How Long It Takes for an Ordinary Node with an Ordinary ID to Output?

In the context of distributed synchronous computing, processors perform in rounds, and the time-complexity of a distributed algorithm is classically defined as the number of rounds before all computing nodes have output. Hence, this complexity measure captures the running time of the slowest node(s). In this paper, we are interested in the running time of the ordinary nodes, to be compared with the running time of the slowest nodes. The node-averaged time-complexity of a distributed algorithm on a given instance is defined as the average, taken over every node of the instance, of the number of rounds before that node output. We compare the node-averaged time-complexity with the classical one in the standard LOCAL model for distributed network computing. We show that there can be an exponential gap between the node-averaged time-complexity and the classical time-complexity, as witnessed by, e.g., leader election. Our first main result is a positive one, stating that, in fact, the two time-complexities behave the same for a large class of problems on very sparse graphs. In particular, we show that, for LCL problems on cycles, the node-averaged time complexity is of the same order of magnitude as the slowest node time-complexity. In addition, in the LOCAL model, the time-complexity is computed as a worst case over all possible identity assignments to the nodes of the network. In this paper, we also investigate the ID-averaged time-complexity, when the number of rounds is averaged over all possible identity assignments. Our second main result is that the ID-averaged time-complexity is essentially the same as the expected time-complexity of randomized algorithms (where the expectation is taken over all possible random bits used by the nodes, and the number of rounds is measured for the worst-case identity assignment). Finally, we study the node-averaged ID-averaged time-complexity.Comment: (Submitted) Journal versio

Anticholinesterase activity of endemic plant extracts from Soqotra

A total of 30 chloroform and methanol extracts from the following endemic Soqotran plants Acridocarpus socotranus Olive, Boswellia socotranao Balf.fil, Boswellia elongata Balf. fil., Caralluma socotrana N. Br, Cephalocroton socotranus Balf.f, Croton socotranus Balf. fil.., Dendrosicycos socotrana Balf.f., Dorstenia gigas Schweinf. ex Balf. fil., Eureiandra balfourii Cogn. & Balf. fil., Kalanchoe farinaceae Balf.f, Limonium sokotranum (Vierh) Radcl. Sm), Oldenlandia pulvinata, Pulicaria diversifolia( Balf. and Pulicaria stephanocarpa Balf. were screened for their acetylcholinesterase inhibitory activity by using in vitro Ellman method at 50 and 200 μg/ml concentrations. Chloroform extracts of Croton socotranus, Boswellia socotrana, Dorstenia gigas, and Pulicaria stephanocarpa as well as methanol extracts of Eureiandra balfourii exhibited inhibitory activities higher than 50 % at concentration of 200 μg. At a concentrations of 50 μg, the chloroform extract of Croton socotranus exhibited an inhibition of 40.6 %.Key words: plant extracts, acetylcholinesterase inhibitors, Soqotra, Alzheimer’s diseas

Five-dimensional AGT Conjecture and the Deformed Virasoro Algebra

We study an analog of the AGT relation in five dimensions. We conjecture that the instanton partition function of 5D N=1 pure SU(2) gauge theory coincides with the inner product of the Gaiotto-like state in the deformed Virasoro algebra. In four dimensional case, a relation between the Gaiotto construction and the theory of Braverman and Etingof is also discussed.Comment: 12 pages, reference added, minor corrections (typos, notation changes, etc

A 5d/3d duality from relativistic integrable system

We propose and prove a new exact duality between the F-terms of supersymmetric gauge theories in five and three dimensions with adjoint matter fields. The theories are compactified on a circle and are subject to the Omega deformation. In the limit proposed by Nekrasov and Shatashvili, the supersymmetric vacua become isolated and are identified with the eigenstates of a quantum integrable system. The effective twisted superpotentials are the Yang-Yang functional of the relativistic elliptic Calogero-Moser model. We show that they match on-shell by deriving the Bethe ansatz equation from the saddle point of the five-dimensional partition function. We also show that the Chern-Simons terms match and extend our proposal to the elliptic quiver generalizations.Comment: 30 pages, 4 figures. v2: typo corrected, references adde

Synthetic seed technology for encapsulation and regrowth of in vitro-derived Acacia hyrid shoot and axillary buds

In this study, various concentrations of sodium alginate solutions and calcium chloride solutions were tested in order to optimize the size, shape and texture of alginate synthetic seeds or beads for Acacia hybrid bud-sprouting. The shoot buds and axillary buds from in vitro Acacia hybrids, as explants were encapsulated with 2 to 5% sodium alginate (w/v) in the Murashige and Skoog (MS) free of calcium salt solution solvent and exposed to 25 to 100 mM calcium chloride solution (CaCl2.2H2O). Rounded beads were observed by the encapsulation with alginate 3% and exposed to 75 to 100 mM CaCl2.2H2O combinations and; the encapsulation with alginate 4 to 5% and exposed to any CaCl2.2H2O combinations. The produced synthetic seeds were then tested on the plantlets regeneration ability. The germination rate was within 73.3 to 100% in the duration of 6 to 20 days. It showed that encapsulation at any alginate concentrations and exposed to any of the CaCl2.2H2O concentrations, gave high germination frequency. These plantlets could then be used as the source of explants for the subsequent experiments. The synthetic seeds have the possibility of being an alternative planting material meant for forestry sector in the future, especially for the highly demanded species.Key word: Acacia hybrid, synthetic seeds, encapsulation, alternative planting material

In vitro propagation of Acacia hybrid through alginate-encapsulated shoots and axillary buds

Seed collected from Acacia hybrid trees yields highly variable and poorly performing offspring and are not commonly used in regeneration. The present study described the incapsulation of Acacia hybrid shoots and axillary buds in the calcium alginate gel. The aim of the study was to evaluate the germination of the buds in vitro on the medium with different concentrations of plant growth regulator and; the performance of the germination under light and darkness. For encapsulation purposes, 3% sodium alginate (w/v) in the Murashige and Skoog (MS) free of calcium salt solution solvent were tested. While for complexation, 100 mM calcium chloride solutions (CaCl2.2H2O) were prepared in liquid MS medium. The encapsulated explants or the beads were cultured into the following media: Modified basal MS supplemented with 6-benzylaminopurine (BAP) ranging from 0 to 2.5 mg/L BAP. High germination rate (100%) was observed within five to eight days in all medium tested. Analysis of variance showed no significant difference in the ability of the synthetic seeds to germinate. This showed that the regeneration of shoots is possible by using basal MS only. It was observed that synthetic seeds needed sucrose more than plant growth regulator for its germination. They were also showing good regeneration and development under light condition.Key words: Acacia hybrid, synthetic seeds, encapsulation, germination, regeneration

Nekrasov Functions and Exact Bohr-Sommerfeld Integrals

In the case of SU(2), associated by the AGT relation to the 2d Liouville theory, the Seiberg-Witten prepotential is constructed from the Bohr-Sommerfeld periods of 1d sine-Gordon model. If the same construction is literally applied to monodromies of exact wave functions, the prepotential turns into the one-parametric Nekrasov prepotential F(a,\epsilon_1) with the other epsilon parameter vanishing, \epsilon_2=0, and \epsilon_1 playing the role of the Planck constant in the sine-Gordon Shroedinger equation, \hbar=\epsilon_1. This seems to be in accordance with the recent claim in arXiv:0908.4052 and poses a problem of describing the full Nekrasov function as a seemingly straightforward double-parametric quantization of sine-Gordon model. This also provides a new link between the Liouville and sine-Gordon theories.Comment: 10 page

Wall Crossing and Instantons in Compactified Gauge Theory

We calculate the leading weak-coupling instanton contribution to the moduli-space metric of N=2 supersymmetric Yang-Mills theory with gauge group SU(2) compactified on R^3 x S^1. The results are in precise agreement with the semiclassical expansion of the exact metric recently conjectured by Gaiotto, Moore and Neitzke based on considerations related to wall-crossing in the corresponding four-dimensional theory.Comment: 24 pages, no figure