Finite Difference Approximation for Linear Stochastic Partial Differential Equations with Method of Lines

A stochastic partial differential equation, or SPDE, describes the dynamics of a stochastic process defined on a space-time continuum. This paper provides a new method for solving SPDEs based on the method of lines (MOL). MOL is a technique that has largely been used for numerically solving deterministic partial differential equations (PDEs). MOL works by transforming the PDE into a system of ordinary differential equations (ODEs) by discretizing the spatial dimension of the PDE. The resulting system of ODEs is then solved by application of either a finite difference or a finite element method. This paper provides a proof that the MOL can be used to provide a finite difference approximation of the boundary value solutions for two broad classes of linear SPDEs, the linear elliptic and parabolic SPDEs.Finite difference approximation; linear stochastic partial differential equations (SPDEs); the method of lines (MOL)

From screen to shelf : perspectives on independent distribution

Of the three broadly defined sectors which make up the British film industry, the academy has tended to focus its attention on production and exhibition, giving comparatively short shrift to matters of distribution. Certainly, the current role of the independent distributor in the UK is, to say the least, under-examined. Academic interest in the work of the distributor tends to stop at their marketing campaigns and, as an extension, their attempts to connect with and sell a film to the public. The relationship between the distributor and the exhibitor, and the process of negotiation which takes place between them, have been largely ignored. Since around 1999, with the burgeoning of the DVD market, UK distributors have gradually expanded their home entertainment divisions, becoming as invested in the retail sector as is the music industry and devoting as much energy (if not as much money) to a film’s release on DVD as to its theatrical launch. Again, academic material on the video and DVD industries is scant, with those studies which do exist, such as Paul McDonald’s Video and DVD Industries (2007), focusing primarily on the US and the major studios

The Computation of Perfect and Proper Equilibrium for Finite Games via Simulated Annealing

This paper exploits an analogy between the “trembles” that underlie the functioning of simulated annealing and the player “trembles” that underlie the Nash refinements known as perfect and proper equilibrium. This paper shows that this relationship can be used to provide a method for computing perfect and proper equilibria of n-player strategic games. This paper also shows, by example, that simulated annealing can be used to locate a perfect equilibrium in an extensive form game.Game Theory

Research Joint Ventures and Optimal Emissions Taxation

This paper performs a comparison of two well known approaches for modelling R&D spillovers associated with investment in E-R&D, namely dAspremont-Jacquemin and Kamien-Muller-Zang. We show that there is little qualitative difference between the models in terms of total surplus delivered when selecting the optimal tax regime when there is precommitment under cooperative regimes in which firms coordinate expenditures to maximize joint profits. However, under non-cooperative regimes there is marked difference, with the model of Kamien- Muller-Zang leading to higher taxation rates when firms share information. Furthermore, we argue that the Kamien-Muller-Zang model is of questionable validity when modelling R&D on emissions reducing technology due to counter intuitive results showing a positive relationhip between R&D spillovers and emissions taxes.

Matthew Baillie's specimens and engravings

In 1799, Matthew Baillie, William Hunter's nephew, published his famous atlas of pathology. It was entitled A Series of Engravings Accompanied with Explanations which are Intended to Illustrate the Morbid Anatomy of Some of the Most Important Parts of the Human Body. The present study aims to match the illustrations to extant specimens in the collections of William and John Hunter, preserved at the University of Glasgow and at the Royal College of Surgeons of England respectively. Baillie's book contains 10 fasciculi, consisting of 73 plates and 206 figures. The specimens Baillie illustrated came from his own collection and those of ten others, including his uncles, William and John Hunter. The book was illustrated by William Clift and engraved by James Basire, William Skelton and James Heath. Excluding eight illustrations of intestinal worms where the provenance of the specimens is uncertain, a total of 98 specimens from William Hunter's collection were illustrated in 104 figures. Eight of the specimens were calculi impossible to identify specifically. Excluding worms and calculi, 72 of William Hunter's specimens illustrated by Baillie are extant in the Hunterian Collection at the University of Glasgow. All but one of the 20 specimens illustrated that had belonged to John Hunter were identified in the on-line catalogue of the Royal College of Surgeons of England. Baillie's own collection was destroyed when the Royal College of Surgeons of England was bombed in 1941. Baillie is credited with being the first to produce an illustrated systematic textbook of morbid anatomy and probably the first to illustrate emphysema and transposition of the great vessels. His book, however, was not comprehensive. It did not cover a number of topics such as muscles and bones and there is little coverage of the nervous system. Baillie's book, however, was an original concept as an atlas of morbid anatomy and showed his deep insight into pathology

The Effect of Connectivity, Proximity and Market Structure on R&D Networks

In a seminal paper, Goyal and Moraga-Gonzalez (2001) use an undirected network to characterize knowledge flows between firms engaging in research in an oligopolistic market. In their paper, firms are regarded as inhabiting a research joint venture (RJV), if they share the same edge of the network. These firms are allowed an R&D spillover of 1; the outside firms (firms not sharing an edge in the network) are permitted a constant knowledge spillover that is less than one. We begin our paper by showing that this last assumption has important consequences when dealing with R&D networks of size greater than or equal to six firms. We present examples of topologically non-equivalent networks that have the same degree of connectivity and generate identical outcomes in terms of R&D effort, firm profits and total welfare. We then modify their model so that R&D spillovers decrease as the number of shortest paths increases between any two firms. We show that under product differentiated Cournot and Bertrand competition, we have different outcomes for all economic variables. We also show that R&D effort increases with respect to the number of collaborative links if firms are in a weakly competitive market, whereas it declines if firms are in a more competitive market where products are closer substitutes. We also find that in more competitive markets there is a conflict between the stability and the efficiency of RJVs.

The political economy of shallow lakes

Shallow lakes display hysteresis in their response to phosphorous loading. Gradual increases in the nutrient content of the lake can appear to have little effect on the oligotrophic state of the lake until a point at which the lake suddenly flips to a eutrophic state. Ecotaxes on phosphorous loading have been suggested as means to maintain the lake in the socially desirable state - oligotrophic or not - when society can agree on a common welfare function. In this paper, we consider the case where society is divided into two interest groups and is thus unable to agree. In particular, the communities that share the use of the lake disagree on the relative importance of the shallow lake acting as a waste sink for phosphorous run-off as opposed to other ecosystem service. A dynamic game in which communities maximize their use of the lake results in a Nash equilibrium where the lake is in a eutrophic state when in fact the Pareto-optimum would be for the lake to be in an oligotrophic state. The tax that would induce, in a non-cooperative context, all of society's members to behave in such a way as to achieve a Pareto-optimal outcome is derived. Further, both types of communities lobby to have their preferred level of tax applied based on their relative preferences for a clean lake and phosphorous loading. The effects of the lobbying on the application of the optimal tax are investigated for particular values of relative preferences and the relative size of each group.Resource /Energy Economics and Policy,

Rent Seeking Behavior and Optimal Taxation of Pollution in Shallow Lakes

In this paper we extend earlier work on the economics of shallow lakes by M\"aler, Xepapadeas and de Zeeuw (2003) to the case where two communities have incommensurable preferences about lake eutrophication. In the case of incommensurable preferences interest group behavior arises, we therefore consider the case where society is divided into two interest groups and is thus unable to agree on a single management objective. In particular, the communities that share the use of the lake disagree on the relative importance of the shallow lake acting as a waste sink for phosphorus run-off as opposed to other ecosystem services. A dynamic game in which communities maximize their use of the lake results in a Nash equilibrium where the lake is in a eutrophic state when in fact the Pareto optimum would be for the lake to be in an oligotrophic state. Our paper differs from previous work by considering two communities or interest groups with different preferences for environmental services. The tax that would induce, in a noncooperative context, all of society's members to behave in such a way as to achieve a Pareto optimal outcome is derived under the assumption that a social planner does not favor one community or another. We then ask whether or not such a tax rate would in fact be implemented if each community were able to bear political pressure on the social planner and the social planner were a public representative seeking re-election. In this case both types of communities lobby to have their preferred level of tax applied based on their relative preferences for a clean lake and phosphorus loading. The effects of the lobbying on the application of the optimal tax are investigated numerically for particular values of relative preferences and the relative size of each group. The representative seeking election proposes a different tax rate in order to maximize their probability of electoral success. This problem is solved numerically assuming that the lake is in a eutrophic equilibrium. It is shown that political representatives have an incentive to propose tax rates that are insufficient to achieve a return to an oligotrophic steady-statePollution of shallow lakes; optimal eco-taxation; dynamic rent seeking

Vasectomy: Morphological and Immunological Effects in the Rat

This thesis examines morphological and immunological effects of vasectomy in inbred Albino Swiss rats. It comprises six separate studies. 1) The response of the regional testicular lvmoh node six and nine months after vasectomy. This work extends a previous study and shows that, while the response to vasectomy of the regional testicular lymph node increased in magnitude up to and including 3 months after operation, it waned through 6 and 9 months. The findings indicate the involvement of the regional lymphatics and lymph nodes in the formation of circulating antisperm antibodies after vasectomy. The response of the testicular nodes varied between individual rats. 2) The lymphatic drainage of the epididymis and of the ductus deferens, with reference to the immune response to vasectomy. The lymphatic drainage pattern of the unoperated reproductive tract is determined. Epididymal lymphatics always united with those of the testis. There is little previous work on lymphatics of the ductus deferens. The more cranial part of the scrotal ductus drained towards the inguinal canal and the iliac nodes. Lymphatics from the more caudal part of the ductus united with those of the epididymis. The results suggested a lymphatic watershed about the middle of the scrotal ductus. The role of variations in the lymphatic drainage of the sperm granuloma, the site of release of spermatozoal antigens, in the variable responses of the testicular lymph node to vasectomy is investigated. Vasectomy did not interrupt the lymphatic drainage of the epididymis. While lymph from epididymal granulomas invariably reached the regional testicular node that from vasal granulomas may occasionally have failed to do so. Variations in the lymphatic drainage of vasal granulomas, but not epididymal ones, may have been partly responsible for the lack of response in certain testicular nodes reported previously. 3) The response of the regional lymph node to epididymal sperm granulomas after vasectomy. The contribution of variations in the lymphatic drainage of vasal sperm granulomas to the variable nodal response to vasectomy is further analysed. By carrying out vasectomy at the junction of the ductus deferens with the epididymal duct, sperm granulomas were induced to form at the epididymis; at this site, their lymph always drains to the testicular node. In spite of the presence of epididymal granulomas in all rats 12 weeks after vasectomy, not all testicular nodes responded. It is concluded that variations in the lymphatic drainage of vasal granulomas had not been wholly responsible for the variations in the response of the testicular lymph node found previously and that additional unknown factors were involved. 4) On the mode of sperm autoantigen presentation to the regional lymph node of the testis after vasectomy. Cytological smears were used to detect whole spermatozoa in the testicular lymph nodes of vasectomised rats. Very few spermatozoa were found; this contrasts with the large numbers reported, by others, in nodes from rams and boars. The basis of this species difference is unclear. 5) A quantitative study of the effect of vasectomy on spermatogenesis. Quantitative studies of the cycle of the seminiferous epithelium and seminiferous tubular dimensions were performed on the testes of rats vasectomised for 6 months. The results indicate that, in functional tubules, there was no alteration in the cycle of the seminiferous epithelium, no tubular distension and no retention of spermatozoa. 6) The effect of testicular biopsy on the regional lymph node of the testis. Testicular biopsy, like vasectomy, damages epithelial barriers of the reproductive tract. This study investigates whether the procedure produces lymph node changes similar to those seen after vasectomy. The testicular lymph nodes of rats 1 and 3 months after testicular biopsy were indistinguishable in every way from those of sham-operated control animals. The absence of lymph node changes following testicular biopsy is likely to reflect the minimal amount of spermatozoal extravasation and inflammation in the testis. The study offers some reassurance about the safety of testicular biopsy in the investigation of male infertility

Optimal taxation in a growth model with public consumption and home production

In a neoclassical growth model with public consumption, we show the following Pareto optimal tax rules. The government should tax leisure and private consumption at the same rate, and subsidize net investment at the same rate it taxes net capital income. Also, it should tax capital income more heavily than labor income. In an extension for home production, the additional rule is to tax investment for home production at the same rate of the tax on private market consumption. These tax and subsidy rates should be constant over time except the initial tax rate on capital income.