Springer

We study the problem of manipulation in voting and extend the individual manipulability results in Favardin and Lepelley for the case of multiple choice, impartial culture, and consider 3, 4, and, for some cases, 5 alternatives. For impartial culture, the results in general are similar to impartial anonymous culture case. For multiple choice and 3 alternatives, results are consistent only for some extension axioms, but for Leximax extension, the Hare and Inverse Borda's rules are among the least manipulable ones. For considered cases for 4 and 5 alternatives, Borda's rule is the least manipulable one for manipulability with reactions (Type IV in Favardin and Lepelley classification).

The applicability of the data on the mean age of death (MAD) of people presented on Wikipedia to determine the survival patterns with respect to professional occupations is considered. The results of previous studies are described. Features of these data related to censorship and the selective nature of their collection are discussed. The proposed approach to account for these features makes it possible to clarify the obtained patterns and to expand the time range of the study.

The phenomenon of multiphasic survival curves found in drosophila is confirmed in experiments on daphnids. Mathematical modeling showed that the multiphasic nature of daphnids survival curves reflected abrupt changes in the death rate of objects during phase transition. The phase of a sharp increase in mortality observed at an early age in intact drosophila occurs in daphnids only as reaction to a negative impact. The induction of reactive changes by weak external signals resulted in decreased survival for young daphnids. A logical conclusion was made about the reaction readiness for each experimental individual. It is proven that the predisposition to reaction in daphnia persists for an indefinitely large number of generations. It is postulated that this reaction has an epigenetic nature. Earlier experimental materials suggest that a reaction of this type is widespread in natural surroundings.

We consider the nonparametric estimation of the extremal index of stochastic processes. The discrepancy method that was proposed by the author as a data-driven smoothing tool for probability density function estimation is extended to find a threshold parameter u for an extremal index estimator in case of heavy-tailed distributions. To this end, the discrepancy statistics are based on the von Mises– Smirnov statistic and the k largest order statistics instead of an entire sample. The asymptotic chi-squared distribution of the discrepancy measure is derived. Its quan8 tiles may be used as discrepancy values. An algorithm to select u for an estimator of the extremal index is proposed. The accuracy of the discrepancy method is checked by a simulation study.

Usually, DEA methods are used for the assessment of a region’s disaster vulnerability. However, most of these methods work with precise values of all the characteristics of the regions. At the same time, in real life, quite often most of the data consists of expert estimates or approximate values. In this regard, we propose to use modified DEA methods, which will take into account inaccuracy of the data. We apply these methods to the evaluation of wildfire preventive measures in the Russian Federation regions.

Рассматривается управляемая система массового обслуживания, в которой число рабочих каналов обслуживания может изменяться в моменты контроля, отстоящие друг от друга на фиксированный временной шаг. При переходе от шага к шагу интенсивность простейшего входящего потока изменяется в соответствии с некоторой марковской цепью. Считается, что в интервале между шагами в системе устанавливается стационарный режим. В качестве целевой функции используется минимизация суммарных средних затрат на многошаговом периоде планирования. Строится стратегия переключения каналов. Выявлена параметрическая структура оптимальной стратегии, что существенно упрощает ее построение.

The paper is devoted to the statistical analysis of the end- to-end (E2E) delay of packet transfers between source and destination nodes in a peer-to-peer (P2P) overlay network. We focus on the iden- tication of the E2E delay and the longest per-hop delay distributions and the stochastic dependence of the associated random process. The E2E delay is determined by the sum of a random number of dependent per-hop (p-h) delays along the links of a considered overlay path and the longest per-hop delay by their maximum. We propose to use the sum of the p-h delays to get a distribution of the maximum which is motivated by the available statistical data of the E2E delays. Based on recent ana- lytic results derived from extreme-value theory we show that such sums and maxima corresponding to different paths may have the same tail and extremal indexes. These indexes determine the heaviness of the dis- tribution tail and the dependence of extremes. Using the extremal index we identify limit distributions of the maxima of the E2E delays and the maxima of the p-h delays at a path among all source-destination paths. Considering real-time applications with stringent E2E-delay constraints, the distributions are used to identify quality-of-service (QoS) metrics of a P2P model like the packet missing probability and the corresponding playback delay as well as the equivalent capacity of a transport channel.

The paper is devoted to the effective information spreading in random complex networks. Our objective is to elect leader nodes or communities of the network, which may spread the content among all nodes faster. We consider a well-known SPREAD algorithm by Mosk- Aoyama and Shah (2006), which provides the spreading and the growth of the node set possessing the information. Assuming that all nodes have asynchronous clocks, the next node is chosen uniformly among nodes of the network by the global clock tick according to a Poisson process. The extremal index measures the clustering tendency of high threshold exceedances. The node extremal index shows the ability to attract highly ranked nodes in the node orbit. Considering a closeness centrality as a measure of a node’s leadership, we find the relation between its extremal index and the minimal spreading time.

We consider the nonparametric estimation of the extremal index of stochastic processes. The discrepancy method that was proposed by the author as a data-driven smoothing tool for probability density function estimation is extended to find a threshold parameter u for an extremal index estimator in case of heavy-tailed distributions. To this end, the discrepancy statistics are based on the von Mises–Smirnov statistic and the k largest order statistics instead of an entire sample. The asymptotic chi-squared distribution of the discrepancy measure is derived. Its quantiles may be used as discrepancy values. An algorithm to select u for an estimator of the extremal index is proposed. The accuracy of the discrepancy method is checked by a simulation study.

We study non-stationary random length sequences of random variables with regularly varying tails. Tail and extremal indexes of their maxima and linear combinations are found. We obtain conditions when both sums and maxima of these sequences have the same tail and extremal indexes. Their extremal index corresponds to the tail index of the most heavy-tailed random variable in the sequence.