Finite-size scaling of the error threshold transition in finite population

The error threshold transition in a stochastic (i.e. finite population) version of the quasispecies model of molecular evolution is studied using finite-size scaling. For the single-sharp-peak replication landscape, the deterministic model exhibits a first-order transition at $Q=Q_c=1/a$, where $Q$ is the probability of exact replication of a molecule of length $L \to \infty$, and $a$ is the selective advantage of the master string. For sufficiently large population size, $N$, we show that in the critical region the characteristic time for the vanishing of the master strings from the population is described very well by the scaling assumption \tau = N^{1/2} f_a \left [ \left (Q - Q_c) N^{1/2} \right ] , where $f_a$ is an $a$-dependent scaling function.Comment: 8 pages, 3 ps figures. submitted to J. Phys.

Baryon spectra with instanton induced forces

Except the vibrational excitations of $K$ and $K^*$ mesons, the main features of spectra of mesons composed of quarks $u$, $d$, and $s$ can be quite well described by a semirelativistic potential model including instanton induced forces. The spectra of baryons composed of the same quarks is studied using the same model. The results and the limitations of this approach are described. Some possible improvements are suggested.Comment: 5 figure

Strong Decays of Strange Quarkonia

In this paper we evaluate strong decay amplitudes and partial widths of strange mesons (strangeonia and kaonia) in the 3P0 decay model. We give numerical results for all energetically allowed open-flavor two-body decay modes of all nsbar and ssbar strange mesons in the 1S, 2S, 3S, 1P, 2P, 1D and 1F multiplets, comprising strong decays of a total of 43 resonances into 525 two-body modes, with 891 numerically evaluated amplitudes. This set of resonances includes all strange qqbar states with allowed strong decays expected in the quark model up to ca. 2.2 GeV. We use standard nonrelativistic quark model SHO wavefunctions to evaluate these amplitudes, and quote numerical results for all amplitudes present in each decay mode. We also discuss the status of the associated experimental candidates, and note which states and decay modes would be especially interesting for future experimental study at hadronic, e+e- and photoproduction facilities. These results should also be useful in distinguishing conventional quark model mesons from exotica such as glueballs and hybrids through their strong decays.Comment: 69 pages, 5 figures, 39 table

Lethal Mutants and Truncated Selection Together Solve a Paradox of the Origin of Life

BACKGROUND: Many attempts have been made to describe the origin of life, one of which is Eigen's cycle of autocatalytic reactions [Eigen M (1971) Naturwissenschaften 58, 465-523], in which primordial life molecules are replicated with limited accuracy through autocatalytic reactions. For successful evolution, the information carrier (either RNA or DNA or their precursor) must be transmitted to the next generation with a minimal number of misprints. In Eigen's theory, the maximum chain length that could be maintained is restricted to 100-1000 nucleotides, while for the most primitive genome the length is around 7000-20,000. This is the famous error catastrophe paradox. How to solve this puzzle is an interesting and important problem in the theory of the origin of life. METHODOLOGY/PRINCIPAL FINDINGS: We use methods of statistical physics to solve this paradox by carefully analyzing the implications of neutral and lethal mutants, and truncated selection (i.e., when fitness is zero after a certain Hamming distance from the master sequence) for the critical chain length. While neutral mutants play an important role in evolution, they do not provide a solution to the paradox. We have found that lethal mutants and truncated selection together can solve the error catastrophe paradox. There is a principal difference between prebiotic molecule self-replication and proto-cell self-replication stages in the origin of life. CONCLUSIONS/SIGNIFICANCE: We have applied methods of statistical physics to make an important breakthrough in the molecular theory of the origin of life. Our results will inspire further studies on the molecular theory of the origin of life and biological evolution

Storage Capacity of Generalized Palimpsests.

A simple analytical study of a short term memory model is performed. This model consists of a symmetric p-neuron interaction between $N$ neurons. Learning is achieved by a generalized Hebb rule. Saturation is prevented by the introduction of a bound A to the couplings. At each time step, an input pattern is drawn at random, independently of the previous ones. The determination of the life time $T$ of a memorized pattern viewed as a function of $A$ and $N$ is accomplished by a statistical study of the dynamic of the learning process which has been made possible under the assumption that the couplings evolve independently. This simplification reduces the determination of $T$ to a one-dimensional problem, by considering energies rather than couplings. The choice of the optimal value $A_{\rm opt}$ of $A$ is a compromise between the success of the learning process and the maximization of $T$. The essential results are expressed by the formulae $T\propto A^2$ and $A_{\rm opt}\propto N^{\frac{p-1}{2}}$