Efficient and Accurate Separable Models for Discretized Material Optimization: A Continuous Perspective Based on Topological Derivatives.

Multi-material design optimization problems can, after discretization, be solved by the iterative solution of simpler sub-problems which approximate the original problem at an expansion point to first order. In particular, models constructed from convex separable first order approximations have a long and successful tradition in the design optimization community and have led to powerful optimization tools like the prominently used method of moving asymptotes (MMA). In this paper, we introduce several new separable approximations to a model problem and examine them in terms of accuracy and fast evaluation.

Counting Arcs in .

An arc in is a set such that no three points of are collinear. We use the method of hypergraph containers to prove several counting results for arcs. Let denote the family of all arcs in .

Isolated Calmness of Perturbation Mappings and Superlinear Convergence of Newton-Type Methods.

In this paper, we characterize Lipschitzian properties of different multiplier-free and multiplier-dependent perturbation mappings associated with the stationarity system of a so-called generalized nonlinear program popularized by Rockafellar. Special emphasis is put on the investigation of the isolated calmness property at and around a point. The latter is decisive for the locally fast convergence of the so-called semismooth* Newton-type method by Gfrerer and Outrata.

Improvements on speed, stability and field of view in adaptive optics OCT for anterior retinal imaging using a pyramid wavefront sensor.

We present improvements on the adaptive optics (AO) correction method using a pyramid wavefront sensor (P-WFS) and introduce a novel approach for closed-loop focus shifting in retinal imaging. The method's efficacy is validated through adaptive optics optical coherence tomography (AO-OCT) imaging in both, healthy individuals and patients with diabetic retinopathy. In both study groups, a stable focusing on the anterior retinal layers is achieved.

Uncertainty Quantification for Scale-Space Blob Detection.

We consider the problem of blob detection for uncertain images, such as images that have to be inferred from noisy measurements. Extending recent work motivated by astronomical applications, we propose an approach that represents the uncertainty in the position and size of a blob by a region in a three-dimensional scale space. Motivated by classic tube methods such as the taut-string algorithm, these regions are obtained from level sets of the minimizer of a total variation functional within a high-dimensional tube.

Towards a transferable fermionic neural wavefunction for molecules.

Deep neural networks have become a highly accurate and powerful wavefunction ansatz in combination with variational Monte Carlo methods for solving the electronic Schrödinger equation. However, despite their success and favorable scaling, these methods are still computationally too costly for wide adoption. A significant obstacle is the requirement to optimize the wavefunction from scratch for each new system, thus requiring long optimization.

A phase-field model for non-small cell lung cancer under the effects of immunotherapy.

Formulating mathematical models that estimate tumor growth under therapy is vital for improving patient-specific treatment plans. In this context, we present our recent work on simulating non-small-scale cell lung cancer (NSCLC) in a simple, deterministic setting for two different patients receiving an immunotherapeutic treatment. At its core, our model consists of a Cahn-Hilliard-based phase-field model describing the evolution of proliferative and necrotic tumor cells.

Variational quantitative phase-field modeling of nonisothermal sintering process.

Phase-field modeling has become a powerful tool in describing the complex pore-structure evolution and the intricate multiphysics in nonisothermal sintering processes. However, the quantitative validity of conventional variational phase-field models involving diffusive processes is a challenge. Artificial interface effects, like the trapping effects, may originate at the interface when the kinetic properties of two opposing phases are different.

Cell to whole organ global sensitivity analysis on a four-chamber heart electromechanics model using Gaussian processes emulators.

Cardiac pump function arises from a series of highly orchestrated events across multiple scales. Computational electromechanics can encode these events in physics-constrained models. However, the large number of parameters in these models has made the systematic study of the link between cellular, tissue, and organ scale parameters to whole heart physiology challenging.

A Unified Approach to Shape and Topological Sensitivity Analysis of Discretized Optimal Design Problems.

We introduce a unified sensitivity concept for shape and topological perturbations and perform the sensitivity analysis for a discretized PDE-constrained design optimization problem in two space dimensions. We assume that the design is represented by a piecewise linear and globally continuous level set function on a fixed finite element mesh and relate perturbations of the level set function to perturbations of the shape or topology of the corresponding design. We illustrate the sensitivity analysis for a problem that is constrained by a reaction-diffusion equation and draw connections between our discrete sensitivities and the well-established continuous concepts of shape and topological derivatives.

Calibration of a three-state cell death model for cardiomyocytes and its application in radiofrequency ablation.

Thermal cellular injury follows complex dynamics and subcellular processes can heal the inflicted damage if insufficient heat is administered during the procedure. This work aims to the identification of irreversible cardiac tissue damage for predicting the success of thermal treatments.Several approaches exist in the literature, but they are unable to capture the healing process and the variable energy absorption rate that several cells display.

Assessing the heterogeneity in the transmission of infectious diseases from time series of epidemiological data.

Structural features and the heterogeneity of disease transmissions play an essential role in the dynamics of epidemic spread. But these aspects can not completely be assessed from aggregate data or macroscopic indicators such as the effective reproduction number. We propose in this paper an index of effective aggregate dispersion (EffDI) that indicates the significance of infection clusters and superspreading events in the progression of outbreaks by carefully measuring the level of relative stochasticity in time series of reported case numbers using a specially crafted statistical model for reproduction.

Synthetic dataset for visco-acoustic imaging.

We provide computationally generated dataset simulating propagation of ultrasonic waves in viscous tissues in two and three dimensional domains. The dataset contains physical parameters of a human breast with a high-contrast inclusion, the acquisition setup with positions of sources and receivers, and the associated pressure-wave data at ultrasonic frequencies. We simulated the wave propagation based on seven different viscous models using the physical parameters of the breast.

Sequences in overpartitions.

This paper is devoted to the study of sequences in overpartitions and their relation to 2-color partitions. An extensive study of a general class of double series is required to achieve these ends.

Tumor Evolution Models of Phase-Field Type with Nonlocal Effects and Angiogenesis.

In this survey article, a variety of systems modeling tumor growth are discussed. In accordance with the hallmarks of cancer, the described models incorporate the primary characteristics of cancer evolution. Specifically, we focus on diffusive interface models and follow the phase-field approach that describes the tumor as a collection of cells.

Mechanoelectric effects in healthy cardiac function and under Left Bundle Branch Block pathology.

Mechanoelectric feedback (MEF) in the heart operates through several mechanisms which serve to regulate cardiac function. Stretch activated channels (SACs) in the myocyte membrane open in response to cell lengthening, while tension generation depends on stretch, shortening velocity, and calcium concentration. How all of these mechanisms interact and their effect on cardiac output is still not fully understood.

Blood flow but not cannula positioning influences the efficacy of Veno-Venous ECMO therapy.

Despite being vital in treating intensive-care patients with lung failure, especially COVID-19 patients, Veno-Venous Extra-Corporeal Membrane Oxygenation does not exploit its full potential, leaving ample room for improvement. The objective of this study is to determine the effect of cannula positioning and blood flow on the efficacy of Veno-Venous Extra-Corporeal Membrane Oxygenation, in particular in relationship with blood recirculation. We performed 98 computer simulations of blood flow and oxygen diffusion in a computerized-tomography-segmented right atrium and venae cavae for different positions of the returning and draining cannulae and ECMO flows of 3 L/min and [Formula: see text].

Weighted cylindric partitions.

Recently Corteel and Welsh outlined a technique for finding new sum-product identities by using functional relations between generating functions for cylindric partitions and a theorem of Borodin. Here, we extend this framework to include very general product-sides coming from work of Han and Xiong. In doing so, we are led to consider structures such as weighted cylindric partitions, symmetric cylindric partitions and weighted skew double-shifted plane partitions.

On convergence rates of adaptive ensemble Kalman inversion for linear ill-posed problems.

In this paper we discuss a deterministic form of ensemble Kalman inversion as a regularization method for linear inverse problems. By interpreting ensemble Kalman inversion as a low-rank approximation of Tikhonov regularization, we are able to introduce a new sampling scheme based on the Nyström method that improves practical performance. Furthermore, we formulate an adaptive version of ensemble Kalman inversion where the sample size is coupled with the regularization parameter.

Meshfree Semi-Lagrangian Methods for Solving Surface Advection PDEs.

We analyze a class of meshfree semi-Lagrangian methods for solving advection problems on smooth, closed surfaces with solenoidal velocity field. In particular, we prove the existence of an embedding equation whose corresponding semi-Lagrangian methods yield the ones in the literature for solving problems on surfaces. Our analysis allows us to apply standard bulk domain convergence theories to the surface counterparts.

Solving the electronic Schrödinger equation for multiple nuclear geometries with weight-sharing deep neural networks.

The Schrödinger equation describes the quantum-mechanical behaviour of particles, making it the most fundamental equation in chemistry. A solution for a given molecule allows computation of any of its properties. Finding accurate solutions for many different molecules and geometries is thus crucial to the discovery of new materials such as drugs or catalysts.

Impact of intraventricular septal fiber orientation on cardiac electromechanical function.

Cardiac fiber direction is an important factor determining the propagation of electrical activity, as well as the development of mechanical force. In this article, we imaged the ventricles of several species with special attention to the intraventricular septum to determine the functional consequences of septal fiber organization. First, we identified a dual-layer organization of the fiber orientation in the intraventricular septum of ex vivo sheep hearts using diffusion tensor imaging at high field MRI.

Oscillations in K(ATP) conductance drive slow calcium oscillations in pancreatic β-cells.

ATP-sensitive K (K(ATP)) channels were first reported in the β-cells of pancreatic islets in 1984, and it was soon established that they are the primary means by which the blood glucose level is transduced to cellular electrical activity and consequently insulin secretion. However, the role that the K(ATP) channels play in driving the bursting electrical activity of islet β-cells, which drives pulsatile insulin secretion, remains unclear. One difficulty is that bursting is abolished when several different ion channel types are blocked pharmacologically or genetically, making it challenging to distinguish causation from correlation.

Systematic Characterization of High-Power Short-Duration Ablation: Insight From an Advanced Virtual Model.

High-power short-duration (HPSD) recently emerged as a new approach to radiofrequency (RF) catheter ablation. However, basic and clinical data supporting its effectiveness and safety is still scarce. We aim to characterize HPSD with an advanced virtual model, able to assess lesion dimensions and complications in multiple conditions and compare it to standard protocols.

An Inverse Problem Involving a Viscous Eikonal Equation with Applications in Electrophysiology.

In this work we discuss the reconstruction of cardiac activation instants based on a viscous Eikonal equation from boundary observations. The problem is formulated as a least squares problem and solved by a projected version of the Levenberg-Marquardt method. Moreover, we analyze the well-posedness of the state equation and derive the gradient of the least squares functional with respect to the activation instants.