Skagerrak populations of Atlantic cod (Gadus morhua L.) have been surveyed at several ¢xed stations since 1919. These coastal populations consist of local stocks with a low age of maturity and a short life span. We investigated 60 time-series of 0-group juveniles (i.e. young of the year) sampled annually from 1945 to 1994. An age-structured model was developed which incorporates asymmetrical interactions between the juvenile cohorts (0-group and 1-group; i.e. one-year-old juveniles) and stochastic reproduction. The model was expressed in delay coordinates in order to estimate model parameters directly from the timeseries and thereby test the model predictions. The autocovariance structure of the time-series was consistent with the delay coordinates model superimposed upon a long-term trend. The model illustrates how both regulatory (density-dependent) and disruptive (stochastic) forces are crucial in shaping the dynamics of the coastal cod populations. The age-structured life cycle acts to resonance the stochasticity inherent in the recruitment process.

Abstract. In this paper we describe an algorithm visiting all numerical semigroups up to a given genus using a well suited representation. The interest of this algorithm is that it fits particularly well the architecture of modern computers allowing very large optimizations: we obtain the number of numerical semigroups of genus g 67 and we confirm the Wilf conjecture for g 60.

Abstract. A result by Dehornoy (1992) says that every nontrivial braid admits a σ -definite expression, defined as a braid word in which the generator σ i with maximal index i appears with exponents that are all positive, or all negative. This is the ground result for ordering braids. In this paper, we enhance this result and prove that every braid admits a σ -definite word expression that, in addition, is quasi-geodesic. This establishes a longstanding conjecture. Our proof uses the dual braid monoid and a new normal form called the rotating normal form.

We analyzed 136 time series (covering from 44 to 73 yr) of juvenile cod to estimate the level of direct and delayed density‐dependent mortality (DDM) of 11 populations from the Norwegian Skagerrak coast. The parameters were estimated using a modeling approach that explicitly incorporates observation errors, so that we could quantify the density‐independent (stochastic) variation in the survival of juvenile cod. Moderate to strong levels of DDM (direct or delayed) were estimated in eight of the 11 populations. Variability in the 0‐group (corrected for observation errors) appeared to be large for most of the populations. Substantial stochastic variability in postsettlement survival was also detected in some areas, indicating that stochastic factors are not only important for egg and larval stages, as stated by the match–mismatch hypothesis, but also for juveniles. We show that the variability in these coastal populations is not only regulated as a function of the strength of DDM processes, but also as an interaction between DDM processes and stochastic factors. We finally postulate that local and regional differences in the strengths of the density‐dependent and stochastic processes are related to differences in the quantity and quality of the bottom flora coverage, which govern both food availability and shelter for juveniles.

Let S ⊆ N be a numerical semigroup with multiplicity m, conductor c and minimal generating set P. Let L = S ∩ [0, c − 1] and W (S) = |P||L| − c. In 1978, Herbert Wilf asked whether W (S) ≥ 0 always holds, a question known as Wilf's conjecture and open since then.A related number W 0 (S), satisfying W 0 (S) ≤ W (S), has recently been introduced. We say that S is a near-miss in Wilf's conjecture if W 0 (S) < 0. Near-misses are very rare. Here we construct infinite families of them, with c = 4m and W 0 (S) arbitrarily small, and we show that the members of these families still satisfy Wilf's conjecture.