Modeling and Analysis of Modal Switching in Networked Transport Systems

We consider networked transport systems defined on directed graphs: the dynamics on the edges correspond to solutions of transport equations with space dimension one. In addition to the graph setting, a major consideration is the introduction and propagation of discontinuities in the solutions when the system may discontinuously switch modes, naturally or as a hybrid control. This kind of switching has been extensively studied for ordinary differential equations, but not much so far for systems governed by partial differential equations. In particular, we give well-posedness results for switching as a control, both in finite horizon open loop operation and as feedback based on sensor measurements in the system.     

Structures induced by collections of subsets: a hypergraph approach

During recent years, much attention has been paid by anthropologists and sociologists to the analysis of social networks. These networks arise from dyadic relationships such as kinship or friendship and they have been studied using techniques derived from graph theory. Although the study of such networks can cast much light on the social structure of a population, many important aspects of this structure cannot be addressed using dyadic relationships alone. For example, group membership gives rise to natural non-dyadic relationships which will be distorted if they are forced into a dyadic mold. The purpose of this paper is to propose an analytical scheme which will permit the study of structure induced by non-dyadic relationships. The concepts used derive from the theory of hypergraphs, and it is shown that these concepts permit a wide variety of structural questions to be posed.     

A convection/reaction/switching system

We consider a spatially distributed hybrid system consisting of a convection/reaction system in which the reaction switches discontinuously in time between modes, independently at each spatial point on reaching “switching thresholds”. The model involves a novel formulation for evolution of the free boundary between the modal regions.     

Selectivity and affinity of DNA triplex forming oligonucleotides containing the nucleoside analogues 2'-O-methyl-5-(3-amino-1-propynyl)uridine and 2'-O-methyl-5-propynyluridine

Triplex forming oligonucleotides (TFOs) containing the nucleoside analogues 2'-O-methyl-5-propynyluridine (1) and 2'-O-methyl-5-(3-amino-1-propynyl)uridine (2) were synthesized. The affinity and selectivity of triplex formation by these TFOs were studied by gel shift analysis, T(m) value measurement, and association rate assays. The results show that the introduction of 1 and 2 into TFOs can improve the stability of the triplexes under physiological conditions. Optimized distribution of 1 or 2 in the TFOs combined with a cluster of contiguous nucleosides with 2'-aminoethoxy sugars resulted in formation of triplexes with further enhanced stability and improved selectivity.     

Comparison of compositional and morphological atom-probe tomography analyses for a multicomponent Fe-Cu steel.

A multicomponent Fe-Cu based steel is studied using atom-probe tomography. The precipitates are identified using two different methodologies and subsequent morphological and compositional results are compared. The precipitates are first identified using a maximum separation distance algorithm, the envelope method, and then by a concentration threshold method, an isoconcentration surface. We discuss in detail the proper selection of the parameters needed to delineate precipitates utilizing both methods. The results of the two methods exhibit a difference of 44 identified precipitates, which can be attributed to differences in the basis of both methods and the sensitivity of our results to user-prescribed parameters. The morphology of the precipitates, characterized by four different precipitate radii and precipitate size distribution functions (PSDs), are compared and evaluated. A variation of less than approximately 8% is found between the different radii. Two types of concentration profiles are compared, giving qualitatively similar results. Both profiles show Cu-rich precipitates containing Fe with elevated concentrations of Ni, Al, and Mn near the heterophase interfaces. There are, however, quantitative disagreements due to differences in the basic foundations of the two analysis methods.     

Two results on exact boundary control of parabolic equations

(1) The known nullcontrollability result for boundary control ofu _t = u_xx + q(x)u is generalized to consider a time-dependent coefficientq. (2) For boundary control ofu _t =Au (where it is known thatC _T : (initial data) (optimal nullcontrol for timeT) exists for allT>0) it is shown that logC _T =145-1 asT 0.