The representation given in Example 3 has an interesting property. The set of matrices {ρ(e), ρ(g)} have common invariant subspaces (other than the trivial ones, namely (0, 0) and C). Indeed, we can eas­ ily verify that the (orthogonal) one­dimensional subspaces given by (t, t) and (t, −t) are invariant under the action of these matrices. Therefore, the restriction of ρ to those subspaces also ...

1 Overview In this lecture, we will • Wrap up Alon-Edmonds-Luby's graph theoretical codes: construction and analysis of distance • Introduce the interplay between codes and computational complexity: open problems and pseudorandomness 2 Alon-Edmonds-Luby The construction of the code depends on three main ingredients: • A binary code C 0 = [d, R 0 d, δ 0 d] 2 , where R 0 and δ 0 are our target ra...

Humans, like all social species, face various collective action problems (difficulties achieving potential benefits from cooperating when coordination is required or individuals have incentives to defect). Humans solve these problems through various means: communication, monitoring, enforcement, and selective incentives. This chapter summarizes the theory and evidence on human cooperation found...

Approximately 50% of patients who undergo resection for Colorectal Cancer will develop recurrent disease within 5 years. The liver is the major site of recurrence and the primary determinant of patient survival. Systematic attempts to resect colorectal liver metastasis were commenced some 40 years ago and subsequently became more widely accepted. A large number of reports showed that resection ...

As early as 1881, de Bary proposed that chemical substances emanating from the oogonia of watermolds triggered the development of antheridial branches and directed their growth toward these cells. This was, on the face of it, an unusually perceptive theory because de Bary did not fully accept the idea that fertilization by antheridia took place in any of the species then known in the family. Kl...

Introduction The estimation of genetic risks to the offspring of consanguineous marriages, especially those of first cousins, has been exhaustively studied in the literature. Even so the subject still remains controversial, as shown by the results of a recent inquiry performed among medical geneticists and genetic counsellors in the United States by Bennett et al. (1999). In fact, analysing the...

More than half a century after the debut of CPM and PERT, we still lack a project scheduling system with calibrated and validated distributions and without requiring complex user input. Modern decision support systems (DSS) for project management are more sophisticated and comprehensive than PERT/CPM. Nonetheless, in terms of stochastic analysis, they show insufficient progress. PERT 21 offers ...

HBV is a noncytopathic hepadnavirus and major human pathogen that causes immune-mediated acute and chronic hepatitis. The immune response to HBV antigens is age dependent: viral clearance occurs in most adults, while neonates and children usually develop chronic infection and liver disease. Here, we characterize an animal model for HBV infection that recapitulates the key differences in viral c...