Finding Maximum Cliques on the D-Wave Quantum Annealer

This paper assesses the performance of the D-Wave 2X (DW) quantum annealer for finding a maximum clique in a graph, one of the most fundamental and important NP-hard problems. Because the size of the largest graphs DW can directly solve is quite small (usually around 45 vertices), we also consider decomposition algorithms intended for larger graphs and analyze their performance. For smaller graphs that fit DW, we provide formulations of the maximum clique problem as a quadratic unconstrained binary optimization (QUBO) problem, which is one of the two input types (together with the Ising model) acceptable by the machine, and compare several quantum implementations to current classical algorithms such as simulated annealing, Gurobi, and third-party clique finding heuristics. We further estimate the contributions of the quantum phase of the quantum annealer and the classical post-processing phase typically used to enhance each solution returned by DW. We demonstrate that on random graphs that fit DW, no quantum speedup can be observed compared with the classical algorithms. On the other hand, for instances specifically designed to fit well the DW qubit interconnection network, we observe substantial speed-ups in computing time over classical approaches.

     

In Silico Identification of Multi-Target Ligands as Promising Hit Compounds for Neurodegenerative Diseases Drug Development

The conventional treatment of neurodegenerative diseases (NDDs) is based on the “one molecule—one target” paradigm. To combat the multifactorial nature of NDDs, the focus is now shifted toward the development of small-molecule-based compounds that can modulate more than one protein target, known as “multi-target-directed ligands” (MTDLs), while having low affinity for proteins that are irrelevant for the therapy. The in silico approaches have demonstrated a potential to be a suitable tool for the identification of MTDLs as promising drug candidates with reduction in cost and time for research and development. In this study more than 650,000 compounds were screened by a series of in silico approaches to identify drug-like compounds with predicted activity simultaneously towards three important proteins in the NDDs symptomatic treatment: acetylcholinesterase (AChE), histone deacetylase 2 (HDAC2), and monoamine oxidase B (MAO-B). The compounds with affinities below 5.0 µM for all studied targets were additionally filtered to remove known non-specifically binding or unstable compounds. The selected four hits underwent subsequent refinement through in silico blood-brain barrier penetration estimation, safety evaluation, and molecular dynamics simulations resulting in two hit compounds that constitute a rational basis for further development of multi-target active compounds against NDDs.     

Polybenzimidazole‐graft‐polyvinylphosphonic acid—proton conducting fuel cell membranes

A new method for the preparation of polybenzimidazole (PBI)‐based membranes, containing high concentrations of immobilized phosphonic acid groups, has been developed. The procedure used is carried out in two steps: (1) Synthesis of modified PBIs, containing 1,2‐dihydroxypropyl groups and preparation of films there from; (2) Introduction of vinylphosphonic acid (VPA) and initiator (cerium ammonium nitrate) in the film, subsequent grafting of VPA from the active sites of the PBI backbone. Membranes with different length of the grafted polyvinylphosphonic acid chains were prepared. The molar ratio grafted VPA units per PBI repeating unit reaches 7.8. Proton conductivity was measured at 120°C and relative humidity (RH) 20–100%. For the membrane with highest concentration of phosphonic acid groups the proton conductivity was 35 mS cm^?1 at 100% RH and 8 mS cm^?1 at 20% RH. © 2012 Wiley Periodicals, Inc. J. Appl. Polym. Sci., 2013     

Multiagent control of self-reconfigurable robots

We demonstrate how multiagent systems provide useful control techniques for modular self-reconfigurable (metamorphic) robots. Such robots consist of many modules that can move relative to each other, thereby changing the overall shape of the robot to suit different tasks. Multiagent control is particularly well-suited for tasks involving uncertain and changing environments. We illustrate this approach through simulation experiments of Proteo, a metamorphic robot system currently under development.     

A classification of slow convergence near parametric periodic points of discrete dynamical systems

We study the phenomenon of slow convergence in families of discrete dynamical systems where the iteration function has a Puiseux series representation. Such occurrence consists in the slow convergence of orbits near non-hyperbolic parametric periodic points. We provide a precise new definition of the slowness of convergence which is based on literature results for the critical exponents associated with parametric periodic points. Such exponents establish a general classification for slow systems and provide a measure of rates of convergence. For dynamical systems whose iteration functions have Taylor series expansions, the new definition is natural with wider applicability. However, it can be also used for iteration functions where a more sophisticated approach, such as a Lagrange expansion, is needed. In addition, we show that even for such iteration functions, the critical exponent can be easily computed. The presented theoretical results are illustrated by numerical examples having different rates of convergence.     

Numerical simulation of multi-species biofilms in porous media for different kinetics

There are bacteria that can form strong biofilms in porous media. These biofilms can be used as biobarriers to restrict the flow of pollutants. For certain contaminants, a second species of bacteria that can actually react with the contaminants can be added to the biobarrier to actually degrade the pollutants. We propose some mathematical models for the formation of these reacting biobarriers under different hypotheses, and numerically solve the resulting equations for the flow, transport and reactions. Qualitative comparisons with some experimental results are also given.     

Developing a Mathematical Model of Intracellular Calcium Dynamics for Evaluating Combined Anticancer Effects of Afatinib and RP4010 in Esophageal Cancer

Targeting dysregulated Ca²⁺ signaling in cancer cells is an emerging chemotherapy approach. We previously reported that store-operated Ca²⁺ entry (SOCE) blockers, such as RP4010, are promising antitumor drugs for esophageal cancer. As a tyrosine kinase inhibitor (TKI), afatinib received FDA approval to be used in targeted therapy for patients with EGFR mutation-positive cancers. While preclinical studies and clinical trials have shown that afatinib has benefits for esophageal cancer patients, it is not known whether a combination of afatinib and RP4010 could achieve better anticancer effects. Since TKI can alter intracellular Ca²⁺ dynamics through EGFR/phospholipase C-γ pathway, in this study, we evaluated the inhibitory effect of afatinib and RP4010 on intracellular Ca²⁺ oscillations in KYSE-150, a human esophageal squamous cell carcinoma cell line, using both experimental and mathematical simulations. Our mathematical simulation of Ca²⁺ oscillations could fit well with experimental data responding to afatinib or RP4010, both separately or in combination. Guided by simulation, we were able to identify a proper ratio of afatinib and RP4010 for combined treatment, and such a combination presented synergistic anticancer-effect evidence by experimental measurement of intracellular Ca²⁺ and cell proliferation. This intracellular Ca²⁺ dynamic-based mathematical simulation approach could be useful for a rapid and cost-effective evaluation of combined targeting therapy drugs.