An elementary proof of an equivalence theorem relevant in the theory of optimization

The authors give an elementary proof of an equivalence theorem of analysis which is often used in optimization theory. The theorem asserts that certain conditions are equivalent to weak convergence in L 1 . One is the Dunford-Pettis condition concerning absolute integrability. Two others are expressed in terms of Nagumo functions, and can be thought of as growth properties. The original proofs of the various parts of the theorem are scattered in different and specialized mathematical publications. The authors feel it useful to present here a straightforward proof of the various parts in terms of standard Lebesgue integration theory.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/45221/1/10957_2004_Article_BF00938425.pd

Einstein's fluctuation formula. A historical overview

A historical overview is given on the basic results which appeared by the year 1926 concerning Einstein's fluctuation formula of black-body radiation, in the context of light-quanta and wave-particle duality. On the basis of the original publications (from Planck's derivation of the black-body spectrum and Einstein's introduction of the photons up to the results of Born, Heisenberg and Jordan on the quantization of a continuum) a comparative study is presented on the first line of thoughts that led to the concept of quanta. The nature of the particle-like fluctuations and the wave-like fluctuations are analysed by using several approaches. With the help of the classical probability theory, it is shown that the infinite divisibility of the Bose distribution leads to the new concept of classical poissonian photo-multiplets or to the binary photo-multiplets of fermionic character. As an application, Einstein's fluctuation formula is derived as a sum of fermion type fluctuations of the binary photo-multiplets.Comment: 34 page

Engineering tyrosine-based electron flow pathways in proteins: The case of aplysia myoglobin

Tyrosine residues can act as redox cofactors that provide an electron transfer ("hole-hopping") route that enhances the rate of ferryl heme iron reduction by externally added reductants, for example, ascorbate. Aplysia fasciata myoglobin, having no naturally occurring tyrosines but 15 phenylalanines that can be selectively mutated to tyrosine residues, provides an ideal protein with which to study such through-protein electron transfer pathways and ways to manipulate them. Two surface exposed phenylalanines that are close to the heme have been mutated to tyrosines (F42Y, F98Y). In both of these, the rate of ferryl heme reduction increased by up to 3 orders of magnitude. This result cannot be explained in terms of distance or redox potential change between donor and acceptor but indicates that tyrosines, by virtue of their ability to form radicals, act as redox cofactors in a new pathway. The mechanism is discussed in terms of the Marcus theory and the specific protonation/deprotonation states of the oxoferryl iron and tyrosine. Tyrosine radicals have been observed and quantified by EPR spectroscopy in both mutants, consistent with the proposed mechanism. The location of each radical is unambiguous and allows us to validate theoretical methods that assign radical location on the basis of EPR hyperfine structure. Mutation to tyrosine decreases the lipid peroxidase activity of this myoglobin in the presence of low concentrations of reductant, and the possibility of decreasing the intrinsic toxicity of hemoglobin by introduction of these pathways is discussed. © 2012 American Chemical Society

Wigner's Dynamical Transition State Theory in Phase Space: Classical and Quantum

A quantum version of transition state theory based on a quantum normal form (QNF) expansion about a saddle-centre-...-centre equilibrium point is presented. A general algorithm is provided which allows one to explictly compute QNF to any desired order. This leads to an efficient procedure to compute quantum reaction rates and the associated Gamov-Siegert resonances. In the classical limit the QNF reduces to the classical normal form which leads to the recently developed phase space realisation of Wigner's transition state theory. It is shown that the phase space structures that govern the classical reaction d ynamicsform a skeleton for the quantum scattering and resonance wavefunctions which can also be computed from the QNF. Several examples are worked out explicitly to illustrate the efficiency of the procedure presented.Comment: 132 pages, 31 figures, corrected version, Nonlinearity, 21 (2008) R1-R11

Deindustrialization in cities of the global south

Recent research by economists has shown that deindustrialization is more severe in Sub-Saharan Africa and Latin America than it ever was in the Organisation for Economic Co-operation and Development (OECD). Nevertheless, most research on deindustrialization is focused on the former centres of Fordist manufacturing in the industrial heartlands of the North Atlantic. In short, there is a mismatch between where deindustrialization is researched and where it is occurring, and the objective of this paper is to shift the geographical focus of research on deindustrialization to the Global South. Case studies from Argentina, India, Tanzania and Turkey demonstrate the variegated nature of deindustrialization beyond the North Atlantic. In the process, it is demonstrated that cities in the Global South can inform wider theoretical discussions on the impacts of deindustrialization at the urban scale

Why Are Clinicians Not Embracing the Results from Pivotal Clinical Trials in Severe Sepsis? A Bayesian Analysis

BACKGROUND: Five pivotal clinical trials (Intensive Insulin Therapy; Recombinant Human Activated Protein C [rhAPC]; Low-Tidal Volume; Low-Dose Steroid; Early Goal-Directed Therapy [EGDT]) demonstrated mortality reduction in patients with severe sepsis and expert guidelines have recommended them to clinical practice. Yet, the adoption of these therapies remains low among clinicians. OBJECTIVES: We selected these five trials and asked: Question 1--What is the current probability that the new therapy is not better than the standard of care in my patient with severe sepsis? Question 2--What is the current probability of reducing the relative risk of death (RRR) of my patient with severe sepsis by meaningful clinical thresholds (RRR >15%; >20%; >25%)? METHODS: Bayesian methodologies were applied to this study. Odds ratio (OR) was considered for Question 1, and RRR was used for Question 2. We constructed prior distributions (enthusiastic; mild, moderate, and severe skeptic) based on various effective sample sizes of other relevant clinical trials (unfavorable evidence). Posterior distributions were calculated by combining the prior distributions and the data from pivotal trials (favorable evidence). MAIN FINDINGS: Answer 1--The analysis based on mild skeptic prior shows beneficial results with the Intensive Insulin, rhAPC, and Low-Tidal Volume trials, but not with the Low-Dose Steroid and EGDT trials. All trials' results become unacceptable by the analyses using moderate or severe skeptic priors. Answer 2--If we aim for a RRR>15%, the mild skeptic analysis shows that the current probability of reducing death by this clinical threshold is 88% for the Intensive Insulin, 62-65% for the Low-Tidal Volume, rhAPC, EGDT trials, and 17% for the Low-Dose Steroid trial. The moderate and severe skeptic analyses show no clinically meaningful reduction in the risk of death for all trials. If we aim for a RRR >20% or >25%, all probabilities of benefits become lower independent of the degree of skepticism. CONCLUSIONS: Our clinical threshold analysis offers a new bedside tool to be directly applied to the care of patients with severe sepsis. Our results demonstrate that the strength of evidence (statistical and clinical) is weak for all trials, particularly for the Low-Dose Steroid and EGDT trials. It is essential to replicate the results of each of these five clinical trials in confirmatory studies if we want to provide patient care based on scientifically sound evidence