Patent policy, patent pools, and the accumulation of claims in sequential innovation

We present a dynamic model where the accumulation of patents generates an increasing number of claims on sequential innovation. We compare innovation activity under three regimes -patents, no-patents, and patent pools- and find that none of them can reach the first best. We find that the first best can be reached through a decentralized tax-subsidy mechanism, by which innovators receive a subsidy when they innovate, and are taxed with subsequent innovations. This finding implies that optimal transfers work in the exact opposite way as traditional patents. Finally, we consider patents of finite duration and determine the optimal patent length.

Misallocation of capital in a model of endogenous financial intermediation and insurance

In this paper we analyze productivity and welfare losses from capital misallocation in a general equilibrium model of occupational choice and endogenous financial intermediation. We study the effects of borrowing and lending, insurance, and risk sharing on the optimal allocation of resources. We find that financial markets together with general equilibrium effects have large impact on entrepreneurs' entry and firm-size decisions. Efficiency gains are increasing in the quality of financial markets, particularly in their ability to alleviate a financing constraint by providing insurance against idiosyncratic risk.

A linear optimization technique for graph pebbling

Graph pebbling is a network model for studying whether or not a given supply of discrete pebbles can satisfy a given demand via pebbling moves. A pebbling move across an edge of a graph takes two pebbles from one endpoint and places one pebble at the other endpoint; the other pebble is lost in transit as a toll. It has been shown that deciding whether a supply can meet a demand on a graph is NP-complete. The pebbling number of a graph is the smallest t such that every supply of t pebbles can satisfy every demand of one pebble. Deciding if the pebbling number is at most k is NP 2 -complete. In this paper we develop a tool, called theWeight Function Lemma, for computing upper bounds and sometimes exact values for pebbling numbers with the assistance of linear optimization. With this tool we are able to calculate the pebbling numbers of much larger graphs than in previous algorithms, and much more quickly as well. We also obtain results for many families of graphs, in many cases by hand, with much simpler and remarkably shorter proofs than given in previously existing arguments (certificates typically of size at most the number of vertices times the maximum degree), especially for highly symmetric graphs. Here we apply theWeight Function Lemma to several specific graphs, including the Petersen, Lemke, 4th weak Bruhat, Lemke squared, and two random graphs, as well as to a number of infinite families of graphs, such as trees, cycles, graph powers of cycles, cubes, and some generalized Petersen and Coxeter graphs. This partly answers a question of Pachter, et al., by computing the pebbling exponent of cycles to within an asymptotically small range. It is conceivable that this method yields an approximation algorithm for graph pebbling.

A parameter-free approach for solving combinatorial optimization problems through biased randomization of efficient heuristics

This paper discusses the use of probabilistic or randomized algorithms for solving combinatorial optimization problems. Our approach employs non-uniform probability distributions to add a biased random behavior to classical heuristics so a large set of alternative good solutions can be quickly obtained in a natural way and without complex conguration processes. This procedure is especially useful in problems where properties such as non-smoothness or non-convexity lead to a highly irregular solution space, for which the traditional optimization methods, both of exact and approximate nature, may fail to reach their full potential. The results obtained are promising enough to suggest that randomizing classical heuristics is a powerful method that can be successfully applied in a variety of cases.

On the stability of the optimal value and the optimal set in optimization problems

The paper develops a stability theory for the optimal value and the optimal set mapping of optimization problems posed in a Banach space. The problems considered in this paper have an arbitrary number of inequality constraints involving lower semicontinuous (not necessarily convex) functions and one closed abstract constraint set. The considered perturbations lead to problems of the same type as the nominal one (with the same space of variables and the same number of constraints), where the abstract constraint set can also be perturbed. The spaces of functions involved in the problems (objective and constraints) are equipped with the metric of the uniform convergence on the bounded sets, meanwhile in the space of closed sets we consider, coherently, the Attouch-Wets topology. The paper examines, in a unified way, the lower and upper semicontinuity of the optimal value function, and the closedness, lower and upper semicontinuity (in the sense of Berge) of the optimal set mapping. This paper can be seen as a second part of the stability theory presented in [17], where we studied the stability of the feasible set mapping (completed here with the analysis of the Lipschitz-like property).

Application of the combined integral method to Stefan problems

In this paper we present a new, accurate form of the heat balance integral method, termed the Combined Integral Method (or CIM). The application of this method to Stefan problems is discussed. For simple test cases the results are compared with exact and asymptotic limits. In particular, it is shown that the CIM is more accurate than the second order, large Stefan number, perturbation solution for a wide range of Stefan numbers. In the initial examples it is shown that the CIM reduces the standard problem, consisting of a PDE defined over a domain specified by an ODE, to the solution of one or two algebraic equations. The latter examples, where the boundary temperature varies with time, reduce to a set of three first order ODEs.

Different approaches to modelling the cost-effectiveness of schistosomiasis control

This paper reviews three different approaches to modelling the cost-effectiveness of schistosomiasis control. Although these approaches vary in their assessment of costs, the major focus of the paper is on the evaluation of effectiveness. The first model presented is a static economic model which assesses effectiveness in terms of the proportion of cases cured. This model is important in highlighting that the optimal choice of chemotherapy regime depends critically on the level of budget constraint, the unit costs of screening and treatment, the rates of compliance with screening and chemotherapy and the prevalence of infection. The limitations of this approach is that it models the cost-effectiveness of only one cycle of treatment, and effectiveness reflects only the immediate impact of treatment. The second model presented is a prevalence-based dynamic model which links prevalence rates from one year to the next, and assesses effectiveness as the proportion of cases prevented. This model was important as it introduced the concept of measuring the long-term impact of control by using a transmission model which can assess reduction in infection through time, but is limited to assessing the impact only on the prevalence of infection. The third approach presented is a theoretical framework which describes the dynamic relationships between infection and morbidity, and which assesses effectiveness in terms of case-years prevented of infection and morbidity. The use of this model in assessing the cost-effectiveness of age-targeted treatment in controlling Schistosoma mansoni is explored in detail, with respect to varying frequencies of treatment and the interaction between drug price and drug efficacy.

An approximate solution method for boundary layer flow of a power law fluid over a flat plate

The work in this paper deals with the development of momentum and thermal boundary layers when a power law fluid flows over a flat plate. At the plate we impose either constant temperature, constant flux or a Newton cooling condition. The problem is analysed using similarity solutions, integral momentum and energy equations and an approximation technique which is a form of the Heat Balance Integral Method. The fluid properties are assumed to be independent of temperature, hence the momentum equation uncouples from the thermal problem. We first derive the similarity equations for the velocity and present exact solutions for the case where the power law index n = 2. The similarity solutions are used to validate the new approximation method. This new technique is then applied to the thermal boundary layer, where a similarity solution can only be obtained for the case n = 1.

Immune Response of Cattle Infected with African Trypanosomes

Trypanosomosis is the most economically important disease constraint to livestock productivity in sub-Saharan Africa and has significant negative impact in other parts of the world. Livestock are an integral component of farming systems and thus contribute significantly to food and economic security in developing countries. Current methods of control for trypanosomosis are inadequate to prevent the enormous socioeconomic losses resulting from this disease. A vaccine has been viewed as the most desirable control option. However, the complexity of the parasite's antigenic repertoire made development of a vaccine based on the variable surface glycoprotein coat unlikely. As a result, research is now focused on identifying invariant trypanosome components as potential targets for interrupting infection or infection-mediated disease. Immunosuppression appears to be a nearly universal feature of infection with African trypanosomes and thus may represent an essential element of the host-parasite relationship, possibly by reducing the host's ability to mount a protective immune response. Antibody, T cell and macrophage/monocyte responses of infected cattle are depressed in both trypanosusceptible and trypanotolerant breeds of cattle. This review describes the specific T cell and monocyte/macrophage functions that are altered in trypanosome-infected cattle and compares these disorders with those that have been described in the murine model of trypanosomosis. The identification of parasite factors that induce immunosuppression and the mechanisms that mediate depressed immune responses might suggest novel disease intervention strategies.

RNA-based gene duplication sheds new light on mammalian sex chromosome evolution

ABSTRACT : Gene duplication is a fundamental source of raw material for the origin of genetic novelty. It has been assumed for a long time that DNA-based gene duplication was the only source of new genes. Recently however, RNA-based gene duplication (retroposition) was shown in multiple organisms to contribute significantly to their genetic diversity. This mechanism produces intronless gene copies (retrocopies) that are inserted in random genomic position, independent of the position of the parental source genes. In human, mouse and fruit fly, it was demonstrated that the X-linked genes spawned an excess of functional retroposed gene copies (retrogenes). In human and mouse, the X chromosome also recruited an excess of retrogenes. Here we further characterized these interesting biases related to the X chromosome in mammals. Firstly, we have confirmed presence of the aforementioned biases in dog and opossum genome. Then based on the expression profile of retrogenes during various spermatogenetic stages, we have provided solid evidence that meiotic sex chromosome inactivation (MSCI) is responsible for an excess of retrogenes stemming from the X chromosome. Moreover, we showed that the X-linked genes started to export an excess of retrogenes just after the split of eutherian and marsupial mammalian lineages. This suggests that MSCI has originated around this time as well. More fundamentally, as MSCI reflects the spread of recombination barrier between the X and Y chromosomes during their evolution, our observation allowed us to re-estimate the age of mammalian sex chromosomes. Previous estimates suggested that they emerged in the common ancestor of all mammals (before the split of monotreme lineage); whereas, here we showed that they originated around the split of marsupial and eutherian lineages, after the divergence of monotremes. Thus, the therian (marsupial and eutherian) sex chromosomes are younger than previously thought. Thereafter, we have characterized the bias related to the recruitment of genes to the X chromosome. Sexually antagonistic forces are most likely driving this pattern. Using our limited retrogenes expression data, it is difficult to determine the exact nature of these forces but some conclusions have been made. Lastly, we looked at the history of this biased recruitment: it commenced around the split of marsupial and eutherian lineages (akin to the biased export of genes out of the X). In fact, the sexually antagonistic forces are predicted to appear just around that time as well. Thereby, the history of the recruitment of genes to the X, provides an indirect evidence that these forces are responsible for this bias.