arXiv subjects

Kim Christensen

Publications and source records attributed to Kim Christensen.

At least 55 records · Page 3Linked to original sources

arXiv2016

Myocardial Architecture and Patient Variability in Clinical Patterns of Atrial Fibrillation

Atrial fibrillation (AF) increases the risk of stroke by a factor of four to five and is the most common abnormal heart rhythm. The progression of AF with age, from short self-terminating episodes to persistence, varies between individuals and is poorly understood. An inability to understand and predict variation in AF progression has resulted in less patient-specific therapy. Likewise, it has been a challenge to relate the microstructural features of heart muscle tissue (myocardial architecture) with the emergent temporal clinical patterns of AF. We use a simple model of activation wavefront propagation on an anisotropic structure, mimicking heart muscle tissue, to show how variation in AF behaviour arises naturally from microstructural differences between individuals. We show that the stochastic nature of progressive transversal uncoupling of muscle strands (e.g., due to fibrosis or gap junctional remodelling), as occurs with age, results in variability in AF episode onset time, frequency, duration, burden and progression between individuals. This is consistent with clinical observations. The uncoupling of muscle strands can cause critical architectural patterns in the myocardium. These critical patterns anchor micro-re-entrant wavefronts and thereby trigger AF. It is the number of local critical patterns of uncoupling as opposed to global uncoupling that determines AF progression. This insight may eventually lead to patient specific therapy when it becomes possible to observe the cellular structure of a patient's heart.

q-bio.TO↗

arXiv2016

Directed Abelian sandpile with multiple downward neighbors

We study the directed Abelian sandpile model on a square lattice, with $K$ downward neighbors per site, $K > 2$. The $K=3$ case is solved exactly, which extends the earlier known solution for the $K=2$ case. For $K>2$, the avalanche clusters can have holes and side-branches and are thus qualitatively different from the $K=2$ case where avalance clusters are compact. However, we find that the critical exponents for $K>2$ are identical with those for the $K=2$ case, and the large scale structure of the avalanches for $K>2$ tends to the $K=2$ case.

cond-mat.stat-mech↗

arXiv2015

A Simple Model for Identifying Critical Structures in Atrial Fibrillation

Atrial fibrillation (AF) is the most common abnormal heart rhythm and the single biggest cause of stroke. Ablation, destroying regions of the atria, is applied largely empirically and can be curative but with a disappointing clinical success rate. We design a simple model of activation wavefront propagation on a structure mimicking the branching network architecture of heart muscle and show how AF emerges spontaneously as age-related parameters change. We identify regions responsible for the initiation and maintenance of AF, the ablation of which terminates AF. The simplicity of the model allows us to calculate analytically the risk of arrhythmia. This analytical result allows us to locate the transition in parameter space and highlights that the transition from regular to fibrillatory behaviour is a finite-size effect present in systems of any size. These clinically testable predictions might inform ablation therapies and arrhythmic risk assessment.

physics.med-ph↗

arXiv2010

Self-similar correlation function in brain resting-state fMRI

Adaptive behavior, cognition and emotion are the result of a bewildering variety of brain spatiotemporal activity patterns. An important problem in neuroscience is to understand the mechanism by which the human brain's 100 billion neurons and 100 trillion synapses manage to produce this large repertoire of cortical configurations in a flexible manner. In addition, it is recognized that temporal correlations across such configurations cannot be arbitrary, but they need to meet two conflicting demands: while diverse cortical areas should remain functionally segregated from each other, they must still perform as a collective, i.e., they are functionally integrated. Here, we investigate these large-scale dynamical properties by inspecting the character of the spatiotemporal correlations of brain resting-state activity. In physical systems, these correlations in space and time are captured by measuring the correlation coefficient between a signal recorded at two different points in space at two different times. We show that this two-point correlation function extracted from resting-state fMRI data exhibits self-similarity in space and time. In space, self-similarity is revealed by considering three successive spatial coarse-graining steps while in time it is revealed by the 1/f frequency behavior of the power spectrum. The uncovered dynamical self-similarity implies that the brain is spontaneously at a continuously changing (in space and time) intermediate state between two extremes, one of excessive cortical integration and the other of complete segregation. This dynamical property may be seen as an important marker of brain well-being both in health and disease.

q-bio.NC↗

arXiv2008

On the scaling of probability density functions with apparent power-law exponents less than unity

We derive general properties of the finite-size scaling of probability density functions and show that when the apparent exponent \tautilde of a probability density is less than 1, the associated finite-size scaling ansatz has a scaling exponent τequal to 1, provided that the fraction of events in the universal scaling part of the probability density function is non-vanishing in the thermodynamic limit. We find the general result that τ>=1 and τ>=\tautilde. Moreover, we show that if the scaling function G(x) approaches a non-zero constant for small arguments, \lim_{x-> 0} G(x) > 0, then τ=\tautilde. However, if the scaling function vanishes for small arguments, \lim_{x-> 0} G(x) = 0, then τ=1, again assuming a non-vanishing fraction of universal events. Finally, we apply the formalism developed to examples from the literature, including some where misunderstandings of the theory of scaling have led to erroneous conclusions.

cond-mat.stat-mech↗

arXiv2007

Multiscaling in the sequence of areas enclosed by coalescing random walkers

We address the question whether the sequence of areas between coalescing random walkers displays multiscaling and in the process calculate the second moment as well as the two point correlation function exactly. The scaling of higher order correlation functions is estimated numerically, indicating a logarithmic dependence on the system size. Together with the analytical results, this confirms the presence of multiscaling.

cond-mat.stat-mech↗

arXiv2006

Evolving networks through deletion and duplication

We introduce a minimalistic model based on dynamic node deletion and node duplication with heterodimerisation. The model is intended to capture the essential features of the evolution of protein interaction networks. We derive an exact two-step rate equation to describe the evolution of the degree distribution. We present results for the case of a fixed-size network. The results are based on the exact numerical solution to the rate equation which are consistent with Monte Carlo simulations of the model's dynamics. Power-law degree distributions with apparent exponents $<1$ were observed for generic parameter choices. However, a proper finite-size scaling analysis revealed that the actual critical exponent in such cases is equal to 1. We present a mean-field argument to determine the asymptotic value of the average degree, illustrating the existence of an attractive fixed point, and corroborate this result with numerical simulations of the first moment of the degree distribution as described by the two-step rate equation. Using the above results, we show that the apparent exponent is determined by the heterodimerisation probability. Our preliminary results are consistent with empirical data for a wide range of organisms, and we believe that through implementing some of the suggested modifications, the model could be well-suited to other types of biological and non-biological networks.

physics.bio-ph↗

arXiv2005

Mean-Field Theory and Sandpile Models

We review and refine the concept of a mean-field theory for the study of sandpile models, which are of central importance in the study of self-organized criticality. By considering the simple one-dimensional random walker with an absorbing and reflecting boundary we are able to construct a complete mean-field picture which we can solve in detail for different types of driving. Using this theory, we are able to clarify the effect of finite driving rate on sandpile models, as well as the observed sensitivity of certain universal quantities on the driving.

cond-mat.stat-mech↗

arXiv2005

Comment on "Earthquakes Descaled"

We show that Bak et al.'s unified scaling law cannot be trivially explained by a single Omori aftershock sequence. On the contrary, the spatial heterogeneity of seismicity plays a fundamental role in the unified scaling law, which implies that the law provides a way to quantify seismic patterns in space.

cond-mat.other↗

arXiv2005

Universality Class of One-Dimensional Directed Sandpile Models

A general n-state directed `sandpile' model is introduced. The stationary properties of the n-state model are derived for n < infty, and analytical arguments based on a central limit theorem show that the model belongs to the universality class of the totally asymmetric Oslo model, with a crossover to uncorrelated branching process behavior for small system sizes. Hence, the central limit theorem allows us to identify the existence of a large universality class of one-dimensional directed sandpile models.

cond-mat.stat-mech↗

arXiv2004

Avalanche Behavior in an Absorbing State Oslo Model

Self-organized criticality can be translated into the language of absorbing state phase transitions. Most models for which this analogy is established have been investigated for their absorbing state characteristics. In this article, we transform the self-organized critical Oslo model into an absorbing state Oslo model and analyze the avalanche behavior. We find that the resulting gap exponent, D, is consistent with its value in the self-organized critical model. For the avalanche size exponent, τ, an analysis of the effect of the external drive and the boundary conditions is required.

cond-mat.stat-mech↗

arXiv2004

Spectral Analysis of Protein-Protein Interactions in Drosophila melanogaster

Within a case study on the protein-protein interaction network (PIN) of Drosophila melanogaster we investigate the relation between the network's spectral properties and its structural features such as the prevalence of specific subgraphs or duplicate nodes as a result of its evolutionary history. The discrete part of the spectral density shows fingerprints of the PIN's topological features including a preference for loop structures. Duplicate nodes are another prominent feature of PINs and we discuss their representation in the PIN's spectrum as well as their biological implications.

q-bio.MN↗

arXiv2004

Sensitivity to initial conditions in self-organized critical systems

We discuss sensitivity to initial conditions in a model for avalanches in granular media displaying self-organized criticality. We show that damage, due to a small perturbation in initial conditions, does not spread. The damage persists in a statistically time-invariant and scale-free form. We argue that the origin of this behavior is the Abelian nature of the model, which generalizes our results to all Abelian models, including the BTW model and the Manna model. An ensemble average of the damage leads to seemingly time dependent damage spreading. Scaling arguments show that this numerical result is due to the time lag before avalanches reach the initial perturbation.

cond-mat.stat-mech↗

arXiv2002

The Tangled Nature model as an evolving quasi-species model

We show that the Tangled Nature model can be interpreted as a general formulation of the quasi-species model by Eigen et al. in a frequency dependent fitness landscape. We present a detailed theoretical derivation of the mutation threshold, consistent with the simulation results, that provides a valuable insight into how the microscopic dynamics of the model determine the observed macroscopic phenomena published previously. The dynamics of the Tangled Nature model is defined on the microevolutionary time scale via reproduction, with heredity, variation, and natural selection. Each organism reproduces with a rate that is linked to the individuals' genetic sequence and depends on the composition of the population in genotype space. Thus the microevolutionary dynamics of the fitness landscape is regulated by, and regulates, the evolution of the species by means of the mutual interactions. At low mutation rate, the macro evolutionary pattern mimics the fossil data: periods of stasis, where the population is concentrated in a network of coexisting species, is interrupted by bursts of activity. As the mutation rate increases, the duration and the frequency of bursts increases. Eventually, when the mutation rate reaches a certain threshold, the population is spread evenly throughout the genotype space showing that natural selection only leads to multiple distinct species if adaptation is allowed time to cause fixation.

cond-mat.stat-mech↗

arXiv2002

Rain: Relaxations in the sky

We demonstrate how, from the point of view of energy flow through an open system, rain is analogous to many other relaxational processes in Nature such as earthquakes. By identifying rain events as the basic entities of the phenomenon, we show that the number density of rain events per year is inversely proportional to the released water column raised to the power 1.4. This is the rain-equivalent of the Gutenberg-Richter law for earthquakes. The event durations and the waiting times between events are also characterised by scaling regions, where no typical time scale exists. The Hurst exponent of the rain intensity signal $H = 0.76 > 0.5$. It is valid in the temporal range from minutes up to the full duration of the signal of half a year. All of our findings are consistent with the concept of self-organised criticality, which refers to the tendency of slowly driven non-equilibrium systems towards a state of scale free behaviour.

cond-mat.soft↗

arXiv2002

Exact enumeration of the Critical States in the Oslo Model

We determine analytically the number $N_{\mathcal{R}}(L)$ of recurrent states in the 1d Oslo model as a function of system size L. The solution $N_{\mathcal{R}}(L) = \frac{1+\sqrt{5}}{2\sqrt{5}}(\frac{3+\sqrt{5}}{2})^L + \frac{\sqrt{5}-1}{2\sqrt{5}}(\frac{3-\sqrt{5}}{2})^L$ is in exact agreement with the number enumerated in computer simulations for $L = 1 - 10$. For $L \gg 1$, the number of allowed metastable states in the attractor increases exponentially as $N_{\mathcal{R}}(L) \approx c_+ λ_+^L$, where $λ_+ = \frac{3+\sqrt{5}}{2}$ is the golden mean. The system is non-ergodic in the sense that the states in the attractor are not equally probable.

cond-mat↗

arXiv2002

Aging and species abundance in the Tangled Nature model of biological evolution

We present an individual based model of evolutionary ecology. The reproduction rate of individuals characterized by their genome depends on the composition of the population in genotype space. Ecological features such as the taxonomy and the macro-evolutionary mode of the dynamics are emergent properties. The macro-dynamics exhibit intermittent two mode switching with a gradually decreasing extinction rate. The generated ecologies become gradually better adapted as well as more complex in a collective sense. The form of the species abundance curve compares well with observed functional forms. The models error threshold can be understood in terms of the characteristics of the two dynamical modes of the system.

cond-mat.stat-mech↗

arXiv2002

A Complexity View of Rainfall

We show that rain events are analogous to a variety of nonequilibrium relaxation processes in Nature such as earthquakes and avalanches. Analysis of high-resolution rain data reveals that power laws describe the number of rain events versus size and number of droughts versus duration. In addition, the accumulated water column displays scale-less fluctuations. These statistical properties are the fingerprints of a self-organized critical process and may serve as a benchmark for models of precipitation and atmospheric processes.

cond-mat.stat-mech↗