Detection of residue contacts in a protein folding intermediate

Protein folding can be described in terms of the development of specific contacts between residues as a highly disordered polypeptide chain converts into the native state. Here we describe an NMR based strategy designed to detect such contacts by observation of nuclear Overhauser effects (NOEs). Experiments with α-lactalbumin reveal the existence of extensive NOEs between aromatic and aliphatic protons in the archetypal molten globule formed by this protein at low pH. Analysis of their time development provides direct evidence for near-native compactness of this state. Through a rapid refolding procedure the NOE intensity can be transferred efficiently into the resolved and assigned spectrum of the native state. This demonstrates the viability of using this approach to map out time-averaged interactions between residues in a partially folded protein.

Well posedness of an integrodifferential kinetic model of Fokker-Planck type for angiogenesis.

Tumor induced angiogenesis processes including the effect of stochastic motion and branching of blood vessels can be described coupling a (nonlocal in time) integrodifferential kinetic equation of Fokker–Planck type with a diffusion equation for the tumor induced ingiogenic factor. The chemotactic force field depends on the flux of blood vessels through the angiogenic factor. We develop an existence and uniqueness theory for this system under natural assumptions on the initial data. The proof combines the construction of fundamental solutions for associated linearized problems with comparison principles, sharp estimates of the velocity integrals and compactness results for this type of kinetic and parabolic operators

Lipschitz compact operators

We introduce the notion of Lipschitz compact (weakly compact, finite-rank, approximable) operators from a pointed metric space X into a Banach space E. We prove that every strongly Lipschitz p-nuclear operator is Lipschitz compact and every strongly Lipschitz p-integral operator is Lipschitz weakly compact. A theory of Lipschitz compact (weakly compact, finite-rank) operators which closely parallels the theory for linear operators is developed. In terms of the Lipschitz transpose map of a Lipschitz operator, we state Lipschitz versions of Schauder type theorems on the (weak) compactness of the adjoint of a (weakly) compact linear operator.

Weighted composition operators on the predual and dual Banach spaces of Beurling algebras on Z

Let vv be a weight sequence on ZZ and let ψ,φψ,φ be complex-valued functions on ZZ such that φ(Z)⊂Zφ(Z)⊂Z. In this paper we study the boundedness, compactness and weak compactness of weighted composition operators Cψ,φCψ,φ on predual Banach spaces c0(Z,1/v)c0(Z,1/v) and dual Banach spaces ℓ∞(Z,1/v)ℓ∞(Z,1/v) of Beurling algebras ℓ1(Z,v)ℓ1(Z,v).

Primal Attainment in Convex Infinite Optimization Duality

This article provides results guarateeing that the optimal value of a given convex infinite optimization problem and its corresponding surrogate Lagrangian dual coincide and the primal optimal value is attainable. The conditions ensuring converse strong Lagrangian (in short, minsup) duality involve the weakly-inf-(locally) compactness of suitable functions and the linearity or relative closedness of some sets depending on the data. Applications are given to different areas of convex optimization, including an extension of the Clark-Duffin Theorem for ordinary convex programs.

Global behavior of the Douglas–Rachford method for a nonconvex feasibility problem

In recent times the Douglas–Rachford algorithm has been observed empirically to solve a variety of nonconvex feasibility problems including those of a combinatorial nature. For many of these problems current theory is not sufficient to explain this observed success and is mainly concerned with questions of local convergence. In this paper we analyze global behavior of the method for finding a point in the intersection of a half-space and a potentially non-convex set which is assumed to satisfy a well-quasi-ordering property or a property weaker than compactness. In particular, the special case in which the second set is finite is covered by our framework and provides a prototypical setting for combinatorial optimization problems.

Should energy efficiency be traded off for other product attributes? : an analysis of air-conditioner regulation in Japan

This paper examines the functioning of energy efficiency standards and labeling policies for air conditioners in Japan. The results of our empirical analysis suggest that consumers respond more to label information, which benchmarks the energy efficiency performance of each product to a pre-specified target, than to direct performance measures. This finding provides justification for the setting, and regular updating, of target standards as well as their use in calculating relative performance measures. We also find, through graphical analysis, that air conditioner manufacturers face a tradeoff between energy efficiency and product compactness when they develop their products. This tradeoff, combined with the semi-regular upward revision of minimum energy efficiency standards, has led to the growth in indoor unit size of air conditioners in recent years. In the face of this phenomenon, regulatory rules were revised so that manufacturers could adhere to less stringent standards if the indoor unit size of their product remains below a certain size. Our demand estimates provide no evidence that larger indoor unit size causes disutility to consumers. It is therefore possible that the regulatory change was not warranted from a consumer welfare point of view.

Partial regularity of minimizers of a functional involving forms and maps

We discuss the partial regularity of minimizers of energy functionals such as (1)/(p)integral(Omega)[sigma(u)dA(p) + (1)/(2)delu(2p)]dx, where u is a map from a domain Omega is an element of R-n into the m-dimensional unit sphere of Rm+1 and A is a differential one-form in Omega.

Positive solutions of a Neumann problem with competing critical nonlinearities

We present existence results for a Neumann problem involving critical Sobolev nonlinearities both on the right hand side of the equation and at the boundary condition.. Positive solutions are obtained through constrained minimization on the Nehari manifold. Our approach is based on the concentration 'compactness principle of P. L. Lions and M. Struwe.

Conservation planning with irreplaceability: does the method matter?

A number of systematic conservation planning tools are available to aid in making land use decisions. Given the increasing worldwide use and application of reserve design tools, including measures of site irreplaceability, it is essential that methodological differences and their potential effect on conservation planning outcomes are understood. We compared the irreplaceability of sites for protecting ecosystems within the Brigalow Belt Bioregion, Queensland, Australia, using two alternative reserve system design tools, Marxan and C-Plan. We set Marxan to generate multiple reserve systems that met targets with minimal area; the first scenario ignored spatial objectives, while the second selected compact groups of areas. Marxan calculates the irreplaceability of each site as the proportion of solutions in which it occurs for each of these set scenarios. In contrast, C-Plan uses a statistical estimate of irreplaceability as the likelihood that each site is needed in all combinations of sites that satisfy the targets. We found that sites containing rare ecosystems are almost always irreplaceable regardless of the method. Importantly, Marxan and C-Plan gave similar outcomes when spatial objectives were ignored. Marxan with a compactness objective defined twice as much area as irreplaceable, including many sites with relatively common ecosystems. However, targets for all ecosystems were met using a similar amount of area in C-Plan and Marxan, even with compactness. The importance of differences in the outcomes of using the two methods will depend on the question being addressed; in general, the use of two or more complementary tools is beneficial.

Achieving completeness: from constructive set theory to large cardinals

This thesis is an exploration of several completeness phenomena, both in the constructive and the classical settings. After some introductory chapters in the first part of the thesis where we outline the background used later on, the constructive part contains a categorical formulation of several constructive completeness theorems available in the literature, but presented here in an unified framework. We develop them within a constructive reverse mathematical viewpoint, highlighting the metatheory used in each case and the strength of the corresponding completeness theorems. The classical part of the thesis focuses on infinitary intuitionistic propositional and predicate logic. We consider a propositional axiomatic system with a special distributivity rule that is enough to prove a completeness theorem, and we introduce weakly compact cardinals as the adequate metatheoretical assumption for this development. Finally, we return to the categorical formulation focusing this time on infinitary first-order intuitionistic logic. We propose a first-order system with a special rule, transfinite transitivity, that embodies both distributivity as well as a form of dependent choice, and study the extent to which completeness theorems can be established. We prove completeness using a weakly compact cardinal, and, like in the constructive part, we study disjunction-free fragments as well. The assumption of weak compactness is shown to be essential for the completeness theorems to hold.

In-fiber microchannel device filled with a carbon nanotube dispersion for passive mode-lock lasing

Fueled by their high third-order nonlinearity and nonlinear saturable absorption, carbon nanotubes (CNT) are expected to become an integral part of next-generation photonic devices such as all-optical switches and passive mode-locked lasers. However, in order to fulfill this expectation it is necessary to identify a suitable platform that allows the efficient use of the optical properties of CNT. In this paper, we propose and implement a novel device consisting of an optofluidic device filled with a dispersion of CNT. By fabricating a microchannel through the core of a conventional fiber and filling it with a homogeneous solution of CNTs on Dimethylformamide (DMF), a compact, all-fiber saturable absorber is realized. The fabrication of the micro-fluidic channel is a two-step process that involves femtosecond laser micro-fabrication and chemical etching of the laser-modified regions. All-fiber high-energy, passive mode-locked lasing is demonstrated with an output power of 13.5 dBm. The key characteristics of the device are compactness and robustness against optical, mechanical and thermal damage.

Influence of downstream processing on the breakage of whey protein precipitates

Whey proteins may be fractionated by isoelectric precipitation followed by centrifugal recovery of the precipitate phase. Transport and processing of protein precipitates may alter the precipitate particle properties, which may affect how they behave in subsequent processes. For example, the transport of precipitate solution through pumps, pipes and valves and into a centrifugal separator may cause changes in particle size and density, which may affect the performance of the separator. This work investigates the effect of fluid flow intensity, flow geometry and exposure time on the breakage of whey protein precipitates: Computational fluid dynamics (CFD) was used to quantify the flow intensity in different geometries. Flow geometry can have a critical impact on particle breakage. Sharp geometrical transitions induce large increases in turbulence that can result in substantial particle breakage. As protein precipitate particles break, they tend to form denser more compact structures. The reduction in particle size and increase in compaction is due to breakage. This makes the particles become more resistant to further breakage as particle compactness increases. The effect of flow intensity on particle breakage is coupled to exposure time, with greater exposure time producing more breakage. However, it is expected that the particles will attain an equilibrium particle size and density after prolonged exposure in a constant flow field where no further breakage will occur with exposure time. © 2005 Institution of Chemical Engineers.

Some Comments on Q-Irresolute and Quasi-Irresolute Functions

The aim of this paper is to continue the study of θ-irresolute and quasi-irresolute functions as well as to give an example of a function which is θ-irresolute but neither quasi-irresolute nor an R-map and thus give an answer to a question posed by Ganster, Noiri and Reilly. We prove that RS-compactness is preserved under open, quasi-irresolute surjections.