Logic-Based Modeling and Solution of Nonlinear Discrete/Continuous Optimization Problems

This paper presents a review of advances in the mathematical programming approach to discrete/continuous optimization problems. We first present a brief review of MILP and MINLP for the case when these problems are modeled with algebraic equations and inequalities. Since algebraic representations have some limitations such as difficulty of formulation and numerical singularities for the nonlinear case, we consider logic-based modeling as an alternative approach, particularly Generalized Disjunctive Programming (GDP), which the authors have extensively investigated over the last few years. Solution strategies for GDP models are reviewed, including the continuous relaxation of the disjunctive constraints. Also, we briefly review a hybrid model that integrates disjunctive programming and mixed-integer programming. Finally, the global optimization of nonconvex GDP problems is discussed through a two-level branch and bound procedure.     

Comparison principles applied to obstacle problems with penalties

Penalty methods form a well known technique to embed elliptic variational inequality problems into a family of variational equations (cf. [6], [13], [17]). Using the specific inverse monotonicity properties of these problems L _∞-bounds for the convergence can be derived by means of comparison solutions. Lagrange duality is applied to estimate parameters involved.

For piecewise linear finite elements applied on weakly acute triangulations in combination with mass lumping the inverse monotonicity of the obstacle problems can be transferred to its discretization. This forms the base of similar error estimations in the maximum norm for the penalty method applied to the discrete problem.

The technique of comparison solutions combined with the uniform boundedness of the Lagrange multipliers leads to decoupled convergence estimations with respect to the discretization and penalization parameters.     

A Branch and Contract Algorithm for Problems with Concave Univariate, Bilinear and Linear Fractional Terms

A new deterministic branch and bound algorithm is presented in this paper for the global optimization of continuous problems that involve concave univariate, bilinear and linear fractional terms. The proposed algorithm, the branch and contract algorithm, relies on the use of a bounds-contraction subproblem that aims at reducing the size of the search region by eliminating portions of the domain in which the objective function takes only values above a known upper bound. The solution of contraction subproblems at selected branch and bound nodes is performed within a finite contraction operation that helps reducing the total number of nodes in the branch and bound solution tree. The use of the proposed algorithm is illustrated with several numerical examples.     

Backward production of the B meson in K−p interactions at 4.2 GeVc

The backward production of the B(1235) meson is studied in the reaction K^?p→Σ^?π⁺ω. This reaction is observed in the final state Σ^?π⁺π⁺π^?π⁰. A π⁺ω mass enhancement is visible in the region of the B meson for events with small |u|K^? →Σ^?) squared four-momentum transfer. The properties of the enhancement agree with those of the B meson. The cross section for K^?p→Σ^?B⁺ at $\text{4.15}\text{GeV}\text{c}$ incident K^? momentum is (3.2 ± 0.5) μb. The backward production of the B meson is compared with similar baryon exchange productions of the A₁ and C(Q₁) axial vector mesons observed in the same experiment.     

Nonlinear and nonlocal transport effects in simple fluids

Correlation function formulae for transport coefficients of 2nd order in arbitrarily dense fluids are derived, using a modified Chapman-Enskog solution of the Liouville equation. Some static correlations are neglected. Approximate evaluation for dilute gases gives essentially the same results as the solution of Boltzmann's equation. As an application higher order transport effects in the critical region are estimated. It is conjectured that they are apparent in sound absorption and the line width of Rayleigh scattering if (T?T_c)/T _c?10^?3.     

Direct Modulation of Small GTPase Activity and Function

Small GTPases are a family of GDP‐/GTP‐binding proteins that serve as biomolecular switches inside cells to control a variety of essential cellular processes. Aberrant function and regulation of small GTPases is associated with a variety of human diseases, thus rendering these proteins highly interesting targets in drug discovery. However, this class of proteins has been considered “undruggable”, as intensive decade‐long efforts did not yield clinically relevant direct modulators of small GTPases. Recently, the targeting of small GTPases has gained fresh impetus through the discovery of novel transient cavities on the protein surfaces and the application of new targeting strategies. Besides Ras proteins, other small GTPases have attracted increased attention since improved biological insight in combination with novel targeting strategies identified them as promising targets in drug discovery. This Review gives an overview of relevant aspects of the superfamily of small GTPases and summarizes recent progress and perspectives for the direct modulation of these challenging targets.