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

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

\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

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

Identification of prostate-enriched proteins by in-depth proteomic analyses of expressed prostatic secretions in urine

Urinary expressed prostatic secretion or \u201cEPS-urine\u201d is proximal tissue fluid that is collected after a digital rectal exam (DRE). EPS-urine is a rich source of prostatederived proteins that can be used for biomarker discovery for prostate cancer (PCa) and other prostatic diseases. We previously conducted a comprehensive proteome analysis of direct expressed prostatic secretions (EPS). In the current study, we defined the proteome of EPS-urine employing Multidimensional Protein Identification Technology (MudPIT) and providing a comprehensive catalogue of this body fluid for future biomarker studies. We identified 1022 unique proteins in a heterogeneous cohort of 11 EPS-urines derived from biopsy negative noncancer diagnoses with some benign prostatic diseases (BPH) and lowgrade PCa, representative of secreted prostate and immune system-derived proteins in a urine background. We further applied MudPIT-based proteomics to generate and compare the differential proteome from a subset of pooled urines (pre-DRE) and EPS-urines (post- DRE) from noncancer and PCa patients. The direct proteomic comparison of these highly controlled patient sample pools enabled us to define a list of prostate-enriched proteins detectable in EPS-urine and distinguishable from a complex urine protein background. A combinatorial analysis of both proteomics data sets and systematic integration with publicly available proteomics data of related body fluids, human tissue transcriptomic data, and immunohistochemistry images from the Human Protein Atlas database allowed us to demarcate a robust panel of 49 prostate-derived proteins in EPS-urine. Finally, we validated the expression of seven of these proteins using Western blotting, supporting the likelihood that they originate from the prostate. The definition of these prostatic proteins in EPS-urine samples provides a reference for future investigations for prostatic-disease biomarker studies

Relative spins and excitation energies of superdeformed bands in 190Hg: Further evidence for octupole vibration

An experiment using the Eurogam Phase II gamma-ray spectrometer confirms the existence of an excited superdeformed (SD) band in 190Hg and its very unusual decay into the lowest SD band over 3-4 transitions. The energies and dipole character of the transitions linking the two SD bands have been firmly established. Comparisons with RPA calculations indicate that the excited SD band can be interpreted as an octupole-vibrational structure.Comment: 12 pages, latex, 4 figures available via WWW at http://www.phy.anl.gov/bgo/bc/hg190_nucl_ex.htm