On the algebra of cornered Floer homology

Bordered Floer homology associates to a parametrized oriented surface a certain differential graded algebra. We study the properties of this algebra under splittings of the surface. To the circle we associate a differential graded 2-algebra, the nilCoxeter sequential 2-algebra, and to a surface with connected boundary an algebra-module over this 2-algebra, such that a natural gluing property is satisfied. Moreover, with a view toward the structure of a potential Floer homology theory of 3-manifolds with codimension-two corners, we present a decomposition theorem for the Floer complex of a planar grid diagram, with respect to vertical and horizontal slicing.Comment: a few minor revision

Hyperbolic Relaxation of Reaction Diffusion Equations with Dynamic Boundary Conditions

Under consideration is the hyperbolic relaxation of a semilinear reaction-diffusion equation on a bounded domain, subject to a dynamic boundary condition. We also consider the limit parabolic problem with the same dynamic boundary condition. Each problem is well-posed in a suitable phase space where the global weak solutions generate a Lipschitz continuous semiflow which admits a bounded absorbing set. We prove the existence of a family of global attractors of optimal regularity. After fitting both problems into a common framework, a proof of the upper-semicontinuity of the family of global attractors is given as the relaxation parameter goes to zero. Finally, we also establish the existence of exponential attractors.Comment: to appear in Quarterly of Applied Mathematic

A path integral leading to higher-order Lagrangians

We consider a simple modification of standard phase-space path integrals and show that it leads in configuration space to Lagrangians depending also on accelerations.Comment: 6 page

Molecular Orbital Tomography using Short Laser Pulses

Recently, a method to image molecular electronic wave functions using high harmonic generation (HHG) was introduced by Itatani \textit{et al.\} [Nature {\textbf{432}}, 876 (2004)]. We show that, while the tomographic reconstruction of general orbitals with arbitrary symmetry cannot be performed with long laser pulses, this becomes possible when extremely short pulses are used. An alternative reconstruction equation based on momentum matrix elements, rather than on dipole matrix elements, is proposed. We present simulations of the procedure for 2D model systems based on numerical solutions of the time-dependent Schr\"{o}dinger equation, and present results from further post-processing of the reconstructed orbitals.Comment: 5 pages, 2 figure

A Survey on the Application of Evolutionary Algorithms for Mobile Multihop Ad Hoc Network Optimization Problems

Evolutionary algorithms are metaheuristic algorithms that provide quasioptimal solutions in a reasonable time. They have been applied to many optimization problems in a high number of scientific areas. In this survey paper, we focus on the application of evolutionary algorithms to solve optimization problems related to a type of complex network likemobilemultihop ad hoc networks. Since its origin, mobile multihop ad hoc network has evolved causing new types of multihop networks to appear such as vehicular ad hoc networks and delay tolerant networks, leading to the solution of new issues and optimization problems. In this survey, we review the main work presented for each type of mobile multihop ad hoc network and we also present some innovative ideas and open challenges to guide further research in this topic

Impact of classical strain improvement of penicillium rubens on amino acid metabolism during β-Lactam production

To produce high levels of β-lactams, the filamentous fungus Penicillium rubens (previously named Penicillium chrysogenum) has been subjected to an extensive classical strain improvement (CSI) program during the last few decades. This has led to the accumulation of many mutations that were spread over the genome. Detailed analysis reveals that several mutations targeted genes that encode enzymes involved in amino acid metabolism, in particular biosynthesis of L-cysteine, one of the amino acids used for β-lactam production. To examine the impact of the mutations on enzyme function, the respective genes with and without the mutations were cloned and expressed in Escherichia coli, purified, and enzymatically analyzed. Mutations severely impaired the activities of a threonine and serine deaminase, and this inactivates metabolic pathways that compete for L-cysteine biosynthesis. Tryptophan synthase, which converts L-serine into L-tryptophan, was inactivated by a mutation, whereas a mutation in 5-aminolevulinate synthase, which utilizes glycine, was without an effect. Importantly, CSI caused increased expression levels of a set of genes directly involved in cysteine biosynthesis. These results suggest that CSI has resulted in improved cysteine biosynthesis by the inactivation of the enzymatic conversions that directly compete for resources with the cysteine biosynthetic pathway, consistent with the notion that cysteine is a key component during penicillin production. IMPORTANCE Penicillium rubens is an important industrial producer of β-lactam antibiotics. High levels of penicillin production were enforced through extensive mutagenesis during a classical strain improvement (CSI) program over 70 years. Several mutations targeted amino acid metabolism and resulted in enhanced L-cysteine biosynthesis. This work provides a molecular explanation for the interrelation between secondary metabolite production and amino acid metabolism and how classical strain improvement has resulted in improved production strains