have been used in this study. Each scenario corresponds to one cognitive bias. Experimental design has been used as the research tool. To see the impact of training, one group of the participants received the scenarios without training and the other group received them with training. The training consists of a brief description of the cognitive bias as well as an example of the cognitive bias. Cognitive reflection is operationalized using cognitive reflection test (CRT). The survey was distributed to students at University of North Texas (UNT). Logistic regression has been employed to analyze data. The research shows that participants show the cognitive biases proposed by Tversky and Kahneman. Moreover, CRT is significant factor to predict the cognitive bias in two scenarios. Finally, providing training in terms of warning helps participants to make more rational decisions in 4 scenarios. This means that although cognitive biases are inherent in the mind of people, management of corporations has the tool to educate its managers and professionals about such biases which helps companies make more rational decisions.