On the rate of convergence of Krasnosel’skiĭ-Mann iterations and their connection with sums of Bernoullis

In this paper we establish an estimate for the rate of convergence of the Krasnosel’ski?-Mann iteration for computing fixed points of non-expansive maps. Our main result settles the Baillon-Bruck conjecture [3] on the asymptotic regularity of this iteration. The proof proceeds by establishing a connection between these iterates and a stochastic process involving sums of non-homogeneous Bernoulli trials. We also exploit a new Hoeffdingtype inequality to majorize the expected value of a convex function of these sums using Poisson distributions.     

Lie and Courant algebroids on foliated manifolds

This is an exposition of the subject, which was developed in the author’s papers [19, 20]. Various results from the theory of foliations (cohomology, characteristic classes, deformations, etc.) are extended to subalgebroids of Lie algebroids that generalize the tangent integrable distributions. We also suggest a definition of foliated Courant algebroids and give some corresponding results and constructions.     

Towards Maintenance‐Free Biosensors for Hundreds of Bind/Release Cycles

A single aptamer bioreceptor layer was formed using a common streptavidin–biotin immobilization strategy and employed for 100–365 bind/release cycles. Chemically induced aptamer unfolding and release of its bound target was accomplished using alkaline solutions with high salt concentrations or deionized (DI) water. The use of DI water scavenged from the ambient atmosphere represents a first step towards maintenance‐free biosensors that do not require the storage of liquid reagents. The aptamer binding affinity was determined by surface plasmon resonance and found to be almost constant over 100–365 bind/release cycles with a variation of less than 5 % relative standard deviation. This reversible operation of biosensors based on immobilized aptamers without storage of liquid reagents introduces a conceptually new perspective in biosensing. Such new biosensing capability will be important for distributed sensor networks, sensors in resource‐limited settings, and wearable sensor applications.     

The Multilevel Splitting algorithm for graph colouring with application to the Potts model

Calculating the partition function of the zero-temperature antiferromagnetic model is an important problem in statistical physics. However, an exact calculation is hard since it is strongly connected to a fundamental combinatorial problem of counting proper vertex colourings in undirected graphs, for which an efficient algorithm is not known to exist. Thus, one has to rely on approximation techniques. In this paper, we formulate the problem of the partition function approximation in terms of rare-event probability estimation and investigate the performance of a particle-based algorithm, called Multilevel Splitting, for handling this setting. The proposed method enjoys a provable probabilistic performance guarantee and our numerical study indicates that this algorithm is capable of delivering accurate results using a relatively modest amount of computational resources.     

Technological applications of BINP industrial electron accelerators with focused beam extracted into atmosphere

Simultaneously with production of industrial accelerators BINP develops new EB technologies. For this purpose the set of equipment based on electron accelerators was installed. The accelerator has an energy range of 0.8–1.5 MeV and a maximum electron beam power of 100 kW. Electron beam is extracted into the atmosphere through the system of diaphragms with output holes about 1 mm in diameter. The operational vacuum in the accelerating tube is provided by a differential pumping system. The extraction device is equipped with additional scanning magnets. It allows the operator to change average beam power density in extra wide region from 10 to 10⁷ Wt/cm². The focused beam has many applications due to its unique properties.     

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Polymeric Sensor Materials: Toward an Alliance of Combinatorial and Rational Design Tools?

Increased selectivity, response speed, and sensitivity in the chemical and biological determinations of gases and liquids are of great interest. Particular attention is paid to polymeric sensor materials, which are applicable to sensors exploiting various energy transduction principles, such as radiant, electrical, mechanical, and thermal energy. Ideally, numerous functional parameters of sensor materials can be tailored to meet specific needs using rational design approaches. However, increasing the structural and functional complexity of polymeric sensor materials makes it more difficult to predict the desired properties. Combinatorial and high-throughput methods have had an impact on all areas of research on polymer-based sensor materials including homo- and copolymers, formulated materials, polymeric structures with engineered morphology, and molecular shape-recognition materials. Herein we report on the state-of-the-art, the development trends, and the remaining knowledge gaps in the area of combinatorial polymeric sensor materials design.     

Production of foamed materials from synthesized silicate glasses

Possibility of obtaining materials with cellular structure directly in syntheses of silicate glasses was demonstrated. It was confirmed that water released in glass formation can serve as a gas-producing agent. The necessity for a deep extent of the topochemical glass-formation process was revealed. A resource-saving solution was suggested for synthesis of foamed glasses, based on the replacement of a part of glass being synthesized from hydrosilicates with a finished sodium-calcium glass.