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This study investigates the barriers to integrating Design for Assembly (DFA) principles within modular product architectures established using the Modular Function Deployment (MFD) method -- a critical stage for deploying mass customization production while reducing costs. Despite the potential benefits of DFA, its application in modular architectures development remains underutilized, due to a mix of challenges. Through content analysis of qualitative data gathered from a focus group and interviews with industry experts and practitioners, we identified four major categories of such challenges, or barriers to adoption of DFA: technological, economic, regulatory, and organizational (TERO). Key challenges include compliance with regulatory requirements for data usage, intellectual property concerns, and limited availability of quantitative data in the initial stages of MFD. The findings reveal that multidisciplinary collaboration is essential to addressing these barriers, as it enhances informed decision making and eases the practical integration of DFA. By analyzing insights from both academic literature and industrial practice, this research develops a conceptual model that describes the main issues of applying DFA in MFD, providing a valuable guide for companies aiming to improve their modular products assembly process. Ultimately, this study provides groundwork to support industry practitioners in overcoming existing barriers, promoting more cost effective, high quality modular design processes with the inclusion of efficient assembly considerations.

The field of visual and physiological optics is undergoing continuous significant advancements, driven by a deeper understanding of the human visual system and the development of cutting-edge optical technologies. This Roadmap, authored by leading experts, delves into critical areas such as corneal biomechanical properties, keratoconus, and advancements in corneal imaging and elastography. It explores the intricate structure-function relationship within the eye lens, offering new perspectives through lens models and ray tracing techniques. The document also covers advancements in retinal imaging, highlighting the current state and future directions, and the role of adaptive optics in evaluating retinal structure and function in both healthy and diseased eyes. Furthermore, it addresses the modelling of ocular surfaces using different mathematical functions and examines the factors affecting peripheral image quality in the human eye, emphasizing the importance of these aspects in visual performance. Additional topics include schematic and functional models of the human eye, the impact of optical and chromatic aberrations, and the design of contact, and intraocular lenses. Finally, the Roadmap addresses the intersection of neurosciences with vision health, presenting a comprehensive overview of current research and future trends aimed at improving visual health and optical performance. Ultimately, this Roadmap aims to serve as a valuable resource for ophthalmologists, optometrists, vision scientists, and engineers dedicated to advancing the field of visual and physiological optics., Comment: This is the pre-peer-review and pre-editing version of the article, as submitted by the author to Journal of Optics

In this paper, we present a telegraph diffusion model with variable exponents for image despeckling. Moving beyond the traditional assumption of a constant exponent in the telegraph diffusion framework, we explore three distinct variable exponents for edge detection. All of these depend on the gray level of the image or its gradient. We rigorously prove the existence and uniqueness of weak solutions of our model in a functional setting and perform numerical experiments to assess how well it can despeckle noisy gray-level images. We consider both a range of natural images contaminated by varying degrees of artificial speckle noise and synthetic aperture radar (SAR) images. We finally compare our method with the nonlocal speckle removal technique and find that our model outperforms the latter at speckle elimination and edge preservation., Comment: 33 pages, 19 figures, 3 tables

Given a set $A$ and an abelian group $B$ with operators in $A$, in the sense of Krull and Noether, we introduce the Ore group extension $B[x ; \delta_B , \sigma_B]$ as the additive group $B[x]$, with $A[x]$ as a set of operators. Here, the action of $A[x]$ on $B[x]$ is defined by mimicking the multiplication used in the classical case where $A$ and $B$ are the same ring. We derive generalizations of Vandermonde's and Leibniz's identities for this construction, and they are then used to establish associativity criteria. Additionally, we prove a version of Hilbert's basis theorem for this structure, under the assumption that the action of $A$ on $B$ is what we call weakly $s$-unital. Finally, we apply these results to the case where $B$ is a left module over a ring $A$, and specifically to the case where $A$ and $B$ coincide with a non-associative ring which is left distributive but not necessarily right distributive.

Accurate imputation is essential for the reliability and success of downstream tasks. Recently, diffusion models have attracted great attention in this field. However, these models neglect the latent distribution in a lower-dimensional space derived from the observed data, which limits the generative capacity of the diffusion model. Additionally, dealing with the original missing data without labels becomes particularly problematic. To address these issues, we propose the Latent Space Score-Based Diffusion Model (LSSDM) for probabilistic multivariate time series imputation. Observed values are projected onto low-dimensional latent space and coarse values of the missing data are reconstructed without knowing their ground truth values by this unsupervised learning approach. Finally, the reconstructed values are fed into a conditional diffusion model to obtain the precise imputed values of the time series. In this way, LSSDM not only possesses the power to identify the latent distribution but also seamlessly integrates the diffusion model to obtain the high-fidelity imputed values and assess the uncertainty of the dataset. Experimental results demonstrate that LSSDM achieves superior imputation performance while also providing a better explanation and uncertainty analysis of the imputation mechanism. The website of the code is \textit{https://github.com/gorgen2020/LSSDM\_imputation}., Comment: 5 pages, conference

Multiple-instance learning (MIL) is an attractive approach for digital pathology applications as it reduces the costs related to data collection and labelling. However, it is not clear how sensitive MIL is to clinically realistic domain shifts, i.e., differences in data distribution that could negatively affect performance, and if already existing metrics for detecting domain shifts work well with these algorithms. We trained an attention-based MIL algorithm to classify whether a whole-slide image of a lymph node contains breast tumour metastases. The algorithm was evaluated on data from a hospital in a different country and various subsets of this data that correspond to different levels of domain shift. Our contributions include showing that MIL for digital pathology is affected by clinically realistic differences in data, evaluating which features from a MIL model are most suitable for detecting changes in performance, and proposing an unsupervised metric named Fr\'echet Domain Distance (FDD) for quantification of domain shifts. Shift measure performance was evaluated through the mean Pearson correlation to change in classification performance, where FDD achieved 0.70 on 10-fold cross-validation models. The baselines included Deep ensemble, Difference of Confidence, and Representation shift which resulted in 0.45, -0.29, and 0.56 mean Pearson correlation, respectively. FDD could be a valuable tool for care providers and vendors who need to verify if a MIL system is likely to perform reliably when implemented at a new site, without requiring any additional annotations from pathologists.

The study of associations between an individual's age and imaging and non-imaging data is an active research area that attempts to aid understanding of the effects and patterns of aging. In this work we have conducted a supervoxel-wise association study between both volumetric and tissue density features in coronary computed tomography angiograms and the chronological age of a subject, to understand the localized changes in morphology and tissue density with age. To enable a supervoxel-wise study of volume and tissue density, we developed a novel method based on image segmentation, inter-subject image registration, and robust supervoxel-based correlation analysis, to achieve a statistical association study between the images and age. We evaluate the registration methodology in terms of the Dice coefficient for the heart chambers and myocardium, and the inverse consistency of the transformations, showing that the method works well in most cases with high overlap and inverse consistency. In a sex-stratified study conducted on a subset of $n=1388$ images from the SCAPIS study, the supervoxel-wise analysis was able to find localized associations with age outside of the commonly segmented and analyzed sub-regions, and several substantial differences between the sexes in the association of age and volume., Comment: 35 pages

The order and chain polytopes are two 0/1-polytopes constructed from a finite poset. In this paper, we study the $f$-vectors of these polytopes. We investigate how the order and chain polytopes behave under disjoint unions and ordinal sums of posets, and how the $f$-vectors of these polytopes are expressed in terms of $f$-vectors of smaller polytopes. Our focus is on comparing the $f$-vectors of the order and chain polytope built from the same poset. In our main theorem we prove that for a family of posets built inductively by taking disjoint unions and ordinal sums of posets, for any poset $\mathcal{P}$ in this family the $f$-vector of the order polytope of $\mathcal{P}$ is component-wise at most the $f$-vector of the chain polytope of $\mathcal{P}$., Comment: Fixed typos, slight change to terminology, added one reference

In this note we derive simple analytical bounds for solutions of $x - \ln x = y -\ln y$ and use them for estimating trajectories following Lotka-Volterra-type integrals. We show how our results imply estimates for the Lambert $W$ function as well as for trajectories of general predator-prey systems, including e.g. Rosenzweig-MacArthur equations.

We use a dynamic programming approach to construct management strategies for a hydropower plant with a dam and a continuously adjustable unit. Along the way, we estimate unknown variables via simple models using historical data and forecasts. Our suggested scheme achieves on average 97.1 % of the theoretical maximum using small computational effort. We also apply our scheme to a Run-of-River hydropower plant and compare the strategies and results to the much more involved PDE-based optimal switching method studied earlier by the authors in (Optimization and Engineering (2021): 1-25); this comparison shows that our simple approach may be preferable if the underlying data is sufficiently rich.

Let $X$ be a magma, that is a set equipped with a binary operation, and consider a function $\alpha : X \to X$. We that $X$ is Hom-associative if for all $x,y,z \in X$, the equality $\alpha(x)(yz) = (xy) \alpha(z)$ holds. For every isomorphism class of magmas of order two, we determine all functions $\alpha$ making $X$ Hom-associative. Furthermore, we find all such $\alpha$ that are endomorphisms of $X$. We also consider versions of these results where the binary operation on $X$ as well as the function $\alpha$ may be only partially defined. We use our findings to construct examples of Hom-associative and multiplicative magma algebras.

The local pivotal method (LPM) is a successful sampling method for taking well-spread samples from discrete populations. We show how the LPM can be utilized to sample from arbitrary continuous distributions and thereby give powerful variance reduction in general cases. The method creates an ``automatic stratification" on any continuous distribution, of any dimension, and selects a ``thin" well-spread sample. We demonstrate the simplicity, generality and effectiveness of the LPM with various examples, including Monte Carlo estimation of integrals, option pricing and stability estimation in non-linear dynamical systems. Additionally, we show how the LPM can be combined with other variance reduction techniques, such as importance sampling, to achieve even greater variance reduction. To facilitate the implementation of the LPM, we provide a quick start guide to using LPM in MATLAB and R, which includes sample code demonstrating how to achieve variance reduction with just a few lines of code.

We investigate properties of group gradings on matrix rings $M_n(R)$, where $R$ is an associative unital ring and $n$ is a positive integer. More precisely, we introduce very good gradings and show that any very good grading on $M_n(R)$ is necessarily epsilon-strong. We also identify a condition that is sufficient to guarantee that $M_n(R)$ is an epsilon-crossed product, i.e. isomorphic to a crossed product associated with a unital twisted partial action. In the case where $R$ has IBN, we are able to provide a characterization of when $M_n(R)$ is an epsilon-crossed product. Our results are illustrated by several examples., Comment: 9 pages

Direct thermal-to-electric energy converters typically operate in the linear regime, where the ratio of actual maximum power relative to the ideal maximum power, the so-called fill factor (FF), is 0.25. By increasing the FF one can potentially increase maximum power by up to four times, but this is only possible in the nonlinear regime of transport and has previously rarely been considered. Here we show, based on fundamental symmetry considerations, that the leading order non-linear terms that can increase the FF require devices with broken spatial symmetry. To experimentally demonstrate such a system, we study nonlinear, thermoelectric transport across an asymmetric energy barrier epitaxially defined in a single semiconductor nanowire. We find in both experiment and theory that we can increase the FF above the linear-response limit of 0.25, accompanied by a drastic increase in short circuit current, open-circuit voltage and maximum power. Our results show that geometric symmetry breaking combined with the design of nonlinear behaviour represent a design strategy for increasing the performance of thermal-to-electric energy converters such as in hot-carrier photovoltaics, thermophotovoltaics or in anisotropic thermoelectric materials., Comment: 11 pages, 3 figures. Submitted to Nature Physics