Individual differences and factors affecting male behaviour in field crickets

Individual differences in male sexual behav~our and the factors influencing calling behaviour were studied in the field crickets Gryllus 2 integer and Q. veletis. In a large (13m) outdoor arena individually numbered adult male ~~ integer started calling at three to five days of age but thereafter the age of individual G. integer males did not affect nightly calling duration. Calling also did not correlate with individual weight. In this study individual male calling was continuously distributed from 0 hrs. per night to 3.5 hrs. per night, on average. A temporal effect on the number of G. integer males calling was observed. The number of males calling through the night was uniform, but a sharp increase in the number calling was observed in the early morning. No difference in calling times was observed between the night and dawn callers. AlsC)' males calling at dawn usually didnotc'all during the preceeding night. Calling and reproductive success in 1979 demonstrated a negative logarithmic relationship while in the 1980(initial) population a negative linear relationship was observed. No relationship was seen in the 1980 high density population. The ratio of non-callers to callers also affected the mating of individuals in the 1979 and1980(initial) densities:-non~callers (males calling .5 hrs. per night, on average, or less) obtained more females when the population contained a high number of callers, this being a negative logarithmic relationship to, No such relationship was observed in the 1980 high density population. Individual displacement varied nightly and was not correlated to amount of calling or reproductive success of individual G. integer males. G. integer males were displa~ed more when in a higher density in the outdoor arena Male G. integer and G. veletis behaviours were also observed in an indoor arena at different densities and, in G. veletis, with respect to female presence. When females were present in the arena, in G. veletis, male calling was reduced. Males of both species called less, on average, when in ~ higher density, than when they were in a lower density. Male displacement of both species increased on average when in a higher density as compared to displacement in a lower density. Aggression was measured by aggressive call-ing and fighting and was studied in regards to density.G. integer demonstrated less aggression in all but one comparison at higher density. No difference was observed in the ratio of aggressive calling to f.ighting comparison in G. integer. G. veletis demonstrated mixed results. No difference in aggression between densities was observed in comparisons. Less.aggression did occur in higher densities when comparisons invol.ved fighting behaviour. Male behaviour represents a competitive strategy against ot~er males, strategy being defined as a genetic (in part) alternative to other strategies. In this sense, the factors of time, density, male-male aggression, and female presence are conditions demonstrated to affect male behaviour in G. integer and G. veletis. Individual male differences and other considerations suggest that alternative male behaviours are represented by at least two conditional strategies. This possibility, and the transient 'or stable nature of genetic polymorphisms in field cricket behaviour are considered.

Male reproductive competition in the field crickets : gryllus veletis and G. pennsylvanicus

Sexual behavior in the field crickets, Gryllus veletis and G. pennsylvanicus , was studied in outdoor arenas (12 m2) at high and low levels of population density in 1983 and 1984. Crickets were weighed, individually marked, and observed from 2200 until 0800 hrs for at least 9 continuous nights. Calling was measured at 5 min intervals, and movement and matings were recorded hourly. Continuous 24 hr observations were also conducted,·and occurrences of aggressive and courtship songs were noted. The timing of males searching, calling, courting, and fighting for females should coincide with female movement and mating patterns. For most samples female movement and matings occurred at night in the 24 hr observations and were randomly distributed with time for both species in the 10 hr observations. Male movement for G. veletis high density only was enhanced at night in the 24 hr observations, however, males called more at night in both species at high and low densities. Male movement was randomly distributed with time in the 10 hr observations, and calling increased at dawn for the G. pennsylvanicus 1984 high density sample, but was randomly distributed in other samples. Most courtship and aggression songs in the 24 hr observations were too infrequent for statistical testing and generally did not coincide with matings. Assuming residual reproductive value, and costs attached to a male trait in terms of future reproductive success decline with age, males should behave in more costly ways with age; by calling and moving more with age. Consequently, mating rates should increase with age. Female behavior may not change with age. G. veletis , females moved more with age at both low density samples, however, crickets moved less with age at high density. G. pennsylvanicus females moved more with age in the 1984 low density sample, whereas crickets moved less with age in the 1983 high density sample. For both species males in the 1984 high density samples called less with age. For G. pennsylvanicus in 1983 calling and mating rates increased with age. Mating rates decreased with age for G. veletis males in the high density sample. Aging may not affect cricket behavior. As population density increases fewer calling sites become available, costs of territoriality increase, and matings resulting from non-calling behavior should increase. For both species the amount of calling and in G. veletis the distance travelled per night was not different between densities. G. pennsylvanicus males and females moved more at low density. At the same deneity levels there were no differences in calling, mating, and, movement rates in G. veletis , however, G. pennsylvanicus males moved more at high density in 1983 than 1984. There was a positive relationship between calling and mating for the G. pennsylvanicus low density sample only, and selection was acting directly to increase calling. For both species no relationships between movement and mating success was found, however, the selection gradient on movement in the G. veletis high density population was significant. The intensity of selection was not significant and was probably due to the inverse relationship between displacement and weight. Larger males should call more, mate more, and move less than smaller males. There were no correlations between calling and individual weight, and an inverse correlation between movement and size in the G. veletis high density population only. In G. pennsylvanicus , there was a positive correlation between individual weight and mating, but, some correlate of weight was under counter selection pressure and-prevented significance of the intensity of selection. In contrast, there was an inverse correlation in the G.·veletis low density B sample. Both measures of selection intensities were significant and showed that weight only was under selection pressures. An inverse correlation between calling and movement was found for G. veletis at low density only. Because males are territorial, females are predicted to move more than males, however, if movement is a mode of male-male reproductive competition then males may move more than females. G. pennsylvanicus males moved more than females in all samples, however, G. veletis males and females moved similar distances at all densities. The variation in relative mating success explained by calling scores, movement, and weight for both species and all samples were not significant In addition, for both species and all samples the intensity of selection never equalled the opportunity for selection.

Sexual selections in the northern fall field cricket, Gryllus pennsylvanicus: a manipulation of the adult sex ratio

The operational sex ratio has long been considered an important constraint on the structure of mating systems. The effects of an experimentally manipulated sex ratio on mating behavior and selection were investigated in a polygynous species, Gryllus pennsylvanicus, where the potential exists for spatial/temporal fluctuations in sex ratio of field populations. Four different sex ratios (males: females, 5:0, 5:2, 5:5, 5:10) were investigated. Observations were conducted in late summer over two field seasons, from 2400 h , to 1000 h EST. Several male characters thought to be associated with male reproduc.tive success were studied: calling duration, searching distance, weight, fighting behavior, courtship frequency, and mating success. Variance in male mating success was used as the indicator for the opportunity for sexual selection. Total selection was estimated as the univariate regression coefficient between relative fitness and the character of interest, while direct selection was estimated as standardized partial regression coefficients generated from a multiple regression of relative fitness on each character. The opportunity for sexual selection was highest at 5:2 and lowest at 5:10. The frequency of fighting behavior was highest at 5:2 and 5:5. Fighting ability (% wins) was determined to be an important correlate of male body weight. Direct selection for increased male body weight was detected at 5:2, while total selection for body weight was seen at 5:5. Selection on male body weight was not detected at 5: 10. Calling duration decreased as sex ratio became more female-biased. Total and direct selection were detected for increased calling at 5:2, only total selection for calling was seen at 5:5, whereas direct selection against calling was detected at 5: 10. Searching distance also decreased as sex ratio became more female-biased, however no form of selection was detected for searching at any of the sex ratios. Data are discussed in terms of sexual selection on male reproductive tactics, the mating system and maintenance of genetic variation in male reproductive behavior.

Philosophiae ad mentem Scoti cursus integer

UANL

Lagrangian-informed mixed integer programming reformulations

La programmation linéaire en nombres entiers est une approche robuste qui permet de résoudre rapidement de grandes instances de problèmes d'optimisation discrète. Toutefois, les problèmes gagnent constamment en complexité et imposent parfois de fortes limites sur le temps de calcul. Il devient alors nécessaire de développer des méthodes spécialisées afin de résoudre approximativement ces problèmes, tout en calculant des bornes sur leurs valeurs optimales afin de prouver la qualité des solutions obtenues. Nous proposons d'explorer une approche de reformulation en nombres entiers guidée par la relaxation lagrangienne. Après l'identification d'une forte relaxation lagrangienne, un processus systématique permet d'obtenir une seconde formulation en nombres entiers. Cette reformulation, plus compacte que celle de Dantzig et Wolfe, comporte exactement les mêmes solutions entières que la formulation initiale, mais en améliore la borne linéaire: elle devient égale à la borne lagrangienne. L'approche de reformulation permet d'unifier et de généraliser des formulations et des méthodes de borne connues. De plus, elle offre une manière simple d'obtenir des reformulations de moins grandes tailles en contrepartie de bornes plus faibles. Ces reformulations demeurent de grandes tailles. C'est pourquoi nous décrivons aussi des méthodes spécialisées pour en résoudre les relaxations linéaires. Finalement, nous appliquons l'approche de reformulation à deux problèmes de localisation. Cela nous mène à de nouvelles formulations pour ces problèmes; certaines sont de très grandes tailles, mais nos méthodes de résolution spécialisées les rendent pratiques.

Integer filling facfor phases and isospin in vertical diatomic artificial molecules

Integer filling factor phases of many-electron vertically coupled diatomic artificial quantum dot molecules are investigated for different values of the interdot coupling. The experimental results are analyzed within local-spin density functional theory for which we have determined a simple lateral confining potential law that can be scaled for the different coupling regimes, and Hartree-Fock theory. Maximum density droplets composed of electrons in both bonding and antibonding or just bonding states are revealed, and interesting isospin-flip physics appears for weak interdot coupling when the systematic depopulation of antibonding states leads to changes in isospin.

The exclusive use of integer-order spots for LEED-IV structure analysis of adsorption systems: p(2×2)-O on Ni{111}

Two different ways of performing low-energy electron diffraction (LEED) structure determinations for the p(2 x 2) structure of oxygen on Ni {111} are compared: a conventional LEED-IV structure analysis using integer and fractional-order IV-curves collected at normal incidence and an analysis using only integer-order IV-curves collected at three different angles of incidence. A clear discrimination between different adsorption sites can be achieved by the latter approach as well as the first and the best fit structures of both analyses are within each other's error bars (all less than 0.1 angstrom). The conventional analysis is more sensitive to the adsorbate coordinates and lateral parameters of the substrate atoms whereas the integer-order-based analysis is more sensitive to the vertical coordinates of substrate atoms. Adsorbate-related contributions to the intensities of integer-order diffraction spots are independent of the state of long-range order in the adsorbate layer. These results show, therefore, that for lattice-gas disordered adsorbate layers, for which only integer-order spots are observed, similar accuracy and reliability can be achieved as for ordered adsorbate layers, provided the data set is large enough.

Generalised prime systems with periodic integer counting function

We study generalised prime systems (both discrete and continuous) for which the `integer counting function' N(x) has the property that N(x) ¡ cx is periodic for some c > 0. We show that this is extremely rare. In particular, we show that the only such system for which N is continuous is the trivial system with N(x) ¡ cx constant, while if N has finitely many discontinuities per bounded interval, then N must be the counting function of the g-prime system containing the usual primes except for finitely many. Keywords and phrases: Generalised prime systems. I

Software-based study of a non-sorting method for median calculation on a set of integer numbers

This paper presents a software-based study of a hardware-based non-sorting median calculation method on a set of integer numbers. The method divides the binary representation of each integer element in the set into bit slices in order to find the element located in the middle position. The method exhibits a linear complexity order and our analysis shows that the best performance in execution time is obtained when slices of 4-bit in size are used for 8-bit and 16-bit integers, in mostly any data set size. Results suggest that software implementation of bit slice method for median calculation outperforms sorting-based methods with increasing improvement for larger data set size. For data set sizes of N > 5, our simulations show an improvement of at least 40%.

Bit-index sort: a fast non-comparison integer sorting algorithm for permutations

This paper describes a fast integer sorting algorithm, herein referred as Bit-index sort, which is a non-comparison sorting algorithm for partial per-mutations, with linear complexity order in execution time. Bit-index sort uses a bit-array to classify input sequences of distinct integers, and exploits built-in bit functions in C compilers supported by machine hardware to retrieve the ordered output sequence. Results show that Bit-index sort outperforms in execution time to quicksort and counting sort algorithms. A parallel approach for Bit-index sort using two simultaneous threads is included, which obtains speedups up to 1.6.

Generalised golden ratios over integer alphabets

It is a well known result that for β ∈ (1,1+√52) and x ∈ (0,1β−1) there exists uncountably many (ǫi)∞i=1 ∈ {0,1}N such that x = P∞i=1ǫiβ−i. When β ∈ (1+√52,2] there exists x ∈ (0,1β−1) for which there exists a unique (ǫi)∞i=1 ∈ {0,1}N such that x=P∞i=1ǫiβ−i. In this paper we consider the more general case when our sequences are elements of {0, . . . , m}N. We show that an analogue of the golden ratio exists and give an explicit formula for it.

Preconditioning 2D integer data for fast convex hull computations

In order to accelerate computing the convex hull on a set of n points, a heuristic procedure is often applied to reduce the number of points to a set of s points, s ≤ n, which also contains the same hull. We present an algorithm to precondition 2D data with integer coordinates bounded by a box of size p × q before building a 2D convex hull, with three distinct advantages. First, we prove that under the condition min(p, q) ≤ n the algorithm executes in time within O(n); second, no explicit sorting of data is required; and third, the reduced set of s points forms a simple polygonal chain and thus can be directly pipelined into an O(n) time convex hull algorithm. This paper empirically evaluates and quantifies the speed up gained by preconditioning a set of points by a method based on the proposed algorithm before using common convex hull algorithms to build the final hull. A speedup factor of at least four is consistently found from experiments on various datasets when the condition min(p, q) ≤ n holds; the smaller the ratio min(p, q)/n is in the dataset, the greater the speedup factor achieved.

An integer linear programming approach for approximate string comparison

We introduce a problem called maximum common characters in blocks (MCCB), which arises in applications of approximate string comparison, particularly in the unification of possibly erroneous textual data coming from different sources. We show that this problem is NP-complete, but can nevertheless be solved satisfactorily using integer linear programming for instances of practical interest. Two integer linear formulations are proposed and compared in terms of their linear relaxations. We also compare the results of the approximate matching with other known measures such as the Levenshtein (edit) distance. (C) 2008 Elsevier B.V. All rights reserved.