Computing shortest closed curves on non-orientable surfaces

We initiate the study of computing shortest non-separating simple closed curves with some given topological properties on non-orientable surfaces. While, for orientable surfaces, any two non-separating simple closed curves are related by a self-homeomorphism of the surface, and computing shortest such curves has been vastly studied, for non-orientable ones the classification of non-separating simple closed curves up to ambient homeomorphism is subtler, depending on whether the curve is one-sided or two-sided, and whether it is orienting or not (whether it cuts the surface into an orientable one). We prove that computing a shortest orienting (weakly) simple closed curve on a non-orientable combinatorial surface is NP-hard but fixed-parameter tractable in the genus of the surface. In contrast, we can compute a shortest non-separating non-orienting (weakly) simple closed curve with given sidedness in $g^{O(1)}\cdot n\log n$ time, where $g$ is the genus and $n$ the size of the surface. For these algorithms, we develop tools that can be of independent interest, to compute a variation on canonical systems of loops for non-orientable surfaces based on the computation of an orienting curve, and some covering spaces that are essentially quotients of homology covers

China-Central Asia Regionalization and Its Impact on the Central Asian Region and Beyond

Since gaining independence, Central Asian countries have maintained stable and friendly relationships with China. Through China-led bilateral, regional, and multilateral projects, China and Central Asia have significantly strengthened their strategic partnership and elevated the importance of their relationship in the region-building process. As a result of these interactions, Central Asia is emerging as an active regional actor. This article characterizes China and Central Asia’s interactions as Warleigh-Lack\u27s (2006) “regionalization” and examines the impact of this process on diffusing China’s model of regionalism in Central Asia. Specifically, the article aims to answer the question: what are the implications of China and Central Asia’s regionalization processes for shaping the region and for the presence of a third actor, Russia? Employing Acharya’s (2004) “norm localization” analytical framework, the article argues that the current Central Asian regional cooperation model can be described as an indirect (recipient-driven) influence of China and Central Asia’s regionalization processes within the scope of the Shanghai Cooperation Agreement (SCO), bilateral strategic partnership agreements and the Belt and Road Initiative (BRI). It posits that, of the various types of indirect diffusion of institutional and policy models of regionalism, the new Central Asian model of regional cooperation entails a “lesson-drawing” diffusion mechanism from the Chinese model of regionalism. La régionalisation Chine-Asie centrale et son impact sur la région d\u27Asie centrale et au-delà Depuis leur accession à l\u27indépendance, les pays d\u27Asie centrale ont entretenu des relations stables et amicales avec la Chine. Grâce à des projets bilatéraux, régionaux et multilatéraux menés par la Chine, la Chine et l\u27Asie centrale ont considérablement renforcé leur partenariat stratégique et accru l\u27importance de leurs relations dans la construction de la région. Grâce à ces interactions, l\u27Asie centrale en tant que telle est en passe de devenir un acteur régional important. L’auteure caractérise les interactions entre la Chine et l\u27Asie centrale comme un exemple de la « régionalisation » de Warleigh-Lack (2006) et examine l\u27impact de ce processus sur la diffusion du modèle chinois de régionalisme en Asie centrale. Quelles sont les implications des processus de régionalisation de la Chine et de l\u27Asie centrale pour la construction de la région et pour la présence d\u27un troisième acteur d’importance, la Russie ? S\u27appuyant sur le cadre analytique de « localisation des normes » d\u27Acharya (2004), l\u27auteure soutient que le modèle actuel de coopération régionale en Asie centrale peut être décrit comme une influence indirecte (par les bénéficiaires) des processus de régionalisation de la Chine et de l\u27Asie centrale dans le cadre de l\u27Accord de coopération de Shanghai (OCS), des accords bilatéraux de partenariat stratégique et de l\u27Initiative route et ceinture (IRC). Elle postule que, parmi les différents types de diffusion indirecte des modèles institutionnels et politiques de régionalisme, le nouveau modèle centrasiatique de coopération régionale implique un modèle de diffusion inspiré du modèle chinois de régionalisme.  

Monte Carlo Models for Eye Plaque Brachytherapy Treatment of Iris Melanoma

Eye plaque brachytherapy is an effective treatment for eye cancer that uses radioactive seeds (that emit low-energy photons) in an applicator. The purpose of this work is to model eye plaques used to treat iris melanoma and evaluate radiation dose (energy deposited per unit mass) using Monte Carlo simulations. The simulations are performed using the egs_brachy code using 125I (OncoSeed 6711) and 103Pd (TheraSeed 200) brachytherapy seeds. The plaques span 180°, 270°and 360°  arcs and are modelled at the center of a 30 cm3  water volume. Dose was scored in a 2.55 cm3 sub-volume made up of 0.5mm3 voxels for simulations with 1010 histories. Voxelized three-dimensional (3D) dose distributions for each plaque are calculated and compared to published BrachyDose data (Thomson et al., 2010). egs_brachy calculated doses are compared to BrachyDose considering absolute dose in gray, dose as a percentage of prescription dose, and dose relative to the TG43 approach currently used in hospitals (Rivard et al., 2004). Statistical analyses show agreement within a 95% confidence interval with published data at 6 points of interest in the eye (cornea, sclera, lens, eye center, macula, and optic disk). Along the plaque central axis, egs_brachy and BrachyDose results agree within statistical uncertainties. In conclusion, eye plaques used for treatment of iris melanoma were successfully modelled and benchmarked. These models will be distributed (open source) with the egs_brachy code on GitHub, enabling state-of-the-art dose calculations in hospitals that will improve patient treatments

Worst-case deterministic fully-dynamic biconnectivity in changeable planar embeddings

We study dynamic planar graphs with $n$ vertices, subject to edge deletion, edge contraction, edge insertion across a face, and the splitting of a vertex in specified corners. We dynamically maintain a combinatorial embedding of such a planar graph, subject to connectivity and 2-vertex-connectivity (biconnectivity) queries between pairs of vertices. Whenever a query pair is connected and not biconnected, we find the first and last cut vertex separating them. Additionally, we allow local changes to the embedding by flipping the embedding of a subgraph that is connected by at most two vertices to the rest of the graph. We support all queries and updates in deterministic, worst-case, $O(\log^2 n)$ time, using an $O(n)$-sized data structure

Was That Use of Force Reasonable? The Public Doesn’t Know

There is a gap between what community members believe is reasonable use of force and what the law defines as reasonable. This divide has led to significant consequences for police departments across the country and society as a whole. In the current study, community members’ assessments of force reasonableness aligned with the legal standard on use of force only about half of the time, partly because legally irrelevant factors influenced their assessments. To reduce the divide between community and legal standards on use of force, police leaders can provide community education, revise departmental policy, and/or deliver de-escalation training

Geometric hitting set for line-constrained disks and related problems

Given a set $P$ of $n$ weighted points and a set $S$ of $m$ disks in the plane, the hitting set problem is to compute a subset $P\u27$ of points of $P$ such that each disk contains at least one point of $P\u27$ and the total weight of all points of $P\u27$ is minimized. The problem is known to be NP-hard. In this paper, we consider a line-constrained version of the problem in which all disks are centered on a line $\ell$. We present an $O((m+n)\log(m+n)+\kappa \log m)$ time algorithm for the problem, where $\kappa$ is the number of pairs of disks that intersect. For the unit-disk case where all disks have the same radius, the running time can be reduced to $O((n + m)\log(m + n))$. In addition, we solve the problem in $O((m + n)\log(m + n))$ time in the $L_{\infty}$ and $L_1$ metrics, in which a disk is a square and a diamond (assuming that $\ell$ is horizontal), respectively. Our techniques can also be used to solve other geometric hitting set problems. For example, given in the plane a set $P$ of $n$ weighted points and a set $S$ of $n$ half-planes, we solve in $O(n^4\log n)$ time the problem of finding a minimum weight hitting set of $P$ for $S$. This improves the previous best algorithm of $O(n^6)$ time by nearly a quadratic factor

New Regional Alignment in the Post-Soviet Space: The EU as an Active Player in the Eastern Partnership Countries (Case of Georgia)

This article examines how the interests, objectives, strategy and policy of the European Union (EU) towards the countries of the Eastern Partnership have changed over time, with a focus on Georgia. The article explains the essence of Europeanization and integration processes in this region, as well as the new role the EU plays in the post-Soviet region. The case of Georgia is used as an example. The article examines how Georgia\u27s status gradually changed from a recipient of EU humanitarian aid to an EU candidate country. The article analyzes various official EU documents that subsequently became guides for the formation of the EU policy about  the Eastern Partnership countries. The article also draws attention to the contradictory geographical identity of individual Eastern Partnership countries, most notably the South Caucasus, including Georgia. The article shows how war became the main variable influencing the fundamental revision of the EU policy towards the Eastern Partnership countries and examples include the Georgian-Russian war of 2008 and the Ukrainian-Russian war. The article examines how the war in both cases became a trigger for the development of new geopolitical projects and concepts on the part of the EU. Nouvel alignement régional dans l\u27espace post-soviétique : L\u27UE en tant qu\u27acteur actif dans les pays du partenariat oriental (Le cas de la Géorgie) Les intérêts, les objectifs, la stratégie et la politique de l\u27Union européenne (UE) à l\u27égard des pays du Partenariat oriental ont évolué au fil du temps. L’auteur étudie cette évolution à travers le cas de la Géorgie. Il explique l\u27essence des processus d\u27européanisation et d\u27intégration dans cette région, ainsi que le nouveau rôle que joue l\u27UE dans la région post-soviétique, montrant que le statut de la Géorgie a progressivement changé, passant de celui de bénéficiaire de l\u27aide humanitaire de l\u27UE à celui de pays candidat à l\u27UE. L\u27analyse porte sur divers documents officiels de l\u27UE qui sont devenus par la suite des guides pour l\u27élaboration de sa politique à l\u27égard des pays du Partenariat oriental et sur les identités géographiques contradictoires des différents pays du Partenariat oriental, notamment dans la région du Caucase du Sud, avec la Géorgie comme exemple clé. L’auteur montre comment la guerre est devenue la variable principale influençant la révision fondamentale de la politique de l\u27UE à l\u27égard des pays du Partenariat oriental, grâce aux exemples de la guerre russo-géorgienne de 2008 et de la guerre russo-ukrainienne de 2022. Enfin, il s’intéresse au fait que la guerre a déclenché, dans les deux cas, de nouveaux projets géopolitiques de la part de l\u27UE, étayés par de nouveaux concepts

Competing Visions and New Regional Order in Central Asia and Caucasus

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