Synchronization in Weighted Uncorrelated Complex Networks in a Noisy Environment: Optimization and Connections with Transport Efficiency

Motivated by synchronization problems in noisy environments, we study the Edwards-Wilkinson process on weighted uncorrelated scale-free networks. We consider a specific form of the weights, where the strength (and the associated cost) of a link is proportional to $(k_{i}k_{j})^{\beta}$ with $k_{i}$ and $k_{j}$ being the degrees of the nodes connected by the link. Subject to the constraint that the total network cost is fixed, we find that in the mean-field approximation on uncorrelated scale-free graphs, synchronization is optimal at $\beta^{*}$$=$-1. Numerical results, based on exact numerical diagonalization of the corresponding network Laplacian, confirm the mean-field results, with small corrections to the optimal value of $\beta^{*}$. Employing our recent connections between the Edwards-Wilkinson process and resistor networks, and some well-known connections between random walks and resistor networks, we also pursue a naturally related problem of optimizing performance in queue-limited communication networks utilizing local weighted routing schemes.Comment: Papers on related research can be found at http://www.rpi.edu/~korniss/Research

Roughening of the (1+1) interfaces in two-component surface growth with an admixture of random deposition

We simulate competitive two-component growth on a one dimensional substrate of $L$ sites. One component is a Poisson-type deposition that generates Kardar-Parisi-Zhang (KPZ) correlations. The other is random deposition (RD). We derive the universal scaling function of the interface width for this model and show that the RD admixture acts as a dilatation mechanism to the fundamental time and height scales, but leaves the KPZ correlations intact. This observation is generalized to other growth models. It is shown that the flat-substrate initial condition is responsible for the existence of an early non-scaling phase in the interface evolution. The length of this initial phase is a non-universal parameter, but its presence is universal. In application to parallel and distributed computations, the important consequence of the derived scaling is the existence of the upper bound for the desynchronization in a conservative update algorithm for parallel discrete-event simulations. It is shown that such algorithms are generally scalable in a ring communication topology.Comment: 16 pages, 16 figures, 77 reference

Diffusion Processes on Small-World Networks with Distance-Dependent Random-Links

We considered diffusion-driven processes on small-world networks with distance-dependent random links. The study of diffusion on such networks is motivated by transport on randomly folded polymer chains, synchronization problems in task-completion networks, and gradient driven transport on networks. Changing the parameters of the distance-dependence, we found a rich phase diagram, with different transient and recurrent phases in the context of random walks on networks. We performed the calculations in two limiting cases: in the annealed case, where the rearrangement of the random links is fast, and in the quenched case, where the link rearrangement is slow compared to the motion of the random walker or the surface. It has been well-established that in a large class of interacting systems, adding an arbitrarily small density of, possibly long-range, quenched random links to a regular lattice interaction topology, will give rise to mean-field (or annealed) like behavior. In some cases, however, mean-field scaling breaks down, such as in diffusion or in the Edwards-Wilkinson process in "low-dimensional" small-world networks. This break-down can be understood by treating the random links perturbatively, where the mean-field (or annealed) prediction appears as the lowest-order term of a naive perturbation expansion. The asymptotic analytic results are also confirmed numerically by employing exact numerical diagonalization of the network Laplacian. Further, we construct a finite-size scaling framework for the relevant observables, capturing the cross-over behaviors in finite networks. This work provides a detailed account of the self-consistent-perturbative and renormalization approaches briefly introduced in two earlier short reports.Comment: 36 pages, 27 figures. Minor revisions in response to the referee's comments. Furthermore, some typos were fixed and new references were adde

Synchronization Landscapes in Small-World-Connected Computer Networks

Motivated by a synchronization problem in distributed computing we studied a simple growth model on regular and small-world networks, embedded in one and two-dimensions. We find that the synchronization landscape (corresponding to the progress of the individual processors) exhibits Kardar-Parisi-Zhang-like kinetic roughening on regular networks with short-range communication links. Although the processors, on average, progress at a nonzero rate, their spread (the width of the synchronization landscape) diverges with the number of nodes (desynchronized state) hindering efficient data management. When random communication links are added on top of the one and two-dimensional regular networks (resulting in a small-world network), large fluctuations in the synchronization landscape are suppressed and the width approaches a finite value in the large system-size limit (synchronized state). In the resulting synchronization scheme, the processors make close-to-uniform progress with a nonzero rate without global intervention. We obtain our results by ``simulating the simulations", based on the exact algorithmic rules, supported by coarse-grained arguments.Comment: 20 pages, 22 figure

The clustering of the first galaxy halos

We explore the clustering properties of high redshift dark matter halos, focusing on halos massive enough to host early generations of stars or galaxies at redshift 10 and greater. Halos are extracted from an array of dark matter simulations able to resolve down to the "mini-halo" mass scale at redshifts as high as 30, thus encompassing the expected full mass range of halos capable of hosting luminous objects and sources of reionization. Halo clustering on large-scales agrees with the Sheth, Mo & Tormen halo bias relation within all our simulations, greatly extending the regime where large-scale clustering is confirmed to be "universal" at the 10-20% level (which means, for example, that 3sigma halos of cluster mass at z=0 have the same large-scale bias with respect to the mass distribution as 3sigma halos of galaxy mass at z=10). However, on small-scales, the clustering of our massive halos (> ~10^9 Msun/h) at these high redshifts is stronger than expected from comparisons with small-scale halo clustering extrapolated from lower redshifts. This implies "non-universality" in the scale-dependence of halo clustering, at least for the commonly used parameterizations of the scale-dependence of bias that we consider. We provide a fit for the scale-dependence of bias in our results. This study provides a basis for using extraordinarily high redshift galaxies (redshift ~10) as a probe of cosmology and galaxy formation at its earliest stages. We show also that mass and halo kinematics are strongly affected by finite simulation volumes. This suggests the potential for adverse affects on gas dynamics in hydrodynamic simulations of limited volumes, such as is typical in simulations of the formation of the "first stars", though further study is warranted.Comment: MNRAS accepte

Association of Typical versus Atypical Antipsychotics with Symptoms and Quality of Life in Schizophrenia

BACKGROUND: Several reports on patients with chronic schizophrenia suggest that atypical versus typical antipsychotics are expected to lead to better quality of life (QOL) and cognitive function. Our aim was to examine the association of chronic treatment with typical or atypical antipsychotics with cognitive function, psychiatric symptoms, QOL, and drug-induced extrapyramidal symptoms in long-hospitalized patients with schizophrenia. METHODOLOGY AND PRINCIPAL FINDINGS: The Hasegawa Dementia Scale-Revised (HDS-R), Brief Psychiatric Rating Scale (BPRS), the Schizophrenia Quality of Life Scale, translated into Japanese (JSQLS), and the Drug-Induced Extrapyramidal Symptoms Scale (DIEPSS) were used to evaluate cognitive function, psychiatric symptoms, QOL, and drug-induced extrapyramidal symptoms. We examined the correlation between the dose of antipsychotics and each measure derived from these psychometric tests. The student t-test was used to compare scores obtained from psychometric tests between patients receiving typical and atypical antipsychotics. Results showed significant correlations between chlorpromazine (CPZ)-equivalent doses of typical antipsychotics and atypical antipsychotics, and the total BPRS score and BPRS subscale scores for positive symptoms. CPZ-equivalent doses of typical antipsychotics were correlated with the JSQLS subscale score for dysfunction of psycho-social activity and DIEPSS score. Furthermore, the total BPRS scores, BPRS subscale score for positive symptoms, the JSQLS subscale score for dysfunction of psycho-social activity, and the DIEPSS score were significantly higher in patients receiving typical antipsychotics than atypical antipsychotics. CONCLUSION AND SIGNIFICANCE: These findings suggest that long-term administration of typical antipsychotics has an unfavorable association with feelings of difficulties mixing in social situations in patients with chronic schizophrenia

Wystepowanie histaminy w zywnosci

Histaminę oznaczano w różnych środkach spożywczych: krajowych i importowanych, dostępnych na naszym rynku, w których istnieje możliwość występowania histaminy. Zbadano łącznie 150 prób. Były to sery, przetwory pomidorowe, kapusta kwaszona, ogórki kwaszone, napoje alkoholowe, mięso i przetwory mięsne. Próby badano bezpośrednio po zakupie oraz podczas przechowywania środków spożywczych w temp. +4°C i +20°C. Histaminę oznaczano metodą kolorymetryczną wg PN-87-A/86784. Wykazano, że zawartość histaminy w środkach spożywczych była poniżej granicy tolerancji, przyjętej za 20 mg histaminy/100 g produktu. Zawartość histaminy w serach przechowywanych w temp. +4°C i +20°C, wykazuje tendencję do narastania. Przechowywanie mięsa i przetworów mięsnych przez 5 dni w temp. +4°C powoduje wzrost zawartości histaminy o 45%. Natomiast warzywa kwaszone, (kapusta i ogórki) pakowane próżniowo, wykazują wyższą zawartość histaminy, niż przechowywanie w beczce.Histamine was estimated in various types of food products, both native and imported ones, available in Poland, with possible histamine presence. 150 samples of various types cheeses, tomato products, sauerkraut, pickled cucumbers, alcoholic beverages, meat and meat products were tested. Samples were tested right after products were purchased and after their storage at +4°C and +20°C. The histamine content was estimated colorimetrically, according to PN-87-A/86784. Estimated histamine content in the tested food products was lower than the level accepted for food, equal to 20 mg/100 g. The histamine content in cheeses was increasing with storage time at +4°C and +20°C. Five-day-storage of meat and meat products at +4°C increase histamine content by 45%. The histamine content in pickled vegetables was higher when vacuum packed than packed in open containers

Statistical Properties of the Simulated Time Horizon

We investigate the universal characteristics of the simulated time horizon of the basic conservative parallel algorithm when implemented on regular lattices. This technique [1, 2] is generically applicable to various physical, biological, or chemical systems where the underlying dynamics is asynchronous. Employing direct simulations, and using standard tools and the concept of dynamic scaling from nonequilibrium surface/interface physics, we identify the universality class of the time horizon and determine its implications for the asymptotic scalability of the basic conservative scheme. Our main finding is that while the simulation converges to an asymptotic nonzero rate of progress, the statistical width of the time horizon diverges with the number of PEs in a power law fashion. This is in contrast with the findings of Ref. [3]. This information can be very useful, e.g., we utilize it to understand optimizing the size of a moving “time window ” to enforce memory constraints. Keywords conservative parallel discrete-event simulation, scalability, non-equilibrium surface growth, Monte Carlo, stochastic processes 1