Formal Projection Research Articles

Emergent Quantum Mechanics and the Origin of Quantum Non-local Correlations

A geometric interpretation for quantum correlations and entanglement according to a particular framework of emergent quantum mechanics is developed. The mechanism described is based on two ingredients: 1. At an hypothetical sub-quantum level description of physical systems, the dynamics has a regime where it is partially ergodic and 2. A formal projection from a two-dimensional time mathematical formalism of the emergent quantum theory to the usual one-dimensional time formalism of quantum dynamics. Observable consequences of the theory are obtained. Among them we show that quantum correlations must be instantaneous from the point of view of the spacetime description, but the spatial distance up to which they can be observed must be bounded. It is argued how our mechanism avoids Bell theorem and Kochen-Specken theorem. Evidence for non-signaling faster than the speed of light in our proposal is discussed.

Active authority or latent legitimacy? The institutional visibility of the university governing body amongst staff as a factor in its effectiveness

This study examines the institutional visibility of the university governing body amongst staff, as an unexplored factor influencing the effectiveness of the body in performing stewardship and strategic responsibilities on behalf of the university. A constructionist view of governance is taken in order to examine the enactment of governing body institutional visibility within the spaces of the university, from the formal projection of its legal and constitutional duties, to communication of the decisions made at governing body meetings, through to governors’ informal encounters and engagement with staff. An institutional visibility spectrum was developed based on governing body ‘apparency’, ‘transparency’ and ‘engagement’, prior to interviewing secretaries and clerks as key actors in the governance system. It was found that governor visibility through engagement and interaction with a range of staff outside the ‘boardroom’ was perceived as a contributor to governing body effectiveness, including governors’ knowledge-building and ability to contribute to strategic initiatives in the host university.

Planning Education and Manpower in the Middle East, 1950s–60s

Education is largely absent in recent work on the history of development and modernization. Yet it was central to the political project of many leaders of decolonization and figured prominently in five-year plans and other development schemes. The article highlights the central role of education in concepts of development and social planning in the Middle East. This could take the form of central plans but also of statistical and computer-generated projections of future educational and manpower needs. After showing how different concepts of planning education were circulated at the level of international organizations, the article investigates the first Egyptian five-year plan. It looks at the Egyptian Institute of National Planning in Cairo, highlighting that Egyptian planners drew on a variety of different experts and institutions from the US and the Soviet Union to the GDR and India. While the late 1960s ushered in more scepticism toward formal planning and projection, the emphasis on expertise, knowledge and skills as central variables of modern societies has endured.

Empathic Imagination: Formal and Experiential Projection

The celebrated architect, educator and author Juhani Pallasmaa is well‐known for having forged a new understanding of perception and the experiential in architecture with his seminal book The Eyes of the Skin: Architecture and the Sensory (3rd edn, Wiley, 2012). Here he describes how ‘imagining human situations’ is at the core of architecture, relying on the interrelationship of physical space, behaviour and the capacity for mental tuning.

Higher-Order Averaging of Fokker--Planck Equations for Nonlinear Fiber Lay-Down Processes

We investigate stochastic models for the lay-down of flexible fibers on a moving conveyor belt for the case of small stochasticity and small belt velocity. Using a suitable scaling we obtain a singularly perturbed problem for a stochastic Hamiltonian system and the corresponding Fokker--Planck equation. These equations are investigated using averaging methods. In the present case the impact of the deterministic forcing, i.e., the belt velocity is not captured by the stochastic averaging theorem. To overcome this problem, a formal energy projection method previously introduced by the authors is used, which allows the computation of higher-order stochastic averages for the present highly nonlinear system. The resulting second-order coefficients are computed numerically and a suitably precise scheme is developed. Finally, we illustrate the results of our method with several examples.

Cues for Interpreting Distortion in Map Projections

The ability to recognize distortions of, for example, areas, angles, and landmass shapes in global-scale map projections, is an important part of critical map reading and use. This study investigates the cues used by individuals when they assess distortion on global-scale map projections. It was hypothesized that landmass shape would be a dominant cue used by individuals with no formal map projection training and that as projection knowledge increased the cues would become more systematic (e.g., use the graticule). Results indicate a tendency for novices to rely on landmass shape as a cue. Some evidence of a systematic evaluation of projections was also found.

Higher Order Averaging of Linear Fokker--Planck Equations with Periodic Forcing

We investigate linear Fokker--Planck equations or stochastic Hamiltonian systems with periodic forcing where the impact of deterministic forcing is not captured by classical stochastic averaging. To overcome this problem, a formal energy projection method is introduced, which splits the corresponding Fokker--Planck equation and allows the computation of higher order stochastic averages. Generally, the resulting averages have to be computed with a numerical scheme. We illustrate the results of our method with two examples: the linear oscillator with periodic forcing and a nonlinear oscillator.

Resolving weak internal layer interactions for the Ginzburg–Landau equation

The internal layer behaviour, in one spatial dimension, associated with two classes of Ginzbug–Landau equation with double-well nonlinearities and small diffusivities is investigated. The problems that are examined are the Ginzburg–Landau equation with and without a constant mass constraint. For the constrained problem, steady-state internal layer solutions are constructed using a formal projection method. This method is also used to derive a differential-algebraic system describing the slow dynamics of the constrained internal layer motion. The dynamics of a two-layer evolution is studied in detail. For the unconstrained problem, a nonlinear WKB-type transformation is introduced that magnifies exponentially weak layer interactions and leads to well-conditioned steady problems. A conventional singular perturbation method, without the need for exponential asymptotics, is used on the resulting transformed problem as an alternative method to construct equilibrium solutions and metastable patterns. Exponentially sensitive steady-state internal layer solutions as well as a one-layer evolution are computed accurately using the transformed problem.

Adiabatic elimination of fast relaxing variables in socio-economic dynamical models

One of the main problems in quantitative dynamic modelling of complex systems is due to the huge number of interacting subsystems. This gives rise not only to large sets of coupled differential equations, whose results are difficult to understand, but makes it almost impossible to give a meaningful set of initial conditions. It is therefore extremely important to investigate projection techniques which allow us to single out a limited subset of relevant variables (order parameters). The effect of the irrelevant variables should then be modelled as some sort of noise, with suitable statistical properties, perturbing the evolution of the order parameters. Such formal projection techniques have been developed for the case where the time evolution of the relevant variables is slower than the time evolution of the irrelevant degrees of freedom, which is a case frequently encountered in practice. We first discuss the simplest of such adiabatic elimination procedures (direct adiabatic elimination). We then discuss a more refined formal procedure, which can be applied to cases where the time scale separation between fast and slow variables is not exceedingly large. We also illustrate the application of adiabatic elimination procedures to a problem which has been stimulated by previous work undertaken by our group (the tourist-environment interaction in a tourist village in Sardinia). However, we greatly simplified the original model assumptions, so the example is to be regarded as illustrative of the adiabatic technique, and should not be considered a case study. We focus our attention on such interesting phenomena as noise induced phase transitions, and discuss also the choice of the correct type of stochastic calculus.

Formal Embedding and Projection Theorems

Formal Embedding and Projection Theorems