Le noyau cellulaire est le siège de réactions chimiques dont le but est l’expression de gènes, la duplication du génome et du maintien et l’intégrité de l’information génétique. Ces réactions sont régulées au cours du cycle cellulaire ou en réponse à un stress. Parmi elles, la transcription permet qu’une séquence d’ADN soit reproduite sous forme d’ARN messager. La transcription est un exemple frappant de processus fondamental pour la cellule impliquant parfois un nombre très faible de molécules. En effet, il n’y a souvent dans un même génome que quelques copies d’un même gène. Le but de cette thèse est d’imager les processus nucléaires dans des cellules humaines à l’échelle de la molécule unique et d’en extraire les grandeurs caractéristiques. Depuis les années 90, des inventeurs de génie ont développé des méthodes simples à partir de microscopes inversés ordinaires pour observer des molécules individuelles jusque dans le noyau des cellules. Nous avons utilisé ces méthodes pour suivre des facteurs de transcription qui régulent la transcription d’un gène. Nos mesures montrent que, bien que hiératique, l’exploration du noyau par les facteurs de transcriptions est régulée par leurs propriétés chimiques. L’agencement des composants du noyau guide les facteurs de transcription dans la recherche d’un gène. Comme exemple de cet agencement, nous nous sommes ensuite intéressés à l’organisation de l’ADN dans le noyau pour montrer qu’elle présentait les caractéristiques d’une structure auto-organisée, une structure fractale. Cette structure change en réponse aux aléas de la vie de la cellule. Dans une dernière étude, nous avons suivi un locus dans le noyau d’une levure. La structure du noyau, qui est révélée par notre méthode, contraint la diffusion du locus à un régime de reptation. Tous ces résultats montrent combien la structure du noyau et les réactions chimiques qui y ont lieu sont interdépendantes. Cette thèse a également permis le développement de méthodes de quantification précises des réactions cellulaires à l’échelle de la molécule unique. / The cell nucleus is a chemical reactor. Nuclear components interact with each other to express genes, duplicate the chromosomes for cell division, and protect DNA from alteration. These reactions are regulated along the cell cycle and in response to stress. One of the fundamental nuclear processes, transcription, enables the production of a messenger RNA from a template DNA sequence. While mandatory for the cell, transcription nevertheless may involve a very small number of molecules. Indeed, a single gene would have only few copies in the genome. During my PhD, I studied nuclear processes in human cells nuclei at the single molecule level with novel imaging techniques. I developed new statistical tools to quantify nuclear components movement that revealed a dynamic nuclear architecture. Since the 90s, simple methods have been developed for the observation of single molecules in the cell. These experiments can be conducted in an ordinary inverted microscope. We used these methods to monitor nuclear molecules called transcription factors (TF) that regulate transcription. From TF dynamics, we concluded that nuclear exploration by transcription factors is regulated by their chemical interactions with partners. The organization of the components of the nucleus guide transcription factors in their search of a gene. As an example of this organization, we then studied chromatin, the de-condensed form of nuclear DNA, proving that it displays the characteristics of a self-organized fractal structure. This structure changes in response to cellular fate and stress. In yeast, we showed that the interminglement of chromatin constrained DNA locus movement in a reptation regime. All these results show the interdependence of the structure of the nucleus and of its chemical reactions. With combination of realistic modeling and high resolution microscopy, we have enlightened the specificity of the nucleus as a chemical reactor. This thesis has also enabled the development of accurate methods for the statistical analysis of single molecule data.

In content-based image retrieval (CBIR) systems, there are two general types of search: target search and category search. Unlike queries in traditional database systems, users in most cases cannot specify an ideal query to retrieve the desired results for either target search or category search in multimedia database systems, and have to rely on iterative feedback to refine their query. Efficient evaluation of such iterative queries can be a challenge, especially when the multimedia database contains a large number of entries, and the search needs many iterations, and when the underlying distance measure is computationally expensive. The overall processing costs, including CPU and disk I/O, are further emphasized if there are numerous concurrent accesses. To address these limitations involved in relevance feedback processing, we propose a generic framework, including a query model, index structures, and query optimization techniques. Specifically, this thesis has five main contributions as follows. The first contribution is an efficient target search technique. We propose four target search methods: naive random scan (NRS), local neighboring movement (LNM), neighboring divide-and-conquer (NDC), and global divide-and-conquer (GDC) methods. All these methods are built around a common strategy: they do not retrieve checked images (i.e., shrink the search space). Furthermore, NDC and GDC exploit Voronoi diagrams to aggressively prune the search space and move towards target images. We theoretically and experimentally prove that the convergence speeds of GDC and NDC are much faster than those of NRS and recent methods. The second contribution is a method to reduce the number of expensive distance computation when answering k-NN queries with non-metric distance measures. We propose an efficient distance mapping function that transfers non-metric measures into metric, and still preserves the original distance orderings. Then existing metric index structures (e.g., M-tree) can be used to reduce the computational cost by exploiting the triangular inequality property. The third contribution is an incremental query processing technique for Support Vector Machines (SVMs). SVMs have been widely used in multimedia retrieval to learn a concept in order to find the best matches. SVMs, however, suffer from the scalability problem associated with larger database sizes. To address this limitation, we propose an efficient query evaluation technique by employing incremental update. The proposed technique also takes advantage of a tuned index structure to efficiently prune irrelevant data. As a result, only a small portion of the data set needs to be accessed for query processing. This index structure also provides an inexpensive means to process the set of candidates to evaluate the final query result. This technique can work with different kernel functions and kernel parameters. The fourth contribution is a method to avoid local optimum traps. Existing CBIR systems, designed around query refinement based on relevance feedback, suffer from local optimum traps that may severely impair the overall retrieval performance. We therefore propose a simulated annealing-based approach to address this important issue. When a stuck-at-a-local-optimum occurs, we employ a neighborhood search technique (i.e., simulated annealing) to continue the search for additional matching images, thus escaping from the local optimum. We also propose an index structure to speed up such neighborhood search. Finally, the fifth contribution is a generic framework to support concurrent accesses. We develop new storage and query processing techniques to exploit sequential access and leverage inter-query concurrency to share computation. Our experimental results, based on the Corel dataset, indicate that the proposed optimization can significantly reduce average response time while achieving better precision and recall, and is scalable to support a large user community. This latter performance characteristic is largely neglected in existing systems making them less suitable for large-scale deployment. With the growing interest in Internet-scale image search applications, our framework offers an effective solution to the scalability problem.

Active particle is a general term used to label a large set of different systems, spanning from a flock of birds flying in a coordinated pattern to a school of fish abruptly changing its direction or to a bacterium self-propelling itself while foraging nourishment. The common property shared by these systems is that their constituent agents, e.g. birds, fishes, or bacteria, are capable of harvesting energy from the surrounding environment and converting it into self-propulsion and directed motion. This peculiar feature characterizes them as out-of-equilibrium systems, in fact, the process of energy consumption and dissipation generates microscopically irreversible dynamics and drives them far from thermal equilibrium. Thanks to their intrinsic out-of-equilibrium nature, active particle systems often display characteristic patterns and behaviors that are not observed in equilibrium physics systems, such as collective motion or motility-induced phase separation. These features prompted the development of theories and algorithms to simulate and study active particles, giving rise to paradigmatic models capable of describing these phenomena, such as the Vicsek model for collective motion, the run-and-tumble model, or the active Brownian particle model. At the same time, synthetic agents have been designed to reproduce the behaviors of these natural active particle systems, and their evolution could play a fundamental role in the nanotechnology of the 21st century and the development of novel medical treatments, in particular controlled drug delivery. A specific type of active particle that uses its directed motion to move at the microscale is called a microswimmer. Examples of these agents are bacteria exploring their surroundings while searching for food or escaping external threats, spermatozoa looking for the egg, or artificial Janus particles designed for specific tasks. Active agents at these scales use different swimming mechanisms, such as rotating flagella or phoretic motion along chemical gradients that they can create. The outcome of their efforts is determined by the interplay of the translational diffusion intrinsic to the dynamics at these scales and the persistent motion that characterizes their self-propulsion. The problem of finding a specific target in a complex environment is essential for microswimmers and active agents in general. Target search is employed by animals and microorganisms for a variety of purposes, from foraging nourishment to escaping potential threats, such as in the case of bacterial chemotaxis. The study of this process is therefore fundamental to characterize the behavior of these systems in nature. Its complete description could then be employed in designing synthetic microswimmers for addressing specific problems, such as the aforementioned targeted drug delivery and the environmental cleansing of soil and polluted water. Here, we provide a detailed study of the target search process for microswimmers exploring complex environments. To this end, we generalize Transition Path Theory, the rigorous statistical mechanics description of transition processes, to the target-search problem. The most general way of modeling a complex environment that the microswimmer has to navigate is through an external potential. This potential can be characterized by high barriers separating metastable states in the system or by the presence of confining boundaries. If a high energy barrier is located between the initial position of the microswimmer and its target, the target search becomes a rare event. Rare events have been thoroughly investigated in equilibrium physics, and several algorithms have been designed to cope with the separation of timescales intrinsic to these problems and enable their investigation via efficient computer simulations. Despite the large set of tools developed for studying passive particles performing rare transitions, the characterization of this process for non-equilibrium systems, such as active particles, is still lacking. One of the main results of this thesis is the generalization to non-equilibrium systems of the Transition Path Sampling (TPS) algorithm, which was originally designed to simulate rare transitions in passive systems. This algorithm relies on the generation of productive trajectories, i.e. trajectories linking the initial state of the particle to the target state, via a Monte Carlo procedure, without the need of simulating long thermal oscillations in metastable states. These trajectories are then accepted according to a Metropolis criterion and are subsequently used to obtain the transition path ensemble, i.e. the ensemble of all reactive paths that completely characterizes the process. The TPS algorithm relies on microscopic reversibility to generate the productive trajectories, therefore its generalization to out-of-equilibrium systems lacking detailed balance and microscopic reversibility has remained a major challenge. Within this work, after deriving a path integral representation for active Brownian particles, we provide a new rule for the generation and acceptance of productive non-equilibrium trajectories, which reduces to the usual expression for passive particles when the activity of the microswimmer is set to zero. This new rule allows us to generalize the TPS algorithm to the case of active Brownian particles and to obtain a first insight into the counterintuitive target-search pathways explored by these particles. In fact, while passive particles perform barrier crossing following the minimum energy path linking the initial state to the target state, we found that active particles, thanks to their activity and persistence of motion, can reach the target more often by surfing higher energy regions of the landscape that lie far from the minimum energy path. The second result of this thesis is a systematic characterization of the target-search path ensemble for an active particle exploring an energy landscape. We do so by analyzing the system’s response to changes in the two adimensional parameters that define the parameter space of the model: the Péclet number and the persistence of the active particle. Our findings show that active Brownian particles can increase their target-finding rates by tuning their Péclet number and their persistence according to the shape and characteristics of the external landscape. We perform this analysis in two different landscapes, namely a double-well potential and the Brown-Müller potential, finding robust features in the target-search patterns. In contrast, other observables of the system, e.g. the target-finding rates, are more responsive to the features of the external environment. Interestingly, our results suggest that, differently from what happens for passive particles, the presence of additional metastable states in the system does not hinder the target-search dynamics of active particles. The third original contribution of this Ph.D. thesis is the generalization of the concept of the committor function to target-search problems. The committor function was first introduced in the framework of Transition Path Theory to study reaction processes. If a definition for a reactant and a product state embedded in the configuration space of the system is provided, the committor function quantifies the probability that a trajectory starting in a given configuration reaches the product state before it can enter the reactant. For this reason, it has been proven to be pivotal for a complete characterization of these events and it is often regarded as the optimal reaction coordinate for thermally activated transitions. The target search problem shares many similarities with transition processes since it is characterized by an initial state from which the agent begins its journey and a target state that the particle is aiming to reach, and often some barriers or obstacles separate the two. Exploiting these similarities, we take advantage of the concept of the committor function to fully characterize a target-search process performed by an active agent. First, we derive the Fokker-Planck equation for an active Brownian particle subject to an external potential, and we use its associated probability current to define the committor function for an active agent. Then, we prove that the active committor satisfies the Backward-Kolmogorov equation analogously to the committor for passive particles. We take advantage of this property to efficiently compute the committor function using a finite-difference algorithm, validating it with brute-force simulations. Finally, we further validate our theory with experiments of a camphor self-propelled disk. This self-propelled disk is capable of moving on a water surface and is studied during its exploration of a circular confining environment. We start by analyzing long recorded trajectories of such a disk moving in a Petri dish, and, after defining a reactant and a product region in the system, we proceed to compute the committor function in three different regions contained in the dish. We analyze all the trajectory slices passing through those regions and we measure how many of them hit the product region and how many hit instead the reactant first, and we obtain the committor in the three regions as a function of the angle. Finally, we simulate a long trajectory of an active Brownian particle exploring a circular confining environment, and we compare the committor as an angular function obtained from brute-force simulations with the committor estimated from experimental data.