The impact of intermediaries on a negotiation: an approach from game theory

Central European Journal of Operations Research - Standard approaches to model interaction networks are limited in their capacity to describe the nuances of real communication. We present a game...     

Inclusion-exclusion: Exact and approximate

It is often required to find the probability of the union of givenn eventsA ₁ ,...,A _n . The answer is provided, of course, by the inclusion-exclusion formula: Pr(A _i )= _i – _i<j Pr(A _i A _j )±.... Unfortunately, this formula has exponentially many terms, and only rarely does one manage to carry out the exact calculation. From a computational point of view, finding the probability of the union is an intractable, #P-hard problem, even in very restricted cases. This state of affairs makes it reasonable to seek approximate solutions that are computationally feasible. Attempts to find such approximate solutions have a long history starting already with Boole [1]. A recent step in this direction was taken by Linial and Nisan [4] who sought approximations to the probability of the union, given the probabilities of allj-wise intersections of the events forj=1,...k. The developed a method to approximate Pr(A _i ), from the above data with an additive error of exp . In the present article we develop an expression that can be computed in polynomial time, that, given the sums _|S|=j Pr( _iS A _i ) forj=1,...k, approximates Pr(A _i ) with an additive error of exp . This error is optimal, up to the logarithmic factor implicit in the notation.The problem of enumerating satisfying assignments of a boolean formula in DNF formF=v _l ^m C _i is an instance of the general problem that had been extensively studied [7]. HereA _i is the set of assignments that satisfyC _i , and Pr( _iS A _i )=a _S /2ⁿ where _iS C _i is satisfied bya _S assignments. Judging from the general results, it is hard to expect a decent approximation ofF's number of satisfying assignments, without knowledge of the numbersa _S for, say, all cardinalities . Quite surprisingly, already the numbersa _S over |S|log(n+1)uniquely determine the number of satisfying assignments for F.We point out a connection between our work and the edge-reconstruction conjecture. Finally we discuss other special instances of the problem, e.g., computing permanents of 0,1 matrices, evaluating chromatic polynomials of graphs and for families of events whose VC dimension is bounded.Work supported in part by a grant of the Binational Israel-US Science Foundation.Work supported in part by a grant of the Binational Israel-US Science Foundation and by the Israel Science Foundation.     

Electronic and vibrational second-order nonlinear optical properties of protein secondary structural motifs

A perturbation theory approach was developed for predicting the vibrational and electronic second-order nonlinear optical (NLO) polarizabilities of materials and macromolecules comprised of many coupled chromophores, with an emphasis on common protein secondary structural motifs. The polarization-dependent NLO properties of electronic and vibrational transitions in assemblies of amide chromophores comprising the polypeptide backbones of proteins were found to be accurately recovered in quantum chemical calculations by treating the coupling between adjacent oscillators perturbatively. A novel diagrammatic approach was developed to provide an intuitive visual means of interpreting the results of the perturbation theory calculations. Using this approach, the chiral and achiral polarization-dependent electronic SHG, isotropic SFG, and vibrational SFG nonlinear optical activities of protein structures were predicted and interpreted within the context of simple orientational models.     

Evidence for a monomeric structure of nonribosomal Peptide synthetases

Nonribosomal peptide synthetases (NRPS) are multimodular biocatalysts that bacteria and fungi use to assemble many complex peptides with broad biological activities. The same modular enzymatic assembly line principles are found in fatty acid synthases (FAS), polyketide synthases (PKS), and most recently in hybrid NRPS/PKS multienzymes. FAS as well as PKS are known to function as homodimeric enzyme complexes, raising the question of whether NRPS may also act as homodimers. To test this hypothesis, biophysical methods (size exclusion chromatography, analytical equilibrium ultracentrifugation, and chemical crosslinking) and biochemical methods (two-affinity-tag-system and complementation studies with enzymes being inactivated in different catalytic domains) were applied to NRPS subunits from the gramicidin S (GrsA-ATE), tyrocidine (TycB(1)-CAT and TycB(2-3)-AT.CATE), and enterobactin (EntF-CATTe) biosynthetic systems. These methods had revealed the dimeric structure of FAS and PKS previously, but all three NRPS systems investigated are functionally active as monomers.     

Tributyl phosphate degradation by immobilized cells of aCitrobacter sp.

Tributyl phosphate (TBP), a plasticizer and solvent, is used in nuclear fuel reprocessing, generating TBP wastes laden with residual uranium. ACitrobacter sp. accumulated heavy metals via a phosphohydrolase(s) that precipitated metals with inorganic phosphate liberated from an organic phosphate “donor” molecule (TBP). Mutant analysis suggested that TBP hydrolysis was not attributable to a previously documented acid phosphatase (monoesterase). Purified monoesterase had little activity against phospho di- and triesters, had no requirement for Mg²⁺ or Mn²⁺, and was EDTA-resistant. Conversely, TBP cleavage by immobilized cells was enhanced by Mg²⁺, and ininhibited by Mn²⁺ and EDTA. A separate phosphotri/diesterase was implicated.     

Polymers for catalytic cation radical chemistry

Cation radical polymers which have cation radical functions at up to 5% of the poly(styrene) monomer sites have been prepared, and their effectiveness in catalyzing the cation radical Diels-Alder reaction is demonstrated.     

Immobilisation of electroactive macrocyclic complexes within titania films

The 4-carboxyphenyl-appended macrocyclic ligand trans-6,13-dimethyl-6-((4-carboxybenzyl)amino)-1,4,8,11-tetraazacyclotetradecane-6-amine (HL10) has been synthesised and complexed with Co(III). The mononuclear complexes [Co(HL10)(CN)]2+ and [CoL10(OH)]+ have been prepared and the crystal structures of their perchlorate salts are presented, where the ligand is bound in a pentadentate mode in each case while the 4-carboxybenzyl-substituted pendent amine remains free from the metal. The cyano-bridged dinuclear complex [CoL10-mu-NC-Fe(CN)5]2- was also prepared and chemisorbed on titania-coated ITO conducting glass. The adsorbed complex is electrochemically active and cyclic voltammetry of the modified ITO working electrode in both water and MeCN solution was undertaken with simultaneous optical spectroscopy. This experiment demonstrates that reversible electrochemical oxidation of the Fe(II) centre is coupled with rapid changes in the optical absorbance of the film.     

Practical and highly selective oxazolidinethione-based asymmetric acetate aldol reactions with aliphatic aldehydes

[reaction: see text] The utility of a valine-derived oxazolidinethione for auxiliary-based asymmetric acetate aldol reactions is reported. Titanium(IV) chloride, along with (-)-sparteine and N-methylpyrrolidinone, is employed for enolization. Subsequent aldol reaction with aliphatic aldehydes occurs with high diastereoselectivity (from 92:8 to 99:1 dr).     

Thermal transformations in phosphorites

The thermal transformations in phosphorites during flash calcination were investigated by FT-IR spectroscopy, X-ray diffraction and chemical analyses. During flash calcination changes occur, both in the composition of the phosphorite and in the crystallochemistry of the fluor-carbonate-apatite (francolite). The former changes include: decomposition of a great part of the calcite in the rock and oxidation of organic matter. The latter changes include: partial removal of the structural carbonate; partial relocation of the remaining carbonate ions in the apatite structure; a new arrangement of hydroxyl groups and fluorine on the hexagonal axis; partial condensation of the orthophosphate groups and increase of crystallite sizes. Isomorphous substitution of PO ₄ ^–3 in apatite by SO ₄ ^–2 and SiO ₄ ^–4 may take place.Dedicated to Prof. Menachem Steinberg on the occasion of his 65th birthdayThe financial support from Rotem-Amfert-Negev Phosphate Co. is gratefully acknowledged. We thank Dr. B. Pregerson of the Rotem-Amfert-Negev for supplying samples