Controlling soliton refraction in optical lattices

We show in the framework of the 1D nonlinear Schrödinger equation that the value of the refraction angle of a fundamental soliton beam passing through an optical lattice can be controlled by adjusting either the shape of an individual waveguide or the relative positions of the waveguides. In the case of the shallow refractive index modulation, we develop a general approach for the calculation of the refraction angle change. The shape of a single waveguide crucially affects the refraction direction due to the appearance of a structural form factor in the expression for the density of emitted waves. For a lattice of scatterers, wave-soliton interference inside the lattice leads to the appearance of an additional geometric form factor. As a result, the soliton refraction is more pronounced for the disordered lattices than for the periodic ones.

Anderson localization in synthetic photonic lattices

We experimentally demonstrate Anderson localization for optical pulses in time domain, using a photonic mesh lattice implemented with coupled optical fiber loops. We also discuss interplay of photonic band-gaps and disorder in such lattices. © OSA 2015.

Nonlinear refraction in optical lattices induced by the wave-soliton interference

In the framework of 1D Nonlinear Shrödinger Equation (NSE) we demonstrate how one can control the refractive angle of a fundamental soliton beam passing through an optical lattice, by adjusting either the shape of an individual waveguide or the relative positions of waveguides. Even for a single scatterer its shape has a nontrivial effect on the refraction direction. In the case of shallow modulation we provide an analytical description based of the effect on the soliton perturbation theory. When one considers a lattice of scatterers, there emanates an additional form factor in the radiation density (RD) of emitted waves referring to the wave-soliton beating and interference inside the lattice. We concentrate on the results for two cases: periodic lattice and disordered lattice of scattering shapes. © 2011 IEEE.

Anderson localization of light in synthetic photonic lattices

We make an comprehensive experimental and theoretical study of an effect of localization of light in photonic lattices realized in time domain with random optical potential. We show that localization occurs in whole range of disorder strength in full agreement with Anderson localization in 1D model. The disorder influence on modes structure is also discussed.

Surface waves in mesh synthetic photonic lattices

Eigenmodes and dispersion curves in different configurations of synthetic photonic lattices are studied numerically. Eigenmodes localized on borders between areas with different optical potential are found. Stability of these eigenmodes against potential disturbances of different type is studied.

Constructing eigenmode excitation spectrum in synthetic photonic lattices using optical heterodyning

A method based on optical heterodyning is proposed for measuring relative optical phases of pulses circulating in a synthetic photonic lattices. The knowledge of the phases can be further used for qualitative reconstruction of an eigenmode excitation spectrum in the synthetic photonic lattice.

Temporal solitonic crystals and non-Hermitian informational lattices

Clusters of temporal optical solitons—stable self-localized light pulses preserving their form during propagation—exhibit properties characteristic of that encountered in crystals. Here, we introduce the concept of temporal solitonic information crystals formed by the lattices of optical pulses with variable phases. The proposed general idea offers new approaches to optical coherent transmission technology and can be generalized to dispersion-managed and dissipative solitons as well as scaled to a variety of physical platforms from fiber optics to silicon chips. We discuss the key properties of such dynamic temporal crystals that mathematically correspond to non-Hermitian lattices and examine the types of collective mode instabilities determining the lifetime of the soliton train. This transfer of techniques and concepts from solid state physics to information theory promises a new outlook on information storage and transmission.

Equilibrium properties of disordered spin models with two-scale interactions

Methods for understanding classical disordered spin systems with interactions conforming to some idealized graphical structure are well developed. The equilibrium properties of the Sherrington-Kirkpatrick model, which has a densely connected structure, have become well understood. Many features generalize to sparse Erdös- Rényi graph structures above the percolation threshold and to Bethe lattices when appropriate boundary conditions apply. In this paper, we consider spin states subject to a combination of sparse strong interactions with weak dense interactions, which we term a composite model. The equilibrium properties are examined through the replica method, with exact analysis of the high-temperature paramagnetic, spin-glass, and ferromagnetic phases by perturbative schemes. We present results of replica symmetric variational approximations, where perturbative approaches fail at lower temperature. Results demonstrate re-entrant behaviors from spin glass to ferromagnetic phases as temperature is lowered, including transitions from replica symmetry broken to replica symmetric phases. The nature of high-temperature transitions is found to be sensitive to the connectivity profile in the sparse subgraph, with regular connectivity a discontinuous transition from the paramagnetic to ferromagnetic phases is apparent.

Evaluation of the sonically induced narrowing of nuclear magnetic resonance spectra of solids

The Nuclear Magnetic Resonance (NMR) spectra of liquids contain a wealth of quantitative information that may be derived, for instance, from chemical shifts and spin-spin couplings. The available information depends on the incoherent rapid molecular motion that causes complicating effects present in the solid state to average to zero. Whereas liquid state NMR spectra show narrow lines, the corresponding NMR spectra from the solid state are normally composed of exceedingly broad resonance lines due to highly restricted molecular motion. It is, therefore, difficult to obtain directly as detailed information from the spectra of solids as from those derived from the liquid state. Studies on a new technique (SINNMR, the sonically induced narrowing of the NMR spectra of solids) to remove line broadening effects in the NMR spectra of the solid state are reported within this thesis. SINNMR involves narrowing the NMR absorptions from solid particles by irradiating them with ultrasound when they are suspended in a support liquid. It is proposed that ultrasound induces incoherent motion of the suspended particles, producing motional characteristics of the particles similar to those of rather large molecules. The first report of apparently successful experiments involving SINNMR[1] emphasised both the irreproducibility of the technique and the uncertainty regarding its true origin. If SINNMR can be made reproducible and the effect definitively attributed to the sonically induced incoherent motional averaging of particles, the technique could offer a simple alternative to the now classical magic-angle spinning (MAS) NMR[2] and the recently reported dynamic angle spinning (DAS)[3] and double rotation (DOR)[4] techniques. Evidence is presented in this thesis to support the proposal that ultrasound may be used to narrow the NMR spectral resonances from solids by inducing incoherent motion of particles suspended in support liquids and, additionally, for some solids, by inducing rotational motion of molecular constituents in the lattices of solids. Successful SINNMR line narrowing using 20 kHz ultrasound is reported for a variety of samples: including trisodium orthophosphate, polytetrafluoroethylene and aluminium alloys. Investigations of SINNMR line narrowing in trisodium phosphate have revealed the relationship between ultrasonic power, particle size and support liquid density for the production of optimum SINNMR conditions. It is also proposed that the incoherent motion of particles induced by 20 kHz ultrasound can originate from interactions between acoustically induced cavitation microjets and particles.

Isotropic compression of mixtures of hard and soft spheres

The compaction behaviour of powders with soft and hard components is of particular interest to the paint processing industry. Unfortunately, at the present time, very little is known about the internal mechanisms within such systems and therefore suitable tests are required to help in the interpretative process. The TRUBAL, Distinct Element Method (D.E.M.) program was the method of investigation used in this study. Steel (hard) and rubber (soft) particles were used in the randomly-generated, binary assemblies because they provided a sharp contrast in physical properties. For reasons of simplicity, isotropic compression of two-dimensional assemblies was also initially considered. The assemblies were first subject to quasi-static compaction, in order to define their behaviour under equilibrium conditions. The stress-strain behaviour of the assemblies under such conditions was found to be adequately described by a second-order polynomial expansion. The structural evolution of the simulation assemblies was also similar to that observed for real powder systems. Further simulation tests were carried out to investigate the effects of particle size on the compaction behaviour of the two-dimensional, binary assemblies. Later work focused on the quasi-static compaction behaviour of three-dimensional assemblies, because they represented more realistic particle systems. The compaction behaviour of the assemblies during the simulation experiments was considered in terms of percolation theory concepts, as well as more familiar macroscopic and microstructural parameters. Percolation theory, which is based on ideas from statistical physics, has been found to be useful in the interpretation of the mechanical behaviour of simple, elastic lattices. However, from the evidence of this study, percolation theory is also able to offer a useful insight into the compaction behaviour of more realistic particle assemblies.

Persistence in a random bond ising model of socio-econo dynamics

We study the persistence phenomenon in a socio-econo dynamics model using computer simulations at a nite temperature on hypercubic lattices in dimensions up to ve. The model includes a \social" local eld which contains the magnetization at time t. The nearest neighbour quenched interactions are drawn from a binary distribution which is a function of the bond concentration, p. The decay of the persistence probability in the model depends on both the spatial dimension and p. We nd no evidence of \blocking" in this model. We also discuss the implications of our results for possible applications in the social and economic elds. It is suggested that the absence, or otherwise, of blocking could be used as a criterion to decide on the validity of a given model in dierent scenarios.

Semantics of query-driven communication of exact values

We address the question of how to communicate among distributed processes valuessuch as real numbers, continuous functions and geometrical solids with arbitrary precision, yet efficiently. We extend the established concept of lazy communication using streams of approximants by introducing explicit queries. We formalise this approach using protocols of a query-answer nature. Such protocols enable processes to provide valid approximations with certain accuracy and focusing on certain locality as demanded by the receiving processes through queries. A lattice-theoretic denotational semantics of channel and process behaviour is developed. Thequery space is modelled as a continuous lattice in which the top element denotes the query demanding all the information, whereas other elements denote queries demanding partial and/or local information. Answers are interpreted as elements of lattices constructed over suitable domains of approximations to the exact objects. An unanswered query is treated as an error anddenoted using the top element. The major novel characteristic of our semantic model is that it reflects the dependency of answerson queries. This enables the definition and analysis of an appropriate concept of convergence rate, by assigning an effort indicator to each query and a measure of information content to eachanswer. Thus we capture not only what function a process computes, but also how a process transforms the convergence rates from its inputs to its outputs. In future work these indicatorscan be used to capture further computational complexity measures. A robust prototype implementation of our model is available.

Shaping acoustic fields as a toolset for microfluidic manipulations in diagnostic technologies

Ultrasonics offers the possibility of developing sophisticated fluid manipulation tools in lab-on-a-chip technologies. Here we demonstrate the ability to shape ultrasonic fields by using phononic lattices, patterned on a disposable chip, to carry out the complex sequence of fluidic manipulations required to detect the rodent malaria parasite Plasmodium berghei in blood. To illustrate the different tools that are available to us, we used acoustic fields to produce the required rotational vortices that mechanically lyse both the red blood cells and the parasitic cells present in a drop of blood. This procedure was followed by the amplification of parasitic genomic sequences using different acoustic fields and frequencies to heat the sample and perform a real-time PCR amplification. The system does not require the use of lytic reagents nor enrichment steps, making it suitable for further integration into lab-on-a-chip point-of-care devices. This acoustic sample preparation and PCR enables us to detect ca. 30 parasites in a microliter-sized blood sample, which is the same order of magnitude in sensitivity as lab-based PCR tests. Unlike other lab-on-a-chip methods, where the sample moves through channels, here we use our ability to shape the acoustic fields in a frequency-dependent manner to provide different analytical functions. The methods also provide a clear route toward the integration of PCR to detect pathogens in a single handheld system.

Editorial overview:new protein production tools for structural biology

Full text: The idea of producing proteins from recombinant DNA hatched almost half a century ago. In his PhD thesis, Peter Lobban foresaw the prospect of inserting foreign DNA (from any source, including mammalian cells) into the genome of a λ phage in order to detect and recover protein products from Escherichia coli [ 1 and 2]. Only a few years later, in 1977, Herbert Boyer and his colleagues succeeded in the first ever expression of a peptide-coding gene in E. coli — they produced recombinant somatostatin [ 3] followed shortly after by human insulin. The field has advanced enormously since those early days and today recombinant proteins have become indispensable in advancing research and development in all fields of the life sciences. Structural biology, in particular, has benefitted tremendously from recombinant protein biotechnology, and an overwhelming proportion of the entries in the Protein Data Bank (PDB) are based on heterologously expressed proteins. Nonetheless, synthesizing, purifying and stabilizing recombinant proteins can still be thoroughly challenging. For example, the soluble proteome is organized to a large part into multicomponent complexes (in humans often comprising ten or more subunits), posing critical challenges for recombinant production. A third of all proteins in cells are located in the membrane, and pose special challenges that require a more bespoke approach. Recent advances may now mean that even these most recalcitrant of proteins could become tenable structural biology targets on a more routine basis. In this special issue, we examine progress in key areas that suggests this is indeed the case. Our first contribution examines the importance of understanding quality control in the host cell during recombinant protein production, and pays particular attention to the synthesis of recombinant membrane proteins. A major challenge faced by any host cell factory is the balance it must strike between its own requirements for growth and the fact that its cellular machinery has essentially been hijacked by an expression construct. In this context, Bill and von der Haar examine emerging insights into the role of the dependent pathways of translation and protein folding in defining high-yielding recombinant membrane protein production experiments for the common prokaryotic and eukaryotic expression hosts. Rather than acting as isolated entities, many membrane proteins form complexes to carry out their functions. To understand their biological mechanisms, it is essential to study the molecular structure of the intact membrane protein assemblies. Recombinant production of membrane protein complexes is still a formidable, at times insurmountable, challenge. In these cases, extraction from natural sources is the only option to prepare samples for structural and functional studies. Zorman and co-workers, in our second contribution, provide an overview of recent advances in the production of multi-subunit membrane protein complexes and highlight recent achievements in membrane protein structural research brought about by state-of-the-art near-atomic resolution cryo-electron microscopy techniques. E. coli has been the dominant host cell for recombinant protein production. Nonetheless, eukaryotic expression systems, including yeasts, insect cells and mammalian cells, are increasingly gaining prominence in the field. The yeast species Pichia pastoris, is a well-established recombinant expression system for a number of applications, including the production of a range of different membrane proteins. Byrne reviews high-resolution structures that have been determined using this methylotroph as an expression host. Although it is not yet clear why P. pastoris is suited to producing such a wide range of membrane proteins, its ease of use and the availability of diverse tools that can be readily implemented in standard bioscience laboratories mean that it is likely to become an increasingly popular option in structural biology pipelines. The contribution by Columbus concludes the membrane protein section of this volume. In her overview of post-expression strategies, Columbus surveys the four most common biochemical approaches for the structural investigation of membrane proteins. Limited proteolysis has successfully aided structure determination of membrane proteins in many cases. Deglycosylation of membrane proteins following production and purification analysis has also facilitated membrane protein structure analysis. Moreover, chemical modifications, such as lysine methylation and cysteine alkylation, have proven their worth to facilitate crystallization of membrane proteins, as well as NMR investigations of membrane protein conformational sampling. Together these approaches have greatly facilitated the structure determination of more than 40 membrane proteins to date. It may be an advantage to produce a target protein in mammalian cells, especially if authentic post-translational modifications such as glycosylation are required for proper activity. Chinese Hamster Ovary (CHO) cells and Human Embryonic Kidney (HEK) 293 cell lines have emerged as excellent hosts for heterologous production. The generation of stable cell-lines is often an aspiration for synthesizing proteins expressed in mammalian cells, in particular if high volumetric yields are to be achieved. In his report, Buessow surveys recent structures of proteins produced using stable mammalian cells and summarizes both well-established and novel approaches to facilitate stable cell-line generation for structural biology applications. The ambition of many biologists is to observe a protein's structure in the native environment of the cell itself. Until recently, this seemed to be more of a dream than a reality. Advances in nuclear magnetic resonance (NMR) spectroscopy techniques, however, have now made possible the observation of mechanistic events at the molecular level of protein structure. Smith and colleagues, in an exciting contribution, review emerging ‘in-cell NMR’ techniques that demonstrate the potential to monitor biological activities by NMR in real time in native physiological environments. A current drawback of NMR as a structure determination tool derives from size limitations of the molecule under investigation and the structures of large proteins and their complexes are therefore typically intractable by NMR. A solution to this challenge is the use of selective isotope labeling of the target protein, which results in a marked reduction of the complexity of NMR spectra and allows dynamic processes even in very large proteins and even ribosomes to be investigated. Kerfah and co-workers introduce methyl-specific isotopic labeling as a molecular tool-box, and review its applications to the solution NMR analysis of large proteins. Tyagi and Lemke next examine single-molecule FRET and crosslinking following the co-translational incorporation of non-canonical amino acids (ncAAs); the goal here is to move beyond static snap-shots of proteins and their complexes and to observe them as dynamic entities. The encoding of ncAAs through codon-suppression technology allows biomolecules to be investigated with diverse structural biology methods. In their article, Tyagi and Lemke discuss these approaches and speculate on the design of improved host organisms for ‘integrative structural biology research’. Our volume concludes with two contributions that resolve particular bottlenecks in the protein structure determination pipeline. The contribution by Crepin and co-workers introduces the concept of polyproteins in contemporary structural biology. Polyproteins are widespread in nature. They represent long polypeptide chains in which individual smaller proteins with different biological function are covalently linked together. Highly specific proteases then tailor the polyprotein into its constituent proteins. Many viruses use polyproteins as a means of organizing their proteome. The concept of polyproteins has now been exploited successfully to produce hitherto inaccessible recombinant protein complexes. For instance, by means of a self-processing synthetic polyprotein, the influenza polymerase, a high-value drug target that had remained elusive for decades, has been produced, and its high-resolution structure determined. In the contribution by Desmyter and co-workers, a further, often imposing, bottleneck in high-resolution protein structure determination is addressed: The requirement to form stable three-dimensional crystal lattices that diffract incident X-ray radiation to high resolution. Nanobodies have proven to be uniquely useful as crystallization chaperones, to coax challenging targets into suitable crystal lattices. Desmyter and co-workers review the generation of nanobodies by immunization, and highlight the application of this powerful technology to the crystallography of important protein specimens including G protein-coupled receptors (GPCRs). Recombinant protein production has come a long way since Peter Lobban's hypothesis in the late 1960s, with recombinant proteins now a dominant force in structural biology. The contributions in this volume showcase an impressive array of inventive approaches that are being developed and implemented, ever increasing the scope of recombinant technology to facilitate the determination of elusive protein structures. Powerful new methods from synthetic biology are further accelerating progress. Structure determination is now reaching into the living cell with the ultimate goal of observing functional molecular architectures in action in their native physiological environment. We anticipate that even the most challenging protein assemblies will be tackled by recombinant technology in the near future.

Generalised Riccati solution and pinning control of complex stochastic networks

This paper considers the global synchronisation of a stochastic version of coupled map lattices networks through an innovative stochastic adaptive linear quadratic pinning control methodology. In a stochastic network, each state receives only noisy measurement of its neighbours' states. For such networks we derive a generalised Riccati solution that quantifies and incorporates uncertainty of the forward dynamics and inverse controller in the derivation of the stochastic optimal control law. The generalised Riccati solution is derived using the Lyapunov approach. A probabilistic approximation type algorithm is employed to estimate the conditional distributions of the state and inverse controller from historical data and quantifying model uncertainties. The theoretical derivation is complemented by its validation on a set of representative examples.