Approximation Algorithms for Generalized MST and TSP in Grid Clusters

We consider a special case of the generalized minimum spanning tree problem (GMST) and the generalized travelling salesman problem (GTSP) where we are given a set of points inside the integer grid (in Euclidean plane) where each grid cell is $1 \times 1$. In the MST version of the problem, the goal is to find a minimum tree that contains exactly one point from each non-empty grid cell (cluster). Similarly, in the TSP version of the problem, the goal is to find a minimum weight cycle containing one point from each non-empty grid cell. We give a $(1+4\sqrt{2}+\epsilon)$ and $(1.5+8\sqrt{2}+\epsilon)$-approximation algorithm for these two problems in the described setting, respectively. Our motivation is based on the problem posed in [7] for a constant approximation algorithm. The authors designed a PTAS for the more special case of the GMST where non-empty cells are connected end dense enough. However, their algorithm heavily relies on this connectivity restriction and is unpractical. Our results develop the topic further

The transferencial relation beyond the interpretation : reflections from the theory of Winnicott.

Este artigo reflete sobre a importância de pensar a relação transferencial na clínica psicanalítica para além da interpretação. Para isso, utiliza-se a concepção de Winnicott como referencial teórico, sendo ressaltadas a noção de holding, a regressão à dependência e a questão do uso de objetos e sua influência sobre a técnica da interpretação. Winnicott revela que na clínica com alguns pacientes, em especial os autistas e psicóticos, o objetivo da análise, antes de fornecer interpretações, é proporcionar um ambiente suficientemente bom a partir do qual o sujeito pode retomar o processo de constituição de si mesmo e da externalidade do mundo.This article reflects about the importance of thinking the transferencial relation in the psychoanalytic clinic beyond the interpretation. For this, the Winnicott’s concept is used as theoretical reference, highlighting the concept of holding, regression to dependence and the question of the use of objects and its influence on the technique of interpretation. Winnicott shows that in the clinic, with some patients, particularly autistic and psychotic, before providing interpretation, the objective of the analysis is to provide a good environment from which the subject can retake the constitution process of himself/herself and of the externality of the world

Political economy of planned relocation: A model of action and inaction in government responses

This is the author accepted manuscript. The final version is available from Elsevier via the DOI in this record.Planned relocation has been shown to have significant impacts on the livelihoods and wellbeing of people and communities, whether the resettlement process is inclusive or coercive. For states, planned relocation represents risks to those communities but also to government investments and political legitimacy. Evaluations of relocations commonly focus on the risks and benefits of government interventions while overlooking the consequences of not intervening. Here we develop a conceptual framework to examine the factors that influence government decision-making about whether or not to undertake planned relocation of populations in the context of environmental change. The study examines planned relocation decisions and non-decisions by government agencies in West Bengal in India for communities seeking relocation due to coastal flooding. It focuses on three localities facing river erosion losing significant land areas in small islands and communities where populations recognize the need for public intervention, but where there has been a diversity of responses from the state authorities. Data are derived from interviews with key respondents involved in planning and implementing relocation and with residents affected by those government decisions (n = 26). These data show that government action is explained by a combination of risk aversion within political systems to avoid perceived negative consequences, and a lack of government accountability. The empirical cases demonstrate the uneven application of action and inaction and the consequent uneven distribution of potential outcomes on populations. The study suggests that while there may be a growing demand for planned relocation in places affected by environmental change, its implementation is likely to be uneven, with profound socioeconomic implications for those living in such localities.International Development Research Centr

On the Sets of Real Numbers Recognized by Finite Automata in Multiple Bases

This article studies the expressive power of finite automata recognizing sets of real numbers encoded in positional notation. We consider Muller automata as well as the restricted class of weak deterministic automata, used as symbolic set representations in actual applications. In previous work, it has been established that the sets of numbers that are recognizable by weak deterministic automata in two bases that do not share the same set of prime factors are exactly those that are definable in the first order additive theory of real and integer numbers. This result extends Cobham's theorem, which characterizes the sets of integer numbers that are recognizable by finite automata in multiple bases. In this article, we first generalize this result to multiplicatively independent bases, which brings it closer to the original statement of Cobham's theorem. Then, we study the sets of reals recognizable by Muller automata in two bases. We show with a counterexample that, in this setting, Cobham's theorem does not generalize to multiplicatively independent bases. Finally, we prove that the sets of reals that are recognizable by Muller automata in two bases that do not share the same set of prime factors are exactly those definable in the first order additive theory of real and integer numbers. These sets are thus also recognizable by weak deterministic automata. This result leads to a precise characterization of the sets of real numbers that are recognizable in multiple bases, and provides a theoretical justification to the use of weak automata as symbolic representations of sets.Comment: 17 page

Forward Analysis and Model Checking for Trace Bounded WSTS

We investigate a subclass of well-structured transition systems (WSTS), the bounded---in the sense of Ginsburg and Spanier (Trans. AMS 1964)---complete deterministic ones, which we claim provide an adequate basis for the study of forward analyses as developed by Finkel and Goubault-Larrecq (Logic. Meth. Comput. Sci. 2012). Indeed, we prove that, unlike other conditions considered previously for the termination of forward analysis, boundedness is decidable. Boundedness turns out to be a valuable restriction for WSTS verification, as we show that it further allows to decide all $\omega$-regular properties on the set of infinite traces of the system

Exploiting the Temporal Logic Hierarchy and the Non-Confluence Property for Efficient LTL Synthesis

The classic approaches to synthesize a reactive system from a linear temporal logic (LTL) specification first translate the given LTL formula to an equivalent omega-automaton and then compute a winning strategy for the corresponding omega-regular game. To this end, the obtained omega-automata have to be (pseudo)-determinized where typically a variant of Safra's determinization procedure is used. In this paper, we show that this determinization step can be significantly improved for tool implementations by replacing Safra's determinization by simpler determinization procedures. In particular, we exploit (1) the temporal logic hierarchy that corresponds to the well-known automata hierarchy consisting of safety, liveness, Buechi, and co-Buechi automata as well as their boolean closures, (2) the non-confluence property of omega-automata that result from certain translations of LTL formulas, and (3) symbolic implementations of determinization procedures for the Rabin-Scott and the Miyano-Hayashi breakpoint construction. In particular, we present convincing experimental results that demonstrate the practical applicability of our new synthesis procedure

A Novel Genome-Wide Association Study Approach Using Genotyping by Exome Sequencing Leads to the Identification of a Primary Open Angle Glaucoma Associated Inversion Disrupting ADAMTS17

Closed breeding populations in the dog in conjunction with advances in gene mapping and sequencing techniques facilitate mapping of autosomal recessive diseases and identification of novel disease-causing variants, often using unorthodox experimental designs. In our investigation we demonstrate successful mapping of the locus for primary open angle glaucoma in the Petit Basset Griffon Vendéen dog breed with 12 cases and 12 controls, using a novel genotyping by exome sequencing approach. The resulting genome-wide association signal was followed up by genome sequencing of an individual case, leading to the identification of an inversion with a breakpoint disrupting the ADAMTS17 gene. Genotyping of additional controls and expression analysis provide strong evidence that the inversion is disease causing. Evidence of cryptic splicing resulting in novel exon transcription as a consequence of the inversion in ADAMTS17 is identified through RNAseq experiments. This investigation demonstrates how a novel genotyping by exome sequencing approach can be used to map an autosomal recessive disorder in the dog, with the use of genome sequencing to facilitate identification of a disease-associated variant

Node-weighted Steiner tree and group Steiner tree in planar graphs

We improve the approximation ratios for two optimization problems in planar graphs. For node-weighted Steiner tree, a classical network-optimization problem, the best achievable approximation ratio in general graphs is Θ [theta] (logn), and nothing better was previously known for planar graphs. We give a constant-factor approximation for planar graphs. Our algorithm generalizes to allow as input any nontrivial minor-closed graph family, and also generalizes to address other optimization problems such as Steiner forest, prize-collecting Steiner tree, and network-formation games. The second problem we address is group Steiner tree: given a graph with edge weights and a collection of groups (subsets of nodes), find a minimum-weight connected subgraph that includes at least one node from each group. The best approximation ratio known in general graphs is O(log3 [superscript 3] n), or O(log2 [superscript 2] n) when the host graph is a tree. We obtain an O(log n polyloglog n) approximation algorithm for the special case where the graph is planar embedded and each group is the set of nodes on a face. We obtain the same approximation ratio for the minimum-weight tour that must visit each group

Antichain Algorithms for Finite Automata

We present a general theory that exploits simulation relations on transition systems to obtain antichain algorithms for solving the reachability and repeated reachability problems. Antichains are more succinct than the sets of states manipulated by the traditional fixpoint algorithms. The theory justifies the correctness of the antichain algorithms, and applications such as the universality problem for finite automata illustrate efficiency improvements. Finally, we show that new and provably better antichain algorithms can be obtained for the emptiness problem of alternating automata over finite and infinite words