On the Necessary Memory to Compute the Plurality in Multi-Agent Systems

We consider the Relative-Majority Problem (also known as Plurality), in which, given a multi-agent system where each agent is initially provided an input value out of a set of $k$ possible ones, each agent is required to eventually compute the input value with the highest frequency in the initial configuration. We consider the problem in the general Population Protocols model in which, given an underlying undirected connected graph whose nodes represent the agents, edges are selected by a globally fair scheduler. The state complexity that is required for solving the Plurality Problem (i.e., the minimum number of memory states that each agent needs to have in order to solve the problem), has been a long-standing open problem. The best protocol so far for the general multi-valued case requires polynomial memory: Salehkaleybar et al. (2015) devised a protocol that solves the problem by employing $O(k 2^k)$ states per agent, and they conjectured their upper bound to be optimal. On the other hand, under the strong assumption that agents initially agree on a total ordering of the initial input values, Gasieniec et al. (2017), provided an elegant logarithmic-memory plurality protocol. In this work, we refute Salehkaleybar et al.'s conjecture, by providing a plurality protocol which employs $O(k^{11})$ states per agent. Central to our result is an ordering protocol which allows to leverage on the plurality protocol by Gasieniec et al., of independent interest. We also provide a $\Omega(k^2)$-state lower bound on the necessary memory to solve the problem, proving that the Plurality Problem cannot be solved within the mere memory necessary to encode the output.Comment: 14 pages, accepted at CIAC 201

Flux networks in metabolic graphs

A metabolic model can be represented as bipartite graph comprising linked reaction and metabolite nodes. Here it is shown how a network of conserved fluxes can be assigned to the edges of such a graph by combining the reaction fluxes with a conserved metabolite property such as molecular weight. A similar flux network can be constructed by combining the primal and dual solutions to the linear programming problem that typically arises in constraint-based modelling. Such constructions may help with the visualisation of flux distributions in complex metabolic networks. The analysis also explains the strong correlation observed between metabolite shadow prices (the dual linear programming variables) and conserved metabolite properties. The methods were applied to recent metabolic models for Escherichia coli, Saccharomyces cerevisiae, and Methanosarcina barkeri. Detailed results are reported for E. coli; similar results were found for the other organisms.Comment: 9 pages, 4 figures, RevTeX 4.0, supplementary data available (excel

Why Global Inequality Matters: Derivative Global Egalitarianism

This article integrates empirical and normative discussions about why global economic inequalities matter in critically examining an approach known as derivative global egalitarianism (DGE). DGE is a burgeoning perspective that opposes excessive global economic inequality not based on the intrinsic value of equality but inequality\u27s negative repercussions on other values. The article aims to advance the research agenda by identifying and critically evaluating four primary varieties of DGE arguments from related but distinct literatures, which span a number of disciplines, including economics, international relations, and political philosophy. Overall, DGE offers a number of persuasive arguments as to why current levels of global inequality are of concern, but aspects of DGE beg further philosophical and empirical examination. By situating DGE within the wider theoretical and empirical contexts, this article provides resources for its critical assessment and theoretical development

Asymptotology of Chemical Reaction Networks

The concept of the limiting step is extended to the asymptotology of multiscale reaction networks. Complete theory for linear networks with well separated reaction rate constants is developed. We present algorithms for explicit approximations of eigenvalues and eigenvectors of kinetic matrix. Accuracy of estimates is proven. Performance of the algorithms is demonstrated on simple examples. Application of algorithms to nonlinear systems is discussed.Comment: 23 pages, 8 figures, 84 refs, Corrected Journal Versio

Неэмпирические расчеты минимальных энергетических путей реакций присоединения молекул H2F2 и H2Cl2 к молекулам ацетилена и метилацетилена

Surfaces of potential energy of gas phase addition reactions of H2F2 and H2Cl2 molecules to acetylene and methyl acetylene molecules were examined. An ab initio calculation of H2F2 and H2Cl2 molecules was carried out. A non-empirical Hartree-Fock-Roothaan method, 6-31 ++G** basis, taking into account electronic correlation in MP2 approximation (Møller-Plesset 2nd order) and Gaussian–03 software were used. Reaction heats and activation energies were calculated. It was established that addition of H2F2 and H2Cl2 molecules to a methyl acetylene molecule according to Markovnikov’s rule with the formation of 2-fluoropropene and HF and 2-chloropropene and HCl respectively is more advantageous both kinetically and thermodynamically.Исследованы поверхности потенциальной энергии газофазных реакций присоединения молекул H2 F2 и H2 Cl2 к молекулам ацетилена и метилацетилена. Проведен ab initio расчет молекул H2 F2 и H2 Cl2.. Использованы неэмпирический метод Хартри-Фока-Рутана, базис 6-31++ G ** с учетом электронной корреляции в приближении МП2 (Меллера-Плессета 2-го порядка), программа Gaussian -03. Рассчитаны теплоты и энергии активации реакций. Установлено, что как кинетически, так и термодинамически более выгодно присоединение молекул H2 F2 и H2 Cl2 к молекуле метилацетилена по правилу Марковникова с образованием 2-фторпропена и HF и соответственно 2-хлорпропена и HCl

Новая колебательная реакция - окислительное карбонилирование фенилацетилена в ангидрид фенилмалеиновой кислоты.

In area of the catalytic reactions with metal complexes new oscillatory process - reaction of phenylacetylene oxidative carbonylation to anhydride of phenylmaleic acid in the system LiBr-PdBr2-CO-O2-(CH3)2CO is found. Independence of a oscillations mode of a gases mixture composition is shown at the percentage of CO no more than 50 %. The preliminary mechanism of process was proposed.области реакций метало-комплексного катализа обнаружен новый колебательный процесс - реакция окислительного карбонилирования фенилацетилена до ангидрида фенилмалеиновой кислоты в системе LiBr-PdBr2-CO-O2-(CH3)2CO; экспериментально показана независимость режима колебаний от состава газовой смеси при содержании СО в ней не более 50%; предложен предварительный механизм процесса

Babes, bones, and isotopes: a stable isotope investigation on non-adults from Aventicum, Roman Switzerland (1st-3rd c. CE)

The study of infant feeding practices in archaeological populations can aid in the understanding of cultural attitudes towards dietary choices and how specific circumstances experienced by mothers and their offspring influence childhood health and survivorship. Breastfeeding and weaning patterns have received increased interest in Roman bioarchaeology, especially through the application of stable isotopic investigation of nitrogen (δ15N) and carbon (δ13C) values. This study presents the stable isotopic results of the first Roman bone sample analyzed from Switzerland (30 non-adults and 9 females), allowing us an unprecedented insight into health and diet at the site of Aventicum/Avenches, the capital city of the territory of Helvetii in Roman times (1st-3rd c. AD). The fact that the majority of the non-adult samples subject to stable isotope analysis were perinates, highlights the complex relationship between their δ15N and δ13C values and those of adult females, as different factors, including variation of fetal and maternal stable isotope values, the possible effects of intrauterine growth, as well as maternal/fetal disease and/or nutritional stress (e.g. nutritional deficiencies such as scurvy, parasitic infections, such as malaria), could have influenced the observed elevated δ15N values

The dynamical Green's function and an exact optical potential for electron-molecule scattering including nuclear dynamics

We derive a rigorous optical potential for electron-molecule scattering including the effects of nuclear dynamics by extending the common many-body Green's function approach to optical potentials beyond the fixed-nuclei limit for molecular targets. Our formalism treats the projectile electron and the nuclear motion of the target molecule on the same footing whereby the dynamical optical potential rigorously accounts for the complex many-body nature of the scattering target. One central result of the present work is that the common fixed-nuclei optical potential is a valid adiabatic approximation to the dynamical optical potential even when projectile and nuclear motion are (nonadiabatically) coupled as long as the scattering energy is well below the electronic excitation thresholds of the target. For extremely low projectile velocities, however, when the cross sections are most sensitive to the scattering potential, we expect the influences of the nuclear dynamics on the optical potential to become relevant. For these cases, a systematic way to improve the adiabatic approximation to the dynamical optical potential is presented that yields non-local operators with respect to the nuclear coordinates.Comment: 22 pages, no figures, accepted for publ., Phys. Rev.