Experiências armazenadas acerca de regularidades passadas permitem a previsão do ambiente e, consequentemente, a possibilidade de ações antecipadas. Esta capacidade cognitiva é expressa em modelos de aprendizagem de sequências, que são capazes de acessar a previsibilidade das sequências de eventos e gerar descrições do desempenho em protocolos experimentais como a tarefa de tempo de reação serial. Nos experimentos 1, 2 e 3 deste trabalho, a abordagem informacional foi aplicada à descrição do desempenho na tarefa de tempo de reação serial. A relação entre medidas de entropia e desempenho na tarefa de tempo de reação serial envolvendo diferentes tipos de sequência foi investigada nos Experimentos 1a e 1b. As medidas de entropia foram feitas pelo processamento das frequências de eventos das sequências (i.e., pares, trios, quadras etc). Os resultados revelaram que a entropia informacional das sequências é um bom descritor do desempenho: (1) sequências de baixa entropia são realizadas mais rapidamente e são mais frequentemente reconhecidas ao final da sessão do que as de alta entropia; (2) uma curva sigmóide relaciona valores de entropia aos de tempo de reação: parâmetros \"min\" (tempo de reação com a previsão total), \"max\" (tempo de reação sem previsão) e \"x50\" (valor de entropia relacionada ao limiar de previsão); (3) o treinamento torna previsíveis sequências de alta entropia (o \"x50\" aumenta com o treinamento); e (4) com o treinamento, mais elementos prévios da sequência passam a ser utilizados para a previsão do próximo elemento. A relação entre desempenho e expectativas probabilísticas geradas durante o treinamento foi investigada no Experimento 2. Esse experimento envolveu múltiplas combinações de sequências de treino e teste, aplicadas a voluntários em sessões únicas. A diferença entre as previsibilidades das sequências de teste e treino foi quantificada pela distância de Kullback-Leibler: pequenas distâncias indicam que o treino proporciona boa previsão sobre o teste. Desconsiderando os efeitos de entropia (descrito no Experimento 1), a distância de Kullback-Leibler entre as sequências de teste e treino está relacionada ao desempenho: (1) distâncias pequenas levam à manutenção das expectativas (prévias) e tempos de reação curtos; (2) distâncias grandes levam à negligência das previsões e tempos de reação intermediários; e (3) distâncias intermediárias estão relacionadas a um conflito entre as estratégias de manutenção e negligência das expectativas, e geram tempos de reação elevados. Portanto, a flexibilidade das previsões ocorre em distâncias pequenas; uma estratégia alternativa, de negligência das previsões, é adotada em distâncias grandes. A estratégia desenvolvida nos Experimentos 1a e 1b foi útil para avaliar, no Experimento 3, a equivalência funcional entre treinamento imaginativo e real na aprendizagem de sequências. Este experimento envolveu voluntários testados na tarefa de tempo de reação serial ao longo de várias sessões de treinamento imaginativo e real. Os desempenhos durante o treinamento imaginativo e real foram descritos e comparados; o experimento mostrou também que a previsibilidade da sequência acessada por meio do treinamento imaginativo pode ser expressa posteriormente no desempenho real da tarefa. No entanto, o limite de previsibilidade das sequências acessado pelo treinamento imaginativo é inferior ao limite acessado por treinamento real, descrita pelo menor \"x50\" do (1) treinamento imaginativo em relação ao treinamento real e (2) desempenho real após o treinamento imaginativo em relação ao desempenho real após o treinamento real. Em conclusão, é possível afirmar que o modelo de entropia informacional é capaz de descrever a variabilidade do desempenho na tarefa de tempo de reação serial. Estes achados apóiam a existência de um princípio geral de acesso à previsibilidade para explicação da aprendizagem e memória. / Stored experiences of past regularities allow the prediction of the environment and, consequently, the possibility of anticipatory actions. This cognitive capacity is expressed in models of sequence learning, which are able to access the predictability of sequences of events and to generate descriptions of performance on experimental protocols as serial reaction time task. In Experiments 1, 2 and 3 of this work the informational framework was applied to the description of performance in serial reaction time task. The relationship between entropy measures and performance on serial reaction time task involving multiple sequence types was investigated on Experiments 1a and 1b. The entropy measures were done by processing the frequencies of events of the sequences (i.e. pairs, triads, quads etc). The results revealed that information entropy of the sequences is an impressively good descriptor of performance: (1) low entropy sequences were performed more rapidly and were more frequently recognized in the end of the session than the high entropy ones; (2) a sigmoid curve relates entropy to reaction time: parameters \"min\" (reaction time with total prediction), \"max\" (reaction time with no prediction) and \"x50\" (entropy value related to threshold of prediction); (3) training makes high entropy sequences predictable (the \"x50\" increases with training); and (4) with training, more previous elements of sequence are used for prediction of the next one. The relationship between performance and probabilistic expectancies generated during training was investigated on Experiment 2. This experiment involved multiple arrangements of training and testing sequences, applied to volunteers on single sessions. The difference between the predictabilities of testing and training sequences was quantified by the Kullback-Leibler divergence: small divergence indicates that training provides good prediction on testing. Disregarding the entropy effects (described on Experiment 1), Kullback-Leibler divergence between training and testing sequences is related to performance: (1) short divergences lead to (previous) predictions maintenance and low reaction times; (2) large divergences lead to predictions negligence and intermediate reaction times; and (3) intermediate divergences are related to conflict between the strategies of maintenance and negligence of predictions, and generate high reaction times. Therefore, the flexibility of predictions occurs on short divergences; an alternative strategy, of predictions negligence, is adopted on large divergences. The strategy developed on Experiments 1a and 1b was useful to evaluate, on Experiment 3, the functional equivalence between imagery and actual training on sequence learning. This experiment involved volunteers tested on serial reaction time task along multiple imagery and actual training sessions. Performances on both imagery and actual training were described and compared; the experiment also showed that the sequence predictability accessed on imagery training can be expressed on posterior actual performance. However, the limit of sequence predictability accessed by imagery training is lower than the limit accessed by actual training, described by the lower \"x50\" of (1) imagery training compared to actual training and (2) actual performance after imagery training compared to actual performance after actual training. In conclusion, it is possible to state that the entropy model is able to describe the variability of performance on serial reaction time task. These findings support the existence of a general principle of accessing the predictability to explain learning and memory.

<p>This thesis consists of four papers on the following topics in analysis and probability: analysis on Wiener space, asymptotic properties of orthogonal polynomials, and convergence rates in the central limit theorem. The first paper gives lower bounds on the constants in the Meyer inequality from the Malliavin calculus. It is shown that both constants grow at least like <i>(p-1)</i>^-1 or like <i>p</i> when <i>p</i> approaches 1 or ∞ respectively. This agrees with known upper bounds. In the second paper, an extremal problem on Wiener chaos motivates an investigation of the <i>L</i>^p-norms of Hermite polynomials. This is followed up by similar computations for Charlier polynomials in the third paper. In both cases, the <i>L</i>^p-norms present a peculiar behaviour with certain threshold values of p, where the growth rate and the dominating intervals undergo a rapid change. The fourth paper analyzes a connection between probability and numerical analysis. More precisely, known estimates on the convergence rate of finite difference equations are "translated" into results on convergence rates of certain functionals in the central limit theorem. These are also extended, using interpolation of Banach spaces as a main tool. Besov spaces play a central role in the emerging results.</p>

This thesis consists of four papers on the following topics in analysis and probability: analysis on Wiener space, asymptotic properties of orthogonal polynomials, and convergence rates in the central limit theorem. The first paper gives lower bounds on the constants in the Meyer inequality from the Malliavin calculus. It is shown that both constants grow at least like (p-1)-1 or like p when p approaches 1 or ∞ respectively. This agrees with known upper bounds. In the second paper, an extremal problem on Wiener chaos motivates an investigation of the Lp-norms of Hermite polynomials. This is followed up by similar computations for Charlier polynomials in the third paper. In both cases, the Lp-norms present a peculiar behaviour with certain threshold values of p, where the growth rate and the dominating intervals undergo a rapid change. The fourth paper analyzes a connection between probability and numerical analysis. More precisely, known estimates on the convergence rate of finite difference equations are "translated" into results on convergence rates of certain functionals in the central limit theorem. These are also extended, using interpolation of Banach spaces as a main tool. Besov spaces play a central role in the emerging results.

Experiências armazenadas acerca de regularidades passadas permitem a previsão do ambiente e, consequentemente, a possibilidade de ações antecipadas. Esta capacidade cognitiva é expressa em modelos de aprendizagem de sequências, que são capazes de acessar a previsibilidade das sequências de eventos e gerar descrições do desempenho em protocolos experimentais como a tarefa de tempo de reação serial. Nos experimentos 1, 2 e 3 deste trabalho, a abordagem informacional foi aplicada à descrição do desempenho na tarefa de tempo de reação serial. A relação entre medidas de entropia e desempenho na tarefa de tempo de reação serial envolvendo diferentes tipos de sequência foi investigada nos Experimentos 1a e 1b. As medidas de entropia foram feitas pelo processamento das frequências de eventos das sequências (i.e., pares, trios, quadras etc). Os resultados revelaram que a entropia informacional das sequências é um bom descritor do desempenho: (1) sequências de baixa entropia são realizadas mais rapidamente e são mais frequentemente reconhecidas ao final da sessão do que as de alta entropia; (2) uma curva sigmóide relaciona valores de entropia aos de tempo de reação: parâmetros \"min\" (tempo de reação com a previsão total), \"max\" (tempo de reação sem previsão) e \"x50\" (valor de entropia relacionada ao limiar de previsão); (3) o treinamento torna previsíveis sequências de alta entropia (o \"x50\" aumenta com o treinamento); e (4) com o treinamento, mais elementos prévios da sequência passam a ser utilizados para a previsão do próximo elemento. A relação entre desempenho e expectativas probabilísticas geradas durante o treinamento foi investigada no Experimento 2. Esse experimento envolveu múltiplas combinações de sequências de treino e teste, aplicadas a voluntários em sessões únicas. A diferença entre as previsibilidades das sequências de teste e treino foi quantificada pela distância de Kullback-Leibler: pequenas distâncias indicam que o treino proporciona boa previsão sobre o teste. Desconsiderando os efeitos de entropia (descrito no Experimento 1), a distância de Kullback-Leibler entre as sequências de teste e treino está relacionada ao desempenho: (1) distâncias pequenas levam à manutenção das expectativas (prévias) e tempos de reação curtos; (2) distâncias grandes levam à negligência das previsões e tempos de reação intermediários; e (3) distâncias intermediárias estão relacionadas a um conflito entre as estratégias de manutenção e negligência das expectativas, e geram tempos de reação elevados. Portanto, a flexibilidade das previsões ocorre em distâncias pequenas; uma estratégia alternativa, de negligência das previsões, é adotada em distâncias grandes. A estratégia desenvolvida nos Experimentos 1a e 1b foi útil para avaliar, no Experimento 3, a equivalência funcional entre treinamento imaginativo e real na aprendizagem de sequências. Este experimento envolveu voluntários testados na tarefa de tempo de reação serial ao longo de várias sessões de treinamento imaginativo e real. Os desempenhos durante o treinamento imaginativo e real foram descritos e comparados; o experimento mostrou também que a previsibilidade da sequência acessada por meio do treinamento imaginativo pode ser expressa posteriormente no desempenho real da tarefa. No entanto, o limite de previsibilidade das sequências acessado pelo treinamento imaginativo é inferior ao limite acessado por treinamento real, descrita pelo menor \"x50\" do (1) treinamento imaginativo em relação ao treinamento real e (2) desempenho real após o treinamento imaginativo em relação ao desempenho real após o treinamento real. Em conclusão, é possível afirmar que o modelo de entropia informacional é capaz de descrever a variabilidade do desempenho na tarefa de tempo de reação serial. Estes achados apóiam a existência de um princípio geral de acesso à previsibilidade para explicação da aprendizagem e memória. / Stored experiences of past regularities allow the prediction of the environment and, consequently, the possibility of anticipatory actions. This cognitive capacity is expressed in models of sequence learning, which are able to access the predictability of sequences of events and to generate descriptions of performance on experimental protocols as serial reaction time task. In Experiments 1, 2 and 3 of this work the informational framework was applied to the description of performance in serial reaction time task. The relationship between entropy measures and performance on serial reaction time task involving multiple sequence types was investigated on Experiments 1a and 1b. The entropy measures were done by processing the frequencies of events of the sequences (i.e. pairs, triads, quads etc). The results revealed that information entropy of the sequences is an impressively good descriptor of performance: (1) low entropy sequences were performed more rapidly and were more frequently recognized in the end of the session than the high entropy ones; (2) a sigmoid curve relates entropy to reaction time: parameters \"min\" (reaction time with total prediction), \"max\" (reaction time with no prediction) and \"x50\" (entropy value related to threshold of prediction); (3) training makes high entropy sequences predictable (the \"x50\" increases with training); and (4) with training, more previous elements of sequence are used for prediction of the next one. The relationship between performance and probabilistic expectancies generated during training was investigated on Experiment 2. This experiment involved multiple arrangements of training and testing sequences, applied to volunteers on single sessions. The difference between the predictabilities of testing and training sequences was quantified by the Kullback-Leibler divergence: small divergence indicates that training provides good prediction on testing. Disregarding the entropy effects (described on Experiment 1), Kullback-Leibler divergence between training and testing sequences is related to performance: (1) short divergences lead to (previous) predictions maintenance and low reaction times; (2) large divergences lead to predictions negligence and intermediate reaction times; and (3) intermediate divergences are related to conflict between the strategies of maintenance and negligence of predictions, and generate high reaction times. Therefore, the flexibility of predictions occurs on short divergences; an alternative strategy, of predictions negligence, is adopted on large divergences. The strategy developed on Experiments 1a and 1b was useful to evaluate, on Experiment 3, the functional equivalence between imagery and actual training on sequence learning. This experiment involved volunteers tested on serial reaction time task along multiple imagery and actual training sessions. Performances on both imagery and actual training were described and compared; the experiment also showed that the sequence predictability accessed on imagery training can be expressed on posterior actual performance. However, the limit of sequence predictability accessed by imagery training is lower than the limit accessed by actual training, described by the lower \"x50\" of (1) imagery training compared to actual training and (2) actual performance after imagery training compared to actual performance after actual training. In conclusion, it is possible to state that the entropy model is able to describe the variability of performance on serial reaction time task. These findings support the existence of a general principle of accessing the predictability to explain learning and memory.

The aim of this study is to evaluate whether the ‘richness’ of the marking on personal names is an adequate indirect measure of a language’s case usage. The method uses parallel texts to identify, and group by lemma, names in over a thousand languages. These groupings are compared with data for case usage from a typological database for those languages for which it is available. This material is then used to test a method for assessing whether a language uses case or not. Results indicate that the maximum number of word types a proprial lemma is attested with in a text is a useful tool for inferring case usage. However, it only yielded clear results for a subset of the languages tested. It was not particularly useful for inferring the absence of case usage. Estimation of number of case categories was also performed. An entropy measure based on word types that a personal name lemma is attested with and the occurrences of these word types was used. It was found to be a fair indicator of number of case categories for languages, if somewhat inaccurate. Markings on languages which had no case were investigated. They were found to be of several types: pragmatic markers, non-case grammatical markers and case-like markers. Two languages with few markings on personal names and with case were investigated. They were found to not use any case marking on their personal names, but still use such markers on common nouns. This contrasts with a tentative generalization that this study is based on: ‘No languages have case marking exclusively in the domain of [personal names] or [common nouns].’ (Handschuh, 2017). / Denna studies syfte är att utvärdera om ’formrikedomen’ hos personnamnslexem är ett fungerande indirekt sätt att undersöka språks kasussystem. Parallella texter användes för att namnen hitta personnamn och gruppera dem efter lexem i över ett tusen språk. För den delmängd av språken där data om deras kasussystem fanns tillgänglig så jämfördes denna med grupperingarna. Resultaten indikerar att det maximala antalet ordformstyper som ett namnlemma observerades i är ett användbart verktyg för att hitta språk som använder kasus, men bara för en delmängd av testade språk. Det var däremot sämre på att hitta språk som inte använder kasus. En entropiuppskattning som var baserat på antalet ordformstyper ett personnamnslemma hittades med och antalet förekomster av dessa ordformstyper användes. Det var en okej indikator för antalet kasuskategorier, dock med något bristande träffsäkerhet. Personnamnsmarkeringar på språk utan kasus undersöktes. De funna typerna av markeringar var pragmatiska, kasuslika, och grammatiska icke-kasus. Två språk med kasus, men med få personnamns, undersöktes. De använder inte kasusmarkering på personnamn, men på sina substantiv, vilket bröt mot en hypotetisk generalisering som denna studie baserades på: Att inga språk har kasusmarkeringar endast på personnamn eller endast på substantiv.

Yes / This paper investigates the interaction phenomena of the coupled axons while the mutual coupling factor is presented as a pairwise description. Based on the Hodgkin-Huxley model and the coupling factor matrix, the membrane potentials of the coupled myelinated/unmyelinated axons are quantified which implies that the neural coupling can be characterised by the presented coupling factor. Meanwhile the equivalent electric circuit is supplied to illustrate the physical meaning of this extended model. In order to estimate the coupling factor, a data-based iterative learning identification algorithm is presented where the Rényi entropy of the estimation error has been minimised. The convergence of the presented algorithm is analysed and the learning rate is designed. To verified the presented model and the algorithm, the numerical simulation results indicate the correctness and the effectiveness. Furthermore, the statistical description of the neural coupling, the approximation using ordinary differential equation, the measurement and the conduction of the nerve signals are discussed respectively as advanced topics. The novelties can be summarised as follows: 1) the Hodgkin-Huxley model has been extended considering the mutual interaction between the neural axon membranes, 2) the iterative learning approach has been developed for factor identification using entropy criterion, and 3) the theoretical framework has been established for this class of system identification problems with convergence analysis. / This work was supported in part by the National Natural Science Foundation of China (NSFC) under Grant 51807010, and in part by the Natural Science Foundation of Hunan under Grant 1541 and Grant 1734. / Research Development Fund Publication Prize Award winner, Nov 2020.

<p>Earth’s ecosystems emerge from interconnected biosphere, geosphere, and atmosphere processes. Changes to any one process ripple through the Earth system, affecting other processes. As global climate change continues, nitrogen deposition is anticipated to increase and precipitation is expected to have varied changes across the globe. These changes to the atmosphere and geosphere will have implications for the biosphere. Namely, vegetation will be impacted by changes to nutrient and precipitation regimes. Vegetation comprises the aggregate strategies of individual plants, which are also influenced by changes in nutrient and water availability. The responses of individual plants to nitrogen, water, and uncertainty are the main focus of this dissertation, as understanding those will be critical to scaling up to the aggregate.</p> <p> First, I describe a mathematical model that predicts grassland root and shoot biomass across carbon, nitrogen, and water gradients. The model simulates competition among plants by dynamically allocating carbon to either root or shoot growth depending on the growth strategy employed by the other plant. I show that the model accurately predicts root net primary productivity (NPP), but performs poorly for shoot and total NPP. At the biome scale, modeled NPP does not vary with water alone but rather water and nitrogen interact to influence NPP. Second, I conduct a greenhouse experiment using <em>Eragrostis capillaris</em> (L.) Nees to examine the predictions of the model mentioned above to answer the question: how do water and nitrogen affect fitness and biomass allocation in a drought-tolerant C4 grass? And ask: what is the nature of the relationship between water and nitrogen as resources? I show that water was important for increasing shoot and total biomass, but that root biomass and root:shoot ratio was influenced interactively by water and nitrogen as predicted by the model. I conclude that the nature of the relationship between water and nitrogen was that of either interacting or hemi-essential resources. That is, additional water was able to partially substitute for limited nitrogen to maintain biomass. Third, I explore how information theory can apply to plants that face uncertainty in resource availability and briefly review the types and sources of information and the mechanisms that plants use to perceive and respond to their environment. Overall, my framework posits that plants interpret information from their surroundings as an emergent property of distributed information processed by a network of cells. I end with a prospectus of directions for future research, including decoding signal from noise, storage of information, strategies to cope with information entropy, additional means of information transmission, and two-way information signaling with biotic partners. Finally, I use the information theory framework discussed above to answer the questions: can plants sense and respond to information entropy? I explore this question using data from an experiment which altered the temporal supply of nutrients and found no support that <em>P. sativum</em> can sense and respond to entropy. Understanding the relationships of water, nitrogen, and uncertainty is critical to predicting plant growth, especially as climate change continues to influence the global system.</p>

<p>Neregularnost prostiranja radio talasa je uobičajeni fenomen koji<br />utiče na kvalitet radio veze u okviru bežične mreže, rezultujući<br />različitim obrascima prostiranja radio talasa. Ova teza daje<br />predlog nekoliko postupaka analize prostiranja radio talasa u cilju<br />bez-senzorskog otkrivanja prisustva i kretanja ljudi unutar postojeće<br />bežične mreže. Indikator primljene snage radio signala predstavlja<br />osnovni element analize, iz kog se izdvajaju informaciono,<br />amplitudsko i frekventno obeležje. Analizom navedenih obeležja<br />moguća je realizacija robusnog postupka bez-senzorske detekcije ljudi<br />koja se može primeniti u različitim rešenjima ambijentalne<br />inteligencije, zahtevajući minimalan broj elemenata fizičke<br />arhitekture, neophodnih za uspostavljanje korisnički svesnog<br />okruženja.</p> / <p>Radio irregularity is a common and non-negligible phenomenon that impacts<br />the connectivity and interference in a wireless network, by introducing<br />disturbances in radio signal&rsquo;s propagation pattern. In order to detect a<br />possible presence of a human subject within the existing radio network<br />sensorlessly, this thesis analyze the irregularity data expressed in a form of<br />received signal strength variation. The received signal strength variation is<br />decomposed into information, amplitude and frequency characteristics. The<br />combination of these three characteristics analysis enables the definition of<br />robust and cost-effective device-free human presence detection method that<br />can be exploited for various ambient intelligence solutions, requiring the<br />minimum hardware add-ons that are necessary for the establishment of a<br />user aware environment.</p>

In the human visual system, one of the most prominent functions of the extensive feedback from the higher brain areas within and outside of the visual cortex is attentional modulation. The feedback helps the brain to concentrate its resources on visual features that are relevant for recognition, i. e. it iteratively selects certain aspects of the visual scene for refined processing by the lower areas until the inference process in the higher areas converges to a single hypothesis about this scene. In order to minimize a number of required selection-refinement iterations, one has to find a short sequence of maximally informative portions of the visual input. Since the feedback is not static, the selection process is adapted to a scene that should be recognized. To find a scene-specific subset of informative features, the adaptive selection process on every iteration utilizes results of previous processing in order to reduce the remaining uncertainty about the visual scene. This phenomenon inspired us to develop a computational algorithm solving a visual classification task that would incorporate such principle, adaptive feature selection. It is especially interesting because usually feature selection methods are not adaptive as they define a unique set of informative features for a task and use them for classifying all objects. However, an adaptive algorithm selects features that are the most informative for the particular input. Thus, the selection process should be driven by statistics of the environment concerning the current task and the object to be classified. Applied to a classification task, our adaptive feature selection algorithm favors features that maximally reduce the current class uncertainty, which is iteratively updated with values of the previously selected features that are observed on the testing sample. In information-theoretical terms, the selection criterion is the mutual information of a class variable and a feature-candidate conditioned on the already selected features, which take values observed on the current testing sample. Then, the main question investigated in this thesis is whether the proposed adaptive way of selecting features is advantageous over the conventional feature selection and in which situations. Further, we studied whether the proposed adaptive information-theoretical selection scheme, which is a computationally complex algorithm, is utilized by humans while they perform a visual classification task. For this, we constructed a psychophysical experiment where people had to select image parts that as they think are relevant for classification of these images. We present the analysis of behavioral data where we investigate whether human strategies of task-dependent selective attention can be explained by a simple ranker based on the mutual information, a more complex feature selection algorithm based on the conventional static mutual information and the proposed here adaptive feature selector that mimics a mechanism of the iterative hypothesis refinement. Hereby, the main contribution of this work is the adaptive feature selection criterion based on the conditional mutual information. Also it is shown that such adaptive selection strategy is indeed used by people while performing visual classification.:1. Introduction 2. Conventional feature selection 3. Adaptive feature selection 4. Experimental investigations of ACMIFS 5. Information-theoretical strategies of selective attention 6. Discussion Appendix Bibliography