Making proofs without Modus Ponens: An introduction to the combinatorics and complexity of cut elimination

This paper is intended to provide an introduction to cut elimination which is accessible to a broad mathematical audience. Gentzen's cut elimination theorem is not as well known as it deserves to be, and it is tied to a lot of interesting mathematical structure. In particular we try to indicate some dynamical and combinatorial aspects of cut elimination, as well as its connections to complexity theory. We discuss two concrete examples where one can see the structure of short proofs with cuts, one concerning feasible numbers and the other concerning "bounded mean oscillation" from real analysis

Some topics concerning homeomorphic parameterizations

In this survey, we consider several questions pertaining to homeomorphisms, including criteria for their existence in certain circumstances, and obstructions to their existence

Coherent photodissociation reactions: Observation by a novel picosecond polarization technique

In this communication, we wish to report on a novel picosecond polarization method for measuring the degree of rotational coherence that is preserved in photodissociation reactions. The systems studied here are jet-cooled van der Waals molecules; stilbene [4-6] bound [5] to He or Ne with a 1:1 composition.[7

War and Remembrance: Walter Place and Ulysses S. Grant

In 1862-1863, General Ulysses S. Grant conducted military operations in the state of Mississippi, culminating in the siege and eventual surrender of the city of Vicksburg. During part of this time, Grant’s wife, Julia, took up residence at Walter Place in Holly Springs, Mississippi. In the years after the Civil War, Walter Place became known not just as an antebellum home, but also as a place with a strong connection to Grant and his family during the Civil War. When Mike and Jorja Lynn purchased the property, they began collecting Grant-related items for display in the home, including modern and historic decorative artifacts, cartes-de-visite, and ephemera. In 2013, Jorja Lynn donated this collection to the Ulysses S. Grant Presidential Library at Mississippi State University Libraries for display and preservation purposes. This article will address the historical background of the collection, the preservation and access plans in place, and the complexities of Civil War memory that create a more nuanced portrait of how the Civil War is represented in the South

Uniqueness and examples of compact toric Sasaki-Einstein metrics

In [11] it was proved that, given a compact toric Sasaki manifold of positive basic first Chern class and trivial first Chern class of the contact bundle, one can find a deformed Sasaki structure on which a Sasaki-Einstein metric exists. In the present paper we first prove the uniqueness of such Einstein metrics on compact toric Sasaki manifolds modulo the action of the identity component of the automorphism group for the transverse holomorphic structure, and secondly remark that the result of [11] implies the existence of compatible Einstein metrics on all compact Sasaki manifolds obtained from the toric diagrams with any height, or equivalently on all compact toric Sasaki manifolds whose cones have flat canonical bundle. We further show that there exists an infinite family of inequivalent toric Sasaki-Einstein metrics on $S^5 \sharp k(S^2 \times S^3)$ for each positive integer $k$.Comment: Statements of the results are modifie

Modified two-potential approach to tunneling problems

One-body quantum tunneling to continuum is treated via the two-potential approach, dividing the tunneling potential into external and internal parts. We show that corrections to this approach can be minimized by taking the separation radius inside the interval determined by simple expressions. The resulting two-potential approach reproduces the resonance energy and its width, both for narrow and wide resonances. We also demonstrate that, without losing its accuracy, the two-potential approach can be modified to a form resembling the R-matrix theory, yet without any uncertainties of the latter related to the choice of the matching radius.Comment: 7 two-column pages, 3 figures, extra-explanation added, Phys. Rev. A, in pres

Null sets of harmonic measure on NTA domains: Lipschitz approximation revisited

We show the David-Jerison construction of big pieces of Lipschitz graphs inside a corkscrew domain does not require its surface measure be upper Ahlfors regular. Thus we can study absolute continuity of harmonic measure and surface measure on NTA domains of locally finite perimeter using Lipschitz approximations. A partial analogue of the F. and M. Riesz Theorem for simply connected planar domains is obtained for NTA domains in space. As a consequence every Wolff snowflake has infinite surface measure.Comment: 22 pages, 6 figure

\epsilon-regularity for systems involving non-local, antisymmetric operators

We prove an epsilon-regularity theorem for critical and super-critical systems with a non-local antisymmetric operator on the right-hand side. These systems contain as special cases, Euler-Lagrange equations of conformally invariant variational functionals as Rivi\`ere treated them, and also Euler-Lagrange equations of fractional harmonic maps introduced by Da Lio-Rivi\`ere. In particular, the arguments presented here give new and uniform proofs of the regularity results by Rivi\`ere, Rivi\`ere-Struwe, Da-Lio-Rivi\`ere, and also the integrability results by Sharp-Topping and Sharp, not discriminating between the classical local, and the non-local situations

Physical and in silico approaches identify DNA-PK in a Tax DNA-damage response interactome

<p>Abstract</p> <p>Background</p> <p>We have initiated an effort to exhaustively map interactions between HTLV-1 Tax and host cellular proteins. The resulting Tax interactome will have significant utility toward defining new and understanding known activities of this important viral protein. In addition, the completion of a full Tax interactome will also help shed light upon the functional consequences of these myriad Tax activities. The physical mapping process involved the affinity isolation of Tax complexes followed by sequence identification using tandem mass spectrometry. To date we have mapped 250 cellular components within this interactome. Here we present our approach to prioritizing these interactions via an <it>in silico </it>culling process.</p> <p>Results</p> <p>We first constructed an <it>in silico </it>Tax interactome comprised of 46 literature-confirmed protein-protein interactions. This number was then reduced to four Tax-interactions suspected to play a role in DNA damage response (Rad51, TOP1, Chk2, 53BP1). The first-neighbor and second-neighbor interactions of these four proteins were assembled from available human protein interaction databases. Through an analysis of betweenness and closeness centrality measures, and numbers of interactions, we ranked proteins in the first neighborhood. When this rank list was compared to the list of physical Tax-binding proteins, DNA-PK was the highest ranked protein common to both lists. An overlapping clustering of the Tax-specific second-neighborhood protein network showed DNA-PK to be one of three bridge proteins that link multiple clusters in the DNA damage response network.</p> <p>Conclusion</p> <p>The interaction of Tax with DNA-PK represents an important biological paradigm as suggested via consensus findings <it>in vivo </it>and <it>in silico</it>. We present this methodology as an approach to discovery and as a means of validating components of a consensus Tax interactome.</p