A new proof for Rockafellar's characterization of maximal monotone operators

We provide a new and short proof for Rockafellar's characterization of maximal monotone operators in reflexive Banach spaces based on S. Fitzpatrick's function and a technique used by R. S. Burachik and B. F. Svaiter for proving their result on the representation of a maximal monotone operator by convex functions.

     

Field theory of mesoscopic fluctuations in superconductor/normal-metal systems

The thermodynamic and transport properties of normal disordered conductors are strongly influenced by the proximity of a superconductor. A cooperation between mesoscopic coherence and Andreev scattering of particles from the superconductor generates new types of interference phenomena. A field theoretic approach is introduced which is capable of exploring both the averaged properties and mesoscopic fluctuations of superconductor/normal-metal systems. As an example the method is applied to the study of the level statistics of a SNS junction. Pis’ma Zh. éksp. Teor. Fiz. 67, No. 1, 21–26 (10 January 1998) Published in English in the original Russian journal. Edited by Steve Torstveit.     

The coupled-cluster method with a multiconfiguration reference state

The coupled-cluster approach to obtaining the bond-state wave functions of many-electron systems is extended, with a set of physically reasonable approximations, to admit a multiconfiguration reference state. This extension permits electronic structure calculations to be performed on correlated closed- or open-shell systems with potentially uniform precision for all molecular geometries. Explicit coupled cluster working equations are derived using a multiconfiguration reference state for the case in which the so-called cluster operator is approximated by its one- and two-particle components. The evaluation of the requisite matrix elements is facilitated by use of the unitary group generators which have recently received wide attention and use in the quantum chemistry community.     

Fractal landscapes in biological systems: long-range correlations in DNA and interbeat heart intervals

Here we discuss recent advances in applying ideas of fractals and disordered systems to two topics of biological interest, both topics having common the appearance of scale-free phenomena, i.e., correlations that have no characteristic length scale, typically exhibited by physical systems near a critical point and dynamical systems far from equilibrium. (i) DNA nucleotide sequences have traditionally been analyzed using models which incorporate the possibility of short-range nucleotide correlations. We found, instead, a remarkably long-range power law correlation. We found such long-range correlations in intron-containing genes and in non-transcribed regulatory DNA sequences as well as intragenomic DNA, but not in cDNA sequences or intron-less genes. We also found that the myosin heavy chain family gene evolution increases the fractal complexity of the DNA landscapes, consistent with the intron-late hypothesis of gene evolution. (ii) The healthy heartbeat is traditionally thought to be regulated according to the classical principle of homeostasis, whereby physiologic systems operate to reduce variability and achieve an equilibrium-like state. We found, however, that under normal conditions, beat-to-beat fluctuations in heart rate display long-range power law correlations.     

Probability and expectation inequalities

Summary This paper introduces a mathematical framework within which a wide variety of known and new inequalities can be viewed from a common perspective. Probability and expectation inequalities of the following types are considered: (a)P(ZA) P(ZA) for some class of setsA, (b)k(Z)k(Z) for some class of functionsk, and (c)l(Z)k(Z) for some class of pairs of functionsl andk. It is shown, sometimes using explicit constructions ofZ andZ, that, in several cases, (a) (b) (c); included here are cases of normal and elliptically contoured distributions. A case where (a) (b) (c) is studied and is expressed in terms ofn monotone functions for (some of) which integral representations are obtained. Also, necessary and sufficient conditions for (c) are given.Research supported by the Air Force Office of Scientific Research under Grants AFOSR-75-2796 and AFOSR-80-0080Research supported by the National Science Foundation under Grants MCS78-01240 and MCS81-00748     

Flow goes forward and cells step backward: endothelial migration

Systemic and pulmonary circulations constitute a complex organ that serves multiple important biological functions. Consequently, any pathological processing affecting the vasculature can have profound systemic ramifications. Endothelial and smooth muscle are the two principal cell types composing blood vessels. Critically, endothelial proliferation and migration are central to the formation and expansion of the vasculature both during embryonic development and in adult tissues. Endothelial populations are quite heterogeneous and are both vasculature type- and organ-specific. There are profound molecular, functional, and phenotypic differences between arterial, venular and capillary endothelial cells and endothelial cells in different organs. Given this endothelial cell population diversity, it has been challenging to determine the origin of endothelial cells responsible for the angiogenic expansion of the vasculature. Recent technical advances, such as precise cell fate mapping, time-lapse imaging, genome editing, and single-cell RNA sequencing, have shed new light on the role of venous endothelial cells in angiogenesis under both normal and pathological conditions. Emerging data indicate that venous endothelial cells are unique in their ability to serve as the primary source of endothelial cellular mass during both developmental and pathological angiogenesis. Here, we review recent studies that have improved our understanding of angiogenesis and suggest an updated model of this process.Subject terms: Cell lineage, Chemotaxis     

A dissipative transformation with a trivial tail-algebra

Summary In [1], an example was given of a measure-preserving dissipative transformation T in a -finite measure space (X, , ), such that T is conservative in the measure space (X, , ) where . Here we shall show that for this transformation we actually have R ={ØX}[].     

Measuring the Michel parameter ξ'

Unlike the majority of Michel parameters which are consistent with the Standard Model V-A interaction, the experimental value of ξ″(=0.65±0.36) [1] is poorly known. Our experiment will measure the longitudinal polarization, P _L , of positrons emitted from the decay of polarized muons. The value of P _L , equal to unity in the Standard Model, will decrease for high energy positrons emitted antiparallel to the muon spin if the combination of Michel parameters ξ″/ξξ′ − 1 deviates from the Standard Model value of zero. This revised version was published online in August 2006 with corrections to the Cover Date.