Hankel operators on Fock spaces

We study Hankel operators on the weighted Fock spaces Fp. The boundedness and compactness of these operators are characterized in terms of BMO and VMO, respectively. Along the way, we also study Berezin transform and harmonic conjugates on the plane. Our results are analogous to Zhu's characterization of bounded and compact Hankel operators on Bergman spaces of the unit disk.

Femtosecond pulse shaping using differential evolutionary algorithm and wavelet operators

Evolutionary meta-algorithms for pulse shaping of broadband femtosecond duration laser pulses are proposed. The genetic algorithm searching the evolutionary landscape for desired pulse shapes consists of a population of waveforms (genes), each made from two concatenated vectors, specifying phases and magnitudes, respectively, over a range of frequencies. Frequency domain operators such as mutation, two-point crossover average crossover, polynomial phase mutation, creep and three-point smoothing as well as a time-domain crossover are combined to produce fitter offsprings at each iteration step. The algorithm applies roulette wheel selection; elitists and linear fitness scaling to the gene population. A differential evolution (DE) operator that provides a source of directed mutation and new wavelet operators are proposed. Using properly tuned parameters for DE, the meta-algorithm is used to solve a waveform matching problem. Tuning allows either a greedy directed search near the best known solution or a robust search across the entire parameter space.

Spectral theory of some non-selfadjoint linear differential operators

We give a characterisation of the spectral properties of linear differential operators with constant coefficients, acting on functions defined on a bounded interval, and determined by general linear boundary conditions. The boundary conditions may be such that the resulting operator is not selfadjoint. We associate the spectral properties of such an operator $S$ with the properties of the solution of a corresponding boundary value problem for the partial differential equation $\partial_t q \pm iSq=0$. Namely, we are able to establish an explicit correspondence between the properties of the family of eigenfunctions of the operator, and in particular whether this family is a basis, and the existence and properties of the unique solution of the associated boundary value problem. When such a unique solution exists, we consider its representation as a complex contour integral that is obtained using a transform method recently proposed by Fokas and one of the authors. The analyticity properties of the integrand in this representation are crucial for studying the spectral theory of the associated operator.

Casimirs and Lax operators from the structure of Lie algebras

This paper uses the structure of the Lie algebras to identify the Casimir invariant functions and Lax operators for matrix Lie groups. A novel mapping is found from the cotangent space to the dual Lie algebra which enables Lax operators to be found. The coordinate equations of motion are given in terms of the structure constants and the Hamiltonian.

A Riemann-Hilbert problem with a vanishing coefficient and applications to Toeplitz operators

We study the homogeneous Riemann-Hilbert problem with a vanishing scalar-valued continuous coefficient. We characterize non-existence of nontrivial solutions in the case where the coefficient has its values along several rays starting from the origin. As a consequence, some results on injectivity and existence of eigenvalues of Toeplitz operators in Hardy spaces are obtained.

Does convective aggregation need to be represented in cumulus parameterizations?

Tropical deep convection exhibits a variety of levels of aggregation over a wide range of scales. Based on a multisatellite analysis, the present study shows at mesoscale that different levels of aggregation are statistically associated with differing large-scale atmospheric states, despite similar convective intensity and large-scale forcings. The more aggregated the convection, the dryer and less cloudy the atmosphere, the stronger the outgoing longwave radiation, and the lower the planetary albedo. This suggests that mesoscale convective aggregation has the potential to affect couplings between moisture and convection and between convection, radiation, and large-scale ascent. In so doing, aggregation may play a role in phenomena such as “hot spots” or the Madden-Julian Oscillation. These findings support the need for the representation of mesoscale organization in cumulus parameterizations; most parameterizations used in current climate models lack any such representation. The ability of a cloud system-resolving model to reproduce observed relationships suggests that such models may be useful to guide attempts at parameterizations of convective aggregation.

The role of plasma membrane STIM1 and Ca(2+)entry in platelet aggregation. STIM1 binds to novel proteins in human platelets.

Ca(2+) elevation is essential to platelet activation. STIM1 senses Ca(2+) in the endoplasmic reticulum and activates Orai channels allowing store-operated Ca(2+) entry (SOCE). STIM1 has also been reported to be present in the plasma membrane (PM) with its N-terminal region exposed to the outside medium but its role is not fully understood. We have examined the effects of the antibody GOK/STIM1, which recognises the N-terminal region of STIM1, on SOCE, agonist-stimulated Ca(2+) entry, surface exposure, in vitro thrombus formation and aggregation in human platelets. We also determined novel binding partners of STIM1 using proteomics. The dialysed GOK/STIM1 antibody failed to reduced thapsigargin- and agonist-mediated Ca(2+) entry in Fura2-labelled cells. Using flow cytometry we detect a portion of STIM1 to be surface-exposed. The dialysed GOK/STIM1 antibody reduced thrombus formation by whole blood on collagen-coated capillaries under flow and platelet aggregation induced by collagen. In immunoprecipitation experiments followed by proteomic analysis, STIM1 was found to extract a number of proteins including myosin, DOCK10, thrombospondin-1 and actin. These studies suggest that PM STIM1 may facilitate platelet activation by collagen through novel interactions at the plasma membrane while the essential Ca(2+)-sensing role of STIM1 is served by the protein in the ER.

On the spectra and pseudospectra of a class of non-self-adjoint random matrices and operators

In this paper we develop and apply methods for the spectral analysis of non-selfadjoint tridiagonal infinite and finite random matrices, and for the spectral analysis of analogous deterministic matrices which are pseudo-ergodic in the sense of E. B. Davies (Commun. Math. Phys. 216 (2001), 687–704). As a major application to illustrate our methods we focus on the “hopping sign model” introduced by J. Feinberg and A. Zee (Phys. Rev. E 59 (1999), 6433–6443), in which the main objects of study are random tridiagonal matrices which have zeros on the main diagonal and random ±1’s as the other entries. We explore the relationship between spectral sets in the finite and infinite matrix cases, and between the semi-infinite and bi-infinite matrix cases, for example showing that the numerical range and p-norm ε - pseudospectra (ε > 0, p ∈ [1,∞] ) of the random finite matrices converge almost surely to their infinite matrix counterparts, and that the finite matrix spectra are contained in the infinite matrix spectrum Σ. We also propose a sequence of inclusion sets for Σ which we show is convergent to Σ, with the nth element of the sequence computable by calculating smallest singular values of (large numbers of) n×n matrices. We propose similar convergent approximations for the 2-norm ε -pseudospectra of the infinite random matrices, these approximations sandwiching the infinite matrix pseudospectra from above and below.

The real-time optimisation of DNO owned storage devices on the LV network for peak reduction

Energy storage is a potential alternative to conventional network reinforcementof the low voltage (LV) distribution network to ensure the grid’s infrastructure remainswithin its operating constraints. This paper presents a study on the control of such storagedevices, owned by distribution network operators. A deterministic model predictive control (MPC) controller and a stochastic receding horizon controller (SRHC) are presented, wherethe objective is to achieve the greatest peak reduction in demand, for a given storagedevice specification, taking into account the high level of uncertainty in the prediction of LV demand. The algorithms presented in this paper are compared to a standard set-pointcontroller and bench marked against a control algorithm with a perfect forecast. A specificcase study, using storage on the LV network, is presented, and the results of each algorithmare compared. A comprehensive analysis is then carried out simulating a large number of LV networks of varying numbers of households. The results show that the performance of each algorithm is dependent on the number of aggregated households. However, on a typical aggregation, the novel SRHC algorithm presented in this paper is shown to outperform each of the comparable storage control techniques.

Control methodologies: Peak reduction algorithms for DNO owned storage devices on the Low Voltage network

The Distribution Network Operators (DNOs) role is becoming more difficult as electric vehicles and electric heating penetrate the network, increasing the demand. As a result it becomes harder for the distribution networks infrastructure to remain within its operating constraints. Energy storage is a potential alternative to conventional network reinforcement such as upgrading cables and transformers. The research presented here in this paper shows that due to the volatile nature of the LV network, the control approach used for energy storage has a significant impact on performance. This paper presents and compares control methodologies for energy storage where the objective is to get the greatest possible peak demand reduction across the day from a pre-specified storage device. The results presented show the benefits and detriments of specific types of control on a storage device connected to a single phase of an LV network, using aggregated demand profiles based on real smart meter data from individual homes. The research demonstrates an important relationship between how predictable an aggregation is and the best control methodology required to achieve the objective.

CLEC-2 is not required for platelet aggregation at arteriolar shear

The C-type lectin receptor CLEC-2 is expressed primarily on the surface of platelets, where it is present as a dimer, and is found at low level on a subpopulation of other hematopoietic cells, including mouse neutrophils [1–4] Clustering of CLEC-2 by the snake venom toxin rhodocytin, specific antibodies or its endogenous ligand, podoplanin, elicits powerful activation of platelets through a pathway that is similar to that used by the collagen receptor glycoprotein VI (GPVI) [4–6]. The cytosolic tail of CLEC-2 contains a conserved YxxL sequence preceded by three upstream acidic amino acid residues, which together form a novel motif known as a hemITAM. Ligand engagement induces tyrosine phosphorylation of the hemITAM sequence providing docking sites for the tandem-SH2 domains of the tyrosine kinase Syk across a CLEC-2 receptor dimer [3]. Tyrosine phosphorylation of Syk by Src family kinases and through autophosphorylation leads to stimulation of a downstream signaling cascade that culminates in activation of phospholipase C γ2 (PLCγ2) [4,6]. Recently, CLEC-2 has been proposed to play a major role in supporting activation of platelets at arteriolar rates of flow [1]. Injection of a CLEC-2 antibody into mice causes a sustained depletion of the C-type lectin receptor from the platelet surface [1]. The CLEC-2-depleted platelets were unresponsive to rhodocytin but underwent normal aggregation and secretion responses after stimulation of other platelet receptors, including GPVI [1]. In contrast, there was a marked decrease in aggregate formation relative to controls when CLEC-2-depleted blood was flowed at arteriolar rates of shear over collagen (1000 s−1 and 1700 s−1) [1]. Furthermore, antibody treatment significantly increased tail bleeding times and mice were unable to occlude their vessels after ferric chloride injury [1]. These data provide evidence for a critical role for CLEC-2 in supporting platelet aggregation at arteriolar rates of flow. The underlying mechanism is unclear as platelets do not express podoplanin, the only known endogenous ligand of CLEC-2. In the present study, we have investigated the role of CLEC-2 in platelet aggregation and thrombus formation using platelets from a novel mutant mouse model that lacks functional CLEC-2.

The environmental setting of Epipalaeolithic aggregation site Kharaneh IV

The archaeological site of Kharaneh IV in Jordan's Azraq Basin, and its relatively near neighbour Jilat 6 show evidence of sustained occupation of substantial size through the Early to Middle Epipalaeolithic (c. 24,000 - 15,000 cal BP). Here we review the geomorphological evidence for the environmental setting in which Kharaneh IV was established. The on-site stratigraphy is clearly differentiated from surrounding sediments, marked visually as well as by higher magnetic susceptibility values. Dating and analysis of off-site sediments show that a significant wetland existed at the site prior to and during early site occupation (~ 23,000 - 19,000 BP). This may explain why such a substantial site existed at this location. This wetland dating to the Last Glacial Maximum also provides important information on the palaeoenvironments and potential palaeoclimatic scenarios for today's eastern Jordanian desert, from where such evidence is scarce.

The sensitivity of convective aggregation to diabatic processes in idealized radiative-convective equilibrium simulations

Idealized explicit convection simulations of the Met Office Unified Model exhibit spontaneous self-aggregation in radiative-convective equilibrium, as seen in other models in previous studies. This self-aggregation is linked to feedbacks between radiation, surface fluxes, and convection, and the organization is intimately related to the evolution of the column water vapor field. Analysis of the budget of the spatial variance of column-integrated frozen moist static energy (MSE), following Wing and Emanuel [2014], reveals that the direct radiative feedback (including significant cloud longwave effects) is dominant in both the initial development of self-aggregation and the maintenance of an aggregated state. A low-level circulation at intermediate stages of aggregation does appear to transport MSE from drier to moister regions, but this circulation is mostly balanced by other advective effects of opposite sign and is forced by horizontal anomalies of convective heating (not radiation). Sensitivity studies with either fixed prescribed radiative cooling, fixed prescribed surface fluxes, or both do not show full self-aggregation from homogeneous initial conditions, though fixed surface fluxes do not disaggregate an initialized aggregated state. A sensitivity study in which rain evaporation is turned off shows more rapid self-aggregation, while a run with this change plus fixed radiative cooling still shows strong self-aggregation, supporting a “moisture memory” effect found in Muller and Bony [2015]. Interestingly, self-aggregation occurs even in simulations with sea surface temperatures (SSTs) of 295 K and 290 K, with direct radiative feedbacks dominating the budget of MSE variance, in contrast to results in some previous studies.