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Isotropic constants and regular polytopes
No full textWe discuss first-order optimality conditions for the isotropic constant and combine them with RS-movements to obtain structural information about polytopal maximizers. Strengthening a result by Rademacher, it is shown that a polytopal local maximizer with a simplicial vertex must be a simplex. A similar statement is shown for a centrally symmetric local maximizer with a simplicial vertex: it has to be a cross-polytope. Moreover, we show that a zonotope that maximizes the isotropic constant and that has a cubical zone must be a cube. Finally, we consider the class of zonotopes with at most n +1 generators and determine the extremals in this class.TU Berlin, Open-Access-Mittel – 2025DFG, 390685689, EXC 2046: MATH+: Berlin Mathematics Research Cente
Computational models for deciphering the evolution of copy-number alterations in human cancers
No full textCancer is an evolutionary process in which cells continuously change, compete, and adapt to their environment. Cancer cells acquire genomic alterations that shape their fitness and drive tumour progression. Among these alterations, somatic copy-number alterations (SCNAs)—gains or losses of genomic segments—play a central role in cancer evolution by amplifying favourable regions and deleting unfavourable ones.
To understand how tumours form and progress, it is essential to uncover the evolutionary forces shaping cancer genomes, how SCNAs arise, and how they affect cellular fitness and selection. These questions are addressed in this thesis through the development of three complementary computational frameworks.
First, I present MEDICC2, an algorithm for reconstructing tumour phylogenies from copy-number data. Using a minimum-evolution principle, MEDICC2 infers evolutionary relationships between multiple tumour samples, providing insight into how copy-number alterations accumulate over time and influence cancer evolution.
Second, I introduce SMITH, a stochastic model that simulates tumour growth under fitness and spatial constraints. By extending classical branching-process models with spatial confinement, SMITH captures distinct evolutionary modes arising from competition between clones within limited space and resources.
Third, I present SPICE, a model to study selection acting on SCNAs across 5,966 cancers from The Cancer Genome Atlas. It infers individual copy-number events and identifies loci under selection, revealing hundreds of novel oncogenes and tumour suppressors.
Together, these projects combine algorithm development, mathematical modelling, machine learning, and large-scale data analysis to provide a unified framework for understanding how somatic copy-number alterations, fitness, and selection jointly shape tumour evolution.Krebs ist ein evolutionärer Prozess, bei dem sich Zellen kontinuierlich verändern, miteinander konkurrieren und an ihre Umgebung anpassen. Krebszellen erwerben fortlaufend genomische Veränderungen, die ihre Fitness beeinflussen und den Wachstum des Tumor vorantreiben. Somatische Kopienzahlaberrationen (somatic copy-number alteration, SCNAs) – Zugewinne oder Verluste von Regionen des Genoms – spielen eine zentrale Rolle in der Krebsentwicklung, indem sie für die Krebszellen vorteilhafte Regionen verstärken und nachteilige entfernen.
Um zu verstehen, wie Tumore entstehen und sich weiterenwickeln, ist es entscheidend, die zugrunde liegenden evolutionären Kräfte zu erfassen. Ebenso ist es wichtig zu verstehen, wie SCNAs entstehen und wie sie die Fitness und Selektion einzelner Krebszellen beeinflussen.
Diese Fragen werden in dieser Dissertation durch die Entwicklung von drei komplementären bioinformatischen Modellen adressiert.
Erstens präsentiere ich mit MEDICC2 einen Algorithmus, der evolutionärer Bäume aus Kopienzahldaten rekonstruiert. Durch die Anwendung eines Prinzip der geringsten Veränderung kann MEDICC2 die evolutionären Beziehungen zwischen verschiedenen Tumorproben präzise rekonstruieren und liefert Einblicke, wie Kopienzahlaberrationen im Verlauf der Krebsentwicklung entstehen und sich anhäufen.
Zweitens stelle ich mit SMITH ein stochastisches Modell vor, welches Tumorwachstum unter Fitness- und räumlichen Einschränkungen simuliert. Durch die Erweiterung klassischer branching-Modelle um räumliche Begrenzungen modelliert SMITH verschiedene evolutionäre Modi, die aus der Konkurrenz zwischen Klonen unter limitierten Bedingungen entstehen.
Drittens präsentiere ich mit SPICE ein Modell zur Untersuchung der evolutionären Selektion von Kopienzahlaberrationen anhand von 5.966 Krebsproben. SPICE rekonstruiert individuelle Kopienzahlaberrationen aus den Daten und identifiziert genomische Loci, welche von evolutionärer Selektion beeinflusst werden. Hierdurch werden Hunderte neue Onkogene und Tumoruppressoren identifiziert.
Gemeinsam verbinden diese Projekte Algorithmusentwicklung, mathematische Modellierung, maschinelles Lernen und großangelegte Datenanalyse zu einem einheitlichen Rahmen, der verdeutlicht, wie somatische Kopienzahlaberrationen, Fitness und Selektion gemeinsam die Tumorevolution beeinflussen.BMFTR, 01IS18025A, Verbundprojekt BIFOLD-BBDC: Berlin Institute for the Foundations of Learning and DataBMFTR, 01IS18037A, Verbundprojekt BIFOLD-BZML: Berlin Institute for the Foundations of Learning and Dat
Improving heat demand forecasting with feature reduction in an Encoder–Decoder LSTM model
No full textAccurate short-term heat demand forecasting is essential for the efficient operation of District Heating Networks (DHNs). However, many forecasting models rely on large sets of engineered or externally forecasted variables, introducing redundancy, computational overhead, and reduced generalizability. This study proposes an Encoder–Decoder (ED) Long Short-Term Memory (LSTM) architecture emphasizing input feature reduction to enhance robustness and accuracy. Using an open-source smart meter dataset, the model is trained and evaluated across ten systematically constructed input feature sets to quantify the influence of each feature group through a feed-forward selection strategy. Results indicate that dimensionality reduction yields substantial performance gains, with MAE and in CV-RMSE reduced by 57% and 64%, respectively. The inclusion of wind speed improves predictive accuracy, while adding solar irradiance results in a degradation of approximately 5 percentage points. The proposed ED-LSTM outperforms benchmark models, including Support Vector Regression (SVR), Seasonal Autoregressive Integrated Moving Average with Exogenous Regressor (SARIMAX), and a baseline two-layer LSTM, with error reductions ranging from 4.8% to 47.1% across MSE, MAE, RMSE, and MAPE metrics. The statistical significance of model performance differences is confirmed through Friedman and Diebold–Mariano tests, supporting the reliability of the comparative results.TU Berlin, Open-Access-Mittel – 2025BMWE, 03EN3062A, EnEff:Stadt: SubWW2 - Innovationswärmeleiter für Wärmeenergiequellen in Agglomerationsgürteln am Beispiel von Konversionsprozessen des Bestandsquartiers "Ortskern Leeste": Phase 2 Umsetzung; Teilvorhaben: Wärmenetzmanagemen
The role of mixing sequence in shaping the 3D-printability of geopolymers
No full textThis paper investigates the influence of sample preparation on a geopolymer composed of fly ash and ground granulated blast furnace slag, specifically designed for extrusion-based 3D printing. We examine the impact of geopolymerisation processes and evaluate their suitability for printing. Various methods, including penetration testing, slow penetration testing, uniaxial unconfined compression testing, ultrasonic wave transmission, heat flow analysis, and compressive strength testing, were employed to assess early structural buildup to gain insights into their effects on printability and buildability. Our results show that the way in which the liquid components are combined with the pecrusors is crucial for influencing the geopolymerisation rate and the geopolymer’s overall performance. By analysing the transition points of yield stress, calculating the Young’s modulus and examining green strength as an early indicator of compressive strength in the yet unset geopolymer, we accurately determine the printability duration using only small-scale laboratory tests, without physical printing tests. When liquid components are added individually, a high OH⁻ concentration locally increases pH and accelerates particle dissolution. By pre-mixing sodium hydroxide with water, the local pH decreases, the geopolymerisation rate is slowed down and the printability is prolonged. A homogeneous distribution of all liquids additionally leads to an even distribution of dissolved silicon ions. This accelerates geopolymerisation that the system becomes unprintable. Our measurements reveal that as structural condensation of the geopolymer begins, the rheological properties shift, rendering the material unsuitable for printing. The results demonstrate that optimised mixing strategies impact the suitability of the geopolymer for extrusion-based 3D printing.TU Berlin, Open-Access-Mittel – 202
S wave velocity and attenuation estimation by using seismic noise data and strong/weak motion recordings in boreholes
No full textA critical element of hazard assessment is the local seismic response, defined as the variation in seismic motion occurring in the upper layers of the earth’s crust, determined by the soil properties that affect the propagation of seismic waves. The implications of this aspect are substantial in practice, as it can lead to varying levels of destruction in urban environments and to loss of human life. Past big earthquakes, such as the great California (USA) earthquake of 1906, the Niigata (Japan) earthquake occurred in 1964, and the 1985 Michoacán (Mexico) earthquake, have highlighted that targeted research is required to enhance the current knowledge base regarding site effects and related parameters. Whereas the shear-wave velocity (Vs) as well as fundamental resonance frequency (f0) have been widely investigated, less studies have been devoted to attenuation and its associated shear-wave quality factor (Qs), perhaps because their estimation from empirical data is more complicated.
Arrays of ambient seismic noise have emerged as a cheap, practical, and non-invasive tool for local seismic response analysis, offering fairly precise values of Vs and, recently, also of Qs. In an attempt to improve current research on attenuation calculation, this dissertation introduces a novel linear inversion methodology to estimate Qs at the local scale based on seismic noise data obtained by arranging temporary seismological stations according to a surface array setup. This approach innovatively leverages the Simultaneous Algebraic Reconstruction Technique (SART) for an easy, rapid, and efficient computation of Qs in studies of local seismic response, particularly within urban settings. After performing reliability tests, the proposed approach is applied in a borehole testing site in northeast Italy, where Vs and Qs values from independent geophysical borehole measurements exist in the literature. Subsequently, at a second borehole site, the consistency between Vs and the factor Qs estimated using the novel approach based on SART, and the same parameters obtained from the analysis of weak motions recorded by seismometers installed within the borehole is evaluated. SART seems to hold great promise and lays the foundation for future advancement in robust estimations of Qs.Ein entscheidendes Element der Gefährdungsbeurteilung hinsichtlich Erdbebenereignissen stellt die lokale seismische Reaktion dar. Letztere wird definiert als die Variation der seismischen Bewegung in den oberen Schichten der Erdkruste, die durch die Bodeneigenschaften bestimmt wird, die ihrerseits die Ausbreitung der seismischen Wellen beeinflussen. Die Auswirkungen dieses Aspekts sind in der Praxis erheblich, da er zu unterschiedlich starken Zerstörungen in städtischen Gebieten und zum Verlust von Menschenleben führen kann. Historische Erdbeben, wie das große Erdbeben in Kalifornien (USA) im Jahr 1906, das Erdbeben in Niigata (Japan) im Jahr 1964, und das Erdbeben in Michoacán (Mexiko) im Jahr 1985, haben die Dringlichkeit einer gezielten Forschung unterstrichen, um das bestehende Wissensdefizit hinsichtlich der Auswirkungen auf den Standort und die damit verbundenen Parameter zu verringern. Obwohl die Scherwellengeschwindigkeit (Vs) und die fundamentale Resonanzfrequenz (f0) bereits umfassend untersucht wurden, wurde der Dämpfung und dem damit verbundenen Scherwellenqualitätsfaktor (Qs) in der Forschung weniger Aufmerksamkeit gewidmet. Diese Vernachlässigung könnte darauf zurückzuführen sein, dass ihre Abschätzung aus empirischen Daten komplizierter ist.
Arrays mit seismischem Umgebungsrauschen haben sich als kostengünstiges, praktikables und nicht-invasives Werkzeug für die Analyse lokaler seismischer Reaktionen erwiesen. Sie gestatten die Ermittlung relativ präziser Werte für Vs und seit kurzem auch für Qs. In einem Versuch, die aktuelle Forschung zur Dämpfungsermittlung zu verbessern, wird in dieser Dissertation eine neuartige lineare Inversionsmethode zur Schätzung von Qs auf lokaler Ebene eingeführt. Diese basiert auf Daten von seismischem Rauschen, die durch die Oberflächenanordnung von temporären seismologischen Stationen gewonnen wurden. Der hier beschriebene Ansatz nutzt auf innovative Weise die Simultane Algebraische Rekonstruktionstechnik (SART) für eine einfache, schnelle und effiziente Berechnung von Qs in Studien über lokale seismische Reaktionen, insbesondere in städtischen Gebieten. Nach Durchführung von Zuverlässigkeitstests wird der vorgeschlagene Ansatz in einem Bohrlochtestgebiet im Nordosten Italiens angewandt, wo Vs- und Qs-Werte aus unabhängigen geophysikalischen Bohrlochmessungen in der Literatur existieren. Anschließend erfolgt an einem zweiten Bohrlochstandort eine Bewertung der Übereinstimmung zwischen Vs und dem Faktor Qs, die mit dem neuartigen, auf SART basierenden Ansatz geschätzt wurden, und denselben Parametern, die aus der Analyse von schwachen Anregungen gewonnen wurden, die von im Bohrloch installierten Seismometern aufgezeichnet wurden. SART zeigt ein hohes Maß an Potenzial und bildet die Grundlage für zukünftige Fortschritte bei der robusten Schätzung von Qs
Perennial roots, lasting structure: how silphium perfoliatum alters pore structure to shape carbon storage and water flow
No full textPerennial cropping systems are increasingly recognized for their potential to enhance soil functions, particularly carbon sequestration and water regulation. However, the structural mechanisms driving these improvements remain poorly understood. In this study, we investigated how ten years of Silphium perfoliatum cultivation altered soil pore architecture compared to a conventionally tilled crop rotation, and how these structural changes affect two key soil functions: soil organic carbon (SOC) accrual and near-saturated water flow.
Using X-ray microtomography, we quantified the three-dimensional pore network across cropping systems, linking structural features to SOC and hydraulic measurements.
S. perfoliatum induced a fundamentally different pore architecture, dominated by small biopores and an organic-rich porous matrix, likely shaped by roots and soil fauna. This structure was closely linked to enhanced SOC accrual in S. perfoliatum, with root-derived particulate organic matter (POM) contributing to the formation of stabilized microsites. Water flow responses were equally distinct. Despite the positive influence of continuous biopores in S. perfoliatum on water flow, the hydraulic conductivity of the topsoil was reduced − likely due to partial blocking with roots and POM. Conversely, in the crop rotation, higher conductivity was associated with abundant small pores and matrix-dominated flow, despite less favorable biopore structure.
Overall, our findings confirm that long-term perennial management leads to the formation of a functionally distinct pore architecture that regulates both carbon storage and water transport. These results highlight the importance of pore structural context in shaping key soil functions and offer mechanistic insight into the long-term benefits of perennial cropping systems.TU Berlin, Open-Access-Mittel – 202
Port-Hamiltonian representations of positive real descriptor systems
No full textThe relationship between port-Hamiltonian and positive real linear time-invariant descriptor systems is investigated. It is well-known that port-Hamiltonian systems are positive real, but the converse implication does not always hold. In Cherifi et al. (2023) sufficient conditions for the converse are presented. We refine these conditions and present for a completely controllable, completely observable and positive real descriptor system a necessary and sufficient condition as well as an explicit method to compute a port-Hamiltonian representation of a general positive real linear time-invariant descriptor system.TU Berlin, Open-Access-Mittel – 202
Non-canonical self-assembly of surfactant/cosurfactant mixtures detected by combining the power of SANS and cryo-TEM
No full textHypothesis
Addition of cosurfactants to surfactant micelles is normally assumed to lead, via a continuous change of the packing parameter, to a transition of spherical micelles to elongated ones, then to wormlike viscoelastic micelles and finally, via a phase transition, to planar lamellae. However, this conventional structural sequence may be different, if surfactants with variable head group size and cosurfactants that favour strongly planar structures are employed.
Experiments
A phase study was done on solutions of the nonionic surfactant Tween-20 (Tw20) with increasing amounts of added cosurfactant 2-ethylhexyl glycerine (EHG). This study was supported by a detailed structural characterisation of the aqueous solutions as a function of added amount of EHG by a combination of small-angle neutron scattering (SANS) and cryo-TEM, which allows uniquely to assign the structures present.
Findings
We found that the initially present small Tw20 micelles become somewhat larger and more oblate with increasing EHG concentration. However, they do not form wormlike micelles, but instead these small oblate micelles arrange themselves into wormlike aggregates of individual micelles, which only show low viscosity. For higher EHG concentration, a two-phase region is found, above which still such wormlike aggregates of small micelles are still observed, which are in equilibrium with bilayer structures. Only at much higher EHG concentrations pure bilayer structures are formed. The latter effect is ascribed to the intrinsic molecular polydispersity of the surfactant head group. However, the overall assembly behaviour arises from having a surfactant that favours to have a highly curved interface, while the cosurfactant favours a rather flat structure.TU Berlin, Open-Access-Mittel – 202
Modeling injection-induced seismicity using a fully coupled poroviscoelasto-dynamic extended finite element approach with stabilized contact and rate-and-state friction
No full textInjection-induced seismicity is of concern for reservoir engineering applications, where fluid flow, in-situ stress, and fault mechanics jointly control fault reactivation. We present a novel two-dimensional, fully coupled poroviscoelasto-dynamic extended finite element (XFEM) model to simulate fault slip and seismicity under realistic injection scenarios. The porous medium is represented by a Kelvin–Voigt (KV) viscoelastic solid in order to allow simultaneous modelling of elastic deformation and intrinsic damping, while inertia effects are included for simulating rupture dynamics and seismic wave propagation. Fault contact is enforced using a Lagrange multiplier (LM) stabilized by the polynomial pressure projection (PPP) method, ensuring stable displacement–contact pressure coupling and preventing spurious oscillations. The fault frictional behavior is governed by a rate-and-state formalism, and the transition between interseismic and coseismic stages is controlled using a modified predictor–corrector algorithm. We additionally present the first implementation of a consistent tangent operator tailored for rate-and-state friction–governed slip, combined with a LM formulation for normal contact, which significantly enhances the convergence of the nonlinear solver. Moreover, a crack-tip enrichment method is employed together with Heaviside functions in the XFEM setting in order to accurately capture stress singularities and tip behavior. An adaptive time-stepping methodology adjusts the temporal resolution based on the solution’s dynamics, thus enabling an efficient and accurate modeling of slip events. The model is verified against benchmark tests and applied to a faulted reservoir, capturing nucleation, rupture propagation, weakening, and stress redistribution. Results confirm the model’s robustness, stability, and efficiency, providing a physically consistent and computationally efficient framework for advancing the mechanistic understanding of injection-induced seismicity in fractured geosystems.TU Berlin, Open-Access-Mittel – 202
Final report on the DFG project “Reduced order modelling of acoustical systems based on measurement data” for the funding period 2022-2025
No full textDas Forschungsvorhaben beschäftigte sich mit der Entwicklung und Validierung einer numerisch robusten Methode zur Identifizierung von reduzierten Zustandsraummodellen auf Basis von hochdimensionalen Messungen von Impulsantworten. Eine effiziente, nutzerfreundliche Implementierung des randomisierten Eigensystem-Realisierungsalgorithmus (ERA) wurde in der quelloffenen Softwarebibliothek pyMOR veröffentlicht und mit einem neuartigen randomisierten Fehlerschätzer versehen, sodass reduzierte Zustandsraummodelle von gewünschter Qualität einfach erstellt werden können. Zur Validierung der Methode wurden mehrere Benchmarkdatensätze erstellt und veröffentlicht. Zwei der Datensätze beinhalten Raumimpulsantworten von einer Quellebene zu einem planaren Mikrofonarray. Mit insgesamt über 3 Millionen Raumimpulsantworten sind diese Datensätze die mit Abstand größten dieser Art. Die untersuchte Methode konnte anhand der Benchmarkdatensätze erfolgreich für sehr große Datensätze validiert werden.
Auf Grundlage der Basismethode wurde eine Erweiterung für Systeme mit Totzeit implementiert. Mithilfe einer Extraktion der ausbreitungsbedingten Totzeit aus den Daten konnte dadurch die Modellqualität bei gleichbleibendem Rechenaufwand verbessert werden. Mit einer Unterteilung der Messdaten in einzelne Frequenzbänder und paralleler Anwendung der Methode kann so auch mit einer frequenzabhängigen Totzeit umgegangen werden, wie sie bei akustischen Systemen mit dispersiver Schallausbreitung vorkommt.
In einem weiteren Schritt wurde untersucht, wie die mit der Methode gewonnenen Modelle zur räumlichen Interpolation der Impulsantworten an nicht gemessenen Orten verwendet werden können. Hierzu wurden verschiedene Matrixinterpolationsmethoden untersucht und außerdem eine neuartige Methode zur rationalen Interpolation von SSM mit dem Loewner-framework vorgestellt. Es konnte beobachtet werden, dass eine Extraktion der Totzeit die Rekonstruktionsqualität des interpolierten Modells deutlich verbessern kann.The research project focused on the development and validation of a numerically robust method for identifying reduced order state space models based on high-dimensional measurements of impulse responses. An efficient, user-friendly implementation of the randomized Eigensysten Realization Algorithm (ERA) was published in the open-source software library pyMOR and equipped with a novel randomized error estimator, allowing reduced state space models of desired quality to be created easily. Several benchmark datasets were created and published to validate the method. Two of the datasets contain room impulse responses from a source plane to a planar microphone array. With a total of over 3 million room impulse responses, these datasets are by far the largest of their kind. The method investigated was successfully validated for very large datasets using the benchmark datasets.
Based on the baseline method, an extension for systems with dead time was implemented. By extracting the propagation-related dead time from the data, the model quality could be improved while maintaining the same computational effort. By dividing the measurement data into individual frequency bands and applying the method in parallel, it is also possible to deal with frequency-dependent dead time, as occurs in acoustic systems with dispersive sound propagation.
In a further step, we investigated how the models obtained using this method can be used for spatial interpolation of impulse responses at unmeasured locations. To this end, we examined various matrix interpolation methods and also presented a novel method for rational interpolation of SSM using the Loewner framework. It was observed that extracting the dead time can significantly improve the reconstruction quality of the interpolated model.DFG, 504367810, Reduzierte Modellierung akustischer Systeme auf der Basis von Messdate