An interval-matrix branch-and-bound algorithm for bounding eigenvalues

We present and explore the behaviour of a branch-and-bound algorithm for calculating valid bounds on the k-th largest eigenvalue of a symmetric interval matrix. Branching on the interval elements of the matrix takes place in conjunction with the application of Rohn’s method (an interval extension of Weyl’s theorem) in order to obtain valid outer bounds on the eigenvalues. Inner bounds are obtained with the use of two local search methods. The algorithm has the theoretical property that it provides bounds to any arbitrary precision > 0 (assuming infinite precision arithmetic) within finite time. In contrast with existing methods, bounds for each individual eigenvalue can be obtained even if its range overlaps with the ranges of other eigenvalues. Performance analysis is carried out through nine examples. In the first example, a comparison of the efficiency of the two local search methods is reported using 4,000 randomly generated matrices. The eigenvalue bounding algorithm is then applied to five randomly generated matrices with overlapping eigenvalue ranges. Valid and sharp bounds are indeed identified given a sufficient number of iterations. Furthermore, most of the range reduction takes place in the first few steps of the algorithm so that significant benefits can be derived without full convergence. Finally, in the last three examples, the potential of the algorithm for use in algorithms to identify index-1 saddle points of nonlinear functions is demonstrated

Influence of sodium chloride on wine yeast fermentation performance

This paper concerns research into the influence of salt (sodium chloride) on growth, viability and fermentation performance in a winemaking strain of the yeast, Saccharomyces cerevisiae. Experimental fermentations were conducted in both laboratory-scale and industrial-scale experiments. Preculturing yeasts in elevated levels of sodium chloride, or salt “preconditioning” led to improved fermentation performance. This was manifest by preconditioned yeasts having an improved capability to ferment high-sugar containing media with increased cell viability and with elevated levels of produced ethanol. Salt-preconditioning most likely influenced the stress-tolerance of yeasts by inducing the synthesis of key metabolites such as trehalose and glycerol. These compounds may act to improve cells’ ability to withstand osmostress and ethanol toxicity during fermentations of grape must. Industrial-scale trials using salt-preconditioned yeasts verified the benefit of this novel physiological cell engineering approach to practical winemaking fermentations

Enclosure of all index-1 saddle points of general nonlinear functions

Transition states (index-1 saddle points) play a crucial role in determining the rates of chemical transformations but their reliable identification remains challenging in many applications. Deterministic global optimization methods have previously been employed for the location of transition states (TSs) by initially finding all stationary points and then identifying the TSs among the set of solutions. We propose several regional tests, applicable to general nonlinear, twice continuously differentiable functions, to accelerate the convergence of such approaches by identifying areas that do not contain any TS or that may contain a unique TS. The tests are based on the application of the interval extension of theorems from linear algebra to an interval Hessian matrix. They can be used within the framework of global optimization methods with the potential of reducing the computational time for TS location. We present the theory behind the tests, discuss their algorithmic complexity and show via a few examples that significant gains in computational time can be achieved by using these tests

Bioethanol Production by Carbohydrate-Enriched Biomass of Arthrospira (Spirulina) platensis

In the present study the potential of bioethanol production using carbohydrate-enriched biomass of the cyanobacterium Arthrospira platensis was studied. For the saccharification of the carbohydrate-enriched biomass, four acids (H2SO4, HNO3, HCl and H3PO4) were investigated. Each acid were used at four concentrations, 2.5 N, 1 N, 0.5 N and 0.25 N, and for each acid concentration the saccharification was conducted under four temperatures (40 °C, 60 °C, 80 °C and 100 °C). Higher acid concentrations gave in general higher reducing sugars (RS) yields (%, gRS/gTotal sugars) with higher rates, while the increase in temperature lead to higher rates at lower acid concentration. The hydrolysates then were used as substrate for ethanolic fermentation by a salt stress-adapted Saccharomyces cerevisiae strain. The bioethanol yield (%, gEtOH/gBiomass) was significantly affected by the acid concentration used for the saccharification of the carbohydrates. The highest bioethanol yields of 16.32% ± 0.90% (gEtOH/gBiomass) and 16.27% ± 0.97% (gEtOH/gBiomass) were obtained in hydrolysates produced with HNO3 0.5 N and H2SO4 0.5 N, respectively

Alleviation of stuck wine fermentations using salt-preconditioned yeast

The influence of salt (sodium chloride) on the cell physiology of wine yeast was investigated. Cellular viability and population growth of three wine-making yeast strains of Saccharomyces cerevisiae, and two non-Saccharomyces yeast strains associated with wine must microflora (Kluyveromyces thermotolerans and K. marxianus) were evaluated following salt pre-treatments. Yeast cells growing in glucose defined media exposed to different sodium chloride concentrations (4, 6 and 10% w/v) exhibited enhanced viabilities compared with nontreated cultures in subsequent trial fermentations. Salt ‘preconditioning’ of wine yeast seed cultures was also shown to alleviate stuck and sluggish fermentations at the winery scale, indicating potential benefits for industrial fermentation processes. It is hypothesized that salt induces specific osmostress response genes to enable yeast cells to better tolerate the rigours of fermentation, particularly in high sugar and alcohol concentrations

Implementing Science Theater

Since 2006, we were implementing a numerous of educational projects on teaching Science - i.e experiments with low-cost materials, developing and using online scenarios, integrating embodied outdoor activities in our physics lesson and engaging the whole school in Interdisciplinary Astronomy Activities. The most fruitful one, in terms of motivating students, was science theater. Science theater - by doing research on scientific topics, writing down the script, organising a play and communicating our efforts - highlights the need of more and systematic (inclusive) thematic learning throughout school topics. Here we will present our last effort, giving a glimpse of our way of work, putting together document theater, science theater and science fiction.

Byzantine and Ottoman Mineral Exploration and Smelting in Eastern Macedonia, Greece and their Implications for Regional Economies

The study outlined here is an investigation of mining and smelting evidence across eastern Macedonia in northern Greece particularly through the Byzantine (AD 324-1453) and Ottoman (AD 1453-1912) periods. Diverse evidence for mineral exploration and metallurgical extraction in the ancient and medieval past exists throughout this region bounded by the Strymon and Nestos river valleys. Through an integrated approach to survey, site characterization and scientific analysis of metallurgical debris it has been intended to approach issues of interrelatedness between subsistence and production sectors, and address questions relating to Byzantine economy and technological complexity. Documentary evidence from antiquity, late Byzantine Mount Athos charters and Ottoman cadastral registers refer to local, large-scale iron production in the region. Although at present there exists no clear understanding of the chronology for the various production sites, surveys and analytical studies carried out elsewhere have been proven enlightening towards that end. Further, the actual practices represented at these sites remains to be established. Although the mainstay of the metallurgical traditions seems to be iron metallurgy, analyses of slag from sites across Macedonia, particularly high arsenic concentrations, and the occurrence of speiss among the debris, suggested that precious metal extraction could have been an important but peripheral activity. This coupled with documentary evidence allows for the potential of eastern Macedonia to be a minor but significant source of precious metals in the Byzantine world. The current study focuses on the survey and sampling of four smelting sites in the region and scientific analysis by various instrumental techniques undertaken in view to characterizing the metallurgical processes represented in each case. The production sites are characterized by spatial and scalar variation reflecting distinct modes of organizing labour and fluctuations in specialization, intensity and time-length of operations. Analytical data provide an overview of the technical parameters which in turn represent human capacities and choices deeply rooted in social and cultural information. Eventually the dynamics of practice and technical choices for organizing seasonal smelting ventures are being perceived as identity forging incidents among the medieval rural communities of the region

Tighter αBB relaxations through a refi nement scheme for the scaled Gerschgorin theorem

Of central importance to the αBB algorithm is the calculation of the α values that guarantee the convexity of the underestimator. Improvement (reduction) of these values can result in tighter underestimators and thus increase the performance of the algorithm. For instance, it was shown by Wechsung et al. (J Glob Optim 58(3):429-438, 2014) that the emergence of the cluster effect can depend on the magnitude of the α values. Motivated by this, we present a refinement method that can improve (reduce) the magnitude of α values given by the scaled Gerschgorin method and thus create tighter convex underestimators for the αBB algorithm. We apply the new method and compare it with the scaled Gerschgorin on randomly generated interval symmetric matrices as well as interval Hessians taken from test functions. As a measure of comparison, we use the maximal separation distance between the original function and the underestimator. Based on the results obtained, we conclude that the proposed refinement method can significantly reduce the maximal separation distance when compared to the scaled Gerschgorin method. This approach therefore has the potential to improve the performance of the αBB algorithm

Optimization-based selection of hydrants and valves control in water distribution networks for fire incidents management

In England and Wales, water utilities reduce hydraulic pressure to a minimum regulatory threshold in order to reduce leakage and avoid financial penalties. However, utilities are not legally bound to guarantee specific flow rates from fire hydrants, thus posing a risk for firefighting. We formulate a biobjective mixed-integer nonlinear program (MINLP) to simultaneously determine control valve settings and the location of fire hydrants to be utilized in a water distribution network during urban fire incidents. The goal is to provide the required flow rate from the fire hydrants while minimizing 1) the distance of the utilized fire hydrants from the fire location and 2) the impact on customer supply. As the solution is required in real-time, we propose an optimization-based heuristic, which relies on iteratively solving a NLP approximation and relaxation of the MINLP formulation. Furthermore, we assess the quality of the heuristic solutions for the presented study case by calculating global optimality bounds. The proposed heuristic is applied to an operational water distribution network