Institute of Mathematical Sciences

Manufacturing operations that emphasize environmental responsibility, product quality and end-of-life (EOL) management are increasingly adopted by firms. These steps are necessary due to increasing environmental legislation and a growing consumer demand for sustainable products. An advantageous approach to effectively addressing returned items within this framework is remanufacturing. The findings of this research explore the dynamic processes involved in the remanufacturing stages, namely the collection, sorting, and testing phase, as well as the development phase, which remanufactures the product, and how they affect the entire supply chain (SC) performance. The current research offers a unified strategy to thoroughly evaluate model responses across a wide range of variables by analysing the impact of key variables within these phases and employing various distribution functions to model their behaviour. A two-stage Data Envelopment Analysis (DEA), an efficient analytical method in Multi-Criteria Decision Making (MCDM), is employed to evaluate the efficiency of the developed models. Research findings indicate that the initial phases of collection, sorting and testing are more efficient than the development phase. Furthermore, the findings show that the cooperative method yields more efficient outcomes than the leader-follower approach in the non-cooperative setting.

Biomolecular condensates formed via liquid-liquid phase separation (LLPS) are essential for cellular organization. α-Synuclein, an amyloidogenic protein linked to Parkinson’s Disease (PD), undergoes phase separation at high concentrations, but the influence of lipid membranes on this process remains unclear. Here, combining in vitro reconstitution, cell biology, and simulations, we show that membranous interfaces promote α-Synuclein condensation at physiologically relevant sub-critical concentrations (~10 nM) without crowding agents. Notably, condensation occurs only on membranes with a specific stoichiometry of lipids, underscoring the role of interfacial potential. These condensates serve as nucleation sites for fibril formation, leading to membrane deformation and rupture. A lattice gas model reveals this behavior as a prewetting-like transition, where an attractive membrane induces local phase separation below the bulk saturation concentration. Indeed altering interfacial potential by lipid composition and membrane depolarization not only drastically changes α-Synuclein puncta size and number but also triggers their release from neurons. These findings reveal the crucial role of lipid membrane interfaces in regulating α-Synuclein condensation, aggregation and release, shedding light on a potential mechanism of their cell-to-cell propagation during neurodegeneration.

Greedy algorithms are central to sparse approximation and stage-wise learning methods such as matching pursuit and boosting. It is known that the Power-Relaxed Greedy Algorithm with step sizes m−α may fail to converge when α>1 in general Hilbert spaces. In this work, we revisit this phenomenon from a sparse learning perspective. We study realizable regression problems with controlled feature coherence and derive explicit lower bounds on the residual norm, showing that over-decaying step-size schedules induce structural stagnation even in low-dimensional sparse settings. Numerical experiments confirm the theoretical predictions and illustrate the role of feature coherence. Our results provide insight into step-size design in greedy sparse learning.

Abstract We investigate the action of Alesker’s Lefschetz operators on translation invariant valuations on convex bodies. For scalar valued valuations, we describe this action on the level of Klain–Schneider functions by a Radon type transform, generalizing a result by Schuster and Wannerer. In the case of rotationally equivariant Minkowski valuations, the Lefschetz operators act on the generating function as a convolution transform. We show that the convolution kernel satisfies a Legendre-type differential equation, and thus, is a strictly positive function that is smooth up to one point.

Recently, several unexpected events of various types (geopolitical, economic, health-related, and weather-related) have had a significant global impact, affecting the lives of millions of people and businesses. Disruptions in supply chains highlight the importance of planning and managing them at various hierarchical levels of decision-making. This paper presents and analyzes supply chain networks (SCNs) for the distribution of soybean and corn in Europe and North Africa, considering the uncertainty of demand and costs along intermodal routes. Transportation and distribution costs for these commodities are minimized by considering the uncertainty of demand and transportation costs. Starting from a deterministic model to establish the SCN, uncertainty is then introduced through stochastic modeling, with the optimization goals redefined accordingly, more specifically in terms of expected cost (EC) and conditional value at risk (CVAR) constraints. The solutions of the bi-objective model, including equivalent average emissions CO2, highlight the strategic positions of the port of Itaqui on the supply side and of the port of Sines as distribution hubs (transshipment) in the design of the networks according to the different objectives. The advantageous position of the port of Sines is analyzed in detail, according to the strategic objective of designing a more efficient intermodal SCN for the distribution of soybean and corn.