Diversity of phage-displayed libraries of peptides during panning and amplification

The amplification of phage-displayed libraries is an essential step in the selection of ligands from these libraries. The amplification of libraries, however, decreases their diversity and limits the number of binding clones that a screen can identify. While this decrease might not be a problem for screens against targets with a single binding site (e.g., proteins), it can severely hinder the identification of useful ligands for targets with multiple binding sites (e.g., cells). This review aims to characterize the loss in the diversity of libraries during amplification. Analysis of the peptide sequences obtained in several hundred screens of peptide libraries shows explicitly that there is a significant decrease in library diversity that occurs during the amplification of phage in bacteria. This loss during amplification is not unique to specific libraries: it is observed in many of the phage display systems we have surveyed. The loss in library diversity originates from competition among phage clones in a common pool of bacteria. Based on growth data from the literature and models of phage growth, we show that this competition originates from growth rate differences of only a few percent for different phage clones. We summarize the findings using a simple two-dimensional "phage phase diagram", which describes how the collapse of libraries, due to panning and amplification, leads to the identification of only a subset of the available ligands. This review also highlights techniques that allow elimination of amplification-induced losses of diversity, and how these techniques can be used to improve phage-display selection and enable the identification of novel ligands.     

Buckling analysis of stringer-stiffened laminated cylindrical shells with nonuniform eccentricity

In this study, the influence of nonuniformity of eccentricity of stringers on the general axial buckling load of stiffened laminated cylindrical shells with simply supported end conditions is investigated. The critical loads are calculated using Love’s First-order Shear Deformation Theory and solved using the Rayleigh-Ritz procedure. The effects of the shell length-to-radius ratio, shell thickness-to-radius ratio, number of stringers, and stringers depth-to-width ratio on the buckling load of nonuniformly eccentric shells, are examined. The research demonstrates that an appropriate nonuniform distribution of eccentricity of stringers leads the buckling load to increase significantly.     

Students’ ways of understanding a proof

We present a model for describing the growth of students’ understandings when reading a proof. The model is composed of two main paths. One is focused on becoming aware of the deductive structure of the proof, in other words, understanding the proof at a semantic level. Generalization, abstraction, and formalization are the most important transitions in this path. The other path focuses on the surface-level form of the proof, and the use of symbolic representations. At the end of this path, students understand how and why symbolic computations formally establish a claim, at a syntactic level. We make distinctions between states in the model and illustrate them with examples from early secondary students’ mathematical activity. We then apply the model to one student’s developing understanding in order to show how the model works in practice. We close with some suggestions for further research.     

A Langevin equation for the rates of currency exchange based on the Markov analysis

We propose a method for analyzing the data for the rates of exchange of various currencies versus the U.S. dollar. The method analyzes the return time series of the data as a Markov process, and develops an effective equation which reconstructs it. We find that the Markov time scale, i.e., the time scale over which the data are Markov-correlated, is one day for the majority of the daily exchange rates that we analyze. We derive an effective Langevin equation to describe the fluctuations in the rates. The equation contains two quantities, D⁽¹⁾ and D⁽²⁾, representing the drift and diffusion coefficients, respectively. We demonstrate how the two coefficients are estimated directly from the data, without using any assumptions or models for the underlying stochastic time series that represent the daily rates of exchange of various currencies versus the U.S. dollar.     

Interactive effects of local smoothing window size and fundamental frequency on shimmer calculation

Slow amplitude modulation of human voice was approximated by a sinusoidal wave. The theoretical effects of smoothing window size, F₀, and modulation frequency on window amplitude average as well as calculated shimmer were mathematically derived. Subsequently, the theoretical predictions were tested using idealized and real voice signals from normal speakers. The theoretical and experimental results suggest that shimmer (when calculated using a smoothing window) is a function of window duration and modulation frequency. Window duration when defined as a constant number of pitch periods varies from speaker to speaker depending on their F₀. It may not be desirable to use local smoothing windows with a constant number of cycles for shimmer computation, especially if voices with known low-frequency amplitude modulations but notably different fundamental frequencies are compared.     

Highly Efficient,Four Component,One-pot Synthesis of Tetrasubstituted Imidazoles Using a Catalytic Amount of FeCl<Subscript>3</Subscript> · 6H<Subscript>2</Subscript>O

Summary. An efficient and improved procedure for the synthesis of tetrasubstituted imidazoles by FeCl₃ · 6H₂O catalyzed four-component one-pot synthesis in refluxing ethanol is described.     

Bounding the performance of tandem queues with finite buffer spaces

We consider a queueing system with three single servers in tandem with two intermediate buffer storages of finite capacity. The processing times are exponentially distributed and the first server has unlimited number of customers in front of it. Using a negative dependence property between the number of customers at the first and second buffer storages we show that a popular form of decomposition approach applied to this model, indeed, provides a lower bound for its performance. The approach used here to establish the bound is new and could be extended to establish bounds for other types of tandem queues with finite buffer spaces.     

Preparation of Co3O4 nanoparticles by nonhydrolytic thermolysis of [Co(Pht)(H2O)]n polymers

Benzenedicarboxylate complexes, especially phthalate ones, can be significant precursors for the preparation of nano-sized metal and metal oxides. The injection of organic surfactants such as oleic acid (OA) and triphenylphosphine into molecular precursors has yielded samples with size control, narrow size distributions and crystallinity of individual nanocrystals. Fourier transform infrared and X-ray photoelectron spectroscopy revealed that the OA molecules were adsorbed on the ferromagnetic nanoparticles by chemisorption. The temperature-dependent magnetization curve in zero-field-cooled and field-cooled exhibit weak ferromagnetism of the Co₃O₄ nanoparticles. At 300 K the remanent magnetization is 0.02 emu/g, the coercive field is 441 Oe and the magnetization at saturation is 1.05 emu/g.     

Tunable optical filter based on Sagnac phase-shift using single optical ring resonator

In this paper, a single optical ring resonator connected to a Sagnac loop is used to demonstrate theoretically a novel narrow band optical filter response that is based on Sagnac phase-shift Δφ. The given filter structure permits the Sagnac rotation to control the filter response. It is shown that by changing the Sagnac rotation rate, we can tune the filter response for desired bandwidths. To increase the wavelength selectivity of the filter, the Sagnac phase-shift should be as small as possible that is limited by the loop length. For Δφ=0.1 rad, the obtained FWHM is 2.63 MHz for tuning loop length of 2 m. The simulation response agrees fairly with the recently reported experimental result.