Attraction Radius Research Articles

Estimating Insect Flight Densities from Attractive Trap Catches and Flight Height Distributions

Methods and equations have not been developed previously to estimate insect flight densities, a key factor in decisions regarding trap and lure deployment in programs of monitoring, mass trapping, and mating disruption with semiochemicals. An equation to estimate densities of flying insects per hectare is presented that uses the standard deviation (SD) of the vertical flight distribution, trapping time, the trap's spherical effective radius (ER), catch at the mean flight height (as estimated from a best-fitting normal distribution with SD), and an estimated average flight speed. Data from previous reports were used to estimate flight densities with the equations. The same equations can use traps with pheromone lures or attractive colors with a measured effective attraction radius (EAR) instead of the ER. In practice, EAR is more useful than ER for flight density calculations since attractive traps catch higher numbers of insects and thus can measure lower populations more readily. Computer simulations in three dimensions with varying numbers of insects (density) and varying EAR were used to validate the equations for density estimates of insects in the field. Few studies have provided data to obtain EAR, SD, speed, and trapping time to estimate flight densities per hectare. However, the necessary parameters can be measured more precisely in future studies.

Analysis of Vertical Distributions and Effective Flight Layers of Insects: Three-Dimensional Simulation of Flying Insects and Catch at Trap Heights

The mean height and standard deviation (SD) of flight is estimated for over 100 insect species from their catches on several trap heights reported in the literature. The iterative equations for calculating mean height and SD are presented. The mean flight height for 95% of the studies varied from 0.17 to 5.40 m, and the SD from 0.12 to 3.83 m. The relationship between SD and mean flight height (X) was SD = 0.711X(-0.7849), n = 123, R(2) = 0.63. In addition, the vertical trap catches were fit to normal distributions and analyzed for skew and kurtosis. The SD was used to calculate an effective flight layer used in transforming the spherical effective attraction radius (EAR) of pheromone-baited traps into a circular EAR(c) for use in two-dimensional encounter rate models of mass trapping and mating disruption using semiochemicals. The EAR/EAR(c) also serves to reveal the attractive strength and efficacy of putative pheromone blends. To determine the reliability of mean flight height and SD calculations from field trapping data, simulations of flying insects in three dimensions (3D) were performed. The simulations used an algorithm that caused individuals to roam freely at random but such that the population distributed vertically according to a normal distribution of specified mean and SD. Within this 3D arena, spherical traps were placed at various heights to determine the effects on catch and SD. The results indicate that data from previous field studies, when analyzed by the iterative equations, should provide good estimates of the population mean height and SD of flight.

Investigating spatial distribution of tourist attractions’ inlinks: A case study of three mountains

In hyperlink analysis, most researchers focus on interpreting hyperlink counts, they seldom concern themselves enough about the significance of spatial distribution of hyperlinks. In this paper, we argue that not only can the inlink count to a tourist attraction’s official website reflect its attractiveness, but also the spatial distribution of its inlinks can reflect the distribution of its tourist source markets. Three mountains in Anhui Province, China, are chosen for the case study. Firstly, the correlation between the spatial distributions of an attraction’s tourist source markets and its official website’s inlinks is investigated. Secondly, the tourism indexes such as the spatial concentration index (SCI) and the attraction radius (AR), which are calculated by inlinks, are compared to the real indexes based on tourist sources. Last, the detailed discussion and analysis are presented and an improved model, which is used to calculate the distribution of inlinks, is proposed.

Correction method on fairs’ attraction radius

At auditing a fair the measure and evaluation of the exhibitors’ distance is a important task and can be used for further promotion of the fair. In analyzing the attraction radius of different fairs one can discover some figures that may raise questions regarding a simple averaging of the attraction distances. According to the research of the author, the bias in the attraction radius can be caused by to factors: the size of the attraction region and the distance from the region’s business center. Authors explored the bias factors and suggest a correction method to remedy it. A theoretical correction model was applied to evaluate three agribusiness fairs. It is established that the corrected attraction radius gives more realistic result than the simple averaging of exhibitors’ distance.

Modeling distributions of flying insects: Effective attraction radius of pheromone in two and three dimensions

The effective attraction radius (EAR) of an attractive pheromone-baited trap was defined as the radius of a passive “sticky” sphere that would intercept the same number of flying insects as the attractant. The EAR for a particular attractant and insect species in nature is easily determined by a catch ratio on attractive and passive (unbaited) traps, and the interception area of the passive trap. The spherical EAR can be transformed into a circular EAR c that is convenient to use in two-dimensional encounter rate models of mass trapping and mating disruption with semiochemicals to control insects. The EAR c equation requires an estimate of the effective thickness of the layer where the insect flies in search of mates and food/habitat. The standard deviation ( SD) of flight height of several insect species was determined from their catches on traps of increasing heights reported in the literature. The thickness of the effective flight layer ( F L ) was assumed to be SD · 2 · π , because the probability area equal to the height of the normal distribution, 1 / ( SD · 2 · π ) , times the F L is equal to the area under the normal curve. To test this assumption, 2000 simulated insects were allowed to fly in a three-dimensional correlated random walk in a 10-m thick layer where an algorithm caused them to redistribute according to a normal distribution with specified SD and mean at the midpoint of this layer. Under the same conditions, a spherical EAR was placed at the center of the 10-m layer and intercepted flying insects distributed normally for a set period. The number caught was equivalent to that caught in another simulation with a uniform flight density in a narrower layer equal to F L , thus verifying the equation to calculate F L . The EAR and F L were used to obtain a smaller EAR c for use in a two-dimensional model that caught an equivalent number of insects as that with EAR in three dimensions. This verifies that the F L estimation equation and EAR to EAR c conversion methods are appropriate.

Active Space of Pheromone Plume and its Relationship to Effective Attraction Radius in Applied Models

The release rate of a semiochemical lure that attracts flying insects has a specific effective attraction radius (EAR) that corresponds to the lure's orientation response strength. EAR is defined as the radius of a passive sphere that intercepts the same number of insects as a semiochemical-baited trap. It is estimated by calculating the ratio of trap catches in the field in baited and unbaited traps and the interception area of the unbaited trap. EAR serves as a standardized method for comparing the attractive strengths of lures that is independent of population density. In two-dimensional encounter rate models that are used to describe insect mass trapping and mating disruption, a circular EAR (EAR(c)) describes a key parameter that affects catch or influence by pheromone in the models. However, the spherical EAR, as measured in the field, should be transformed to an EAR(c) for appropriate predictions in such models. The EAR(c) is calculated as (pi/2EAR(2))/F (L), where F (L) is the effective thickness of the flight layer where the insect searches. F (L) was estimated from catches of insects (42 species in the orders Coleoptera, Lepidoptera, Diptera, Hemiptera, and Thysanoptera) on traps at various heights as reported in the literature. The EAR(c) was proposed further as a simple but equivalent alternative to simulations of highly complex active-space plumes with variable response surfaces that have proven exceedingly difficult to quantify in nature. This hypothesis was explored in simulations where flying insects, represented as coordinate points, moved about in a correlated random walk in an area that contained a pheromone plume, represented as a sector of active space composed of a capture probability surface of variable complexity. In this plume model, catch was monitored at a constant density of flying insects and then compared to simulations in which a circular EAR(c) was enlarged until an equivalent rate was caught. This demonstrated that there is a circular EAR(c), where all insects that enter are caught, which corresponds in catch effect to any plume. Thus, the EAR(c), based on the field-observed EAR, can be used in encounter rate models to develop effective control programs based on mass trapping and/or mating disruption.

Simulation of Mating Disruption and Mass Trapping with Competitive Attraction and Camouflage

Simulation models of mass trapping and mating disruption were developed based on correlated random walks (CRW) of flying male moths searching for females. Males encountered pheromone plumes, transformed into a circular probability surface represented as an effective attraction radius (EAR), from females and from dispensers with or without traps. In simulations, parameters of dispenser EAR and density, female EAR and density, female stationary periods, male density, and male orienting times in EAR of dispensers or females were varied, whereas the male CRW parameters (speed, turning angle, and step size) remained constant to evaluate effects on the percentages of females mating. When male orienting time was constant regardless of EAR, the models indicated no difference in mating disruption efficacy between either a higher density of dispensers with smaller EAR or a lower density of dispensers with a compensating larger EAR. However, when the orienting time was increased in proportion to dispenser EAR, fewer dispensers with larger EAR were more effective in reducing female mating than were more numerous ones with smaller EAR. When costs of pheromone are substantial, however, more numerous dispensers of smaller EAR would be more economical because dose-response curves in previous studies indicate release rate must increase exponentially to achieve a linear increase in EAR. The models are useful in understanding the variables affecting the success of insect control programs. More precise measurements of the above parameters in the field are needed before the models can precisely predict outcomes of mating disruption and mass trapping.

Nodes and field of tourist origins to ancient village —A case study of Huangcheng Village in Shanxi Province of China

Based on Hagget’s theory of spatial structure, researches on the nodes and field of tourist origins to Huangcheng Village in Shanxi Province of China have been explored. Nodal hierarchy structure of tourist origins is analyzed with cluster analysis and the gravity model. And field of tourist origins is analyzed with attraction radius index (R) and geography concentration index (G). In the field analysis, R and G of Huangcheng Village are compared with Xidi Village that is a world heritage located in Huangshan City of Anhui Province in China. According to comparison of locations of two areas, influential factors for field area of Huangcheng Village are identified. It is concluded that: 1) cluster analysis and gravity model can be complementary methods to each other for nodal hierarchy structure analysis of tourist origins; and 2) as far as location is concerned, the weak intensity effect of tourism resources in the tourist region is a major cause for explaining why tourist origins to Huangcheng Village are mainly its neighboring areas. Moreover, it is suggested that the regional effect of tourist resources should be regarded as a component of destination attractiveness when applying gravity model.

Impacts of Yulong Mountain glacier on tourism in Lijiang

The glacier on the Yulong Mountain is one of the most important attractions in Lijiang, Yunnan, China. But it keeps retreating these years due to global warming, which is bound to influence regional tourism significantly in Lijiang. This study estimates the effects of the glacier retreat of the Yulong Mountains on tourism there. Primary data were collected through a visitor survey including demographics, motives, lengths of stay, and opinions about each tourism resource from tourists to Lijiang, as well as questions about which scenic spot(s) they had visited or would visit, how much they expended per day during their visit and how their visiting behavior would be changed upon the hypothesis that the glacier would disappear. These data were used to analyze the proportion of the contribution of glacier to the tourism in Lijiang and estimate the impact of glacier on the regional tourism quantitatively. According to the survey, it could be concluded that three quarters of the tourists to Lijiang were interested in the Yulong Mountain glacier, indicating that the glacier possesses notable appeal for sightseeing tourists. The results of our analysis showed that about 689,013∼1,508,247 tourists, accounting for 19.63∼42.97 % of the total 3,510,000 domestic tourists to Lijiang in 2004, would not come to Lijiang in the absence of the glacier, resulting in a possible direct economic loss of 84,382,508 ∼ 184,713,011 USD (viz. 700,374,824 ∼ 1,533,117,993 RMB) and a markedly decrease in the attraction radius.

Feasibility of light-trapping in community research on moths: attraction radius of light, completeness of samples, nightly flight times and seasonality of Southeast-Asian hawkmoths (Lepidoptera: Sphingidae)

Experimental data and quantitative samples of Sphingid assemblages from tropical Southeast-Asia were analyzed to investigate methodologically relevant topics of light-trapping. MarkRelease-Recapture experiments revealed differences between lepidopteran families in the attraction radius of a light source, but no such differences could be found between 18 species within the family Sphingidae. Attraction radii (for 50% return rate within 5 minutes) were generally below 30 meters, which confirms results from previously published studies. Arrival of Sphingidae individuals at a light source was symmetrically distributed around midnight, and species differed significantly in median arrival time. No evolutionary hypothesis for such flight time differences (such as avoidance of interspecific mating or an effect of body size) could be confirmed from our data. At appropriately chosen sample sites (avoiding dense undergrowth), all-night sampling with a 125 Watt mercuryvapor lamp yielded more than 3⁄4 of the expected species richness of Sphingidae in an average of 5-6 sample nights. Seasonality and temporal changes of local assemblages can probably be neglected for samples from largely non-seasonal regions like Borneo if data stem from a relatively short study time of a few years. In conclusion, (1) there are no indications that light trapping ‘draws’ specimens from distant habitats to the sampling site, (2) we did not find proof that species within the family Sphingidae are differentially drawn to light, which would lead to biases if light-trapping data are used as a measure of relative abundance in the habitat, (3) such biases, on the other hand, probably exist between taxonomically or morphologically more diverse taxa (e.g. for different families), and must be considered for a proper interpretation of results, and (4) light-trapping is an effective means of assessing species composition and relative abundances of Sphingid assemblages in Southeast-Asia, but sampling has to be carried out all night in order to maximize catch size and avoid biases due to different flight times of species.

Two-stage clustering via neural networks

This paper presents a two-stage approach that is effective for performing fast clustering. First, a competitive neural network (CNN) that can harmonize mean squared error and information entropy criteria is employed to exploit the substructure in the input data by identifying the local density centers. A Gravitation neural network (GNN) then takes the locations of these centers as initial weight vectors and undergoes an unsupervised update process to group the centers into clusters. Each node (called gravi-node) in the GNN is associated with a finite attraction radius and would be attracted to a nearby centroid simultaneously during the update process, creating the Gravitation-like behavior without incurring complicated computations. This update process iterates until convergence and the converged centroid corresponds to a cluster. Compared to other clustering methods, the proposed clustering scheme is free of initialization problem and does not need to pre-specify the number of clusters. The two-stage approach is computationally efficient and has great flexibility in implementation. A fully parallel hardware implementation is very possible.

Melting of two-dimensional systems: Dependence of the type of transition on the radius of the potential

In the framework of the two-dimensional melting theory based on the density functional approach, we use a Monte Carlo computer simulation to study melting of a two-dimensional hard disk system with a rectangular-well attraction potential. We show that depending on the attraction radius, the melting can occur via a single first-order transition as well as continuously in accordance with the Kosterlitz–Thouless–Halperin–Nelson–Young theory.

Pattern Recognition by High-Capacity Polynomial Bidirectional Hetero-Associative Network

This investigation presents a novel method of image processing using the polynomial bidirectional hetero-associative network (PBHAN). This network can be used for industrial application of optical character recognition. According to the results of detailed simulations, the PBHAN has a higher capacity for pattern pair storage than do the conventional bidirectional associative memories and fuzzy memories. The practical capacity of a PBHAN considering fault tolerance is discussed. The fault tolerance requirement leads to the discovery of the attraction radius of the basin for each stored pattern pair. PBHAN takes advantage of fuzzy characteristics in evolution equations such that the signal-noise-ratio is significantly increased. In this work, we apply the result of this research to pattern recognition problems. The practical capacity of fuzzy data recognition using PBHAN and considering fault tolerance in the worst case is also estimated. Simulation results are presented to verify the derived theory.

VQ-agglomeration: a novel approach to clustering

A novel approach called ‘VQ-agglomeration’ capable of performing fast and autonomous clustering is presented. The approach involves a vector quantisation (VQ) process followed by an agglomeration algorithm that treats codewords as initial prototypes. Each codeword is associated with a gravisphere that has a well defined attraction radius. The agglomeration algorithm requires that each codeword be moved directly to the centroid of its neighbouring codewords. The movements of codewords in the feature space are synchronous, and will converge quickly to certain sets of concentric circles for which the centroids identify the resulting clusters. Unlike other techniques, such as the k-means and the fuzzy C-means, the proposed approach is free of the initial prototype problem and it does not need pre-specification of the number of clusters. Properties of the agglomeration algorithm are characterised and its convergence is proved.

EFFECTS OF ATTRACTION RADIUS AND FLIGHT PATHS ON CATCH OF SCOLYTID BEETLES DISPERSING OUTWARD THROUGH RINGS OF PHEROMONE TRAPS

Results were analyzed from six previous studies in which marked bark and ambrosia beetles, Ips typographus, I. paraconfusus, and Trypodendron lineatum (Coleoptera: Scolytidae), were released at the center of concentric rings of pheromone traps. Assuming nearly straight flight paths, a “filtering” equation model predicts recapture percentages on several trap rings of specified radii, trap numbers, and effective attraction radius (EAR) of a pheromone trap. Equations were used to calculate recapture percentages on concentric trap rings as a function of increasing EAR and gave polynomial relationships for each ring with terms equal to the number of inner rings plus one. Results were confirmed by computer simulations. Filtering equations were iterated with increasing EAR values to find one that gave a recapture percentage for the innermost trap ring that matched the field results. The estimated EAR for a synthetic pheromone bait of I. typographus was similar in five tests (range 1.39–1.78 m), but in two other tests was larger (3.27 and 15.9 m). The EAR for pheromone of 75 male I. paraconfusus in ponderosa pine logs ranged from 0.35 to 34.5 m (mean of 4.7 m) and was generally larger for previously pheromone-responding beetles than for freshly emerged ones. For T. lineatum, the EAR of lineatin-baited traps at 100-m radius was 2.43 m. Recaptures of I. typographus were reasonably predicted by the estimated EARs in the filtering model. To obtain perfect fits, another model assumed the EAR could vary with ring radius (dispersal distance) and found that the EAR for I. typographus decreased with dispersal distance in four experiments, but increased or was variable in two others. However, in I. paraconfusus and T. lineatum, the EAR increased with dispersal distance. Simulations that varied combinations of the EAR and random angles of maximum turning (AMT) of beetles stepwise showed that a nearly straight flight path for I. typographus explained observed catches on trap rings best, while a higher AMT of 36° was better to explain catches of T. lineatum. Simulations show that catch per trap ring in relation to radial distance can be influenced by the beetle's AMT (still unobserved in the field). A conceptual model of dispersal and host selection in “aggressive” bark beetles with regard to pioneer and joiner colonization strategies is presented.

Long-term attraction in higher order neural networks

Recent results on the memory storage capacity of higher order neural networks indicate a significant improvement compared to the limited capacity of the Hopfield model. However, such results have so far been obtained under the restriction that only a single iteration is allowed to converge. This paper presents a indirect convergence (long-term attraction) analysis of higher order neural networks. Our main result is that for any kappa(d)<d!2(d-1)/(2d)!, and 0< or =rho<1/2, a Hebbian higher order neural network of order d with n neurons can store a random set of kappa(d)n(d)/log n fundamental memories such that almost all memories have an attraction radius of size rhon. If kappa(d)<d!2(d-1)/((2d)!(d+1)), then all memories possess this property simultaneously. It indicates that the lower bounds on the long-term attraction capacities are larger than the corresponding direct convergence capacities by a factor of 1/(1-2rho) (2d). In addition we upper bound the convergence rate (number of iterations required to converge). This bound is asymptotically independent of n. Similar results are obtained for zero diagonal higher order neural networks.

Increasing Attraction of Pseudo-Inverse Autoassociative Networks

We show how partial reduction of self-connections of the network designed with the pseudo-inverse learning rule increases the direct attraction radius of the network. Theoretical formula is obtained. Data obtained by simulation are presented.

Global Convergence and Asymptotic Stability of Asymmetric Hopfield Neural Networks

The global convergence and asymptotic stability of Hopfield neural networks are known to be bases of successful applications of networks in various computing and recognition tasks. However, all previous studies on the networks assumed that the interconnection matrix is symmetric or antisymmetric. In this paper the two fundamental properties of the networks are studied without a symmetry assumption. It is proved that the networks will be globally convergent to a stable state if the interconnection matrix is weakly diagonally dominant in a sense to be defined. Furthermore, under any one of conditions assuring global convergence of the network, the maximal attraction radius of any one of stable states is found to be half of the distribution distance of the state to the network. The obtained results not only generalize the existing results, but also provide a theoretical foundation of performance analysis and new applications of the Hopfield networks.

Nondirect convergence radius and number of iterations of the Hopfield associative memory

Considers a Hopfield associative memory consisting of n neurons, designed to store an m-set of n-dimensional /spl plusmn/1 statistically independent uniformly distributed random vectors (fundamental memories), using a connection matrix, constructed by the usual Hebbian rule. Previous results have indicated that the maximal value of m, such that almost all m vectors are stable points of the memory, in probability (i.e., with probability approaching one as n approaches infinity), is n/(2 log n)(n/(4 log n) if all m vectors must be stable simultaneously, in probability). Previous work further analyzed the direct convergence (i.e., convergence in one iteration) error-correcting power of the Hopfield memory. The present authors rigorously analyze the general case of nondirect convergence, and prove that in the m=n/(2 log n) case, independently of the operation mode used (synchronous or asynchronous), almost all memories have an attraction radius of size n/2 around them (in the n/(4 log n) case, all memories have such an attraction radius, in probability). This result, which was conjectured in the past but was never proved rigorously, combined with an old converse result that the network cannot store more than n/(2 log n)(n/(4 log n)) fundamental memories, gives a full picture of the error-correcting power of the Hebbian Hopfield network. The authors also upper bound the number of iterations required to achieve convergence.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Attraction Radii in Binary Hopfield Nets are Hard to Compute

We prove that it is an NP-hard problem to determine the attraction radius of a stable vector in a binary Hopfield memory network, and even that the attraction radius is hard to approximate. Under synchronous updating, the problems are already NP-hard for two-step attraction radii; direct (one-step) attraction radii can be computed in polynomial time.