Embryonic development in Clarias gariepinus under laboratory conditions

The embryonic development in Clarias gariepinus was studied under laboratory conditions. The developmental stages of eggs starting from first cleavage were examined microscopically. Photomicroscope was used to take important stages of segmentation, blastulation, differentiation of embryo and hatching. The films of the photograph were developed and printed for each stage produced. The accurate timing and detailed description of each stage was done. The results show that the blastodisc (Polar cap) appeared about 35 minutes after fertilization and the first cleavage dividing the blastodisc into two blastomeres occurs 15 minutes after polar cap formation. Details of the developmental stages of embryos and the timing from one stage to the other were described. The larva shook off the shell and emerged completely from the egg case about 22 hours after fertilization at a water temperature of 25.1 degree C. The accurate determination of the time of initiation of first mitosis is of great importance in fish culture and breeding especially in the production of tetraploids

Regulation in Uganda's Lake Victoria fishery: historical and contemporary conditions

This paper sets out to explore how Uganda's lake Victoria fishery has been managed. It explores the management of the fishery during the protectorate period, and argues that the apparent success of regulation during this time may be attributed to the very heightened controls arising from Sleeping Sickness Controls. Once these were removed, entry into the fishery was rapid and uncontrolled, and the resultant impact on fish stocks was quickly felt. With its huge area, considerable shoreline, and innumerable islands, the lake Victoria fisheries service was quickly overwhelmed and disbanded as a result. In the early independence years, the Republic's government focused on developing the fishery, plans thwarted by turmoil of, and following, Idi Amin's reign. More recently, the fishery has prospered from Uganda's entry into the Nile perch fillet export market, which ahs adversely affected stocks. We present and comment on recently collected data that considers fishers' impressions of the status of the fishery, regulations and future managerial possibilities, and comment on these in the light of recent changes to Uganda's fisheries administration

Water in silicate glasses

The speciation of water in a variety of hydrous silicate glasses, including simple and rhyolitic compositions, synthesized over a range of experimental conditions with up to 11 weight percent water has been determined using infrared spectroscopy. This technique has been calibrated with a series of standard glasses and provides a precise and accurate method for determining the concentrations of molecular water and hydroxyl groups in these glasses.

For all the compositions studied, most of the water is dissolved as hydroxyl groups at total water contents less than 3-4 weight percent; at higher total water contents, molecular water becomes the dominant species. For total water contents above 3-4 weight percent, the amount of water dissolved as hydroxyl groups is approximately constant at about 2 weight percent and additional water is incorporated as molecular water. Although there are small but measurable differences in the ratio of molecular water to hydroxyl groups at a given total water content among these silicate glasses, the speciation of water is similar over this range of composition. The trends in the concentrations of the H-bearing species in the hydrous glasses included in this study are similar to those observed in other silicate glasses using either infrared or NMR spectroscopy.

The effects of pressure and temperature on the speciation of water in albitic glasses have been investigated. The ratio of molecular water to hydroxyl groups at a given total water content is independent of the pressure and temperature of equilibration for albitic glasses synthesized in rapidly quenching piston cylinder apparatus at temperatures greater than 1000°C and pressures greater than 8 kbar. For hydrous glasses quenched from melts cooled at slower rates (i.e., in internally heated or in air-quench cold seal pressure vessels), there is an increase in the ratio of molecular water to hydroxyl group content that probably reflects reequilibration of the melt to lower temperatures during slow cooling.

Molecular water and hydroxyl group concentrations in glasses provide information on the dissolution mechanisms of water in silicate liquids. Several mixing models involving homogeneous equilibria of the form H_2O + O = 20H among melt species have been explored for albitic melts. These models can account for the measured species concentrations if the effects of non-ideal behavior or mixing of polymerized units are included, or by allowing for the presence of several different types of anhydrous species.

A thermodynamic model for hydrous albitic melts has been developed based on the assumption that the activity of water in the melt is equal to the mole fraction of molecular water determined by infrared spectroscopy. This model can account for the position of the watersaturated solidus of crystalline albite, the pressure and temperature dependence of the solubility of water in albitic melt, and the volumes of hydrous albitic melts. To the extent that it is successful, this approach provides a direct link between measured species concentrations in hydrous albitic glasses and the macroscopic thermodynamic properties of the albite-water system.

The approach taken in modelling the thermodynamics of hydrous albitic melts has been generalized to other silicate compositions. Spectroscopic measurements of species concentrations in rhyolitic and simple silicate glasses quenched from melts equilibrated with water vapor provide important constraints on the thermodynamic properties of these melt-water systems. In particular, the assumption that the activity of water is equal to the mole fraction of molecular water has been tested in detail and shown to be a valid approximation for a range of hydrous silicate melts and the partial molar volume of water in these systems has been constrained. Thus, the results of this study provide a useful thermodynamic description of hydrous melts that can be readily applied to other melt-water systems for which spectroscopic measurements of the H-bearing species are available.

Exact solutions and transformation properties of nonlinear partial differential equations from general relativity

Various families of exact solutions to the Einstein and Einstein-Maxwell field equations of General Relativity are treated for situations of sufficient symmetry that only two independent variables arise. The mathematical problem then reduces to consideration of sets of two coupled nonlinear differential equations.

The physical situations in which such equations arise include: a) the external gravitational field of an axisymmetric, uncharged steadily rotating body, b) cylindrical gravitational waves with two degrees of freedom, c) colliding plane gravitational waves, d) the external gravitational and electromagnetic fields of a static, charged axisymmetric body, and e) colliding plane electromagnetic and gravitational waves. Through the introduction of suitable potentials and coordinate transformations, a formalism is presented which treats all these problems simultaneously. These transformations and potentials may be used to generate new solutions to the Einstein-Maxwell equations from solutions to the vacuum Einstein equations, and vice-versa.

The calculus of differential forms is used as a tool for generation of similarity solutions and generalized similarity solutions. It is further used to find the invariance group of the equations; this in turn leads to various finite transformations that give new, physically distinct solutions from old. Some of the above results are then generalized to the case of three independent variables.

Numerical solution of parabolic equations by the box scheme

The box scheme proposed by H. B. Keller is a numerical method for solving parabolic partial differential equations. We give a convergence proof of this scheme for the heat equation, for a linear parabolic system, and for a class of nonlinear parabolic equations. Von Neumann stability is shown to hold for the box scheme combined with the method of fractional steps to solve the two-dimensional heat equation. Computations were performed on Burgers' equation with three different initial conditions, and Richardson extrapolation is shown to be effective.

Non-linear dispersive waves with a small dissipation

The general theory of Whitham for slowly-varying non-linear wavetrains is extended to the case where some of the defining partial differential equations cannot be put into conservation form. Typical examples are considered in plasma dynamics and water waves in which the lack of a conservation form is due to dissipation; an additional non-conservative element, the presence of an external force, is treated for the plasma dynamics example. Certain numerical solutions of the water waves problem (the Korteweg-de Vries equation with dissipation) are considered and compared with perturbation expansions about the linearized solution; it is found that the first correction term in the perturbation expansion is an excellent qualitative indicator of the deviation of the dissipative decay rate from linearity.

A method for deriving necessary and sufficient conditions for the existence of a general uniform wavetrain solution is presented and illustrated in the plasma dynamics problem. Peaking of the plasma wave is demonstrated, and it is shown that the necessary and sufficient existence conditions are essentially equivalent to the statement that no wave may have an amplitude larger than the peaked wave.

A new type of fully non-linear stability criterion is developed for the plasma uniform wavetrain. It is shown explicitly that this wavetrain is stable in the near-linear limit. The nature of this new type of stability is discussed.

Steady shock solutions are also considered. By a quite general method, it is demonstrated that the plasma equations studied here have no steady shock solutions whatsoever. A special type of steady shock is proposed, in which a uniform wavetrain joins across a jump discontinuity to a constant state. Such shocks may indeed exist for the Korteweg-de Vries equation, but are barred from the plasma problem because entropy would decrease across the shock front.

Finally, a way of including the Landau damping mechanism in the plasma equations is given. It involves putting in a dissipation term of convolution integral form, and parallels a similar approach of Whitham in water wave theory. An important application of this would be towards resolving long-standing difficulties about the "collisionless" shock.

Bifurcation theory of nonlinear boundary value problems

The theory of bifurcation of solutions to two-point boundary value problems is developed for a system of nonlinear first order ordinary differential equations in which the bifurcation parameter is allowed to appear nonlinearly. An iteration method is used to establish necessary and sufficient conditions for bifurcation and to construct a unique bifurcated branch in a neighborhood of a bifurcation point which is a simple eigenvalue of the linearized problem. The problem of bifurcation at a degenerate eigenvalue of the linearized problem is reduced to that of solving a system of algebraic equations. Cases with no bifurcation and with multiple bifurcation at a degenerate eigenvalue are considered.

The iteration method employed is shown to generate approximate solutions which contain those obtained by formal perturbation theory. Thus the formal perturbation solutions are rigorously justified. A theory of continuation of a solution branch out of the neighborhood of its bifurcation point is presented. Several generalizations and extensions of the theory to other types of problems, such as systems of partial differential equations, are described.

The theory is applied to the problem of the axisymmetric buckling of thin spherical shells. Results are obtained which confirm recent numerical computations.

Liquid silicate equation of state : using shock waves to understand the properties of the deep Earth

The equations of state (EOS) of several geologically important silicate liquids have been constrained via preheated shock wave techniques. Results on molten Fe₂SiO₄ (fayalite), Mg₂SiO₄ (forsterite), CaFeSi₂O₆ (hedenbergite), an equimolar mixture of CaAl₂Si₂O₈-CaFeSi₂O₆ (anorthite-hedenbergite), and an equimolar mixture of CaAl₂Si₂O₈-CaFeSi₂O₆-CaMgSi₂O₆(anorthite-hedenbergite-diopside) are presented. This work represents the first ever direct EOS measurements of an iron-bearing liquid or of a forsterite liquid at pressures relevant to the deep Earth (> 135 GPa). Additionally, revised EOS for molten CaMgSi₂O₆ (diopside), CaAl₂Si₂O₈ (anorthite), and MgSiO₃ (enstatite), which were previously determined by shock wave methods, are also presented.

The liquid EOS are incorporated into a model, which employs linear mixing of volumes to determine the density of compositionally intermediate liquids in the CaO-MgO-Al₂O₃-SiO₂-FeO major element space. Liquid volumes are calculated for temperature and pressure conditions that are currently present at the core-mantle boundary or that may have occurred during differentiation of a fully molten mantle magma ocean.

The most significant implications of our results include: (1) a magma ocean of either chondrite or peridotite composition is less dense than its first crystallizing solid, which is not conducive to the formation of a basal mantle magma ocean, (2) the ambient mantle cannot produce a partial melt and an equilibrium residue sufficiently dense to form an ultralow velocity zone mush, and (3) due to the compositional dependence of Fe2+ coordination, there is a threshold of Fe concentration (molar X_Fe ≤ 0.06) permitted in a liquid for which its density can still be approximated by linear mixing of end-member volumes.

Exchange energy shifts under dense plasma conditions

The variation of the energy interval between the intercombination line ( 1s2p(P-3(1))-> 1s(2)) and the resonance line ( 1s2p(P-1(1))-> 1s(2)) of He-like aluminium with plasma density and temperature is investigated. Since such energy interval is equivalent to the exchange energy of the state 1s2p(P-3(1)), we consider the dependence of this energy shift on the plasma environment. It was found that the shifts of exchange energy increase ( decrease) with the increase of electron density ( electron temperature), and the shifts of exchange energy become more sensitive to the electron density as the electron temperature decreases, i. e. in the strongly coupled plasma regime. An approximately linear relation is found between the shifts of exchange energy and the electron density. The results show that dense plasma effects are very important for the simulation of the spectral fine structure. The relative shifts between the intercombination ( 1s2p(P-3(1))-> 1s(2)) and the resonance line ( 1s2p(P-1(1))-> 1s(2)) are discussed for diagnostic applications.

On the Mumford-Tate conjecture for Abelian varieties with reduction conditions

In this thesis we study Galois representations corresponding to abelian varieties with certain reduction conditions. We show that these conditions force the image of the representations to be "big," so that the Mumford-Tate conjecture (:= MT) holds. We also prove that the set of abelian varieties satisfying these conditions is dense in a corresponding moduli space.

The main results of the thesis are the following two theorems.

Theorem A: Let A be an absolutely simple abelian variety, End° (A) = k : imaginary quadratic field, g = dim(A). Assume either dim(A) ≤ 4, or A has bad reduction at some prime ϕ, with the dimension of the toric part of the reduction equal to 2r, and gcd(r,g) = 1, and (r,g) ≠ (15,56) or (m -1, m(m+1)/2). Then MT holds.

Theorem B: Let M be the moduli space of abelian varieties with fixed polarization, level structure and a k-action. It is defined over a number field F. The subset of M(Q) corresponding to absolutely simple abelian varieties with a prescribed stable reduction at a large enough prime ϕ of F is dense in M(C) in the complex topology. In particular, the set of simple abelian varieties having bad reductions with fixed dimension of the toric parts is dense.

Besides this we also established the following results:

(1) MT holds for some other classes of abelian varieties with similar reduction conditions. For example, if A is an abelian variety with End° (A) = Q and the dimension of the toric part of its reduction is prime to dim( A), then MT holds.

(2) MT holds for Ribet-type abelian varieties.

(3) The Hodge and the Tate conjectures are equivalent for abelian 4-folds.

(4) MT holds for abelian 4-folds of type II, III, IV (Theorem 5.0(2)) and some 4-folds of type I.

(5) For some abelian varieties either MT or the Hodge conjecture holds.

Anatomical and developmental patterns of interleukin-2 gene expression in the mouse: analysis of IL-2 expressing cells and partial characterization of interactions involved in mediating IL-2 gene expression in vivo

Interleukin-2 (IL-2) is an important mediator in the vertebrate immune system. IL-2 is a potent growth factor that mature T lymphocytes use as a proliferation signal and the production of IL-2 is crucial for the clonal expansion of antigen-specific T cells in the primary immune response. IL-2 driven proliferation is dependent on the interaction of the lymphokine with its cognate multichain receptor. IL-2 expression is induced only upon stimulation and transcriptional activation of the IL-2 gene relies extensively on the coordinate interaction of numerous inducible and constitutive trans-acting factors. Over the past several years, thousands of papers have been published regarding molecular and cellular aspects of IL-2 gene expression and IL-2 function. The vast majority of these reports describe work that has been carried out in vitro. However, considerably less is known about control of IL-2 gene expression and IL-2 function in vivo.

To gain new insight into the regulation of IL-2 gene expression in vivo, anatomical and developmental patterns of IL-2 gene expression in the mouse were established by employing in situ hybridization and immunohistochemical staining methodologies to tissue sections generated from normal mice and mutant animals in which T -cell development was perturbed. Results from these studies revealed several interesting aspects of IL-2 gene expression, such as (1) induction of IL-2 gene expression and protein synthesis in the thymus, the primary site of T-cell development in the body, (2) cell-type specificity of IL-2 gene expression in vivo, (3) participation of IL-2 in the extrathymic expansion of mature T cells in particular tissues, independent of an acute immune response to foreign antigen, (4) involvement of IL-2 in maintaining immunologic balance in the mucosal immune system, and (5) potential function of IL-2 in early events associated with hematopoiesis.

Extensive analysis of IL-2 mRNA accumulation and protein production in the murine thymus at various stages of development established the existence of two classes of intrathymic IL-2 producing cells. One class of intrathymic IL-2 producers was found exclusively in the fetal thymus. Cells belonging to this subset were restricted to the outermost region of the thymus. IL-2 expression in the fetal thymus was highly transient; a dramatic peak ofiL-2 mRNA accumulation was identified at day 14.5 of gestation and maximal IL-2 protein production was observed 12 hours later, after which both IL-2 mRNA and protein levels rapidly decreased. Significantly, the presence of IL-2 expressing cells in the day 14-15 fetal thymus was not contingent on the generation of T-cell receptor (TcR) positive cells. The second class of IL-2 producing cells was also detectable in the fetal thymus (cells found in this class represented a minority subset of IL-2 producers in the fetal thymus) but persist in the thymus during later stages of development and after birth. Intrathymic IL-2 producers in postnatal animals were located in the subcapsular region and cortex, indicating that these cells reside in the same areas where immature T cells are consigned. The frequency of IL-2 expressing cells in the postnatal thymus was extremely low, indicating that induction of IL-2 expression and protein synthesis are indicative of a rare activation event. Unlike the fetal class of intrathymic IL-2 producers, the presence of IL-2 producing cells in the postnatal thymus was dependent on to the generation of TcR+ cells. Subsequent examination of intrathymic IL-2 production in mutant postnatal mice unable to produce either αβ or γδ T cells showed that postnatal IL-2 producers in the thymus belong to both αβ and γδ lineages. Additionally, further studies indicated that IL-2 synthesis by immature αβ -T cells depends on the expression of bonafide TcR αβ-heterodimers. Taken altogether, IL-2 production in the postnatal thymus relies on the generation of αβ or γδ-TcR^+ cells and induction of IL-2 protein synthesis can be linked to an activation event mediated via the TcR.

With regard to tissue specificity of IL-2 gene expression in vivo, analysis of whole body sections obtained from normal neonatal mouse pups by in situ hybridization demonstrated that IL-2 mRNA^+ cells were found in both lymphoid and nonlymphoid tissues with which T cells are associated, such as the thymus (as described above), dermis and gut. Tissues devoid of IL-2 mRNA^+ cells included brain, heart, lung, liver, stomach, spine, spinal cord, kidney, and bladder. Additional analysis of isolated tissues taken from older animals revealed that IL-2 expression was undetectable in bone marrow and in nonactivated spleen and lymph nodes. Thus, it appears that extrathymic IL-2 expressing cells in nonimmunologically challenged animals are relegated to particular epidermal and epithelial tissues in which characterized subsets of T cells reside and thatinduction of IL-2 gene expression associated with these tissues may be a result of T-cell activation therein.

Based on the neonatal in situ hybridization results, a detailed investigation into possible induction of IL-2 expression resulting in IL-2 protein synthesis in the skin and gut revealed that IL-2 expression is induced in the epidermis and intestine and IL-2 protein is available to drive cell proliferation of resident cells and/or participate in immune function in these tissues. Pertaining to IL-2 expression in the skin, maximal IL-2 mRNA accumulation and protein production were observed when resident Vγ_3^+ T-cell populations were expanding. At this age, both IL-2 mRNA^+ cells and IL-2 protein production were intimately associated with hair follicles. Likewise, at this age a significant number of CD3ε^+ cells were also found in association with follicles. The colocalization of IL-2 expression and CD3ε^+ cells suggests that IL-2 expression is induced when T cells are in contact with hair follicles. In contrast, neither IL-2 mRNA nor IL-2 protein were readily detected once T-cell density in the skin reached steady-state proportions. At this point, T cells were no longer found associated with hair follicles but were evenly distributed throughout the epidermis. In addition, IL-2 expression in the skin was contingent upon the presence of mature T cells therein and induction of IL-2 protein synthesis in the skin did not depend on the expression of a specific TcR on resident T cells. These newly disclosed properties of IL-2 expression in the skin indicate that IL-2 may play an additional role in controlling mature T-cell proliferation by participating in the extrathymic expansion of T cells, particularly those associated with the epidermis.

Finally, regarding IL-2 expression and protein synthesis in the gut, IL-2 producing cells were found associated with the lamina propria of neonatal animals and gut-associated IL-2 production persisted throughout life. In older animals, the frequency of IL-2 producing cells in the small intestine was not identical to that in the large intestine and this difference may reflect regional specialization of the mucosal immune system in response to enteric antigen. Similar to other instances of IL-2 gene expression in vivo, a failure to generate mature T cells also led to an abrogation of IL-2 protein production in the gut. The presence of IL-2 producing cells in the neonatal gut suggested that these cells may be generated during fetal development. Examination of the fetal gut to determine the distribution of IL-2 producing cells therein indicated that there was a tenfold increase in the number of gut-associated IL-2 producers at day 20 of gestation compared to that observed four days earlier and there was little difference between the frequency of IL-2 producing cells in prenatal versus neonatal gut. The origin of these fetally-derived IL-2 producing cells is unclear. Prior to the immigration of IL-2 inducible cells to the fetal gut and/or induction of IL-2 expression therein, IL-2 protein was observed in the fetal liver and fetal omentum, as well as the fetal thymus. Considering that induction of IL-2 protein synthesis may be an indication of future functional capability, detection of IL-2 producing cells in the fetal liver and fetal omentum raises the possibility that IL-2 producing cells in the fetal gut may be extrathymic in origin and IL-2 producing cells in these fetal tissues may not belong solely to the T lineage. Overall, these results provide increased understanding of the nature of IL-2 producing cells in the gut and how the absence of IL-2 production therein and in fetal hematopoietic tissues can result in the acute pathology observed in IL-2 deficient animals.

Three-dimensional models of mantle convection : influence of phase transitions and temperature-dependent viscosity

Two of the most important questions in mantle dynamics are investigated in three separate studies: the influence of phase transitions (studies 1 and 2), and the influence of temperature-dependent viscosity (study 3).

(1) Numerical modeling of mantle convection in a three-dimensional spherical shell incorporating the two major mantle phase transitions reveals an inherently three-dimensional flow pattern characterized by accumulation of cold downwellings above the 670 km discontinuity, and cylindrical 'avalanches' of upper mantle material into the lower mantle. The exothermic phase transition at 400 km depth reduces the degree of layering. A region of strongly-depressed temperature occurs at the base of the mantle. The temperature field is strongly modulated by this partial layering, both locally and in globally-averaged diagnostics. Flow penetration is strongly wavelength-dependent, with easy penetration at long wavelengths but strong inhibition at short wavelengths. The amplitude of the geoid is not significantly affected.

(2) Using a simple criterion for the deflection of an upwelling or downwelling by an endothermic phase transition, the scaling of the critical phase buoyancy parameter with the important lengthscales is obtained. The derived trends match those observed in numerical simulations, i.e., deflection is enhanced by (a) shorter wavelengths, (b) narrower up/downwellings (c) internal heating and (d) narrower phase loops.

(3) A systematic investigation into the effects of temperature-dependent viscosity on mantle convection has been performed in three-dimensional Cartesian geometry, with a factor of 1000-2500 viscosity variation, and Rayleigh numbers of 10^5-10^7. Enormous differences in model behavior are found, depending on the details of rheology, heating mode, compressibility and boundary conditions. Stress-free boundaries, compressibility, and temperature-dependent viscosity all favor long-wavelength flows, even in internally heated cases. However, small cells are obtained with some parameter combinations. Downwelling plumes and upwelling sheets are possible when viscosity is dependent solely on temperature. Viscous dissipation becomes important with temperature-dependent viscosity.

The sensitivity of mantle flow and structure to these various complexities illustrates the importance of performing mantle convection calculations with rheological and thermodynamic properties matching as closely as possible those of the Earth.

Essays on cooperation and reciprocity

This dissertation comprises three essays that use theory-based experiments to gain understanding of how cooperation and efficiency is affected by certain variables and institutions in different types of strategic interactions prevalent in our society.

Chapter 2 analyzes indefinite horizon two-person dynamic favor exchange games with private information in the laboratory. Using a novel experimental design to implement a dynamic game with a stochastic jump signal process, this study provides insights into a relation where cooperation is without immediate reciprocity. The primary finding is that favor provision under these conditions is considerably less than under the most efficient equilibrium. Also, individuals do not engage in exact score-keeping of net favors, rather, the time since the last favor was provided affects decisions to stop or restart providing favors.

Evidence from experiments in Cournot duopolies is presented in Chapter 3 where players indulge in a form of pre-play communication, termed as revision phase, before playing the one-shot game. During this revision phase individuals announce their tentative quantities, which are publicly observed, and revisions are costless. The payoffs are determined only by the quantities selected at the end under real time revision, whereas in a Poisson revision game, opportunities to revise arrive according to a synchronous Poisson process and the tentative quantity corresponding to the last revision opportunity is implemented. Contrasting results emerge. While real time revision of quantities results in choices that are more competitive than the static Cournot-Nash, significantly lower quantities are implemented in the Poisson revision games. This shows that partial cooperation can be sustained even when individuals interact only once.

Chapter 4 investigates the effect of varying the message space in a public good game with pre-play communication where player endowments are private information. We find that neither binary communication nor a larger finite numerical message space results in any efficiency gain relative to the situation without any form of communication. Payoffs and public good provision are higher only when participants are provided with a discussion period through unrestricted text chat.