This House Proves that Debating is Harder than Soccer

During the last twenty years, a lot of research was conducted on the sport elimination problem: Given a sports league and its remaining matches, we have to decide whether a given team can still possibly win the competition, i.e., place first in the league at the end. Previously, the computational complexity of this problem was investigated only for games with two participating teams per game. In this paper we consider Debating Tournaments and Debating Leagues in the British Parliamentary format, where four teams are participating in each game. We prove that it is NP-hard to decide whether a given team can win a Debating League, even if at most two matches are remaining for each team. This contrasts settings like football where two teams play in each game since there this case is still polynomial time solvable. We prove our result even for a fictitious restricted setting with only three teams per game. On the other hand, for the common setting of Debating Tournaments we show that this problem is fixed parameter tractable if the parameter is the number of remaining rounds $k$. This also holds for the practically very important question of whether a team can still qualify for the knock-out phase of the tournament and the combined parameter $k + b$ where $b$ denotes the threshold rank for qualifying. Finally, we show that the latter problem is polynomial time solvable for any constant $k$ and arbitrary values $b$ that are part of the input.Comment: 18 pages, to appear at FUN 201

Parameterized Approximation Schemes for Independent Set of Rectangles and Geometric Knapsack

The area of parameterized approximation seeks to combine approximation and parameterized algorithms to obtain, e.g., (1+epsilon)-approximations in f(k,epsilon)n^O(1) time where k is some parameter of the input. The goal is to overcome lower bounds from either of the areas. We obtain the following results on parameterized approximability: - In the maximum independent set of rectangles problem (MISR) we are given a collection of n axis parallel rectangles in the plane. Our goal is to select a maximum-cardinality subset of pairwise non-overlapping rectangles. This problem is NP-hard and also W[1]-hard [Marx, ESA\u2705]. The best-known polynomial-time approximation factor is O(log log n) [Chalermsook and Chuzhoy, SODA\u2709] and it admits a QPTAS [Adamaszek and Wiese, FOCS\u2713; Chuzhoy and Ene, FOCS\u2716]. Here we present a parameterized approximation scheme (PAS) for MISR, i.e. an algorithm that, for any given constant epsilon>0 and integer k>0, in time f(k,epsilon)n^g(epsilon), either outputs a solution of size at least k/(1+epsilon), or declares that the optimum solution has size less than k. - In the (2-dimensional) geometric knapsack problem (2DK) we are given an axis-aligned square knapsack and a collection of axis-aligned rectangles in the plane (items). Our goal is to translate a maximum cardinality subset of items into the knapsack so that the selected items do not overlap. In the version of 2DK with rotations (2DKR), we are allowed to rotate items by 90 degrees. Both variants are NP-hard, and the best-known polynomial-time approximation factor is 2+epsilon [Jansen and Zhang, SODA\u2704]. These problems admit a QPTAS for polynomially bounded item sizes [Adamaszek and Wiese, SODA\u2715]. We show that both variants are W[1]-hard. Furthermore, we present a PAS for 2DKR. For all considered problems, getting time f(k,epsilon)n^O(1), rather than f(k,epsilon)n^g(epsilon), would give FPT time f\u27(k)n^O(1) exact algorithms by setting epsilon=1/(k+1), contradicting W[1]-hardness. Instead, for each fixed epsilon>0, our PASs give (1+epsilon)-approximate solutions in FPT time. For both MISR and 2DKR our techniques also give rise to preprocessing algorithms that take n^g(epsilon) time and return a subset of at most k^g(epsilon) rectangles/items that contains a solution of size at least k/(1+epsilon) if a solution of size k exists. This is a special case of the recently introduced notion of a polynomial-size approximate kernelization scheme [Lokshtanov et al., STOC\u2717]

Astrocytes as a Source for Extracellular Matrix Molecules and Cytokines

Research of the past 25 years has shown that astrocytes do more than participating and building up the blood-brain barrier and detoxify the active synapse by reuptake of neurotransmitters and ions. Indeed, astrocytes express neurotransmitter receptors and, as a consequence, respond to stimuli. Within the tripartite synapse, the astrocytes owe more and more importance. Besides the functional aspects the differentiation of astrocytes has gained a more intensive focus. Deeper knowledge of the differentiation processes during development of the central nervous system might help explaining and even help treating neurological diseases like Alzheimer’s disease, Amyotrophic lateral sclerosis, Parkinsons disease, and psychiatric disorders in which astrocytes have been shown to play a role. Specific differentiation of neural stem cells toward the astroglial lineage is performed as a multi-step process. Astrocytes and oligodendrocytes develop from a multipotent stem cell that prior to this has produced primarily neuronal precursor cells. This switch toward the more astroglial differentiation is regulated by a change in receptor composition on the cell surface and responsiveness to Fibroblast growth factor and Epidermal growth factor (EGF). The glial precursor cell is driven into the astroglial direction by signaling molecules like Ciliary neurotrophic factor, Bone Morphogenetic Proteins, and EGF. However, the early astrocytes influence their environment not only by releasing and responding to diverse soluble factors but also express a wide range of extracellular matrix (ECM) molecules, in particular proteoglycans of the lectican family and tenascins. Lately these ECM molecules have been shown to participate in glial development. In this regard, especially the matrix protein Tenascin C (Tnc) proved to be an important regulator of astrocyte precursor cell proliferation and migration during spinal cord development. Nevertheless, ECM molecules expressed by reactive astrocytes are also known to act mostly in an inhibitory fashion under pathophysiological conditions. Thus, we further summarize resent data concerning the role of chondroitin sulfate proteoglycans and Tnc under pathological conditions

Dynamic Approximate Maximum Independent Set of Intervals, Hypercubes and Hyperrectangles

Independent set is a fundamental problem in combinatorial optimization. While in general graphs the problem is essentially inapproximable, for many important graph classes there are approximation algorithms known in the offline setting. These graph classes include interval graphs and geometric intersection graphs, where vertices correspond to intervals/geometric objects and an edge indicates that the two corresponding objects intersect. We present dynamic approximation algorithms for independent set of intervals, hypercubes and hyperrectangles in d dimensions. They work in the fully dynamic model where each update inserts or deletes a geometric object. All our algorithms are deterministic and have worst-case update times that are polylogarithmic for constant d and ?>0, assuming that the coordinates of all input objects are in [0, N]^d and each of their edges has length at least 1. We obtain the following results: - For weighted intervals, we maintain a (1+?)-approximate solution. - For d-dimensional hypercubes we maintain a (1+?)2^d-approximate solution in the unweighted case and a O(2^d)-approximate solution in the weighted case. Also, we show that for maintaining an unweighted (1+?)-approximate solution one needs polynomial update time for d ? 2 if the ETH holds. - For weighted d-dimensional hyperrectangles we present a dynamic algorithm with approximation ratio (1+?)log^{d-1}N

Karl Schlögel / Karl-Konrad Tschäpe (Hrsg.), Die Russische Revolution und das Schicksal der russischen Juden. Eine Debatte in Berlin 1922/23. Berlin, Matthes & Seitz 2014. 762 S., € 49,90

Dieser Beitrag ist mit Zustimmung des Rechteinhabers aufgrund einer (DFG-geförderten) Allianz- bzw. Nationallizenz frei zugänglich.Peer Reviewe

ChaeRan Y. Freeze / Jay M. Harris (Eds.), Everyday Jewish Life in Imperial Russia. Select Documents (1772–1914). (Tauber Institute Series for the Study of European Jewry.) Waltham, MA, Brandeis University Press 2013

Peer Reviewe