Numerical experiments with MALDI Imaging data

This article does not present new mathematical results, it solely aims at discussing some numerical experiments with MALDI Imaging data. However, these experiments are based on and could not be done without the mathematical results obtained in the UNLocX project. They tackle two obstacles which presently prevent clinical routine applications of MALDI Imaging technology. In the last decade, matrix-assisted laser desorption/ionization imaging mass spectrometry (MALDI-IMS) has developed into a powerful bioanalytical imaging modality. MALDI imaging data consists of a set of mass spectra, which are measured at different locations of a flat tissue sample. Hence, this technology is capable of revealing the full metabolic structure of the sample under investigation. Sampling resolution as well as spectral resolution is constantly increasing, presently a conventional 2D MALDI Imaging data requires up to 100 GB per dataset. A major challenge towards routine applications of MALDI Imaging in pharmaceutical or medical workflows is the high computational cost for evaluating and visualizing the information content of MALDI imaging data. This becomes even more critical in the near future when considering cohorts or 3D applications. Due to its size and complexity MALDI Imaging constitutes a challenging test case for high performance signal processing. In this article we will apply concepts and algorithms, which were developed within the UNLocX project, to MALDI Imaging data. In particular we will discuss a suitable phase space model for such data and report on implementations of the resulting transform coders using GPU technology. Within the MALDI Imaging workflow this leads to an efficient baseline removal and peak picking. The final goal of data processing in MALDI Imaging is the discrimination of regions having different metabolic structures. We introduce and discuss so-called soft-segmentation maps which are obtained by non-negative matrix factorization incorporating sparsity constraints.     

Using the near-field coupling of a sharp tip to tune fluorescence-emission fluctuations during quantum-dot blinking

We demonstrate that the cycling between internal states of quantum dots during fluorescence blinking can be used to tune the near-field coupling with a sharp tip. In particular, the fluorescence emission from states with high quantum yield is quenched due to energy transfer, while that from low-yield states is elevated due to field enhancement. Thus, as a quantum dot blinks, its emission fluctuations are progressively suppressed upon approach of a tip.     

Structural elucidation of amino amide‐type local anesthetic drugs and their main metabolites in urine by LC‐MS after derivatization and its application for differentiation between positional isomers of prilocaine

The demand for clinical toxicology analytical methods for identifying drugs of abuse and medicinal drugs is steadily increasing. Structural elucidation of amino amide‐type local anesthetic drugs and their main metabolites by GC‐EI‐MS and LC‐ESI‐MS/MS is of great analytical challenge. These compounds exhibit only/mostly fragments/product ions representing the amine‐containing residue, while the aromatic amide moiety remains unidentified. This task becomes even more complicated when discrimination between positional isomers of such compounds is required. Here, we report the development of a derivatization procedure for the differentiation and structural elucidation of a mixture of local anesthetic drugs and their metabolites that possess tertiary and secondary amines in water and urine. A method based on two sequential “in‐vial” instantaneous derivatization processes at ambient temperature followed by LC‐ESI‐MS/MS analysis was developed. 2,2,2‐Trichloro‐1,1‐dimethylethyl chloroformate (TCDMECF) was utilized to selectively convert the secondary amines into their carbamate derivatives, followed by hydrogen peroxide addition to produce the corresponding tertiary amine oxides. The resulting derivatives exhibited rich fragmentation patterns, enabling improved structural elucidation of the original compounds. The developed method was successfully applied to the differentiation and structural elucidation of prilocaine and its four positional isomers, which all possess similar GC and LC retention times and four of them exhibit almost identical EI‐MS and ESI‐MS/MS spectra, enabling their structural elucidation in a single LC‐ESI‐MS/MS analysis. The developed technique is fast and simple and enables discrimination between isomers based on different diagnostic ions/fragmentation patterns.     

The Langlands parameter of a simple supercuspidal representation: symplectic groups

The Ramanujan Journal - Let $$\pi $$ be a simple supercuspidal representation of the symplectic group $${\mathrm {Sp}}_{2l}(F)$$, over a p-adic field F. In this work, we explicitly compute the...     

On the maximum number of edges in quasi-planar graphs

A topological graph is quasi-planar, if it does not contain three pairwise crossing edges. Agarwal et al. [P.K. Agarwal, B. Aronov, J. Pach, R. Pollack, M. Sharir, Quasi-planar graphs have a linear number of edges, Combinatorica 17 (1) (1997) 1-9] proved that these graphs have a linear number of edges. We give a simple proof for this fact that yields the better upper bound of 8n edges for n vertices. Our best construction with 7n−O(1) edges comes very close to this bound. Moreover, we show matching upper and lower bounds for several relaxations and restrictions of this problem. In particular, we show that the maximum number of edges of a simple quasi-planar topological graph (i.e., every pair of edges have at most one point in common) is 6.5n−O(1), thereby exhibiting that non-simple quasi-planar graphs may have many more edges than simple ones.     

Use of sol-gel entrapment techniques for the resolution of itaconic acid biosynthetic pathway in Aspergillus terreus

A new technique of investigation of labile metabolic pathways using immobilization of the pathway in sol-gel derived silicate matrices was demonstrated. The biosynthetic pathway of itaconic acid in Aspergillus terreus is believed to proceed through decarboxylation of cis-aconitate catalyzed by an unstable enzyme aconitate decarboxylase, E.C. 4.1.1.6. Stabilization of this pathway in sol-gel derived silicate matrix enabled the elucidation of the correct sequence of biosynthetic steps. The decarboxylation of cis-aconitate does not lead directly to itaconate, but rather to citraconate. The latter is then isomerized to itaconate by a previously unknown enzyme.     

Infrared laser enhancement of the reaction of sulfur hexafluoride with sodium vapor

The vibrational energy dependence of the rate of the gas phase reaction of Na with SF₆ has been determined in a diffusion cloud experiment using CO₂ laser excitation. The “conversion efficiency” of ca. 40% for vibrational energy suggests a preference for vibrational over the translational energy when compared with “prior” statistical expectation.     

Harmonic Pinnacles in the Discrete Gaussian Model

The 2D Discrete Gaussian model gives each height function \({\eta : {\mathbb{Z}^2\to\mathbb{Z}}}\) a probability proportional to \({\exp(-\beta \mathcal{H}(\eta))}\), where \({\beta}\) is the inverse-temperature and \({\mathcal{H}(\eta) = \sum_{x\sim y}(\eta_x-\eta_y)^2}\) sums over nearest-neighbor bonds. We consider the model at large fixed \({\beta}\), where it is flat unlike its continuous analog (the Discrete Gaussian Free Field). We first establish that the maximum height in an \({L\times L}\) box with 0 boundary conditions concentrates on two integers M, M + 1 with \({M\sim \sqrt{(1/2\pi\beta)\log L\log\log L}}\). The key is a large deviation estimate for the height at the origin in \({\mathbb{Z}^{2}}\), dominated by “harmonic pinnacles”, integer approximations of a harmonic variational problem. Second, in this model conditioned on \({\eta\geq 0}\) (a floor), the average height rises, and in fact the height of almost all sites concentrates on levels H, H + 1 where \({H\sim M/\sqrt{2}}\). This in particular pins down the asymptotics, and corrects the order, in results of Bricmont et al. (J. Stat. Phys. 42(5–6):743–798, 1986), where it was argued that the maximum and the height of the surface above a floor are both of order \({\sqrt{\log L}}\). Finally, our methods extend to other classical surface models (e.g., restricted SOS), featuring connections to p-harmonic analysis and alternating sign matrices.     

Effect of the Solvent on the Conformation of Isolated MEH‐PPV Chains Intercalated Into SnS2

Photophysical processes in conjugated polymers are influenced by two competing effects: the extent of excited state delocalization along a chain, and the electronic interaction between chains. Experimentally, it is often difficult to separate the two because both are controlled by chain conformation. Here we demonstrate that it is possible to modify intra‐chain delocalization without inducing inter‐chain interactions by intercalating polymer monolayers between the sheets of an inorganic layered matrix. The red‐emitting conjugated polymer, MEH‐PPV, is confined to the interlayer space of layered SnS₂. The formation of isolated polymer monolayers between the SnS₂ sheets is confirmed by X‐ray diffraction measurements. Photoluminescence excitation (PLE) and photoluminescence (PL) spectra of the incorporated MEH‐PPV chains reveal that the morphology of the incorporated chains can be varied through the choice of solvent used for chain intercalation. Incorporation from chloroform results in more extended conformations compared to intercalation from xylene. Even highly twisted conformations can be achieved when the incorporation occurs from a methanol:chloroform mixture. The PL spectra of the MEH‐PPV incorporated SnS₂ nanocomposites using the different solvents are in good agreement with the PL spectra of the same solutions, indicating that the conformation of the polymer chains in the solutions is retained upon intercalation into the inorganic host. Therefore, intercalation of conjugated polymer chains into layered hosts enables the study of intra‐chain photophysical processes as a function of chain conformation.