The Computational Complexity of the Game of Set and its Theoretical Applications

The game of SET is a popular card game in which the objective is to form Sets using cards from a special deck. In this paper we study single- and multi-round variations of this game from the computational complexity point of view and establish interesting connections with other classical computational problems. Specifically, we first show that a natural generalization of the problem of finding a single Set, parameterized by the size of the sought Set is W-hard; our reduction applies also to a natural parameterization of Perfect Multi-Dimensional Matching, a result which may be of independent interest. Second, we observe that a version of the game where one seeks to find the largest possible number of disjoint Sets from a given set of cards is a special case of 3-Set Packing; we establish that this restriction remains NP-complete. Similarly, the version where one seeks to find the smallest number of disjoint Sets that overlap all possible Sets is shown to be NP-complete, through a close connection to the Independent Edge Dominating Set problem. Finally, we study a 2-player version of the game, for which we show a close connection to Arc Kayles, as well as fixed-parameter tractability when parameterized by the number of rounds played

Monomial Testing and Applications

In this paper, we devise two algorithms for the problem of testing $q$-monomials of degree $k$ in any multivariate polynomial represented by a circuit, regardless of the primality of $q$. One is an $O^*(2^k)$ time randomized algorithm. The other is an $O^*(12.8^k)$ time deterministic algorithm for the same $q$-monomial testing problem but requiring the polynomials to be represented by tree-like circuits. Several applications of $q$-monomial testing are also given, including a deterministic $O^*(12.8^{mk})$ upper bound for the $m$-set $k$-packing problem.Comment: 17 pages, 4 figures, submitted FAW-AAIM 2013. arXiv admin note: substantial text overlap with arXiv:1302.5898; and text overlap with arXiv:1007.2675, arXiv:1007.2678, arXiv:1007.2673 by other author

Protocol: optimised electrophyiological analysis of intact guard cells from arabidopsis

Genetic resources available for Arabidopsis thaliana make this species particularly attractive as a model for molecular genetic studies of guard cell homeostasis, transport and signalling, but this facility is not matched by accessible tools for quantitative analysis of transport in the intact cell. We have developed a reliable set of procedures for voltage clamp analysis of guard cells from Arabidopsis leaves. These procedures greatly simplify electrophysiological recordings, extending the duration of measurements and scope for analysis of the predominant K+ and anion channels of intact stomatal guard cells to that achieved previously in work with Vicia and tobacco guard cells

Reducing Urban Pollution Exposure from Road Transport(RUPERT)

This paper presents the preliminary results of a two-year study on reducing urban pollution exposure from road transport (RUPERT). The main aim of this project is to develop a new modelling framework for nitrogen dioxide, carbon monoxide and particulate matter to simulate exposures of different population groups across a city, and to assess the impact of roadside concentrations on these exposures. This will be achieved by modelling the frequency distribution of personal exposures (PEFDs) as a function of urban background and roadside concentrations, under different traffic conditions. The modelling approach combines new and existing models relating traffic and air pollution data, with particular emphasis of the impact of congestion, and the probabilistic modelling framework of personal exposure. Modelling of roadside concentrations consists of two main elements, namely the analysis of concentrations patterns at different roadside sites and of the relationship between traffic conditions and added roadside pollution. Roadside concentrations are predicted using empirically derived relationships; statistical models, novel statistics and artificial neural networks namely feed forward neural network and radial basis neural network. The exposure modelling is carried out by linking two models: the INDAIR model, which is designed to simulate probabilistically diurnal profiles of air pollutant concentrations in a range of microenvironments, and the EXPAIR model, which is designed to simulate population exposure patterns based on population time-activity patterns and a library of micro-environmental concentrations derived from the INDAIR model

Characterization of Grain Boundaries in Superplastically Deformed Y-TZP Ceramics

The effects of compressive deformation on the grain boundary characteristics of fine-grained Y-TZP have been investigated using surface spectroscopy, impedance analysis, and transmission electron microscopy. After sintering at low temperature (1150°C), the grain boundaries are covered by an ultrathin (1nm) yttrium-rich amorphous film. After deformation at 1200°–1300°C under low stress, some grain boundaries are no longer covered by the amorphous film. Yttrium segregation seems to occur only at wetted grain boundaries. Evidence has been found that the extent of dewetting increases with increasing applied stress

Use of hydraulic rating to set environmental flows in the Zhangxi River, China

Ningbo city, China, is a rapidly growing residential and industrial centre, with a current population of 4 million. Its development has required a major water supply expansion programme providing 400,000 m3 of water per day from the upper reaches of the Zhangxi River by means of a cascade of reservoirs. Water resources management is achieved through operation of two major reservoirs, Jiaokou (75 million m3) and Zhougongzhai (93 million m3). Water is released from the reservoirs, via turbines (generating hydropower), for local industry, irrigated agriculture and public supply along the lower reaches of the River and to maintain the river ecosystem. Surveys of local residents along the Zhangxi River showed its important role in aspects of life, social activity, culture and leisure. Analysis of ecological monitoring data demonstrated the diverse nature of fish, plants and invertebrates within the river. Some elements of the ecosystem have a high local economic value to local people. This paper reports an assessment of the environmental flow needed to support key species in the river ecosystem. It employs hydraulic ratings to define sections of the river where flow velocity reaches 0.5 ms-1, required to stimulate spawning of the moonlight fish, an economically important and indicator species in the river. In two out of 6 cross-sections studied, flow releases from the reservoirs meet the needs of fish. The reservoirs reduce flood flows, which may lead to a loss of deep pools that are essential for the fish to survive during winter month

Entropy spectrum of a Kerr anti-de Sitter black hole

The entropy spectrum of a spherically symmetric black hole was derived without the quasinormal modes in the work of Majhi and Vagenas. Extending this work to rotating black holes, we quantize the entropy and the horizon area of a Kerr anti-de Sitter black hole by two methods. The spectra of entropy and area are obtained via the Bohr-Sommerfeld quantization rule and the adiabatic invariance in the first way. By addressing the wave function of emitted (absorbed) particles, the entropy and the area are quantized in the second one. Both results show that the entropy and the area spectra are equally spaced.Comment: Accepted for publication in The European Physical Journal C, Volume 72, Issue

The zero exemplar distance problem

Given two genomes with duplicate genes, \textsc{Zero Exemplar Distance} is the problem of deciding whether the two genomes can be reduced to the same genome without duplicate genes by deleting all but one copy of each gene in each genome. Blin, Fertin, Sikora, and Vialette recently proved that \textsc{Zero Exemplar Distance} for monochromosomal genomes is NP-hard even if each gene appears at most two times in each genome, thereby settling an important open question on genome rearrangement in the exemplar model. In this paper, we give a very simple alternative proof of this result. We also study the problem \textsc{Zero Exemplar Distance} for multichromosomal genomes without gene order, and prove the analogous result that it is also NP-hard even if each gene appears at most two times in each genome. For the positive direction, we show that both variants of \textsc{Zero Exemplar Distance} admit polynomial-time algorithms if each gene appears exactly once in one genome and at least once in the other genome. In addition, we present a polynomial-time algorithm for the related problem \textsc{Exemplar Longest Common Subsequence} in the special case that each mandatory symbol appears exactly once in one input sequence and at least once in the other input sequence. This answers an open question of Bonizzoni et al. We also show that \textsc{Zero Exemplar Distance} for multichromosomal genomes without gene order is fixed-parameter tractable if the parameter is the maximum number of chromosomes in each genome.Comment: Strengthened and reorganize

Holographic description of Kerr-Bolt-AdS-dS Spacetimes

We show that there exists a holographic 2D CFT description of a Kerr-Bolt-AdS-dS spacetime. We first consider the wave equation of a massless scalar field propagating in extremal Kerr-Bolt-AdS-dS spacetimes and find in the "near region", the wave equation in extremal limit could be written in terms of the $SL(2,R)$ quadratic Casimir. This suggests that there exist dual CFT descriptions of these black holes. In the probe limit, we compute the scattering amplitudes of the scalar off the extremal black holes and find perfect agreement with the CFT prediction. Furthermore we study the holographic description of the generic four dimensional non-extremal Kerr-Bolt-AdS-dS black holes. We find that if focusing on the near-horizon region, for the massless scalar scattering in the low-frequency limit, the radial equation could still be rewritten as the $SL(2,R)$ quadratic Casimir, suggesting the existence of dual 2D description. We read the temperatures of the dual CFT from the conformal coordinates and obtain the central charges by studying the near-horizon geometry of near-extremal black holes. We recover the macroscopic entropy from the microscopic counting. We also show that for the superradiant scattering, the retarded Green's functions and the corresponding absorption cross sections are in perfect match with CFT prediction.Comment: 17 pages, typos corrected, references adde

Permissive Controller Synthesis for Probabilistic Systems

We propose novel controller synthesis techniques for probabilistic systems modelled using stochastic two-player games: one player acts as a controller, the second represents its environment, and probability is used to capture uncertainty arising due to, for example, unreliable sensors or faulty system components. Our aim is to generate robust controllers that are resilient to unexpected system changes at runtime, and flexible enough to be adapted if additional constraints need to be imposed. We develop a permissive controller synthesis framework, which generates multi-strategies for the controller, offering a choice of control actions to take at each time step. We formalise the notion of permissivity using penalties, which are incurred each time a possible control action is disallowed by a multi-strategy. Permissive controller synthesis aims to generate a multi-strategy that minimises these penalties, whilst guaranteeing the satisfaction of a specified system property. We establish several key results about the optimality of multi-strategies and the complexity of synthesising them. Then, we develop methods to perform permissive controller synthesis using mixed integer linear programming and illustrate their effectiveness on a selection of case studies