More Than 1700 Years of Word Equations

Geometry and Diophantine equations have been ever-present in mathematics. Diophantus of Alexandria was born in the 3rd century (as far as we know), but a systematic mathematical study of word equations began only in the 20th century. So, the title of the present article does not seem to be justified at all. However, a linear Diophantine equation can be viewed as a special case of a system of word equations over a unary alphabet, and, more importantly, a word equation can be viewed as a special case of a Diophantine equation. Hence, the problem WordEquations: "Is a given word equation solvable?" is intimately related to Hilbert's 10th problem on the solvability of Diophantine equations. This became clear to the Russian school of mathematics at the latest in the mid 1960s, after which a systematic study of that relation began. Here, we review some recent developments which led to an amazingly simple decision procedure for WordEquations, and to the description of the set of all solutions as an EDT0L language.Comment: The paper will appear as an invited address in the LNCS proceedings of CAI 2015, Stuttgart, Germany, September 1 - 4, 201

Government-Industry Cooperative Fisheries Research in the North Pacific under the MSFCMA

The National Marine Fisheries Service’s Alaska Fisheries Science Center (AFSC) has a long and successful history of conducting research in cooperation with the fishing industry. Many of the AFSC’s annual resource assessment surveys are carried out aboard chartered commercial vessels and the skill and experience of captains and crew are integral to the success of this work. Fishing companies have been contracted to provide vessels and expertise for many different types of research, including testing and evaluation of survey and commercial fishing gear and development of improved methods for estimating commercial catch quantity and composition. AFSC scientists have also participated in a number of industry-initiated research projects including development of selective fishing gears for bycatch reduction and evaluating and improving observer catch composition sampling. In this paper, we describe the legal and regulatory provisions for these types of cooperative work and present examples to illustrate the process and identify the requirements for successful cooperative research

Generalized Fock spaces and the Stirling numbers

The Bargmann-Fock-Segal space plays an important role in mathematical physics, and has been extended into a number of directions. In the present paper we imbed this space into a Gelfand triple. The spaces forming the Fr\'echet part (i.e. the space of test functions) of the triple are characterized both in a geometric way and in terms of the adjoint of multiplication by the complex variable, using the Stirling numbers of the second kind. The dual of the space of test functions has a topological algebra structure, of the kind introduced and studied by the first named author and G. Salomon.Comment: revised versio

Recombinant luminescent bacteria for measuring bioavailable arsenite and antimonite

Luminescent bacterial strains for the measurement of bioavailable arsenite and antimony were constructed, The expression of firefly luciferase was controlled by the regulatory unit of the ars operon of Staphylococcus aureus plasmid pI258 in recombinant plasmid pT0021, with S. aureus RN4220, Bacillus subtilis BR151, and Escherichia coli MC1061 as host strains, Strain RN4220(pT0021) was found to be the most sensitive for metal detection responding to arsenite, antimonite, and cadmium, the lowest detectable concentrations being 100, 33, and 330 nhl, respectively, Strains BR151(pT0021) and MC1061(pT0021) responded to arsenite, arsenate, antimonite, and cadmium, the lowest detectable concentrations being 3.3 and 330 mu M and 330 and 330 nM with BR151(pT0021), respectively, and 3.3, 33, 3.3, and 33 CIM with MC1061(pT0021), respectively, In the absence of the mentioned ions, the expression of luciferase was repressed and only a small amount of background light was emitted, Other ions did not notably interfere with the measurement in any of the strains tested, Freeze-drying of the cells did not decrease the sensitivity of the detection of arsenite; however, the induction coefficients were somewhat lower

Luminescent bacterial sensor for cadmium and lead

A sensor plasmid was constructed by inserting the regulation unit from the cadA determinant of plasmid pI258 to control the expression of firefly luciferase. The resulting sensor plasmid pTOO24 is capable of replicating in Gram-positive and Gram-negative bacteria. The expression of the reporter gene as a function of added extracellular heavy metals was studied in Staphylococcus aureus strain RN4220 and Bacillus subtilis strain BR151. Strain RN4220(pTOO24) mainly responded to cadmium, lead and antimony, the lowest detectable concentrations being 10 nM, 33 nM and 1 nM respectively. Strain BR151(pTOO24) responded to cadmium, antimony, zinc and tin at concentrations starting from 3.3 nM, 33 nM, 1 mu M and 100 mu M, respectively. The luminescence ratios between induced and uninduced cells, the induction coefficients, of strains RN4220(pTOO24) and BR151(pTOO24) were 23-50 and about 5, respectively. These results were obtained with only 2-3 h incubation times. Freeze-drying of the sensor strains had only moderate effects on the performance with respect to sensitivity or induction coefficients. (C) 1998 Elsevier Science S.A. All rights reserved

Genetic Algorithm with Optimal Recombination for the Asymmetric Travelling Salesman Problem

We propose a new genetic algorithm with optimal recombination for the asymmetric instances of travelling salesman problem. The algorithm incorporates several new features that contribute to its effectiveness: (i) Optimal recombination problem is solved within crossover operator. (ii) A new mutation operator performs a random jump within 3-opt or 4-opt neighborhood. (iii) Greedy constructive heuristic of W.Zhang and 3-opt local search heuristic are used to generate the initial population. A computational experiment on TSPLIB instances shows that the proposed algorithm yields competitive results to other well-known memetic algorithms for asymmetric travelling salesman problem.Comment: Proc. of The 11th International Conference on Large-Scale Scientific Computations (LSSC-17), June 5 - 9, 2017, Sozopol, Bulgari

Fast Searching in Packed Strings

Given strings $P$ and $Q$ the (exact) string matching problem is to find all positions of substrings in $Q$ matching $P$. The classical Knuth-Morris-Pratt algorithm [SIAM J. Comput., 1977] solves the string matching problem in linear time which is optimal if we can only read one character at the time. However, most strings are stored in a computer in a packed representation with several characters in a single word, giving us the opportunity to read multiple characters simultaneously. In this paper we study the worst-case complexity of string matching on strings given in packed representation. Let $m \leq n$ be the lengths $P$ and $Q$, respectively, and let $\sigma$ denote the size of the alphabet. On a standard unit-cost word-RAM with logarithmic word size we present an algorithm using time O\left(\frac{n}{\log_\sigma n} + m + \occ\right). Here \occ is the number of occurrences of $P$ in $Q$. For $m = o(n)$ this improves the $O(n)$ bound of the Knuth-Morris-Pratt algorithm. Furthermore, if $m = O(n/\log_\sigma n)$ our algorithm is optimal since any algorithm must spend at least \Omega(\frac{(n+m)\log \sigma}{\log n} + \occ) = \Omega(\frac{n}{\log_\sigma n} + \occ) time to read the input and report all occurrences. The result is obtained by a novel automaton construction based on the Knuth-Morris-Pratt algorithm combined with a new compact representation of subautomata allowing an optimal tabulation-based simulation.Comment: To appear in Journal of Discrete Algorithms. Special Issue on CPM 200

Determining the Solution Space of Vertex-Cover by Interactions and Backbones

To solve the combinatorial optimization problems especially the minimal Vertex-cover problem with high efficiency, is a significant task in theoretical computer science and many other subjects. Aiming at detecting the solution space of Vertex-cover, a new structure named interaction between nodes is defined and discovered for random graph, which results in the emergence of the frustration and long-range correlation phenomenon. Based on the backbones and interactions with a node adding process, we propose an Interaction and Backbone Evolution Algorithm to achieve the reduced solution graph, which has a direct correspondence to the solution space of Vertex-cover. By this algorithm, the whole solution space can be obtained strictly when there is no leaf-removal core on the graph and the odd cycles of unfrozen nodes bring great obstacles to its efficiency. Besides, this algorithm possesses favorable exactness and has good performance on random instances even with high average degrees. The interaction with the algorithm provides a new viewpoint to solve Vertex-cover, which will have a wide range of applications to different types of graphs, better usage of which can lower the computational complexity for solving Vertex-cover

Spectral backscattering properties of marine phytoplankton cultures

The backscattering properties of marine phytoplankton, which are assumed to vary widely with differences in size, shape, morphology and internal structure, have been directly measured in the laboratory on a very limited basis. This work presents results from laboratory analysis of the backscattering properties of thirteen phytoplankton species from five major taxa. Optical measurements include portions of the volume scattering function (VSF) and the absorption and attenuation coefficients at nine wavelengths. The VSF was used to obtain the backscattering coefficient for each species, and we focus on intra- and interspecific variability in spectral backscattering in this work. Ancillary measurements included chlorophyll-a concentration, cell concentration, and cell size, shape and morphology via microscopy for each culture. We found that the spectral backscattering properties of phytoplankton deviate from theory at wavelengths where pigment absorption is significant. We were unable to detect an effect of cell size on the spectral shape of backscattering, but we did find a relationship between cell size and both the backscattering ratio and backscattering crosssection. While particulate backscattering at 555 nm was well correlated to chlorophyll-a concentration for any given species, the relationship was highly variable between species. Results from this work indicate that phytoplankton cells may backscatter light at significantly higher efficiencies than what is predicted by Mie theory, which has important implications for closing the underwater and remotely sensed light budget