Winfried Just

Computational Complexity of Multiple Sequence Alignment with SP-Score

It is shown that the multiple alignment problem with SP-score is NP-hard for each scoring matrix in a broad class M that includes most scoring matrices actually used in biological applications. The problem remains NP-hard even if sequences can only be shifted relative to each other and no internal gaps are allowed. It is also shown that there is a scoring matrix M(0) such that the multiple alignment problem for M(0) is MAX-SNP-hard, regardless of whether or not internal gaps are allowed.

Set theory of the continuum

Primarily consisting of talks presented at a workshop sponsored by the Mathematical Sciences Research Institute, this volume reflects a spectrum of activities in set theory. It includes a variety of research papers on the relation of set theory to algebra and topology.

The Napoleon Complex: why smaller males pick fights

Does it ever pay for smaller animals to initiate fights even when they are likely to lose? Asymmetry in payoffs between opponents or a suboptimal strategy resulting from likely losers misperceiving themselves as likely winners have both been proposed as possible explanations for the aggressive behavior of smaller males. The model presented here suggests that in some cases, even without a payoff asymmetry and allowing for only a small error in perception, likely losers are expected to attack first. If the value of the resource exceeds the cost of losing a fight, the cost of displaying is sufficiently small, and assessment of resource holding power is reasonably accurate but not perfect, the evolutionarily stable strategy (ESS) prompts those contestants who perceive themselves as the likely losers to initiate fights, while it prompts those contestants who perceive themselves as the likely winners to wait for the adversary to attack or retreat.

The number and probability of canalizing functions

Canalizing functions have important applications in physics and biology. For example, they represent a mechanism capable of stabilizing chaotic behavior in Boolean network models of discrete dynamical systems. When comparing the class of canalizing functions to other classes of functions with respect to their evolutionary plausibility as emergent control rules in genetic regulatory systems, it is informative to know the number of canalizing functions with a given number of input variables. This is also important in the context of using the class of canalizing functions as a constraint during the inference of genetic networks from gene expression data. To this end, we derive an exact formula for the number of canalizing Boolean functions of n variables. We also derive a formula for the probability that a random Boolean function is canalizing for any given bias p of taking the value 1. In addition, we consider the number and probability of Boolean functions that are canalizing for exactly k variables. Finally, we provide an algorithm for randomly generating canalizing functions with a given bias p and any number of variables, which is needed for Monte Carlo simulations of Boolean networks.

On certain Boolean algebras #7B-P (ω)/I

On considere des isomorphismes possibles entre des algebres de la forme #7B-P(ω)/I; en supposant CH

Sharp bases and weakly uniform bases versus point-countable bases

Abstract A base B for a topological space X is said to be sharp if for every x∈X and every sequence (U n ) n∈ω of pairwise distinct elements of B with x∈U n for all n the set {⋂ i U i : n∈ω} forms a base at x . Sharp bases of T 0 -spaces are weakly uniform. We investigate which spaces with sharp bases or weakly uniform bases have point-countable bases or are metrizable. In particular, Davis, Reed, and Wage had constructed in a 1976 paper a consistent example of a Moore space with weakly uniform base, but without a point-countable base. They asked whether such an example can be constructed in ZFC. We partly answer this question by showing that under CH, every first-countable space with a weakly uniform base and at most ℵ ω isolated points has a point-countable base.

Some conditions under which tri-quotient or compact-covering maps are inductively perfect☆

Abstract We solve two problems posed by E. Michael (1981) concerning whether certain compact-covering maps are inductively perfect, we generalize a theorem of A. Ostrovsky on a condition under which tri-quotient maps are inductively perfect and we present an example which answers a more recent question of Michael in the same general area.

The evolution of aggressive losers

We examine the question of when aggressive behavior of likely losers should be part of an evolutionarily stable strategy. We modified an earlier model by the authors that found situations where likely losers initiate aggressive interactions more often than likely winners. The modifications allowed us to examine the robustness of the previous study by including an unusually high number of possible strategies (n=81) and to examine a wide range of parameter settings. First, we show that restricting attention to only a few most plausible strategies may change the overall results. Second, within the space where escalation is predicted, for a large percentage of the parameter settings (85%), an ESS exists that leads to a somewhat counterintuitive situation where escalation is more often initiated by the likely loser than by the likely winner of the contest. In contrast, an ESS that favors escalation by likely winners was found only for about 3% of parameter settings. Furthermore, we use simulations of evolution in a finite population to verify for certain parameter settings that the analytically predicted ESSs could in fact evolve. Our results suggest that ESSs in which the likely loser rather than the likely winner is expected to initiate escalation are generic and ESSs in which the opposite is true need to be explained by incorporating specific features of the biology of a given species into more detailed models.

Some results on property (a)

Abstract A space X has property (a) if for every open cover U of X and for each dense D⫅X there is a closed discrete F⫅D such that St(F, U)=X . In this paper, the relationship between property (a) and normality is investigated. A consistent example of a normal space without property (a) is constructed. A weakening of property (a) is defined and studied. Examples of nonmetrizable Moore spaces with property (a) are given. The question for which spaces X with property (a) the product X×(ω+1) also has property (a) is studied.

Multiple Sequence Alignment as a Facility-Location Problem

A connection is made between certain multiple-sequence alignment problems and facility-location problems, and the existence of a PTAS (polynomial-time approximation scheme) for these problems is shown. Moreover, it is shown that multiple sequence alignment with SP-score and fixed gap penalties is MAX SNP-hard.