Rigorous conditions for food-web intervality in high-dimensional trophic niche spaces

Food webs represent trophic (feeding) interactions in ecosystems. Since the late 1970s, it has been recognized that food-webs have a surprisingly close relationship to interval graphs. One interpretation of food-web intervality is that trophic niche space is low-dimensional, meaning that the trophic character of a species can be expressed by a single or at most a few quantitative traits. In a companion paper we demonstrated, by simulating a minimal food-web model, that food webs are also expected to be interval when niche-space is high-dimensional. Here we characterize the fundamental mechanisms underlying this phenomenon by proving a set of rigorous conditions for food-web intervality in high-dimensional niche spaces. Our results apply to a large class of food-web models, including the special case previously studied numerically.

Food-web structure in low- and high-dimensional trophic niche spaces

A question central to modelling and, ultimately, managing food webs concerns the dimensionality of trophic niche space, that is, the number of independent traits relevant for determining consumer-resource links. Food-web topologies can often be interpreted by assuming resource traits to be specified by points along a line and each consumer's diet to be given by resources contained in an interval on this line. This phenomenon, called intervality, has been known for 30 years and is widely acknowledged to indicate that trophic niche space is close to one-dimensional. We show that the degrees of intervality observed in nature can be reproduced in arbitrary-dimensional trophic niche spaces, provided that the processes of evolutionary diversification and adaptation are taken into account. Contrary to expectations, intervality is least pronounced at intermediate dimensions and steadily improves towards lower- and higher-dimensional trophic niche spaces.

Infinite Dimensional Banach spaces of functions with nonlinear properties

The aim of this paper is to show that there exist infinite dimensional Banach spaces of functions that, except for 0, satisfy properties that apparently should be destroyed by the linear combination of two of them. Three of these spaces are: a Banach space of differentiable functions on Rn failing the Denjoy-Clarkson property; a Banach space of non Riemann integrable bounded functions, but with antiderivative at each point of an interval; a Banach space of infinitely differentiable functions that vanish at infinity and are not the Fourier transform of any Lebesgue integrable function.

The level sets of the resolvent norm and convexity properties of Banach spaces

We construct a bounded linear operator on a separable, reflexive and strictly convex Banach space whose resolvent norm is constant in a neighbourhood of zero.

1-amenability of A(X) for Banach spaces with 1-unconditional bases

The main result of the note is a characterization of 1-amenability of Banach algebras of approximable operators for a class of Banach spaces with 1-unconditional bases in terms of a new basis property. It is also shown that amenability and symmetric amenability are equivalent concepts for Banach algebras of approximable operators, and that a type of Banach space that was long suspected to lack property A has in fact the property. Some further ideas on the problem of whether or not amenability (in this setting) implies property A are discussed.

Sensing Spaces:A Body-oriented Architectural Design Education

The contemporary dominance of visuality has turned our understanding of space into a mode of unidirectional experience that externalizes other sensual capacities of the body while perceiving the built environment. This affects not only architectural practice but also architectural education when an introduction to the concept of space is often challenging, especially for the students who have limited spatial and sensual training. Considering that an architectural work is not perceived as a series of retinal pictures but as a repeated multi-sensory experience, the problem definitions in the design studio need to be disengaged from the dominance of a ‘focused vision’ and be re-constructed in a holistic manner. A method to address this approach is to enable the students to refer to their own sensual experiences of the built environment as a part of their design processes. This paper focuses on a particular approach to the second year architectural design teaching which has been followed in the Department of Architecture at Izmir University of Economics for the last three years. The very first architectural project of the studio and the program, entitled ‘Sensing Spaces’, is conducted as a multi-staged design process including ‘sense games, analyses of organs and their interpretations into space’. The objectives of this four-week project are to explore the sense of space through the design of a three-dimensional assembly, to create an awareness of the significance of the senses in the design process and to experiment with re-interpreted forms of bodily parts. Hence, the students are encouraged to explore architectural space through their ‘tactile, olfactory, auditory, gustative and visual stimuli’. In this paper, based on a series of examples, architectural space is examined beyond its boundaries of structure, form and function, and spatial design is considered as an activity of re-constructing the built environment through the awareness of bodily senses.

Mesoscale flux-closure domain formation in single-crystal BaTiO3

Over 60 years ago, Charles Kittel predicted that quadrant domains should spontaneously form in small ferromagnetic platelets. He expected that the direction of magnetization within each quadrant should lie parallel to the platelet surface, minimizing demagnetizing fields, and that magnetic moments should be configured into an overall closed loop, or flux-closure arrangement. Although now a ubiquitous observation in ferromagnets, obvious flux-closure patterns have been somewhat elusive in ferroelectric materials. This is despite the analogous behaviour between these two ferroic subgroups and the recent prediction of dipole closure states by atomistic simulations research. Here we show Piezoresponse Force Microscopy images of mesoscopic dipole closure patterns in free-standing, single-crystal lamellae of BaTiO3. Formation of these patterns is a dynamical process resulting from system relaxation after the BaTiO3 has been poled with a uniform electric field. The flux-closure states are composed of shape conserving 90° stripe domains which minimize disclination stresses.

Polarization Closure in PbZr(0.42)Ti(0.58)O3 Nanodots

Domain states in PbZr(0.42)Ti(0.58)O3 single-crystal ferroelectric nanodots, formed on cooling through the Curie temperature, were imaged by transmission electron microscopy. In the majority of cases, 90o stripe domains were found to form into four distinct “bundles” or quadrants. Detailed analysis of the dipole orientations in the system was undertaken, using both dark-field imaging and an assumption that charged domain walls were energetically unfavorable in comparison to uncharged walls. On this basis, we conclude that the dipoles in these nanodots are arranged such that the resultant polarizations, associated with the four quadrant domain bundles, form into a closed loop. This “polarization closure” pattern is reminiscent of the flux-closure already commonly observed in soft ferromagnetic microdots but to date unseen in analogous ferroelectric dots.

The spaces of knowledge: Contributions towards a historical geography of science

Reprinted in Trevor Barnes and Derek Gregory (eds), Reading Human Geography: The Poetics and Politics of Inquiry, (London: Arnold, 1997), pp. 27-48

Perceiving and acting upon spaces in a VR rugby task: Expertise effects in affordance detection and task achievement

This study used a virtual simulated 3vs3 rugby task to investigate whether gaps opening in particular running channels promote different actions by the ball-carrier player and whether an effect of rugby expertise is verified. We manipulated emergent gaps in three different locations: gap1 in the participant’s own running channel, gap 2 in the 1st receiver's running channel, and gap3 in the 2nd receiver's running channel. Recreational, intermediate, professional and non-rugby players performed the task. They could i) run with the ball, ii) make a short pass, or iii) make a long pass. All actions were digitally recorded. Results revealed that the emergence of gaps in the defensive line with respect to the participant’s own position significantly influenced action selection. Namely, ‘run’ was most often the action performed in gap 1, ‘short pass’ in gap 2, and ‘long pass’ in gap 3 trials. Furthermore, a strong positive relationship between expertise and task achievement was found.

“Voices, Spaces and Processes in Constitutionalism - Editorial"

(With C. Harvey, J. Shaw .)