mm-bigness in compatible systems

Taylor-Wiles type lifting theorems allow one to deduce that for $\rho$ a "sufficiently nice" $l$-adic representation of the absolute Galois group of a number field whose semi-simplified reduction modulo $l$, denoted $\overline{\rho}$, comes from an automorphic representation then so does $\rho$. The recent lifting theorems of Barnet-Lamb-Gee-Geraghty-Taylor impose a technical condition, called \emph{$m$-big}, upon the residual representation $\overline{\rho}$. Snowden-Wiles proved that for a sufficiently irreducible compatible system of Galois representations, the residual images are \emph{big} at a set of places of Dirichlet density $1$. We demonstrate the analogous result in the \emph{$m$-big} setting using a mild generalization of their argument

pp-adic Langlands functoriality for the definite unitary group

We formalise a notion of $p$-adic Langlands functoriality for the definite unitary group. This extends the classical notion of Langlands functoriality to the setting of eigenvarieties. We apply some results of Chenevier to obtain some cases of $p$-adic Langlands functoriality by interpolating known cases of classical Langlands functoriality

A Model for Creation: Part II

In Part I we developed a model, called system P, for constructing the physical universe. In the present paper (Part II) we explore the hypothesis that something exists prior to the physical universe; i.e. we suppose that there exists a sequence of projections (and levels) that is prior to the sequence that constructs the physical universe itself. To avoid an infinite regress, this prior sequence must be finite, meaning that the whole chain of creative projections must begin at some primal level which is itself uncreated. So, from this primal level emanates a primal sequence of projections, which yields a first-created system; by definition, there is no creation prior to this first system. Proceeding from this basis, we use the template of our previous work in constructing entities in the physical universe to outline the construction of entities in this first-created system. Next, we seek an interpretation of this first system and its entities. Since our "primal level" is an uncreated state of being from which all creation springs, it draws obvious allusions to the concept of "God". So at this point the model bumps head-on into theology, and we are forced to ask: Is there some metaphysically- or theologically-related work that can help us to interpret this first-created system and its entities? Indeed, such a work, and consequent interpretations, will be put forth --- from which much more then follows

A Model for Creation: Part I

Four initial postulates are presented (with two more added later), which state that construction of the physical universe proceeds from a sequence of discrete steps or "projections" --- a process that yields a sequence of discrete levels (labeled 0, 1, 2, 3, 4). At or above level 2 the model yields a (3+1)-dimensional structure, which is interpreted as ordinary space and time. As a result, time does not exist below level 2 of the system, and thus the quantum of action, h, which depends on time (since its unit is time•energy), also does not exist below level 2. This implies that the quantum of action is not fundamental, and thus e.g. that the physical universe cannot have originated from a quantum fluctuation. When the gravitational interaction for the model is developed, it is seen that the basic ingredient for gravity is already operating at level 1 of the system, which implies that gravity, too, is not fundamentally quantum mechanical (since, as stated, h only kicks in at level 2) --- perhaps obviating the need for a quantum theory of gravity. Further arguments along this line lead to the conclusion that quantum fluctuations cannot be a source of gravity, and thus cannot contribute to the cosmological constant --- thereby averting the cosmological constant problem. Along the way, the model also provides explanations for dark energy, the beginning and ending of inflation, quark confinement, and more. Although the model dethrones the quantum, it nevertheless elevates an idea in physics that was engendered by quantum mechanics: the necessary role of "observers" in constructing the world

Productivity and Proximity

Abstract: Papers examining a developed nation’s labour productivity frequently ignore spatial effects. We present empirical results indicating that geographical proximity matters for plant-level productivity.distance; labour productivity

Evaluating Mobile Device Cleaning Policies in the NHS

Introduction The use of mobile devices within healthcare settings by staff, patients and visitors is widespread and growing. DoH guidance states that patients should be allowed the widest possible use of mobile phones. For staff mobile devices have become an essential aspect of their day-to-day professional and personal lives. There is, however, clear evidence that phones/tablets can be contaminated with pathogens, which may survive for prolonged periods before being transferred onto hands or other surfaces.   Methods A FoI request for “all current policies or guidelines that make reference to the use and management of mobile phones and tablet devices in the healthcare environment, by staff, service users, and visitors – this applies to both personal and institutionally-owned devices”, was sent to NHS institutions across England, Scotland and Wales with a response rate of 96% (n=252).   Results 22% of organisations had no policy in place, with ≈11% stating that this would be considered policy reviews. Organisations that acknowledged the issue responded that staff were informed of disinfection procedures: e.g. ‘the normal cleaning schedule’ or the use of universal sanitizing/detergent wipes. Many organisations referred to their Cleaning and Decontamination policy, however none of these explicitly mentioned mobile devices. Instead, the general advice for electrical devices was to follow manufacturer’s instructions, as using any other process might invalidate warranties. Where specific cleaning policies were in place they advocated the use of ‘general purpose/universal detergent wipes’ without any technical justification. Multiple organisations suggested that existing hand decontamination procedures were sufficient to address this issue.   Discussion There is no consistency in infection control advice regarding the potential risks posed by the use of mobile devices. Regular cleaning may be a solution, but there is little evidence evaluating the available methods. The literature in this field calls for clear evidence-based guidelines for cleaning and disinfecting mobile devices

Regional Input Output Models and the FLQ Formula: A Case Study of Finland

This paper examines the use of location quotients (LQs) in constructing regional input-output models. Its focus is on the augmented FLQ formula (AFLQ) proposed by Flegg and Webber, 2000, which takes regional specialization explicitly into account. In our case study, we examine data for 20 Finnish regions, ranging in size from very small to very large, in order to assess the relative performance of the AFLQ formula in estimating regional imports, total intermediate inputs and output multipliers, and to determine an appropriate value for the parameter ? used in this formula. In this assessment, we use the Finnish survey-based national and regional input-output tables for 1995, which identify 37 separate sectors, as a benchmark. The results show that, in contrast with the other LQ-based formulae examined, the AFLQ is able to produce adequate estimates of output multipliers in all regions. However, some variation is required in the value of ? across regions in order to obtain satisfactory estimates. The case study also reveals that the AFLQ and its predecessor, the FLQ, yield very similar results. This finding indicates that the inclusion of a measure of regional specialization in the AFLQ formula is not helpful in terms of generating superior results.Regional input-output models Finland FLQ formula Location quotients

Review of 3D model development with application to groundwater studies in New Zealand 1996 – 2011

Three dimensional geological modelling techniques have been applied since 1996 with an aim to characterise the lithological and chronological units of New Zealand’s many diverse aquifers. Models of property-scattered data have also been applied to assess physical properties of aquifers and the distribution of groundwater chemistry, including groundwater age, to inform an understanding of groundwater systems. These models, fundamental to understanding groundwater recharge, flow and discharge have found many uses as outlined in this paper

Concordant Convergence Empirics

We present a new model to test the convergence hypothesis based on the ideas of concordance and then employ the model to test empirically for GDP per capita convergence across 97 countries. Our results suggest the presence of switching, while there is more ‘strong divergence’ than ‘strong convergence’.Convergence; Concordance; Income per capita.

Convergence towards a Steady State Distribution

The convergence literature frequently presupposes some unidentified steady state distribution. This paper presents a new method to identify the presence and rate of convergence to a steady state distribution. The method is illustrated with application to UK regional male wages.Convergence; Steady state; Average UK regional male wages