Quasinormal resonances of near-extremal Kerr–Newman black holes

We study analytically   the fundamental resonances of near-extremal, slowly rotating Kerr–Newman black holes. We find a simple analytic expression for these black-hole quasinormal frequencies in terms of the black-hole physical parameters: ω=mΩ−2iπTBH(l+1+n)$\omega =m\Omega -2i\pi T_{\mathrm{BH}}(l+1+n)$, where TBH$T_{\mathrm{BH}}$ and Ω are the temperature and angular velocity of the black hole. The mode parameters l and m   are the spheroidal harmonic index and the azimuthal harmonic index of a co-rotating mode, respectively. This analytical formula is valid in the regime ℑω?ℜω?M⁻¹$\Im \omega ?\Re \omega ?M^{\mathrm{-1}}$, where M is the black-hole mass.     

Return of the quantum cosmic censor

The influential theorems of Hawking and Penrose demonstrate that spacetime singularities are ubiquitous features of general relativity, Einstein's theory of gravity. The utility of classical general relativity in describing gravitational phenomena is maintained by the cosmic censorship principle. This conjecture, whose validity is still one of the most important open questions in general relativity, asserts that the undesirable spacetime singularities are always hidden inside of black holes. In this Letter we reanalyze extreme situations which have been considered as counterexamples to the cosmic censorship hypothesis. In particular, we consider the absorption of fermion particles by a spinning black hole. Ignoring quantum effects may lead one to conclude that an incident fermion wave may over spin the black hole, thereby exposing its inner singularity to distant observers. However, we show that when quantum effects are properly taken into account, the integrity of the black-hole event horizon is irrefutable. This observation suggests that the cosmic censorship principle is intrinsically a quantum phenomena.     

Communication Efficient Algorithms for Bounding and Approximating the Empirical Entropy in Distributed Systems

The empirical entropy is a key statistical measure of data frequency vectors, enabling one to estimate how diverse the data are. From the computational point of view, it is important to quickly compute, approximate, or bound the entropy. In a distributed system, the representative (“global”) frequency vector is the average of the “local” frequency vectors, each residing in a distinct node. Typically, the trivial solution of aggregating the local vectors and computing their average incurs a huge communication overhead. Hence, the challenge is to approximate, or bound, the entropy of the global vector, while reducing communication overhead. In this paper, we develop algorithms which achieve this goal.     

On closures of orbits and arithmetic of quaternions

ForG=PGL₂(ℚ _p )×PGL₂ ℚ we study the closures of orbits under the maximal split Cartan subgroup ofG in homogeneous spacesΓ\G. We show that if a closure of an orbit contains a closed orbit then the orbit is either dense or closed. We show the relation of this to divisibility properties of integral quaternions and other lattices. Sponsored in part by the Edmund Landau Center for Research in Mathematical Analysis supported by the Minerva Foundation (Germany). Research at MSRI supported by NSF grant DMS8505550.     

Chemical Synthesis of Proteins with Non‐Strategically Placed Cysteines Using Selenazolidine and Selective Deselenization

Although native chemical ligation has enabled the synthesis of hundreds of proteins, not all proteins are accessible through typical ligation conditions. The challenging protein, 125‐residue human phosphohistidine phosphatase 1 (PHPT1), has three cysteines near the C‐terminus, which are not strategically placed for ligation. Herein, we report the first sequential native chemical ligation/deselenization reaction. PHPT1 was prepared from three unprotected peptide segments using two ligation reactions at cysteine and alanine junctions. Selenazolidine was utilized as a masked precursor for N‐terminal selenocysteine in the middle segment, and, following ligation, deselenization provided the native alanine residue. This approach was used to synthesize both the wild‐type PHPT1 and an analogue in which the active‐site histidine was substituted with the unnatural and isosteric amino acid β‐thienyl‐l ‐alanine. The activity of both proteins was studied and compared, providing insights into the enzyme active site.     

PNA versus DNA: effects of structural fluctuations on electronic structure and hole-transport mechanisms

The effects of structural fluctuations on charge transfer in double-stranded DNA and peptide nucleic acid (PNA) are investigated. A palindromic sequence with two guanine bases that play the roles of hole donor and acceptor, separated by a bridge of two adenine bases, was analyzed using combined molecular dynamics (MD) and quantum-chemical methods. Surprisingly, electronic structure calculations on individual MD snapshots show significant frontier orbital electronic population on the bridge in approximately 10% of the structures. Electron-density delocalization to the bridge is found to be gated by fluctuations of the covalent conjugated bond structure of the aromatic rings of the nucleic bases. It is concluded, therefore, that both thermal hopping and superexchange should contribute significantly to charge transfer even in short DNA/PNA fragments. PNA is found to be more flexible than DNA, and this flexibility is predicted to produce larger rates of charge transfer.     

On weakly bounded empirical processes

Let F be a class of functions on a probability space (Ω, μ) and let X ₁,...,X _k be independent random variables distributed according to μ. We establish an upper bound that holds with high probability on for every t > 0, and that depends on a natural geometric parameter associated with F. We use this result to analyze the supremum of empirical processes of the form for p > 1 using the geometry of F. We also present some geometric applications of this approach, based on properties of the random operator 〈X _i , ·〉e _i , where are sampled according to an isotropic, log-concave measure on .     

Molecular design of porphyrin-based nonlinear optical materials

Nonlinear optical chromophores containing (porphyrinato)Zn(II), proquinoid, and (terpyridyl)metal(II) building blocks were optimized in a library containing approximately 10(6) structures using the linear combination of atomic potentials (LCAP) methodology. We report here the library design and molecular property optimizations. Two basic structural types of large beta(0) chromophores were examined: linear and T-shaped motifs. These T-shaped geometries suggest a promising NLO chromophoric architecture for experimental investigation and further support the value of performing LCAP searches in large chemical spaces.     

A subgaussian embedding theorem

We prove a subgaussian extension of a Gaussian result on embedding subsets of a Euclidean space into normed spaces. Using the concentration of a random subgaussian vector around its mean we obtain an isomorphic (rather than almost isometric) result, under an additional cotype assumption on the normed space considered. Partially supported by an Australian Research Council Discovery grant. This author holds the Canada Research Chair in Geometric Analysis.