Phosphorus based inhibitors of matrix metalloproteinases

This article reviews the current state of phosphorus-based matrix metalloproteinase (MMP) inhibitors. MMPs are a potentially harmful group of enzymes and their successful inhibition can be expected to alleviate a large diversity of severe pathologies that are listed in the beginning of the review. More than 20 years of worldwide search by the scientific and industrial community for a clinically useful inhibitor have resulted in failure because of toxic side effects or lack of in vivo efficacy of the tested molecules. In the majority of inhibitors reviewed in this article, the phosphorus plays the role of zinc bonding, as most MMP inhibitors are designed to do, since the catalytic zinc ion is crucial for the functioning of these enzymes. The main classes of phosphorus based MMP inhibitors are: bisphosphonates, phosphonamidates, phosphinamidates, phosphinates, phosphonates and carbamoylphosphonates.     

Optimal algorithms for the α-neighbor p-center problem

Assigning multiple service facilities to demand points is important when demand points are required to withstand service facility failures. Such failures may result from a multitude of causes, ranging from technical difficulties to natural disasters. The α-neighbor p-center problem deals with locating p service facilities. Each demand point is assigned to its nearest α service facilities, thus it is able to withstand up to α − 1 service facility failures. The objective is to minimize the maximum distance between a demand point and its αth nearest service facility. We present two optimal algorithms for both the continuous and discrete α-neighbor p-center problem. We present experimental results comparing the performance of the two optimal algorithms for α = 2. We also present experimental results showing the performance of the relaxation algorithm for α = 1, 2, 3.     

Effective chiral magnetic currents, topological magnetic charges, and microwave vortices in a cavity with an enclosed ferrite disk

In microwaves, a TE-polarized rectangular-waveguide resonator with an inserted thin ferrite disk gives an example of a nonintegrable system. The interplay of reflection and transmission at the disk interfaces together with the material gyrotropy effect gives rise to whirlpool-like electromagnetic vortices in the proximity of the ferromagnetic resonance. Based on numerical simulation, we show that a character of microwave vortices in a cavity can be analyzed by means of consideration of equivalent magnetic currents. Maxwell equations allows introduction of a magnetic current as a source of the electromagnetic field. Specifically, we found that in such nonintegrable structures, magnetic gyrotropy and geometrical factors leads to the effect of symmetry breaking resulting in effective chiral magnetic currents and topological magnetic charges. As an intriguing fact, one can observe precessing behavior of the electric-dipole polarization inside a ferrite disk.     

Randomized Algorithms with Splitting: Why the Classic Randomized Algorithms Do Not Work and How to Make them Work

We show that the original classic randomized algorithms for approximate counting in NP-hard problems, like for counting the number of satisfiability assignments in a SAT problem, counting the number of feasible colorings in a graph and calculating the permanent, typically fail. They either do not converge at all or are heavily biased (converge to a local extremum). Exceptions are convex counting problems, like estimating the volume of a convex polytope. We also show how their performance could be dramatically improved by combining them with the classic splitting method, which is based on simulating simultaneously multiple Markov chains. We present several algorithms of the combined version, which we simple call the splitting algorithms. We show that the most advance splitting version coincides with the cloning algorithm suggested earlier by the author. As compared to the randomized algorithms, the proposed splitting algorithms require very little warm-up time while running the MCMC from iteration to iteration, since the underlying Markov chains are already in steady-state from the beginning. What required is only fine tuning, i.e. keeping the Markov chains in steady-state while moving from iteration to iteration. We present extensive simulation studies with both the splitting and randomized algorithms for different NP-hard counting problems.     

Using fractional primal–dual to schedule split intervals with demands

We consider the problem of scheduling jobs that are given as groups of non-intersecting intervals on the real line. Each job j is associated with a t-interval (which consists of up to t segments, for some t≥1), a demand, d_j[0,1], and a weight, w(j). A feasible schedule is a collection of jobs such that, for every , the total demand of the jobs in the schedule whose t-interval contains s does not exceed 1. Our goal is to find a feasible schedule that maximizes the total weight of scheduled jobs.We present a 6t-approximation algorithm for this problem that uses a novel extension of the primal–dual schema called fractional primal–dual. The first step in a fractional primal–dual r-approximation algorithm is to compute an optimal solution, x^*, of an LP relaxation of the problem. Next, the algorithm produces an integral primal solution x, and a new LP, denoted by P′, that has the same objective function as the original problem, but contains inequalities that may not be valid with respect to the original problem. Moreover, x^* is a feasible solution of P′. The algorithm also computes a solution y to the dual of P′. The solution x is r-approximate, since its weight is bounded by the value of y divided by r.We present a fractional local ratio interpretation of our 6t-approximation algorithm. We also discuss the connection between fractional primal–dual and the fractional local ratio technique. Specifically, we show that the former is the primal–dual manifestation of the latter.     

Scale-free networks on lattices

We suggest a method for embedding scale-free networks, with degree distribution Pk approximately k(-lambda), in regular Euclidean lattices accounting for geographical properties. The embedding is driven by a natural constraint of minimization of the total length of the links in the system. We find that all networks with lambda>2 can be successfully embedded up to a (Euclidean) distance xi which can be made as large as desired upon the changing of an external parameter. Clusters of successive chemical shells are found to be compact (the fractal dimension is df=d), while the dimension of the shortest path between any two sites is smaller than 1: dmin=(lambda-2)/(lambda-1-1/d), contrary to all other known examples of fractals and disordered lattices.     

Reference-wave solutions for high-frequency fields propagating in random media

Ray theory plays an important role in determining the propagation properties of high-frequency fields and their statistical measures in complicated random environments. According to the ray approach, the field at the observer can be synthesized from a variety of field species arriving along multiple ray trajectories resulting from refraction and scattering from boundaries and from scattering centers embedded in the random medium. For computations of the statistical measures, it is desirable therefore to possess a solution for the high-frequency field propagating along an isolated ray trajectory. For this reason, a new reference-wave method was developed to provide an analytic solution of the parabolic-wave equation.     

Energy transfer between coronene and rhodamine 6G in PMMA matrices

The fluorescence lifetime of coronene and the rate of dipole-dipole energy transfer from coronene to rhodamine 6G in PMMA matrices were found to be temperature dependent. For both these photophysical processes an activation energy of about 500 cm^?1 is obtained. The energy transfer results can be analyzed in terms of a model involving thermally activated energy transfer from excited states of coronene.     

On finite sets of points inP 3

Given a finite set of points Γ₀ which span a projective spaceP ³, we show here that a plane spanned by points of Γ₀ can be a neighbour of at most eight points of Γ₀, these being the vertices of a projective cube; the common neighbour plane is then elementary with the three only points of Γ₀ in it being diagonal points of the cube. This extends toP ³ some results of L. M. Kelly and W. O. J. Moser in the planeP ².