An Open Mapping Theorem

It is proved that any surjective morphism $f: \mathbb{Z}^\kappa \to K$ onto a locally compact group $K$ is open for every cardinal $\kappa$. This answers a question posed by Karl Heinrich Hofmann and the second author

Functional Regression

Functional data analysis (FDA) involves the analysis of data whose ideal units of observation are functions defined on some continuous domain, and the observed data consist of a sample of functions taken from some population, sampled on a discrete grid. Ramsay and Silverman's 1997 textbook sparked the development of this field, which has accelerated in the past 10 years to become one of the fastest growing areas of statistics, fueled by the growing number of applications yielding this type of data. One unique characteristic of FDA is the need to combine information both across and within functions, which Ramsay and Silverman called replication and regularization, respectively. This article will focus on functional regression, the area of FDA that has received the most attention in applications and methodological development. First will be an introduction to basis functions, key building blocks for regularization in functional regression methods, followed by an overview of functional regression methods, split into three types: [1] functional predictor regression (scalar-on-function), [2] functional response regression (function-on-scalar) and [3] function-on-function regression. For each, the role of replication and regularization will be discussed and the methodological development described in a roughly chronological manner, at times deviating from the historical timeline to group together similar methods. The primary focus is on modeling and methodology, highlighting the modeling structures that have been developed and the various regularization approaches employed. At the end is a brief discussion describing potential areas of future development in this field

Genomic and proteomic profiling for cancer diagnosis in dogs

Global gene expression, whereby tumours are classified according to similar gene expression patterns or ‘signatures’ regardless of cell morphology or tissue characteristics, is being increasingly used in both the human and veterinary fields to assist in cancer diagnosis and prognosis. Many studies on canine tumours have focussed on RNA expression using techniques such as microarrays or next generation sequencing. However, proteomic studies combining two-dimensional polyacrylamide gel electrophoresis or two-dimensional differential gel electrophoresis with mass spectrometry have also provided a wealth of data on gene expression in tumour tissues. In addition, proteomics has been instrumental in the search for tumour biomarkers in blood and other body fluids

The lived experience of Diabulimia. Individuals with Type 1 Diabetes using insulin for weight control

Diabulimia is the term given to the intentional restriction of insulin for the purposes of weight loss in individuals with Type 1 Diabetes Mellites (T1DM). Diabulimia can be life-threatening, and prevalence rates in T1DM are high, yet there is a lack of research exploring how best to support individuals with this difficulty. Currently, individuals restricting their insulin appear in care and support pathways which do not always attend to specific psychological factors associated with T1DM. Recent literature has named the importance of understanding the physical and psychological issues related to insulin restriction to provide effective care. Exploring the lived experience of diabulimia stands to provide much needed information to healthcare professionals working alongside this population. Which in turn, may inform psychological support, future research, and support pathways. Subsequently, this research aims to explore the lived experience of diabulimia. Through Interpretative Phenomenological Analysis (IPA), five females and one male shared their subjective lived experience of using insulin for weight control through semi-structured interviews, which led to the identification of four superordinate themes: (1) Go count your carbs and take your jabs; (2) A deadly love; (3) It is so much deeper than just insulin, and (4) There is recovery. The analysis revealed the relational nature of diabulimia which encapsulated the participants longing for relational depth with healthcare professionals and peers. Recommendations based on the research findings include incorporating an existential-phenomenological and relational psychoanalytic approach to therapeutic work, as well as utilising the participant’s motivation to pursue recovery for the other. Future research would benefit from exploring the male experience of diabulimia, as well as enquiring into the construction of self-identity when using insulin for weight control

Electroconvection in a Suspended Fluid Film: A Linear Stability Analysis

A suspended fluid film with two free surfaces convects when a sufficiently large voltage is applied across it. We present a linear stability analysis for this system. The forces driving convection are due to the interaction of the applied electric field with space charge which develops near the free surfaces. Our analysis is similar to that for the two-dimensional B\'enard problem, but with important differences due to coupling between the charge distribution and the field. We find the neutral stability boundary of a dimensionless control parameter ${\cal R}$ as a function of the dimensionless wave number ${\kappa}$. ${\cal R}$, which is proportional to the square of the applied voltage, is analogous to the Rayleigh number. The critical values ${{\cal R}_c}$ and ${\kappa_c}$ are found from the minimum of the stability boundary, and its curvature at the minimum gives the correlation length ${\xi_0}$. The characteristic time scale ${\tau_0}$, which depends on a second dimensionless parameter ${\cal P}$, analogous to the Prandtl number, is determined from the linear growth rate near onset. ${\xi_0}$ and ${\tau_0}$ are coefficients in the Ginzburg-Landau amplitude equation which describes the flow pattern near onset in this system. We compare our results to recent experiments.Comment: 36 pages, 7 included eps figures, submitted to Phys Rev E. For more info, see http://mobydick.physics.utoronto.ca

Conformal anomaly from gauge fields without gauge fixing

We show how the Weyl anomaly generated by gauge fields, can be computed from manifestly gauge invariant and diffeomorphism invariant exact renormalization group equations, without having to fix the gauge at any stage. Regularisation is provided by covariant higher derivatives and by embedding the Maxwell field into a spontaneously broken $U(1|1)$ supergauge theory. We first provide a realisation that leaves behind two versions of the original $U(1)$ gauge field, and then construct a manifestly $U(1|1)$ supergauge invariant flow equation which leaves behind only the original Maxwell field in the spontaneously broken regime.Comment: 24 page

Scheme Independence to all Loops

The immense freedom in the construction of Exact Renormalization Groups means that the many non-universal details of the formalism need never be exactly specified, instead satisfying only general constraints. In the context of a manifestly gauge invariant Exact Renormalization Group for SU(N) Yang-Mills, we outline a proof that, to all orders in perturbation theory, all explicit dependence of beta function coefficients on both the seed action and details of the covariantization cancels out. Further, we speculate that, within the infinite number of renormalization schemes implicit within our approach, the perturbative beta function depends only on the universal details of the setup, to all orders.Comment: 18 pages, 8 figures; Proceedings of Renormalization Group 2005, Helsinki, Finland, 30th August - 3 September 2005. v2: Published in jphysa; minor changes / refinements; refs. adde