The 2-intersection number of paths and bounded-degree trees

We represent a graph by assigning each vertex a finite set such that vertices are adjacent if and only if the corresponding sets have at least two common elements. The 2-intersection number θ₂(G) of a graph G is the minimum size of the union of sets in such a representation. We prove that the maximum order of a path that can be represented in this way using t elements is between (t² - 19t + 4)/4 and (t² - t + 6)/4, making θ₂(P_n) asymptotic to 2√n. We also show the existence of a constant c depending on ? such that, for any tree T with maximum degree at most d, θ₂(T) ≤ c(√n)^1+?. When the maximum degree is not bounded, there is an n-vertex tree T with θ₂(T) > .945n^2/3. © 1995 John Wiley & Sons, Inc.     

Analyzing the performance of simultaneous generalized hill climbing algorithms

Simultaneous generalized hill climbing (SGHC) algorithms provide a framework for using heuristics to simultaneously address sets of intractable discrete optimization problems where information is shared between the problems during the algorithm execution. Many well-known heuristics can be embedded within the SGHC algorithm framework. This paper shows that the solutions generated by an SGHC algorithm are a stochastic process that satisfies the Markov property. This allows problem probability mass functions to be formulated for particular sets of problems based on the long-term behavior of the algorithm. Such results can be used to determine the proportion of iterations that an SGHC algorithm will spend optimizing over each discrete optimization problem. Sufficient conditions that guarantee that the algorithm spends an equal number of iterations in each discrete optimization problem are provided. SGHC algorithms can also be formulated such that the overall performance of the algorithm is independent of the initial discrete optimization problem chosen. Sufficient conditions are obtained guaranteeing that an SGHC algorithm will visit the globally optimal solution for each discrete optimization problem. Lastly, rates of convergence for SGHC algorithms are reported that show that given a rate of convergence for the embedded GHC algorithm, the SGHC algorithm can be designed to preserve this rate.     

Metaheuristics for a Flexible Assembly System Design Problem

Flexibility has become an important priority in the formulation and implementation of manufacturing strategies. This in turn has opened up a new class of design problems for such systems. Flexible assembly systems (FAS), consisting of a variety of processors and operations, provide the opportunity for improving product manufacturing flexibility, hence gaining competitive advantages. This paper considers a particular design decision problem for FAS. A matrix-based, polynomial-time lower bound algorithm is presented. Simulated annealing and tabu search metaheuristics are formulated to address the problems. Computational experience with these metaheuristics is reported.     

Polymeric Nanoparticles with a Glutathione‐Sensitive Heterodimeric Multifunctional Prodrug for In Vivo Drug Monitoring and Synergistic Cancer Therapy

Polymeric micelle‐based drug delivery systems have dramatically improved the delivery of small molecular drugs, yet multiple challenges remain to be overcome. A polymeric nanomedicine has now been engineered that possesses an ultrahigh loading (59 %) of a glutathione (GSH)‐sensitive heterodimeric multifunctional prodrug (HDMP) to effectively co‐deliver two synergistic drugs to tumors. An HDMP comprising of chemotherapeutic camptothecin (CPT) and photosensitizer 2‐(1‐hexyloxyethyl)‐2‐devinyl pyropheophorbide‐α (HPPH) was conjugated via a GSH‐cleavable linkage. The intrinsic fluorogenicity and label‐free radio‐chelation (⁶⁴Cu) of HPPH enabled direct drug monitoring by fluorescence imaging and positron emission tomography (PET). Through quantitative PET imaging, HDMP significantly improves drug delivery to tumors. The high synergistic therapeutic efficacy of HDMP‐loaded NPs highlights the rational design of HDMP, and presents exciting opportunities for polymer NP‐based drug delivery.     

A Criterion for Stability of Two-Term Recurrence Sequences Modulo 2

The authors describe a technique for characterizing stable two-term recurrence sequences and apply the technique to identify stable sequences that were not previously known to be stable.