Explicit Error Bounds for Spline Interpolation on a Uniform Partition

AbstractThis paper considers the optimality and the evaluation of the constants that appear in the expressions of error bounds for interpotating spline functions over a uniform mesh of the real line when the nodes are uniformly shifted

Generalized Heisenberg algebras and k-generalized Fibonacci numbers

It is shown how some of the recent results of de Souza et al. [1] can be generalized to describe Hamiltonians whose eigenvalues are given as k-generalized Fibonacci numbers. Here k is an arbitrary integer and the cases considered by de Souza et al. corespond to k=2.Comment: 8 page

Selective changes in inhibition as determinants for limited hyperexcitability in the insular cortex of epileptic rats

The insular cortex (IC) is involved in the generalization of epileptic discharges in temporal lobe epilepsy (TLE), while seizures originating in IC can mimic the epileptic phenotype seen in some TLE patients. Few studies have however addressed the changes occurring in the IC in TLE animal models. Here, we analyzed the immunohistochemical and electrophysiological properties of IC networks in non-epileptic control and pilocarpine-treated epileptic rats. Neurons identified with a neuron-specific nuclear protein antibody showed similar counts in the two types of tissue but parvalbumin- and neuropeptide Y-positive interneurons were significantly decreased (parvalbumin, approx. -35%; neuropeptide Y, approx. -38%; P<0.01) in the epileptic IC. Non-adapting neurons were more frequently seen in the epileptic IC during intracellular injection of depolarizing current pulses. In addition, single-shock electrical stimuli elicited network-driven epileptiform responses in 87% of epileptic and in 22% of non-epileptic control neurons (P<0.01) but spontaneous postsynaptic potentials had similar amplitude, duration and intervals of occurrence in the two groups. Finally, pharmacologically isolated, GABAA receptor-mediated inhibitory postsynaptic potentials had more negative reversal potential (P<0.01) and higher peak conductance (P<0.05) in epileptic tissue. These data reveal moderate increased network excitability in the IC of pilocarpine-treated epileptic rats. We propose that such limited degree of hyperexcitability originates from loss of parvalbumin- and neuropeptide Y-positive interneurons that is compensated by an increased drive for GABAA receptor-mediated inhibition

Facilitation of epileptic activity during sleep is mediated by high amplitude slow waves

Epileptic discharges in focal epilepsy are frequently activated during non-rapid eye movement sleep. Sleep slow waves are present during this stage and have been shown to include a deactivated ('down', hyperpolarized) and an activated state ('up', depolarized). The 'up' state enhances physiological rhythms, and we hypothesize that sleep slow waves and particularly the 'up' state are the specific components of non-rapid eye movement sleep that mediate the activation of epileptic activity. We investigated eight patients with pharmaco-resistant focal epilepsies who underwent combined scalp-intracerebral electroencephalography for diagnostic evaluation. We analysed 259 frontal electroencephalographic channels, and manually marked 442 epileptic spikes and 8487 high frequency oscillations during high amplitude widespread slow waves, and during matched control segments with low amplitude widespread slow waves, non-widespread slow waves or no slow waves selected during the same sleep stages (total duration of slow wave and control segments: 49 min each). During the slow waves, spikes and high frequency oscillations were more frequent than during control segments (79% of spikes during slow waves and 65% of high frequency oscillations, both P ~ 0). The spike and high frequency oscillation density also increased for higher amplitude slow waves. We compared the density of spikes and high frequency oscillations between the 'up' and 'down' states. Spike and high frequency oscillation density was highest during the transition from the 'up' to the 'down' state. Interestingly, high frequency oscillations in channels with normal activity expressed a different peak at the transition from the 'down' to the 'up' state. These results show that the apparent activation of epileptic discharges by non-rapid eye movement sleep is not a state-dependent phenomenon but is predominantly associated with specific events, the high amplitude widespread slow waves that are frequent, but not continuous, during this state of sleep. Both epileptic spikes and high frequency oscillations do not predominate, like physiological activity, during the 'up' state but during the transition from the 'up' to the 'down' state of the slow wave, a period of high synchronization. Epileptic discharges appear therefore more associated with synchronization than with excitability. Furthermore, high frequency oscillations in channels devoid of epileptic activity peak differently during the slow wave cycle from those in channels with epileptic activity. This property may allow differentiating physiological from pathological high frequency oscillations, a problem that is unresolved until now

Effect of Mono and Di-rhamnolipids on Biofilms Pre-formed by Bacillus subtilis BBK006.

Different microbial inhibition strategies based on the planktonic bacterial physiology have been known to have limited efficacy on the growth of biofilms communities. This problem can be exacerbated by the emergence of increasingly resistant clinical strains. Biosurfactants have merited renewed interest in both clinical and hygienic sectors due to their potential to disperse microbial biofilms. In this work, we explore the aspects of Bacillus subtilis BBK006 biofilms and examine the contribution of biologically derived surface-active agents (rhamnolipids) to the disruption or inhibition of microbial biofilms produced by Bacillus subtilis BBK006. The ability of mono-rhamnolipids (Rha-C10-C10) produced by Pseudomonas aeruginosa ATCC 9027 and the di-rhamnolipids (Rha-Rha-C14-C14) produced by Burkholderia thailandensis E264, and phosphate-buffered saline to disrupt biofilm of Bacillus subtilis BBK006 was evaluated. The biofilm produced by Bacillus subtilis BBK006 was more sensitive to the di-rhamnolipids (0.4 g/L) produced by Burkholderia thailandensis than the mono-rhamnolipids (0.4 g/L) produced by Pseudomonas aeruginosa ATCC 9027. Rhamnolipids are biologically produced compounds safe for human use. This makes them ideal candidates for use in new generations of bacterial dispersal agents and useful for use as adjuvants for existing microbial suppression or eradication strategies

Genome-scale screen for DNA methylation-based detection markers for ovarian cancer.

The identification of sensitive biomarkers for the detection of ovarian cancer is of high clinical relevance for early detection and/or monitoring of disease recurrence. We developed a systematic multi-step biomarker discovery and verification strategy to identify candidate DNA methylation markers for the blood-based detection of ovarian cancer

The receptor tyrosine kinase EphB4 is overexpressed in ovarian cancer, provides survival signals and predicts poor outcome

EphB4 is a member of the largest family of transmembrane receptor tyrosine kinases and plays critical roles in axonal pathfinding and blood vessel maturation. We wanted to determine the biological role of EphB4 in ovarian cancer. We studied the expression of EphB4 in seven normal ovarian specimens and 85 invasive ovarian carcinomas by immunohistochemistry. EphB4 expression was largely absent in normal ovarian surface epithelium, but was expressed in 86% of ovarian cancers. EphB4 expression was significantly associated with advanced stage of disease and the presence of ascites. Overexpression of EphB4 predicted poor survival in both univariate and multivariate analyses. We also studied the biological significance of EphB4 expression in ovarian tumour cells lines in vitro and in vivo. All five malignant ovarian tumour cell lines tested expressed higher levels of EphB4 compared with the two benign cell lines. Treatment of malignant, but not benign, ovarian tumour cell lines with progesterone, but not oestrogen, led to a 90% reduction in EphB4 levels that was associated with 50% reduction in cell survival. Inhibition of EphB4 expression by specific siRNA or antisense oligonucleotides significantly inhibited tumour cell viability by inducing apoptosis via activation of caspase-8, and also inhibited tumour cell invasion and migration. Furthermore, EphB4 antisense significantly inhibited growth of ovarian tumour xenografts and tumour microvasculature in vivo. Inhibition of EphB4 may hence have prognostic and therapeutic utility in ovarian carcinoma