Chemical Solutions in a Quantum Solvent: Anionic Electrolytes in 4He Nanodroplets

Variational and diffusion Monte Carlo (VMC and DMC) calculations are presented for anionic electrolytes solvated in ⁴He. The electrolytes have the general structure X^?(He)_N, with X=F, Cl, Br and I, and N varying up to 40 (41 for I^?). The overall interaction potential is obtained from accurate ab initio data for the two‐body components and then using the sum‐of‐potentials approximation. Our computational scheme is a robust procedure, giving us accurate trial wavefunctions that can be used to perform high‐quality DMC calculations. The results indicate very marked delocalization and permanence of the liquid‐like quantum features of the solvent adatoms surrounding the anionic impurities. This finding stands in contrast to the more structured, solid‐like behavior of the quantum solutions with alkali metal cations embedded in He nanodroplets. While other negatively charged species such as H^? have shown an overall repulsive interaction with He, the present calculations clearly indicate that the halogen anions remain solvated within liquid‐like solvent “bubbles” of species‐dependent size.     

On the number of anisotropic simple submodules in modules with a form

Let G be a finite group, and V a finite-dimensional semisimple G-module over a finite field. Assume that V is endowed with a nonsingular bilinear form which is symmetric or symplectic, and which is invariant under the action of G. In this setting, we compute the number of anisotropic simple submodules of V.Received: 25 May 2004     

One-way multiparty communication lower bound for pointer jumping with applications

In this paper we study the one-way multiparty communication model, in which every party speaks exactly once in its turn. For every k, we prove a tight lower bound of Ω(n ^1/(k?1)}) on the probabilistic communication complexity of pointer jumping in a k-layered tree, where the pointers of the i-th layer reside on the forehead of the i-th party to speak. The lower bound remains nontrivial even for k = (logn)^1/2?? parties, for any constant ? > 0. Previous to our work a lower bound was known only for k =3 (Wigderson, see [7]), and in restricted models for k>3 [2},24,18,4,13]. Our results have the following consequences to other models and problems, extending previous work in several directions. The one-way model is strong enough to capture general (not one-way) multiparty protocols with a bounded number of rounds. Thus we generalize two problem areas previously studied in the 2-party model (cf. [30,21,29]). The first is a rounds hierarchy: we give an exponential separation between the power of r and 2r rounds in general probabilistic k-party protocols, for any k and r. The second is the relative power of determinism and nondeterminism: we prove an exponential separation between nondeterministic and deterministic communication complexity for general k-party protocols with r rounds, for any k,r. The pointer jumping function is weak enough to be a special case of the well-studied disjointness function. Thus we obtain a lower bound of Ω(n ^1/(k?1)) on the probabilistic complexity of k-set disjointness in the one-way model, which was known only for k = 3 parties. Our result also extends a similar lower bound for the weaker simultaneous model, in which parties simultaneously send one message to a referee [12]. Finally, we infer an exponential separation between the power of any two different orders in which parties send messages in the one-way model, for every k. Previous results [29, 7] separated orders based on who speaks first. Our lower bound technique, which handles functions of high discrepancy over cylinder intersections, provides a “party-elimination” induction, based on a restricted form of a direct-product result, specific to the pointer jumping function.     

An experimental comparison of four graph drawing algorithms

In this paper we present an extensive experimental study comparing four general-purpose graph drawing algorithms. The four algorithms take as input general graphs (with no restrictions whatsoever on connectivity, planarity, etc.) and construct orthogonal grid drawings, which are widely used in software and database visualization applications. The test data (available by anonymous ftp) are 11,582 graphs, ranging from 10 to 100 vertices, which have been generated from a core set of 112 graphs used in “real-life” software engineering and database applications. The experiments provide a detailed quantitative evaluation of the performance of the four algorithms, and show that they exhibit trade-offs between “aesthetic” properties (e.g., crossings, bends, edge length) and running time.     

The communication complexity of addition

Suppose each of k≤n ^o(1) players holds an n-bit number x _i in its hand. The players wish to determine if ∑ _i≤k x _i =s. We give a public-coin protocol with error 1% and communication O(k logk). The communication bound is independent of n, and for k≥3 improves on the O(k logn) bound by Nisan (Bolyai Soc. Math. Studies; 1993).     

Controlled self assembly of collagen nanoparticle

In recent years carrier-mediated drug delivery has emerged as a powerful methodology for the treatment of various pathologies. The therapeutic index of traditional and novel drugs is enhanced via the increase of specificity due to targeting of drugs to a particular tissue, cell or intracellular compartment, the control over release kinetics, the protection of the active agent, or a combination of the above. Collagen is an important biomaterial in medical applications and ideal as protein-based drug delivery platform due to its special characteristics, such as biocompatibility, low toxicity, biodegradability, and weak antigenicity. While some many attempts have been made, further work is needed to produce fully biocompatible collagen hydrogels of desired size and able to release drugs on a specific target. In this article we propose a novel method to obtain spherical particles made of polymerized collagen surrounded by DMPC liposomes. The liposomes allow to control both the particles dimension and the gelling environment during the collagen polymerization. Furthermore, an optical based method to visualize and quantify each step of the proposed protocol is detailed and discussed.     

On the Violation of Ohm’s Law for Bounded Interactions: a One Dimensional System

We consider an infinite Hamiltonian system in one space dimension, given by a charged particle subjected to a constant electric field and interacting with an infinitely extended system of particles. We discuss conditions on the particle/medium interaction which are necessary for the charged particle to reach a finite limiting velocity. We assume that the background system is initially in an equilibrium Gibbs state and we prove that for bounded interactions the average velocity of the charged particle increases linearly in time. This statement holds for any positive intensity of the electric field, thus contradicting Ohms law.Work partially supported by the GNFM-INDAM and the Italian Ministry of the University.