Optimal random search for a single hidden target

A single target is hidden at a location chosen from a predetermined probability distribution. Then, a searcher must find a second probability distribution from which random search points are sampled such that the target is found in the minimum number of trials. Here it will be shown that if the searcher must get very close to the target to find it, then the best search distribution is proportional to the square root of the target distribution. For a Gaussian target distribution, the optimum search distribution is approximately a Gaussian with a standard deviation that varies inversely with how close the searcher must be to the target to find it. For a network, where the searcher randomly samples nodes and looks for the fixed target along edges, the optimum is to either sample a node with probability proportional to the square root of the out degree plus one or not at all.Comment: 13 pages, 5 figure

Writing Devotions for the Classroom

For faculty considering faith integration in the classroom, devotion time is one of the best opportunities to share and engage with the student about God and Scripture. There is a lack of literature on writing devotions for the classroom. This paper adds a possible structure for online and onsite business devotions. Preparing students with reflective questions for reading and absorbing devotional material is useful for their entire lives

A Universal Property of Axonal and Dendritic Arbors

SummaryAxonal and dendritic arbors can be characterized statistically by their spatial density function, a function that specifies the probability of finding a branch of a particular arbor at each point in a neural circuit. Based on an analysis of over a thousand arbors from many neuron types in various species, we have discovered an unexpected simplicity in arbor structure: all of the arbors we have examined, both axonal and dendritic, can be described by a Gaussian density function truncated at about two standard deviations. Because all arbors are characterized by density functions with this single functional form, only four parameters are required to specify an arbor's size and shape: the total length of its branches and the standard deviations of the Gaussian in three orthogonal directions. This simplicity in arbor structure can have implications for the developmental wiring of neural circuits

Eye Movement and Pupil Measures: A Review

Our subjective visual experiences involve complex interaction between our eyes, our brain, and the surrounding world. It gives us the sense of sight, color, stereopsis, distance, pattern recognition, motor coordination, and more. The increasing ubiquity of gaze-aware technology brings with it the ability to track gaze and pupil measures with varying degrees of fidelity. With this in mind, a review that considers the various gaze measures becomes increasingly relevant, especially considering our ability to make sense of these signals given different spatio-temporal sampling capacities. In this paper, we selectively review prior work on eye movements and pupil measures. We first describe the main oculomotor events studied in the literature, and their characteristics exploited by different measures. Next, we review various eye movement and pupil measures from prior literature. Finally, we discuss our observations based on applications of these measures, the benefits and practical challenges involving these measures, and our recommendations on future eye-tracking research directions

Synthesis and homopolymerization studies of vinylimidazolium salts

The preparations and characterizations of several monomeric vinylimidazolium salts are presented from the quaternizations of 1-vinylimidazole and 2-methyl-1-vinylimidazole with n-alkyl iodides and with dimethyl sulphate. Although vinylimidazolium salts have been reported in the patent literature, many of these salts were not isolated and characterized prior to their polymerization. From the reactions of 1-vinylimidazole with n-alkyl iodides, a homologous series of 3-n-alkyl-1-vinylimidazolium iodides were prepared in which the longer chain derivatives appeared to form micelles in aqueous solution. Dicationic crosslinking agents were also prepared through similar quaternization reactions. All the cationic vinyl monomers were homopolymerized in aqueous solution by free radical initiation. The solution behaviour of the resulting polyions indicated that the longer side-chain polyions had polysoap properties.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/33769/1/0000021.pd