Optimization with binet matrices

This paper deals with linear and integer programming problems in which the constraint matrix is a binet matrix. Linear programs can be solved with the generalized network simplex method, while integer programs are converted to a matching problem. It is also proved that an integral binet matrix has strong Chvátal rank 1.     

A combinatorial-probabilistic analysis of bitcoin attacks*

In 2008, Satoshi Nakamoto famously invented bitcoin, and in his (or her, or their, or its) white paper sketched an approximate formula for the probability of a successful double spending attack by a dishonest party. This was corrected by Meni Rosenfeld, who, under more realistic assumptions, gave the exact probability (missing a foundational proof); and another formula (along with foundational proof), in terms of the Incomplete Beta function, was given later by Cyril Grunspan and Ricardo Pérez-Marco, that enabled them to derive an asymptotic formula for that quantity. Using Wilf-Zeilberger algorithmic proof theory, we continue in this vein and present a recurrence equation for the above-mentioned probability of success, that enables a very fast compilation of these probabilities. We next use this recurrence to derive (in algorithmic fashion) higher-order asymptotic formulas, extending the formula of Grunspan and Pérez-Marco who did the leading term. We then study the statistical properties (expectation, variance, etc.) of the duration of a successful attack.     

Atomic and Molecular Decomposition of Homogeneous Spaces of Distributions Associated to Non-negative Self-Adjoint Operators

We deal with homogeneous Besov and Triebel–Lizorkin spaces in the setting of a doubling metric measure space in the presence of a non-negative self-adjoint operator whose heat kernel has Gaussian localization and the Markov property. The class of almost diagonal operators on the associated sequence spaces is developed and it is shown that this class is an algebra. The boundedness of almost diagonal operators is utilized for establishing smooth molecular and atomic decompositions for the above homogeneous Besov and Triebel–Lizorkin spaces. Spectral multipliers for these spaces are established as well.

     

Fluxes of physical quantities and ozone concentration within a fruit tree

Summary Implicit to an understanding of the eco-physiological behaviour and yield of cultivated plants is a knowledge of air-vegetation interaction. One of the basic factors controlling the quantity and quality of plant growth is the turbulent exchange of such physical quantities as temperature and humidity, a fact making the impact assessment of gaseous pollutant deposition also important. Oxidants such as ozone are potentially harmful to plants via metabolic responses and cell injury and, once the threshold of adaptation is exceeded, the death of the plant may even ensue. Experimental application of the micrometeorological gradient method to a peach tree so as to determine the in-canopy transfer coefficients and to derive the fluxes of physical quantities and ozone is reported.     

Preliminary analysis of surface radiation measurements recorded at the Nansen ice sheet (Antarctica)

Summary An experiment on radiation and surface energy balance was conducted during the 9th Italian expedition in Antarctica at the Nansen ice sheet, a glacier situated close to the Italian base at Terra Nova Bay, to correlate surface balances to the formation and development of katabatic winds. Measurements were taken by radiometers covering the whole spectra of solar and terrestrial emissions and by fast sensors of atmospheric wind velocity and humidity for the application of the eddy correlation technique. A preliminary analysis of the radiotive energy balance during the Antarctic summer in clear-sky conditions is reported and discussed. The findings show the very low available energy (mean about 1 W/m²), in terms of net radiation, for the physical processes such as sensible- and latent-heat fluxes. Long-wave radiation balance was applied to estimate the reliability of the Swinbank's parametrization, relative to general conditions of the atmosphere.     

A dynamically adaptive wavelet approach to stochastic computations based on polynomial chaos – capturing all scales of random modes on independent grids

In stochastic computations, or uncertainty quantification methods, the spectral approach based on the polynomial chaos expansion in random space leads to a coupled system of deterministic equations for the coefficients of the expansion. The size of this system increases drastically when the number of independent random variables and/or order of polynomial chaos expansions increases. This is invariably the case for large scale simulations and/or problems involving steep gradients and other multiscale features; such features are variously reflected on each solution component or random/uncertainty mode requiring the development of adaptive methods for their accurate resolution. In this paper we propose a new approach for treating such problems based on a dynamically adaptive wavelet methodology involving space-refinement on physical space that allows all scales of each solution component to be refined independently of the rest. We exemplify this using the convection–diffusion model with random input data and present three numerical examples demonstrating the salient features of the proposed method. Thus we establish a new, elegant and flexible approach for stochastic problems with steep gradients and multiscale features based on polynomial chaos expansions.     

Virtually Biautomatic Groups

We introduce virtually biautomatic groups (groups with finite index biautomatic subgroups) and generalize results of Gersten and Short [3 Gersten , S. , Short , H. ( 1991 ). Rational subgroups of biautomatic groups . Annals of Mathematics 134 : 125 – 128 .[Crossref], [Web of Science ®] , [Google Scholar]] and Mosher [5 Mosher , L. ( 1997 ). Central quotients of biautomatic groups . Comment. Math. Helv. 72 ( 1 ): 16 – 29 .[Crossref], [Web of Science ®] , [Google Scholar]] on centralizers, normalizers, and quotients to virtually biautomatic groups.     

Flexible long-term capacity planning in closed-loop supply chains with remanufacturing

We deal with long-term demand-driven capacity planning policies in the reverse channel of closed-loop supply chains (CLSCs) with remanufacturing, under high capacity acquisition cost coupled with uncertainty in actual demand, sales patterns, quality and timing of end-of-use product returns. The objective is to facilitate the decision-making when the management faces the dilemma of implementing either a strategy of early large-scale investments to benefit from economies of scale and capacity readiness, or a flexible strategy of low volume but more frequent capacity expansions. We consider a CLSC with two sequential product-types. We study the system’s response in terms of transient flows, actual/desired capacity level, capacity expansions/contractions and total supply chain profit, employing a simulation-based system dynamics optimization approach. Extensive numerical investigation covers a broad range of real-world remanufacturable products under alternative scenarios in relation to the market preference over product-types. The key findings propose flexible policies as improved alternatives to large-scale capacity expansions/contractions in terms of adaptability to the actual pattern of end-of-use product returns and involved risk in the investments’ turnover. Flexible policies are also proposed as practices to avoid overcapacity phenomena in collection and remanufacturing capacity and as robust policies to product demand. Their implementation is revealed to be even more important for the case of remanufacturing, when a high capacity acquisition unit-cost ratio (remanufacturing/collection) is coupled with strong economies of scale. Finally, results under different information sharing structures show changes in remanufacturing policies, thus justifying the importance of coordination between the decision-maker and the distributor.     

Modelling the semi-batch vinyl acetate emulsion polymerization in a real-life industrial reactor

A detailed dynamic model of the polymerization reaction of vinyl acetate in a real-life industrial reactor is presented. With the recipe and the operating procedures observed in the factory as inputs, the model predicts with reasonable accuracy the final conversion, the average particle diameter, the solid content and the viscosity. The manual and semi-manual operations, and the decision process followed by the operator, are also modelled in order to replicate closely the process carried out in the factory. The model provides further insight into the reaction kinetics and allows us to make knowledge-based decisions. The model is intended to be used for the optimization of the policy of adding monomer in order to reduce the batch time.