2,574 research outputs found
Classical and quantum algorithms for scaling problems
This thesis is concerned with scaling problems, which have a plethora of connections to different areas of mathematics, physics and computer science. Although many structural aspects of these problems are understood by now, we only know how to solve them efficiently in special cases.We give new algorithms for non-commutative scaling problems with complexity guarantees that match the prior state of the art. To this end, we extend the well-known (self-concordance based) interior-point method (IPM) framework to Riemannian manifolds, motivated by its success in the commutative setting. Moreover, the IPM framework does not obviously suffer from the same obstructions to efficiency as previous methods. It also yields the first high-precision algorithms for other natural geometric problems in non-positive curvature.For the (commutative) problems of matrix scaling and balancing, we show that quantum algorithms can outperform the (already very efficient) state-of-the-art classical algorithms. Their time complexity can be sublinear in the input size; in certain parameter regimes they are also optimal, whereas in others we show no quantum speedup over the classical methods is possible. Along the way, we provide improvements over the long-standing state of the art for searching for all marked elements in a list, and computing the sum of a list of numbers.We identify a new application in the context of tensor networks for quantum many-body physics. We define a computable canonical form for uniform projected entangled pair states (as the solution to a scaling problem), circumventing previously known undecidability results. We also show, by characterizing the invariant polynomials, that the canonical form is determined by evaluating the tensor network contractions on networks of bounded size
Algorithms and complexity for approximately counting hypergraph colourings and related problems
The past decade has witnessed advancements in designing efficient algorithms for approximating the number of solutions to constraint satisfaction problems (CSPs), especially in the local lemma regime. However, the phase transition for the computational tractability is not known. This thesis is dedicated to the prototypical problem of this kind of CSPs, the hypergraph colouring. Parameterised by the number of colours q, the arity of each hyperedge k, and the vertex maximum degree Î, this problem falls into the regime of LovĂĄsz local lemma when Î âČ qá”. In prior, however, fast approximate counting algorithms exist when Î âČ qá”/Âł, and there is no known inapproximability result. In pursuit of this, our contribution is two-folded, stated as follows.
âą When q, k â„ 4 are evens and Î â„ 5·qá”/ÂČ, approximating the number of hypergraph colourings is NP-hard.
âą When the input hypergraph is linear and Î âČ qá”/ÂČ, a fast approximate counting algorithm does exist
LIPIcs, Volume 251, ITCS 2023, Complete Volume
LIPIcs, Volume 251, ITCS 2023, Complete Volum
Exploration autonome et efficiente de chantiers miniers souterrains inconnus avec un drone filaire
Abstract: Underground mining stopes are often mapped using a sensor located at the end of a pole that the operator introduces into the stope from a secure area. The sensor emits laser beams that provide the distance to a detected wall, thus creating a 3D map. This produces shadow zones and a low point density on the distant walls. To address these challenges, a research team from the UniversitĂ© de Sherbrooke is designing a tethered drone equipped with a rotating LiDAR for this mission, thus benefiting from several points of view. The wired transmission allows for unlimited flight time, shared computing, and real-time communication. For compatibility with the movement of the drone after tether entanglements, the excess length is integrated into an onboard spool, contributing to the drone payload. During manual piloting, the human factor causes problems in the perception and comprehension of a virtual 3D environment, as well as the execution of an optimal mission. This thesis focuses on autonomous navigation in two aspects: path planning and exploration. The system must compute a trajectory that maps the entire environment, minimizing the mission time and respecting the maximum onboard tether length. Path planning using a Rapidly-exploring Random Tree (RRT) quickly finds a feasible path, but the optimization is computationally expensive and the performance is variable and unpredictable. Exploration by the frontier method is representative of the space to be explored and the path can be optimized by solving a Traveling Salesman Problem (TSP) but existing techniques for a tethered drone only consider the 2D case and do not optimize the global path. To meet these challenges, this thesis presents two new algorithms. The first one, RRT-Rope, produces an equal or shorter path than existing algorithms in a significantly shorter computation time, up to 70% faster than the next best algorithm in a representative environment. A modified version of RRT-connect computes a feasible path, shortened with a deterministic technique that takes advantage of previously added intermediate nodes. The second algorithm, TAPE, is the first 3D cavity exploration method that focuses on minimizing mission time and unwound tether length. On average, the overall path is 4% longer than the method that solves the TSP, but the tether remains under the allowed length in 100% of the simulated cases, compared to 53% with the initial method. The approach uses a 2-level hierarchical architecture: global planning solves a TSP after frontier extraction, and local planning minimizes the path cost and tether length via a decision function. The integration of these two tools in the NetherDrone produces an intelligent system for autonomous exploration, with semi-autonomous features for operator interaction. This work opens the door to new navigation approaches in the field of inspection, mapping, and Search and Rescue missions.La cartographie des chantiers miniers souterrains est souvent rĂ©alisĂ©e Ă lâaide dâun capteur situĂ© au bout dâune perche que lâopĂ©rateur introduit dans le chantier, depuis une zone sĂ©curisĂ©e. Le capteur Ă©met des faisceaux laser qui fournissent la distance Ă un mur dĂ©tectĂ©, crĂ©ant ainsi une carte en 3D. Ceci produit des zones dâombres et une faible densitĂ© de points sur les parois Ă©loignĂ©es. Pour relever ces dĂ©fis, une Ă©quipe de recherche de lâUniversitĂ© de Sherbrooke conçoit un drone filaire Ă©quipĂ© dâun LiDAR rotatif pour cette mission, bĂ©nĂ©ficiant ainsi de plusieurs points de vue. La transmission filaire permet un temps de vol illimitĂ©, un partage de calcul et une communication en temps rĂ©el. Pour une compatibilitĂ© avec le mouvement du drone lors des coincements du fil, la longueur excĂ©dante est intĂ©grĂ©e dans une bobine embarquĂ©e, qui contribue Ă la charge utile du drone. Lors dâun pilotage manuel, le facteur humain entraĂźne des problĂšmes de perception et comprĂ©hension dâun environnement 3D virtuel, et dâexĂ©cution dâune mission optimale. Cette thĂšse se concentre sur la navigation autonome sous deux aspects : la planification de trajectoire et lâexploration. Le systĂšme doit calculer une trajectoire qui cartographie lâenvironnement complet, en minimisant le temps de mission et en respectant la longueur maximale de fil embarquĂ©e. La planification de trajectoire Ă lâaide dâun Rapidly-exploring Random Tree (RRT) trouve rapidement un chemin rĂ©alisable, mais lâoptimisation est coĂ»teuse en calcul et la performance est variable et imprĂ©visible. Lâexploration par la mĂ©thode des frontiĂšres est reprĂ©sentative de lâespace Ă explorer et le chemin peut ĂȘtre optimisĂ© en rĂ©solvant un Traveling Salesman Problem (TSP), mais les techniques existantes pour un drone filaire ne considĂšrent que le cas 2D et nâoptimisent pas le chemin global. Pour relever ces dĂ©fis, cette thĂšse prĂ©sente deux nouveaux algorithmes. Le premier, RRT-Rope, produit un chemin Ă©gal ou plus court que les algorithmes existants en un temps de calcul jusquâĂ 70% plus court que le deuxiĂšme meilleur algorithme dans un environnement reprĂ©sentatif. Une version modifiĂ©e de RRT-connect calcule un chemin rĂ©alisable, raccourci avec une technique dĂ©terministe qui tire profit des noeuds intermĂ©diaires prĂ©alablement ajoutĂ©s. Le deuxiĂšme algorithme, TAPE, est la premiĂšre mĂ©thode dâexploration de cavitĂ©s en 3D qui minimise le temps de mission et la longueur du fil dĂ©roulĂ©. En moyenne, le trajet global est 4% plus long que la mĂ©thode qui rĂ©sout le TSP, mais le fil reste sous la longueur autorisĂ©e dans 100% des cas simulĂ©s, contre 53% avec la mĂ©thode initiale. Lâapproche utilise une architecture hiĂ©rarchique Ă 2 niveaux : la planification globale rĂ©sout un TSP aprĂšs extraction des frontiĂšres, et la planification locale minimise le coĂ»t du chemin et la longueur de fil via une fonction de dĂ©cision. LâintĂ©gration de ces deux outils dans le NetherDrone produit un systĂšme intelligent pour lâexploration autonome, dotĂ© de fonctionnalitĂ©s semi-autonomes pour une interaction avec lâopĂ©rateur. Les travaux rĂ©alisĂ©s ouvrent la porte Ă de nouvelles approches de navigation dans le domaine des missions dâinspection, de cartographie et de recherche et sauvetage
Immune contexture monitoring in solid tumors focusing on Head and Neck Cancer
Forti evidenze dimostrano una stretta interazione tra il sistema immunitario e lo sviluppo biologico e la progressione clinica dei tumori solidi. L'effetto che il microambiente immunitario del tumore puĂČ avere sul comportamento clinico della malattia Ăš indicato come "immunecontexture". Nonostante ciĂČ, l'attuale gestione clinica dei pazienti affetti da cancro non tiene conto di alcuna caratteristica immunologica nĂ© per la stadiazione nĂ© per le scelte terapeutiche. Il tumore della testa e del collo (HNSCC) rappresenta il 7° tumore piĂč comune al mondo ed Ăš caratterizzato da una prognosi relativamente sfavorevole e dall'effetto negativo dei trattamenti sulla qualitĂ della vita dei pazienti. Oltre alla chirurgia e alla radioterapia, sono disponibili pochi trattamenti sistemici, rappresentati principalmente dalla chemioterapia a base di platino-derivati o dal cetuximab. L'immunoterapia Ăš una nuova strategia terapeutica ancora limitata al setting palliativo (malattia ricorrente non resecabile o metastatica). La ricerca di nuovi biomarcatori o possibili nuovi meccanismi target Ăš molto rilevante quindi nel contesto clinico dell'HNSCC. In questa tesi ci si concentrerĂ sullo studio di tre possibili popolazioni immunitarie pro-tumorali studiate nell'HNSCC: i neutrofili tumore-associati (TAN), le cellule B intratumorali con fenotipo immunosoppressivo e i T-reg CD8+. Particolare attenzione Ăš data all'applicazione di moderne tecniche biostatistiche e bioinformatiche per riassumere informazioni complesse derivate da variabili cliniche e immunologiche multiparametriche e per validare risultati derivati ââin situ, attraverso dati di espressione genica derivati da dataset pubblici. Infine, la seconda parte della tesi prenderĂ in considerazione progetti di ricerca clinica rilevanti, volti a migliorare l'oncologia di precisione nell'HNSCC, sviluppando modelli predittivi di sopravvivenza, confrontando procedure oncologiche alternative, validando nuovi classificatori o testando l'uso di nuovi protocolli clinici come l'uso dell'immunonutrizione.Strong evidences demonstrate a close interplay between the immune system and the biological development and clinical progression of solid tumors. The effect that the tumor immune microenvironment can have on the clinical behavior of the disease is referred as the immuno contexture. Nevertheless, the current clinical management of patients affected by cancer does not take into account any immunological features either for the staging or for the treatment choices. Head and Neck Cancer (HNSCC) represents the 7th most common cancer worldwide and it is characterized by a relatively poor prognosis and detrimental effect of treatments on the quality of life of patients. Beyond surgery and radiotherapy, few systemic treatments are available, mainly represented by platinum-based chemotherapy or cetuximab. Immunotherapy is a new therapeutical strategy still limited to the palliative setting (recurrent not resectable or metastatic disease). The search for new biomarkers or possible new targetable mechanisms is meaningful especially in the clinical setting of HNSCC. In this thesis a focus will be given on the study of three possible pro-tumoral immune populations studied in HNSCC: the tumor associated neutrophils (TAN), intratumoral B-cells with a immunosuppressive phenotype and the CD8+ T-regs. Biostatistical and bioinformatical techniques are applied to summarize complex information derived from multiparametric clinical and immunological variables and to validate in-situ derived findings through gene expression data of public available datasets. Lastly, the second part of the thesis will take into account relevant clinical research projects, aimed at improving the precision oncology in HNSCC developing survival prediction models, comparing alternative oncological procedures, validating new classifiers or testing the use of novel clinical protocols as the use of immunnutrition
Automated Distinct Bone Segmentation from Computed Tomography Images using Deep Learning
Large-scale CT scans are frequently performed for forensic and diagnostic purposes, to plan and
direct surgical procedures, and to track the development of bone-related diseases. This often
involves radiologists who have to annotate bones manually or in a semi-automatic way, which is
a time consuming task. Their annotation workload can be reduced by automated segmentation
and detection of individual bones. This automation of distinct bone segmentation not only has
the potential to accelerate current workflows but also opens up new possibilities for processing
and presenting medical data for planning, navigation, and education.
In this thesis, we explored the use of deep learning for automating the segmentation of all
individual bones within an upper-body CT scan. To do so, we had to find a network architec-
ture that provides a good trade-off between the problemâs high computational demands and the
resultsâ accuracy. After finding a baseline method and having enlarged the dataset, we set out
to eliminate the most prevalent types of error. To do so, we introduced an novel method called
binary-prediction-enhanced multi-class (BEM) inference, separating the task into two: Distin-
guishing bone from non-bone is conducted separately from identifying the individual bones.
Both predictions are then merged, which leads to superior results. Another type of error is tack-
led by our developed architecture, the Sneaky-Net, which receives additional inputs with larger
fields of view but at a smaller resolution. We can thus sneak more extensive areas of the input
into the network while keeping the growth of additional pixels in check.
Overall, we present a deep-learning-based method that reliably segments most of the over
one hundred distinct bones present in upper-body CT scans in an end-to-end trained matter
quickly enough to be used in interactive software. Our algorithm has been included in our
groups virtual reality medical image visualisation software SpectoVR with the plan to be used
as one of the puzzle piece in surgical planning and navigation, as well as in the education of
future doctors
Design of decorative 3D models: from geodesic ornaments to tangible assemblies
L'obiettivo di questa tesi Ăš sviluppare strumenti utili per creare opere d'arte decorative digitali in 3D. Uno dei processi decorativi piĂč comunemente usati prevede la creazione di pattern decorativi, al fine di abbellire gli oggetti. Questi pattern possono essere dipinti sull'oggetto di base o realizzati con l'applicazione di piccoli elementi decorativi. Tuttavia, la loro realizzazione nei media digitali non Ăš banale. Da un lato, gli utenti esperti possono eseguire manualmente la pittura delle texture o scolpire ogni decorazione, ma questo processo puĂČ richiedere ore per produrre un singolo pezzo e deve essere ripetuto da zero per ogni modello da decorare. D'altra parte, gli approcci automatici allo stato dell'arte si basano sull'approssimazione di questi processi con texturing basato su esempi o texturing procedurale, o con sistemi di riproiezione 3D. Tuttavia, questi approcci possono introdurre importanti limiti nei modelli utilizzabili e nella qualitĂ dei risultati. Il nostro lavoro sfrutta invece i recenti progressi e miglioramenti delle prestazioni nel campo dell'elaborazione geometrica per creare modelli decorativi direttamente sulle superfici. Presentiamo una pipeline per i pattern 2D e una per quelli 3D, e dimostriamo come ognuna di esse possa ricreare una vasta gamma di risultati con minime modifiche dei parametri. Inoltre, studiamo la possibilitĂ di creare modelli decorativi tangibili. I pattern 3D generati possono essere stampati in 3D e applicati a oggetti realmente esistenti precedentemente scansionati. Discutiamo anche la creazione di modelli con mattoncini da costruzione, e la possibilitĂ di mescolare mattoncini standard e mattoncini custom stampati in 3D. CiĂČ consente una rappresentazione precisa indipendentemente da quanto la voxelizzazione sia approssimativa. I principali contributi di questa tesi sono l'implementazione di due diverse pipeline decorative, un approccio euristico alla costruzione con mattoncini e un dataset per testare quest'ultimo.The aim of this thesis is to develop effective tools to create digital decorative 3D artworks. Real-world art often involves the use of decorative patterns to enrich objects. These patterns can be painted on the base or might be realized with the application of small decorative elements. However, their creation in digital media is not trivial. On the one hand, users can manually perform texture paint or sculpt each decoration, in a process that can take hours to produce a single piece and needs to be repeated from the ground up for every model that needs to be decorated. On the other hand, automatic approaches in state of the art rely on approximating these processes with procedural or by-example texturing or with 3D reprojection. However, these approaches can introduce significant limitations in the models that can be used and in the quality of the results. Instead, our work exploits the recent advances and performance improvements in the geometry processing field to create decorative patterns directly on surfaces. We present a pipeline for 2D and one for 3D patterns and demonstrate how each of them can recreate a variety of results with minimal tweaking of the parameters. Furthermore, we investigate the possibility of creating decorative tangible models. The 3D patterns we generate can be 3D printed and applied to previously scanned real-world objects. We also discuss the creation of models with standard building bricks and the possibility of mixing standard and custom 3D-printed bricks. This allows for a precise representation regardless of the coarseness of the voxelization. The main contributions of this thesis are the implementation of two different decorative pipelines, a heuristic approach to brick construction, and a dataset to test the latter
Subgroup discovery for structured target concepts
The main object of study in this thesis is subgroup discovery, a theoretical framework for finding subgroups in dataâi.e., named sub-populationsâ whose behaviour with respect to a specified target concept is exceptional when compared to the rest of the dataset. This is a powerful tool that conveys crucial information to a human audience, but despite past advances has been limited to simple target concepts. In this work we propose algorithms that bring this framework to novel application domains. We introduce the concept of representative subgroups, which we use not only to ensure the fairness of a sub-population with regard to a sensitive trait, such as race or gender, but also to go beyond known trends in the data. For entities with additional relational information that can be encoded as a graph, we introduce a novel measure of robust connectedness which improves on established alternative measures of density; we then provide a method that uses this measure to discover which named sub-populations are more well-connected. Our contributions within subgroup discovery crescent with the introduction of kernelised subgroup discovery: a novel framework that enables the discovery of subgroups on i.i.d. target concepts with virtually any kind of structure. Importantly, our framework additionally provides a concrete and efficient tool that works out-of-the-box without any modification, apart from specifying the Gramian of a positive definite kernel. To use within kernelised subgroup discovery, but also on any other kind of kernel method, we additionally introduce a novel random walk graph kernel. Our kernel allows the fine tuning of the alignment between the vertices of the two compared graphs, during the count of the random walks, while we also propose meaningful structure-aware vertex labels to utilise this new capability. With these contributions we thoroughly extend the applicability of subgroup discovery and ultimately re-define it as a kernel method.Der Hauptgegenstand dieser Arbeit ist die Subgruppenentdeckung (Subgroup Discovery), ein theoretischer Rahmen fĂŒr das Auffinden von Subgruppen in Datenâd. h. benannte Teilpopulationenâderen Verhalten in Bezug auf ein bestimmtes Targetkonzept im Vergleich zum Rest des Datensatzes auĂergewöhnlich ist. Es handelt sich hierbei um ein leistungsfĂ€higes Instrument, das einem menschlichen Publikum wichtige Informationen vermittelt. Allerdings ist es trotz bisherigen Fortschritte auf einfache Targetkonzepte beschrĂ€nkt. In dieser Arbeit schlagen wir Algorithmen vor, die diesen Rahmen auf neuartige Anwendungsbereiche ĂŒbertragen. Wir fĂŒhren das Konzept der reprĂ€sentativen Untergruppen ein, mit dem wir nicht nur die Fairness einer Teilpopulation in Bezug auf ein sensibles Merkmal wie Rasse oder Geschlecht sicherstellen, sondern auch ĂŒber bekannte Trends in den Daten hinausgehen können. FĂŒr EntitĂ€ten mit zusĂ€tzlicher relationalen Information, die als Graph kodiert werden kann, fĂŒhren wir ein neuartiges MaĂ fĂŒr robuste Verbundenheit ein, das die etablierten alternativen DichtemaĂe verbessert; anschlieĂend stellen wir eine Methode bereit, die dieses MaĂ verwendet, um herauszufinden, welche benannte Teilpopulationen besser verbunden sind. Unsere BeitrĂ€ge in diesem Rahmen gipfeln in der EinfĂŒhrung der kernelisierten Subgruppenentdeckung: ein neuartiger Rahmen, der die Entdeckung von Subgruppen fĂŒr u.i.v. Targetkonzepten mit praktisch jeder Art von Struktur ermöglicht. Wichtigerweise, unser Rahmen bereitstellt zusĂ€tzlich ein konkretes und effizientes Werkzeug, das ohne jegliche Modifikation funktioniert, abgesehen von der Angabe des Gramian eines positiv definitiven Kernels. FĂŒr den Einsatz innerhalb der kernelisierten Subgruppentdeckung, aber auch fĂŒr jede andere Art von Kernel-Methode, fĂŒhren wir zusĂ€tzlich einen neuartigen Random-Walk-Graph-Kernel ein. Unser Kernel ermöglicht die Feinabstimmung der Ausrichtung zwischen den Eckpunkten der beiden unter-Vergleich-gestelltenen Graphen wĂ€hrend der ZĂ€hlung der Random Walks, wĂ€hrend wir auch sinnvolle strukturbewusste Vertex-Labels vorschlagen, um diese neue FĂ€higkeit zu nutzen. Mit diesen BeitrĂ€gen erweitern wir die Anwendbarkeit der Subgruppentdeckung grĂŒndlich und definieren wir sie im Endeffekt als Kernel-Methode neu
Probabilistic Inference for Model Based Control
Robotic systems are essential for enhancing productivity, automation, and performing hazardous tasks. Addressing the unpredictability of physical systems, this thesis advances robotic planning and control under uncertainty, introducing learning-based methods for managing uncertain parameters and adapting to changing environments in real-time.
Our first contribution is a framework using Bayesian statistics for likelihood-free inference of model parameters. This allows employing complex simulators for designing efficient, robust controllers. The method, integrating the unscented transform with a variant of information theoretical model predictive control, shows better performance in trajectory evaluation compared to Monte Carlo sampling, easing the computational load in various control and robotics tasks.
Next, we reframe robotic planning and control as a Bayesian inference problem, focusing on the posterior distribution of actions and model parameters. An implicit variational inference algorithm, performing Stein Variational Gradient Descent, estimates distributions over model parameters and control inputs in real-time. This Bayesian approach effectively handles complex multi-modal posterior distributions, vital for dynamic and realistic robot navigation.
Finally, we tackle diversity in high-dimensional spaces. Our approach mitigates underestimation of uncertainty in posterior distributions, which leads to locally optimal solutions. Using the theory of rough paths, we develop an algorithm for parallel trajectory optimisation, enhancing solution diversity and avoiding mode collapse. This method extends our variational inference approach for trajectory estimation, employing diversity-enhancing kernels and leveraging path signature representation of trajectories. Empirical tests, ranging from 2-D navigation to robotic manipulators in cluttered environments, affirm our method's efficiency, outperforming existing alternatives
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