The role of Mittag-Leffler functions in anomalous relaxation

The inertia-corrected Debye model of rotational Brownian motion of polar molecules was generalized by Coffey et al. [Phys. Rev. E, 65, 32 102 (2002)] to describe fractional dynamics and anomalous rotational diffusion. The linear- response theory of the normalized complex susceptibility was given in terms of a Laplace transform and as a function of frequency. The angular-velocity correlation function was parametrized via fractal Mittag-Leffler functions. Here we apply the latter method and complex-contour integral- representation methods to determine the original time-dependent amplitude as an inverse Laplace transform using both analytical and numerical approaches, as appropriate. (C) 2004 Elsevier B.V. All rights reserved.

Self-affine crossover length in a layered silicate deposit

Self-affine dehydrated colloidal deposits on fresh mica surfaces of the synthetic layered silicate 2:1 smectite clay laponite have been studied by means of atomic force microscopy (AFM). AFM images of these prepared assemblies of sol and gel aggregates have been analyzed both by means of standard AFM Fourier software and a wavelet method. The deposited surfaces show a persistence to antipersistent crossover with a clay concentration dependent crossover length. It is concluded that the crossover length is associated with aggregate size, and further that the persistent roughness at small length scales signals near compact clusters of fractal dimension three, whereas the antipersistent roughness at large length scales signals a sedimentation process.

Periodically loaded 1-D metallodielectric electromagnetic bandgap structures for miniaturisation and bandwidth enhancement

Periodic loading of 1-D metallodielectric electromagnetic bandgap (MEBG) structures has been rigorously investigated. Miniaturised and broadband MEBG structures have been produced by means of periodically loading a dipole array. A study has been carried out with regard to the loading mechanism, the number of stubs, the topology of the structure and the order of loading. Simulations have been carried out using a method of moments based software. First order uniform loading stubs have yielded a significant size reduction of the MEBG array and the bandwidth has doubled. Good agreement between simulations and measurements has been achieved. The current distribution on the proposed structure has been studied, yielding valuable insight. An interdigital topology has resulted in further miniaturisation and bandwidth enhancement. Fractal-type arrays have been produced after applying second order loading. A maximum miniaturisation of 2.5:1 has been achieved.

Burrow architecture and digging activity in the Cape dune mole rat

While females are traditionally thought to invest more time and energy into parental care than males, males often invest more resources into searching and displaying for mates, obtaining mates and in male-male conflict. Solitary subterranean mammals perform these activities in a particularly challenging niche, necessitating energetically expensive burrowing to both search for mates and forage for food. This restriction presumably affects males more than females as the former are thought to dig longer tunnels that cover greater distances to search for females. We excavated burrow systems of male and female Cape dune mole rats Bathyergus suillus the, largest truly subterranean mammal, to investigate whether male burrows differ from those of females in ways that reflect mate searching by males. We consider burrow architecture (length, internal dimensions, fractal dimension of tunnel systems, number of nesting chambers and mole mounds on the surface) in relation to mating strategy. Males excavated significantly longer burrow systems with higher fractal dimensions and larger burrow areas than females. Male burrow systems were also significantly farther from one another than females were from other females' burrow systems. However, no sex differences were evident in tunnel cross-sectional area, mass of soil excavated per mound, number of mounds produced per unit burrow length or mass of soil excavated per burrow system. Hence, while males may use their habitat differently from females, they do not appear to differ in the dimensions of the tunnels they create. Thus, exploration and use of the habitat differs between the sexes, which may be a consequence of sex differences in mating behaviour and greater demands for food.

Recent advances in the analysis of behavioural organization and interpretation as indicators of animal welfare

While the incorporation of mathematical and engineering methods has greatly advanced in other areas of the life sciences, they have been under-utilized in the field of animal welfare. Exceptions are beginning to emerge and share a common motivation to quantify 'hidden' aspects in the structure of the behaviour of an individual, or group of animals. Such analyses have the potential to quantify behavioural markers of pain and stress and quantify abnormal behaviour objectively. This review seeks to explore the scope of such analytical methods as behavioural indicators of welfare. We outline four classes of analyses that can be used to quantify aspects of behavioural organization. The underlying principles, possible applications and limitations are described for: fractal analysis, temporal methods, social network analysis, and agent-based modelling and simulation. We hope to encourage further application of analyses of behavioural organization by highlighting potential applications in the assessment of animal welfare, and increasing awareness of the scope for the development of new mathematical methods in this area.

Multi-epoch high-resolution spectroscopy of SN2011fe - Linking the progenitor to its environment

This study attempts to establish a link between the reasonably well known nature of the progenitor of SN2011fe and its surrounding environment. This is done with the aim of enabling the identification of similar systems in the vast majority of the cases, when distance and epoch of discovery do not allow a direct approach. To study the circumstellar environment of SN2011fe we have obtained high-resolution spectroscopy of SN2011fe on 12 epochs, from 8 to 86 days after the estimated date of explosion, targeting in particular at the time evolution of CaII and NaI. Three main absorption systems are identified from CaII and NaI, one associated to the Milky Way, one probably arising within a high-velocity cloud, and one most likely associated to the halo of M101. The Galactic and host galaxy reddening, deduced from the integrated equivalent widths (EW) of the NaI lines are E(B-V)=0.011+/-0.002 and E(B-V)=0.014+/-0.002 mag, respectively. The host galaxy absorption is dominated by a component detected at the same velocity measured from the 21-cm HI line at the projected SN position (~180 km/s). During the ~3 months covered by our observations, its EW changed by 15.6+/-6.5 mA. This small variation is shown to be compatible with the geometric effects produced by therapid SN photosphere expansion coupled to the patchy fractal structure of the ISM. The observed behavior is fully consistent with ISM properties similar to those derived for our own Galaxy, with evidences for structures on scales

Retinal microvascular network attenuation in Alzheimer's disease

INTRODUCTION:Cerebral small-vessel disease has been implicated in the development of Alzheimer’sdisease (AD). The retinal microvasculature enables non-invasive visualization andevaluation of the systemic microcirculation. We evaluated retinal microvascular parametersin a case-control study of AD patients and cognitively-normal controls. 

METHODS:Retinal images were computationally analyzed and quantitative retinal parameters (caliber,fractal dimension, tortuosity, and bifurcation) measured. Regression models were used tocompute odds ratios (OR) and confidence intervals (CI) for AD with adjustment forconfounders. 

RESULTS:Retinal images were available in 213 AD participants and 294 cognitively-normal controls.Persons with lower venular fractal dimension (OR per standard deviation [SD] increase, 0.77[CI: 0.62–0.97]) and lower arteriolar tortuosity (OR per SD increase, 0.78 [CI: 0.63–0.97])were more likely to have AD following appropriate adjustment. 
DISCUSSION:Patients with AD have a sparser retinal microvascular network and retinal microvascularvariation may represent similar pathophysiological events within the cerebralmicrovasculature of patients with AD.

Intermittent and Scale-Invariant Intensity Fluctuations in Hot Coronal Loops

ABSTRACT BODY: To resolve outstanding questions on heating of coronal loops, we study intensity fluctuations in inter-moss portions of active region core loops as observed with AIA/SDO. The 94Å fluctuations (Figure 1) have structure on timescales shorter than radiative and conductive cooling times. Each of several strong 94Å brightenings is followed after ~8 min by a broader peak in the cooler 335Å emission. This indicates that we see emission from the hot component of the 94Å contribution function. No hotter contributions appear, and we conclude that the 94Å intensity can be used as a proxy for energy injection into the loop plasma. The probability density function of the observed 94Å intensity has 'heavy tails' that approach zero more slowly than the tails of a normal distribution. Hence, large fluctuations dominate the behavior of the system. The resulting 'intermittence' is associated with power-law or exponential scaling of the related variables, and these in turn are associated with turbulent phenomena. The intensity plots in Figure 1 resemble multifractal time series, which are common to various forms of turbulent energy dissipation. In these systems a single fractal dimension is insufficient to describe the dynamics and instead there is a spectrum of fractal dimensions that quantify the self-similar properties. Figure 2 shows the multifractal spectrum from our data to be invariant over timescales from 24 s to 6.4 min. We compare these results to outputs from theoretical energy dissipation models based on MHD turbulence, and in some cases we find substantial agreement, in terms of intermittence, multifractality and scale invariance. Figure 1. Time traces of 94A intensity in the inter-moss portions of four AR core loops. Figure 2. Multifractal spectra showing timescale invariance. The four cases of Figure 1 are included.

Coherence and discontinuity in the scaling of species' distribution patterns

The spatial distribution of a species can be characterized at many different spatial scales, from fine-scale measures of local population density to coarse-scale geographical-range structure. Previous studies have shown a degree of correlation in species' distribution patterns across narrow ranges of scales, making it possible to predict fine-scale properties from coarser-scale distributions. To test the limits of such extrapolation, we have compiled distributional information on 16 species of British plants, at scales ranging across six orders of magnitude in linear resolution (1 in to 100 km). As expected, the correlation between patterns at different spatial scales tends to degrade as the scales become more widely separated. There is, however, an abrupt breakdown in cross-scale correlations across intermediate (ca. 0.5 km) scales, suggesting that local and regional patterns are influenced by essentially non-overlapping sets of processes. The scaling discontinuity may also reflect characteristic scales of human land use in Britain, suggesting a novel method for analysing the 'footprint' of humanity on a landscape.

Evaluation of the Retinal Vasculature in Hypertension and Chronic Kidney Disease in an elderly population of Irish nuns

Background: Chronic kidney disease (CKD) and hypertension are global public health problems associated with considerable morbidity, premature mortality and attendant healthcare costs. Previous studies have highlighted that non-invasive examination of the retinal microcirculation can detect microvascular pathology that is associated with systemic disorders of the circulatory system such as hypertension. We examined the associations between retinal vessel caliber (RVC) and fractal dimension (DF), with both hypertension and CKD in elderly Irish nuns.

Methods: Data from 1233 participants in the cross-sectional observational Irish Nun Eye Study (INES) were assessed from digital photographs with a standardized protocol using computer-assisted software. Multivariate regression analyses were used to assess associations with hypertension and CKD, with adjustment for age, body mass index (BMI), refraction, fellow eye RVC, smoking, alcohol consumption, ischemic heart disease (IHD), cerebrovascular accident (CVA), diabetes and medication use.

Results: In total, 1122 (91%) participants (mean age: 76.3 [range: 56-100] years) had gradable retinal images of sufficient quality for blood vessel assessment. Hypertension was significantly associated with a narrower central retinal arteriolar equivalent (CRAE) in a fully adjusted analysis (P = 0.002; effect size= -2.16 μm; 95% confidence intervals [CI]: -3.51, -0.81 μm). No significant associations between other retinal vascular parameters and hypertension or between any retinal vascular parameters and CKD were found.

Conclusions: Individuals with hypertension have significantly narrower retinal arterioles which may afford an earlier opportunity for tailored prevention and treatment options to optimize the structure and function of the microvasculature, providing additional clinical utility. No significant associations between retinal vascular parameters and CKD were detected.

Existência de minimizantes relaxados e fenómeno de Lavrentiev

Neste trabalho prova-se a existência de minimizantes relaxados em problemas de controlo óptimo não convexos usando técnicas de compactificação. Faz-se a extensão do exemplo de Manià a dimensão dois, obtendo-se uma classe de problemas variacionais em 2D que apresentam Fenómeno de Lavrentiev. Prova-se que o fenómeno persiste a certas perturbações, obtendo- -se assim uma classe de funcionais cujos Lagrangianos são coercivos e convexos em relação ao gradiente. Adicionalmente, apresentam-se exemplos de problemas do cálculo das variações com diferentes condições de fronteira, e em diferentes tipos de domínios (incluindo domínios com fronteira fractal), que exibem Fenómeno de Lavrentiev.

Gorgonians of the South of Portugal: biology, ecology and conservation

O papel ecológico das gorgónias (Octocorallia: Alcyonacea) nos fundos marinhos rochosos é mundialmente reconhecido. Contudo, a informação acerca da ecologia e biologia das espécies de gorgónias nas zonas temperadas do NE Atlântico é manifestamente escassa, especialmente tendo em consideração as actuais perturbações globais, regionais e locais. Nos fundos rochosos da costa algarvia até aos 30 m, verificouse que várias espécies de gorgónias são abundantes e frequentes, nomeadamente Eunicella labiata, Eunicella gazella, Eunicella verrucosa, Leptogorgia lusitanica e Leptogorgia sarmentosa. As populações de gorgónias são co-dominadas por diferentes espécies que apresentaram elevados índices de associação, indicando reduzidos níveis de competição entre elas. Em todo o caso, a estrutura dos povoamentos diferiu com as condições locais. Todas as espécies evidenciaram padrões de distribuição semelhantes ao longo do gradiente de profundidade, i.e. a abundância aumenta significamente com a profundidade após os 15 m. A profundidades mais baixas (até aos 15 m), a distribuição das gorgónias parece ser condicionada por factores abióticos e pela competição com algas. Com efeito, os padrões de distribuição espacial das espécies de gorgónias na costa algarvia são determinados pela interacção de pressões naturais e antropogénicas (ex. pesca). Ainda que as colónias de maior tamanho não tenham sido restritas a áreas menos pescadas, em áreas mais perturbadas pela pesca, a distribuição dos tamanhos das colónias estava maioritariamente desviada para tamanhos mais pequenos. Os efeitos das perturbações naturais nas populações de gorgónias foram evidenciados pela ocorrência de padrões demográficos distintos em áreas vizinhas sujeitas a níveis semelhantes de pressões antropogénicas. Estes estudos demonstraram, ainda, que os efeitos na distribuição de frequências de tamanho das colónias são dependentes das espécies de gorgónias em causa: Eunicella labiata não parece ser afectada; Leptogorgia sarmentosa é tendencialmente afectada por pressões antropogénicas; Eunicella gazella e Leptogorgia lusitanica aparentam ser afectadas, quer por pressões naturais, quer por pressões antropogénicas. Os efeitos verificados nos padrões da distribuição de frequências de tamanho, particularmente a tendência para o desvio destas frequências para tamanhos mais pequenos em áreas sujeitas a perturbações, poderão ter consequências para a biodiversidade dos fundos sublitorais rochosos na costa algarvia. Com efeito, o presente estudo apoia o paradigma geral de que os corais são habitats que suportam comunidades de elevada biodiversidade e abundância. Num dos poucos estudos que examinam a relação entre as gorgónias e as suas comunidades de invertebrados epibentónicos, foi verificado que as gorgónias (Eunicella gazella e Leptogorgia lusitanica) sustentam comunidades ricas (11 phyla, 181 taxa) e abundantes (7284 indivíduos). Estas comunidades são dominadas por anfípodes, mas os poliquetas tiveram um grande contributo para os níveis elevados de biodiversidade. Verificou-se, igualmente, que o tamanho da colónia desempenha um papel fundamental na biodiversidade, na medida em que as colónias de menor tamanho apresentaram um contributo mais baixo, comparativamente às médias e grandes. Ainda que ambas as gorgónias partilhem a maioria das espécies amostradas, 11 e 18 taxa foram exclusivos de Eunicella gazella e Leptogorgia lusitanica, respectivamente (excluindo indivíduos com presenças únicas). No entanto, a maioria destes taxa eram ou pouco abundantes ou pouco frequentes. A excepção foi a presença de planárias (Turbellaria) de coloração branca nas colónias de Eunicella gazella, provavelmente beneficiando do efeito de camuflagem proporcionado pelos ramos com a mesma coloração. Com efeito, a complementaridade entre as comunidades epibentónicas associadas a ambas as gorgónias diminuiu quando usados os dados de presença/ausência, sugerindo que os padrões de biodiversidade são mais afectados pelas alterações na abundância relativa das espécies dominantes do que pela composição faunística. As comunidades de epifauna bentónica associadas a estas gorgónias não só apresentaram valores elevados de ®-diversidade, como de ¯- diversidade, resultantes de padrões intrincados de variabilidade na sua composição e estrutura. Ainda que o conjunto de espécies disponíveis para colonização seja, na generalidade, o mesmo para ambos os locais, cada colónia apresenta uma parte deste conjunto. Na sua totalidade, as colónias de gorgónias poderão funcionar como uma metacomunidade, mas a estrutura das comunidades associadas a cada colónia (ex. número total de espécies e abundância) parecem depender dos atributos da colónia, nomeadamente superfície disponível para colonização (altura, largura e área), complexidade e heterogeneidade (dimensão fractal e lacunaridade, respectivamente) e cobertura epibentónica “colonial” (ex. fauna colonial e algas macroscópicas; CEC). Numa primeira tentativa para quantificar a relação entre as gorgónias e os invertebrados epibentónicos a elas associados (em termos de abundância e riqueza específica), verificou-se que a natureza e a intensidade destas relações dependem da espécie hospedeira e variam para os grupos taxonómicos principais. No entanto, independentemente do grupo taxonómico, a riqueza específica e a abundância estão significativamente correlacionadas com a CEC. Com efeito, a CEC provavelmente devido a um efeito trófico (aumento da disponibilidade alimentar directo ou indirecto), combinado com a superfície disponível para colonização (efeito espécies-área) foram as variáveis mais relacionadas com os padrões de abundância e riqueza específica. Por outro lado, ainda que a complexidade estrutural seja frequentemente indicada como um dos factores responsáveis pela elevada diversidade e abundância das comunidades bentónicas associadas a corais, a dimensão fractal e a lacunaridade apenas foram relevantes nas comunidades associadas a Leptogorgia lusitanica. A validade do paradigma que defende que a complexidade estrutural promove a biodiversidade poderá ser, então, dependente da escala a que se realizam os estudos. No caso das gorgónias, o efeito da complexidade ao nível dos agregados de gorgónias poderá ser muito mais relevante do que ao nível da colónia individual, reforçando a importância da sua conservação como um todo, por forma a preservar a diversidade de espécies hospedeiras, o seu tamanho e estrutura. Actividades antropogénicas como a pesca, podem, ainda, ter efeitos negativos ao nível da reprodução de espécies marinhas. Analogamente ao verificado para os padrões de distribuição espacial das populações de gorgónias na costa algarvia, a informação relativa à sua reprodução é igualmente escassa. Os estudos realizados em populações de Eunicella gazella a 16m de profundidade, demonstraram que o desenvolvimento anual das estruturas reprodutivas é altamente sincronizado entre os sexos. A razão entre sexos na população foi de 1.09 (F:M), encontrando-se perto da paridade. A espermatogénese estende-se por 6 a 8 meses, enquanto que a oogénese é mais demorada, levando mais de um ano para que os oócitos se desenvolvam até estarem maduros. Antes da libertação dos gâmetas, foi observada uma elevada fecundidade nas fêmeas (27.30§13.24 oócitos pólipo−1) e nos machos (49.30§31.14 sacos espermáticos pólipo−1). Estes valores encontram-se entre os mais elevados reportados à data para zonas temperadas. A libertação dos gâmetas (não há evidência de desenvolvimento larvar, nem à superfície da colónia, nem no seu interior) occorre em Setembro/ Outubro, após um período de elevada temperatura da água do mar. As fêmeas emitem oócitos maduros de elevadas dimensões, retendo, todavia, os oócitos imaturos que se desenvolvem apenas na época seguinte. Ainda que o efeito da pesca nas populações de gorgónias da costa do Algarve seja perceptível, às taxas actuais, o mergulho recreativo não aparenta afectar seriamente estas populações. Contudo, sendo uma indústria em expansão e conhecendo-se a preferência de mergulhadores por áreas rochosas naturais ricas em espécies bentónicas, futuramente poderá vir a afectar estes habitats. A monitorização de mergulhadores na costa algarvia mostrou que a sua maioria (88.6 %) apresenta comportamentos que podem impactar o habitat, com uma taxa média de contactos de 0.340§0.028 contactos min−1. Esta taxa foi mais elevada em mergulhadores com moderada experiência e na fase inicial do mergulho (0–10 min). Os contactos com as barbatanas e mãos foram comuns, resultando, maioritariamente, na resuspensão do sedimento, mas geralmente apresentando um impacto reduzido. Todavia, a fauna também foi afectada, quer por danos físicos, quer pela interacção com os mergulhadores, e num cenário de expansão significativa desta actividade, os impactos na fauna local poderão aumentar, com consequências para os ecossistemas de fundos rochosos da costa sul de Portugal. Na sua globalidade, a informação recolhida nos estudos que contemplam esta tese, por ser em grande parte totalmente nova para a região, espera-se que contribua para a gestão da zona costeira do Algarve.

Emerging Technologies

This book, written when Walker was Visiting Professor at the Technical University Munich in 2011, describes his research on the effects of digital technology on architectural design and construction, and on the development of ‘digital craft’. The primary example given is The Swarm, a digitally designed and manufactured pavilion, produced with students while Walker was at TU Munich. It now stands outside the Bayerischen Architektenkammer (Bavarian Chamber of Architects) in Munich. Through such research-by-design, Walker asks larger questions: what can designers craft without a master craftsman’s skills, and how can craft skills be recovered through digital fabrication? Another example in the book is the Swoosh Pavilion, one of two public-space-scale architectural pavilion prototypes Walker developed between 2008 and 2009 at the Architectural Association (AA), using applied digital modelling and CNC techniques to investigate methods of teaching and testing digital processes through making. Swoosh (2008) and a second AA pavilion, Driftwood (2009), were discussed by Walker and Martin Self, his co-investigator, in ‘Fractal, bad hair, Swoosh and Driftwood pavilions of Intermediate Unit 2, 2006–2009’, published in the AD reader, Manufacturing the Bespoke (2012), which includes essays by well-known critics and designers such as Mathias Kohler and Michael Stacey. Both AA pavilions were sponsored by FinnForest Merk, Arup, HOK and Building Design Magazine, and were seen by large international audiences in Bedford Square, London during the 2008–9 ‘AA Projects Review’ shows. The book Making Pavilions (Walker and Self, AA Agenda No. 9, Architectural Association Press, 2011) also discusses their work over seven years of teaching at the Architectural Association. At the same time, Walker collaborated on a series of Serpentine pavilions, commissioned annually by the Serpentine Gallery, London, co-designing these experimental structures with internationally renowned architects Daniel Libeskind, Oscar Niemeyer, Toyo Ito and Alvaro Siza.

The world without outside

The world is all that there is. In the world, ontology and epistemology coincide. The thing and the perspective are part of it, scale is ingested in its multiplicity, communication stops at the world's edge. By reading together Deleuze and Guattari's plane of immanence and Niklas Luhmann's proto-global concept of Weltgesellschaft (“world society”), I suggest a conceptualisation of the world as the materiality of the multiple spaces of creation in an insular, all-inclusive immanence. Deprived of an outside, the world pushes its own understanding of circumference through, first, the expansion of its own limits through the process of worlding, and, second, the multiplication of modes of material (self-)production through its process of othering. Thus, the world swells up from the inside and expands on both the material and the semantic level, producing a multiplicity of fractal microcosms. Issues of responsibility and justice arise that are intricately linked to the materiality of the world and take place in and between the various bodies and spaces of the world but without an overarching hierarchy or principle. This approach is a way of counteracting the all-pervasive Hegelian understanding of synthesis, arguing instead for a plenitude that brims with positivity and that can never become fully complete. The world remains its own infinite process of worlding.