Correction to: Mathematical models of neuronal growth.

Correction to: Biomechanics and Modeling in Mechanobiology (2022) 21:89-118 https://doi.org/10.1007/s10237-021-01539-0.

Extended correlation functions for spatial analysis of multiplex imaging data.

Imaging platforms for generating highly multiplexed histological images are being continually developed and improved. Significant improvements have also been made in the accuracy of methods for automated cell segmentation and classification. However, less attention has focused on the quantification and analysis of the resulting point clouds, which describe the spatial coordinates of individual cells.

Oscillations in three-reaction quadratic mass-action systems.

It is known that rank-two bimolecular mass-action systems do not admit limit cycles. With a view to understanding which small mass-action systems admit oscillation, in this paper we study rank-two networks with bimolecular source complexes but allow target complexes with higher molecularities. As our goal is to find oscillatory networks of minimal size, we focus on networks with three reactions, the minimum number that is required for oscillation.

Assessing the complementary information from an increased number of biologically relevant features in liquid biopsy-derived RNA-Seq data.

Liquid biopsy-derived RNA sequencing (lbRNA-seq) exhibits significant promise for clinic-oriented cancer diagnostics due to its non-invasiveness and ease of repeatability. Despite substantial advancements, obstacles like technical artefacts and process standardisation impede seamless clinical integration. Alongside addressing technical aspects such as normalising fluctuating low-input material and establishing a standardised clinical workflow, the lack of result validation using independent datasets remains a critical factor contributing to the often low reproducibility of liquid biopsy-detected biomarkers.

Modeling the extracellular matrix in cell migration and morphogenesis: a guide for the curious biologist.

The extracellular matrix (ECM) is a highly complex structure through which biochemical and mechanical signals are transmitted. In processes of cell migration, the ECM also acts as a scaffold, providing structural support to cells as well as points of potential attachment. Although the ECM is a well-studied structure, its role in many biological processes remains difficult to investigate comprehensively due to its complexity and structural variation within an organism.

Gluing GAP to RAS Mutants: A New Approach to an Old Problem in Cancer Drug Development.

Mutated genes may lead to cancer development in numerous tissues. While more than 600 cancer-causing genes are known today, some of the most widespread mutations are connected to the RAS gene; RAS mutations are found in approximately 25% of all human tumors. Specifically, KRAS mutations are involved in the three most lethal cancers in the U.

Bias of the additive hazard model in the presence of causal effect heterogeneity.

Hazard ratios are prone to selection bias, compromising their use as causal estimands. On the other hand, if Aalen's additive hazard model applies, the hazard difference has been shown to remain unaffected by the selection of frailty factors over time. Then, in the absence of confounding, observed hazard differences are equal in expectation to the causal hazard differences.

Integrative processing in artificial and biological vision predicts the perceived beauty of natural images.

Previous research shows that the beauty of natural images is already determined during perceptual analysis. However, it is unclear which perceptual computations give rise to the perception of beauty. Here, we tested whether perceived beauty is predicted by spatial integration across an image, a perceptual computation that reduces processing demands by aggregating image parts into more efficient representations of the whole.

A multiscale computational framework for the development of spines in molluscan shells.

From mathematical models of growth to computer simulations of pigmentation, the study of shell formation has given rise to an abundant number of models, working at various scales. Yet, attempts to combine those models have remained sparse, due to the challenge of combining categorically different approaches. In this paper, we propose a framework to streamline the process of combining the molecular and tissue scales of shell formation.

Coherent categorical information triggers integration-related alpha dynamics.

To create coherent visual experiences, the brain spatially integrates the complex and dynamic information it receives from the environment. We previously demonstrated that feedback-related alpha activity carries stimulus-specific information when two spatially and temporally coherent naturalistic inputs can be integrated into a unified percept. In this study, we sought to determine whether such integration-related alpha dynamics are triggered by categorical coherence in visual inputs.

Using a probabilistic approach to derive a two-phase model of flow-induced cell migration.

Interstitial fluid flow is a feature of many solid tumors. In vitro experiments have shown that such fluid flow can direct tumor cell movement upstream or downstream depending on the balance between the competing mechanisms of tensotaxis (cell migration up stress gradients) and autologous chemotaxis (downstream cell movement in response to flow-induced gradients of self-secreted chemoattractants). In this work we develop a probabilistic-continuum, two-phase model for cell migration in response to interstitial flow.

Optimal control of collective electrotaxis in epithelial monolayers.

Epithelial monolayers are some of the best-studied models for collective cell migration due to their abundance in multicellular systems and their tractability. Experimentally, the collective migration of epithelial monolayers can be robustly steered using electric fields, via a process termed electrotaxis. Theoretically, however, the question of how to design an electric field to achieve a desired spatiotemporal movement pattern is underexplored.

Multifractal Analysis of Measures Arising from Random Substitutions.

We study regularity properties of frequency measures arising from random substitutions, which are a generalisation of (deterministic) substitutions where the substituted image of each letter is chosen independently from a fixed finite set. In particular, for a natural class of such measures, we derive a closed-form analytic formula for the -spectrum and prove that the multifractal formalism holds. This provides an interesting new class of measures satisfying the multifractal formalism.

Clinical Predictive Modeling of Heart Failure: Domain Description, Models' Characteristics and Literature Review.

This study attempts to identify and briefly describe the current directions in applied and theoretical clinical prediction research. Context-rich chronic heart failure syndrome (CHFS) telemedicine provides the medical foundation for this effort. In the chronic stage of heart failure, there are sudden exacerbations of syndromes with subsequent hospitalizations, which are called acute decompensation of heart failure (ADHF).

The K41 theory and turbulence in 1D Burgers equation.

This work is a review of a group of results on the stochastic Burgers equation with small viscosity, obtained during the last two decades. These results jointly show that the equation makes a good model of hydrodynamical turbulence. The model provides natural and rigorously justified analogies of a number of key predictions of the theory of turbulence, including the main assertions of the Kolmogorov approach to turbulence, known as the K41 theory.

The Dirac equation across the horizons of the 5D Myers-Perry geometry: separation of variables, radial asymptotic behaviour and Hamiltonian formalism.

We analytically extend the 5D Myers-Perry metric through the event and Cauchy horizons by defining Eddington-Finkelstein-type coordinates. Then, we use the orthonormal frame formalism to formulate and perform separation of variables on the massive Dirac equation, and analyse the asymptotic behaviour at the horizons and at infinity of the solutions to the radial ordinary differential equation (ODE) thus obtained. Using the essential self-adjointness result of Finster-Röken and Stone's formula, we obtain an integral spectral representation of the Dirac propagator for spinors with low masses and suitably bounded frequency spectra in terms of resolvents of the Dirac Hamiltonian, which can in turn be expressed in terms of Green's functions of the radial ODE.

Association of sugar intake from different sources with cardiovascular disease incidence in the prospective cohort of UK Biobank participants.

Background: The relation between incident cardiovascular disease (CVD) and sugar might not only depend on the quantity consumed but also on its source. This study aims to assess the association between various sources of dietary sugars and CVD incidence in the prospective population-based UK Biobank cohort.

Methods: A total of 176,352 participants from the UK Biobank with at least one web-based dietary questionnaire (Oxford WebQ) for assessment of sugar intake were included in this study.

2'-Fucosyllactose helps butyrate producers outgrow competitors in infant gut microbiota simulations.

A reduced capacity for butyrate production by the early infant gut microbiota is associated with negative health effects, such as inflammation and the development of allergies. Here, we develop new hypotheses on the effect of the prebiotic galacto-oligosaccharides (GOS) or 2'-fucosyllactose (2'-FL) on butyrate production by the infant gut microbiota using a multiscale, spatiotemporal mathematical model of the infant gut. The model simulates a community of cross-feeding gut bacteria in metabolic detail.

Diverse collections in matroids and graphs.

We investigate the parameterized complexity of finding diverse sets of solutions to three fundamental combinatorial problems. The input to the Weighted Diverse Bases problem consists of a matroid , a weight function , and integers . The task is to decide if there is a collection of of such that the weight of the symmetric difference of any pair of these bases is at least .

Early language dissociation in bilingual minds: magnetoencephalography evidence through a machine learning approach.

Does neural activity reveal how balanced bilinguals choose languages? Despite using diverse neuroimaging techniques, prior studies haven't provided a definitive solution to this problem. Nonetheless, studies involving direct brain stimulation in bilinguals have identified distinct brain regions associated with language production in different languages. In this magnetoencephalography study with 45 proficient Spanish-Basque bilinguals, we investigated language selection during covert picture naming and word reading tasks.

Enhanced perfusion following exposure to radiotherapy: A theoretical investigation.

Tumour angiogenesis leads to the formation of blood vessels that are structurally and spatially heterogeneous. Poor blood perfusion, in conjunction with increased hypoxia and oxygen heterogeneity, impairs a tumour's response to radiotherapy. The optimal strategy for enhancing tumour perfusion remains unclear, preventing its regular deployment in combination therapies.

The built-in selection bias of hazard ratios formalized using structural causal models.

It is known that the hazard ratio lacks a useful causal interpretation. Even for data from a randomized controlled trial, the hazard ratio suffers from so-called built-in selection bias as, over time, the individuals at risk among the exposed and unexposed are no longer exchangeable. In this paper, we formalize how the expectation of the observed hazard ratio evolves and deviates from the causal effect of interest in the presence of heterogeneity of the hazard rate of unexposed individuals (frailty) and heterogeneity in effect (individual modification).