Information Theories with Adversaries,Intrinsic Information,and Entanglement

There are aspects of privacy theory that are analogous to quantum theory. In particular one can define distillable key and key cost in parallel to distillable entanglement and entanglement cost. We present here classical privacy theory as a particular case of information theory with adversaries, where similar general laws hold as in entanglement theory. We place the result of Renner and Wolf—that intrinsic information is lower bound for key cost—into this general formalism. Then we show that the question of whether intrinsic information is equal to key cost is equivalent to the question of whether Alice and Bob can create a distribution product with Eve using I_M bits of secret key. We also propose a natural analogue of relative entropy of entanglement in privacy theory and show that it is equal to the intrinsic information. We also provide a formula analogous to the entanglement of formation for classical distributions. It is our pleasure to dedicate this paper to Asher Peres on the occasion of his seventieth birthday.     

Model-Independent Normalization Condition for Gamow Vectors

Two comments on the theory of Gamow states are presented. First, it is shown that Gamow states may be viewed as two resonating states which correspond to two different eigenproblems for the same real value of energy. Second, a universal normalization condition for all Gamow states is derived.     

On biharmonic maps and their generalizations

We give a new proof of regularity of biharmonic maps from four-dimensional domains into spheres, showing first that the biharmonic map system is equivalent to a set of bilinear identities in divergence form. The method of reverse Hölder inequalities is used next to prove continuity of solutions and higher integrability of their second order derivatives. As a byproduct, we also prove that a weak limit of biharmonic maps into a sphere is again biharmonic. The proof of regularity can be adapted to biharmonic maps on the Heisenberg group, and to other functionals leading to fourth order elliptic equations with critical nonlinearities in lower order derivatives.Received: 6 February 2003, Accepted: 12 March 2003, Published online: 16 May 2003Mathematics Subject Classification (2000): 35J60, 35H20Pawel Strzelecki: Current address (till September 2003): Mathematisches Institut der Universität Bonn, Beringstr. 1, 53115 Bonn, Germany (email: strzelec@math.uni-bonn.de). The author is partially supported by KBN grant no. 2-PO3A-028-22;he gratefully acknowledgesthe hospitality of his colleagues from Bonn,and the generosity of Humboldt Foundation.     

Ranking Beta Sheet Topologies with Applications to Protein Structure Prediction

One reason why ab initio protein structure predictors do not perform very well is their inability to reliably identify long-range interactions between amino acids. To achieve reliable long-range interactions, all potential pairings of β-strands (β-topologies) of a given protein are enumerated, including the native β-topology. Two very different β-topology scoring methods from the literature are then used to rank all potential β-topologies. This has not previously been attempted for any scoring method. The main result of this paper is a justification that one of the scoring methods, in particular, consistently top-ranks native β-topologies. Since the number of potential β-topologies grows exponentially with the number of β-strands, it is unrealistic to expect that all potential β-topologies can be enumerated for large proteins. The second result of this paper is an enumeration scheme of a subset of β-topologies. It is shown that native-consistent β-topologies often are among the top-ranked β-topologies of this subset. The presence of the native or native-consistent β-topologies in the subset of enumerated potential β-topologies relies heavily on the correct identification of β-strands. The third contribution of this paper is a method to deal with the inaccuracies of secondary structure predictors when enumerating potential β-topologies. The results reported in this paper are highly relevant for ab initio protein structure prediction methods based on decoy generation. They indicate that decoy generation can be heavily constrained using top-ranked β-topologies as they are very likely to contain native or native-consistent β-topologies.     

Synthesis and characterization of hyperbranched polyesters from glycerol‐based AB2 monomer

This article describes the synthesis of a new glycerol‐based AB₂ type monomer—ethyl{3‐[2‐hydroxy‐1‐(hydroxymethyl)ethoxy]propyl}thioacetate ( 4 ) and its application for the preparation of hyperbranched polyesters. The polycondensation of 4 has been performed over a wide range of catalysts and reaction conditions leading to polymers containing solely primary hydroxyl groups. The polycondensation progress has been monitored by means of ¹H NMR. The degree of branching of the polymers showed to be in the range of 0.5 ± 0.03. The obtained polyesters easily undergo hydrolysis or alcoholysis and may be of interest as recycled materials. © 2009 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 47: 3860–3868, 2009     

A note on wavelet density deconvolution for weakly dependent data

In this paper we investigate the performance of a linear wavelet-type deconvolution estimator for weakly dependent data. We show that the rates of convergence which are optimal in the case of i.i.d. data are also (almost) attained for strongly mixing observations, provided the mixing coefficients decay fast enough. The results are applied to a discretely observed continuous-time stochastic volatility model.     

Liquid scintillation counters calibration stability over long timescales

Liquid scintillation spectrometry is widely used for the analysis of alpha and beta emitting radionuclides. Robust calibration of liquid scintillation (LS) spectrometers is fundamental to accurate LS measurement but at the same time is time consuming and costly, particularly if a wide range of radionuclides are analysed by the laboratory. The frequency of the calibration varies in different laboratories and is based on many practical and operational factors. This work summarizes the observations regarding variations in 1220 Quantulus spectrometers efficiency calibrations performed annually using various radionuclides: ³H ⁶³Ni, ⁵⁵Fe, ³⁶Cl, ⁴⁵Ca, ¹⁴⁷Pm, ²⁴¹Pu, ⁹⁹Tc for a period of 9 years and discusses the implication to calibration frequency.

     

Controlled sulfur oxygenation of the ruthenium dithiolate (4,7-bis-(2'-methyl-2'-mercaptopropyl)-1-thia-4,7-diazacyclononane)RuPPh(3) under limiting O(2) conditions yields thiolato/sulfinato, sulfenato/sulfinato, and bis-sulfinato derivatives

The ruthenium(II) dithiolate complex (bmmp-TASN)RuPPh(3) (1) reacts with O(2) under limiting conditions to yield isolable sulfur oxygenated derivatives as a function of reaction time. With this approach, a family of sulfur-oxygenates has been prepared and isolated without the need for O-atom transfer agents or column chromatography. Addition of 5 equiv of O(2) to 1 yields the thiolato/sulfinato complex (bmmp-O(2)-TASN)RuPPh(3) (2) in 70% yield within 5 min. Increasing the reaction time to 12 h yields the sulfenato/sulfinato derivative (bmmp-O(3)-TASN)RuPPh(3) (3) in 82% yield. Longer reaction times and/or additional O(2) exposure yield the bis-sulfinato complex (bmmp-O(4)-TASN)RuPPh(3) (4). All products remain in the Ru(II) oxidation state under the conditions employed. Stoichiometric hydrolysis of acetonitrile to acetamide by 2 and 3 is observed in mixed acetonitrile, methanol, PIPES buffer (pH = 7.0) mixtures. The Ru(III)/(II) reduction potential of -0.85 V (versus ferrocenium/ferrocene) for 1 shifts to -0.39 and -0.26 V for 2 and 3, respectively, because of the decreased donor ability of sulfur upon oxygenation. X-ray diffraction studies reveal a decrease in Ru-S bond distances upon oxygenation by 0.045(1) and 0.158(1) ? for the sulfenato and sulfinato donors, respectively. Conversely, sulfur-oxygenation increases the Ru-P bond distance by 0.061(1) ? from 1 to 2 and an additional 0.027(1) ? from 2 to 3. Density functional theory investigations using the BP86 and B3LYP functionals with a LANL2DZ basis set for Ru and the 6-31G(d) basis set for all other atoms reveal a direct correlation between the oxygenation level and the Ru-P distance with an increase of 0.031 ? per O-atom.     

One-pot highly enantioselective catalytic Mannich-type reactions between aldehydes and stable α-amido sulfones: asymmetric synthesis of β-amino aldehydes and β-amino acids

A highly enantioselective catalytic route to carbamate- and benzoate-protected β-amino aldehydes and β-amino acids is presented. The amino acid-catalyzed one-pot asymmetric reaction between unmodified aldehydes and α-amido sulfones gives the corresponding β-amino compounds with up to 95:5 dr and 97->99% ee.