Proof of the Double Bubble Conjecture in R^n

The least-area hypersurface enclosing and separating two given volumes in R^n is the standard double bubble.Comment: 20 pages, 22 figure

Pole Assignment for a Vibrating System with Aerodynamic Effect

This paper deals with a pole assignment problem by single-input state feedback control arising from a one-dimensional vibrating system with aerodynamic effect. On the practical side, we derive explicit formulae for the required controlling force terms, which can reassign part of the spectrum to the desired values while leaving the remaining spectrum unchanged. On the mathematical side, unlike the classical Sturm–Liouville problem, our eigenvalue problem is associated with a cubic pencil with unbounded operators as coefficients and has many interesting new features, one of which is that a new controllability condition appears. This condition together with the known controllability condition in the quadratic case are necessary and sufficient. This sheds light on the adjustment of the model parameters. We also analyze the spectrum of the associated noncompact operator and in particular show that the discrete spectrums of controlled and uncontrolled systems lie outside a closed interval on the negative real axis

On the geometry of mixed states and the Fisher information tensor

In this paper, we will review the co-adjoint orbit formulation of finite dimensional quantum mechanics, and in this framework, we will interpret the notion of quantum Fisher information index (and metric). Following previous work of part of the authors, who introduced the definition of Fisher information tensor, we will show how its antisymmetric part is the pullback of the natural Kostant-Kirillov-Souriau symplectic form along some natural diffeomorphism. In order to do this, we will need to understand the symmetric logarithmic derivative as a proper 1-form, settling the issues about its very definition and explicit computation. Moreover, the fibration of co-adjoint orbits, seen as spaces of mixed states, is also discussed.Comment: 27 pages; Accepted Manuscrip

mRNA Display Selection of a High-Affinity, Modification-Specific Phospho-IκBα-Binding Fibronectin

The complexity of the human proteome is greatly expanded by post-translational modifications. New tools capable of recognizing these modifications in a sequence-specific fashion provide a route to purify these modified proteins, to alter protein trafficking, and to visualize signal transduction in real time. Here, we have evolved novel, modification-specific ligands that target phosphorylated IκBα. To do this, we employed mRNA display-based in vitro selection using a 30-trillion-member protein library based on the fibronectin type III domain. The selection yielded one fibronectin molecule, 10C17C25, that binds a phospho-IκBα peptide with Kd = 18 nM and is over 1000-fold specific compared to the nonphosphorylated peptide. 10C17C25 specifically recognizes endogenous phosphorylated IκBα from mammalian cell extract and stabilizes phospho-IκBα in vivo. We also incorporated 10C17C25 into a FRET indicator that detects IκB kinase (IKK) activity in vitro, demonstrating the utility of selecting designed adaptors for kinase activity sensors

Puzzles in BB physics

I discuss some puzzles observed in exclusive $B$ meson decays, concentrating on the large difference between the direct CP asymmetries in the $B^0\to \pi^\mp K^\pm$ and $B^\pm\to \pi^0 K^\pm$ modes, the large $B^0\to\pi^0\pi^0$ branching ratio, and the large deviation of the mixing-induced CP asymmetries in the $b\to sq\bar q$ penguins from those in the $b\to c\bar c s$ trees.Comment: 6 pages, 1 figure, talk presented at the 9th Workshop on High Energy Physics Phenomenology, Bhubaneswar, Orissa, India, Jan. 3-14, 2006; reference adde

Efficient and seamless DNA recombineering using a thymidylate synthase A selection system in Escherichia coli

λ-Red system-based recombinogenic engineering is a powerful new method to engineer DNA without the need for restriction enzymes or ligases. Here, we report the use of a single selectable marker to enhance the usefulness of this approach. The strategy is to utilize the thymidylate synthase A (thyA) gene, which encodes an enzyme involved in the synthesis of thymidine 5′-triphosphate, for both positive and negative selection. With this approach, we successfully created point mutations in plasmid and bacterial artificial chromosome (BAC) DNA containing the mouse Col10a1 gene. The results showed that the thyA selection system is highly efficient and accurate, giving an average of >90% selection efficiency. This selection system produces DNA that is free from permanent integration of unwanted sequences, thus allowing unlimited rounds of modifications if required

mRNA Display Selection of a High-Affinity, Modification-Specific Phospho-IκBα-Binding Fibronectin

The complexity of the human proteome is greatly expanded by post-translational modifications. New tools capable of recognizing these modifications in a sequence-specific fashion provide a route to purify these modified proteins, to alter protein trafficking, and to visualize signal transduction in real time. Here, we have evolved novel, modification-specific ligands that target phosphorylated IκBα. To do this, we employed mRNA display-based in vitro selection using a 30-trillion-member protein library based on the fibronectin type III domain. The selection yielded one fibronectin molecule, 10C17C25, that binds a phospho-IκBα peptide with Kd = 18 nM and is over 1000-fold specific compared to the nonphosphorylated peptide. 10C17C25 specifically recognizes endogenous phosphorylated IκBα from mammalian cell extract and stabilizes phospho-IκBα in vivo. We also incorporated 10C17C25 into a FRET indicator that detects IκB kinase (IKK) activity in vitro, demonstrating the utility of selecting designed adaptors for kinase activity sensors

Exotic smooth structures and symplectic forms on closed manifolds

We give a short proof of the (known) result that there are no Kaehler structures on exotic tori. This yields a negative solution to a problem posed by Benson and Gordon. W discuss the symplectic version of the problem and analyze results which yield an evidence for the conjecture that there are no symplectic structures on exotic tori.Comment: AMSLaTeX, 16 pages, a new version. A survey of the symplectic version of the problem is adde