The vanishing ideal of a finite set of points with multiplicity structures

Given a finite set of arbitrarily distributed points in affine space with arbitrary multiplicity structures, we present an algorithm to compute the reduced Groebner basis of the vanishing ideal under the lexicographic ordering. Our method discloses the essential geometric connection between the relative position of the points with multiplicity structures and the quotient basis of the vanishing ideal, so we will explicitly know the set of leading terms of elements of I. We split the problem into several smaller ones which can be solved by induction over variables and then use our new algorithm for intersection of ideals to compute the result of the original problem. The new algorithm for intersection of ideals is mainly based on the Extended Euclidean Algorithm.Comment: 12 pages,12 figures,ASCM 201

From 2D to 3D: novel nanostructured scaffolds to investigate signalling in reconstructed neuronal networks

To recreate in vitro 3D neuronal circuits will ultimately increase the relevance of results from cultured to whole-brain networks and will promote enabling technologies for neuro-engineering applications. Here we fabricate novel elastomeric scaffolds able to instruct 3D growth of living primary neurons. Such systems allow investigating the emerging activity, in terms of calcium signals, of small clusters of neurons as a function of the interplay between the 2D or 3D architectures and network dynamics. We report the ability of 3D geometry to improve functional organization and synchronization in small neuronal assemblies. We propose a mathematical modelling of network dynamics that supports such a result. Entrapping carbon nanotubes in the scaffolds remarkably boosted synaptic activity, thus allowing for the first time to exploit nanomaterial/cell interfacing in 3D growth support. Our 3D system represents a simple and reliable construct, able to improve the complexity of current tissue culture models

A Glucose Fuel Cell for Implantable Brain–Machine Interfaces

We have developed an implantable fuel cell that generates power through glucose oxidation, producing steady-state power and up to peak power. The fuel cell is manufactured using a novel approach, employing semiconductor fabrication techniques, and is therefore well suited for manufacture together with integrated circuits on a single silicon wafer. Thus, it can help enable implantable microelectronic systems with long-lifetime power sources that harvest energy from their surrounds. The fuel reactions are mediated by robust, solid state catalysts. Glucose is oxidized at the nanostructured surface of an activated platinum anode. Oxygen is reduced to water at the surface of a self-assembled network of single-walled carbon nanotubes, embedded in a Nafion film that forms the cathode and is exposed to the biological environment. The catalytic electrodes are separated by a Nafion membrane. The availability of fuel cell reactants, oxygen and glucose, only as a mixture in the physiologic environment, has traditionally posed a design challenge: Net current production requires oxidation and reduction to occur separately and selectively at the anode and cathode, respectively, to prevent electrochemical short circuits. Our fuel cell is configured in a half-open geometry that shields the anode while exposing the cathode, resulting in an oxygen gradient that strongly favors oxygen reduction at the cathode. Glucose reaches the shielded anode by diffusing through the nanotube mesh, which does not catalyze glucose oxidation, and the Nafion layers, which are permeable to small neutral and cationic species. We demonstrate computationally that the natural recirculation of cerebrospinal fluid around the human brain theoretically permits glucose energy harvesting at a rate on the order of at least 1 mW with no adverse physiologic effects. Low-power brain–machine interfaces can thus potentially benefit from having their implanted units powered or recharged by glucose fuel cells

Carboxylic ester hydrolases from hyperthermophiles

Carboxylic ester hydrolyzing enzymes constitute a large group of enzymes that are able to catalyze the hydrolysis, synthesis or transesterification of an ester bond. They can be found in all three domains of life, including the group of hyperthermophilic bacteria and archaea. Esterases from the latter group often exhibit a high intrinsic stability, which makes them of interest them for various biotechnological applications. In this review, we aim to give an overview of all characterized carboxylic ester hydrolases from hyperthermophilic microorganisms and provide details on their substrate specificity, kinetics, optimal catalytic conditions, and stability. Approaches for the discovery of new carboxylic ester hydrolases are described. Special attention is given to the currently characterized hyperthermophilic enzymes with respect to their biochemical properties, 3D structure, and classification

Demographic, clinical and antibody characteristics of patients with digital ulcers in systemic sclerosis: data from the DUO Registry

OBJECTIVES: The Digital Ulcers Outcome (DUO) Registry was designed to describe the clinical and antibody characteristics, disease course and outcomes of patients with digital ulcers associated with systemic sclerosis (SSc). METHODS: The DUO Registry is a European, prospective, multicentre, observational, registry of SSc patients with ongoing digital ulcer disease, irrespective of treatment regimen. Data collected included demographics, SSc duration, SSc subset, internal organ manifestations, autoantibodies, previous and ongoing interventions and complications related to digital ulcers. RESULTS: Up to 19 November 2010 a total of 2439 patients had enrolled into the registry. Most were classified as either limited cutaneous SSc (lcSSc; 52.2%) or diffuse cutaneous SSc (dcSSc; 36.9%). Digital ulcers developed earlier in patients with dcSSc compared with lcSSc. Almost all patients (95.7%) tested positive for antinuclear antibodies, 45.2% for anti-scleroderma-70 and 43.6% for anticentromere antibodies (ACA). The first digital ulcer in the anti-scleroderma-70-positive patient cohort occurred approximately 5 years earlier than the ACA-positive patient group. CONCLUSIONS: This study provides data from a large cohort of SSc patients with a history of digital ulcers. The early occurrence and high frequency of digital ulcer complications are especially seen in patients with dcSSc and/or anti-scleroderma-70 antibodies