# Martin Homer's research while affiliated with University of Bristol and other places

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## Publications (70)

Organoids offer a powerful model to study cellular self-organisation, the growth of specific tissue morphologies in-vitro, and to assess potential medical therapies. However, the intrinsic mechanisms of these systems are not entirely understood yet, which can result in variability of organoids due to differences in culture conditions and basement m...

The sewed focus is one of the singularities of planar piecewise smooth dynamical systems. Defined by Filippov in his book 'Differential Equations with Discontinuous Righthand Sides' (Kluwer, 1988), it consists of two invisible tangencies either side of the switching manifold. In the case of analytic focus-like behaviour, Filippov showed that the ap...

The sewed focus is one of the singularities of planar piecewise smooth dynamical systems. Defined by Filippov in his book (Differential Equations with Discontinuous Righthand Sides, Kluwer, 1988), it consists of two invisible tangencies either side of the switching manifold. In the case of analytic focus-like behaviour, Filippov showed that the app...

Organoids offer a powerful model to study cellular self-organisation, the growth of specific tissue morphologies in-vitro, and to assess potential medical therapies. However, the intrinsic mechanisms of these systems are not entirely understood yet, which can result in variability of organoids due to differences in culture conditions and basement m...

Consider a cooperation game on a spatial network of habitat patches, where players can relocate between patches if they judge the local conditions to be unfavorable. In time, the relocation events may lead to a homogeneous state where all patches harbor the same relative densities of cooperators and defectors, or they may lead to self-organized pat...

This paper is concerned with computational modelling of fluid mixing by arrays of villi-like actuators. We are motivated by intestinal villi: small finger-like projections that densely line the small intestine, and exhibit co-ordinated motions that enhance digestion via local mixing. Despite promising applications for artificial villi, such as next...

Objectives
To illustrate the epidemiologic and cost-effectiveness impact of shifting the focus from population-based screening toward a targeted management approach for genital chlamydia infection.
Design
Modeling study, implementing an individual-based, stochastic, dynamic network model.
Setting
Hong Kong.
Population
A hypothetical sample netwo...

Consider a cooperation game on a spatial network of habitat patches, where players can relocate between habitats if they judge the local conditions to be unfavorable. In time, the relocation events may lead to a homogeneous state where all patches harbor the same densities of cooperators and defectors or they may lead to self-organized patterns, wh...

Intestinal crypts are responsible for the total cell renewal of the lining of the intestines; this turnover is governed by the interplay between signalling pathways and the cell cycle. The role of Wnt signalling in cell proliferation and differentiation in the intestinal crypt has been extensively studied, with increased signalling found towards th...

Organoids are engineered three-dimensional tissue cultures derived from stem cells and capable of self-renewal and self-organization into a variety of progenitors and differentiated cell types. An organoid resembles the cellular structure of an organ and retains some of its functionality, while still being amenable to in vitro experimental study. C...

Background Antimicrobial-resistant (AMR) gonorrhoea is a global public health threat. Discriminatory point-of-care tests (POCT) to detect drug sensitivity are under development, enabling individualised resistance-guided therapy.
Methods:
An individual-based dynamic transmission model of gonorrhoea infection in MSM living in London has been develo...

Background
Antimicrobial resistant (AMR) gonorrhoea is a global public health threat. Diagnoses of gonorrhoea have increased in England over the last decade. Guidelines in UK now recommend single dose ceftriaxone, so preserving the efficacy of ceftriaxone is essential. In England, over half of tested isolates remain sensitive to previously recommen...

Intestinal crypts are responsible for the total cell renewal of the lining of the intestines; this turnover is governed by the interplay between signalling pathways and the cell cycle. The role of Wnt signalling in governing cell proliferation and differentiation in the intestinal crypt has been extensively studied, with increased signalling found...

Among the main issues with the implementation of Dielectric Elastomer Generators (DEGs) is the need for pre-charging to perform mechanical-to-electrical energy conversion. In cases when energy harvesting has to be performed in an environment with unpredictable characteristics (e.g., wind, waves, human walking), defining the best times for charge in...

During development, pluripotency is a transient state describing a cell’s ability to give rise to all three germ layers and germline. Recent studies have shown that, in vitro, pluripotency is highly dynamic: exogenous stimuli provided to cultures of mouse embryonic stem cells, isolated from pre-implantation blastocysts, significantly affect the spe...

The yellow fever mosquito Aedes aegypti forms aerial swarms that serve as mating aggregations [1]. Despite lacking the remarkable collective order of other animal ensembles, such as fish and birds [2], the kinematic properties of these swarms bear the hallmarks of local interaction and global cohesion [3,4]. However, the mechanisms responsible for...

Discontinuities are a common feature of physical models in engineering and biological systems, e.g. stick-slip due to friction, electrical relays or gene regulatory networks. The computation of basins of attraction of such nonsmooth systems is challenging and requires special treatments, especially regarding numerical integration. In this paper, we...

Introduction
Antimicrobial resistant (AMR) gonorrhoea is a global public health threat. In London, diagnoses in men who have sex with men (MSM) have more than quadrupled from 2010 to 2015. Importantly, our last-line treatment (ceftriaxone) is used in first-line dual therapy. However, over half of tested isolates are still sensitive to older drugs,...

Micro-mechanical cantilevers are increasingly being used as a characterisation tool in both material and biological sciences. New non-destructive applications are being developed that rely on the information encoded within the cantilever's higher oscillatory modes, such as atomic force microscopy techniques that measure the non-topographic properti...

Dielectric elastomer generators (DEGs) are an emerging technology for the conversion of mechanical into electrical energy. Despite many advantageous characteristics, there are still issues to overcome, including the need for charging at every cycle to produce an electrical output. Self-priming circuits (SPCs) are one possible solution, storing part...

We present two codimension-one bifurcations that occur when an equilibrium collides with a discontinuity in a piecewise smooth dynamical system. These simple cases appear to have escaped recent classifications. We present them here to highlight some of the powerful results from Filippov’s book Differential Equations with Discontinuous Righthand Sid...

Atomic force microscopes have proved to be fundamental research tools in many situations where a gentle imaging process is required, and in a variety of environmental conditions, such as the study of biological samples. Among the possible modes of operation, intermittent contact mode is one that causes less wear to both the sample and the instrumen...

A key problem in the study and design of complex systems is the apparent disconnection between the microscopic and the macroscopic. It is not straightforward to identify the local interactions that give rise to an observed global phenomenon, nor is it simple to design a system that will exhibit some desired global property using only local knowledg...

This article analyses the hearing and behaviour of mosquitoes in the context of inter-individual acoustic interactions. The acoustic interactions of tethered live pairs of Aedes aegypti mosquitoes, from same and opposite sex mosquitoes of the species, are recorded on independent and unique audio channels, together with the response of tethered indi...

One of the main challenges for the practical implementation of dielectric elastomer generators (DEGs) is supplying high voltages. To address this issue, systems using self-priming circuits (SPCs) — which exploit the DEG voltage swing to increase its supplied voltage — have been used with success. A self-priming circuit consists of a charge pump imp...

Erythropoietin is essential for the production of mature erythroid cells, promoting both proliferation and survival. Whether erythropoietin and other cytokines can influence lineage commitment of hematopoietic stem and progenitor cells is of significant interest. To study lineage restriction of the common myeloid progenitor to the megakaryocyte/ery...

A key problem in the study and design of complex systems is the apparent
disconnection between the microscopic and the macroscopic. It is not
straightforward to identify the local interactions that give rise to an
observed global phenomenon, nor is it simple to design a system that will
exhibit some desired global property using only local knowledg...

Dielectric
Elastomer Generators (DEGs) have been claimed as one promising technology for renewable mechanical to electrical energy harvesting, due to their lightweight, low cost, and high energy density. Dielectric
elastomers have a dual behavior, able to convert electrical energy into mechanical if charged electrostatically and to convert mechanic...

Cephalopods employ their chromomorphic skins for rapid and versatile active camouflage and signalling effects. This is achieved using dense networks of pigmented, muscle-driven chromatophore cells which are neurally stimulated to actuate and affect local skin colouring. This allows cephalopods to adopt numerous dynamic and complex skin patterns, mo...

A simple nonlinear transmission-line model of the cochlea with longitudinal
coupling is introduced that can reproduce Basilar membrane response and neural
tuning in the chinchilla. It is found that the middle ear has little effect on
cochlear resonances, and hence conclude that the theory of coherent reflections
is not applicable to the model. The...

Techniques for estimating temporal variation in the frequency content of acoustic tones based on short-time fast Fourier transforms are fundamentally limited by an inherent time-frequency trade-off. This paper presents an alternative methodology, based on Hilbert spectral analysis, which is not affected by this weakness, and applies it to the accur...

Progress in theoretical physics is often made by the investigation of toy models, the model organisms of physics, which provide benchmarks for new methodologies. For complex systems, one such model is the adaptive voter model. Despite its simplicity, the model is hard to analyze. Only inaccurate results are obtained from well-established approximat...

Plants display a range of striking architectural adaptations when grown at elevated temperatures. In the model plant Arabidopsis thaliana, these include elongation of petioles, and increased petiole and leaf angles from the soil surface. The potential physiological significance of these architectural changes remains speculative. We address this iss...

In the investigation of network dynamics a prominent role is played by
analytical coarse-graining schemes. A very powerful class of these schemes are
the so-called heterogeneous approximations, which describe the dynamics of an
agent-based network model by an infinite-dimensional system of differential
equations. Here, we propose a widely applicabl...

Various simple mathematical models of the dynamics of the organ of Corti in the mammalian cochlea are analyzed and their dynamics compared. The specific models considered are phenomenological Hopf and cusp normal forms, a recently proposed description combining active hair-bundle motility and somatic motility, a reduction thereof, and finally a mod...

During high-speed contact mode atomic force microscopy, higher eigenmode flexural oscillations of the cantilever have been identified as the main source of noise in the resultant topography images. We show that by selectively filtering out the frequencies corresponding to these oscillations in the time domain prior to transforming the data into the...

Understanding the modal response of an atomic force microscope is important for the identification of image artefacts captured using contact-mode atomic force microscopy (AFM). As the scan rate of high speed AFM increases, these modes present themselves as ever clearer noise patterns as the frequency of cantilever vibration falls under the frequenc...

Using scanning laser Doppler vibrometer we have identified sources of noise in contact mode high-speed atomic force microscope images and the cantilever dynamics that cause them. By analysing reconstructed animations of the entire cantilever passing over various surfaces, we identified higher eigenmode oscillations along the cantilever as the cause...

A synthesis is presented of two recent studies on modelling the nonlinear neuro- mechanical hearing processes in mosquitoes and in mammals. In each case, a hierarchy of models is considered in attempts to understand data that shows nonlinear amplification and compression of incoming sound signals. The insect’s hearing is tuned to the vicinity of a...

This paper reviews current understanding and presents new results on some of the nonlinear processes that underlie the function of the mammalian cochlea. These processes occur within mechano-sensory hair cells that form part of the organ of Corti. After a general overview of cochlear physiology, mathematical modelling results are presented in three...

In this paper we introduce a simple cochlear model with outer hair cell somatic motility as the active process. The model includes longitudinal feed‐forward coupling mechanism of the basilar membrane to the hair bundle of the outer hair cell. Our analysis indicates that the compressive nonlinearity is greatly enhanced by this coupling mechanism. To...

In this paper we compare and contrast the effects of longitudinal coupling and temporal delay on a fluid-structure transmission-line model of the mammalian cochlea. This work is based on recent reports that, in order to qualitatively explain experimental data, models of the basilar membrane impedance must include an exponential term that represents...

A simple microscopic mechanistic model is described of the active
amplification within the Johnston's organ of the mosquito species
Toxorhynchites brevipalpis. The model is based on the description of the
antenna as a forced-damped oscillator coupled to a set of active threads
(ensembles of scolopidia) that provide an impulsive force when they
twit...

The mammalian cochlea is a remarkable organ that is able to provide up to 60dB amplification of low amplitude sound with sharp tuning. It has been proposed that in order qualitatively to explain experimental data, models of the basilar membrane impedance must include an exponential term that represents a delayed feedback. There are also models that...

We report the use of a laser Doppler vibrometer to measure the motion of an atomic force microscope contact mode cantilever during continuous line scans of a mica surface. With a sufficiently high density of measurement points the dynamics of the entire cantilever beam, from the apex to the base, can be reconstructed. We demonstrate nanosecond reso...

A synthesis is presented of two recent studies on modelling the nonlinear neuro-mechanical hearing processes in mosquitoes and in mammals. In each case, a hierarchy of models is considered in attempts to understand data that shows nonlinear amplification and compression of incoming sound signals. The insect’s hearing is tuned to the vicinity of a s...

We investigate a mathematical model of tapping mode atomic force microscopy (AFM), which includes surface interaction vi both van der Waals and meniscus forces. We also take particular care to include a realistic representation of the integra control inherent to the real microscope. Varying driving amplitude, amplitude setpoint and driving frequenc...

Insects have evolved diverse and delicate morphological structures in order to capture the inherently low energy of a propagating sound wave. In mosquitoes, the capture of acoustic energy and its transduction into neuronal signals are assisted by the active mechanical participation of the scolopidia. We propose a simple microscopic mechanistic mode...

A revised version of an earlier preprint paper This paper is concerned with the computation of the basins of attraction of a simple one degree-of-freedom backlash oscillator using cell-to-cell mapping techniques. This analysis is motivated by the modelling of order vibration in geared systems. We consider both a piecewise linear stiffness model and...

Lightly damped backlash systems have been shown to exhibit unwanted noise and vibration problems and we present a nonlinear analysis of this behaviour. As a representative example, we derive a simple model for a pair of meshing spur gears as a single-degree-of-freedom oscillator with backlash. We consider the behaviour of such a system with low dam...

In this paper we present a model of impact dynamics in large dimensional systems. We describe a hybrid method, based on graph theory and probability theory, which enables us qualitatively to model the statistics of global dynamics as parameters are varied. Direct numerical simulation reveals a sudden jump from no impacts within the system to many r...

This paper is concerned with the modelling of gear rattle in Roots blower vacuum pumps. Analysis of experimental data reveals that the source of the noise and vibration problem is the backlash nonlinearity due to gear teeth losing and re-establishing contact. We develop non-smooth ordinary differential equation models for the dynamics of the pump....

This paper proposes a strategy for the classification of codimension-two discontinuity-induced bifurcations of limit cycles in piecewise smooth systems of ordinary differential equations. Such nonsmooth transitions (also known as C-bifurcations) occur when the cycle interacts with a discontinuity boundary of phase space in a nongeneric way, such as...

In this brief, we consider methods to improve the performance of chaotic communication schemes. We study a system using a receiver which explicitly includes the presence of noise in the channel. We show how the choice of chaotic dynamical system generating the transmitted signal is crucial. We observe a large variation in bit error rate performance...

Motivated by recent experimental results, an explanation is sought for the asymmetry in the radial profile of basilar membrane vibrations in the inner ear. A sequence of one-dimensional beam models is studied which take into account variations in the bending stiffness of the basilar membrane as well as the potential presence of structural hinges. T...

This paper examines the behaviour of piecewise-smooth, continuous, one-dimensional maps that have been derived in the literature as normal forms for grazing and sliding bifurcations. These maps are linear for negative values of the parameter and non-linear for positive values of the parameter. Both C1 and C2 maps of this form are considered. These...

Nonlinear dynamics has been successful in explaining complicated phenomena in well-defined low-dimensional systems. Now it is time to focus on real-life problems that are high-dimensional or ill-defined, for example, due to delay, spatial extent, stochasticity, or the limited nature of available data. How can one understand the dynamics of such sys...

simple model of impact dynamics in many dimensional

In this paper we present a simple hybrid model of impact dynamics in heat exchangers. The method, based on graph theory and probability theory, enables us to model the variation in global dynamics as measurable local parameters are changed. We find a sudden jump from no to many repeated impacts, in agreement with numerical and experimental evidence...

This paper is concerned with the analysis of non-standard bifurcations in piecewise smooth (PWS) dynamical systems. These systems are particularly relevant in many areas of engineering and applied science and have been shown to exhibit a large variety of nonlinear phenomena including chaos. While there is a complete understanding of local bifurcati...

Ideas from graph theory are used systematically to uncover periodic orbits in piecewise smooth dynamical systems of arbitrary dimension. The method is illustrated by its application to one low dimensional system (a confined rocking block) and to one high dimensional system (a heat exchanger). In the latter case the number of possible periodic orbit...

Ideas from graph theory are used to systematically uncover all possible periodic orbits in piecewise continuous mechanical systems of arbitrary dimension. The method is illustrated by its application to one low dimensional system (a confined rocking block) and to one high dimensional system (a heat exchanger). In the latter case the number of possi...

## Citations

... Interestingly, these results depend only on the first derivatives of functions fðu; vÞ and gðu; vÞ coupled to the diffusion coefficients. Therefore, there exists a whole class of systems where such instability may emerge, from chemical reactions [51][52][53] or biological morphogenesis [3,54] to ecosystems [55][56][57][58] and game theory applied to ecological systems [59,60]. In ecology, one such model is the Mimura-Murray model [56]. ...

... Flow past multiple tandem cylinders has been studied to reveal the effect of the presence of bluff bodies upstream on the flow structure. [95][96][97][98] For two cylinders, depending on the distance between the objects, there are three possible scenarios: extended-body flow, reattachment flow, and co-shedding flow. 23,46 When the pitch distance between the two objects is large enough, a two-row shear layer structure is formed and co-shedding flow is represented, whereas, for smaller distances, the frontal cylinder does not produce its independent vortex street. ...

... 6 In settings where sexual partners are not required to test before they take their antibiotic, sexual partners might receive treatment unnecessarily. 7 Overconsumption of antibiotics could exacerbate antimicrobial resistance in other sexually transmitted infections (eg, gonorrhoea, Mycoplasma genitalium, and syphilis) and cause collateral damage to microbiota. Thus, providing access to highly accurate home-based tests for chlamydia to rapidly determine the need for treatment of sexual partners would be ideal. ...

... The regulation of ISC stemness by the Foxo signaling pathway has been noted in the past [37]. Studies have reported crosstalk between Foxo and Wnt and Notch signaling in the intestine (i.e., the downregulation of Foxo1 and Foxo3 inhibits ISC proliferation and differentiation) [38]. In addition, Foxo1 can bind to the CSL element in the Hes1 promoter to promote neural stem cell differentiation [39]. ...

... Moreover, computational modeling approaches, including ordinary differential equations (ODEs), partial differential equations (PDEs), agent-based models, and network modeling, can simulate and predict the behaviors of complex systems like organoids (Gonçalves and García-Aznar, 2023;Pleyer and Fleck, 2023;Wen and Chaolu, 2023). These models integrate known biological mechanisms and parameters to study emergent properties, test hypotheses, and explore the effects of perturbations on organoid development, functionality, and response to external factors (Montes-Olivas et al., 2019). For example, models of intestinal organoids have been developed to investigate the distribution of cell populations and growth patterns in response to signaling dynamics (Buske et al., 2012;Thalheim et al., 2018), to study the biomechanical interactions between cells in crypts (Langlands et al., 2016;Almet et al., 2018), and to evaluate the effect of exogenous substances in the growth pattern of colon cancer organoids (Yan et al., 2018). ...

Reference: Organoids as complex (bio)systems

... We adapted an individual-based, stochastic, dynamic network model of a sexually transmitted infection, previously developed and parameterised for gonorrhea among men who have sex with men (MSM) in the UK (12). This model was originally used to examine antimicrobial-resistant gonorrhea strain development, and we adapted it to represent chlamydia transmission dynamics in a Hong Kong context. ...

... A preliminary analysis of the existence of attractors in the system can be done by evaluating the rate of volume contraction (or expansion) in the state space [21][22][23][24] of the model (system (3)). Recall that the rate contraction (or expansion) of the volume of a continuous time dynamic system is defined as the sum of the derivatives with respect to the state variables and is given by expression (5): ...

... These works discovered that eyes and skin have the same structure [64] and can detect light intensity, and change the colour according to light changings [65]. The results of the genome studies enables the creation of artificial skin and skin-cells with all appropriate features [66], [67], [68]. ...

... The active camouflage used by cephalopods like octopi and cuttlefish to opportunistically mimic substrates has drawn intense interest (199) due among other things to its rapidity, with chromatophores that can flash different colors roughly five times every second (51). Cephalopod chromatophore cells have inspired the development of artificial skin (200,201), paint-like coatings that can be triggered to change color (202,203), and artificial chromatophores (204,205). ...

... Fixing the parameters of the harvesting circuit (namely the value of the storage capacitor C s , and the priming voltage V 2' ) does not require measuring the effective deformation with external sensors or a self-sensing scheme (Rizzello et al., 2018). It can be argued that the harvesting circuit described in Figure 2 requires active measurement of the deformation for proper operation of the switches S 1 and S 2 . ...