Computing roadmaps of semi-algebraic sets on a variety

We consider a semi-algebraic set defined by polynomials in variables which is contained in an algebraic variety . The variety is assumed to have real dimension the polynomial and the polynomials defining have degree at most . We present an algorithm which constructs a roadmap on . The complexity of this algorithm is . We also present an algorithm which, given a point of defined by polynomials of degree at most , constructs a path joining this point to the roadmap. The complexity of this algorithm is These algorithms easily yield an algorithm which, given two points of defined by polynomials of degree at most , decides whether or not these two points of lie in the same semi-algebraically connected component of and if they do computes a semi-algebraic path in connecting the two points.

     

On Projections of Semi-Algebraic Sets Defined by Few Quadratic Inequalities

Let S⊂ℝ ^k+m be a compact semi-algebraic set defined by P ₁≥0,…,P _ℓ ≥0, where P _i ∈ℝ[X ₁,…,X _k ,Y ₁,…,Y _m ], and deg (P _i )≤2, 1≤i≤ℓ. Let π denote the standard projection from ℝ ^k+m onto ℝ ^m . We prove that for any q>0, the sum of the first q Betti numbers of π(S) is bounded by (k+m) ^{O(q ℓ)}. We also present an algorithm for computing the first q Betti numbers of π(S), whose complexity is . For fixed q and ℓ, both the bounds are polynomial in k+m. The author was supported in part by an NSF Career Award 0133597 and a Sloan Foundation Fellowship.     

Analysis of conducting-system frequency response data for an interfacial amorphous phase of copper-core oxide-shell nanocomposites

Complex electrical-conductivity experimental data sets for the interfacial amorphous phase in copper-core-copper-oxide-shell nanostructured composites have been analyzed using two Kohlrausch-related frequency response models recently developed for analysis of the dispersive electrical response of conductive materials. Such analysis has been carried out for both the precursor (herein referred to as the reference) glass as well as the glass in which the core-shell nanostructure was developed after suitable heat treatment. Complex nonlinear-least-squares data fitting at each temperature employed composite Kohlrausch models that included electrode effects. Because of the lack of sufficient high-frequency data, it was necessary to use fixed, rather than free, values of the shape parameter beta1 of the model. On the basis of topological considerations, its values were set at 13 and 23 for the reference glass and the core-shell structured glass, respectively. The activation energies of resistivity for the reference and the treated glasses were found to have values of about 2 and 0.4 eV, respectively, indicating two different mechanisms of electrical conduction. A blocking-electrode measurement on the reference glass indicated the presence of an electronic as well as an ionic component of the electrical conductivity, with the ionic part dominating at the temperatures for which the present analyses were carried out.     

Search for DeltaS = 2 nonleptonic hyperon decays

A sensitive search for the rare decays Omega(-)--> Lambdapi(-) and Xi(0)--> ppi(-) has been performed using data from the 1997 run of the HyperCP (Fermilab E871) experiment. Limits on other such processes do not exclude the possibility of observable rates for |DeltaS| = 2 nonleptonic hyperon decays, provided the decays occur through parity-odd operators. We obtain the branching-fraction limits B(Omega(-)-->Lambdapi(-)) < 2.9 x 10(-6) and B(Xi(0)--> ppi(-)) < 8.2 x 10(-6), both at 90% confidence level.     

Template based growth of nanoscaled films: a brief review

Growth of ultrathin films of metals and inorganic materials using various templates — both solid and liquid has been reviewed. Such nanoscaled films have been found to be effective in fabrication of devices and sensors. Use of crystal nanochannels of some inorganic compounds has been found to induce novel properties to the films grown within them. It is expected the latter approach will lead to the synthesis of materials with hitherto unknown properties.     

Bacterial adhesion on hybrid cationic nanoparticle-polymer brush surfaces: ionic strength tunes capture from monovalent to multivalent binding

This paper describes the creation of hybrid surfaces containing cationic nanoparticles and biocompatible PEG (polyethylene glycol) brushes that manipulate bacterial adhesion for potential diagnostic and implant applications. Here, ～10 nm cationically functionalized gold nanoparticles are immobilized randomly on negative silica surfaces at tightly controlled surface loadings, and the remaining areas are functionalized with a hydrated PEG brush, using a graft copolymer of poly-l-lysine and PEG (PLL-PEG), containing 2000 molecular weight PEG chains and roughly 30% functionalization of the PLL. The cationic nanoparticles attract the negative surfaces of suspended Staphylococcus aureus bacteria while the PEG brush exerts a steric repulsion. With the nanoparticle and PEG brush heights on the same lengthscale, variations in ionic strength are demonstrated to profoundly influence the capture of S. aureus on these surfaces. For bacteria captured from gentle flow, a crossover from multivalent to univalent binding is demonstrated as the Debye length is increased from 1 to 4 nm. In the univalent regime, 1 um diameter spherical bacteria are captured and held by single nanoparticles. In the multivalent regime, there is an adhesion threshold in the surface density of nanoparticles needed for bacterial capture. The paper also documents an interesting effect concerning the relaxations in the PLL-PEG brush itself. For brushy surfaces containing no nanoparticles, bacterial adhesion persists on newly formed brushes, but is nearly eliminated after these brushes relax, at constant mass in buffer for 12h. Thus brushy relaxations increase biocompatibility.     

Chemistry of metal-bound anion radicals. A family of mono- and bis(azopyridine) chelates of bivalent ruthenium

The reaction of the dihydride [RuII(H)2(CO)(PPh3)3], 3, with excess azo-2,2'-bipyridine (abp) in boiling dry benzene has afforded the diradical bischelate [RuII(abp.-)2(CO)(PPh3)], 4, and the hydridic monochelate monoradical [RuII(abp.-)(H)(CO)(PPh3)2], 5. A similar reaction between 3 and 2-(p-chlorophenylazo)pyridine (Clpap) did not yield a bischelate, but the hydridic monoradical [RuII(Clpap.-)(H)(CO)(PPh3)2], 6, has been isolated. Upon treatment of 4-6 with NH4PF6 in a wet dichloromethane-acetonitrile medium, the one-electron-oxidized salts 4+PF6-, 5+PF6-, and 6+PF6- are isolated, H+ being the oxidizing agent. The X-ray structures of 4+PF6-.CH2Cl2, 5+PF6-.H2O, and 6+PF6- have been determined. In the monoradical 4+ the azo N-N bond lengths in the two chelate rings are 1.284(6) and 1.336(6) A, showing that the radical electron is localized in the latter ring. The half-filled extended Hückel HOMO is indeed found to be so localized, and it has a large azo character. Complexes 4-6 display radical redox couples with E1/2 in the range -0.5 to +0.10 V vs SCE. The E1/2 values qualitatively correlate with corresponding vco values (1900-2000 cm-1). The monoradicals (S = 1/2) 4+, 5, and 6 uniformly display a strong EPR signal near g = 2.00. Metal-mediated magnetic interaction makes the EPR-silent diradical 4 strongly antiferromagnetic with J = -299 cm-1. Crystal data are as follows: (4+PF6-.CH2Cl2, C40H33Cl2F6N8-OP2Ru) monoclinic, space group P2(1)/c (no. 14), a = 14.174(6) A, b = 16.451(4) A, c = 18.381(4) A, beta = 98.00(3) degrees, Z = 4; (5+PF6-.H2O, C47H41F6N4O2P3Ru) monoclinic, space group P2(1)/n (no. 14), a = 9.433(2) A, b = 38.914(17) A, c = 13.084(3) A, beta = 103.47(2) degrees, Z = 4; (6+PF6-, C48H39ClF6N3OP3Ru) monoclinic, space group P2(1)/n (no. 14), a = 10.496(5) A, b = 22.389(8) A, c = 19.720(6) A, beta = 90.53(3) degrees, Z = 4.