Modular Frobenius manifolds and their invariant flows

The space of Frobenius manifolds has a natural involutive symmetry on it: there exists a map $I$ which send a Frobenius manifold to another Frobenius manifold. Also, from a Frobenius manifold one may construct a so-called almost dual Frobenius manifold which satisfies almost all of the axioms of a Frobenius manifold. The action of $I$ on the almost dual manifolds is studied, and the action of $I$ on objects such as periods, twisted periods and flows is studied. A distinguished class of Frobenius manifolds sit at the fixed point of this involutive symmetry, and this is made manifest in certain modular properties of the various structures. In particular, up to a simple reciprocal transformation, for this class of modular Frobenius manifolds, the flows are invariant under the action of $I\,.

Feminist institutionalism and women’s political leadership in Scotland: successes and failures

Jenny Morrison and Ewan Gibbs write that Scottish feminists’ experiences of organising in the Women’s Liberation Movement pointed to the importance of pragmatically working towards shared goals across traditional divisions. This emphasis on consensus decision-making has moulded a centre-left framing for Scottish women’s leadership that rejects both conservatism and left-wing radicalism

Modular Frobenius manifolds

This thesis studies how a symmetry defined on the solution space to the WDVV equations, called the inversion symmetry, singles out a special class of solution: those that lie at its fixed points. We will learn how demanding invariance of the solution under this symmetry forces it to take on a very rich form: that of a quasi-modular function. We will also study how the corresponding principal hierarchies inherit this symmetry from the solution to the WDVV equations. More specifically, Chapter 1 is introductory material on the theory of Frobenius manifolds. We provide motivation, basic examples and tools that will be useful to us later. As such it contains no original material. The references [1,16,17,18,19,35,37] were extremely useful in the preparation of this chapter. Chapter 2 is based on [45], which was written in collaboration with Professor Ian Strachan. It appeared in Physica D: Nonlinear Phenomena. We study those solutions to WDVV that lie at the fixed points the inversion symmetry. By studying the transformation and homogeneity properties that such solutions must have, we set out a program for classification, with complete results presented for dimensions three and four, together with partial results for dimension five. We show how various examples that have appeared in the literature fit into our framework. Any material here that is not original is clearly referenced. Chapter 3 is background material on integrable systems. It begins with a little history of the KdV equation, and explores some of the key properties that make it interesting [15,13]. We move on to the construction of Poisson brackets on loop spaces [48,24], and more specifically Poisson brackets of hydrodynamic type. We then sketch Dubrovin's construction [16] of the principal hierarchy from the geometry of the Frobenius manifold. Chapter 4 is based on [44], a joint work with Professor Ian Strachan which appeared in International Mathematics Research Notices. We study how the inversion symmetry defined on the solution space to the WDVV equations lifts to the principal hierarchy. It turns out that the action is an example of a so-called reciprocal transformation, introduced by Rogers [52]. These results were obtained independently in [41], and more recently in [26]. There is also some background material which has been tailored from Dubrovin's work [10] on so-called almost dual solutions to WDVV. We give a definition of the inversion symmetry for these solutions and study how the inversion symmetry acts on the associated hydrodynamic systems. Chapter 5 is a very natural continuation of the results obtained in Chapter 4. Motivated by the Witten-Kontsevich theorem, Dubrovin & Zhang [23] showed how the inclusion of the elliptic Gromov-Witten invariants into the tau-function perturbs the equations of the hierarchy. The results of Chapter 5 show how to extend the symmetry found at the level of the hydrodynamic equations to these first order, (or genus one), deformations

Polynomial Modular Frobenius Manifolds

The moduli space of Frobenius manifolds carries a natural involutive symmetry, and a distinguished class - so-called modular Frobenius manifolds - lie at the fixed points of this symmetry. In this paper a classification of semi-simple modular Frobenius manifolds which are polynomial in all but one of the variables is begun, and completed for three and four dimensional manifolds. The resulting examples may also be obtained from higher dimensional manifolds by a process of folding. The relationship of these results with orbifold quantum cohomology is also discussed

A MAPK/c-Jun-mediated switch regulates the initial adaptive and cell death responses to mitochondrial damage in a neuronal cell model

Parkinson’s disease (PD) is defined by the progressive loss of dopaminergic neurons. Mitochondrial dysfunction and oxidative stress are associated with PD although it is not fully understood how neurons respond to these stresses. How adaptive and apoptotic neuronal stress response pathways are regulated and the thresholds at which they are activated remains ambiguous. Utilising SH-SY5Y neuroblastoma cells, we show that MAPK/AP-1 pathways are critical in regulating the response to mitochondrial uncoupling. Here we found the AP-1 transcription factor cJun can act in either a pro- or anti-apoptotic manner, depending on the level ofstress. JNK-mediated cell death in differentiated cells only occurred once a threshold of stress was surpassed. We also identified a novel feedback loop between Parkin activity and the c-Jun response, suggesting defective mitophagy may initiate MAPK/c-Jun-mediated neuronal loss observed in PD. Our data supports the hypothesis that blocking cell death pathways upstream of c-Jun as a therapeutic target in PD may not be appropriate due to crossover of the pro- and anti-apoptotic responses. Boosting adaptive responses or targeting specific aspects of the neuronal death response may therefore represent more viable therapeutic strategie

A deep Chandra observation of the poor cluster AWM 4 - I. Properties of the central radio galaxy and its effects on the intracluster medium

Using observations from the Chandra X-ray Observatory and Giant Metrewave Radio Telescope, we examine the interaction between the intracluster medium and central radio source in the poor cluster AWM 4. In the Chandra observation a small cool core or galactic corona is resolved coincident with the radio core. This corona is capable of fuelling the active nucleus, but must be inefficiently heated by jet interactions or conduction, possibly precluding a feedback relationship between the radio source and cluster. A lack of clearly detected X-ray cavities suggests that the radio lobes are only partially filled by relativistic plasma. We estimate a filling factor of phi=0.21 (3 sigma upper limit phi<0.42) for the better constrained east lobe. We consider the particle population in the jets and lobes, and find that the standard equipartition assumptions predict pressures and ages which agree poorly with X-ray estimates. Including an electron population extending to low Lorentz factors either reduces (gamma_min=100) or removes (gamma_min=10) the pressure imbalance between the lobes and their environment. Pressure balance can also be achieved by entrainment of thermal gas, probably in the first few kiloparsecs of the radio jets. We estimate the mechanical power output of the radio galaxy, and find it to be marginally capable of balancing radiative cooling.Comment: Accepted for publication in MNRAS, 18 pages, 9 postscript figures

Improving soil moisture prediction of a high-resolution land surface model by parameterising pedotransfer functions through assimilation of SMAP satellite data

Pedotransfer functions are used to relate gridded databases of soil texture information to the soil hydraulic and thermal parameters of land surface models. The parameters within these pedotransfer functions are uncertain and calibrated through analyses of point soil samples. How these calibrations relate to the soil parameters at the spatial scale of modern land surface models is unclear because gridded databases of soil texture represent an area average. We present a novel approach for calibrating such pedotransfer functions to improve land surface model soil moisture prediction by using observations from the Soil Moisture Active Passive (SMAP) satellite mission within a data assimilation framework. Unlike traditional calibration procedures, data assimilation always takes into account the relative uncertainties given to both model and observed estimates to find a maximum likelihood estimate. After performing the calibration procedure, we find improved estimates of soil moisture and heat flux for the Joint UK Land Environment Simulator (JULES) land surface model (run at a 1 km resolution) when compared to estimates from a cosmic-ray soil moisture monitoring network (COSMOS-UK) and three flux tower sites. The spatial resolution of the COSMOS probes is much more representative of the 1 km model grid than traditional point-based soil moisture sensors. For 11 cosmic-ray neutron soil moisture probes located across the modelled domain, we find an average 22 % reduction in root mean squared error, a 16 % reduction in unbiased root mean squared error and a 16 % increase in correlation after using data assimilation techniques to retrieve new pedotransfer function parameters

Runx1 deficiency protects against adverse cardiac remodeling following myocardial infarction

Background: Myocardial infarction (MI) is a leading cause of heart failure and death worldwide. Preservation of contractile function and protection against adverse changes in ventricular architecture (cardiac remodeling) are key factors to limiting progression of this condition to heart failure. Consequently, new therapeutic targets are urgently required to achieve this aim. Expression of the Runx1 transcription factor is increased in adult cardiomyocytes after MI; however, the functional role of Runx1 in the heart is unknown. Methods: To address this question, we have generated a novel tamoxifen-inducible cardiomyocyte-specific Runx1-deficient mouse. Mice were subjected to MI by means of coronary artery ligation. Cardiac remodeling and contractile function were assessed extensively at the whole-heart, cardiomyocyte, and molecular levels. Results: Runx1-deficient mice were protected against adverse cardiac remodeling after MI, maintaining ventricular wall thickness and contractile function. Furthermore, these mice lacked eccentric hypertrophy, and their cardiomyocytes exhibited markedly improved calcium handling. At the mechanistic level, these effects were achieved through increased phosphorylation of phospholamban by protein kinase A and relief of sarco/endoplasmic reticulum Ca2+-ATPase inhibition. Enhanced sarco/endoplasmic reticulum Ca2+-ATPase activity in Runx1-deficient mice increased sarcoplasmic reticulum calcium content and sarcoplasmic reticulum–mediated calcium release, preserving cardiomyocyte contraction after MI. Conclusions: Our data identified Runx1 as a novel therapeutic target with translational potential to counteract the effects of adverse cardiac remodeling, thereby improving survival and quality of life among patients with MI

EB1 Is Required for Spindle Symmetry in Mammalian Mitosis

Most information about the roles of the adenomatous polyposis coli protein (APC) and its binding partner EB1 in mitotic cells has come from siRNA studies. These suggest functions in chromosomal segregation and spindle positioning whose loss might contribute to tumourigenesis in cancers initiated by APC mutation. However, siRNA-based approaches have drawbacks associated with the time taken to achieve significant expression knockdown and the pleiotropic effects of EB1 and APC gene knockdown. Here we describe the effects of microinjecting APC- or EB1- specific monoclonal antibodies and a dominant-negative EB1 protein fragment into mammalian mitotic cells. The phenotypes observed were consistent with the roles proposed for EB1 and APC in chromosomal segregation in previous work. However, EB1 antibody injection also revealed two novel mitotic phenotypes, anaphase-specific cortical blebbing and asymmetric spindle pole movement. The daughters of microinjected cells displayed inequalities in microtubule content, with the greatest differences seen in the products of mitoses that showed the severest asymmetry in spindle pole movement. Daughters that inherited the least mobile pole contained the fewest microtubules, consistent with a role for EB1 in processes that promote equality of astral microtubule function at both poles in a spindle. We propose that these novel phenotypes represent APC-independent roles for EB1 in spindle pole function and the regulation of cortical contractility in the later stages of mitosis. Our work confirms that EB1 and APC have important mitotic roles, the loss of which could contribute to CIN in colorectal tumour cells

NuMA Overexpression in Epithelial Ovarian Cancer

Highly aneuploid tumours are common in epithelial ovarian cancers (EOC). We investigated whether NuMA expression was associated with this phenomenon