Fractal dimension of dried foods : a correlation between microstructure and porosity

The quality of dried food is affected by a number of factors including quality of raw material, initial microstructure, and drying conditions. The structure of the food materials goes through deformations due to the simultaneous effect of heat and mass transfer during the drying process. Shrinkage and changes in porosity, microstructure and appearance are some of the most remarkable features that directly influence overall product quality. Porosity and microstructure are the important material properties in relation to the quality attributes of dried foods. Fractal dimension (FD) is a quantitative approach of measuring surface, pore characteristics, and microstructural changes [1]. However, in the field of fractal analysis, there is a lack of research in developing relationship between porosity, shrinkage and microstructure of different solid food materials in different drying process and conditions [2-4]. Establishing a correlation between microstructure and porosity through fractal dimension during convective drying is the main objective of this work.

Lattice basis delegation in fixed dimension and shorter-ciphertext hierarchical IBE

We present a technique for delegating a short lattice basis that has the advantage of keeping the lattice dimension unchanged upon delegation. Building on this result, we construct two new hierarchical identity-based encryption (HIBE) schemes, with and without random oracles. The resulting systems are very different from earlier lattice-based HIBEs and in some cases result in shorter ciphertexts and private keys. We prove security from classic lattice hardness assumptions.

The why dimension - opening frontiers for digital learning

Digital learning has come a long way from the days of simple 'if-then' queries. It is now enabled by countless innovations that support knowledge sharing, openness, flexibility, and independent inquiry. Set against an evolutionary context this study investigated innovations that directly support human inquiry. Specifically, it identified five activities that together are defined as the 'why dimension' – asking, learning, understanding, knowing, and explaining why. Findings highlight deficiencies in mainstream search-based approaches to inquiry, which tend to privilege the retrieval of information as distinct from explanation. Instrumental to sense-making, the 'why dimension' provides a conceptual framework for development of 'sense-making technologies'.

Navigating the social dimension of sustainability decision making of mega-projects

Until recently, sustainable development was perceived as essentially an environmental issue, relating to the integration of environmental concerns into economic decision-making. As a result, environmental considerations have been the primary focus of sustainability decision making during the economic development process for major projects, and the assessment and preservation of social and cultural systems has been arguably too limited. The practice of social impact and sustainability assessment is an established and accepted part of project planning, however, these practices are not aimed at delivering sustainability outcomes for social systems, rather they are designed to minimise ‘unsustainability’ and contribute to project approval. Currently, there exists no widely recognised standard approach for assessing social sustainability and accounting for positive externalities of existing social systems in project decision making. As a result, very different approaches are applied around the world, and even by the same organisations from one project to another. This situation is an impediment not only to generating a shared understanding of the social implications as related to major projects, but more importantly, to identifying common approaches to help improve social sustainability outcomes of proposed activities. This paper discusses the social dimension of sustainability decision making of mega-projects, and argues that to improve accountability and transparency of project outcomes it is important to understand the characteristics that make some communities more vulnerable than others to mega-project development. This paper highlights issues with current operational level approaches to social sustainability assessment at the project level, and asserts that the starting point for project planning and sustainability decision making of mega-projects needs to include the preservation, maintenance, and enhancement of existing social and cultural systems. It draws attention to the need for a scoping mechanism to systematically assess community vulnerability (or sensitivity) to major infrastructure development during the feasibility and planning stages of a project.

On the relations and differences between Popper dimension, exclusion dimension and VC-Dimension

A high-level relationPopper dimension—( Exclusion dimension—( VC dimension—( between Karl Popper’s ideas on “falsifiability of scientific theories” and the notion of “overfitting”Overfitting in statistical learning theory can be easily traced. However, it was pointed out that at the level of technical details the two concepts are significantly different. One possible explanation that we suggest is that the process of falsification is an active process, whereas statistical learning theory is mainly concerned with supervised learningSupervised learning, which is a passive process of learning from examples arriving from a stationary distribution. We show that concepts that are closer (although still distant) to Karl Popper’s definitions of falsifiability can be found in the domain of learning using membership queries, and derive relations between Popper’s dimension, exclusion dimension, and the VC-dimensionVC dimension.

Canards in advection-reaction-diffusion systems in one spatial dimension

This thesis contains a mathematical investigation of the existence of travelling wave solutions to singularly perturbed advection-reaction-diffusion models of biological processes. An enhanced mathematical understanding of these solutions and models is gained via the identification of canards (special solutions of fast/slow dynamical systems) and their role in the existence of the most biologically relevant, shock-like solutions. The analysis focuses on two existing models. A new proof of existence of a whole family of travelling waves is provided for a model describing malignant tumour invasion, while new solutions are identified for a model describing wound healing angiogenesis.

Quantitative characterization of kaolinite dispersibility in styrene–butadiene rubber composites by fractal dimension

A fractal method was introduced to quantitatively characterize the dispersibility of modified kaolinite (MK) and precipitated silica (PS) in styrene–butadiene rubber (SBR) matrix based on the lower magnification transmission electron microscopic images. The fractal dimension (FD) is greater, and the dispersion is worse. The fractal results showed that the dispersibility of MK in the latex blending sample is better than that in the mill blending samples. With the increase of kaolinite content, the FD increases from 1.713 to 1.800, and the dispersibility of kaolinite gradually decreases. There is a negative correlation between the dispersibility and loading content. With the decrease of MK and increase of PS, the FD significantly decreases from 1.735 to 1.496 and the dipersibility of kaolinite remarkably increases. The hybridization can improve the dispersibility of fillers in polymer matrix. The FD can be used to quantitatively characterize the aggregation and dispersion of kaolinite sheets in rubber matrix.

A quasi-likelihood method for fractal-dimension estimation

We propose a simple method of constructing quasi-likelihood functions for dependent data based on conditional-mean-variance relationships, and apply the method to estimating the fractal dimension from box-counting data. Simulation studies were carried out to compare this method with the traditional methods. We also applied this technique to real data from fishing grounds in the Gulf of Carpentaria, Australia

Multiresolution Area-based Fractal Dimension Estimation of Signals Applied to EEG Data

In this paper, we present an approach to estimate fractal complexity of discrete time signal waveforms based on computation of area bounded by sample points of the signal at different time resolutions. The slope of best straight line fit to the graph of log(A(rk)A / rk(2)) versus log(l/rk) is estimated, where A(rk) is the area computed at different time resolutions and rk time resolutions at which the area have been computed. The slope quantifies complexity of the signal and it is taken as an estimate of the fractal dimension (FD). The proposed approach is used to estimate the fractal dimension of parametric fractal signals with known fractal dimensions and the method has given accurate results. The estimation accuracy of the method is compared with that of Higuchi's and Sevcik's methods. The proposed method has given more accurate results when compared with that of Sevcik's method and the results are comparable to that of the Higuchi's method. The practical application of the complexity measure in detecting change in complexity of signals is discussed using real sleep electroencephalogram recordings from eight different subjects. The FD-based approach has shown good performance in discriminating different stages of sleep.

Signal Characterization using Fractal Dimension

Fractal Dimensions (FD) are popular metrics for characterizing signals. They are used as complexity measuresin signal analysis applications in various fields. However, proper interpretation of such analyses has not been thoroughly addressed. In this paper, we study the effect of various signal properties on FD and interpret results in terms of classical signal processing concepts such as amplitude, frequency,number of harmonics, noise power and signal bandwidth. We have used Higuchi’s method for estimating FDs. This study helps in gaining a better understanding of the FD complexity measure for various signal parameters. Our results indicate that FD is a useful metric in estimating various signal properties. As an application of the FD measure in real world scenario, the FD is used as a feature in discriminating seizures from seizure free intervals in intracranial EEG data recordings and the FD feature has given good discrimination performance.

Consonance in urban form: The architectural dimension of urban morphology

Consonance in urban form is contingent on the continuity of the fine grain architectural features that are imbued in the commodity of the evolved historic urban fabric. A city's past can be viewed therefore as a repository of urban form characteristics from which concise architectural responses can result in a congruent urban landscape. This thesis proposes new methods to evaluate the interplay of architectural elements that can be traced throughout the lifespan of the particular evolving urban areas under scrutiny, and postulates a theory of how the mapping of historical urban form can correlate with deriving parameters for new buildings.

Exact calculations of survival probability for diffusion on growing lines, disks, and spheres: The role of dimension

Unlike standard applications of transport theory, the transport of molecules and cells during embryonic development often takes place within growing multidimensional tissues. In this work, we consider a model of diffusion on uniformly growing lines, disks, and spheres. An exact solution of the partial differential equation governing the diffusion of a population of individuals on the growing domain is derived. Using this solution, we study the survival probability, S(t). For the standard nongrowing case with an absorbing boundary, we observe that S(t) decays to zero in the long time limit. In contrast, when the domain grows linearly or exponentially with time, we show that S(t) decays to a constant, positive value, indicating that a proportion of the diffusing substance remains on the growing domain indefinitely. Comparing S(t) for diffusion on lines, disks, and spheres indicates that there are minimal differences in S(t) in the limit of zero growth and minimal differences in S(t) in the limit of fast growth. In contrast, for intermediate growth rates, we observe modest differences in S(t) between different geometries. These differences can be quantified by evaluating the exact expressions derived and presented here.