Construction of a New Class of Tetracycline Lead Structures with Potent Antibacterial Activity through Biosynthetic Engineering

Antimicrobial resistance and the shortage of novel antibiotics have led to an urgent need for new antibacterial drug leads. Several existing natural product scaffolds (including chelocardins) have not been developed because their suboptimal pharmacological properties could not be addressed at the time. It is demonstrated here that reviving such compounds through the application of biosynthetic engineering can deliver novel drug candidates. Through a rational approach, the carboxamido moiety of tetracyclines (an important structural feature for their bioactivity) was introduced into the chelocardins, which are atypical tetracyclines with an unknown mode of action. A broad‐spectrum antibiotic lead was generated with significantly improved activity, including against all Gram‐negative pathogens of the ESKAPE panel. Since the lead structure is also amenable to further chemical modification, it is a platform for further development through medicinal chemistry and genetic engineering.     

A Tensile Strain Hardening Test Indicator of Environmental Stress Cracking Resistance

Environmental stress cracking resistance (ESCR) is an important indicator of performance for high density polyethylene (HDPE) in structural and polymer pipe applications. The commonly used test for determining ESCR of HDPE can be time consuming and rather imprecise. A tensile strain hardening test was recently proposed to offer a faster way to characterize ESCR of polyethylene. In this paper, a practical approach is adopted whereby the test is extended to room temperature and shown to relate reliably to the ESCR of HDPE. Several HDPE resins (including pipe‐grade resins) are analyzed at strain rates of 0.5 mm/min and 7 mm/min to compare the effect of strain rate. Comparisons between the conventional ESCR test method and the strain hardening test show that strain hardening can be used to rank ESCR of HDPE in a reliable fashion. In our study the more direct measure of “hardening stiffness” is used to compare resins instead of strain hardening modulus. Because no true stress‐strain measurement is needed, this is a much simpler test method than other methods previously suggested. In addition, the use of the natural drawing ratio (NDR) as ESCR ranking indicator is examined. Results show that NDR can also be employed as a strain rate‐independent indicator of ESCR of HDPE. The test proposed herein is practical, simple and precise, and hence a more reliable indicator of ESCR performance of HDPE.     

A Nondifferentiable Optimization Algorithm for Structural Problems with Eigenvalue Inequality Constraints*

This paper presents a nondifferentiable optimization algorithm for solution of structural optimal design problems with eigenvalue inequality constraints. The algorithm is shown to be convergent both in the L _∞ and in the sequence space topologies.     

Fourier transform versus Hilbert transform

Certain relations between the Fourier transform of a function and the Hilbert transform of its derivative are revealed. They concern the integrability/non-integrability of both transforms. Certain applications are discussed.     

An Algorithm Based on Active Sets and Smoothing for Discretized Semi-Infinite Minimax Problems

We present a new active-set strategy which can be used in conjunction with exponential (entropic) smoothing for solving large-scale minimax problems arising from the discretization of semi-infinite minimax problems. The main effect of the active-set strategy is to dramatically reduce the number of gradient calculations needed in the optimization. Discretization of multidimensional domains gives rise to minimax problems with thousands of component functions. We present an application to minimizing the sum of squares of the Lagrange polynomials to find good points for polynomial interpolation on the unit sphere in ℝ³. Our numerical results show that the active-set strategy results in a modified Armijo gradient or Gauss-Newton like methods requiring less than a quarter of the gradients, as compared to the use of these methods without our active-set strategy. Finally, we show how this strategy can be incorporated in an algorithm for solving semi-infinite minimax problems.     

On the Convergence of the Pshenichnyi-Pironneau-Polak Minimax Algorithm with an Active Set Strategy

The purpose of this technical note is to present a proof of convergence of the Pshenichnyi-Pironneau-Polak (PPP) minimax algorithm (see Algorithm 2.4.1 in Polak, Optimization: Algorithms and Consistent Approximations, Springer, [1997]), modified to use an active set strategy. This active set strategy was formally derived in Polak (Optimization: Algorithms and Consistent Approximations, Springer, [1997]) from those used in the methods of feasible directions developed by Zoutendijk (Methods of Feasible Directions, Elsevier, [1960]) and Polak (Computational Methods in Optimization: A Unified Approach, Academic, [1971]). The resulting ε-Active PPP algorithm was presented as Algorithm 2.4.34, in Polak (Optimization: Algorithms and Consistent Approximations, Springer, [1997]), without any proofs.     

Algorithms for Finite and Semi-Infinite Min–Max–Min Problems Using Adaptive Smoothing Techniques

We develop two implementable algorithms, the first for the solution of finite and the second for the solution of semi-infinite min-max-min problems. A smoothing technique (together with discretization for the semi-infinite case) is used to construct a sequence of approximating finite min-max problems, which are solved with increasing precision. The smoothing and discretization approximations are initially coarse, but are made progressively finer as the number of iterations is increased. This reduces the potential ill-conditioning due to high smoothing precision parameter values and computational cost due to high levels of discretization. The behavior of the algorithms is illustrated with three semi-infinite numerical examples.