Successive projections on hyperplanes

AbstractAny sequence of points in Rn obtained by successive projections of a point on elements of a finite set of hyperplanes is bounded

Convex Independence in Permutation Graphs

A set C of vertices of a graph is P_3-convex if every vertex outside C has at most one neighbor in C. The convex hull \sigma(A) of a set A is the smallest P_3-convex set that contains A. A set M is convexly independent if for every vertex x \in M, x \notin \sigma(M-x). We show that the maximal number of vertices that a convexly independent set in a permutation graph can have, can be computed in polynomial time

Predicting the effects of deep brain stimulation using a reduced coupled oscillator model

This is the final version. Available on open access from Public Library of Science via the DOI in this recordData Availability: The data analysed in this manuscript is available from MRC BNDU Data Sharing platform at: https://data.mrc.ox.ac.uk/data-set/tremor-data-measured-essential-tremor-patients-subjected-phase-locked-deep-brain DOI: 10.5287/bodleian:xq24eN2KmDeep brain stimulation (DBS) is known to be an effective treatment for a variety of neurological disorders, including Parkinson’s disease and essential tremor (ET). At present, it involves administering a train of pulses with constant frequency via electrodes implanted into the brain. New ‘closed-loop’ approaches involve delivering stimulation according to the ongoing symptoms or brain activity and have the potential to provide improvements in terms of efficiency, efficacy and reduction of side effects. The success of closed-loop DBS depends on being able to devise a stimulation strategy that minimizes oscillations in neural activity associated with symptoms of motor disorders. A useful stepping stone towards this is to construct a mathematical model, which can describe how the brain oscillations should change when stimulation is applied at a particular state of the system. Our work focuses on the use of coupled oscillators to represent neurons in areas generating pathological oscillations. Using a reduced form of the Kuramoto model, we analyse how a patient should respond to stimulation when neural oscillations have a given phase and amplitude, provided a number of conditions are satisfied. For such patients, we predict that the best stimulation strategy should be phase specific but also that stimulation should have a greater effect if applied when the amplitude of brain oscillations is lower. We compare this surprising prediction with data obtained from ET patients. In light of our predictions, we also propose a new hybrid strategy which effectively combines two of the closed-loop strategies found in the literature, namely phase-locked and adaptive DBS

Evoked resonant neural activity in subthalamic local field potentials reflects basal ganglia network dynamics.

Evoked resonant neural activity (ERNA) is induced by subthalamic deep brain stimulation (DBS) and was recently suggested as a marker of lead placement and contact selection in Parkinson's disease. Yet, its underlying mechanisms and how it is modulated by stimulation parameters are unclear. Here, we recorded local field potentials from 27 Parkinson's disease patients, while leads were externalised to scrutinise the ERNA. First, we show that ERNA in the time series waveform and spectrogram likely represent the same activity, which was contested before. Second, our results show that the ERNA has fast and slow dynamics during stimulation, consistent with the synaptic failure hypothesis. Third, we show that ERNA parameters are modulated by different DBS frequencies, intensities, medication states and stimulation modes (continuous DBS vs. adaptive DBS). These results suggest the ERNA might prove useful as a predictor of the best DBS frequency and lowest effective intensity in addition to contact selection. Changes with levodopa and DBS mode suggest that the ERNA may indicate the state of the cortico-basal ganglia circuit making it a putative biomarker to track clinical state in adaptive DBS

Preparation and characterization of polypyrrole/graphene nanocomposite films and their electrochemical performance

A one-step electrochemical process had been employed to synthesize nanocomposite films of polypyrrole/graphene (PPy/GR) by electrochemical polymerisation on indium tin oxide (ITO) from an aqueous solution containing pyrrole monomer, graphene oxide (GO) nanosheets and sodium p-toluenesulfonate (NapTS). The X-ray diffraction (XRD) patterns showed that the typical peak of GO at 9.9o was missing from the nanocomposite’s diffraction pattern, suggesting that the GO had been stripped off of its oxygenous groups after the reaction. We postulated that a nanocomposite film was produced through a layer-by-layer deposition based on field emission scanning electron microscope (FESEM) images. The Raman spectroscopy profiles exhibited that the D/G intensity ratio (ID/IG) of PPy was not altered by the inclusion of GO due to the low concentration of the material used. However, the concentration was sufficient to increase the specific capacitance of the nanocomposite by 20 times compared to that of pure PPy, reflecting a synergistic effect between PPy and GR, as analysed by a three-electrode electrochemical cell. The electrochemical performance of the nanocomposites was affected by varying the deposition parameters such as concentrations of pyrrole and GO, scan rate, deposition time and deposition potential

Orally Administered P22 Phage Tailspike Protein Reduces Salmonella Colonization in Chickens: Prospects of a Novel Therapy against Bacterial Infections

One of the major causes of morbidity and mortality in man and economically important animals is bacterial infections of the gastrointestinal (GI) tract. The emergence of difficult-to-treat infections, primarily caused by antibiotic resistant bacteria, demands for alternatives to antibiotic therapy. Currently, one of the emerging therapeutic alternatives is the use of lytic bacteriophages. In an effort to exploit the target specificity and therapeutic potential of bacteriophages, we examined the utility of bacteriophage tailspike proteins (Tsps). Among the best-characterized Tsps is that from the Podoviridae P22 bacteriophage, which recognizes the lipopolysaccharides of Salmonella enterica serovar Typhimurium. In this study, we utilized a truncated, functionally equivalent version of the P22 tailspike protein, P22sTsp, as a prototype to demonstrate the therapeutic potential of Tsps in the GI tract of chickens. Bacterial agglutination assays showed that P22sTsp was capable of agglutinating S. Typhimurium at levels similar to antibodies and incubating the Tsp with chicken GI fluids showed no proteolytic activity against the Tsp. Testing P22sTsp against the three major GI proteases showed that P22sTsp was resistant to trypsin and partially to chymotrypsin, but sensitive to pepsin. However, in formulated form for oral administration, P22sTsp was resistant to all three proteases. When administered orally to chickens, P22sTsp significantly reduced Salmonella colonization in the gut and its further penetration into internal organs. In in vitro assays, P22sTsp effectively retarded Salmonella motility, a factor implicated in bacterial colonization and invasion, suggesting that the in vivo decolonization ability of P22sTsp may, at least in part, be due to its ability to interfere with motility… Our findings show promise in terms of opening novel Tsp-based oral therapeutic approaches against bacterial infections in production animals and potentially in humans

Hydrogen physisorption based on the dissociative hydrogen chemisorption at the sulphur vacancy of MoS2 surface

We provide a new insight that the sulphur-depleted MoS2 surface can store hydrogen gas at room temperature. Our findings reveal that the sulphur-vacancy defects preferentially serve as active sites for both hydrogen chemisorption and physisorption. Unexpectedly the sulphur vacancy instantly dissociates the H-2 molecules and strongly binds the split hydrogen at the exposed Mo atoms. Thereon the additional H-2 molecule is adsorbed with enabling more hydrogen physisorption on the top sites around the sulphur vacancy. Furthermore, the increase of the sulphur vacancy on the MoS2 surface further activates the dissociative hydrogen chemisorption than the H-2 physisorption