In this paper we propose a new simplicial partition-based deterministic algorithm for global optimization of Lipschitz-continuous functions without requiring any knowledge of the Lipschitz constant. Our algorithm is motivated by the well-known Direct algorithm which evaluates the objective function on a set of points that tries to cover the most promising subregions of the feasible region. Almo...

Abstract Involution Schubert polynomials represent cohomology classes of K -orbit closures in the complete flag variety, where is orthogonal or symplectic group. We show they also $\mathsf {T}$ -equivariant subvarieties defined by upper-left rank conditions spaces symmetric skew-symmetric matrices. This geometry implies that these are positive combinations monomials variables $x_i + x_j$ , and ...

We have investigated the role of IL-6 in the initiation and progression of mouse mammary gland involution in IL-6-null mice. This study was based on the hypothesis that IL-6 is the activating cytokine for signal transducer and activator of transcription 3 (Stat), the transcription factor whose presence is required for controlled mammary gland involution. We now show that expression of IL-6 is l...

We define an invariant of torsors under adjoint linear algebraic groups of type Cn—equivalently, central simple algebras of degree 2n with symplectic involution—for n divisible by 4 that takes values in H(k, μ2). The invariant is distinct from the few known examples of cohomological invariants of torsors under adjoint groups. We also prove that the invariant detects whether a central simple alg...

Involution is the process of post-lactational mammary gland regression to quiescence and it involves secretory epithelial cell death, stroma remodeling and gland repopulation by adipocytes. Though reportedly accompanying apoptosis, the role of autophagy in involution has not yet been determined. We now report that autophagy-related (ATG) proteins mediate dead cell clearance and suppress inflamm...

Recent pregnancy correlates with decreased survival for breast cancer patients compared with non-pregnancy-associated breast cancer. We hypothesize that postpartum mammary involution induces metastasis through wound-healing programs known to promote cancer. It is unknown whether alternatively activated M2 macrophages, immune cells important in wound-healing and experimental tumorigenesis that a...