An Abstraction of Whitney's Broken Circuit Theorem

We establish a broad generalization of Whitney's broken circuit theorem on the chromatic polynomial of a graph to sums of type $\sum_{A\subseteq S} f(A)$ where $S$ is a finite set and $f$ is a mapping from the power set of $S$ into an abelian group. We give applications to the domination polynomial and the subgraph component polynomial of a graph, the chromatic polynomial of a hypergraph, the characteristic polynomial and Crapo's beta invariant of a matroid, and the principle of inclusion-exclusion. Thus, we discover several known and new results in a concise and unified way. As further applications of our main result, we derive a new generalization of the maximums-minimums identity and of a theorem due to Blass and Sagan on the M\"obius function of a finite lattice, which generalizes Rota's crosscut theorem. For the classical M\"obius function, both Euler's totient function and its Dirichlet inverse, and the reciprocal of the Riemann zeta function we obtain new expansions involving the greatest common divisor resp. least common multiple. We finally establish an even broader generalization of Whitney's broken circuit theorem in the context of convex geometries (antimatroids).Comment: 18 page

The opportunity cost of negative screening in socially responsible investing

This paper investigates the impact of negative screening on the investment universe as well as on financial performance. We come up with a novel identification process and as such depart from mainstream socially responsible investing literature by concentrating on individual firms’ conduct and by studying a much wider range of issues. Firstly, we study the size and financial performance of fourteen potentially controversial issues: abortion, adult entertainment, alcohol, animal testing, contraceptives, controversial weapons, fur, gambling, genetic engineering, meat, nuclear power, pork, (embryonic) stem cells, and tobacco. We investigate an international sample of more than 1,600 stocks for more than twenty years. We then analyze the impact of applying negative screens to a market portfolio. Our findings suggest that the choice for negative screening strategies does matter for the size of the investment universe as well as for risk-adjusted return performance. Investing in controversial stocks in many cases results in additional risk-adjusted returns, whereas excluding them may reduce financial performance. These findings suggest that there are opportunity costs to negative screening.Publisher PDFPeer reviewe

Hepatitis C virus resistance to the new direct-acting antivirals

Introduction: The treatment of hepatitis C virus (HCV) infection has dramatically improved in recent years with the widespread use of interferon-free combination regimens. Despite the high sustained virological response (SVR) rates (over 90%) obtained with direct-acting antivirals (DAAs), drug resistance has emerged as a potential challenge. The high replication rate of HCV and the low fidelity of its RNA polymerase result in a high degree of genetic variability in the HCV population, which ultimately explains the rapid selection of drug resistance associated variants (RAVs). Areas covered: Results from clinical trials and real-world experience have both provided important information on the rate and clinical significance of RAVs. They can be present in treatment-naive patients as natural polymorphisms although more frequently they are selected upon treatment failure. In patients engaged in high-risk behaviors, RAVs can be transmitted. Expert opinion: Although DAA failures generally occur in less than 10% of treated chronic hepatitis C patients, selection of drug resistance is the rule in most cases. HCV re-treatment options are available, but first-line therapeutic strategies should be optimized to efficiently prevent DAA failure due to baseline HCV resistance. Considerable progress is being made and next-generation DAAs are coming with pangenotypic activity and higher resistance barrier.Fil: Esposito, Isabella. Hospital Universitario La Paz; EspañaFil: Trinks, Julieta. Hospital Italiano. Instituto de Ciencias Básicas y Medicina Experimental; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Soriano, Vicente. Hospital Universitario La Paz; Españ

Falling for Rising Temperatures?:finance in a carbon-constrained world

Mitigating climate change requires significant societal change. But global action to keep temperature rise within safe bounds is still highly deficient. A heated debate exists about the role that firms and financial markets play in contributing to a solution. However, why and to what extent would firms and investors care about rising temperatures? Based on a financial-economic framework of risk management, this thesis empirically investigates the relevance of climate-related factors for investment behavior and financial performance.Attention is given to the perspectives of investors, firms, and public policy and institutions. I zoom in on a key investor practice that accounts for climate change, namely fossil fuel divestment, and study its implications for risk and return in investment portfolios. Next, I investigate how firms’ carbon footprint impacts financial risk in individual assets and stock portfolios. I then take an in-depth look into firms’ carbon emissions from a productive efficiency perspective and study associations with financial performance. Finally, I explore to what extent expectations and uncertainty about future carbon constraints induce firms to use internal carbon prices. Overall, this thesis highlights that risk management provides firms and investors with an important reason to care about rising temperatures