Phenol-derived chiral phosphine–phosphite ligands in the rhodium-catalyzed enantioselective hydrogenation of functionalized olefins

A set of 15 chiral Taddol- and Binol-based phosphine–phosphite ligands were tested in the Rh-catalyzed asymmetric hydrogenation of three olefins, methyl 2-hydroxymethyl-acrylate, 1-phenylvinyl acetate, and α-methyl cinnamic acid. The best enantioselectivities (up to 92% ee) were observed in the hydrogenation of methyl 2-hydroxymethyl-acrylate using Binol-based ligands. As previously observed in other applications of this class of modular chiral ligand in enantioselective catalysis, the stereochemical outcome of the reactions greatly depended on the substituents at the ligand aryl backbone in the ortho-position to the chiral phosphite unit.     

Thermal activation of polyethylene@silica particles: towards ceramic surfactants

The fabrication of “switch-on” amphiphilic submicrometer hybrid particles of cross-linked polyethylene (XPE)@silica is described. The synthesis of the particles is based on the simultaneous cross-linking of PE and the polycondensation of tetraethoxysilane in hot, surfactant-stabilized O/W micelles. Thermal activation of the particles results in particles with amphiphilic behavior. It is proposed that the thermal activation triggers partial phase-separation which pushes some of the PE chain to the surface, in a heterogeneous way. By this, on each particle two halves can be identified which differ in their degree of hydrophobicity (“Janus” structure), thus giving rise to the surfactant activity. The particles were intensively characterized before and after the thermal activation and their amphiphilic behavior was demonstrated. By the approach described in the paper it is in principle possible to design a library of functionalities out of a single surface active agent species. This was demonstrated by the thermal activation of functionalized composite particles of dyes@XPE@silica and of the triple hybrid Ag@XPE@silica. Full material characterization is provided, including SEM, TGA, surface area analysis, antibacterial tests and zeta potential measurements.     

Solution of the Propeller Conjecture in \mathbb R ^3

It is shown that every measurable partition $\{A_1,\ldots , A_k\}$ { A 1 , … , A k } of $\mathbb R ^3$ R 3 satisfies 1 $$\begin{aligned} \sum _{i=1}^k\big \Vert \int _{A_i} x\mathrm{{e}}^{-\frac{1}{2}\Vert x\Vert _2^2}\mathrm{{d}}x\big \Vert _2^2\leqslant 9\pi ^2. \end{aligned}$$ ∑ i = 1 k ‖ ∫ A i x e - 1 2 ‖ x ‖ 2 2 d x ‖ 2 2 ? 9 π 2 . Let $\{P_1,P_2,P_3\}$ { P 1 , P 2 , P 3 } be the partition of $\mathbb R ^2$ R 2 into $120^{\circ }$ 120 ° sectors centered at the origin. The bound (1) is sharp, with equality holding if $A_i=P_i\times \mathbb R $ A i = P i × R for $i\in \{1,2,3\}$ i ∈ { 1 , 2 , 3 } and $A_i=\emptyset $ A i = ? for $i\in \{4,\ldots ,k\}$ i ∈ { 4 , … , k } . This settles positively the $3$ 3 -dimensional Propeller Conjecture of Khot and Naor [(Mathematika 55(1-2):129–165, 2009 (FOCS 2008)]. The proof of (1) reduces the problem to a finite set of numerical inequalities which are then verified with full rigor in a computer-assisted fashion. The main consequence (and motivation) of (1) is complexity-theoretic: the unique games hardness threshold of the kernel clustering problem with $4\times 4$ 4 × 4 centered and spherical hypothesis matrix equals $\frac{2\pi }{3}$ 2 π 3 .     

Engineering Aqueous Fiber Assembly into Silk‐Elastin‐Like Protein Polymers

Self‐assembled peptide/protein nanofibers are valuable 1D building blocks for creating complex structures with designed properties and functions. It is reported that the self‐assembly of silk‐elastin‐like protein polymers into nanofibers or globular aggregates in aqueous solutions can be modulated by tuning the temperature of the protein solutions, the size of the silk blocks, and the charge of the elastin blocks. A core‐sheath model is proposed for nanofiber formation, with the silk blocks in the cores and the hydrated elastin blocks in the sheaths. The folding of the silk blocks into stable cores—affected by the size of the silk blocks and the charge of the elastin blocks—plays a critical role in the assembly of silk‐elastin nanofibers. Furthermore, enhanced hydrophobic interactions between the elastin blocks at elevated temperatures greatly influence the nanoscale features of silk‐elastin nanofibers.

     

The bond-algebraic approach to dualities

An algebraic theory of dualities is developed based on the notion of bond algebras. It deals with classical and quantum dualities in a unified fashion explaining the precise connection between quantum dualities and the low temperature (strong-coupling)/high temperature (weak-coupling) dualities of classical statistical mechanics (or (Euclidean) path integrals). Its range of applications includes discrete lattice, continuum field and gauge theories. Dualities are revealed to be local, structure-preserving mappings between model-specific bond algebras that can be implemented as unitary transformations, or partial isometries if gauge symmetries are involved. This characterization permits us to search systematically for dualities and self-dualities in quantum models of arbitrary system size, dimensionality and complexity, and any classical model admitting a transfer matrix or operator representation. In particular, special dualities such as exact dimensional reduction, emergent and gauge-reducing dualities that solve gauge constraints can be easily understood in terms of mappings of bond algebras. As a new example, we show that the ?₂ Higgs model is dual to the extended toric code model in any number of dimensions. Non-local transformations such as dual variables and Jordan–Wigner dictionaries are algorithmically derived from the local mappings of bond algebras. This permits us to establish a precise connection between quantum dual and classical disorder variables. Our bond-algebraic approach goes beyond the standard approach to classical dualities, and could help resolve the long-standing problem of obtaining duality transformations for lattice non-Abelian models. As an illustration, we present new dualities in any spatial dimension for the quantum Heisenberg model. Finally, we discuss various applications including location of phase boundaries, spectral behavior and, notably, we show how bond-algebraic dualities help constrain and realize fermionization in an arbitrary number of spatial dimensions.     

Ultrametric subsets with large Hausdorff dimension

It is shown that for every ε∈(0,1), every compact metric space (X,d) has a compact subset S?X that embeds into an ultrametric space with distortion O(1/ε), and $$\dim_H(S)\geqslant (1-\varepsilon)\dim_H(X),$$ where dim _H (?) denotes Hausdorff dimension. The above O(1/ε) distortion estimate is shown to be sharp via a construction based on sequences of expander graphs.     

Eigen‐frequencies in thin elastic 3‐D domains and Reissner–Mindlin plate models

The eigen‐frequencies of elastic three‐dimensional thin plates are addressed and compared to the eigen‐frequencies of two‐dimensional Reissner–Mindlin plate models obtained by dimension reduction. The qualitative mathematical analysis is supported by quantitative numerical data obtained by the p‐version finite element method. The mathematical analysis establishes an asymptotic expansion for the eigen‐frequencies in power series of the thickness parameter. Such results are new for orthotropic materials and for the Reissner–Mindlin model. The 3‐D and R–M asymptotics have a common first term but differ in their second terms. Numerical experiments for clamped plates show that for isotropic materials and relatively thin plates the Reissner–Mindlin eigen‐frequencies provide a good approximation to the three‐dimensional eigen‐frequencies. However, for some anisotropic materials this is no longer the case, and relative errors of the order of 30 per cent are obtained even for relatively thin plates. Moreover, we showed that no shear correction factor is known to be optimal in the sense that it provides the best approximation of the R–M eigen‐frequencies to their 3‐D counterparts uniformly (for all relevant thicknesses range). Copyright © 2002 John Wiley & Sons, Ltd.     

Bit commitment using pseudorandomness

We show how a pseudorandom generator can provide a bit-commitment protocol. We also analyze the number of bits communicated when parties commit to many bits simultaneously, and show that the assumption of the existence of pseudorandom generators suffices to assure amortized O(1) bits of communication per bit commitment.Part of this work was done while the author was at the University of California at Berkeley. This research was supported by NSF Grant CCR 88-13632.     

On the rate of convergence in the entropic central limit theorem

We study the rate at which entropy is produced by linear combinations of independent random variables which satisfy a spectral gap condition.Mathematics Subjects Classification (2000):94A17; 60F05Supported in part by the EU Grant HPMT-CT-2000-00037, The Minkowski center for Geometry and the Israel Science Foundation.Supported in part by NSF Grant DMS-9796221.Supported in part by EPSRC Grant GR/R37210.Supported in part by the BSF, Clore Foundation and EU Grant HPMT-CT-2000-00037.     

Non-Cooperative Multicast and Facility Location Games

We consider a multicast game with selfish non- cooperative players. There is a special source node and each player is interested in connecting to the source by making a routing decision that minimizes its payment. The mutual influence of the players is determined by a cost sharing mechanism, which in our case evenly splits the cost of an edge among the players using it. We consider two different models: an integral model, where each player connects to the source by choosing a single path, and a fractional model, where a player is allowed to split the flow it receives from the source between several paths. In both models we explore the overhead incurred in network cost due to the selfish behavior of the users, as well as the computational complexity of finding a Nash equilibrium. The existence of a Nash equilibrium for the integral model was previously established by the means of a potential function. We prove that finding a Nash equilibrium that minimizes the potential function is NP-hard. We focus on the price of anarchy of a Nash equilibrium resulting from the best-response dynamics of a game course, where the players join the game sequentially. For a game with in players, we establish an upper bound of O(radicnlog² n) on the price of anarchy, and a lower bound of Omega(log n/log log n). For the fractional model, we prove the existence of a Nash equilibrium via a potential function and give a polynomial time algorithm for computing an equilibrium that minimizes the potential function. Finally, we consider a weighted extension of the multicast game, and prove that in the fractional model, the game always has a Nash equilibrium.