Quantitative Small Subgraph Conditioning

We revisit the method of small subgraph conditioning, used to establish that random regular graphs are Hamiltonian a.a.s. We refine this method using new technical machinery for random $d$-regular graphs on $n$ vertices that hold not just asymptotically, but for any values of $d$ and $n$. This lets us estimate how quickly the probability of containing a Hamiltonian cycle converges to 1, and it produces quantitative contiguity results between different models of random regular graphs. These results hold with $d$ held fixed or growing to infinity with $n$. As additional applications, we establish the distributional convergence of the number of Hamiltonian cycles when $d$ grows slowly to infinity, and we prove that the number of Hamiltonian cycles can be approximately computed from the graph's eigenvalues for almost all regular graphs.Comment: 59 pages, 5 figures; minor changes for clarit

Structured Linearization of Discrete Mechanical Systems for Analysis and Optimal Control

Variational integrators are well-suited for simulation of mechanical systems because they preserve mechanical quantities about a system such as momentum, or its change if external forcing is involved, and holonomic constraints. While they are not energy-preserving they do exhibit long-time stable energy behavior. However, variational integrators often simulate mechanical system dynamics by solving an implicit difference equation at each time step, one that is moreover expressed purely in terms of configurations at different time steps. This paper formulates the first- and second-order linearizations of a variational integrator in a manner that is amenable to control analysis and synthesis, creating a bridge between existing analysis and optimal control tools for discrete dynamic systems and variational integrators for mechanical systems in generalized coordinates with forcing and holonomic constraints. The forced pendulum is used to illustrate the technique. A second example solves the discrete LQR problem to find a locally stabilizing controller for a 40 DOF system with 6 constraints.Comment: 13 page

The Dreyfus-McDowell Debate and the Limits of Reason

In the Dreyfus-McDowell debate, John McDowell makes the claim that what makes us distinctively human is our all-pervasive conceptual rationality. Hubert Dreyfus, on the other hand, argues that we are, at our best, absorbed in the world and only ‘part time’ rational animals. Who is right? I appraise the debate, and proceed to then focus my analysis on two core issues: the Linguistic Community of McDowell, and the non-qualitative phenomenology of Dreyfus. I conclude that Dreyfus and McDowell cannot explain how we ‘step back from’ and ‘step in to’ the world, respectively. I propose a mediatory account between Dreyfus and McDowell’s claim through Helmuth Plessner’s concept of ‘eccentric positionality’. In employing psychopathological research, providing Plessner’s eccentric positionality as an instructive model, I suggest that we can see the disruption of eccentricity as a cornerstone of the ‘ontological confusion’ of personhood found in people with schizophrenia. Furthermore, I will propose that in this disruption of eccentricity, we are led to similar issues found in Dreyfus’ non-qualitative phenomenology, and the issues faced with McDowell’s linguistic community. This suggests a need for a reconciliation of both of their claims, which can be made through Plessner’s eccentric positionality. Therefore, I will suggest that both Dreyfus and McDowell are describing reciprocal aspects of the nature of the human being, which are in fact complementary and necessary to one another. However, these two positions need to be consolidated through Plessner’s eccentric positionality to account for the human being, for, to be the human, is to be eccentric

Eastern South Dakota Wetlands

Diverse and extensive wetland resources have always been familiar parts of the landscape to farmers, hunters, and residents of eastern South Dakota. The journals and oral histories of adventurers, trappers, and natives and immigrants reveal how wetlands shaped the wildlife and the people who lived on and modified the land to meet their own needs. The history of South Dakota wetlands parallels the history and interactions of people and wetlands elsewhere in North America and the world. This interaction can best be characterized as constant conflict. Driven primarily by economics, farmers the world over expended tremendous energy to reclaim and rehabilitate wet soils and wetlands. Their efforts alerted wildlife biologists, who sounded clear alarms in the 1950s about the loss of wetlands and about what that loss implied for the future of waterfowl and hunting. Eventually, farmers became aware that drainage districts, their costs, and their failures were adversely affecting farm families as often as they helped them. This report deals with the present. It outlines the true abundance and characteristics of eastern South Dakota wetlands, whether still pristine, modified, or constructed by man. It provides a clear statement of the kinds and numbers of wetlands and why they are important. It is a foundation for reasoned dialog about the future of wetlands. The past decade has seen unprecedented public debate about wetlands, with issues of property rights and anti-government sentiment woven in. Underlying this heated public dialog is the knowledge that wetlands have tremendous values, ranging from financial returns to flood control and wildlife habitat. These values become real and measurable in South Dakota. If wetlands are eliminated and the land no longer can absorb excess snowmelt or precipitation) the water overruns the land here and then goes downstream to flood someone else. Constant drainage can kill the golden goose of economic returns from hunting and other recreation. Landowners and biologists are now trying to undo harmful wetland modifications of the past. The future of many of these wetlands is still to be played out in eastern South Dakota and elsewhere. That future still holds the key to the majestic flights of waterfowl through future wet and dry cycles. Almost a million water bodies of all kinds are present in eastern South Dakota; this report is a powerful reminder of their dominant role in the lives of people and wildlife. [Forward by Rollin D. Sparrowe, Wildlife Management Institute]https://openprairie.sdstate.edu/nrm_book/1003/thumbnail.jp

Amplitude Modulation and Relaxation-Oscillation of Counterpropagating Rolls within a Broken-Symmetry Laser-Induced Electroconvection Strip

We report a liquid-crystal pattern-formation experiment in which we break the lateral (translational) symmetry of a nematic medium with a laser-induced thermal gradient. The work is motivated by an improved measurement (reported here) of the temperature dependence of the electroconvection threshold voltage in planar-nematic 4-methoxybenzylidene-4-butylaniline (MBBA). In contrast with other broken-symmetry-pattern studies that report a uniform drift, we observe a strip of counterpropagating rolls that collide at a sink point, and a strong temporally periodic amplitude modulation within a width of 3-4 rolls about the sink point. The time dependence of the amplitude at a fixed position is periodic but displays a nonsinusoidal relaxation-oscillation profile. After reporting experimental results based on spacetime contours and wavenumber profiles, along with a measurement of the change in the drift frequency with applied voltage at a fixed control parameter, we propose some potential guidelines for a theoretical model based on saddle-point solutions for Eckhaus-unstable states and coupled complex Ginzburg-Landau equations. Published in PRE 73, 036317 (2006).Comment: Published in Physical Review E in March 200

Temperament and self-based correlates of cooperative, competitive and individualistic learning preferences

People vary in the extent to which they prefer cooperative, competitive or individualistic achievement tasks. In the present research, we conducted two studies designed to investigate correlates and possible roots of these social interdependence orientations, namely approach and avoidance temperament, general self-efficacy, implicit theories of intelligence, and contingencies of self-worth based in others’ approval, competition, and academic competence. The results indicated that approach temperament, general self-efficacy, and incremental theory were positively, and entity theory was negatively related to cooperative preferences (|r| range from .11 to .41); approach temperament, general self-efficacy, competition contingencies, and academic competence contingencies were positively related to competitive preferences (|r| range from .16 to .46); and avoidance temperament, entity theory, competitive contingencies, and academic competence contingencies were positively related, and incremental theory was negatively related to individualistic preferences (|r| range from .09 to .15). The findings are discussed with regard to the meaning of each of the three social interdependence orientations, cultural differences among the observed relations, and implications for practicioners

The development of metaphorical language comprehension in typical development and in Williams syndrome

The domain of figurative language comprehension was used to probe the developmental relation between language and cognition in typically developing individuals and individuals with Williams syndrome. Extending the work of Vosniadou and Ortony, the emergence of nonliteral similarity and category knowledge was investigated in 117 typically developing children between 4 and 12 years of age, 19 typically developing adults, 15 children with Williams syndrome between 5 and 12 years of age, and 8 adults with Williams syndrome. Participants were required to complete similarity and categorization statements by selecting one of two words (e.g., either “The sun is like ___” or “The sun is the same kind of thing as ___”) with word pairs formed from items that were literally, perceptually, or functionally similar to the target word or else anomalous (e.g., moon, orange, oven, or chair, respectively). Results indicated that individuals with Williams syndrome may access different, less abstract knowledge in figurative language comparisons despite the relatively strong verbal abilities found in this disorder

Canola seed as affected by swathing time

Non-Peer ReviewedYield, weight, protein content (oil-free meal) and oil content of canola seed increased as seeds developed. Maximum values were obtained between 45-49 days after flowering, when seed moisture was 29-38%. Fatty acid composition of canola seed oil changed during seed development. The proportion of oleic (C18:1) and linolenic (C18:3) acids increased, while that of most other fatty acids decreased, as seeds developed, while Eicosenoic (C20:1) and erucic (C22:1) acids did not show a clear trend. Fatty-acids tended to stabilize by the 49th day after flowering. Early seeding resulted in higher seed yield, larger seeds, lower seed protein content and higher seed oil content, when compared to late seeding

Augmented Inhibition from Cannabinoid-Sensitive Interneurons Diminishes CA1 Output after Traumatic Brain Injury

The neurological impairments associated with traumatic brain injury include learning and memory deficits and increased risk of seizures. The hippocampus is critically involved in both of these phenomena and highly susceptible to damage by traumatic brain injury. To examine network activity in the hippocampal CA1 region after lateral fluid percussion injury, we used a combination of voltage-sensitive dye, field potential, and patch clamp recording in mouse hippocampal brain slices. When the stratum radiatum (SR) was stimulated in slices from injured mice, we found decreased depolarization in SR and increased hyperpolarization in stratum oriens (SO), together with a decrease in the percentage of pyramidal neurons firing stimulus-evoked action potentials. Increased hyperpolarization in SO persisted when glutamatergic transmission was blocked. However, we found no changes in SO responses when the alveus was stimulated to directly activate SO. These results suggest that the increased SO hyperpolarization evoked by SR stimulation was mediated by interneurons that have cell bodies and/or axons in SR, and form synapses in stratum pyramidale and SO. A low concentration (100 nM) of the synthetic cannabinoid WIN55,212-2, restored CA1 output in slices from injured animals. These findings support the hypothesis that increased GABAergic signaling by cannabinoid-sensitive interneurons contributes to the reduced CA1 output following traumatic brain injury

A Toolbox for Spatiotemporal Analysis of Voltage-Sensitive Dye Imaging Data in Brain Slices

Voltage-sensitive dye imaging (VSDI) can simultaneously monitor the spatiotemporal electrical dynamics of thousands of neurons and is often used to identify functional differences in models of neurological disease. While the chief advantage of VSDI is the ability to record spatiotemporal activity, there are no tools available to visualize and statistically compare activity across the full spatiotemporal range of the VSDI dataset. Investigators commonly analyze only a subset of the data, and a majority of the dataset is routinely excluded from analysis. We have developed a software toolbox that simplifies visual inspection of VSDI data, and permits unaided statistical comparison across spatial and temporal dimensions. First, the three-dimensional VSDI dataset (x,y,time) is geometrically transformed into a two-dimensional spatiotemporal map of activity. Second, statistical comparison between groups is performed using a non-parametric permutation test. The result is a 2D map of all significant differences in both space and time. Here, we used the toolbox to identify functional differences in activity in VSDI data from acute hippocampal slices obtained from epileptic Arx conditional knock-out and control mice. Maps of spatiotemporal activity were produced and analyzed to identify differences in the activity evoked by stimulation of each of two axonal inputs to the hippocampus: the perforant pathway and the temporoammonic pathway. In mutant hippocampal slices, the toolbox identified a widespread decrease in spatiotemporal activity evoked by the temporoammonic pathway. No significant differences were observed in the activity evoked by the perforant pathway. The VSDI toolbox permitted us to visualize and statistically compare activity across the spatiotemporal scope of the VSDI dataset. Sampling error was minimized because the representation of the data is standardized by the toolbox. Statistical comparisons were conducted quickly, across the spatiotemporal scope of the data, without a priori knowledge of the character of the responses or the likely differences between them