Generalized Sampling and Infinite-Dimensional Compressed Sensing

We introduce and analyze a framework and corresponding method for compressed sensing in infinite dimensions. This extends the existing theory from finite-dimensional vector spaces to the case of separable Hilbert spaces. We explain why such a new theory is necessary by demonstrating that existing finite-dimensional techniques are ill suited for solving a number of key problems. This work stems from recent developments in generalized sampling theorems for classical (Nyquist rate) sampling that allows for reconstructions in arbitrary bases. A conclusion of this paper is that one can extend these ideas to allow for significant subsampling of sparse or compressible signals. Central to this work is the introduction of two novel concepts in sampling theory, the stable sampling rate and the balancing property, which specify how to appropriately discretize an infinite-dimensional problem.     

Central-to-axial chirality transfer in the benzannulation reaction of optically pure Fischer carbene complexes in the synthesis of allocolchicinoids

A method for the synthesis of allocolchicinoids is explored that involves the benzannulation reaction of Fischer chromium carbene complexes with alkynes. The benzannulation reaction is employed to install the aromatic C-ring via the reaction of an α,β-unsaturated carbene complex in which the carbene complex is attached to a seven-membered ring that is to become the B-ring of the allocolchicinoids. Two different regioisomeric series can be accessed depending on which position the carbene complex is on the seven-membered ring. A key issue that is addressed is the stereochemistry of the newly formed axis of chirality that results from a stereo-relay from an existing chiral center on the seven-membered ring at the position destined to be C(7) in the allocolchicinoids. The level of stereochemistry is dependent on the position of the carbene complex on the seven-membered ring. A mechanism is proposed to account for this stereochemical dependence and to account for the observed effects of temperature and solvent on the stereoselectivity. Finally, the benzannulation reactions of optically pure complexes are examined and quite surprisingly one, but not both, of the diastereomeric products is racemized. The racemization can be prevented with the proper choice of solvent and temperature. A mechanism is proposed to account for the racemization of only one of the diastereomers of the product that involves the intermediacy of an o-quinone methide chromium tricarbonyl complex.     

Prediction of pH-dependent aqueous solubility of Histone Deacetylase (HDAC) inhibitors

Recently we developed a model for prediction of pH-dependent aqueous solubility of drugs and drug like molecules. In the present work, the model was applied on a series of novel Histone Deacetylases (HDAC) inhibitors discovered at TopoTarget. The applicability of our model was evaluated on the series of HDAC inhibitors by use of Self-Organizing Maps (SOM) and 2D-projection of the HDAC inhibitors on the chemical space of the training data set of the artificial neural network (ANN) module. The model was refined for the particular chemical space of interest, which led to two modifications in the training data set of the ANN. The performance of the original and the two modified versions of the model were evaluated against the commercial software from Simulations-plus and pH-dependent solubility measurements for representative compounds of the series. The results of the evaluation indicate that one can develop models that are more accurate in predicting differences in the solubility of structurally very similar compounds than models that have been trained on structurally unbiased, diverse data sets. Such 'tailor-made' models have the potential to become trustworthy enough to replace time-consuming and expensive medium- and high-throughput solubility experiments by providing results of similar or even better quality.     

Comparison of algorithms for the calculation of molecular vibrational level densities

Level densities of vibrational degrees of freedom are calculated numerically with formulas based on the inversion of the canonical vibrational partition function. The calculated level densities are compared with other approximate equations from literature and with the exact Beyer-Swinehart values, for which a simplified but equivalent version is given. All approximate equations agree at high excitation energies, but our results are vastly superior at low energies for large molecules. The results presented here are therefore of particular relevance for thermal processes of very large molecules, e.g., of biological nature, for which the exact state counting can be prohibitively slow. Furthermore, it is valid for situations where anharmonic motion significantly influences the thermal properties.     

Large exposure estimation through automatic business group identification

Large exposure rules are considered critical for financial institutions, as they directly restrict the lending activity of banks to clients. However, empirical evidence suggests that those rules are difficult both for regulators to enforce and for financial institutions to implement. We present a data-driven analytical model that automatically and algorithmically creates groups of related parties based on ownership information, financial dependencies, business associations, and family ties. We develop a methodology based on linear algebra and networks to group clients, highlight missing critical information, and identify unreported business partners. The approach can be used both prospectively by banking institutions analyzing credit risk and by regulators. We include a case study, applying the methodology retrospectively to highlight large exposure violations and systemic risk leading up to the 2008 banking crises in Iceland.     

Liouville Property,Wiener’s Test and Unavoidable Sets for Hunt Processes

Let \((X,\mathcal {W})\) be a balayage space, \(1\in \mathcal {W}\), or – equivalently – let \(\mathcal W\) be the set of excessive functions of a Hunt process on a locally compact space X with countable base such that \(\mathcal {W}\) separates points, every function in \(\mathcal {W}\) is the supremum of its continuous minorants and there exist strictly positive continuous \(u,v\in \mathcal {W}\) such that u/v → 0 at infinity. We suppose that there is a Green function G > 0 for X, a metric ρ for X and a decreasing function \(g\colon [0,\infty )\to (0,\infty ]\) having the doubling property such that G ≈ g ° ρ. Assuming that the constant function 1 is harmonic and balls of (X, ρ) are relatively compact, it is shown that every positive harmonic function on X is constant (Liouville property) and that Wiener’s test at infinity shows, if a given set A in X is unavoidable, that is, if the process hits A with probability one, wherever it starts. An application yields that locally finite unions of pairwise disjoint balls B(z, r_z), z ∈ Z, which have a certain separation property with respect to a suitable measure λ on X are unavoidable if and only if, for some/any point x₀ ∈ X, the series \({\sum }_{z\in Z} g(\rho (x_{0},z))/g(r_{z}) \) diverges. The results generalize and, exploiting a zero-one law for hitting probabilities, simplify recent work by S. Gardiner and M. Ghergu, A. Mimica and Z. Vondra?ek, and the author.     

Adsorption of amylase enzyme on ultrafiltration membranes

A method to measure the static adsorption on membrane surfaces has been developed and described. The static adsorption of amylase-F has been measured on two different ultrafiltration membranes, both with a cutoff value of 10 kDa (a PES membrane and the ETNA10PP membrane, which is a surface-modified PVDF membrane). The adsorption follows the Langmuir adsorption theory. Thus, the static adsorption consists of monolayer coverage and is expressed both as a permeability drop and an adsorption resistance. From the adsorption isotherms, the maximum static permeability drops and the maximum static adsorption resistances are determined. The maximum static permeability drop for the hydrophobic PES membrane is 75%, and the maximum static adsorption resistance is 0.014 m2.h.bar/L. The maximum static permeability drop for the hydrophilic surface-modified PVDF membrane (ETNA10PP) is 23%, and the maximum static adsorption resistance is 0.0046 m2.h.bar/L. The difference in maximum static adsorption, by a factor of around 3, affects the performance during the filtration of a 5 g/L amylase-F solution at 2 bar. The two membranes behave very similarly during filtration with almost equal fluxes and retentions even though the initial water permeability of the PES membrane is around 3 times larger than the initial water permeability of the ETNA10PP membrane. This is mainly attributed to the larger maximum static adsorption of the PES membrane. The permeability drop during filtration exceeds the maximum static permeability drop, indicating that the buildup layer on the membranes during filtration exceeds monolayer coverage, which is also seen by the increase in fouling resistance during filtration. The accumulated layer on the membrane surface can be described as a continually increasing cake-layer thickness, which is independent of the membrane type. At higher concentrations of enzyme, concentration polarization effects cannot be neglected. Therefore, stagnant film theory and the osmotic pressure model can describe the relationship between flux and bulk concentration.     

Structural engineering of pMHC reagents for T cell vaccines and diagnostics

MHC class I peptide complexes (pMHC) are routinely used to enumerate T cell populations and are currently being evaluated as vaccines to tumors and specific pathogens. Herein, we describe the structures of three generations of single-chain pMHC progressively designed for the optimal presentation of covalently associated epitopes. Our ultimate design employs a versatile disulfide trap between an invariant MHC residue and a short C-terminal peptide extension. This general strategy is nondisruptive of native pMHC conformation and T cell receptor engagement. Indeed, cell-surface-expressed MHC complexes with disulfide-trapped epitopes are refractory to peptide exchange, suggesting they will make safe and effective vaccines. Furthermore, we find that disulfide-trap stabilized, recombinant pMHC reagents reliably detect polyclonal CD8 T cell populations as proficiently as conventional reagents and are thus well suited to monitor or modulate immune responses during pathogenesis.     

Error bounds for stochastic shortest path problems

For stochastic shortest path problems, error bounds for value iteration due to Bertsekas elegantly generalize the classic MacQueen–Porteus error bounds for discounted infinite-horizon Markov decision problems, but incur prohibitive computational overhead. We derive bounds on these error bounds that can be computed with little or no overhead, making them useful in practice—especially so, since easily-computed error bounds have not previously been available for this class of problems.