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Project WEAR: Developing a methodological framework for functional analysis on stone tools through controlled experiments and computational modelling of shape transformations through use
No full textThe WEAR project is developing an integrative methodology to analyse and predict use-related shape transformation of Neolithic stone axes from Central Europe with mathematical methods and experimental archaeology
Similarity-based fuzzy clustering scientific articles: potentials and challenges from mathematical and computational perspectives
No full textFuzzy clustering, which allows an article to belong to multiple clusters with soft membership degrees, plays a vital role in analyzing publication data. This problem can be formulated as a constrained optimization model, where the goal is to minimize the discrepancy between the similarity observed from data and the similarity derived from a predicted distribution. While this approach benefits from leveraging state-of-the-art optimization algorithms, tailoring them to work with real, massive databases like OpenAlex or Web of Science - containing about 70 million articles and a billion citations - poses significant challenges. We analyze potentials and challenges of the approach from both mathematical and computational perspectives. Among other things, second-order optimality conditions are established, providing new theoretical insights, and practical solution methods are proposed by exploiting the structure of the problem. Specifically, we accelerate the gradient projection method using GPU-based parallel computing to efficiently handle large-scale data
Data-driven Reduction of Transfer Operators for Particle Clustering Dynamics
No full textWe develop an operator-based framework to coarse-grain interacting particle systems that exhibit clustering dynamics. Starting from the particle-based transfer operator, we first construct a sequence of reduced representations: the operator is projected onto concentrations and then further reduced by representing the concentration dynamics on a geometric low-dimensional manifold and an adapted finite-state discretization. The resulting coarse-grained transfer operator is finally estimated from dynamical simulation data by inferring the transition probabilities between the Markov states. Applied to systems with multichromatic and Morse interaction potentials, the reduced model reproduces key features of the clustering process, including transitions between cluster configurations and the emergence of metastable states. Spectral analysis and transition-path analysis of the estimated operator reveal implied time scales and dominant transition pathways, providing an interpretable and efficient description of particle-clustering dynamics
Novel image registration approach for combining 2D Osterix and collagen bundles images with 3D µCT
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Importance sampling of unbounded random stopping times: computing committor functions and exit rates without reweighting
No full textRare events in molecular dynamics are often related to noise-induced transitions between different macroscopic states (e.g., in protein folding). A common feature of these rare transitions is that they happen on timescales that are on average exponentially long compared to the characteristic timescale of the system, with waiting time distributions that have (sub)exponential tails and infinite support. As a result, sampling such rare events can lead to trajectories that can be become arbitrarily long, with not too low probability, which makes the reweighting of such trajectories a real challenge. Here, we discuss rare event simulation by importance sampling from a variational perspective, with a focus on applications in molecular dynamics, in particular the computation of committor functions. The idea is to design importance sampling schemes that (a) reduce the variance of a rare event estimator while controlling the average length of the trajectories and (b) that do not require the reweighting of possibly very long trajectories. In doing so, we study different stochastic control formulations for committor and mean first exit times, which we compare both from a theoretical and a computational point of view, including numerical studies of some benchmark examples
Correlative light and electron microscopy reveals the fine circuit structure underlying evidence accumulation in larval zebrafish
No full textAccumulating information is a critical component of most circuit computations in the brain across species, yet its precise implementation at the synaptic level remains poorly understood. Dissecting such neural circuits in vertebrates requires precise knowledge of functional neural properties and the ability to directly correlate neural dynamics with the underlying wiring diagram in the same animal. Here we combine functional calcium imaging with ultrastructural circuit reconstruction, using a visual motion accumulation paradigm in larval zebrafish. Using connectomic analyses of functionally identified cells and computational modeling, we show that bilateral inhibition, disinhibition, and recurrent connectivity are prominent motifs for sensory accumulation within the anterior hindbrain. We also demonstrate that similar insights about the structure-function relationship within this circuit can be obtained through complementary methods involving cell-specific morphological labeling via photo-conversion of functionally identified neuronal response types. We used our unique ground truth datasets to train and test a novel classifier algorithm, allowing us to assign functional labels to neurons from morphological libraries where functional information is lacking. The resulting feature-rich library of neuronal identities and connectomes enabled us to constrain a biophysically realistic network model of the anterior hindbrain that can reproduce observed neuronal dynamics and make testable predictions for future experiments. Our work exemplifies the power of hypothesis-driven electron microscopy paired with functional recordings to gain mechanistic insights into signal processing and provides a framework for dissecting neural computations across vertebrates
Reconstructing Ambient Temperature in Forensic Death Time Estimation
No full textIn medicolegal practice, time since death is estimated to assess alibi for homicide cases. Ambient temperature TA has a strong impact on cooling and therefore on temperature based time since death estimation (TTDE). At many crimescenes the ambient temperature TA1 is lowered instantaneously from a start value TA0 to a value TA1 at a certain time t0 during investigations due to human intervention such as window or door opening or body transport. Usually TA0 and t0 are unknown to the investigators. In this paper we focus on reconstruction of the unknown parameters TA0 and t0.
Our approach is inspired by TTDE literature remarks of detecting said changes by measuring temperatures in closed compartments as e.g. cupboards or neighboring rooms of the crime scene, where TA0 could have been ‘preserved’ after t0. We aim to estimate t0 and TA0 from temperature measurements TZ(t) in closed compartments Z at times t > t0.
We got results even under the most trivial assumption of Newtonian cooling for boxes filled with air, with heaps of clothes or even with books in two different experimental scenarios. Two different parameter estimators, (t0^, TA0^) using a single quadruple temperature measurement in two boxes and (t0*, TA0*) on the basis of weighted averaging the results of a series of N quadruple measurements during cooling of the two boxes respectively, were tested.
Our results were partially appropriate for TTDE input. For example a sudden decline at time t0 from TA0 = 22.5°C to TA1 = 14°C of the ambient temperature in a climate chamber could be reconstructed at t = t0 + 95min with relative deviations ρt0^ = 27% and ρTA0^ = 19% of the estimators relative to t - t0 and TA0 – TA1 respectively, only based on N = 1 quadruple measurement with a span of Δt = 50min. In case of N = 200 quadruple measurements starting at t = t0 + 95min and ending at t = t0 + 295min we found for weighted mean estimators distinctively reduced relative deviations ρt0^ = 5% and ρTA0^ = 11% with the same quadruple span Δt = 50min.
Further research is necessary to guarantee applicability in routine case work. We will investigate more elaborate cooling models, estimation algorithms and evaluation localization