Can Liars Ever Prosper.

The paper compares the optimal financial contracts of a firm which has private information over its expost revenues when the finance can be provided by either a single or two groups of investors. When they are the only investors we use a financial contract with non-contractible monitoring, in which the probabilities of cheating by the entrepreneur/firm and monitoring by investors are mutual best responses. The contract is written by the entrepreneur knowing that this equilibrium will subsequently occur. With a second group of investors who have no monitoring rights, we analyse a truth telling contract and a misrepresentation contract in which cheating and monitoring probabilities are chosen in a similar way to those of the single investor contract. The non monitoring investors learn the results of any monitoring for free. Our main results are that: the two investor group truth-telling contract achieves the second best despite the lack of commitment; this contract is only feasible under limited liability of investors if low state revenues are high enough. When low state revenues are too low for this then the two investor misrepresentation contract is optimal. This contract has a negative correlation between repayments to the two investor groups: the contract uses the non-monitoring group to smooth out the repayments of the entrepreneur optimally. This reduces his incentive to make false reports and mitigates the investor's incentive to monitor. A second result is that the two investor scenario is Pareto superior to the single investor model. We show that with unlimited liability on investor groups, the two investor misrepresentation contract is as good as the second best. Generally in this misrepresentation contract investors may have to make repayments to the firm rather than receive them. A further result is that the three party contract is always renegotiation-proof, as well as collusion-proof so long as the low state revenues are below the expected repayments of the monitor. Last we show that under limited liability the share of finance provided by the two is strictly positive and uniquely determined.financial contracts; multiple investors; no commitment.

General solution of an exact correlation function factorization in conformal field theory

We discuss a correlation function factorization, which relates a three-point function to the square root of three two-point functions. This factorization is known to hold for certain scaling operators at the two-dimensional percolation point and in a few other cases. The correlation functions are evaluated in the upper half-plane (or any conformally equivalent region) with operators at two arbitrary points on the real axis, and a third arbitrary point on either the real axis or in the interior. This type of result is of interest because it is both exact and universal, relates higher-order correlation functions to lower-order ones, and has a simple interpretation in terms of cluster or loop probabilities in several statistical models. This motivated us to use the techniques of conformal field theory to determine the general conditions for its validity. Here, we discover a correlation function which factorizes in this way for any central charge c, generalizing previous results. In particular, the factorization holds for either FK (Fortuin-Kasteleyn) or spin clusters in the Q-state Potts models; it also applies to either the dense or dilute phases of the O(n) loop models. Further, only one other non-trivial set of highest-weight operators (in an irreducible Verma module) factorizes in this way. In this case the operators have negative dimension (for c < 1) and do not seem to have a physical realization.Comment: 7 pages, 1 figure, v2 minor revision

How is coaching being used within schools? Does coaching have an impact on improvement in school settings?

Within this report we are seeking to investigate how coaching is being used within school, who is doing it and how it is evaluated by those using it. Without such information it is difficult to offer informed support to teachers and schools in this field. The results of this work will identify the potential that a sample of head teachers see for coaching as a development tool for the future and indicate where schools are finding value in the coaching approach. Primarily we hope this will inform head teachers and those responsible for teacher development so they have access to the experience of others building best practice in the area. This information may also help to inform decisions of policy and strategy at all levels. It may help to shape the training offered by those with commissioning and provider roles for the development of teachers and leaders in schools. The findings of this report may help tailor provision to the specific needs of teachers and schools rather than using the generic commercial models of coaching currently on offer

Determination of thermodynamic properties of AeroZINE-50, phase 1

Literature survey of, and test procedure for determination of thermodynamic properties of AeroZINE-5

Simulation of How Jack Pine Budworm (Lepidoptera: Tortricidae) Affects Economic Returns From Jack Pine Timber Production in Michigan

The impact of jack pine budworm on economic returns from jack pine timber production in Lower Michigan and management actions that might be taken to reduce this impact were evaluated with a simulation model. Results indicate that current jack pine rotation ages arc excessive and should be reduced. Insecticide application is not a viable strategy for reducing jack pine budworm impact

Temporal and Spatial Activity Patterns of an Adult Parasitoid, Glypta fumiferanae (Hymenoptera: Ichneumonidae), and their Influence on Parasitism

Temporal and spatial activity patterns of adult Glypta fumiferanae (Vierick) were assessed through use of malaise traps placed in tree canopies and on the forest floor. Many parasitoids were trapped in the tree canopies while none was caught on the forest floor. A model that related malaise trap catches to weather was used to draw inferences from these data. It was concluded that cool wet weather inhibited activity of the parasitoid. Historical data on interaction between G. fumiferanae and its host were used to illustrate the possibility that reductions in parasite activity due to weather factors led to reductions in rates of parasitis

Errors Incurred When Using Iwao's Sequential Decision Rule in Insect Sampling

Sequential decision rules based upon defining a relationship between the mean and variance of a population and using this relationship in a confidence interval about a sum of counts on sample units have been developed and used for sampling insect pests. The actual error rates that arise from the use of these rules are much larger than the nominal ones. This occurs for three reasons: The confidence interval is incorrectly used as a sequential decision rule; it is assumed that random variables are normally distributed; and variances are not constant. If these sequential decision rules are to be used, we suggest that actual error rates be determined through simulatio

Microlensing of Circumstellar Disks

We investigate the microlensing effects on a source star surrounded by a circumstellar disk, as a function of wavelength. The microlensing light curve of the system encodes the geometry and surface brightness profile of the disk. In the mid- and far-infrared, the emission of the system is dominated by the thermal emission from the cold dusty disk. For a system located at the Galactic center, we find typical magnifications to be of order 10-20% or higher, depending on the disk surface brightness profile, and the event lasts over one year. At around 20 microns, where the emission for the star and the disk are comparable, the difference in the emission areas results in a chromatic microlensing event. Finally, in the near-infrared and visible, where the emission of the star dominates, the fraction of star light directly reflected by the disk slightly modifies the light curve of the system which is no longer that of a point source. In each case, the corresponding light curve can be used to probe some of the disk properties. A fraction of 0.1% to 1% optical microlensing events are expected to be associated with circumstellar disk systems. We show that the lensing signal of the disk can be detected with sparse follow-up observations of the next generation space telescopes. While direct imaging studies of circumstellar disks are limited to the solar neighborhood, this microlensing technique can probe very distant disk systems living in various environments and has the potential to reveal a larger diversity of circumstellar disks.Comment: 9 pages, 7 figures. Accepted for publication in Ap

Chromatic number, clique subdivisions, and the conjectures of Haj\'os and Erd\H{o}s-Fajtlowicz

For a graph $G$, let $\chi(G)$ denote its chromatic number and $\sigma(G)$ denote the order of the largest clique subdivision in $G$. Let H(n) be the maximum of $\chi(G)/\sigma(G)$ over all $n$-vertex graphs $G$. A famous conjecture of Haj\'os from 1961 states that $\sigma(G) \geq \chi(G)$ for every graph $G$. That is, $H(n) \leq 1$ for all positive integers $n$. This conjecture was disproved by Catlin in 1979. Erd\H{o}s and Fajtlowicz further showed by considering a random graph that $H(n) \geq cn^{1/2}/\log n$ for some absolute constant $c>0$. In 1981 they conjectured that this bound is tight up to a constant factor in that there is some absolute constant $C$ such that $\chi(G)/\sigma(G) \leq Cn^{1/2}/\log n$ for all $n$-vertex graphs $G$. In this paper we prove the Erd\H{o}s-Fajtlowicz conjecture. The main ingredient in our proof, which might be of independent interest, is an estimate on the order of the largest clique subdivision which one can find in every graph on $n$ vertices with independence number $\alpha$.Comment: 14 page