<p>Sustained attention, the ability to direct and maintain attentional focus on tasks and stimuli, emerges during infancy and undergoes rapid development throughout early childhood. Abnormal patterns of sustained attention are implicated in several childhood psychological disorders. Improving our measurement of infant sustained attention may clarify how child psychopathology develops and inform targeted prevention and early intervention efforts. While several behavioral and psychophysiological measures index infant sustained attention, previous studies have employed these measures in isolation, focused on analyses at short timescales of milliseconds to a few seconds, and examined synchronous associations among these measures. Therefore, the associations and temporal relationships across multiple, concurrent behavioral and psychophysiological measures of infant sustained attention remain unclear, particularly at long timescales. The present study assessed sustained attention in 12-month-old infants using behavioral (looking), cardiac (heart rate), and neural (theta and alpha oscillations) measures to investigate two temporal aspects of infant sustained attention. First, we examined whether associations among infant sustained attention measures were similar or different across short (1-second) and long (10-second) timescales. Covariation analyses indicated largely similar association patterns among these measures across the two timescales. Second, we evaluated whether specific infant sustained attention measures temporally preceded other measures. Cross-correlation analyses broadly revealed that short-timescale measures exhibited asynchronous temporal relationships, such that looking behaviors preceded neural oscillations that in turn preceded cardiac responses. Our findings highlight the value of considering the temporal dimension when studying and measuring infant sustained attention. Additional multimodal research may yield greater insights into dynamic biobehavioral processes that underlie infant sustained attention and enhance clinical interventions aimed at promoting optimal outcomes for young children with abnormalities in sustained attention.</p>

Diese Dissertation befaßt sich mit kinetischen und dynamischen Analysen an spinmarkierten Proteinen mittels Elektronenspinresonanz-Spektroskopie (ESR-S) in Kombination mit weiteren biophysikalischen Methoden. Die Spinmarkierung der hier untersuchten Proteine (z.B. Bakteriorhodopsin (EF-loop) bzw. Reverse Transkriptase) erfolgt durch spezifische Substitution ausgewählter Aminosäure-Seitenketten durch eine radikalische Seitenkette ("R1", MTS-Spinlabel an Cystein gebunden). Der Schwerpunkt dieser Arbeit liegt in der Methodenentwicklung eines neuen Simulationsverfahrens für ESR-Spektren basierend auf einer speziellen Molekulardynamik-Simulation (MD-S). Das Verfahren nutzt den von Robinson et al. (J.Chem.Phys.96:2609-2616) vorgeschlagenen Trajektorien-basierten Berechnungsalgorithmus für ESR-Spektren. Hierfür sind zahlreiche Trajektorien der umgebungsabhängigen Umorientierungsdynamik von R1 mit Längen von jeweils über 700 ns erforderlich. Diese Trajektorien werden im hier präsentierten Simulationsverfahren mit minimalem Zeitaufwand in drei Stufen generiert: i) statistisch korrekte Erfassung des gesamten verfügbaren Konformationsraums von R1 in positionsspezifischer Proteinumgebung mittels einer kurzen (ca. 10 ns) speziellen MD-S (in-vacuo, 600 Kelvin); ii) Berechnung eines Potentials im Eulerwinkelraum welches das spezifische Umorientierungsverhalten der radikalischen R1-Kopfgruppe widerspiegelt; iii) Trajektorienberechnung mittels Simulation der potentialabhängigen Brownschen Umorientierungsdynamik eines virtuellen Teilchens bei 300 Kelvin (Einteilchen-Simulation). Die Statistiken wichtiger dynamischer Prozesse während der speziellen MD-S werden analysiert und mit Langzeit-Dynamiken aus herkömmlichen MD-S unter physiologischen Bedingungen verglichen. Zusätzlich wird ein Simulationsverfahren zur Identifikation von Wasserstoff-Brücken vorgestellt. In einem weiteren Kapitel dieser Arbeit werden Konzeption, Aufbau und Test einer Temperatursprung-ESR-Anlage beschrieben.

One main goal of this thesis is to show that for every K it is possible to find K consecutive natural numbers that cannot be written as sums of three nonnegative cubes. Since it is believed that approximately 10% of all natural numbers can be written in this way, this result indicates that the sums of three cubes distribute unevenly on the real line. These sums have been studied for almost a century, in relation with Waring's problem, but the existence of ``arbitrarily long gaps'' between them was not known. We will provide two proofs for this theorem. The first is relatively elementary and is based on the observation that the sums of three cubes have a positive bias towards being cubic residues modulo primes of the form p=1+3k. Thus, our first method to find consecutive non-sums of three cubes consists in searching them among the natural numbers that are non-cubic residues modulo ``many'' primes congruent to 1 modulo 3. Our second proof is more technical: it involves the computation of the Sato-Tate distribution of the underlying cubic Fermat variety {x^3+y^3+z^3=0}, via Jacobi sums of cubic characters and equidistribution theorems for Hecke L-functions of the Eisenstein quadratic number field Q(\sqrt{-3}). The advantage of the second approach is that it provides a nearly optimal quantitative estimate for the size of gaps: if N is large, there are >>\sqrt{log N}/(log log N)^4 consecutive non-sums of three cubes that are less than N. According to probabilistic models, an optimal estimate would be of the order of log N / log log N. In this thesis we also study other gap problems, e.g. between sums of four fourth powers, and we give an application to the arithmetic of cubic and biquadratic theta series. We also provide the following additional contributions to Number Theory and Combinatorics: a derivation of cubic identities from a parameterization of the pseudo-automorphisms of binary quadratic forms; a multiplicity estimate for multiprojective Chow forms, with applications to Transcendental Number Theory; a complete solution of a problem on planar graphs with everywhere positive combinatorial curvature.

A leading theory for why we sleep focuses on memory consolidation - the process of stabilizing and strengthening newly acquired memories into long-term storage. Consolidation of memory for cognitive strategies and problem-solving skills is enhanced as compared to a period of daytime wakefulness. Importantly, sleep preferentially enhances memory for the cognitive strategy per se, over-and-above the motor skills that are used to execute the strategy. Although it has been known for some time that sleep benefits this type of memory, it is not known how this process unfolds during sleep, or how sleep transforms this memory trace in the brain. Sleep is classified into rapid eye movement (REM) sleep and non-REM (NREM) sleep. The role of REM sleep for consolidation of memory for problem-solving skills remains controversial. In addition, little attention has been paid to the possible distinct roles of phasic REM sleep (i.e., when bursts of eye movements occur) and tonic REM sleep (i.e., the presence of isolated eye movements and the absence of eye movement bursts). REM sleep might favour procedural memory consolidation for cognitive strategies and problem-solving skills, and the specific role of REM sleep in this process might be discernible only by differentiating between phasic and tonic REM states. In addition, fMRI studies have revealed that sleep-related consolidation of the memory trace for simple motor procedural skills is associated with strengthened activity of, and functional connectivity between, key memory-related brain areas (i.e., hippocampal, striatal, and neocortex). However, fMRI techniques have not yet been employed to investigate sleep-related consolidation of procedural memory for cognitive strategies and problem-solving skills. Participants (n=60) performed a procedural memory task involving a cognitive strategy while undergoing functional magnetic resonance imaging (fMRI) before and after a condition of Sleep, Nap, or Wake. Those in the Sleep and Nap condition underwent polysomnography (PSG) to further study the learning-related changes in sleep macrostructure and microstructure. This thesis not only shows that a period of sleep or a nap afford a greater benefit to memory consolidation of a procedural strategy than a period of wake, but more specifically: In Study 1, during sleep, phasic REM sleep theta power was directly associated with overnight improvement on the task, whereas tonic REM sleep sensorimotor rhythm power was greater following a night of learning compared to a non-learning control night. In Study 2, we show that distinct hippocampal, striatal, and cortical areas associated with strategy learning are preferentially enhanced. Study 3 reveals that the functional communication among these brain areas is greater following sleep compared to a daytime nap or day of wakefulness. Sleep-related changes in brain activation and functional connectivity were both correlated with improved performance from before to after a period of sleep. Overall, findings from this thesis support the benefit of sleep at the behavioural and systems level for consolidating procedural memory involving cognitive strategies used to solve problems. The findings suggest that the multifaceted nature of REM sleep must be examined separately by its phasic and tonic states, to identify the active role of REM sleep for consolidating memory. Further, the consolidation of the memory trace is reflected through activation of, and communication between hippocampal, striatal, and neocortical brain areas. In summary, this thesis shows that sleep actively consolidates memory for cognitive strategies and problem-solving skills.

Introduction: Memory is a complex cognitive process formerly linked to mechanisms of brain plasticity that can be estimated in the left dorsolateral prefrontal cortex (DLPFC) using transcranial magnetic stimulation and electroencephalography (TMS-EEG). Also, cortical thickness in the DLPFC may be a potential proxy measure of brain plasticity as previous literature reports a link between better memory and thicker cortex. However, the link between brain plasticity and memory performance as well as DLPFC thickness remains to be clarified. Methods: Intermittent theta burst stimulation (iTBS) probed plasticity-like mechanisms in the left DLPFC in 17 cognitively healthy participants. TMS-EEG recordings were performed before and after sham and active iTBS to quantify plasticity via transcranial magnetic stimulation-evoked potentials (TEPs). Composite memory scores for each domain (verbal episodic, visual episodic and working memory) were obtained using the Cambridge Neuropsychological Test Automated Battery. Anatomical T1 images were acquired by magnetic resonance imaging and processed by open-source software (CIVET) and the Automated Anatomical Labeling atlas to extract cortical thickness of the DLPFC. All statistical analyses (linear mixed model, Tukey's post hoc test and Pearson's correlations) were completed in R Studio. Results: iTBS resulted in increased TEP amplitude P30 (F= 5.239, p = 0.029), as shown by a significant interaction between condition (iTBS, sham) and time (pre- and post-condition). Specifically, Tukey's post hoc test revealed that the P30 increase was near trending significant post-iTBS compared to pre-iTBS for the active condition (p = 0.166) but not for the sham condition (p = 0.294). A trending significant relationship was observed between the magnitude of P30 change post-iTBS and thicker left DLPFC (r = 0.488; p = 0.108). Lastly, no significant relationships between P30 change and memory performance were observed. Conclusion: These preliminary findings suggest there could be a relationship between increased capacity for brain plasticity and a thicker left DLPFC. To further investigate these relationships, we plan to recruit additional cognitively healthy participants. Our preliminary findings support the foundation for future clinical studies in which DLPFC thickness could be explored as a predictive factor for response to plasticity-targeting iTBS treatment.

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<p>The primary somatosensory cortex (SI) is important for hand function and influences motor circuitry in the primary motor cortex (M1). Areas 3a, 1 and 2 of SI have direct connectivity with M1. Much of our present knowledge of this connectivity and its relevance to hand function is based on animal research. However, less is known about the neural mechanisms that underpin hand function in humans. The present study investigated the influence of SI on corticospinal excitability as well as inhibitory and excitatory neural circuitry within M1 before and after continuous theta-burst stimulation (cTBS). Additionally, stimulation parameters influence the direction and magnitude of cTBS after-effects. Thus, current direction and frequency of cTBS were manipulated. Two experiments were performed. In Experiment 1, motor-evoked potentials (MEPs) were recorded from the first-dorsal interosseous (FDI) muscle bilaterally before and after 50 Hz cTBS over left SI. In a second condition, the orientation of cTBS was reversed. Experiment 2 measured MEPs, short-latency intracortical inhibition (SICI) and intracortical facilitation (ICF) from the right FDI following a modified 30 Hz cTBS over left SI or M1. The results of Experiment 1 and 2 demonstrate that SI influences M1 circuitry such that MEPs are facilitated following cTBS over SI. However, MEPs are suppressed when the current direction is reversed. CTBS at 30 Hz delivered over M1 suppressed excitatory circuitry that generates MEPs and ICF. The findings from the thesis suggest that SI influences hand motor circuitry and is likely a mechanism by which somatosensory information modulates hand motor function.</p> / Bachelor of Science (BSc)

Encoding and consolidation of memories are two processes within the hippocampus, and connected cortical networks, that recruit different circuit level dynamics to effectively process and pass information from brain region to brain region. In the hippocampal CA1 pyramidal layer local field potential (LFP), these processes take the form of theta and sharp wave ripples (SPW-Rs) for encoding and consolidation, respectively. As an animal runs through an environment, neurons become active at specific locations in the environment (place cells) increasing their firing rate, functionally representing these specific locations. These firing rate increases are organized within the local theta oscillations and sequential activation of many place cells creates a map of the environment. Once the animal stops moving and begins consummatory behaviors, such as eating, drinking, or grooming, theta activity diminishes, and large irregular activity (LIA) begins to dominate the LFP. Spontaneously, with the LIA, the place cells active during the experience are replayed during SPW-Rs in the same spatial order they were encountered in the environment. Both theta and SPW-R oscillations and their associated neuronal firing are necessary for effective place recognition as well as learning and memory. As such, interruption or termination of SPW-R events results in decreased learning performance over days. During exploration, the associated theta and sequential place cell activity is thought to encode the experience. During quiet restfulness or slow wave sleep (SWS), SPW-R events, that replay experience specific place sequences, are thought to be the signal by which systems consolidation progresses and the hippocampus guides cortical synaptic reorganization. The granular retrosplenial cortex (gRSC) is an associational area that exhibits high frequency oscillations (HFOs) during both hippocampal theta and SPW-Rs, and is potentially a period when the gRSC interprets incoming content from the hippocampus during encoding and systems consolidation. However, the precise laminar organization of synaptic currents supporting HFOs, whether the local gRSC circuitry can support HFOs without patterned input, and the precise coupling of hippocmapla oscillations to gRSC HFOs across brain states remains unknown. We aimed to answer these questions using in vivo, awake electrophysiological recordings in head-fixed mice that were trained to run for water rewards in a 1D virtual environment. We show that gRSC synaptic currents supporting HFOs, across all awake brain states, are exclusively localized to layer 2/3 (L2/3), even when events are detected within layer 5 (L5). Using focal optogenetics, both L2/3 and L5 can generate induced HFOs given a strong enough broad stimulation. Spontaneous gRSC HFOs occurring outside of SPW-Rs are highly comodulated with medial entorhinal cortex (MEC) generated high gamma in hippocampal stratum lacunosum moleculare. gRSC HFOs may serve a necessary role in communication between the hippocampus during SPW-Rs states and between the hippocampus, gRSC, and MEC during theta states to support memory consolidation and memory encoding, respectively. / Doctor of Philosophy / As an animal moves through an environment, individual neurons in the hippocampus, known as place cells, increase and decrease their firing rate as the animal enters and exits specific locations in the environment. Within an environment, multiple neurons become active in different locations, this cooperation of spiking in various locations creates a place map of the environment. Now let's say when the animal moved from one corner of the environment to another, place cells 'A', 'C', 'B', 'E', and 'D' became active in that order. This means, at any given point in the environment, the animal is standing in a venn-diagram-esque overlap of place fields, or locations individual place cells represent. A key question that entranced researchers for many years was how do these neurons know when to be active to not impinge on their neighbor's locations? The answer to this question rested with population electrical activity, known as the local field potential (LFP), that place cell activity is paced to. During active navigation through an environment, place cells activity is coupled to the phase of a slow ~8 hertz (Hz) theta oscillation. Within one theta cycle, or peak to peak, multiple place cells are active, representing the venn diagram of location the animal is in. Importantly, this theta activity and encoding of place cell activity is largely seen during active running or rapid eye movement (REM) sleep. During slow wave sleep (SWS), after an animal has experienced a specific environment and has created a place map, place cells are reactivated in the same order the animal experienced them in. From our previous example, the content of this reactivation would be the place cells 'A', 'C', 'B', 'E', and 'D' which all would be reactivated in that same order. These reactivations or replays occur during highly synchronous and fast LFP oscillations known as sharp wave-ripples (SPW-Rs). SPW-Rs are thought to be a key LFP event that drives memory consolidation and the eventual conversion of short-term memory into long-term memory. However, for consolidation to occur, connected cortical regions need to be able to receive and interpret the information within SPW-Rs. The granular retrosplenial cortex (gRSC) is one proposed region that serves this role. During SPW-Rs the superficial gRSC has been shown to exhibit high frequency oscillations (HFOs), which potentially serve the purpose for interpreting SPW-R content. However, HFOs have been reported during hippocampal theta, suggesting HFOs serve multiple purposes in interregional communication across different states. In this study, we found that naturally occurring gRSC HFOs occur exclusively in layer 2/3 across all awake brain states. Using focal optogenetic excitation we were able to evoke HFOs in both layer 2/3 and 5. Spontaneous gRSC HFOs occurring without SPW-Rs were highly comodulated with medial entorhinal cortex (MEC) generated high gamma in hippocampal stratum lacunosum moleculare. gRSC HFOs may serve a general role in supporting hippocampo-cortical dialogue during SPW-R and theta brain states to support memory consolidation and encoding, respectively.

Les principaux objets étudiés dans cette thèse sont les équations décrivant le morphisme de groupe sur une variété abélienne, plongée dans un espace projectif, et leurs applications en cryptographie. Notons g sa dimension et k son corps de définition. Ce mémoire est composé de deux parties. La première porte sur l'étude des courbes d'Edwards, un modèle pour les courbes elliptiques possédant un sous-groupe de points k-rationnels cyclique d'ordre 4, connues en cryptographie pour l'efficacité de leur loi d'addition et la possibilité qu'elle soit définie pour toute paire de points k-rationnels (loi d'addition k-complète). Nous en donnons une interprétation géométrique et en déduisons des formules explicites pour le calcul du couplage de Tate réduit sur courbes d'Edwards tordues, dont l'efficacité rivalise avec les modèles elliptiques couramment utilisés. Cette partie se conclut par la génération, spécifique au calcul de couplages, de courbes d'Edwards dont les tailles correspondent aux standards cryptographiques actuellement en vigueur. Dans la seconde partie nous nous intéressons à la notion de complétude introduite ci-dessus. Cette propriété est cryptographiquement importante car elle permet d'éviter des attaques physiques, comme les attaques par canaux cachés, sur des cryptosystèmes basés sur les courbes elliptiques ou hyperelliptiques. Un précédent travail de Lange et Ruppert, basé sur la cohomologie des fibrés en droite, permet une approche théorique des lois d'addition. Nous présentons trois résultats importants : tout d'abord nous généralisons un résultat de Bosma et Lenstra en démontrant que le morphisme de groupe ne peut être décrit par strictement moins de g+1 lois d'addition sur la clôture algébrique de k. Ensuite nous démontrons que si le groupe de Galois absolu de k est infini, alors toute variété abélienne peut être plongée dans un espace projectif de manière à ce qu'il existe une loi d'addition k-complète. De plus, l'utilisation des variétés abéliennes nous limitant à celles de dimension un ou deux, nous démontrons qu'une telle loi existe pour leur plongement projectif usuel. Finalement, nous développons un algorithme, basé sur la théorie des fonctions thêta, calculant celle-ci dans P^15 sur la jacobienne d'une courbe de genre deux donnée par sa forme de Rosenhain. Il est désormais intégré au package AVIsogenies de Magma. / The main objects we study in this PhD thesis are the equations describing the group morphism on an abelian variety, embedded in a projective space, and their applications in cryptograhy. We denote by g its dimension and k its field of definition. This thesis is built in two parts. The first one is concerned by the study of Edwards curves, a model for elliptic curves having a cyclic subgroup of k-rational points of order 4, known in cryptography for the efficiency of their addition law and the fact that it can be defined for any couple of k-rational points (k-complete addition law). We give the corresponding geometric interpretation and deduce explicit formulae to calculate the reduced Tate pairing on twisted Edwards curves, whose efficiency compete with currently used elliptic models. The part ends with the generation, specific to pairing computation, of Edwards curves with today's cryptographic standard sizes. In the second part, we are interested in the notion of completeness introduced above. This property is cryptographically significant, indeed it permits to avoid physical attacks as side channel attacks, on elliptic -- or hyperelliptic -- curves cryptosystems. A preceeding work of Lange and Ruppert, based on cohomology of line bundles, brings a theoretic approach of addition laws. We present three important results: first of all we generalize a result of Bosma and Lenstra by proving that the group morphism can not be described by less than g+1 addition laws on the algebraic closure of k. Next, we prove that if the absolute Galois group of k is infinite, then any abelian variety can be projectively embedded together with a k-complete addition law. Moreover, a cryptographic use of abelian varieties restricting us to the dimension one and two cases, we prove that such a law exists for their classical projective embedding. Finally, we develop an algorithm, based on the theory of theta functions, computing this addition law in P^15 on the Jacobian of a genus two curve given in Rosenhain form. It is now included in AVIsogenies, a Magma package.

No description available.