On the mathematical modeling of wound healing angiogenesis in skin as a reaction-transport process

Over the last 30 years, numerous research groups have attempted to provide mathematical descriptions of the skin wound healing process. The development of theoretical models of the interlinked processes that underlie the healing mechanism has yielded considerable insight into aspects of this critical phenomenon that remain difficult to investigate empirically. In particular, the mathematical modeling of angiogenesis, i.e., capillary sprout growth, has offered new paradigms for the understanding of this highly complex and crucial step in the healing pathway. With the recent advances in imaging and cell tracking, the time is now ripe for an appraisal of the utility and importance of mathematical modeling in wound healing angiogenesis research. The purpose of this review is to pedagogically elucidate the conceptual principles that have underpinned the development of mathematical descriptions of wound healing angiogenesis, specifically those that have utilized a continuum reaction-transport framework, and highlight the contribution that such models have made toward the advancement of research in this field. We aim to draw attention to the common assumptions made when developing models of this nature, thereby bringing into focus the advantages and limitations of this approach. A deeper integration of mathematical modeling techniques into the practice of wound healing angiogenesis research promises new perspectives for advancing our knowledge in this area. To this end we detail several open problems related to the understanding of wound healing angiogenesis, and outline how these issues could be addressed through closer cross-disciplinary collaboration.

5-year Chlamydia vaccination programme could reverse disease-related koala population decline: Predictions from a mathematical model using field data

BACKGROUND Many koala populations around Australia are in serious decline, with a substantial component of this decline in some Southeast Queensland populations attributed to the impact of Chlamydia. A Chlamydia vaccine for koalas is in development and has shown promise in early trials. This study contributes to implementation preparedness by simulating vaccination strategies designed to reverse population decline and by identifying which age and sex category it would be most effective to target. METHODS We used field data to inform the development and parameterisation of an individual-based stochastic simulation model of a koala population endemic with Chlamydia. The model took into account transmission, morbidity and mortality caused by Chlamydia infections. We calibrated the model to characteristics of typical Southeast Queensland koala populations. As there is uncertainty about the effectiveness of the vaccine in real-world settings, a variety of potential vaccine efficacies, half-lives and dosing schedules were simulated. RESULTS Assuming other threats remain constant, it is expected that current population declines could be reversed in around 5-6 years if female koalas aged 1-2 years are targeted, average vaccine protective efficacy is 75%, and vaccine coverage is around 10% per year. At lower vaccine efficacies the immunological effects of boosting become important: at 45% vaccine efficacy population decline is predicted to reverse in 6 years under optimistic boosting assumptions but in 9 years under pessimistic boosting assumptions. Terminating a successful vaccination programme at 5 years would lead to a rise in Chlamydia prevalence towards pre-vaccination levels. CONCLUSION For a range of vaccine efficacy levels it is projected that population decline due to endemic Chlamydia can be reversed under realistic dosing schedules, potentially in just 5 years. However, a vaccination programme might need to continue indefinitely in order to maintain Chlamydia prevalence at a sufficiently low level for population growth to continue.

Amplified stories: Digital technology and representations of lived experiences

New media technologies and the narrative turn in qualitative research has expanded the methods through which we gather data about and share findings of groups who have traditionally been written about by others rather than telling their own stories to reveal the complexities of their experiences. This chapter explores two projects that use storytelling and technology in an effort to change public perceptions about disadvantaged a community or cohort that have specific circumstances but are a result of policies beyond their control.

A mathematical framework for expanding a railway’s theoretical capacity

Analytical techniques for measuring and planning railway capacity expansion activities have been considered in this article. A preliminary mathematical framework involving track duplication and section sub divisions is proposed for this task. In railways these features have a great effect on network performance and for this reason they have been considered. Additional motivations have also arisen from the limitations of prior models that have not included them.

An integrated mathematical approach to measure the capacity of MMTS

This article focusses upon multi-modal transportation systems (MMTS) and the issues surrounding the determination of system capacity. For that purpose a multi-objective framework is advocated that integrates all the different modes and many different competing capacity objectives. This framework is analytical in nature and facilitates a variety of capacity querying and capacity expansion planning.

Honey flows through fertile valleys : The cognitive and evolutionary foundations of paradise representations

The aim of the study is to explain how paradise beliefs are born from the viewpoint of mental functions of the human mind. The focus is on the observation that paradise beliefs across the world are mutually more similar than dissimilar. By using recent theories and results from the cognitive and evolutionary study of religion as well as from studies of environmental preferences, I suggest that this is because pan-human unconscious motivations, the architecture of mind, and the way the human mind processes information constrain the possible repertoire of paradise beliefs. The study is divided into two parts, theoretical and empirical. The arguments in the theoretical part are tested with data in the empirical part with two data sets. The first data set was collected using an Internet survey. The second data set was derived from literary sources. The first data test the assumption that intuitive conceptions of an environment of dreams generally follow the outlines set by evolved environmental preferences, but that they can be tweaked by modifying the presence of desirable elements. The second data test the assumption that familiarity is a dominant factor determining the content of paradise beliefs. The results of the study show that in addition to the widely studied belief in supernatural agents, belief in supernatural environments wells from the natural functioning of the human mind attesting the view that religious thinking and ideas are natural for human species and are produced by the same mental mechanisms as other cultural information. The results also help us to understand that the mental structures behind the belief in the supernatural have a wider scope than has been previously acknowledged.

The Unable Individual : The Actantial Analyses of Three Chinese Films and Discussion on Their Representations of the Individual’s Position in Contemporary Chinese Society

The thesis studies three contemporary Chinese films, Incense (Xianghuo 2003), Beijing Bicycle (Shiqi sui de danche, 2001), and South of the Clouds (Yun de nanfang, 2004). The aim of the thesis is to find out how these films represent the individual, his relationships with others, and his possibilities in society. The films all portray a male individual setting out to pursue a goal, facing one obstacle after the other in the process, and in the end failing to achieve his goal. The other characters in the films are also primarily either unable or unwilling to help the lead character. In the thesis these features of the films are analysed by applying A.J. Greimas’s structuralist semiotic theory about the actantial structure of discourses. The questions about the individual’s position are answered by defining which instances in the films actually represent the actantial positions of the sender, receiver, subject, object, helper and opponent. The results of the actantial analyses of the three films are further discussed in the light of theories regarding individualization. The focus is on the theories of Ulrich Beck, Elisabeth Beck-Gernsheim and Zygmunt Bauman, who see a development towards individualization in societies following the disintegration of traditional social structures. For the most part, these theories do seem to be applicable to the films’ representations of the individual’s position, especially regarding the increased responsibility of the individual. For example, the position of the family is represented as either insignificant or negative in all of the films, which fits with the description of the individualized society, contradicting the idea of traditional Chinese society. On the other hand, the identities and goals of the characters in the films are not represented as fragmented in the way the theories would suggest.

Simplified Mathematical Model for Effects of Freezing on the Low-Temperature Performance of the Lead-Acid Battery

Discharge periods of lead-acid batteries are significantly reduced at subzero centigrade temperatures. The reduction is more than what can he expected due to decreased rates of various processes caused by a lowering of temperature and occurs despite the fact that active materials are available for discharge. It is proposed that the major cause for this is the freezing of the electrolyte. The concentration of acid decreases during battery discharge with a consequent increase in the freezing temperature. A battery freezes when the discharge temperature falls below the freezing temperature. A mathematical model is developed for conditions where charge-transfer reaction is the rate-limiting step. and Tafel kinetics are applicable. It is argued that freezing begins from the midplanes of electrodes and proceeds toward the reservoir in-between. Ionic conduction stops when one of the electrodes freezes fully and the time taken to reach that point, namely the discharge period, is calculated. The predictions of the model compare well to observations made at low current density (C/5) and at -20 and -40 degrees C. At higher current densities, however, diffusional resistances become important and a more complicated moving boundary problem needs to be solved to predict the discharge periods. (C) 2009 The Electrochemical Society.

Gauge theory of a group of diffeomorphisms. I. General principles

Any (N+M)-parameter Lie group G with an N-parameter subgroup H can be realized as a global group of diffeomorphisms on an M-dimensional base space B, with representations in terms of transformation laws of fields on B belonging to linear representations of H. The gauged generalization of the global diffeomorphisms consists of general diffeomorphisms (or coordinate transformations) on a base space together with a local action of H on the fields. The particular applications of the scheme to space-time symmetries is discussed in terms of Lagrangians, field equations, currents, and source identities. Journal of Mathematical Physics is copyrighted by The American Institute of Physics.

Neuronal oscillations in gamma- and alpha-frequency bands: from object representations to sensory awareness

The synchronization of neuronal activity, especially in the beta- (14-30 Hz) /gamma- (30 80 Hz) frequency bands, is thought to provide a means for the integration of anatomically distributed processing and for the formation of transient neuronal assemblies. Thus non-stimulus locked (i.e. induced) gamma-band oscillations are believed to underlie feature binding and the formation of neuronal object representations. On the other hand, the functional roles of neuronal oscillations in slower theta- (4 8 Hz) and alpha- (8 14 Hz) frequency bands remain controversial. In addition, early stimulus-locked activity has been largely ignored, as it is believed to reflect merely the physical properties of sensory stimuli. With human neuromagnetic recordings, both the functional roles of gamma- and alpha-band oscillations and the significance of early stimulus-locked activity in neuronal processing were examined in this thesis. Study I of this thesis shows that even the stimulus-locked (evoked) gamma oscillations were sensitive to high-level stimulus features for speech and non-speech sounds, suggesting that they may underlie the formation of early neuronal object representations for stimuli with a behavioural relevance. Study II shows that neuronal processing for consciously perceived and unperceived stimuli differed as early as 30 ms after stimulus onset. This study also showed that the alpha band oscillations selectively correlated with conscious perception. Study III, in turn, shows that prestimulus alpha-band oscillations influence the subsequent detection and processing of sensory stimuli. Further, in Study IV, we asked whether phase synchronization between distinct frequency bands is present in cortical circuits. This study revealed prominent task-sensitive phase synchrony between alpha and beta/gamma oscillations. Finally, the implications of Studies II, III, and IV to the broader scientific context are analysed in the last study of this thesis (V). I suggest, in this thesis that neuronal processing may be extremely fast and that the evoked response is important for cognitive processes. I also propose that alpha oscillations define the global neuronal workspace of perception, action, and consciousness and, further, that cross-frequency synchronization is required for the integration of neuronal object representations into global neuronal workspace.

Mathematical model of arterial stenosis

A mathematical model for pulsatile flow in a partially occluded tube is presented. The problem has applications in studying the effects of blood flow characteristics on atherosclerotic development. The model brings out the importance of the pulsatility of blood flow on separation and the stress distribution. The results obtained show fairly good agreement with the available experimental results.

Cortical representations for phonological quantity

Different languages use temporal speech cues in different linguistic functions. In Finnish, speech-sound duration is used as the primary cue for the phonological quantity distinction ― i.e., a distinction between short and long phonemes. For the second-language (L2) learners of Finnish, quantity is often difficult to master if speech-sound duration plays a less important role in the phonology of their native language (L1). The present studies aimed to investigate the cortical representations for phonological quantity in native speakers and L2 users of Finnish by using behavioral and electrophysiological methods. Since long-term memory representations for different speech units have been previously shown to participate in the elicitation of the mismatch negativity (MMN) brain response, MMN was used to compare the neural representation for quantity between native speakers and L2 users of Finnish. The results of the studies suggested that native Finnish speakers' MMN response to quantity was determined by the activation of native-language phonetic prototypes rather than by phoneme boundaries. In addition, native speakers seemed to process phoneme quantity and quality independently from each other by separate brain representations. The cross-linguistic MMN studies revealed that, in native speakers of Finnish, the MMN response to duration or quantity-degree changes was enhanced in amplitude selectively in speech sounds, whereas this pattern was not observed in L2 users. Native speakers' MMN enhancement is suggested to be due to the pre-attentive activation of L1 prototypes for quantity. In L2 users, the activation of L2 prototypes or other L2 learning effects were not reflected in the MMN, with one exception. Even though L2 users failed to show native-like brain responses to duration changes in a vowel that was similar in L1 and L2, their duration MMN response was native-like for an L2 vowel with no counterpart in L1. Thus, the pre-attentive activation of L2 users' representations was determined by the degree of similarity of L2 sounds to L1 sounds. In addition, behavioral experiments suggested that the establishment of representations for L2 quantity may require several years of language exposure.

Mathematical modelling of the impaction and spreading of spray droplets on leaves

This thesis concerns the development of mathematical models to describe the interactions that occur between spray droplets and leaves. Models are presented that not only provide a contribution to mathematical knowledge in the field of fluid dynamics, but are also of utility within the agrichemical industry. The thesis is presented in two parts. First, thin film models are implemented with efficient numerical schemes in order to simulate droplets on virtual leaf surfaces. Then the interception event is considered, whereby energy balance techniques are employed to instantaneously predict whether an impacting droplet will bounce, splash, or adhere to a leaf.

Mathematical models of calcium and tight junctions in normal and reconstructed epidermis

This project investigated the calcium distributions of the skin, and the growth patterns of skin substitutes grown in the laboratory, using mathematical models. The research found that the calcium distribution in the upper layer of the skin is controlled by three different mechanisms, not one as previously thought. The research also suggests that tight junctions, which are adhesions between neighbouring skin cells, cannot be solely responsible for the differences in the growth patterns of skin substitutes and normal skin.

Application of Mathematical Programming to the Plywood Design and Manufacturing Problem

Plywood manufacture includes two fundamental stages. The first is to peel or separate logs into veneer sheets of different thicknesses. The second is to assemble veneer sheets into finished plywood products. At the first stage a decision must be made as to the number of different veneer thicknesses to be peeled and what these thicknesses should be. At the second stage, choices must be made as to how these veneers will be assembled into final products to meet certain constraints while minimizing wood loss. These decisions present a fundamental management dilemma. Costs of peeling, drying, storage, handling, etc. can be reduced by decreasing the number of veneer thicknesses peeled. However, a reduced set of thickness options may make it infeasible to produce the variety of products demanded by the market or increase wood loss by requiring less efficient selection of thicknesses for assembly. In this paper the joint problem of veneer choice and plywood construction is formulated as a nonlinear integer programming problem. A relatively simple optimal solution procedure is developed that exploits special problem structure. This procedure is examined on data from a British Columbia plywood mill. Restricted to the existing set of veneer thicknesses and plywood designs used by that mill, the procedure generated a solution that reduced wood loss by 79 percent, thereby increasing net revenue by 6.86 percent. Additional experiments were performed that examined the consequences of changing the number of veneer thicknesses used. Extensions are discussed that permit the consideration of more than one wood species.