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

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

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

The presence of Au and Ag in Pb-rich slags from Hellenistic Pistyros, N. Greece: some observations

Pistyros, in NE Greece, is a small fortified urban settlement founded by Thasians on the mainland in the 7th c. BCE; it displays, uniquely for the region, a considerable amount of well contextualized and dated (4th-3rd c. BCE) metallurgical waste (in excess of 1.2 tons); further, the Pb-based metallurgical waste displays presence of Au and Ag. In an area famous, both on historical and geological grounds, for its base (Cu, Pb, Fe) and precious (Au, Ag) metals deposits, there exists, still today, no good evidence for their routine extraction and processing and on a large scale. The questions that arise are related to what was urban Pistyros’ main function. Was it intent on making metals and which ones? Was it making only metals or metal derivatives (oxides or carbonates) as well? We have at this stage no definitive answers. In this paper we focus on the presentation of EPMA (Electron Probe Micro Analysis) results from three slag sample-types (silicate slag, iron arsenides, lead oxides). We examine the presence and distribution of Au and Ag within, and suggest that the two metals probably play a secondary role to the site’s main involvement, i.e. Pb-based metallurgy; be it for the production of antimonial lead and its ‘purification’ for the production of lead oxide and/or for the further processing of iron arsenides. Pistyros polymetallic metallurgical waste interpretation requires careful assessment of what it means to carry out high temperature metallurgical activities for the purpose of acquiring not just metals but possibly, also, metallic mineral derivatives within urban centers; such centers tend to be rare, nuanced, and certainly challenge us to look beyond the ‘precious metal-for-coinage’ axis we have been accustomed to

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

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

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

Assessment of flood hazard areas at a regional scale using an index-based approach and Analytical Hierarchy Process: Application in Rhodope–Evros region, Greece

AbstractThe present study introduces a multi-criteria index to assess flood hazard areas in a regional scale. Accordingly, a Flood Hazard Index (FHI) has been defined and a spatial analysis in a GIS environment has been applied for the estimation of its value.The developed methodology processes information of seven parameters namely flow accumulation, distance from the drainage network, elevation, land use, rainfall intensity and geology. The initials of these criteria gave the name to the developed method: “FIGUSED”. The relative importance of each parameter for the occurrence and severity of flood has been connected to weight values. These values are calculated following an “Analytical Hierarchy Process”, a method originally developed for the solution of Operational Research problems. According to their weight values, information of the different parameters is superimposed, resulting to flood hazard mapping. The accuracy of the method has been supported by a sensitivity analysis that examines a range for the weights' values and corresponding to alternative scenarios.The presented methodology has been applied to an area in north-eastern Greece, where recurring flood events have appeared. Initially FIGUSED method resulted to a Flood Hazard Index (FHI) and a corresponding flood map. A sensitivity analysis on the parameters' values revealed some interesting information on the relative importance of each criterion, presented and commented in the Discussion section. Moreover, the sensitivity analysis concluded to a revised index FHIS (methodology named FIGUSED-S) and flood mapping, supporting the robustness of FIGUSED methodology. A comparison of the outcome with records of historical flood events confirmed that the proposed methodology provides valid results