Quantifying chaos: practical estimation of the correlation dimension

Be it a physical object or a mathematical model, a nonlinear dynamical system can display complicated aperiodic behavior, or "chaos." In many cases, this chaos is associated with motion on a strange attractor in the system's phase space. And the dimension of the strange attractor indicates the effective number of degrees of freedom in the dynamical system.

In this thesis, we investigate numerical issues involved with estimating the dimension of a strange attractor from a finite time series of measurements on the dynamical system.

Of the various definitions of dimension, we argue that the correlation dimension is the most efficiently calculable and we remark further that it is the most commonly calculated. We are concerned with the practical problems that arise in attempting to compute the correlation dimension. We deal with geometrical effects (due to the inexact self-similarity of the attractor), dynamical effects (due to the nonindependence of points generated by the dynamical system that defines the attractor), and statistical effects (due to the finite number of points that sample the attractor). We propose a modification of the standard algorithm, which eliminates a specific effect due to autocorrelation, and a new implementation of the correlation algorithm, which is computationally efficient.

Finally, we apply the algorithm to chaotic data from the Caltech tokamak and the Texas tokamak (TEXT); we conclude that plasma turbulence is not a low- dimensional phenomenon.

Influence of number of valves on catch composition of a fishing pot trap (Lege) in River Rima, north western Nigeria

Three types of prototype (Lege) traps with different numbers of entrance valves were evaluated in River Rima, north western Nigeria. The traps contained 4,6 and 8 valves, tagged 4-V, 6-V and 8-V respectively. The experiment was carried out in a randomized complete block design with one factor each replicated three times. Data collected on fish diversity, number biomass and sizes were subjected to descriptive statistics and analysis of variance. The results of the catch composition showed close diversity index of 0.86 for 6-V, 0.80 for 8-V and 0.60 for 4-V Lege traps. However, the number (41%) and biomass 48%) of fish caught in the 6-V Lege trap were significantly (P0.05) higher than those caught in the other traps. There was no definite trend in the sizes (length and girth) of fish caught in the traps. On the basis of species diversity, and the number and biomass of fish caught, the 6-V Lege showed preference for adoption than the other two traps. However, further studies are recommended on the appropriate mesh size net for the trap in line with the provisions of fisheries edicts

Influence of number of valves on catch composition of a fishing pot trap (Lege) in River Rima, north western Nigeria

Three types of prototype (Lege) traps with different numbers of entrance valves were evaluated in River Rima, north western Nigeria. The traps contained 4,6 and 8 valves, tagged 4-V, 6-V and 8-V respectively. The experiment was carried out in a randomized complete block design with one factor each replicated three times. Data collected on fish diversity, number, biomass and sizes were subjected to descriptive statistics and analysis of variance. The results of the catch composition showed close diversity index of 0.86 for 6-V, 0.80 for 8-V and 0.60 for 4-V Lege traps. However, the number (41%) and biomass (48%) of fish caught in the 6-V Lege trap were significantly (P<0.05) higher than those caught in the other traps. There was no definite trend in the sizes (length and girth) of fish caught in the traps. On the basis of species diversity, and the number and biomass of fish caught, the 6-V Lege showed preference for adoption than the other two traps. However, further studies are recommended on the appropriate mesh size net for the trap in line with the provisions of fisheries edicts

Radioautographic method of determination of number of bacteria in water-bodies [Translation from: Informatsionnyi Byulleten Biologiya Vnutrennikh Vod No.26, 65-67, 1975]

The radioautographic method of determination of the number of autotrophic microorganisms was initially suggested for counting methane-oxidizing bacteria. With the help of this method colonies of hydrogen-oxidizing bacteria are differentiated even more clearly from heterotrophic. Under laboratory conditions it was shown that colonies grown on membrane filters from a pure culture of thionic bacteria on a nutrient medium with radio- active carbonate, give better prints on film. This method was tested by the authors for determining the number of these bacteria in the meromictic Lake Vae de San Juan during the expedition to Cuba in the summer of 1973. The study showed that that the thionic bacteria are found throughout the pelagial. It proved that the thionic bacteria can be well considered in water-bodies by the radioautographic method.

Number of phase levels of a Talbot array illuminator

The number of phase levels of a Talbot array illuminator is an important factor in the estimation of practical fabrication complexity and cost. We show that the number it) of phase levels of a Talbot array illuminator has a simple relationship to the prime number. When there is an alternative pi -phase modulation in the output array, the relations are similar. (C) 2001 Optical Society of America OCIS codes: 070.6760, 050.1950, 050.1980.

On the number of generations of tendipes in collective ponds in Kuibyshchevskoi district [Translation from: C.R. Acad.Sci. U.R.S.S. 95, 1113-1115, 1954]

Three ponds were chosen for this study. The two lower ones were of 2 - 4 hectares in area, the depth of the littoral zone was 2.5 - 3 metres at the time of maximum flooding and the mud which covered the floor of the ponds was homogeneous and autochthonous in nature with very few vegetable remnants. The ponds which were originally set up in 1950. were intended for water supply and populated with Crucian Carp (for human consumption). A survey was done in the ponds in order to establish number and biomass of Tendipes semireductus. The author concludes that in these ponds T.semireductus has 2-3 generations per year.

Population structure, long-term connectivity, and effective size of mutton snapper (Lutjanus analis) in the Caribbean Sea and Florida Keys

Genetic structure and average long-term connectivity and effective size of mutton snapper (Lutjanus analis) sampled from offshore localities in the U.S. Caribbean and the Florida Keys were assessed by using nuclear-encoded microsatellites and a fragment of mitochondrial DNA. No significant differences in allele, genotype (microsatellites), or haplotype (mtDNA) distributions were detected; tests of selective neutrality (mtDNA) were nonsignificant after Bonferroni correction. Heuristic estimates of average long-term rate of migration (proportion of migrant individuals/generation) between geographically adjacent localities varied from 0.0033 to 0.0054, indicating that local subpopulations could respond independently of environmental perturbations. Estimates of average longterm effective population sizes varied from 341 to 1066 and differed significantly among several of the localities. These results indicate that over time larval drift and interregional adult movement may not be sufficient to maintain population sustainability across the region and that there may be different demographic stocks at some of the localities studied. The estimate of long-term effective population size at the locality offshore of St. Croix was below the minimum threshold size considered necessary to maintain the equilibrium between the loss of adaptive genetic variance from genetic drift and its replacement by mutation. Genetic variability in mutton snapper likely is maintained at the intraregional level by aggregate spawning and random mating of local populations. This feature is perhaps ironic in that aggregate spawning also renders mutton snapper especially vulnerable to overexploitation.

Effective herding of flatfish by cables with minimal seafloor contact

Otter trawls are very effective at capturing flatfish, but they can affect the seaf loor ecosystems where they are used. Alaska f latf ish trawlers have very long cables (called sweeps) between doors and net to herd fish into the path of the trawl. These sweeps, which ride on and can disturb the seaf loor, account for most of the area affected by these trawls and hence a large proportion of the potential for damage to seaf loor organisms. We examined modifications to otter trawls, such that disk clusters were installed at 9-m intervals to raise trawl sweeps small distances above the seafloor, greatly reducing the area of direct seafloor contact. A critical consideration was whether flatfish would still be herded effectively by these sweeps. We compared conventional and modified sweeps using a twin trawl system and analyzed the volume and composition of the resulting catches. We tested sweeps raised 5, 7.5, and 10 cm and observed no significant losses of flatfish catch until sweeps were raised 10 cm, and those losses were relatively small (5–10%). No size composition changes were detected in the flatfish catches. Alaska pollock (Theragra chalcogramma) were captured at higher rates with two versions of the modified sweeps. Sonar observations of the sweeps in operation and the seaf loor after passage confirmed that the area of direct seafloor contact was greatly reduced by the modified sweep

Population structure of chum salmon (Oncorhynchus keta) across the Pacific Rim, determined from microsatellite analysis

The Pacific Rim population structure of chum salmon (Oncorhynchus keta) was examined with a survey of microsatellite variation to describe the distribution of genetic variation and to evaluate whether chum salmon may have originated from two or more glacial refuges following dispersal to newly available habitat after glacial retreat. Variation at 14 microsatellite loci was surveyed for over 53,000 chum salmon sampled from over 380 localities ranging from Korea through Washington State. An index of genetic differentiation, FST, over all populations and loci was 0.033, with individual locus values ranging from 0.009 to 0.104. The most genetically diverse chum salmon were observed from Asia, particularly Japan, whereas chum salmon from the Skeena River and Queen Charlotte Islands in northern British Columbia and those from Washington State displayed the fewest number of alleles compared with chum salmon in other regions. Differentiation in chum salmon allele frequencies among regions and populations within regions was approximately 18 times greater than that of annual variation within populations. A regional structuring of populations was the general pattern observed, with chum salmon spawning in different tributaries within a major river drainage or spawning in smaller rivers in a geographic area generally more similar to each other than to populations in different major river drainages or geographic areas. Population structure of chum salmon on a Pacific Rim basis supports the concept of a minimum of two refuges, northern and southern, during the last glaciation, but four possible refuges fit better the observed distribution of genetic variation. The distribution of microsatellite variation of chum salmon on a Pacific Rim basis likely reflects the origins of salmon radiating from refuges after the last glaciation period.

Number of Players and Relative Pitch Area per Player: Comparing Their Influence on Heart Rate and Physical Demands in Under-12 and Under-13 Football Players

The aim of the present study is to analyse the influence of different large-sided games (LSGs) on the physical and physiological variables in under-12s (U12) and -13s (U13) soccer players. The effects of the combination of different number of players per team, 7, 9, and 11 (P7, P9, and P11, respectively) with three relative pitch areas, 100, 200, and 300 m(2) (A100, A200, and A300, respectively), were analysed in this study. The variables analysed were: 1) global indicator such as total distance (TD); work:rest ratio (W:R); player-load (PL) and maximal speed (V-max); 2) heart rate (HR) mean and time spent in different intensity zones of HR (<75%, 75-84%, 84-90% and >90%), and; 3) five absolute (<8, 8-13, 13-16 and >16 Km h(-1)) and three relative speed categories (<40%, 40-60% and >60% V-max). The results support the theory that a change in format (player number and pitch dimensions) affects no similarly in the two players categories. Although it can seem that U13 players are more demanded in this kind of LSG, when the work load is assessed from a relative point of view, great pitch dimensions and/or high number of player per team are involved in the training task to the U12 players. The results of this study could alert to the coaches to avoid some types of LSGs for the U12 players such as:P11 played in A100, A200 or A300, P9 played in A200 or A300 and P7 played in A300 due to that U13>U12 in several physical and physiological variables (W:R, time spent in 84-90% HRmax, distance in 8-13 and 13-16 Km h(-1) and time spent in 40-60% V-max). These results may help youth soccer coaches to plan the progressive introduction of LSGs so that task demands are adapted to the physiological and physical development of participants.

Restricted Access vs. Open Access Methods of Management: Toward More Effective Regulation of Fishing Effort

This paper gives an overview of the economic rationale for limited entry as a method of fishery management and discusses general advantages and disadvantages of license limitation and catch rights as the two primary methods of restricting access to marine fisheries. Traditional open-access methods of regulation (e.g., gear restrictions, size limits, trip limits, quotas, and closures) can be temporarily effective in protecting fish populations, but they generally fail to provide lasting biological or economic benefits to fishermen because they do not restrict access to the fishery. The general result of regulation with unrestricted access to a fishery is additional and more costly and complex regulations as competition increases for dwindling fishery resources. Regulation that restricts access to a fishery in conjunction with selected traditional methods of regulation would encourage efficient resource usage and minimize the need for future regulatory adjustments, provided that enforcement and monitoring costs are not too great. In theory, catch rights are superior to license limitation as a means of restricting access to a fishery.