TY - JOUR AB - The growth function of populations is central in biomathematics. The main dogma is the existence of density-dependence mechanisms, which can be modelled with distinct functional forms that depend on the size of the Population. One important class of regulatory functions is the theta-logistic, which generalizes the logistic equation. Using this model as a motivation, this paper introduces a simple dynamical reformulation that generalizes many growth functions. The reformulation consists of two equations, one for population size, and one for the growth rate. Furthermore, the model shows that although population is density-dependent, the dynamics of the growth rate does not depend either on population size, nor on the carrying capacity. Actually, the growth equation is uncoupled from the population size equation, and the model has only two parameters, a Malthusian parameter rho and a competition coefficient theta. Distinct sign combinations of these parameters reproduce not only the family of theta-logistics, but also the van Bertalanffy, Gompertz and Potential Growth equations, among other possibilities. It is also shown that, except for two critical points, there is a general size-scaling relation that includes those appearing in the most important allometric theories, including the recently proposed Metabolic Theory of Ecology. With this model, several issues of general interest are discussed such as the growth of animal population, extinctions, cell growth and allometry, and the effect of environment over a population. (c) 2005 Elsevier Ltd. All rights reserved. AU - de Vladar, Harold ID - 4237 IS - 2 JF - Journal of Theoretical Biology TI - Density-dependence as a size-independent regulatory mechanism VL - 238 ER - TY - JOUR AU - Harold Vladar AU - González,J. A ID - 4235 JF - Journal of Theoretical Biology TI - Dynamic response of cancer under the influence of immunological activity and therapy ER - TY - JOUR AB - In finite populations, genetic drift generates interference between selected loci, causing advantageous alleles to be found more often on different chromosomes than on the same chromosome, which reduces the rate of adaptation. This “Hill–Robertson effect” generates indirect selection to increase recombination rates. We present a new method to quantify the strength of this selection. Our model represents a new beneficial allele (A) entering a population as a single copy, while another beneficial allele (B) is sweeping at another locus. A third locus affects the recombination rate between selected loci. Using a branching process model, we calculate the probability distribution of the number of copies of A on the different genetic backgrounds, after it is established but while it is still rare. Then, we use a deterministic model to express the change in frequency of the recombination modifier, due to hitchhiking, as A goes to fixation. We show that this method can give good estimates of selection for recombination. Moreover, it shows that recombination is selected through two different effects: it increases the fixation probability of new alleles, and it accelerates selective sweeps. The relative importance of these two effects depends on the relative times of occurrence of the beneficial alleles. AU - Roze, Denis AU - Nicholas Barton ID - 4248 IS - 3 JF - Genetics TI - The Hill-Robertson effect and the evolution of recombination VL - 173 ER - TY - GEN AB - A recent analysis has shown that divergence between human and chimpanzee varies greatly across the genome. Although this is consistent with ‘hybridisation’ between the diverging human and chimp lineages, such observations can be explained more simply by the null model of allopatric speciation. AU - Nicholas Barton ID - 4250 IS - 16 T2 - Current Biology TI - Evolutionary Biology: How did the human species form? VL - 16 ER - TY - CONF AU - Thomas Wies AU - Kuncak, Viktor AU - Lam,Patrick AU - Podelski,Andreas AU - Rinard,Martin ID - 4359 TI - Field Constraint Analysis ER - TY - CONF AU - Maler, Oded AU - Dejan Nickovic AU - Pnueli,Amir ID - 4373 TI - Real Time Temporal Logic: Past, Present, Future ER - TY - CONF AU - Maler, Oded AU - Dejan Nickovic AU - Pnueli,Amir ID - 4374 TI - From MITL to Timed Automata ER - TY - CONF AB - We propose and evaluate a new algorithm for checking the universality of nondeterministic finite automata. In contrast to the standard algorithm, which uses the subset construction to explicitly determinize the automaton, we keep the determinization step implicit. Our algorithm computes the least fixed point of a monotone function on the lattice of antichains of state sets. We evaluate the performance of our algorithm experimentally using the random automaton model recently proposed by Tabakov and Vardi. We show that on the difficult instances of this probabilistic model, the antichain algorithm outperforms the standard one by several orders of magnitude. We also show how variations of the antichain method can be used for solving the language-inclusion problem for nondeterministic finite automata, and the emptiness problem for alternating finite automata. AU - De Wulf, Martin AU - Doyen, Laurent AU - Thomas Henzinger AU - Raskin, Jean-François ID - 4406 TI - Antichains: A new algorithm for checking universality of finite automata VL - 4144 ER - TY - CONF AU - Alur, Rajeev AU - Pavol Cerny AU - Zdancewic,Steve ID - 4401 TI - Preserving Secrecy Under Refinement ER - TY - CONF AB - The synthesis of reactive systems requires the solution of two-player games on graphs with ω-regular objectives. When the objective is specified by a linear temporal logic formula or nondeterministic Büchi automaton, then previous algorithms for solving the game require the construction of an equivalent deterministic automaton. However, determinization for automata on infinite words is extremely complicated, and current implementations fail to produce deterministic automata even for relatively small inputs. We show how to construct, from a given nondeterministic Büchi automaton, an equivalent nondeterministic parity automaton that is good for solving games with objective . The main insight is that a nondeterministic automaton is good for solving games if it fairly simulates the equivalent deterministic automaton. In this way, we omit the determinization step in game solving and reactive synthesis. The fact that our automata are nondeterministic makes them surprisingly simple, amenable to symbolic implementation, and allows an incremental search for winning strategies. AU - Thomas Henzinger AU - Piterman, Nir ID - 4437 TI - Solving games without determinization VL - 4207 ER -