2,493 research outputs found

    Classical and quantum algorithms for scaling problems

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    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

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    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 Δ, this problem falls into the regime of LovĂĄsz local lemma when Δ â‰Č qᔏ. In prior, however, fast approximate counting algorithms exist when Δ â‰Č qᔏ/Âł, and there is no known inapproximability result. In pursuit of this, our contribution is two-folded, stated as follows. ‱ When q, k ≄ 4 are evens and Δ ≄ 5·qᔏ/ÂČ, approximating the number of hypergraph colourings is NP-hard. ‱ When the input hypergraph is linear and Δ â‰Č qᔏ/ÂČ, a fast approximate counting algorithm does exist

    LIPIcs, Volume 251, ITCS 2023, Complete Volume

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    LIPIcs, Volume 251, ITCS 2023, Complete Volum

    Effects of municipal smoke-free ordinances on secondhand smoke exposure in the Republic of Korea

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    ObjectiveTo reduce premature deaths due to secondhand smoke (SHS) exposure among non-smokers, the Republic of Korea (ROK) adopted changes to the National Health Promotion Act, which allowed local governments to enact municipal ordinances to strengthen their authority to designate smoke-free areas and levy penalty fines. In this study, we examined national trends in SHS exposure after the introduction of these municipal ordinances at the city level in 2010.MethodsWe used interrupted time series analysis to assess whether the trends of SHS exposure in the workplace and at home, and the primary cigarette smoking rate changed following the policy adjustment in the national legislation in ROK. Population-standardized data for selected variables were retrieved from a nationally representative survey dataset and used to study the policy action’s effectiveness.ResultsFollowing the change in the legislation, SHS exposure in the workplace reversed course from an increasing (18% per year) trend prior to the introduction of these smoke-free ordinances to a decreasing (−10% per year) trend after adoption and enforcement of these laws (ÎČ2 = 0.18, p-value = 0.07; ÎČ3 = −0.10, p-value = 0.02). SHS exposure at home (ÎČ2 = 0.10, p-value = 0.09; ÎČ3 = −0.03, p-value = 0.14) and the primary cigarette smoking rate (ÎČ2 = 0.03, p-value = 0.10; ÎČ3 = 0.008, p-value = 0.15) showed no significant changes in the sampled period. Although analyses stratified by sex showed that the allowance of municipal ordinances resulted in reduced SHS exposure in the workplace for both males and females, they did not affect the primary cigarette smoking rate as much, especially among females.ConclusionStrengthening the role of local governments by giving them the authority to enact and enforce penalties on SHS exposure violation helped ROK to reduce SHS exposure in the workplace. However, smoking behaviors and related activities seemed to shift to less restrictive areas such as on the streets and in apartment hallways, negating some of the effects due to these ordinances. Future studies should investigate how smoke-free policies beyond public places can further reduce the SHS exposure in ROK

    Agnostic proper learning of monotone functions: beyond the black-box correction barrier

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    We give the first agnostic, efficient, proper learning algorithm for monotone Boolean functions. Given 2O~(n/Δ)2^{\tilde{O}(\sqrt{n}/\varepsilon)} uniformly random examples of an unknown function f:{±1}n→{±1}f:\{\pm 1\}^n \rightarrow \{\pm 1\}, our algorithm outputs a hypothesis g:{±1}n→{±1}g:\{\pm 1\}^n \rightarrow \{\pm 1\} that is monotone and (opt+Δ)(\mathrm{opt} + \varepsilon)-close to ff, where opt\mathrm{opt} is the distance from ff to the closest monotone function. The running time of the algorithm (and consequently the size and evaluation time of the hypothesis) is also 2O~(n/Δ)2^{\tilde{O}(\sqrt{n}/\varepsilon)}, nearly matching the lower bound of Blais et al (RANDOM '15). We also give an algorithm for estimating up to additive error Δ\varepsilon the distance of an unknown function ff to monotone using a run-time of 2O~(n/Δ)2^{\tilde{O}(\sqrt{n}/\varepsilon)}. Previously, for both of these problems, sample-efficient algorithms were known, but these algorithms were not run-time efficient. Our work thus closes this gap in our knowledge between the run-time and sample complexity. This work builds upon the improper learning algorithm of Bshouty and Tamon (JACM '96) and the proper semiagnostic learning algorithm of Lange, Rubinfeld, and Vasilyan (FOCS '22), which obtains a non-monotone Boolean-valued hypothesis, then ``corrects'' it to monotone using query-efficient local computation algorithms on graphs. This black-box correction approach can achieve no error better than 2opt+Δ2\mathrm{opt} + \varepsilon information-theoretically; we bypass this barrier by a) augmenting the improper learner with a convex optimization step, and b) learning and correcting a real-valued function before rounding its values to Boolean. Our real-valued correction algorithm solves the ``poset sorting'' problem of [LRV22] for functions over general posets with non-Boolean labels

    Two Source Extractors for Asymptotically Optimal Entropy, and (Many) More

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    A long line of work in the past two decades or so established close connections between several different pseudorandom objects and applications. These connections essentially show that an asymptotically optimal construction of one central object will lead to asymptotically optimal solutions to all the others. However, despite considerable effort, previous works can get close but still lack one final step to achieve truly asymptotically optimal constructions. In this paper we provide the last missing link, thus simultaneously achieving explicit, asymptotically optimal constructions and solutions for various well studied extractors and applications, that have been the subjects of long lines of research. Our results include: Asymptotically optimal seeded non-malleable extractors, which in turn give two source extractors for asymptotically optimal min-entropy of O(log⁡n)O(\log n), explicit constructions of KK-Ramsey graphs on NN vertices with K=log⁡O(1)NK=\log^{O(1)} N, and truly optimal privacy amplification protocols with an active adversary. Two source non-malleable extractors and affine non-malleable extractors for some linear min-entropy with exponentially small error, which in turn give the first explicit construction of non-malleable codes against 22-split state tampering and affine tampering with constant rate and \emph{exponentially} small error. Explicit extractors for affine sources, sumset sources, interleaved sources, and small space sources that achieve asymptotically optimal min-entropy of O(log⁡n)O(\log n) or 2s+O(log⁡n)2s+O(\log n) (for space ss sources). An explicit function that requires strongly linear read once branching programs of size 2n−O(log⁡n)2^{n-O(\log n)}, which is optimal up to the constant in O(⋅)O(\cdot). Previously, even for standard read once branching programs, the best known size lower bound for an explicit function is 2n−O(log⁡2n)2^{n-O(\log^2 n)}.Comment: Fixed some minor error

    Exploration autonome et efficiente de chantiers miniers souterrains inconnus avec un drone filaire

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    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  l’aide d’un capteur situĂ© au bout d’une perche que l’opĂ©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 d’ombres et une faible densitĂ© de points sur les parois Ă©loignĂ©es. Pour relever ces dĂ©fis, une Ă©quipe de recherche de l’UniversitĂ© de Sherbrooke conçoit un drone filaire Ă©quipĂ© d’un 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 d’un pilotage manuel, le facteur humain entraĂźne des problĂšmes de perception et comprĂ©hension d’un environnement 3D virtuel, et d’exĂ©cution d’une mission optimale. Cette thĂšse se concentre sur la navigation autonome sous deux aspects : la planification de trajectoire et l’exploration. Le systĂšme doit calculer une trajectoire qui cartographie l’environnement complet, en minimisant le temps de mission et en respectant la longueur maximale de fil embarquĂ©e. La planification de trajectoire Ă  l’aide d’un Rapidly-exploring Random Tree (RRT) trouve rapidement un chemin rĂ©alisable, mais l’optimisation est coĂ»teuse en calcul et la performance est variable et imprĂ©visible. L’exploration par la mĂ©thode des frontiĂšres est reprĂ©sentative de l’espace 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 n’optimisent 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 jusqu’à 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 d’exploration 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. L’approche 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. L’intĂ©gration de ces deux outils dans le NetherDrone produit un systĂšme intelligent pour l’exploration autonome, dotĂ© de fonctionnalitĂ©s semi-autonomes pour une interaction avec l’opĂ©rateur. Les travaux rĂ©alisĂ©s ouvrent la porte Ă  de nouvelles approches de navigation dans le domaine des missions d’inspection, de cartographie et de recherche et sauvetage

    Bridging Sports Nutrition & Diabetes Care: Assessing the Role of Protein Intake and Timing on Glycemia During and Following Physical Activity Among Adolescents and Adults with Type 1 Diabetes

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    For people with type 1 diabetes (T1D), the risk of experiencing hypoglycemia is elevated during and up to 24 hours following physical activity, the fear of which is a leading barrier to physical activity among this population. Increasing dietary protein intake, as recommended by sports nutrition guidelines, may promote a mild, prolonged hyperglycemic effect which may mitigate the risk of exercise-related hypoglycemia. Therefore, the goal of this dissertation was to evaluate the role of protein intake and timing on exercise-related glycemia among adolescents and adults with T1D. Data from the Flexible Lifestyles Empowering Change (FLEX) study were used to evaluate the role of pre-exercise, post-exercise, and daily protein intake on glycemia during and following bouts of moderate-to-vigorous physical activity (MVPA) among adolescents with T1D (n=112) utilizing mixed effects regression modeling. Dietary intake and MVPA were quantified using 24-hour dietary recalls and previous day physical activity records, respectively. Percent time in recommended glucose range (TIR, 70-180mg/dL), percent time below range (TBR, 180mg/dL) during MVPA bouts as well as from bout cessation until the following morning were calculated from continuous glucose monitoring (CGM) data. Additional secondary analyses were conducted using data from an exercise pilot study to evaluate the role of post-exercise protein intake on post-exercise glycemia among adults with T1D following supervised bouts of moderate-intensity continuous training (MICT) or high-intensity interval training (HIIT) performed following an overnight fast. Dietary intake was quantified using 3-day food records and TIR, TBR and TAR were calculated using CGM data. Protein intakes of at least 10g or 0.125g/kg consumed within 4 hours prior to MVPA were associated with reduced TBR among adolescents with T1D. Additionally, daily protein intakes within sports nutrition guidelines (1.2-2.0g/kg/day) were associated with reduced TAR and increased TIR following MVPA, with stronger associations identified for adolescents with overweight or obesity, those using multiple daily insulin injections, and females. Furthermore, there was a trend (p=0.05) towards reduced TBR following MICT, but not HIIT among adults with T1D. Following sports nutrition guidelines for protein intake may improve the glycemic response to exercise for people living with T1D.Doctor of Philosoph
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