Firms, destinations, and aggregate fluctuations

This paper uses a database covering the universe of French firms for the period 1990-2007 to provide a forensic account of the role of individual firms in generating aggregatefluctuations. We set up a simple multi-sector model of heterogeneous firms selling tomultiple markets to motivate a theoretically-founded decomposition of firms' annualsales growth rate into different components. We find that the firm-specific componentcontributes substantially to aggregate sales volatility, mattering about as much as thecomponents capturing shocks that are common across firms within a sector or country.We then decompose the firm-specific component to provide evidence on two mechanismsthat generate aggregate fluctuations from microeconomic shocks highlighted in the recentliterature: (i) when the firm size distribution is fat-tailed, idiosyncratic shocks tolarge firms directly contribute to aggregate fluctuations; and (ii) aggregate fluctuationscan arise from idiosyncratic shocks due to input-output linkages across the economy.Firm linkages are approximately three times as important as the direct effect of firmshocks in driving aggregate fluctuations.

The minimum tree for a given zero-entropy period

We answer the following question: given any n∈ℕ, which is the minimum number of endpoints en of a tree admitting a zero-entropy map f with a periodic orbit of period n? We prove that en=s1s2…sk−∑i=2ksisi+1…sk, where n=s1s2…sk is the decomposition of n into a product of primes such that si≤si+1 for 1≤iof period m with em>e, then the topological entropy of f is positive

Binding free energy differences in a TCR-peptide-MHC complex induced by a peptide mutation: a simulation analysis.

Recognition by the T-cell receptor (TCR) of immunogenic peptides presented by class I major histocompatibility complexes (MHCs) is the determining event in the specific cellular immune response against virus-infected cells or tumor cells. It is of great interest, therefore, to elucidate the molecular principles upon which the selectivity of a TCR is based. These principles can in turn be used to design therapeutic approaches, such as peptide-based immunotherapies of cancer. In this study, free energy simulation methods are used to analyze the binding free energy difference of a particular TCR (A6) for a wild-type peptide (Tax) and a mutant peptide (Tax P6A), both presented in HLA A2. The computed free energy difference is 2.9 kcal/mol, in good agreement with the experimental value. This makes possible the use of the simulation results for obtaining an understanding of the origin of the free energy difference which was not available from the experimental results. A free energy component analysis makes possible the decomposition of the free energy difference between the binding of the wild-type and mutant peptide into its components. Of particular interest is the fact that better solvation of the mutant peptide when bound to the MHC molecule is an important contribution to the greater affinity of the TCR for the latter. The results make possible identification of the residues of the TCR which are important for the selectivity. This provides an understanding of the molecular principles that govern the recognition. The possibility of using free energy simulations in designing peptide derivatives for cancer immunotherapy is briefly discussed.