A critical branching process model for biodiversity

Motivated as a null model for comparison with data, we study the following model for a phylogenetic tree on $n$ extant species. The origin of the clade is a random time in the past, whose (improper) distribution is uniform on $(0,\infty)$. After that origin, the process of extinctions and speciations is a continuous-time critical branching process of constant rate, conditioned on having the prescribed number $n$ of species at the present time. We study various mathematical properties of this model as $n \to \infty$ limits: time of origin and of most recent common ancestor; pattern of divergence times within lineage trees; time series of numbers of species; number of extinct species in total, or ancestral to extant species; and "local" structure of the tree itself. We emphasize several mathematical techniques: associating walks with trees, a point process representation of lineage trees, and Brownian limits.Comment: 31 pages, 7 figure

Contractual savings for housing : How suitable are they for transitional economies?

Problems of developing financial services for housing are acute in transitional socialist economies. The authors examine contractual savings for housing (CSH), which are often advocated as a primary solution, especially in Central and Eastern European countries. A CSH instrument links a phase of contractual savings remunerated at below-market rate to the promise of a housing loan at a rate also fixed below market at the time the contract is signed. This contract can contain a variety of options. CSH were used very successfully in Europe after World War II. The issue today is not whether such specialized instruments can work. They clearly can under low inflation. The issue is whether CSH systems are advisable today in latecomer countries with vastly different financial technology and financial policy environments. The authors focus on two influential CSH systems: the"closed"German Bausparsystem and the"open"French epargne-logement. In a"closed"CSH system, access to a housing loan is based on queuing: a loan can be made only if funds are available in the specialist institution. In an"open"system, the saver can legally call his or her loan at contract maturity, regardless of the liquidity conditions in the CSH system. From the perspective of households, CSH contracts facilitate the accumulation of equity and offer the prospect of a low-interest loan. They promote savings discipline and provide a concrete goal that many households find important. But CSH instruments leave the objective of providing a primary loan unmet. In additon, even moderate inflation quickly leads to very low loan-to-value ratios for CSH loans and a large financing gap for housing purchases. From the perspective of financial institutions, CSH can help overcome the severe information asymmetries they face in transitional socialist economies, where there are no retail financial markets, no credit bureaus, problematic income reporting. CSH are very effective in screening, monitoring, and establishing the reputation of steady savers as future borrowers, and they are good at lowering credit risks. With their saving periods of four to five years, CSH also help bridge the gap between long-term loans and short-term deposits. Finally, CSH can be an important commercial tool for developing cross-lending activities. But CSH can be risky. When the interest rate on outstanding contracts is low compared with current market rates, holders of mature contracts will want to call their loans. And new savers will be reluctant to sign on at very low contract rates. Eliminating this liquidity risk with a"closed"CSH system erodes the attractiveness of CSH. From the perspective of government, a CSH instrument can work in a noninflationary environment, yet a CSH system would have no justification in fully developed and competitive financial markets today. CSH instruments can play a useful but not a dominant role in housingfinance. After stabilization, they can overcome information constraints on financial contracts, and contribute to higher financial savings rates. CSH instruments are best used to finance home improvements. They can also be used as part of a social policy to reach targeted social groups.Financial Intermediation,Banks&Banking Reform,Payment Systems&Infrastructure,Public Sector Economics&Finance,Housing Finance,Public Sector Economics&Finance,Banks&Banking Reform,Housing Finance,Financial Intermediation,Non Bank Financial Institutions

Nonequilibrium many-body quantum dynamics: from full random matrices to real systems

We present an overview of our studies on the nonequilibrium dynamics of quantum systems that have many interacting particles. Our emphasis is on systems that show strong level repulsion, referred to as chaotic systems. We discuss how full random matrices can guide and support our studies of realistic systems. We show that features of the dynamics can be anticipated from a detailed analysis of the spectrum and the structure of the initial state projected onto the energy eigenbasis. On the other way round, if we only have access to the dynamics, we can use it to infer the properties of the spectrum of the system. Our focus is on the survival probability, but results for other observables, such as the spin density imbalance and Shannon entropy are also mentioned.Comment: 14 pages, 7 figures, chapter for the book "Thermodynamics in the Quantum Regime - Recent Progress and Outlook

Current knowledge and recent advances in understanding metabolism of the model cyanobacterium Synechocystis sp. PCC 6803

Cyanobacteria are key organisms in the global ecosystem, useful models for studying metabolic and physiological processes conserved in photosynthetic organisms, and potential renewable platforms for production of chemicals. Characterising cyanobacterial metabolism and physiology is key to understanding their role in the environment and unlocking their potential for biotechnology applications. Many aspects of cyanobacterial biology differ from heterotrophic bacteria. For example, most cyanobacteria incorporate a series of internal thylakoid membranes where both oxygenic photosynthesis and respiration occur, while CO2 fixation takes place in specialised compartments termed carboxysomes. In this review, we provide a comprehensive summary of our knowledge on cyanobacterial physiology and the pathways in Synechocystis sp. PCC 6803 (Synechocystis) involved in biosynthesis of sugar-based metabolites, amino acids, nucleotides, lipids, cofactors, vitamins, isoprenoids, pigments and cell wall components, in addition to the proteins involved in metabolite transport. While some pathways are conserved between model cyanobacteria, such as Synechocystis, and model heterotrophic bacteria like Escherichia coli, many enzymes and/or pathways involved in the biosynthesis of key metabolites in cyanobacteria have not been completely characterised. These include pathways required for biosynthesis of chorismate and membrane lipids, nucleotides, several amino acids, vitamins and cofactors, and isoprenoids such as plastoquinone, carotenoids, and tocopherols. Moreover, our understanding of photorespiration, lipopolysaccharide assembly and transport, and degradation of lipids, sucrose, most vitamins and amino acids, and heme, is incomplete. We discuss tools that may aid characterisation of cyanobacterial metabolism, notably CyanoSource, a barcoded library of targeted Synechocystis mutants, which will significantly accelerate characterisation of individual proteins