Asymptotic approximation of eigenvalues of vector equations

A vectorial extension of the Keller-Rubinow method of computing asymptotic approximations of eigenvalues in bounded domains is presented. The method is applied to the problem of a multimode step-profile cylindrical optical fibre, including the effects of polarisation. A comparison of the asymptotic results with the exact eigenvalues is made when these are available, and the agreement is shown to be good

Improved bounds for the crossing numbers of K_m,n and K_n

It has been long--conjectured that the crossing number cr(K_m,n) of the complete bipartite graph K_m,n equals the Zarankiewicz Number Z(m,n):= floor((m-1)/2) floor(m/2) floor((n-1)/2) floor(n/2). Another long--standing conjecture states that the crossing number cr(K_n) of the complete graph K_n equals Z(n):= floor(n/2) floor((n-1)/2) floor((n-2)/2) floor((n-3)/2)/4. In this paper we show the following improved bounds on the asymptotic ratios of these crossing numbers and their conjectured values: (i) for each fixed m >= 9, lim_{n->infty} cr(K_m,n)/Z(m,n) >= 0.83m/(m-1); (ii) lim_{n->infty} cr(K_n,n)/Z(n,n) >= 0.83; and (iii) lim_{n->infty} cr(K_n)/Z(n) >= 0.83. The previous best known lower bounds were 0.8m/(m-1), 0.8, and 0.8, respectively. These improved bounds are obtained as a consequence of the new bound cr(K_{7,n}) >= 2.1796n^2 - 4.5n. To obtain this improved lower bound for cr(K_{7,n}), we use some elementary topological facts on drawings of K_{2,7} to set up a quadratic program on 6! variables whose minimum p satisfies cr(K_{7,n}) >= (p/2)n^2 - 4.5n, and then use state--of--the--art quadratic optimization techniques combined with a bit of invariant theory of permutation groups to show that p >= 4.3593.Comment: LaTeX, 18 pages, 2 figure

Phase transition in a super superspin glass

We here confirm the occurrence of spin glass phase transition and extract estimates of associated critical exponents of a highly monodisperse and densely compacted system of bare maghemite nanoparticles. This system has earlier been found to behave like an archetypal spin glass, with e.g. a sharp transition from paramagnetic to non-equilibrium behavior, suggesting that this system undergoes a spin-glass phase transition at a relatively high temperature, $T_g$ $\sim$ 140 K.Comment: 4 pages, 3 figure

Dual tasking in Parkinson's disease: cognitive consequences while walking

Published in final edited form as: Neuropsychology. 2017 September; 31(6): 613–623. doi:10.1037/neu0000331.OBJECTIVE: Cognitive deficits are common in Parkinson's disease (PD) and exacerbate the functional limitations imposed by PD's hallmark motor symptoms, including impairments in walking. Though much research has addressed the effect of dual cognitive-locomotor tasks on walking, less is known about their effect on cognition. The purpose of this study was to investigate the relation between gait and executive function, with the hypothesis that dual tasking would exacerbate cognitive vulnerabilities in PD as well as being associated with gait disturbances. METHOD: Nineteen individuals with mild-moderate PD without dementia and 13 age- and education-matched normal control adults (NC) participated. Executive function (set-shifting) and walking were assessed singly and during dual tasking. RESULTS: Dual tasking had a significant effect on cognition (reduced set-shifting) and on walking (speed, stride length) for both PD and NC, and also on stride frequency for PD only. The impact of dual tasking on walking speed and stride frequency was significantly greater for PD than NC. Though the group by condition interaction was not significant, PD had fewer set-shifts than NC on dual task. Further, relative to NC, PD showed significantly greater variability in cognitive performance under dual tasking, whereas variability in motor performance remained unaffected by dual tasking. CONCLUSIONS: Dual tasking had a significantly greater effect in PD than in NC on cognition as well as on walking. The results suggest that assessment and treatment of PD should consider the cognitive as well as the gait components of PD-related deficits under dual-task conditions. (PsycINFO Database Record)

An exact approach for the vehicle routing problem with two-dimensional loading constraints

We consider a special case of the symmetric capacitated vehicle routing problem, in which a fleet of K identical vehicles must serve n customers, each with a given demand consisting in a set of rectangular two-dimensional weighted items. The vehicles have a two-dimensional loading surface and a maximum weight capacity. The aim is to find a partition of the customers into routes of minimum total cost such that, for each vehicle, the weight capacity is taken into account and a feasible two-Dimensional allocation of the items into the loading surface exists. The problem has several practical applications in freight transportation, and it is -hard in the strong sense. We propose an exact approach, based on a branch-and-cut algorithm, for the minimization of the routing cost that iteratively calls a branch-and-bound algorithm for checking the feasibility of the loadings. Heuristics are also used to improve the overall performance of the algorithm. The effectiveness of the approach is shown by means of computational results

Environmental Inequality Dataset

The Disaggreated RSEI model data (also known as RSEI-GM, or Geographic Microdata) version 2.3.4 was downloaded from the Amazon Web Service created by EPA. The RSEI-GM provides detailed air model results from EPA’s Risk-Screening Environmental Indicators (RSEI) model. The results include chemical concentration, toxicity-weighted concentration and score, calculated for each 810 meter square grid cell in a 49-km circle around the emitting facility, for every year from 1988 through 2014. The data can be used to examine trends in air pollution from industrial facilities over time and across geographies. In order to allow for evaluation of toxic-weighted concentration over time, we used only the core chemicals and industries that have been consistently required to report since 1988. Thus we filtered the RSEI-GM disaggregated dataset to exclude additional chemicals and industries added after 1988. Crosswalks to translate data from the RSEI grid cell system to U.S. census block geographies, provided by EPA, were used to combine RSEI results with census data and aggregate the results to the census tract level. We used the Longitudinal Tract Database created by Brown University, which adjusts data from previous years to 2010 census tract boundaries, to combine census demographic information for years 1989 through 2004. We used the 2006-2010 American Community Survey (ACS) for years 2005 through 2009 and the 2010-2014 ACS for years 2010 through 2014. This data were then used to calculate measures of environmental inequality. The ZIP file with the dataset is available below under additional files

Participatory Plant Breeding: A New Challenge in the Generation and Appropriation of Potato Varieties by Farmers in Bolivia

Experiments on participatory plant breeding were carried out with the active participation of farmers from the Morochata Region in Bolivia

su(1,1) Algebraic approach of the Dirac equation with Coulomb-type scalar and vector potentials in D + 1 dimensions

We study the Dirac equation with Coulomb-type vector and scalar potentials in D + 1 dimensions from an su(1, 1) algebraic approach. The generators of this algebra are constructed by using the Schr\"odinger factorization. The theory of unitary representations for the su(1, 1) Lie algebra allows us to obtain the energy spectrum and the supersymmetric ground state. For the cases where there exists either scalar or vector potential our results are reduced to those obtained by analytical techniques

Eye movement control during visual pursuit in Parkinson's disease

BACKGROUND: Prior studies of oculomotor function in Parkinson’s disease (PD) have either focused on saccades without considering smooth pursuit, or tested smooth pursuit while excluding saccades. The present study investigated the control of saccadic eye movements during pursuit tasksand assessed the quality of binocular coordinationas potential sensitive markers of PD. METHODS: Observers fixated on a central cross while a target moved toward it. Once the target reached the fixation cross, observers began to pursue the moving target. To further investigate binocular coordination, the moving target was presented on both eyes (binocular condition), or on one eye only (dichoptic condition). RESULTS: The PD group made more saccades than age-matched normal control adults (NC) both during fixation and pursuit. The difference between left and right gaze positions increased over time during the pursuit period for PD but not for NC. The findings were not related to age, as NC and young-adult control group (YC) performed similarly on most of the eye movement measures, and were not correlated with classical measures of PD severity (e.g., Unified Parkinson’s Disease Rating Scale (UPDRS) score). DISCUSSION: Our results suggest that PD may be associated with impairment not only in saccade inhibition, but also in binocular coordination during pursuit, and these aspects of dysfunction may be useful in PD diagnosis or tracking of disease course.This work was supported in part by grants from the National Science Foundation (NSF SBE-0354378 to Arash Yazdanbakhsh and Bo Cao) and Office of Naval Research (ONR N00014-11-1-0535 to Bo Cao, Chia-Chien Wu, and Arash Yazdanbakhsh). There was no additional external funding received for this study. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. (SBE-0354378 - National Science Foundation (NSF); ONR N00014-11-1-0535 - Office of Naval Research)Published versio