Fast Consensus under Eventually Stabilizing Message Adversaries

This paper is devoted to deterministic consensus in synchronous dynamic networks with unidirectional links, which are under the control of an omniscient message adversary. Motivated by unpredictable node/system initialization times and long-lasting periods of massive transient faults, we consider message adversaries that guarantee periods of less erratic message loss only eventually: We present a tight bound of $2D+1$ for the termination time of consensus under a message adversary that eventually guarantees a single vertex-stable root component with dynamic network diameter $D$, as well as a simple algorithm that matches this bound. It effectively halves the termination time $4D+1$ achieved by an existing consensus algorithm, which also works under our message adversary. We also introduce a generalized, considerably stronger variant of our message adversary, and show that our new algorithm, unlike the existing one, still works correctly under it.Comment: 13 pages, 5 figures, updated reference

Cooling and Heating Functions of Photoionized Gas

Cooling and heating functions of cosmic gas are a crucial ingredient for any study of gas dynamics and thermodynamics in the interstellar and intergalactic medium. As such, they have been studied extensively in the past under the assumption of collisional ionization equilibrium. However, for a wide range of applications, the local radiation field introduces a non-negligible, often dominant, modification to the cooling and heating functions. In the most general case, these modifications cannot be described in simple terms, and would require a detailed calculation with a large set of chemical species using a radiative transfer code (the well-known code Cloudy, for example). We show, however, that for a sufficiently general variation in the spectral shape and intensity of the incident radiation field, the cooling and heating functions can be approximated as depending only on several photoionization rates, which can be thought of as representative samples of the overall radiation field. This dependence is easy to tabulate and implement in cosmological or galactic-scale simulations, thus economically accounting for an important but rarely-included factor in the evolution of cosmic gas. We also show a few examples where the radiation environment has a large effect, the most spectacular of which is a quasar that suppresses gas cooling in its host halo without any mechanical or non-radiative thermal feedback.Comment: replaced with the accepted version; note that the revised version differs substantially from the original draf

Fibrations of genus two on complex surfaces

We consider fibrations of genus 2 over complex surfaces. The purpose of this paper is primarily to provide a geometric description of the possible structures of the fibration on a neighborhood of a singular fiber. In particular it is shown that the "geometric data" of the singular fiber determines the fibration on its neighborhood up to a transversely holomorphic $C^{\infty}$-diffeomorphism. The method employed is quite flexible and it applies to good extent to fibrations of arbitrary genus.Comment: This is the final version, June 201

Convergence of Quantum Annealing with Real-Time Schrodinger Dynamics

Convergence conditions for quantum annealing are derived for optimization problems represented by the Ising model of a general form. Quantum fluctuations are introduced as a transverse field and/or transverse ferromagnetic interactions, and the time evolution follows the real-time Schrodinger equation. It is shown that the system stays arbitrarily close to the instantaneous ground state, finally reaching the target optimal state, if the strength of quantum fluctuations decreases sufficiently slowly, in particular inversely proportionally to the power of time in the asymptotic region. This is the same condition as the other implementations of quantum annealing, quantum Monte Carlo and Green's function Monte Carlo simulations, in spite of the essential difference in the type of dynamics. The method of analysis is an application of the adiabatic theorem in conjunction with an estimate of a lower bound of the energy gap based on the recently proposed idea of Somma et. al. for the analysis of classical simulated annealing using a classical-quantum correspondence.Comment: 6 pages, minor correction

Convergence theorems for quantum annealing

We prove several theorems to give sufficient conditions for convergence of quantum annealing, which is a protocol to solve generic optimization problems by quantum dynamics. In particular the property of strong ergodicity is proved for the path-integral Monte Carlo implementation of quantum annealing for the transverse Ising model under a power decay of the transverse field. This result is to be compared with the much slower inverse-log decay of temperature in the conventional simulated annealing. Similar results are proved for the Green's function Monte Carlo approach. Optimization problems in continuous space of particle configurations are also discussed.Comment: 19 page

Effect of cactus pear cultivation after Mediterranean maquis on soil carbon stock, δ13C spatial distribution and root turnover

croplands and orchards leading to strong soil degradation. Organic carbon is usually accumulated in soils under maquis leading to partial regeneration of fertility for future agricultural use. The aim of this work was to investigate the effect of land use change from maquis to agriculture on soil organic carbon (SOC) stock and its spatial distribution in a Mediterranean system. Three Mediterranean land use systems (seminatural vegetation, cactus pear crop and olive grove) were selected in Sicily and analysed for soil C stocks and their δ13C. Total SOC and δ13C were measured up to 75 cm soil depth within and between the rows of cactus pear and olive grove and along a similar transect in maquis, in order to evaluate the distribution of new and old C derived from roots. The land use change from Mediterranean maquis (C3 plant) to cactus pear (CAM plant) lead to a SOC decrease of 65% after 28 years of cultivation, and a further decrease for 14% after 7 years after the change from cactus pear to olive grove (C3 plant). Considering these SOC losses as well as the periods after the land use changes we calculated the mean residence time (MRT) of soil organic matter. TheMRT of C under Mediterranean maquis was about 142 years, but was just 10 years under cactus pear. Root biomass of cactus pear was used for a new approach to estimate root turnover. The root turnover rate of cactus decreased along the soil profile from 7.1% per year in 0–15 cm to 3.7% in 60–75 cm soil depth. Along the transect, the average of root turnover values was highest in the middle of the intra-row. Root turnover and C inputwere correlated with SOC stocks to evaluate C sequestration potential of soils depending on land use and managements. Weconclude that the SOC under maquis is higher and has longer residence time compared to permanent agricultural crops like cactus pear and olives

Anomalous diffusion in a symbolic model

We address this work to investigate some statistical properties of symbolic sequences generated by a numerical procedure in which the symbols are repeated following a power law probability density. In this analysis, we consider that the sum of n symbols represents the position of a particle in erratic movement. This approach revealed a rich diffusive scenario characterized by non-Gaussian distributions and, depending on the power law exponent and also on the procedure used to build the walker, we may have superdiffusion, subdiffusion or usual diffusion. Additionally, we use the continuous-time random walk framework to compare with the numerical data, finding a good agreement. Because of its simplicity and flexibility, this model can be a candidate to describe real systems governed by power laws probabilities densities.Comment: Accepted for publication in Physica Script

Glutamate-mediated blood-brain barrier opening. implications for neuroprotection and drug delivery

The blood-brain barrier is a highly selective anatomical and functional interface allowing a unique environment for neuro-glia networks. Blood-brain barrier dysfunction is common in most brain disorders and is associated with disease course and delayed complications. However, the mechanisms underlying blood-brain barrier opening are poorly understood. Here we demonstrate the role of the neurotransmitter glutamate in modulating early barrier permeability in vivo Using intravital microscopy, we show that recurrent seizures and the associated excessive glutamate release lead to increased vascular permeability in the rat cerebral cortex, through activation of NMDA receptors. NMDA receptor antagonists reduce barrier permeability in the peri-ischemic brain, whereas neuronal activation using high-intensity magnetic stimulation increases barrier permeability and facilitates drug delivery. Finally, we conducted a double-blind clinical trial in patients with malignant glial tumors, using contrast-enhanced magnetic resonance imaging to quantitatively assess blood-brain barrier permeability. We demonstrate the safety of stimulation that efficiently increased blood-brain barrier permeability in 10 of 15 patients with malignant glial tumors. We suggest a novel mechanism for the bidirectional modulation of brain vascular permeability toward increased drug delivery and prevention of delayed complications in brain disorders. SIGNIFICANCE STATEMENT: In this study, we reveal a new mechanism that governs blood-brain barrier (BBB) function in the rat cerebral cortex, and, by using the discovered mechanism, we demonstrate bidirectional control over brain endothelial permeability. Obviously, the clinical potential of manipulating BBB permeability for neuroprotection and drug delivery is immense, as we show in preclinical and proof-of-concept clinical studies. This study addresses an unmet need to induce transient BBB opening for drug delivery in patients with malignant brain tumors and effectively facilitate BBB closure in neurological disorders