Parameterized Two-Player Nash Equilibrium

We study the problem of computing Nash equilibria in a two-player normal form (bimatrix) game from the perspective of parameterized complexity. Recent results proved hardness for a number of variants, when parameterized by the support size. We complement those results, by identifying three cases in which the problem becomes fixed-parameter tractable. Our results are based on a graph-theoretic representation of a bimatrix game, and on applying graph-theoretic tools on this representation.     

On problems without polynomial kernels

Kernelization is a strong and widely-applied technique in parameterized complexity. A kernelization algorithm, or simply a kernel, is a polynomial-time transformation that transforms any given parameterized instance to an equivalent instance of the same problem, with size and parameter bounded by a function of the parameter in the input. A kernel is polynomial if the size and parameter of the output are polynomially-bounded by the parameter of the input.In this paper we develop a framework which allows showing that a wide range of FPT problems do not have polynomial kernels. Our evidence relies on hypothesis made in the classical world (i.e. non-parametric complexity), and revolves around a new type of algorithm for classical decision problems, called a distillation algorithm, which is of independent interest. Using the notion of distillation algorithms, we develop a generic lower-bound engine that allows us to show that a variety of FPT problems, fulfilling certain criteria, cannot have polynomial kernels unless the polynomial hierarchy collapses. These problems include k-Path, k-Cycle, k-Exact Cycle, k-Short Cheap Tour, k-Graph Minor Order Test, k-Cutwidth, k-Search Number, k-Pathwidth, k-Treewidth, k-Branchwidth, and several optimization problems parameterized by treewidth and other structural parameters.     

W-Hierarchies Defined by Symmetric Gates

The classes of the W-hierarchy are the most important classes of intractable problems in parameterized complexity. These classes were originally defined via the weighted satisfiability problem for Boolean circuits. Here, besides the Boolean connectives we consider connectives such as majority, not-all-equal, and unique. For example, a gate labelled by the majority connective outputs true if more than half of its inputs are true. For any finite set C\mathcal{C} of connectives we construct the corresponding W( C\mathcal{C} )-hierarchy. We derive some general conditions which guarantee that the W-hierarchy and the W( C\mathcal{C} )-hierarchy coincide levelwise. If C\mathcal{C} only contains the majority connective then the first levels of the hierarchies coincide. We use this to show that a variant of the parameterized vertex cover problem, the majority vertex cover problem, is W[1]-complete.     

Prediction of landslide occurrence in urban areas located on volcanic ash soils in Pereira, Colombia

As a result of the 25 January 1999 Armenia earthquake, the city of Pereira (400,000 inhabitants), located on a volcanic ash-covered alluvial fan in the western limit of the Central Cordillera (Colombia), suffered 250 slope movements. After a complete inventory, a monitoring process of unstable areas was designed, based on repeated topographic surveys, soil pore saturation levels and visual inspections. The participation of the communities was crucial and permitted the prediction of slope movements between 2 weeks and 3 months in advance and the evacuation of the inhabitants. Three specific examples are discussed. The method could be improved by excavating observation trenches and observing in detail local rainfall. In all cases, the strong involvement of the community was considered indispensable for the success of the process.     

Erosional and depositional features produced by a convulsive event,San Carlos,Colombia, September 21, 1990

The upper catchment, of the San Carlos River, located on the eastern slope of the Colombian Central Cordillera, was affected by a rainstorm which had no historic equivalent in the area, caused 20 deaths and important destruction and therefore might be called convulsive in the sense of Clifton (1988). Steep upper slopes suffered more than one hundred shallow mudflows. In the catchment channel deepening and widening cut through older torrential and slope deposits and weathered granodiorite, A large amount of material was eroded including blocks up to 8 m in diameter. Resultings deposits show the well-known differentiation: blocks accumulated in the upper part, coarse and settled in the intermediate course and clay was carried to the Punchinà Reservois about 20 km downstream. A volcanic ash layer which covers the older torrential deposits shows mineral assemblages which may enable its correlation with other ashes found eastward with an age estimated in about 10.500 years BP.     

Ordering in recognition memory after ambiguous initial or recognition displays.

Asked 57 deaf and 40 hearing 7-13 yr olds to recognize the order of 3 visually-presented digits in 2 conditions. In 1 condition, 3 numbers were exposed successively in 3 windows in temporally- and spatially-incongruent orders. This was followed by a recognition display in which the numbers appeared successively in 1 window, placed below the others. In the 2nd condition, the 1-window display was presented 1st and was followed by an incongruently ordered set of the same numbers in 3 windows for recognition. While hearing Ss recognized the digits in serial order, many deaf Ss gave left-to-right ordered recognition responses. No relationship was found between either implicit verbalization or level of articulation ability and temporal ordering. (French summary) (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Discrimination and reversal learning in imbeciles.

"Imbecile children matched for mental age with normal five-year-olds learned a size discrimination problem with more difficulty than the normals, but showed greater facility in the appropriate reversed task. An explanation of this phenomenon in terms of the verbal regulation of motor behavior was offered and tested." (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Operationalising resilience for disaster medicine practitioners: capability development through training,simulation and reflection

Cognition, Technology & Work - Resilience has in recent decades been introduced as a term describing a new perspective within the domains of disaster management and safety management. Several...