Brainstem atrophy in focal epilepsy destabilizes brainstem-brain interactions: Preliminary findings.

BACKGROUND: MR Imaging has shown atrophy in brainstem regions that were linked to autonomic dysfunction in epilepsy patients. The brainstem projects to and modulates the activation state of several wide-spread cortical/subcortical regions. The goal was to investigate 1. Impact of brainstem atrophy on gray matter connectivity of cortical/subcortical structures and autonomic control. 2. Impact on the modulation of cortical/subcortical functional connectivity. METHODS: 11 controls and 18 patients with non-lesional focal epilepsy (FE) underwent heart rate variability (HRV) measurements and a 3 T MRI (T1 in all subjects, task-free fMRI in 7 controls/ 12 FE). The brainstem was extracted, and atrophy assessed using deformation-based-morphometry. The age-corrected z-scores of the mean Jacobian determinants were extracted from 71 5x5x5 mm grids placed in brainstem regions associated with autonomic function. Cortical and non-brainstem subcortical gray matter atrophy was assessed with voxel-based-morphometry and mean age corrected z-scores of the modulated gray matter volumes extracted from 380 cortical/subcortical rois. The profile similarity index was used to characterize the impact of brainstem atrophy on gray matter connectivity. The fMRI was preprocessed in SPM12/Conn17 and the BOLD signal extracted from 398 ROIs (16 brainstem). A dynamic task-free analysis approach was used to identify activation states. Connectivity HRV relationship were assessed with Spearman rank correlations. RESULTS: HRV was negatively correlated with reduced brainstem right hippocampus/parahippocampus gray matter connectivity in controls (p \u3c .05, FDR) and reduced brainstem to right parietal cortex, lingual gyrus, left hippocampus/amygdala, parahippocampus, temporal pole, and bilateral anterior thalamus connectivity in FE (p \u3c .05, FDR). Dynamic task-free fMRI analysis identified 22 states. The strength of the functional brainstem/cortical connectivity of state 15 was negatively associated with HRV (r = -0.5, p = .03) and positively with decreased brainstem-cortical (0.49, p = .03) gray matter connectivity. CONCLUSION: The findings of this small pilot study suggest that impaired brainstem-cortex gray matter connectivity in FE negatively affects the brainstem\u27s ability to control cortical activation

Nonlinear Integral-Equation Formulation of Orthogonal Polynomials

The nonlinear integral equation P(x)=\int_alpha^beta dy w(y) P(y) P(x+y) is investigated. It is shown that for a given function w(x) the equation admits an infinite set of polynomial solutions P(x). For polynomial solutions, this nonlinear integral equation reduces to a finite set of coupled linear algebraic equations for the coefficients of the polynomials. Interestingly, the set of polynomial solutions is orthogonal with respect to the measure x w(x). The nonlinear integral equation can be used to specify all orthogonal polynomials in a simple and compact way. This integral equation provides a natural vehicle for extending the theory of orthogonal polynomials into the complex domain. Generalizations of the integral equation are discussed.Comment: 7 pages, result generalized to include integration in the complex domai

Calculation of some determinants using the s-shifted factorial

Several determinants with gamma functions as elements are evaluated. This kind of determinants are encountered in the computation of the probability density of the determinant of random matrices. The s-shifted factorial is defined as a generalization for non-negative integers of the power function, the rising factorial (or Pochammer's symbol) and the falling factorial. It is a special case of polynomial sequence of the binomial type studied in combinatorics theory. In terms of the gamma function, an extension is defined for negative integers and even complex values. Properties, mainly composition laws and binomial formulae, are given. They are used to evaluate families of generalized Vandermonde determinants with s-shifted factorials as elements, instead of power functions.Comment: 25 pages; added section 5 for some examples of application

Virtual patients design and its effect on clinical reasoning and student experience : a protocol for a randomised factorial multi-centre study

Background Virtual Patients (VPs) are web-based representations of realistic clinical cases. They are proposed as being an optimal method for teaching clinical reasoning skills. International standards exist which define precisely what constitutes a VP. There are multiple design possibilities for VPs, however there is little formal evidence to support individual design features. The purpose of this trial is to explore the effect of two different potentially important design features on clinical reasoning skills and the student experience. These are the branching case pathways (present or absent) and structured clinical reasoning feedback (present or absent). Methods/Design This is a multi-centre randomised 2x2 factorial design study evaluating two independent variables of VP design, branching (present or absent), and structured clinical reasoning feedback (present or absent).The study will be carried out in medical student volunteers in one year group from three university medical schools in the United Kingdom, Warwick, Keele and Birmingham. There are four core musculoskeletal topics. Each case can be designed in four different ways, equating to 16 VPs required for the research. Students will be randomised to four groups, completing the four VP topics in the same order, but with each group exposed to a different VP design sequentially. All students will be exposed to the four designs. Primary outcomes are performance for each case design in a standardized fifteen item clinical reasoning assessment, integrated into each VP, which is identical for each topic. Additionally a 15-item self-reported evaluation is completed for each VP, based on a widely used EViP tool. Student patterns of use of the VPs will be recorded. In one centre, formative clinical and examination performance will be recorded, along with a self reported pre and post-intervention reasoning score, the DTI. Our power calculations indicate a sample size of 112 is required for both primary outcomes

The value of urban green space in Britain: A methodological framework for spatially referenced benefit transfer

Author version of article. The final publication is available at Springer via http://dx.doi.org/10.1007/s10640-013-9665-8.© Springer Science+Business Media Dordrecht 2013A meta-analysis of studies valuing urban greenspace in the UK is undertaken to yield spatially sensitive marginal value functions. A geographical information system (GIS) is used to apply these functions to spatial data detailing the location of such greenspace resources in five British cities and monetary values are computed. This procedure is repeated for the six future scenarios used in the UK National Ecosystem Assessment and changes in values calculated for the period 2010-60. These findings are then extrapolated to all major British cities to obtain per household and aggregate valuation estimates for each scenario both with and without distributional weights. While subject to a number of shortcomings in both data availability and methodology, this represents the first systematic and comprehensive attempt to value marginal changes in urban greenspace while accounting for spatial heterogeneity.Economic and Social Research Council (ESRC

Spectral singularities for Non-Hermitian one-dimensional Hamiltonians: puzzles with resolution of identity

We examine the completeness of bi-orthogonal sets of eigenfunctions for non-Hermitian Hamiltonians possessing a spectral singularity. The correct resolutions of identity are constructed for delta like and smooth potentials. Their form and the contribution of a spectral singularity depend on the class of functions employed for physical states. With this specification there is no obstruction to completeness originating from a spectral singularity.Comment: 25 pages, more refs adde

Global Electric Circuit Implications of Combined Aircraft Storm Electric Current Measurements and Satellite-Based Diurnal Lightning Statistics

Using rotating vane electric field mills and Gerdien capacitors, we measured the electric field profile and conductivity during 850 overflights of thunderstorms and electrified shower clouds (ESCs) spanning regions including the Southeastern United States, the Western Atlantic Ocean, the Gulf of Mexico, Central America and adjacent oceans, Central Brazil, and the South Pacific. The overflights include storms over land and ocean, and with positive and negative fields above the storms. Over three-quarters (78%) of the land storms had detectable lightning, while less than half (43%) of the oceanic storms had lightning. Integrating our electric field and conductivity data, we determined total conduction currents and flash rates for each overpass. With knowledge of the storm location (land or ocean) and type (with or without lightning), we determine the mean currents by location and type. The mean current for ocean thunderstorms is 1.7 A while the mean current for land thunderstorms is 1.0 A. The mean current for ocean ESCs 0.41 A and the mean current for land ESCs is 0.13 A. We did not find any significant regional or latitudinal based patterns in our total conduction currents. By combining the aircraft derived storm currents and flash rates with diurnal flash rate statistics derived from the Lightning Imaging Sensor (LIS) and Optical Transient Detector (OTD) low Earth orbiting satellites, we reproduce the diurnal variation in the global electric circuit (i.e., the Carnegie curve) to within 4% for all but two short periods of time. The agreement with the Carnegie curve was obtained without any tuning or adjustment of the satellite or aircraft data. Given our data and assumptions, mean contributions to the global electric circuit are 1.1 kA (land) and 0.7 kA (ocean) from thunderstorms, and 0.22 kA (ocean) and 0.04 (land) from ESCs, resulting in a mean total conduction current estimate for the global electric circuit of 2.0 kA. Mean storm counts are 1100 for land thunderstorms, 530 for ocean ESCs, 390 for ocean thunderstorms, and 330 for land ESCs

Flash Detection Efficiencies of Long Range Lightning Detection Networks During GRIP

We flew our Lightning Instrument Package (LIP) on the NASA Global Hawk as a part of the Genesis and Rapid Intensification Processes (GRIP) field program. The GRIP program was a NASA Earth science field experiment during the months of August and September, 2010. During the program, the LIP detected lighting from 48 of the 213 of the storms overflown by the Global Hawk. The time and location of tagged LIP flashes can be used as a "ground truth" dataset for checking the detection efficiency of the various long or extended range ground-based lightning detection systems available during the GRIP program. The systems analyzed included Vaisala Long Range (LR), Vaisala GLD360, the World Wide Lightning Location Network (WWLLN), and the Earth Networks Total Lightning Network (ENTLN). The long term goal of our research is to help understand the advantages and limitations of these systems so that we can utilize them for both proxy data applications and cross sensor validation of the GOES-R Geostationary Lightning Mapper (GLM) sensor when it is launched in the 2015 timeframe

Fuels treatment and wildfire effects on runoff from Sierra Nevada mixed-conifer forests

We applied an eco-hydrologic model (Regional Hydro-Ecologic Simulation System [RHESSys]), constrained with spatially distributed field measurements, to assess the impacts of forest-fuel treatments and wildfire on hydrologic fluxes in two Sierra Nevada firesheds. Strategically placed fuels treatments were implemented during 2011–2012 in the upper American River in the central Sierra Nevada (43 km2) and in the upper Fresno River in the southern Sierra Nevada (24 km2). This study used the measured vegetation changes from mechanical treatments and modelled vegetation change from wildfire to determine impacts on the water balance. The well-constrained headwater model was transferred to larger catchments based on geologic and hydrologic similarities. Fuels treatments covered 18% of the American and 29% of the Lewis catchment. Averaged over the entire catchment, treatments in the wetter central Sierra Nevada resulted in a relatively light vegetation decrease (8%), leading to a 12% runoff increase, averaged over wet and dry years. Wildfire with and without forest treatments reduced vegetation by 38% and 50% and increased runoff by 55% and 67%, respectively. Treatments in the drier southern Sierra Nevada also reduced the spatially averaged vegetation by 8%, but the runoff response was limited to an increase of less than 3% compared with no treatment. Wildfire following treatments reduced vegetation by 40%, increasing runoff by 13%. Changes to catchment-scale water-balance simulations were more sensitive to canopy cover than to leaf area index, indicating that the pattern as well as amount of vegetation treatment is important to hydrologic response

Asymptotic behavior of the least common multiple of consecutive arithmetic progression terms

Let $l$ and $m$ be two integers with $l>m\ge 0$, and let $a$ and $b$ be integers with $a\ge 1$ and $a+b\ge 1$. In this paper, we prove that $\log {\rm lcm}_{mn<i\le ln}\{ai+b\} =An+o(n)$, where $A$ is a constant depending on $l, m$ and $a$.Comment: 8 pages. To appear in Archiv der Mathemati