arXiv subjects

Timo de Wolff

Publications and source records attributed to Timo de Wolff.

At least 19 recordsLinked to original sources

arXiv2026

Automatic ply-specific analyses of CFRP micrographs using shortest-path-based ply distinction

We present an automated approach to distinguish between ply instances in semantic segmentation masks of high-resolution carbon-fiber reinforced polymer micrographs. Interpreting the segmentation mask as a graph with pixels as vertices, enables us to use a shortest-path algorithm yielding the ply-separating paths. Thereby, we bridge the gap between semantic segmentation and ply instance segmentation using global information. We successfully apply our approach on high-resolution micrographs featuring a broad range of characteristics like artificially added gaps in single or multiple plies, different stacking sequences and ply traversing cracks. Assigning each fiber pixel to a ply based on the calculated paths, allows for a comprehensive, quantitative ply analysis with respect to its microstructural properties like the local fiber volume fraction as well as locally resolved ply and interleaf layer thickness. These insights help to reveal manufacturing-induced inhomogeneities, draw conclusions on manufacturing parameters and link mechanical properties to underlying microstructural imperfections.

cs.CV↗

arXiv2026

Voronoi-Based Vacuum Leakage Detection in Composite Manufacturing

In this article, we investigate vacuum leakage detection problems in composite manufacturing. Our approach uses Voronoi diagrams, a well-known structure in discrete geometry. The Voronoi diagram of the vacuum connection positions partitions the component surface. We use this partition to narrow down potential leak locations to a small area, making an efficient manual search feasible. To further reduce the search area, we propose refined Voronoi diagrams. We evaluate both variants using a novel dataset consisting of several hundred one- and two-leak positions along with their corresponding flow values. Our experimental results demonstrate that Voronoi-based predictive models are highly accurate and have the potential to resolve the leakage detection bottleneck in composite manufacturing.

math.MG↗

arXiv2025

IMProofBench: Benchmarking AI on Research-Level Mathematical Proof Generation

As the mathematical capabilities of large language models (LLMs) improve, it becomes increasingly important to evaluate their performance on research-level tasks at the frontier of mathematical knowledge. However, existing benchmarks are limited, as they focus solely on final-answer questions or high-school competition problems. To address this gap, we introduce IMProofBench, a private benchmark consisting of 77 peer-reviewed problems developed by expert mathematicians. Each problem requires a detailed proof and is paired with subproblems that have final answers, supporting both an evaluation by human experts and a large-scale quantitative analysis through automated grading. Furthermore, unlike prior benchmarks, the evaluation setup simulates a realistic research environment: models operate in an agentic framework with tools like web search for literature review and mathematical software such as SageMath. Our results show that current LLMs can already solve a significant percentage of research-level questions. IMProofBench will continue to evolve as a dynamic benchmark in collaboration with the mathematical community, ensuring its relevance for evaluating the next generation of LLMs.

cs.CL↗

arXiv2025

Nonnegativity of signomials with Newton simplex over $\mathcal{A}$-convex sets

We study a class of signomials whose positive support is the set of vertices of a simplex and which may have several negative support points in the simplex. Various groups of authors have provided an exact characterization for the global nonnegativity of a signomial in this class in terms of circuit signomials and that characterization provides a tractable nonnegativity test. We generalize this characterization to the constrained nonnegativity over a set $X$ under an additional convexity precondition in the exponential moment space. This provides a tractable nonnegativity test over $X$ for the class in terms of a power cone program. Our proof methods rely on a variant of the convex cone of constrained SAGE signomials (sums of arithmetic-geometric exponentials) and the duality theory.

math.CO↗

arXiv2025

Benchmarking of quantum and classical SDP relaxations for QUBO formulations of real-world logistics problems

Quadratic unconstrained binary optimization problems (QUBOs) are intensively discussed in the realm of quantum computing and polynomial optimization. We provide a vast experimental study of semidefinite programming (SDP) relaxations of QUBOs using sums of squares methods and on Hamiltonian Updates. We test on QUBO reformulations of industry-based instances of the (open) vehicle routing problem and the (affinity-based) slotting problem -- two common combinatorial optimization problems in logistics. Beyond comparing the performance of various methods and software, our results reaffirm that optimizing over non-generic, real-world instances provides additional challenges. In consequence, this study underscores recent developments towards structure exploitation and specialized solver development for the used methods and simultaneously shows that further research is necessary in this direction both on the classical and the quantum side.

math.OC↗

arXiv2025

Solving quadratic binary optimization problems using quantum SDP methods: Non-asymptotic running time analysis

Quantum computers can solve semidefinite programs (SDPs) using resources that scale better than state-of-the-art classical methods as a function of the problem dimension. At the same time, the known quantum algorithms scale very unfavorably in the precision, which makes it non-trivial to find applications for which the quantum methods are well-suited. Arguably, precision is less crucial for SDP relaxations of combinatorial optimization problems (such as the Goemans-Williamson algorithm), because these include a final rounding step that maps SDP solutions to binary variables. With this in mind, Brand\~ao, Fran\c{c}a, and Kueng have proposed to use quantum SDP solvers in order to achieve an end-to-end speed-up for obtaining approximate solutions to combinatorial optimization problems. They did indeed succeed in identifying an algorithm that realizes a polynomial quantum advantage in terms of its asymptotic running time. However, asymptotic results say little about the problem sizes for which advantages manifest. Here, we present an analysis of the non-asymptotic resource requirements of this algorithm. The work consists of two parts. First, we optimize the original algorithm with a particular emphasis on performance for realistic problem instances. In particular, we formulate a version with adaptive step-sizes, an improved detection criterion for infeasible instances, and a more efficient rounding procedure. In a second step, we benchmark both the classical and the quantum version of the algorithm. The benchmarks did not identify a regime where even the optimized quantum algorithm would beat standard classical approaches for input sizes that can be realistically solved at all. In the absence of further significant improvements, these algorithms therefore fall into a category sometimes called galactic: Unbeaten in their asymptotic scaling behavior, but not practical for realistic problems.

quant-ph↗

arXiv2024

Revealing hidden physical nonclassicality with nonnegative polynomials

Understanding quantum phenomena which go beyond classical concepts is a focus of modern quantum physics. Here, we show how the theory of nonnegative polynomials emerging around Hilbert's 17th problem, can be used to optimally exploit data capturing the nonclassical nature of light. Specifically, we show that nonnegative polynomials can reveal nonclassicality in data even when it is hidden from standard detection methods up to now. Moreover, the abstract language of nonnegative polynomials also leads to a unified mathematical approach to nonclassicality for light and spin systems, allowing us to map methods for one to the other. Conversely, the physical problems arising also inspire several mathematical insights into characterisation of nonnegative polynomials.

quant-ph↗

arXiv2024

A Speed-up for Helsgaun's TSP Heuristic by Relaxing the Positive Gain Criterion

The Traveling Salesman Problem (TSP) is one of the most extensively researched and widely applied combinatorial optimization problems. It is NP-hard even in the symmetric and metric case. Building upon elaborate research, state-of-the-art exact solvers such as CONCORDE can solve TSP instances with several ten thousand vertices. A key ingredient for these integer programming approaches are fast heuristics to find a good initial solution, in particular the Lin-Kernighan-Helsgaun (LKH) heuristic. For instances with few hundred vertices heuristics like LKH often find an optimal solution. In this work we develop variations of LKH that perform significantly better on large instances. LKH repeatedly improves an initially random tour by exchanging edges along alternating circles. Thereby, it respects several criteria designed to quickly find alternating circles that give a feasible improvement of the tour. Among those criteria, the positive gain criterion stayed mostly untouched in previous research. It requires that, while constructing an alternating circle, the total gain has to be positive after each pair of edges. We relax this criterion carefully leading to improvement steps hitherto undiscovered by LKH. We confirm this improvement experimentally via extensive simulations on various benchmark libraries for TSP. Our computational study shows that for large instances our method is on average 13% faster than the latest version of LKH.

math.OC↗

arXiv2023

Realistic Runtime Analysis for Quantum Simplex Computation

In recent years, strong expectations have been raised for the possible power of quantum computing for solving difficult optimization problems, based on theoretical, asymptotic worst-case bounds. Can we expect this to have consequences for Linear and Integer Programming when solving instances of practically relevant size, a fundamental goal of Mathematical Programming, Operations Research and Algorithm Engineering? Answering this question faces a crucial impediment: The lack of sufficiently large quantum platforms prevents performing real-world tests for comparison with classical methods. In this paper, we present a quantum analog for classical runtime analysis when solving real-world instances of important optimization problems. To this end, we measure the expected practical performance of quantum computers by analyzing the expected gate complexity of a quantum algorithm. The lack of practical quantum platforms for experimental comparison is addressed by hybrid benchmarking, in which the algorithm is performed on a classical system, logging the expected cost of the various subroutines that are employed by the quantum versions. In particular, we provide an analysis of quantum methods for Linear Programming, for which recent work has provided asymptotic speedup through quantum subroutines for the Simplex method. We show that a practical quantum advantage for realistic problem sizes would require quantum gate operation times that are considerably below current physical limitations.

quant-ph↗

arXiv2023

Initial Application of SONC to Lyapunov Stability of Dynamical Systems

Certifying the stability of dynamical systems is a central and challenging task in control theory and systems analysis. To tackle these problems we present an algorithmic approach to finding polynomial Lyapunov functions. Our method relies on sums of nonnegative circuit functions (SONC), a certificate of nonnegativity of real polynomials. We show that both the problem of verifying as well as the more difficult task of finding Lyapunov functions can be carried out via relative entropy programming when using SONC certificates. This approach is analogue yet independent to finding Lyapunov functions via sums of squares (SOS) certificates and semidefinite programming. Furthermore, we explore whether using the related, recently introduced DSONC certificate is advantageous compared to SONC for this type of problem. We implemented our results, and present examples to show their applicability.

math.OC↗

arXiv2022

A Generalized Muirhead Inequality and Symmetric Sums of Nonnegative Circuits

Circuit polynomials are a certificate of nonnegativity for real polynomials, which can be derived via a generalization of the classical inequality of arithmetic and geometric means. In this article, we show that similarly nonnegativity of symmetric real polynomials can be certified via a generalization of the classical Muirhead inequality. Moreover, we show that a nonnegative symmetric polynomial admits a decomposition into sums of nonnegative circuit polynomials if and only if it satisfies said generalized Muirhead condition. The latter re-proves a result by Moustrou, Naumann, Riener, Theobald, and Verdure for the case of the symmetric group in a shortened and more elementary way.

math.AG↗

arXiv2022

Learning Variational Models with Unrolling and Bilevel Optimization

In this paper we consider the problem of learning variational models in the context of supervised learning via risk minimization. Our goal is to provide a deeper understanding of the two approaches of learning of variational models via bilevel optimization and via algorithm unrolling. The former considers the variational model as a lower level optimization problem below the risk minimization problem, while the latter replaces the lower level optimization problem by an algorithm that solves said problem approximately. Both approaches are used in practice, but unrolling is much simpler from a computational point of view. To analyze and compare the two approaches, we consider a simple toy model, and compute all risks and the respective estimators explicitly. We show that unrolling can be better than the bilevel optimization approach, but also that the performance of unrolling can depend significantly on further parameters, sometimes in unexpected ways: While the stepsize of the unrolled algorithm matters a lot (and learning the stepsize gives a significant improvement), the number of unrolled iterations plays a minor role.

stat.ML↗

arXiv2022

Parameter region for multistationarity in $n-$site phosphorylation networks

Multisite phosphorylation is a signaling mechanism well known to give rise to multiple steady states, a property termed multistationarity. When phosphorylation occurs in a sequential and distributive manner, we obtain a family of networks indexed by the number of phosphorylation sites $n$. This work addresses the problem of understanding the parameter region where this family of networks displays multistationarity, by focusing on the projection of this region onto the set of kinetic parameters. The problem is phrased in the context of real algebraic geometry and reduced to studying whether a polynomial, defined as the determinant of a parametric matrix of size three, attains negative values over the positive orthant. The coefficients of the polynomial are functions of the kinetic parameters. For any $n$, we provide sufficient conditions for the polynomial to be positive and hence, preclude multistationarity, and also sufficient conditions for it to attain negative values and hence, enable multistationarity. These conditions are derived by exploiting the structure of the polynomial, its Newton polytope, and employing circuit polynomials. A relevant consequence of our results is that the set of kinetic parameters that enable or preclude multistationarity are both connected for all $n$.

q-bio.MN↗

arXiv2022

The Duality of SONC: Advances in Circuit-based Certificates

The cone of sums of nonnegative circuits (SONCs) is a subset of the cone of nonnegative polynomials / exponential sums, which has been studied extensively in recent years. In this article, we construct a subset of the SONC cone which we call the DSONC cone. The DSONC cone can be seen as an extension of the dual SONC cone; membership can be tested via linear programming. We show that the DSONC cone is a proper, full-dimensional cone, we provide a description of its extreme rays, and collect several properties that parallel those of the SONC cone. Moreover, we show that functions in the DSONC cone cannot have real zeros, which yields that DSONC cone does not intersect the boundary of the SONC cone. Furthermore, we discuss the intersection of the DSONC cone with the SOS and SDSOS cones. Finally, we show that circuit functions in the boundary of the DSONC cone are determined by points of equilibria, which hence are the analogues to singular points in the primal SONC cone, and relate the DSONC cone to tropical geometry.

math.AG↗

arXiv2021

Re-entrant tensegrity: A three-periodic, chiral, tensegrity structure that is auxetic

We present a three-periodic, chiral, tensegrity structure and demonstrate that it is auxetic. Our tensegrity structure is constructed using the chiral symmetry {\Pi}+ cylinder packing, transforming the cylinders themselves to the elastic elements and cylinder contacts to incompressible rods. The resulting structure displays local re-entrant geometry at its vertices, and is shown to be auxetic when modelled as an equilibrium configuration of spatial constraints subject to a quasi-static deformation. When the tensegrity structure is subsequently modelled as a lattice material with elastic elements, the auxetic behaviour is again confirmed through finite element modelling as well as demonstrated with a 3d printed example. The cubic symmetry of the structure means that the behaviour is independent of the chosen stretching direction and the auxetic behaviour is observed in both perpendicular directions. This structure could be the simplest three-dimensional analogue to the two-dimensional re-entrant honeycomb. This, alongside the chirality of the structure, make it an interesting design target for multifunctional materials.

cond-mat.mtrl-sci↗

arXiv2020

Global Optimization via the Dual SONC Cone and Linear Programming

Using the dual cone of sums of nonnegative circuits (SONC), we provide a relaxation of the global optimization problem to minimize an exponential sum and, as a special case, a multivariate real polynomial. Our approach builds on two key observations. First, that the dual SONC cone is contained in the primal one. Hence, containment in this cone is a certificate of nonnegativity. Second, we show that membership in the dual cone can be verified by a linear program. We implement the algorithm and present initial experimental results comparing our method to existing approaches.

math.OC↗

arXiv2020

Evaluation of Pool-based Testing Approaches to Enable Population-wide Screening for COVID-19

Background: Rapid testing for an infection is paramount during a pandemic to prevent continued viral spread and excess morbidity and mortality. This study aimed to determine whether alternative testing strategies based on sample pooling can increase the speed and throughput of screening for SARS-CoV-2. Methods: A mathematical modelling approach was chosen to simulate six different testing strategies based on key input parameters (infection rate, test characteristics, population size, testing capacity etc.). The situations in five countries (US, DE, UK, IT and SG) currently experiencing COVID-19 outbreaks were simulated to reflect a broad variety of population sizes and testing capacities. The primary study outcome measurements that were finalised prior to any data collection were time and number of tests required; number of cases identified; and number of false positives. Findings: The performance of all tested methods depends on the input parameters, i.e. the specific circumstances of a screening campaign. To screen one tenth of each country's population at an infection rate of 1% - e.g. when prioritising frontline medical staff and public workers -, realistic optimised testing strategies enable such a campaign to be completed in ca. 29 days in the US, 71 in the UK, 25 in Singapore, 17 in Italy and 10 in Germany (ca. eight times faster compared to individual testing). When infection rates are considerably lower, or when employing an optimal, yet logistically more complex pooling method, the gains are more pronounced. Pool-based approaches also reduces the number of false positive diagnoses by 50%. Interpretation: The results of this study provide a clear rationale for adoption of pool-based testing strategies to increase speed and throughput of testing for SARS-CoV-2. The current individual testing approach unnecessarily wastes valuable time and resources.

q-bio.PE↗

arXiv2020

Computing the Real Isolated Points of an Algebraic Hypersurface

Let $\mathbb{R}$ be the field of real numbers. We consider the problem of computing the real isolated points of a real algebraic set in $\mathbb{R}^n$ given as the vanishing set of a polynomial system. This problem plays an important role for studying rigidity properties of mechanism in material designs. In this paper, we design an algorithm which solves this problem. It is based on the computations of critical points as well as roadmaps for answering connectivity queries in real algebraic sets. This leads to a probabilistic algorithm of complexity $(nd)^{O(n\log(n))}$ for computing the real isolated points of real algebraic hypersurfaces of degree $d$. It allows us to solve in practice instances which are out of reach of the state-of-the-art.

cs.CG↗