Targeting Cellular DNA Damage Responses: Predicting in vivo treatment responses using an in vitro-calibrated agent-based **mathematical** **model**.

**mathematical**framework and

**model**parameters intact, the

**mathematic**al model can first be calibrated by in vitro data and thereafter be used to successfully predict treatment responses in human tumour xenografts in vivo qualitatively, and quantitatively... Expand abstract.

**mathematical**

**model**is governed by a set of empirically observable rules. By adjusting only the rules, whilst keeping the fundamental

**mathematical**framework and

**model**parameters intact, the

**mathematical**

**model**can first be calibrated by in vitro data and thereafter be used to successfully predict treatment responses in human tumour xenografts in vivo qualitatively, and quantitatively up to approximately 10 days post tumour injection.

8/10 relevant

bioRxiv

Finite element simulation of ionicelectrodiffusion in cellular geometries

**Mathematical**

**models**for excitable cells are commonly based on cable theory, which considers a homogenized domain and spatially constant ionic concentrations. Expand abstract.

**Mathematical**

**models**for excitable cells are commonly based on cable theory, which considers a homogenized domain and spatially constant ionic concentrations. Although such

**models**provide valuable insight, the effect of altered ion concentrations or detailed cell morphology on the electrical potentials cannot be captured. In this paper, we discuss an alternative approach to detailed modelling of electrodiffusion in neural tissue. The

**mathematical**

**model**describes the distribution and evolution of ion concentrations in a geometrically-explicit representation of the intra- and extracellular domains. As a combination of the electroneutral Kirchhoff-Nernst-Planck (KNP)

**model**and the Extracellular-Membrane-Intracellular (EMI) framework, we refer to this

**model**as the KNP-EMI

**model**. Here, we introduce and numerically evaluate a new, finite element-based numerical scheme for the KNP-EMI model, capable of efficiently and flexibly handling geometries of arbitrary dimension and arbitrary polynomial degree. Moreover, we compare the electrical potentials predicted by the KNP-EMI and EMI

**models**. Finally, we study ephaptic coupling induced in an unmyelinated axon bundle and demonstrate how the KNP-EMI framework can give new insights in this setting.

7/10 relevant

arXiv

Amplitude effects allow short jetlags and large seasonal phase shifts in minimal clock **models**

**Mathematical**

**models**of varying complexity have helped shed light on different aspects of circadian clock function. Expand abstract.

**Mathematical**

**models**of varying complexity have helped shed light on different aspects of circadian clock function. In this work, we question whether minimal clock

**models**(Goodwin models) are sufficient to reproduce essential phenotypes of the clock: a small phase response curve (PRC), fast jetlag and seasonal phase shifts. Instead of building a single best model, we take an approach where we study the properties of a set of

**models**satisfying certain constraints; here a PRC to a one-hour pulse of three hours and clock periods between 22h and 26h. Surprisingly, almost all these randomly parameterized

**models**showed a phase shift of about four hours between long and short days and jetlag durations of three to seven days in advance and delay. Moreover, intrinsic clock period influenced jetlag duration and entrainment amplitude and phase. Fast jetlag was realized in this

**model**by means of a novel amplitude effect: the association between clock amplitude and clock period termed `twist'. This twist allows amplitude changes to speed up and slow down clocks enabling faster shifts. These findings were robust to the addition of additional positive feedback to the

**model**. In summary, the known design principles of rhythm generation -- negative feedback, long delay and switch-like inhibition (we review these in detail) -- are sufficient to reproduce the essential clock phenotypes. Furthermore, amplitudes play a role in determining clock properties and must be always considered, although they are difficult to measure.

5/10 relevant

bioRxiv

**Mathematical** **model**ing the protective coloration of animals with usage of parameters of diversity and evenness

**mathematical**

**models**of the performance of the protective coloration of animals, depending on the specific situations of their adaptation to a particular area. Expand abstract.

**mathematical**

**models**of the performance of the protective coloration of animals, depending on the specific situations of their adaptation to a particular area. The results of the study can be used to create remote technologies for detecting animals of certain species at a considerable distance.

4/10 relevant

bioRxiv

Discovery of the prickle patterning on the stem of rose and the **mathematical** **model** of the pattern.

**mathematical**

**model**based on diffusion to explain the process via which the patterns emerged. Expand abstract.

**mathematical**

**model**based on diffusion to explain the process via which the patterns emerged. The

**model**assumed the presence of diffusion factors from primordia that suppress the development of prickles. As a result, this

**model**shows the prickle patterning similar to those observed on live specimens. Moreover, by changing the

**model**parameters of the assumed factors, we reproduce the pattern that is on other plant species. The finding indicates that the patterns of prickles in the kingdom Plantae are organized by similar diffuse systems. Further investigation will provide various insights into the molecular mechanism of prickle development and the role of the prickle patterning.

7/10 relevant

bioRxiv

A Stochastic Automata Network Description for Spatial DNA-Methylation
**Models**

**mathematical**

**models**that consider only one cytosine and its partner on the opposite DNA-strand (CpG), in order to include such neighborhood dependencies. Expand abstract.

**mathematical**

**models**that consider only one cytosine and its partner on the opposite DNA-strand (CpG), in order to include such neighborhood dependencies. One approach is to describe the system as a stochastic automata network (SAN) with functional transitions. We show that single-CpG

**models**can successfully be generalized to multiple CpGs using the SAN description and verify the results by comparing them to results from extensive Monte-Carlo simulations.

4/10 relevant

arXiv

Grinding Kinetics of Slag and Effect of Final Particle Size on the Compressive Strength of Alkali Activated Materials

**mathematical**

**models**used to simulate the particle size distribution, Rosin-Rammler (RR) was found to be the most suitable. Expand abstract.

**model**grinding of a Polish slag and evaluate the particle size distributions of the products obtained after different grinding times. Then, selected products were alkali activated in order to investigate the effect of particle size on the compressive strength of the produced alkali activated materials (AAMs). Other parameters affecting alkali activation, i.e. temperature, curing and ageing time were also examined. Among the different

**mathematical**

**models**used to simulate the particle size distribution, Rosin-Rammler (RR) was found to be the most suitable. When piecewise regression analysis was applied to experimental data it was found that the particle size distribution of the slag products exhibits multi fractal character. In addition, grinding of slag exhibits non-first-order behavior and the reduction rate of each size is time dependent. The grinding rate and consequently the grinding efficiency increases when the particle size increases, but drops sharply near zero after prolonged grinding periods. Regarding alkali activation, it is deduced that among the parameters studied, particle size (and the respective specific surface area) of the raw slag product and curing temperature have the most noticeable impact on the compressive strength of the produced AAMs.

4/10 relevant

Preprints.org

Variational autoencoder reconstruction of complex many-body physics

**mathematical**

**models**to study realistic systems and their coupling to their environment that constrains their dynamics, both analytical approaches and numerical methods that build on these

**model**s, show limitations in scope or applicability. Expand abstract.

**mathematical**

**models**to study realistic systems and their coupling to their environment that constrains their dynamics, both analytical approaches and numerical methods that build on these models, show limitations in scope or applicability. On the other hand, machine learning, i.e. data-driven, methods prove to be increasingly efficient for the study of complex quantum systems. Deep neural networks in particular have been successfully applied to many-body quantum dynamics simulations and to quantum matter phase characterization. In the present work, we show how to use a variational autoencoder (VAE) -- a state-of-the-art tool in the field of deep learning for the simulation of probability distributions of complex systems. More precisely, we transform a quantum mechanical problem of many-body state reconstruction into a statistical problem, suitable for VAE, by using informationally complete positive operator-valued measure. We show with the paradigmatic quantum Ising

**model**in a transverse magnetic field, that the ground-state physics, such as, e.g., magnetization and other mean values of observables, of a whole class of quantum many-body systems can be reconstructed by using VAE learning of tomographic data, for different parameters of the Hamiltonian, and even if the system undergoes a quantum phase transition. We also discuss challenges related to our approach as entropy calculations pose particular difficulties.

4/10 relevant

arXiv

**Models** and algorithms for the Flying Sidekick Traveling Salesman Problem

**mathematical**

**models**struggle to provide either good heuristic solution or strong lower bounds. Expand abstract.

**mathematical**

**models**struggle to provide either good heuristic solution or strong lower bounds.

5/10 relevant

arXiv

Genetic interactions derived from high-throughput phenotyping of 7,350 yeast cell cycle mutants

**mathematical**

**models**of the regulatory networks controlling the division of eukaryotic cells. Expand abstract.

**mathematical**

**models**of the regulatory networks controlling the division of eukaryotic cells. These

**models**capture data resulting from two complementary experimental approaches: low-throughput experiments aimed at extensively characterizing the functions of small numbers of genes, and large-scale genetic interaction screens that provide a systems-level perspective on the cell division process. The former is insufficient to capture the interconnectivity of the genetic control network, while the latter is fraught with irreproducibility issues. Here, we describe a hybrid approach in which the genetic interactions between 36 cell-cycle genes are quantitatively estimated by high-throughput phenotyping with an unprecedented number of biological replicates. Using this approach, we identify a subset of high-confidence genetic interactions, which we use to refine a previously published

**mathematical**

**model**of the cell cycle. We also present a quantitative dataset of the growth rate of these mutants under six different media conditions in order to inform future cell cycle

**models**.

7/10 relevant

bioRxiv