The model of population protocols refers to the growing in popularity theoretical framework suitable for studying pairwise interactions within a large collection of simple indistinguishable entities, frequently called agents. In this paper the emphasis is on the space complexity in fast leader election via population protocols governed by the random scheduler, which uniformly at random selects pairwise interactions from the population of n agents.The main result of this paper is a new fast and space optimal leader election protocol. The new protocol operates in parallel time O(log 2 n) equivalent to O(n log 2 n) sequential pairwise interactions, in which each agent utilises O(log log n) states. This double logarithmic space utilisation matches asymptotically the lower bound 1 2 log log n on the number of states utilised by agents in any leader election algorithm with the running time o( n polylog n ), see [7]. Our solution relies on the concept of phase clocks, a fundamental synchronisation and coordination tool in the field of Distributed Computing. We propose a new fast and robust population protocol for initialisation of phase clocks to be run simultaneously in multiple modes and intertwined with the leader election process. We also provide the reader with the relevant formal argumentation indicating that our solution is always correct and fast with high probability.
Metabolic disorders occurring in menopause, including dyslipidemia, disorders of carbohydrate metabolism (impaired glucose tolerance – IGT, type 2 diabetes mellitus – T2DM) or components of metabolic syndrome, constitute risk factors for cardiovascular disease in women. A key role could be played here by hyperinsulinemia, insulin resistance and visceral obesity, all contributing to dyslipidemia, oxidative stress, inflammation, alter coagulation and atherosclerosis observed during the menopausal period. Undiagnosed and untreated, metabolic disorders may adversely affect the length and quality of women's life. Prevention and treatment preceded by early diagnosis should be the main goal for the physicians involved in menopausal care. This article represents a short review of the current knowledge concerning metabolic disorders (e.g. obesity, polycystic ovary syndrome or thyroid diseases) in menopause, including the role of a tailored menopausal hormone therapy (HT). According to current data, HT is not recommend as a preventive strategy for metabolic disorders in menopause. Nevertheless, as part of a comprehensive strategy to prevent chronic diseases after menopause, menopausal hormone therapy, particularly estrogen therapy may be considered (after balancing benefits/risks and excluding women with absolute contraindications to this therapy). Life-style modifications, with moderate physical activity and healthy diet at the forefront, should be still the first choice recommendation for all patients with menopausal metabolic abnormalities.
The model of population protocols refers to a large collection of simple indistinguishable entities, frequently called agents. The agents communicate and perform computation through pairwise interactions. We study fast and space efficient leader election in population of cardinality n governed by a random scheduler, where during each time step the scheduler uniformly at random selects for interaction exactly one pair of agents.We propose the first o(log 2 n)-time leader election protocol. Our solution operates in expected parallel time O(log n log log n) which is equivalent to O(n log n log log n) pairwise interactions. This is the fastest currently known leader election algorithm in which each agent utilises asymptotically optimal number of O(log log n) states. The new protocol incorporates and amalgamates successfully the power of assorted synthetic coins with variable rate phase clocks.
The Signal-to-Interference-and-Noise-Ratio model (SINR) is currently the most popular model for analyzing communication in wireless networks. Roughly speaking, it allows receiving a message if the strength of the signal carrying the message dominates over the combined strength of the remaining signals and the background noise at the receiver. There is a large volume of analysis done under the SINR model in the centralized setting, when both network topology and communication tasks are provided as a part of the common input, but surprisingly not much is known in the ad hoc setting, when nodes have very limited knowledge about the network topology. In particular, there is no theoretical study of deterministic solutions to multi-hop communication tasks, i.e., tasks in which packets often have to be relayed in order to reach their destinations. These kinds of problems, including broadcasting, routing, group communication, leader election, and many others, are important from perspective of development of future multi-hop wireless and mobile technologies, such as MANET, VANET, Internet of Things.In this paper we initiate a study of distributed deterministic broadcasting in ad-hoc wireless networks with uniform transmission powers under the SINR model. We design algorithms in two settings: with and without local knowledge about immediate neighborhood. In the former setting, our solution has almost optimal O(D log 2 n) time cost, where n is the size of a network, D is the eccentricity of the network and {1, . . . , N } is the set of possible node IDs. In the latter case, we prove an Ω(n log N ) lower bound and develop an algorithm matching this formula, where n is the number of network nodes. As one of the conclusions, we derive that the inherited cost of broadcasting techniques in wireless networks is much smaller, by factor around min{n/D, ∆}, than the cost of learning the immediate neighborhood. Finally, we develop a O(D∆ log 2 N ) algorithm for the setting without local knowledge, where ∆ is the upper bound on the degree of the communication graph of a network. This algorithm is close to a lower bound Ω(D∆).In the model without local knowledge, we take advantage of the fact that efficient deterministic distributed communication is possible (in the SINR model) between stations which are very close, despite large amount of interferences caused by other transmitters. This feature somehow compensates inconveniences caused by distant interferences and makes it possible to obtain a broadcasting algorithm with efficiency similar to that obtained for UDG radio networks. However, unlike in the UDG radio networks model, the (lower) bounds apply also for randomized solutions. In other words, randomization does not substantially help in ad hoc distributed broadcasting in a large class of networks.Recent development of deterministic protocols for wireless communication, e.g., CDMA-based technologies, and rapidly growing scale of ad hoc wireless networks, poses new challenges for design of efficient deterministic distributed proto...
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