On the complexity of project scheduling to minimize exposed time

We consider project scheduling where the project manager’s objective is to minimize the time from when an adversary discovers the project until the completion of the project. We analyze the complexity of the problem identifying both polynomially solvable and NP-hard versions of the problem. The complexity of the problem is seen to be dependent on the nature of renewable resource constraints, precedence constraints, and the ability to crash activities in the project.     

An extension of the truth table method to cross products

This paper provides a graphical (technical) exhaustive search algorithm for elements which belong to expressions containing cross products of sets. Initial tests suggest that this technique, an extension of the truth table technique, is superior to the currently employed method of verbal (symbolic) inclusion check. The method allows routine treatment of complicated expressions which contain cross products, utilizing the basic table     

Using bid data for the management of sequential,multi-unit,online auctions with uniformly distributed bidder valuations

Internet auctions for consumers’ goods are an increasingly popular selling venue. We have observed that many sellers, instead of offering their entire inventory in a single auction, split it into sequential auctions of smaller lots, thereby reducing the negative market impact of larger lots. Information technology also makes it possible to collect and analyze detailed bid data from online auctions. In this paper, we develop and test a new model of sequential online auctions to explore the potential benefits of using real bid data from earlier auctions to improve the management of future auctions. Assuming a typical truth-revealing auction model, we quantify the effect of the lot size on the closing price and derive a closed-form solution for the problem of allocating inventory across multiple auctions when bidder valuation distributions are known. We also develop a decision methodology for allocating inventory across multiple auctions that dynamically incorporates the results of previous auctions as feedback into the management of subsequent auctions, and updating the lot size and number of auctions. We demonstrate how information signals from previous auctions can be used to update the auctioneer’s beliefs about the customers’ valuation distribution, and then to significantly increase the seller’s profit potential. We use several examples to reveal the benefits of using detailed transaction data for the management of sequential, multi-unit, online auctions and we demonstrate how these benefits are influenced by the inventory holding costs, the number of bidders, and the dispersion of consumers’ valuations.     

Matrix-based autologous chondrocyte implantation for cartilage repair: noninvasive monitoring by high-resolution magnetic resonance imaging

OBJECTIVE: Monitoring of articular cartilage repair after matrix-associated autologous chondrocyte implantation (MACI) by a new grading and point-scale system based on noninvasive cartilage-specific magnetic resonance imaging (MRI) protocol. PATIENTS AND METHODS: In 20 patients, postoperative high-resolution MRI follow-up examinations at 4, 12, 24 and 52 weeks after matrix-based ACI for cartilage repair were initiated. The repair tissue was described with separate variables: degree of defect repair in width and length, surface, structure and signal intensity of the repair tissue, and status of the subchondral lamina and bone. For these variables, a grading system with point-scale evaluation was applied, and the mean average values were calculated for every follow-up MR exam of each patient. RESULTS: In 10 patients, an incomplete filling of the defect improved to complete filling (6 patients) or less incomplete (4 patients) filling of the defect. Three cases of implant hypertrophy returned to normal within 1 year. Complete filling of the defect by repair tissue was found in 2 patients from the beginning. Integration was complete in 10 cases. Improvement of incomplete to complete integration was found in 3 patients. The signal intensity of the implant developed to native cartilage signal in 13 patients. The mean average values increased from the 4th to the 52 nd week in 17 of 20 patients and decreased in 3 of 20 patients. CONCLUSION: High-resolution MRI provides a noninvasive tool for monitoring the development of cartilage repair tissue in MACI over time and helps to differentiate abnormal repair tissue from a normal maturation process.     

Are cerebral cavernomas truly nonenhancing lesions and thereby distinguishable from arteriovenous malformations?: MRI findings and histopathological correlation

PURPOSE: The aim of this study was to determine whether cerebral cavernomas are truly nonenhancing lesions on magnetic resonance imaging (MRI), whether they can be distinguished from arteriovenous malformations (AVM) on that basis and to evaluate the incidence of their association with developmental venous anomalies (DVA). PATIENTS AND METHODS: Thirty-two patients who underwent neurosurgical operation for a cerebral vascular malformation and had a standard MRI conclusive of cerebral cavernoma were retrospectively evaluated for size of the lesions, contrast enhancement of the lesion and the coexistence of DVA. The contrast uptake of these lesions was investigated, and contrast enhancement was classified as none, moderate or marked. The incidence of an associated DVA was also investigated. The radiological findings were subsequently correlated with neurohistopathological findings. RESULTS: No difference was found between the contrast enhancement of cavernomas and AVMs. Cross tables were calculated for contrast enhancement and size, which demonstrated no statistically significant correlation. Cross tables were calculated for contrast enhancement and histopathological diagnosis, which revealed that both entities presented variable degrees of contrast enhancement and were thereby not distinguishable from each other on the basis of contrast enhancement. We found an association of cavernoma with DVA in 30% of cases. CONCLUSION: Neither a correlation between the absence of contrast enhancement and the histopathological diagnosis of cavernoma nor the size and contrast enhancement was found. We conclude that cavernomas present with variable degrees of contrast enhancement on MRI and, thus, are definitely not distinguishable from AVM on the basis of contrast enhanced MRI. We found an association between cavernomas and DVA in approximately one third of patients.     

The concept ‘model’ and its potential role in mathematics education

Under the general term ‘mathematical models’ is now subsumed a sufficiently diversified collection of distinct types of models to merit categorization and an attempt at a unified definition. In this study a broad ‘working definition’ for the concept ‘model’ is proposed; basic types of models are identified and illustrated, and the impact of conscious instruction of models on mathematics education is analysed.