Singularities and semistable degenerations for symplectic topology

We overview our work [7], [8], [9], [10], [11], [6] defining and studying normal crossings varieties and subvarieties in symplectic topology. This work answers a question of Gromov on the feasibility of introducing singular (sub)varieties into symplectic topology in the case of normal crossings singularities. It also provides a necessary and sufficient condition for smoothing normal crossings symplectic varieties. In addition, we explain some connections with other areas of mathematics and discuss a few directions for further research.     

Functional Generalized Additive Models

We introduce the functional generalized additive model (FGAM), a novel regression model for association studies between a scalar response and a functional predictor. We model the link-transformed mean response as the integral with respect to t of F{X(t), t} where F( ·, ·) is an unknown regression function and X(t) is a functional covariate. Rather than having an additive model in a finite number of principal components as by Müller and Yao (2008 Müller, H.G., and Yao, F. (2008), “Functional Additive Models,” Journal of the American Statistical Association, 103, 1534–1544.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]), our model incorporates the functional predictor directly and thus our model can be viewed as the natural functional extension of generalized additive models. We estimate F( ·, ·) using tensor-product B-splines with roughness penalties. A pointwise quantile transformation of the functional predictor is also considered to ensure each tensor-product B-spline has observed data on its support. The methods are evaluated using simulated data and their predictive performance is compared with other competing scalar-on-function regression alternatives. We illustrate the usefulness of our approach through an application to brain tractography, where X(t) is a signal from diffusion tensor imaging at position, t, along a tract in the brain. In one example, the response is disease-status (case or control) and in a second example, it is the score on a cognitive test. The FGAM is implemented in R in the refund package. There are additional supplementary materials available online.     

Possibilities for human skin characterization based on strongly reduced Raman spectroscopic information

Loss‐of‐function mutations in the gene coding for filaggrin are the single most important risk factor for development of atopic dermatitis and associated allergic rhinitis and asthma. Filaggrin is enzymatically degraded to natural moisturizing factor (NMF) in the stratum corneum (SC). In vivo Raman spectra of human skin can be used to quantify the NMF concentration in SC and thereby identify carriers of a loss‐of‐function mutation in the gene coding for filaggrin, which results in decreased NMF content. Here, we demonstrate that strongly reduced Raman spectral information is sufficient to make this differentiation. This is an important step towards development of a dedicated diagnostic device of reduced complexity, size and cost as compared to current state‐of‐the‐art Raman equipment. A genetic algorithm was used to select the spectral regions needed to classify skin based on normal or reduced NMF content in SC. Using the NMF content based on full spectral information as gold standard, only four Raman regions were required to create a linear discriminant analysis model that can differentiate between skin with low NMF and skin with normal NMF with a prediction accuracy of 93 %. Copyright © 2013 John Wiley & Sons, Ltd.     

Graded Nilpotent Algebras and Eggert's Conjecture

A group G is (l,m,n)-generated if it is a quotient group of the triangle group T(l,m,n) = (x,y,z|x ^l= y ^m= z ⁿ= xyz= 1). In [8] the problem is posed to find all possible (l,m,n)-generations for the non-abelian finite simple groups. In this paper we partially answer this question for the Janko group J ₃. We find all (2, 3, t)-generations as well as (2, 2,2,p)-generations, p a prime, for J ₃     

Design and Synthesis of Imidazole and Triazole Pyrazoles as Mycobacterium Tuberculosis CYP121A1 Inhibitors

The emergence of untreatable drug-resistant strains of Mycobacterium tuberculosis is a major public health problem worldwide, and the identification of new efficient treatments is urgently needed. Mycobacterium tuberculosis cytochrome P450 CYP121A1 is a promising drug target for the treatment of tuberculosis owing to its essential role in mycobacterial growth. Using a rational approach, which includes molecular modelling studies, three series of azole pyrazole derivatives were designed through two synthetic pathways. The synthesized compounds were biologically evaluated for their inhibitory activity towards M. tuberculosis and their protein binding affinity (K_D). Series 3 biarylpyrazole imidazole derivatives were the most effective with the isobutyl ( 10 f ) and tert-butyl ( 10 g ) compounds displaying optimal activity (MIC 1.562 μg/mL, K_D 0.22 μM ( 10 f ) and 4.81 μM ( 10 g )). The spectroscopic data showed that all the synthesised compounds produced a type II red shift of the heme Soret band indicating either direct binding to heme iron or (where less extensive Soret shifts are observed) putative indirect binding via an interstitial water molecule. Evaluation of biological and physicochemical properties identified the following as requirements for activity: LogP >4, H-bond acceptors/H-bond donors 4/0, number of rotatable bonds 5–6, molecular volume >340 ų, topological polar surface area <40 Ų.     

Development of a Neutral Diketopyrrolopyrrole Phosphine Oxide for the Selective Bioimaging of Mitochondria at the Nanomolar Level

Development of novel bioimaging materials that exhibit organelle specific accumulation continues to be at the forefront of research interests and efforts. Among the various subcellular organelles, mitochondria, which are found in the cytoplasm of eukaryotic cells, are of particular interest in relation to their vital function. To date, most molecular probes that target mitochondria utilise delocalised lipophilic cations such as triphenylphosphonium and pyridinium. However, the use of such charged motifs is known to be detrimental to the working function of the mitochondrial transmembrane potential and there remains a strong case for development of neutral mitochondrial fluorescent probes. Herein, we demonstrate for the first time the exploitation of diketopyrrolopyrrole-based chemistries for the realisation of a neutral fluorescent probe that exhibits organelle specific accumulation within the mitochondria at the nanomolar level. The synthesised probe, which bears a neutral triphenylphosphine oxide moiety, exhibits a large Stokes shift and high fluorescence quantum yield in water, both highly sought-after properties in the development of bioimaging agents. In vitro studies reveal no interference with cell metabolism when tested for the human MCF7 breast cancer cell and nanomolar subcellular organelle colocalisation with commercially available mitochondrial staining agent Mitotracker Red. In light of its novelty, neutral structure and the preferential accumulation at nanomolar concentrations we anticipate this work to be of significant interest for the increasingly larger community devoted to the realisation of neutral mitochondrial selective systems and more widely to those engaged in the rational development of superior organic architectures in the biological field.     

Dual copper- and photoredox-catalysed reactions

The merger of transition metal catalysis with visible light photoredox catalysis in a cooperative fashion has recently emerged as a versatile way of developing new synthetic methodologies. This review will focus on the relatively new but fast expanding area of dual copper- and photoredox-catalysis, detailing recent developments in the area.     

Purification of monoclonal antibody from tobacco extract using membrane-based bioseparation techniques

Transgenic plants offer a promising system for large-scale production of therapeutic proteins such as monoclonal antibodies (mAbs). This paper describes a membrane-based process suitable for purification of a humanized mAb expressed in tobacco. Most monoclonal antibody purification schemes rely on the use of Protein A as the affinity ligand for antibody capture. The main objective of our work was to develop non-Protein A-based purification methods to avoid some of the problems and limitations associated with this ligand, e.g. cost, immunotoxicity, and antibody aggregation during elution. Ion exchange membrane chromatography (IEMC) was used for primary capture and preliminary purification of the mAb from tobacco juice. Hydrophobic interaction membrane chromatography (HIMC) was then used for high-resolution purification, followed by ultrafiltration for polishing, desalting and buffer exchange. Using this scheme, both high mAb purity (single peak in size exclusion chromatogram, i.e., ca. 100% purity) and high recovery (77% of mAb spiked into the tobacco extract) were achieved. Membrane chromatography is generally considered unsuitable for resolving bound proteins by gradient elution and is therefore commonly used in the bind and elute mode with a single-step change of mobile phase. We show that the gradient elution process in the HIMC step can be optimized to increase the resolution and thereby obtain product of high purity.