LOWLAD: a locally weightedL 1 smoothing spline algorithm with cross validated choice of smoothing parameters

The computation ofL ₁ smoothing splines on large data sets is often desirable, but computationally infeasible. A locally weighted, LAD smoothing spline based smoother is suggested, and preliminary results will be discussed. Specifically, one can seek smoothing splines in the spacesW _m (D), with [0, 1] ⁿ D. We assume data of the formy _i =f(t _i )+ _i ,i=1,..., N with {t _i } _i=1 ^N D, the _i are errors withE( _i )=0, andf is assumed to be inW _m . An LAD smoothing spline is the solution,s , of the following optimization problem

AnL 1 smoothing spline algorithm with cross validation

We propose an algorithm for the computation ofL ₁ (LAD) smoothing splines in the spacesW _M (D), with . We assume one is given data of the formy _i =(f(t _i ) + _i , i=1,...,N with {itt_i} _i=1 ^{N D} , the _i are errors withE( _i )=0, andf is assumed to be inW _M . The LAD smoothing spline, for fixed smoothing parameter0, is defined as the solution,s , of the optimization problem (1/N) _i=1 ^N ¦y _i –g(t _i ¦+J _M (g), whereJ _M (g) is the seminorm consisting of the sum of the squaredL ₂ norms of theMth partial derivatives ofg. Such an LAD smoothing spline,s , would be expected to give robust smoothed estimates off in situations where the _i are from a distribution with heavy tails. The solution to such a problem is a thin plate spline of known form. An algorithm for computings is given which is based on considering a sequence of quadratic programming problems whose structure is guided by the optimality conditions for the above convex minimization problem, and which are solved readily, if a good initial point is available. The data driven selection of the smoothing parameter is achieved by minimizing aCV() score of the form .The combined LAD-CV smoothing spline algorithm is a continuation scheme in 0 taken on the above SQPs parametrized in, with the optimal smoothing parameter taken to be that value of at which theCV() score first begins to increase. The feasibility of constructing the LAD-CV smoothing spline is illustrated by an application to a problem in environment data interpretation.     

Free Radicals as a Double-Edged Sword: The Cancer Preventive and Therapeutic Roles of Curcumin

Free radicals, generally composed of reactive oxygen species (ROS) and reactive nitrogen species (RNS), are generated in the body by various endogenous and exogenous systems. The overproduction of free radicals is known to cause several chronic diseases including cancer. However, increased production of free radicals by chemotherapeutic drugs is also associated with apoptosis in cancer cells, indicating the dual nature of free radicals. Among various natural compounds, curcumin manifests as an antioxidant in normal cells that helps in the prevention of carcinogenesis. It also acts as a prooxidant in cancer cells and is associated with inducing apoptosis. Curcumin quenches free radicals, induces antioxidant enzymes (catalase, superoxide dismutase, glutathione peroxidase), and upregulates antioxidative protein markers–Nrf2 and HO-1 that lead to the suppression of cellular oxidative stress. In cancer cells, curcumin aggressively increases ROS that results in DNA damage and subsequently cancer cell death. It also sensitizes drug-resistant cancer cells and increases the anticancer effects of chemotherapeutic drugs. Thus, curcumin shows beneficial effects in prevention, treatment and chemosensitization of cancer cells. In this review, we will discuss the dual role of free radicals as well as the chemopreventive and chemotherapeutic effects of curcumin and its analogues against cancer.     

Diversification of a β-Lactam Pharmacophore via Allylic C-H Amination: Accelerating Effect of Lewis Acid Co-Catalyst

This report describes the use of Pd(II)/bis-sulfoxide 1 catalyzed intra- and intermolecular allylic C-H amination reactions to rapidly diversify structures containing a sensitive β-lactam core similar to that found in the monobactam antibiotic Aztreonam. Pharmacologically interesting oxazolidinone, oxazinanone, and linear amine motifs are rapidly installed with predictable and high selectivities under conditions that use limiting amounts of substrate. Additionally, we demonstrate for the first time that intramolecular C-H amination processes may be accelerated using catalytic amounts of a Lewis acid co-catalyst [Cr(III)(salen)Cl 2].     

A polynomially bounded algorithm for a singly constrained quadratic program

This paper presents a characterization of the solutions of a singly constrained quadratic program. This characterization is then used in the development of a polynomially bounded algorithm for this class of problems.     

THE COLORS OF FIREFLY BIOLUMINESCENCE—II EXPERIMENTAL EVIDENCE FOR THE OPTIMIZATION MODEL*

Abstract— The shapes, the peak wavelengths and the close matching of bioluminescence colors to visual spectral sensitivities in North American firefly species are consistent with the predictions of a spectral optimization model for selection in evolution (Seliger et al., 1982). A screening pigment found by microspectrophotometry in the rhabomeres of Photinus pyralis has the absorbancc characteristics predicted by the model. The biologically effective adaptation, a dimensionless ratio proportional to the relative advantage of a species to detect bioluminescence during twilight. has been calculated from experimentally determined distributions of ambient spectral radiances, visual spectral sensitivities and bioluminescence emissions and is shown to correlate both with color of bioluminescence and with the timing of initiation of flashing activity. The colors of firefly bioluminescence are therefore species-specific adaptations to optimize the detection of bioluminescence in the different photic environments in which the species have evolved.