Load balancing via random local search in closed and open systems

In this paper, we analyze the performance of random load resampling and migration strategies in parallel server systems. Clients initially attach themselves to an arbitrary server, but may switch servers independently at random instants of time in an attempt to improve their service rate. This approach to load balancing contrasts with traditional approaches where clients make smart server selections upon arrival (e.g., Join-the-Shortest-Queue policy and variants thereof). Load resampling is particularly relevant in scenarios where clients cannot predict the load of a server before being actually attached to it. An important example is in wireless spectrum sharing where clients try to share a set of frequency bands in a distributed manner. We first analyze the natural Random Local Search (RLS) strategy. Under this strategy, after sampling a new server randomly, clients only switch to it if their service rate is improved. In closed systems, where the client population is fixed, we derive tight estimates of the time it takes under RLS strategy to balance the load across servers. We then study open systems where clients arrive according to a random process and leave the system upon service completion. In this scenario, we analyze how client migrations within the system interact with the system dynamics induced by client arrivals and departures. We compare the load-aware RLS strategy to a load-oblivious strategy in which clients just randomly switch server without accounting for the server loads. Surprisingly, we show that both load-oblivious and load-aware strategies stabilize the system whenever this is at all possible. We use large-system asymptotics to characterize system performance, and augment this with simulations, which suggest that the average client sojourn time under the load-oblivious strategy is not considerably reduced when clients apply smarter load-aware strategies.     

Efficient and strategy-proof social choice when preferences are single-dipped

We study the problem of locating a single public good along a segment when agents have single-dipped preferences. We ask whether there are unanimous and strategy-proof rules for this model. The answer is positive and we characterize all such rules. We generalize our model to allow the set of alternatives to be unbounded. If the set of alternatives does not have a maximal and a minimal element, there is no meaningful notion of efficiency. However, we show that the range of every strategy-proof rule has a maximal and a minimal element. We then characterize all strategy-proof rules.     

PMMA–cellulose acetate phthalate nanocomposites reinforced with silane-treated nanoclay

A blend of cellulose acetate phthalate with poly (methyl methacrylate) has been developed by reinforcing it with silane-treated nanoclay. In order to enhance interactions between the nanoclay and blend components, maleic anhydride was added as the coupling agent. The mechanical properties were enhanced and were further analyzed by theoretical models. The thermal properties and water absorption characteristics were also assessed.     

Use of polystyrene brushes to investigate the role of interface between substrates and thin homogeneous films

The viscoelastic properties of thin polystyrene (PS) films depend on confinement, as it can modify the molecular dynamics affecting the glass transition. In the recent past, the authors have investigated the region next to the free interface by means of an atomic force microscope suitably modified to monitor the indentation of a tip into a film during a given lapse of time while applying a constant load. Herein, to explore the interface with the substrate, the authors report on experiments in which PS brushes grafted to native silicon oxide were used. It was found that the film wettability on brushes and H‐terminated silicon can be highly improved when compared with native silicon oxide. In addition, the glass transition temperature of thin films increases up to the bulk value in the case of film/brush combinations with high molecular weight or films with high molecular weight on H‐terminated silicon. Data are discussed according to hypotheses such as residual solvent presence, interface free volume, and molecular mechanical coupling. These observations can be of great interest for nanotechnological applications, especially in those instances where one needs to tailor the temperature dependence of viscoelastic properties of thin films. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2013, 51, 1149–1156     

Monomials, binomials and Riemann–Roch

The Riemann–Roch theorem on a graph G is related to Alexander duality in combinatorial commutative algebra. We study the lattice ideal given by chip firing on G and the initial ideal whose standard monomials are the G-parking functions. When G is a saturated graph, these ideals are generic and the Scarf complex is a minimal free resolution. Otherwise, syzygies are obtained by degeneration. We also develop a self-contained Riemann–Roch theory for Artinian monomial ideals.     

Biginelli-type reaction: Efficient synthesis of 5-unsubstituted 3,4-dihydropyrimidin-2-ones and thiones from gem-dibromomethylarenes

In the present study, we are reporting a simple and efficient method for the one-pot synthesis of the biologically important heterocyclic molecules 5-unsubstituted 3,4-dihydropyrimidin-2-ones and thiones using gem-dibromomethylarenes, oxalacetic acid, and urea or thiourea. Gem-dibromomethylarenes are used as aldehyde equivalent for the efficient synthesis of 3,4-dihydropyrimidin-2-ones/thiones. This reaction offers advantages for the synthesis of these compounds, including ready availability of the starting materials, experimental simplicity and in good yields. Besides, the synthesized molecules are interesting for their biological and pharmacological actions.