A Chemical Proteomic Probe for Detecting Dehydrogenases: \u3cem\u3eCatechol Rhodanine\u3c/em\u3e

The inherent complexity of the proteome often demands that it be studied as manageable subsets, termed subproteomes. A subproteome can be defined in a number of ways, although a pragmatic approach is to define it based on common features in an active site that lead to binding of a common small molecule ligand (ex. a cofactor or a cross-reactive drug lead). The subproteome, so defined, can be purified using that common ligand tethered to a resin, with affinity chromatography. Affinity purification of a subproteome is described in the next chapter. That subproteome can then be analyzed using a common ligand probe, such as a fluorescent common ligand that can be used to stain members of the subproteome in a native gel. Here, we describe such a fluorescent probe, based on a catechol rhodanine acetic acid (CRAA) ligand that binds to dehydrogenases. The CRAA ligand is fluorescent and binds to dehydrogenases at pH \u3e 7, and hence can be used effectively to stain dehydrogenases in native gels to identify what subset of proteins in a mixture are dehydrogenases. Furthermore, if one is designing inhibitors to target one or more of these dehydrogenases, the CRAA staining can be performed in a competitive assay format, with or without inhibitor, to assess the selectivity of the inhibitor for the targeted dehydrogenase. Finally, the CRAA probe is a privileged scaffold for dehydrogenases, and hence can easily be modified to increase affinity for a given dehydrogenase

S-Lemma with Equality and Its Applications

Let $f(x)=x^TAx+2a^Tx+c$ and $h(x)=x^TBx+2b^Tx+d$ be two quadratic functions having symmetric matrices $A$ and $B$. The S-lemma with equality asks when the unsolvability of the system $f(x)<0, h(x)=0$ implies the existence of a real number $\mu$ such that $f(x) + \mu h(x)\ge0, ~\forall x\in \mathbb{R}^n$. The problem is much harder than the inequality version which asserts that, under Slater condition, $f(x)<0, h(x)\le0$ is unsolvable if and only if $f(x) + \mu h(x)\ge0, ~\forall x\in \mathbb{R}^n$ for some $\mu\ge0$. In this paper, we show that the S-lemma with equality does not hold only when the matrix $A$ has exactly one negative eigenvalue and $h(x)$ is a non-constant linear function ($B=0, b\not=0$). As an application, we can globally solve $\inf\{f(x)\vert h(x)=0\}$ as well as the two-sided generalized trust region subproblem $\inf\{f(x)\vert l\le h(x)\le u\}$ without any condition. Moreover, the convexity of the joint numerical range $\{(f(x), h_1(x),\ldots, h_p(x)):~x\in\Bbb R^n\}$ where $f$ is a (possibly non-convex) quadratic function and $h_1(x),\ldots,h_p(x)$ are affine functions can be characterized using the newly developed S-lemma with equality.Comment: 34 page

Radial basis function classifier construction using particle swarm optimisation aided orthogonal forward regression

We develop a particle swarm optimisation (PSO) aided orthogonal forward regression (OFR) approach for constructing radial basis function (RBF) classifiers with tunable nodes. At each stage of the OFR construction process, the centre vector and diagonal covariance matrix of one RBF node is determined efficiently by minimising the leave-one-out (LOO) misclassification rate (MR) using a PSO algorithm. Compared with the state-of-the-art regularisation assisted orthogonal least square algorithm based on the LOO MR for selecting fixednode RBF classifiers, the proposed PSO aided OFR algorithm for constructing tunable-node RBF classifiers offers significant advantages in terms of better generalisation performance and smaller model size as well as imposes lower computational complexity in classifier construction process. Moreover, the proposed algorithm does not have any hyperparameter that requires costly tuning based on cross validation

Sparse kernel density estimation technique based on zero-norm constraint

A sparse kernel density estimator is derived based on the zero-norm constraint, in which the zero-norm of the kernel weights is incorporated to enhance model sparsity. The classical Parzen window estimate is adopted as the desired response for density estimation, and an approximate function of the zero-norm is used for achieving mathemtical tractability and algorithmic efficiency. Under the mild condition of the positive definite design matrix, the kernel weights of the proposed density estimator based on the zero-norm approximation can be obtained using the multiplicative nonnegative quadratic programming algorithm. Using the -optimality based selection algorithm as the preprocessing to select a small significant subset design matrix, the proposed zero-norm based approach offers an effective means for constructing very sparse kernel density estimates with excellent generalisation performance

Probability density estimation with tunable kernels using orthogonal forward regression

A generalized or tunable-kernel model is proposed for probability density function estimation based on an orthogonal forward regression procedure. Each stage of the density estimation process determines a tunable kernel, namely, its center vector and diagonal covariance matrix, by minimizing a leave-one-out test criterion. The kernel mixing weights of the constructed sparse density estimate are finally updated using the multiplicative nonnegative quadratic programming algorithm to ensure the nonnegative and unity constraints, and this weight-updating process additionally has the desired ability to further reduce the model size. The proposed tunable-kernel model has advantages, in terms of model generalization capability and model sparsity, over the standard fixed-kernel model that restricts kernel centers to the training data points and employs a single common kernel variance for every kernel. On the other hand, it does not optimize all the model parameters together and thus avoids the problems of high-dimensional ill-conditioned nonlinear optimization associated with the conventional finite mixture model. Several examples are included to demonstrate the ability of the proposed novel tunable-kernel model to effectively construct a very compact density estimate accurately

A Direct Elliptic Solver Based on Hierarchically Low-rank Schur Complements

A parallel fast direct solver for rank-compressible block tridiagonal linear systems is presented. Algorithmic synergies between Cyclic Reduction and Hierarchical matrix arithmetic operations result in a solver with $O(N \log^2 N)$ arithmetic complexity and $O(N \log N)$ memory footprint. We provide a baseline for performance and applicability by comparing with well known implementations of the $\mathcal{H}$-LU factorization and algebraic multigrid with a parallel implementation that leverages the concurrency features of the method. Numerical experiments reveal that this method is comparable with other fast direct solvers based on Hierarchical Matrices such as $\mathcal{H}$-LU and that it can tackle problems where algebraic multigrid fails to converge