Projections on Convex Sets in the Relaxed Limit

The paper establishes the continuity of the best approximation, or the projection, of a function in L _p for p[1,), on a closed convex set in the space, when the set varies and converges to a limit set in the Young-measure relaxation of the space. To this end a strong-type convergence and a convexity structure are identified on the space of Young measures. The appropriate convergence of sets with respect to which the continuity holds is the Mosco convergence of sets associated with the strong-type convergence of functions.     

Continuum regularization of gauge theory with fermions

The covariant-derivative regularization program is discussed ford-dimensional gauge theory coupled to fermions in an arbitrary representation.     

On the complexity of the exchange algorithm for minimax optimization problems

We present an exchange algorithm for the solution of minimax optimization problems involving convex functions. For a certain class of functions, the complexity of this algorithm is shown to be either linear in the number of functions, or at least squared in that number.     

The gravity p-median model

In this paper we propose a new model for the p-median problem. In the standard p-median problem it is assumed that each demand point is served by the closest facility. In many situations (for example, when demand points are communities of customers and each customer makes his own selection of the facility) demand is divided among the facilities. Each customer selects a facility which is not necessarily the closest one. In the gravity p-median problem it is assumed that customers divide their patronage among the facilities with the probability that a customer patronizes a facility being proportional to the attractiveness of that facility and to a decreasing utility function of the distance to the facility.     

A note on the Weber location problem

In this note, we collect some interesting and useful results about the Weber problem. We investigate an accelerated Weiszfeld procedure which increases the step size and find a formula for the step size that empirically produces the fastest convergence rate. We also derive an estimate for the optimal cost of the system.     

Disorder induced granularity in an amorphous superconductor

We present experimental evidence that shows that the transport mechanism on the insulating side of the superconductor to insulator transition may be modified by the presence of small “droplets” of non-percolating superconducting regions. From the conductivity point of view, the system behaves as a granular system despite the fact that the underlying structure is essentially amorphous.     

ERYTHROPOIETIC PROTOPORPHYRIA: PHOTODYNAMIC TRANSFER OF PROTOPORPHYRIN FROM INTACT ERYTHROCYTES TO OTHER CELLS

Erythrocytes in patients with erythropoietic protoporphyria (EPP) contain large amounts of protoporphyrin and are regarded as the main source of protoporphyrin in this disease. Cells in the skin of EPP patients accumulate protoporphyrin released from the erythrocytes and upon sun exposure endothelial cells are photodamaged. In the present study a light-induced transfer of protoporphyrin directly from EPP erythrocytes to cultured cells is demonstrated. Erythrocytes were layered upon cultured cells and irradiated. The nearness of erythrocyte and cultured cell membranes potentiated the transfer of protoporphyrin between these cells. This transfer was rapid and preceded the release of protoporphyrin to proteins in the medium. Further irradiation of the protoporphyrin-enriched cultured cells, after removal of the erythrocytes, caused severe photodamage to the cells and survival was dependent on both the amount of protoporphyrin transferred and on the light fluence. Clinical observations and the results of this study indicate that light energy may be involved in two steps in the pathophysiology of EPP: (A) light-induced release of protoporphyrin from erythrocytes to endothelial cells and (B) photodynamic damage to protoporphyrin-enriched endothelial cells.     

A Multivariate Approach to Estimating the Completion Time for PERT Networks

Stochastic PERT is typically treated as a critical path problem, with the critical path having a univariate probability distribution. A method has been developed to treat the PERT problem as a multivariate problem taking into consideration correlation among paths, thereby providing a more accurate analysis of the network and its corresponding probabilities for completion time.     

Efficient algorithms for finding minimum spanning trees in undirected and directed graphs

Recently, Fredman and Tarjan invented a new, especially efficient form of heap (priority queue). Their data structure, theFibonacci heap (or F-heap) supports arbitrary deletion inO(logn) amortized time and other heap operations inO(1) amortized time. In this paper we use F-heaps to obtain fast algorithms for finding minimum spanning trees in undirected and directed graphs. For an undirected graph containingn vertices andm edges, our minimum spanning tree algorithm runs inO(m logβ (m, n)) time, improved fromO(mβ(m, n)) time, whereβ(m, n)=min {i|log⁽ⁱ⁾ n ≦m/n}. Our minimum spanning tree algorithm for directed graphs runs inO(n logn + m) time, improved fromO(n log n +m log log log_(m/n+2) n). Both algorithms can be extended to allow a degree constraint at one vertex. Research supported in part by National Science Foundation Grant MCS-8302648. Research supported in part by National Science Foundation Grant MCS-8303139. Research supported in part by National Science Foundation Grant MCS-8300984 and a United States Army Research Office Program Fellowship, DAAG29-83-GO020.