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In the last few years, large improvements in image clustering have been driven by the recent advances in deep learning. However, due to the architectural complexity of deep neural networks, there is no mathematical theory that explains the…
The optical properties of nanoparticle clusters vary with the spatial arrangement of the constituent particles, but also the overall orientation of the cluster with respect to the incident light. This is particularly important in the…
Spontaneous self-assembly of hard convex polyhedra are known to form orientationally disordered crystalline phases, where particle orientations do not follow the same pattern as the positional arrangement of the crystal. A distinct type of…
From atomic crystals to bird flocks, most forms of order are captured by the concept of spontaneous symmetry breaking. This paradigm was challenged by the discovery of topological order, in materials where the number of accessible states is…
Complex networks are a recent type of frameworks used to study complex systems with many interacting elements, such as Self-Organized Criticality (SOC). The network node's tendency to link to other nodes of similar type is characterized by…
Order-invariant formulas access an ordering on a structure's universe, but the model relation is independent of the used ordering. Order invariance is frequently used for logic-based approaches in computer science. Order-invariant formulas…
Packing optimization is a prevalent problem that necessitates robust and efficient algorithms that are also simple to implement. One group of approaches is the raster methods, which rely on approximating the objects with pixelated…
We show that macro-molecular self-assembly can recognize and classify high-dimensional patterns in the concentrations of $N$ distinct molecular species. Similar to associative neural networks, the recognition here leverages dynamical…
Particle-based shape modeling (PSM) is a family of approaches that automatically quantifies shape variability across anatomical cohorts by positioning particles (pseudo landmarks) on shape surfaces in a consistent configuration. Recent…
Humans effortlessly identify objects by leveraging a rich understanding of the surrounding scene, including spatial relationships, material properties, and the co-occurrence of other objects. In contrast, most computational object…
Self-Organizing Map algorithms have been used for almost 40 years across various application domains such as biology, geology, healthcare, industry and humanities as an interpretable tool to explore, cluster and visualize high-dimensional…
This tutorial article introduces the physics of quantum information scrambling in quantum many-body systems. The goals are to understand how to precisely quantify the spreading of quantum information and how causality emerges in complex…
Recently, convex nested stochastic composite optimization (NSCO) has received considerable attention for its applications in reinforcement learning and risk-averse optimization. The current NSCO algorithms have worse stochastic oracle…
This article investigates the interplay of rounding objective coefficients in binary programs and almost symmetries. Empirically, reducing the number of significant bits through rounding often leads to instances that are easier to solve.…
Tailoring the functional properties of advanced organic/inorganic heterogeonous devices to their intended technological applications requires knowledge and control of the microscopic structure inside the device. Atomistic quantum mechanical…
System-on-Chip (SoC) designs are used in every aspect of computing and their optimization is a difficult but essential task in today's competitive market. Data taken from SoCs to achieve this is often characterised by very long concurrent…
Self-consistent field theory (SCFT) and strong segregation theory (SST) are used to explore the parameter space governing the self-assembly of cylinder forming block copolymers (BCPs) on a modulated substrate. The stability of in-plane…
Block copolymer are ideal matrices to control the localisation of colloids. Furthermore, anisotropic nanoparticles such as Janus nanoparticles possess an additional orientational degree of freedom that can play a crucial role in the…
Accurate modeling of gravitational interactions is fundamental to the analysis, prediction, and control of space systems. While the Newtonian point-mass approximation suffices for many preliminary studies, real celestial bodies exhibit…
We consider programmable matter that consists of computationally limited devices (called particles) that are able to self-organize in order to achieve some collective goal without the need for central control or external intervention. We…