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

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

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

Сравнение сорбционной способности активированных углей, цеолитов и промышленных образцов оксида алюминия по отношению к оксиду азота(II) в воздухе

This investigation studied the sorption of NO by activated carbons, zeolites and aluminum oxide at ambient temperature. It was found that γ-Al2O3 has the highest sorption capacity (45-50%). Among the studied activated carbons only AG-3 sample proved to be competitive with samples of γ-Al2O3. The NO sorption degree of the studied zeolites was less than 7%.В динамическом режиме изучена сорбция оксида азота (II) из воздуха активированными углями, цеолитами и образцами оксида алюминия. Установлено, что максимальную скорость сорбции NO (степень поглощения 45-50%) обеспечивают различные образцы γ-оксида алюминия. Из исследованных активированных углей только образец марки АГ-3 оказался конкурентоспособным с образцами γ-Al2O3. Изученные цеолиты обеспечивают степень поглощения NO не более 7%

О МЕХАНИЗМАХ ФОРМИРОВАНИЯ КАТАЛИТИЧЕСКИ АКТИВНЫХ В ОКИСЛЕНИИ ОЛЕФИНОВ КАТИОННЫХ КОМПЛЕКСОВ Pd(II) В СРЕДЕ ВОДА-АЦЕТОНИТРИЛ-ХЛОРНАЯ КИСЛОТА

The catalytic system Pd (OAc)2-HClO4--CH3CN (AN)-H2O of olefins oxidation was studied. Information about the ways of forming catalytic active cationic palladium complexes was detected. Analysis of the electron spectroscopy data shows the probability of existence complexes [Pd(AN)(H2O)3]2+ (λmax = 360-365 nm), [Pd(AN)2(H2O)2]2+ (λmax = 335-345 nm) in catalytic system. The preparation method of stable and sufficient active catalytic system for obtaining reproducible kinetic data was designed.В результате исследования системы Pd(OAc)2-HClO4-CH3CN (АN)-H2O, проявляющей каталитическую активность в реакции окисления олефинов, получена информация о путях формирования каталитически активных катионных комплексов палладия. Методом электронной спектроскопии показано, что с большой вероятностью в системе существуют комплексы состава [Pd(AN)(H2O)3]2 (λmax = 360-365 нм), [Pd(AN)2(H2O)2]2+ (λmax = 335-345 нм). Предложена методика приготовления стабильной и достаточно активной исходной каталитической системы для получения воспроизводимых кинетических данных

Влияние состава бинарного растворителя CH3CN-H2O на кинетику окисления циклогексена п-бензохиноном в растворах катионных комплексов палладия(II)

During the study of cyclohexene oxidation by p-benzoquinones into cyclohexanone in water-organic solutions of cationic complexes of palladium(II) it was demonstrated that the initial reaction rate R0 depends complicatedly on water molar fraction for three studied solvents: acetonitrile (AN), dimethylformamide, and dimethylsulfoxide. In order to explain the obtained bimodal dependence for the example of AN-water system, modeling of phase equilibrium in the studied system was performed. The existence of two- and three-phase immiscibility areas as well as a three-component heteroazeotrope was found. By UV spectroscopy it was stated that varying of water molar fraction in the binary solvent substantially changes the state of starting cationic complexes [Pd(АН)x(H2O)4-x]2+. For mathematical description of medium effect on R0 value three models were proposed taking into account different factors, such as: a) physico-chemical properties of binary solvent; b) composition of possible associates AN-water; c) composition of starting [Pd(АН)x(H2O)4-x]2+ complexes. The adequate description of bimodal dependency was obtained in the model considering the changes of [Pd(АН)x(H2O)4-x]2+ complexes composition with simultaneous presence of an associate of (АН)2(H2O) composition.В ходе изучения кинетики окисления циклогексена п-бензохиноном до циклогексанона в водно-органических растворах катионных комплексов палладия(II) показано, что начальная скорость реакции R0 сложным образом зависит от мольной доли воды для трех изученных растворителей: ацетонитрил (АН), диметилформамид и диметилсульфоксид. На примере системы ацетонитрил-вода проведено моделирование фазовых равновесий в исследуемой системе, позволившее выявить наличие областей двух- и трехфазного расслаивания, а также трехкомпонентного гетероазеотропа. Методом УФ-спектроскопии установлено, что изменение мольной доли воды в бинарном растворителе существенно меняет состояние исходных катионных комплексов [Pd(АН)x(H2O)4-x]2+. Для математического описания эффектов влияния среды на величину R0 предложены три модели, учитывающие такие факторы, как: а) физико-химические свойства бинарного растворителя, б) состав возможных ассоциатов ацетонитрил-вода, в) состав исходных комплексов Pd(II). Адекватное описание бимодальной зависимости получено в рамках модели, рассматривающей изменение состава комплексов [Pd(АН)x(H2O)4-x]2+ с одновременным присутствием ассоциата состава (АН)2(H2O)

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.

Окисление монооксида углерода кислородом в водно-ацетонитрильных растворах бромидных комплексов палладия(II) в присутствии фталоцианинатов Со(II), Fe(II) и Mn(III)

Objectives. The objective of this paper was to compare acetylene oxidative dicarbonylation that leads to maleic anhydride with a side reaction of CO oxidation by oxygen in a PdBr2-LiBr-H2C-CH3CN system and in the presence of insoluble (Co) and soluble (Co, Fe, and Mn) phthalocyaninates (PcM).Methods. To study the oxidation of CO to CO2, a kinetics method was used; UV and IR spectroscopy was used to determine the concentrations of initial and intermediate compounds.Results. The knetics of CO to CO2 oxidation were investigated and the reactivity series of PcM in CO oxidation and maleic anhydride synthesis was characterized. A satisfactory correlation was observed between reaction rates and PcM concentration, as well as the nature of metal, in both processes. The IR measurements of concentrations of Pd(II) and Pd(I) intermediate carbonyl complexes, and CO2 concentrations, have made it possible to hypothesize the mechanism of CO2 generation. The effect of PcM concentration on the concentrations of Pd(II)(CO) in CO oxidation has been shown.Conclusions. Based on the data regarding CO oxidation and acetylene oxidative dicarbonylation, certain conditions have been proposed to effectively produce double-labeled maleic anhydride with 13C (from 13CO).Цели. Сравнение результатов изучения процесса окислительного дикарбонилирования ацетилена до малеинового ангидрида (МА) с закономерностями побочной реакции окисления СО кислородом в системе PdBr2–LiBr–Н2О–ацетонитрил в присутствии нерастворимых (Со) и растворимых (Co, Fe и Mn) фталоцианинатов (РсМ).Методы. Использованы кинетический метод для изучения реакции окисления СО до СО2 и УФ- и ИК-спектроскопия для контроля за концентрациями исходных и промежуточных соединений.Результаты. Изучена кинетика образования CO2. Установлены ряды активности РсМ в реакции окисления СО и получения МА и показана удовлетворительная корреляция характера зависимостей скоростей RCO2 и RMA от [PcM] и от природы металла в обоих процессах. По результатам измерения концентраций промежуточных карбонильных комплексов Pd(II) и Pd(I) и концентраций СО2 в ходе процесса м.етодом ИК-спектроскопии предложены гипотезы о механизме образования СО2, а также установлено влияние [PcM] на концентрацию [PdII](CO) в стационарных условиях в ходе каталитического процесса окисления СО.Заключение. По результатам изучения модельной реакции окисления СО и закономерностей окислительного дикарбонилирования ацетилена предложены рекомендации по условиям эффективного процесса получения дваждыы13С-меченного малеинового ангидрида (из 13СО)