Search results for "Nonlinear"

2016

AbstractThe different factors involved in the growth process of complex networks imprint valuable information in their observable topologies. How to exploit this information to accurately predict structural network changes is the subject of active research. A recent model of network growth sustains that the emergence of properties common to most complex systems is the result of certain trade-offs between node birth-time and similarity. This model has a geometric interpretation in hyperbolic space, where distances between nodes abstract this optimisation process. Current methods for network hyperbolic embedding search for node coordinates that maximise the likelihood that the network was pro…

Weakly coupled map lattice models for multicellular patterning and collective normalization of abnormal single-cell states

2017

We present a weakly coupled map lattice model for patterning that explores the effects exerted by weakening the local dynamic rules on model biological and artificial networks composed of two-state building blocks (cells). To this end, we use two cellular automata models based on: (i) a smooth majority rule (model I) and (ii) a set of rules similar to those of Conway's Game of Life (model II). The normal and abnormal cell states evolve according with local rules that are modulated by a parameter $\kappa$. This parameter quantifies the effective weakening of the prescribed rules due to the limited coupling of each cell to its neighborhood and can be experimentally controlled by appropriate e…

Intermittent targeted therapies and stochastic evolution in patients affected by chronic myeloid leukemia

2016

Front line therapy for the treatment of patients affected by chronic myeloid leukemia (CML) is based on the administration of tyrosine kinase inhibitors, namely imatinib or, more recently, axitinib. Although imatinib is highly effective and represents an example of a successful molecular targeted therapy, the appearance of resistance is observed in a proportion of patients, especially those in advanced stages. In this work, we investigate the appearance of resistance in patients affected by CML, by modeling the evolutionary dynamics of cancerous cell populations in a simulated patient treated by an intermittent targeted therapy. We simulate, with the Monte Carlo method, the stochastic evolu…

Wavelength selection of rippling patterns in myxobacteria

2016

Rippling patterns of myxobacteria appear in starving colonies before they aggregate to form fruiting bodies. These periodic traveling cell density waves arise from the coordination of individual cell reversals, resulting from an internal clock regulating them, and from contact signaling during bacterial collisions. Here we revisit a mathematical model of rippling in myxobacteria due to Igoshin et al.\ [Proc. Natl. Acad. Sci. USA {\bf 98}, 14913 (2001) and Phys. Rev. E {\bf 70}, 041911 (2004)]. Bacteria in this model are phase oscillators with an extra internal phase through which they are coupled to a mean-field of oppositely moving bacteria. Previously, patterns for this model were obtaine…

On the growth and form of cortical convolutions

2016

International audience; The rapid growth of the human cortex during development is accompanied by the folding of the brain into a highly convoluted structure1-3. Recent studies have focused on the genetic and cellular regulation of cortical growth4-8, but understanding the formation of the gyral and sulcal convolutions also requires consideration of the geometry and physical shaping of the growing brain9-15. To study this, we use magnetic resonance images to build a 3D-printed layered gel mimic of the developing smooth fetal brain; when immersed in a solvent, the outer layer swells relative to the core, mimicking cortical growth. This relative growth puts the outer layer into mechanical com…

New Approach of Controlling Cardiac Alternans

2018

The alternans of the cardiac action potential duration is a pathological rhythm. It is considered to be relating to the onset of ventricular fibrillation and sudden cardiac death. It is well known that, the predictive control is among the control methods that use the chaos to stabilize the unstable fixed point. Firstly, we show that alternans (or period-2 orbit) can be suppressed temporally by the predictive control of the periodic state of the system. Secondly, we determine an estimation of the size of a restricted attraction's basin of the unstable equilibrium point representing the unstable regular rhythm stabilized by the control. This result allows the application of predictive control…

Nonlinear trade-offs allow the cooperation game to evolve from Prisoner's Dilemma to Snowdrift.

2017

[EN] The existence of cooperation, or the production of public goods, is an evolutionary problem. Cooperation is not favoured because the Prisoner s Dilemma (PD) game drives cooperators to extinction. We have re-analysed this problem by using RNA viruses to motivate a model for the evolution of cooperation. Gene products are the public goods and group size is the number of virions co-infecting the same host cell. Our results show that if the trade-off between replication and production of gene products is linear, PD is observed. However, if the trade-off is nonlinear, the viruses evolve into separate lineages of ultra-defectors and ultra-cooperators as group size is increased. The nonlinear…

Mathematical investigation of innate immune responses to lung cancer: The role of macrophages with mixed phenotypes

2021

Abstract Macrophages’ role in the evolution of solid tumours is a well accepted fact, with the M1-like macrophages having an anti-tumour role and the M2-like macrophages having a pro-tumour role. Despite the fact that some clinical studies on lung tumours have emphasised also the presence of macrophages with mixed M1 and M2 phenotypes in addition to macrophages with distinct phenotypes, the majority of studies still use the distinct M1-M2 classification to predict the evolution of tumours and patient survival. In this theoretical study we use a mathematical modelling and computational approach to investigate the role of macrophages with mixed phenotype on growth/control/elimination of lung …

Collective Cell Migration in a Fibrous Environment: A Hybrid Multiscale Modelling Approach

2021

International audience; The specific structure of the extracellular matrix (ECM), and in particular the density and orientation of collagen fibres, plays an important role in the evolution of solid cancers. While many experimental studies discussed the role of ECM in individual and collective cell migration, there are still unanswered questions about the impact of nonlocal cell sensing of other cells on the overall shape of tumour aggregation and its migration type. There are also unanswered questions about the migration and spread of tumour that arises at the boundary between different tissues with different collagen fibre orientations. To address these questions, in this study we develop …

Observation of elastic anisotropy in strained optical nanofibers using Brillouin spectroscopy

2019

Optical nanofibers (ONFs) are excellent nanophotonic platforms for many applications such as optical sensing, quantum photonics, and nonlinear optics, due to both tight optical confinement and their evanescent field. From an acoustic viewpoint, it has recently been reported the observation of a new class of Brillouin acoustic resonances in optical nanofibers, including hybrid shear/longitudinal acoustic waves (HAWs) and surface acoustic waves (SAWs) [1–2]. It has been later shown that, under axial tensile strain, the Brillouin frequency shifts (BFS) of these elastic resonances are fundamentally different from that of standard optical fibers [3]. This is principally due to the hybrid nature …