Correct ordering in the Zipf-Poisson ensemble

We consider a Zipf--Poisson ensemble in which X_i\sim\poi(Ni^{-\alpha}) for $\alpha>1$ and $N>0$ and integers $i\ge 1$. As $N\to\infty$ the first $n'(N)$ random variables have their proper order $X_1>X_2>...>X_{n'}$ relative to each other, with probability tending to 1 for $n'$ up to $(AN/\log(N))^{1/(\alpha+2)}$ for an explicit constant $A(\alpha)\ge 3/4$. The rate $N^{1/(\alpha+2)}$ cannot be achieved. The ordering of the first $n'(N)$ entities does not preclude $X_m>X_{n'}$ for some interloping $m>n'$. The first $n"$ random variables are correctly ordered exclusive of any interlopers, with probability tending to 1 if $n"\le (BN/\log(N))^{1/(\alpha+2)}$ for $B<A$. For a Zipf--Poisson model of the British National Corpus, which has a total word count of $100{,}000{,}000$, our result estimates that the 72 words with the highest counts are properly ordered

The importance of incorporating technological advancements into the artificial eye process: a perspective commentary

Application of technology into healthcare has typically been targeted to high demand illnesses and treatments. However, with an increasing need to meet patient’s expectations combined with increased accessibility and reduced costs, smaller healthcare fields are starting to investigate its function and usability. Services have historically been led by skills and expertise, and recent developments are being seen by ocularists in the field of prosthetic eyes who acknowledge the potential benefit from technological advancement. Utilising the technologies recently investigated in maxillofacial prosthesis can start the evolutionary process where products are continually re-designed and re-developed to achieve excellent patient outcome and satisfaction levels

Exploring the evolution of a trade-off between vigilance and foraging in group-living organisms

Despite the fact that grouping behavior has been actively studied for over a century, the relative importance of the numerous proposed fitness benefits of grouping remain unclear. We use a digital model of evolving prey under simulated predation to directly explore the evolution of gregarious foraging behavior according to one such benefit, the "many eyes" hypothesis. According to this hypothesis, collective vigilance allows prey in large groups to detect predators more efficiently by making alarm signals or behavioral cues to each other, thereby allowing individuals within the group to spend more time foraging. Here, we find that collective vigilance is sufficient to select for gregarious foraging behavior as long there is not a direct cost for grouping (e.g., competition for limited food resources), even when controlling for confounding factors such as the dilution effect. Further, we explore the role of the genetic relatedness and reproductive strategy of the prey, and find that highly related groups of prey with a semelparous reproductive strategy are the most likely to evolve gregarious foraging behavior mediated by the benefit of vigilance. These findings, combined with earlier studies with evolving digital organisms, further sharpen our understanding of the factors favoring grouping behavior.Comment: 26 pages (double-spaced, single column), 6 figures, 2 SI figure

Empirical stationary correlations for semi-supervised learning on graphs

In semi-supervised learning on graphs, response variables observed at one node are used to estimate missing values at other nodes. The methods exploit correlations between nearby nodes in the graph. In this paper we prove that many such proposals are equivalent to kriging predictors based on a fixed covariance matrix driven by the link structure of the graph. We then propose a data-driven estimator of the correlation structure that exploits patterns among the observed response values. By incorporating even a small fraction of observed covariation into the predictions, we are able to obtain much improved prediction on two graph data sets.Comment: Published in at http://dx.doi.org/10.1214/09-AOAS293 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Predator confusion is sufficient to evolve swarming behavior

Swarming behaviors in animals have been extensively studied due to their implications for the evolution of cooperation, social cognition, and predator-prey dynamics. An important goal of these studies is discerning which evolutionary pressures favor the formation of swarms. One hypothesis is that swarms arise because the presence of multiple moving prey in swarms causes confusion for attacking predators, but it remains unclear how important this selective force is. Using an evolutionary model of a predator-prey system, we show that predator confusion provides a sufficient selection pressure to evolve swarming behavior in prey. Furthermore, we demonstrate that the evolutionary effect of predator confusion on prey could in turn exert pressure on the structure of the predator's visual field, favoring the frontally oriented, high-resolution visual systems commonly observed in predators that feed on swarming animals. Finally, we provide evidence that when prey evolve swarming in response to predator confusion, there is a change in the shape of the functional response curve describing the predator's consumption rate as prey density increases. Thus, we show that a relatively simple perceptual constraint--predator confusion--could have pervasive evolutionary effects on prey behavior, predator sensory mechanisms, and the ecological interactions between predators and prey.Comment: 11 pages, 6 figures. Supplementary information (including video files S1 and S5) in ancillary material. Videos S2-S4 are available from the authors upon reques

Scoping Review of the development of artificial eyes throughout the years

Losing an eye following trauma can lead to profound psychosocial difficulties making it imperative for the wearer to be fitted with an aesthetically pleasing custom-made artificial eye. Despite recent technological advancements, current design and manufacturing processes have remained unchanged in over 55 years. With the aim of portraying current knowledge regarding the development of artificial eyes in order to aid future development, a scooping review was conducted. Six online search engines were used: Scopus, PubMed, MedLine Complete, Web of Science, Science Direct and Google Scholar. Thirty-eight articles met the inclusion criteria and underwent numerical and thematic analysis with three thematic themes emerging. History and the current process of artificial eyes has been well documented, however, the impact of wearing artificial eyes is sparse. On-going research and development into the design and manufacturing processes of artificial eyes and the psychosocial impact of wearing an artificial eye is needed

The role of follow-on contracts in government-sponsored research and development

Role of follow-on contracts in government sponsored research and developmen

Retinoblastoma: Identifying the Diagnostic Signs for Early Treatment

Retinoblastoma is a rare but significant cause of childhood eye cancer world-wide. The prognosis depends upon early diagnosis and treatment but also upon accurate classification of the tumours. Unilateral incidence is normally non-hereditary compared with bilateral incidence where secondary tumours are more common. Survivorship is much better for unilateral compared with bilateral and trilateral retinoblastoma. Early signs are important to detect and photography can assist in identifying no return of “red-eye” during flash photography and yellow appearance of the tumour. Treatment options are discussed together with new psycho-oncology approaches that address potential trauma in the survivor as well as in the family of the survivor

Combustion of hydrogen injected into a supersonic airstream (a guide to the HISS computer program)

A computer program based on a finite-difference, implicit numerical integration scheme is described for the prediction of hydrogen injected into a supersonic airstream at an angle ranging from normal to parallel to the airstream main flow direction. Results of calculations for flow and thermal property distributions were compared with 'cold flow data' taken by NASA/Langley and show excellent correlation. Typical results for equilibrium combustion are presented and exhibit qualitatively plausible behavior. Computer time required for a given case is approximately one minute on a CDC 7600. A discussion of the assumption of parabolic flow in the injection region is given which demonstrates that improvement in calculation in this region could be obtained by a partially-parabolic procedure which has been developed. It is concluded that the technique described provides an efficient and reliable means for analyzing hydrogen injection into supersonic airstreams and the subsequent combustion

A Dichotomy Theorem for Homomorphism Polynomials

In the present paper we show a dichotomy theorem for the complexity of polynomial evaluation. We associate to each graph H a polynomial that encodes all graphs of a fixed size homomorphic to H. We show that this family is computable by arithmetic circuits in constant depth if H has a loop or no edge and that it is hard otherwise (i.e., complete for VNP, the arithmetic class related to #P). We also demonstrate the hardness over the rational field of cut eliminator, a polynomial defined by B\"urgisser which is known to be neither VP nor VNP-complete in the field of two elements, if VP is not equal to VNP (VP is the class of polynomials computable by arithmetic circuit of polynomial size)