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Multi-Input data ASsembly for joint Analysis (MIASA): A framework for the joint analysis of disjoint sets of variables
No full textBranch and cut for partitioning a graph into a cycle of clusters
No full textIn this paper we study formulations and algorithms for the cycle clustering problem, a partitioning problem over the vertex set of a directed graph with nonnegative arc weights that is used to identify cyclic behavior in simulation data generated from nonreversible Markov state models. Here, in addition to partitioning the vertices into a set of coherent clusters, the resulting clusters must be ordered into a cycle such as to maximize the total net flow in the forward direction of the cycle. We provide a problem-specific binary programming formulation and compare it to a formulation based on the reformulation-linearization technique (RLT). We present theoretical results on the polytope associated with our custom formulation and develop primal heuristics and separation routines for both formulations. In computational experiments on simulation data from biology we find that branch and cut based on the problem-specific formulation outperforms the one based on RLT
CoDA: Interactive Segmentation and Morphological Analysis of Dendroid Structures Exemplified on Stony Cold-Water Corals
No full textDendroid stony corals build highly complex colonies that develop from a single coral polyp sitting in a cup-like skeleton, called corallite, by asexual reproduction, resulting in a tree-like branching pattern of its skeleton. Despite their beauty and ecological importance as reef builders in tropical shallow-water reefs as well as in cold-water coral mounds in the deep ocean, systematic studies investigating the ontogenetic morphological development of such coral colonies are largely missing. One reason for this is the sheer number of corallites – up to several thousands in a single coral colony. Another limiting factor, especially for the analysis of dendroid cold-water corals, is the existence of many secondary joints in the ideally tree-like structure that make a reconstruction of the skeleton tree extremely tedious.
Herein, we present CoDA, the Coral Dendroid structure Analyzer, a visual analytics suite that allows for the first time to investigate the ontogenetic morphological development of complex dendroid coral colonies, exemplified on three important framework-forming dendroid cold-water corals: Lophelia pertusa (Linnaeus, 1758), Madrepora oculata (Linnaeus, 1758), and Goniocorella dumosa (Alcock, 1902). Input to CoDA is an initial instance segmentation of the coral polyp cavities (calices), from which it estimates the skeleton tree of the colony and extracts classical morphological measurements and advanced shape features of the individual corallites. CoDA also works as a proofreading and error correction tool by helping to identify wrong parts in the skeleton tree and providing tools to quickly correct these errors. The final skeleton tree enables the derivation of additional information about the calices/corallite instances that otherwise could not be obtained, including their ontogenetic generation and branching patterns – the basis of a fully quantitative statistical analysis of the coral colony morphology. Part of CoDA is CoDA.Graph, a feature-rich link-and-brush user interface for visualizing the extracted features and 2D graph layouts of the skeleton tree, enabling the real-time exploration of complex coral colonies and their building blocks, the individual corallites and branches.
In the future, we expect CoDA to greatly facilitate the analysis of large stony corals of different species and morphotypes, as well as other dendroid structures, enabling new insights into the influence of genetic and environmental factors on their ontogenetic morphological development
Dynamical Measure Transport and Neural PDE Solvers for Sampling
No full textThe task of sampling from a probability density can be approached as transporting a tractable density function to the target, known as dynamical measure transport. In this work, we tackle it through a principled unified framework using deterministic or stochastic evolutions described by partial differential equations (PDEs). This framework incorporates prior trajectory-based sampling methods, such as diffusion models or Schrödinger bridges, without relying on the concept of time-reversals. Moreover, it allows us to propose novel numerical methods for solving the transport task and thus sampling from complicated targets without the need for the normalization constant or data samples. We employ physics-informed neural networks (PINNs) to approximate the respective PDE solutions, implying both conceptional and computational advantages. In particular, PINNs allow for simulation- and discretization-free optimization and can be trained very efficiently, leading to significantly better mode coverage in the sampling task compared to alternative methods. Moreover, they can readily be fine-tuned with Gauss-Newton methods to achieve high accuracy in sampling
Understanding the Origins of Life - A Machine learning approach to estimate reaction mechanisms of biotic precursors
No full textLife as we know it is the result of billions of years of evolution; yet, understanding how the very first organisms came into existence is a challenge that has yet to be solved. One theory states that components of the first biotic molecules may not have formed on Earth. Rather, they may have initially formed in the interstellar medium (ISM) and been transported to Earth, as supported by recorded instances of organic molecules detected in space. The ISM, with its low temperatures and specific collision processes, allows for molecular stability and the formation of biotic precursors that would otherwise be unlikely in Earth's prebiotic conditions. Understanding how these molecules formed in the ISM may be the key to determining how life began.
The goal of this research is to develop a new model for solving astrobiophysical problems by studying the formation mechanisms of biomolecules found in the ISM. Although such pathways have been studied individually, there has not yet been a comprehensive method to understand all the formation reactions that can occur in ISM. Several quantum chemical and numerical methods are available for finding transition states (TS) and energy barriers (E) of chemical reactions but are time-consuming and can hardly be applied to systems with more than a few atoms. Our main interest is to develop a a machine learning approach to approximate TS, and E, requiring as input only estimates of geometry and energies of reactants and products. Using a complete dataset 300 reaction features are computed, and an estimate of E is obtained by fitting a Kernel Ridge Regression (KRR) model with Laplacian kernel, and a fully connected Artificial Neural Network (ANN) to estimate reaction energy barriers
Modelling altered signalling of G-protein coupled receptors in inflamed environment to advance drug design
No full textWe previously reported the successful design, synthesis and testing of the prototype opioid painkiller NFEPP that does not elicit adverse side effects. The design process of NFEPP was based on mathematical modelling of extracellular interactions between G-protein coupled receptors (GPCRs) and ligands, recognizing that GPCRs function differently under pathological versus healthy conditions. We now present an additional and novel stochastic model of GPCR function that includes intracellular dissociation of G-protein subunits and modulation of plasma membrane calcium channels and their dependence on parameters of inflamed and healthy tissue (pH, radicals). The model is validated against in vitro experimental data for the ligands NFEPP and fentanyl at different pH values and radical concentrations. We observe markedly reduced binding affinity and calcium channel inhibition for NFEPP at normal pH compared to lower pH, in contrast to the effect of fentanyl. For increasing radical concentrations, we find enhanced constitutive G-protein activation but reduced ligand binding affinity. Assessing the different effects, the results suggest that, compared to radicals, low pH is a more important determinant of overall GPCR function in an inflamed environment. Future drug design efforts should take this into account
Function spaces, time derivatives and compactness for evolving families of Banach spaces with applications to PDEs
No full textWe develop a functional framework suitable for the treatment of partial differential equations and variational problems posed on evolving families of Banach spaces. We propose a definition for the weak time derivative which does not rely on the availability of an inner product or Hilbertian structure and explore conditions under which the spaces of weakly differentiable functions (with values in an evolving Banach space) relate to the classical Sobolev--Bochner spaces. An Aubin--Lions compactness result in this setting is also proved. We then analyse several concrete examples of function spaces over time-evolving spatial domains and hypersurfaces for which we explicitly provide the definition of the time derivative and verify isomorphism properties with the aforementioned Sobolev--Bochner spaces. We conclude with the formulation and proof of well posedness for a class of nonlinear monotone problems on an abstract evolving space (generalising in particular the evolutionary p-Laplace equation on a moving domain or surface) and identify some additional evolutionary problems that can be appropriately formulated with the abstract setting developed in this work
Sampling-Dependent Transition Paths of Iceland-Scotland Overflow Water
No full textIn this note, we apply Transition Path Theory (TPT) from Markov chains to shed light on the problem of Iceland-Scotland Overflow Water (ISOW) equatorward export. A recent analysis of observed trajectories of submerged floats demanded revision of the traditional abyssal circulation theory, which postulates that ISOW should steadily flow along a deep boundary current (DBC) around the subpolar North Atlantic prior to exiting it. The TPT analyses carried out here allow to focus the attention on the portions of flow from the origin of ISOW to the region where ISOW exits the subpolar North Atlantic and suggest that insufficient sampling may be biasing the aforementioned demand. The analyses, appropriately adapted to represent a continuous input of ISOW, are carried out on three time-homogeneous Markov chains modeling the ISOW flow. One is constructed using a high number of simulated trajectories homogeneously covering the flow domain. The other two use much fewer trajectories which heterogeneously cover the domain. The trajectories in the latter two chains are observed trajectories or simulated trajectories subsampled at the observed frequency. While the densely sampled chain supports a well-defined DBC, the more heterogeneously sampled chains do not, irrespective of whether observed or simulated trajectories are used. Studying the sampling sensitivity of the Markov chains, we can give recommendations for enlarging the existing float dataset to improve the significance of conclusions about time-asymptotic aspects of the ISOW circulation
Approximating the RSRP with Predictive Maintenance
No full textWe study the solution of the rolling stock rotation problem with predictive maintenance (RSRP-PM) by an iterative refinement approach that is based on a state-expanded event-graph. In this graph, the states are parameters of a failure distribution, and paths correspond to vehicle rotations with associated health state approximations. An optimal set of paths including maintenance can be computed by solving an integer linear program. Afterwards, the graph is refined and the procedure repeated. An associated linear program gives rise to a lower bound that can be used to determine the solution quality. Computational results for two instances derived from real world timetables of a German railway company are presented. The results show the effectiveness of the approach and the quality of the solutions
Rate-limiting recovery processes in neurotransmission under sustained stimulation
No full textAt chemical synapses, an arriving electric signal induces the fusion of vesicles with the presynaptic membrane, thereby releasing neurotransmitters into the synaptic cleft. After a fusion event, both the release site and the vesicle undergo a recovery process before becoming available for reuse again. Of central interest is the question which of the two restoration steps acts as the limiting factor during neurotrans-mission under high-frequency sustained stimulation. In order to investigate this question, we introduce a novel non-linear reaction network which involves explicit recovery steps for both the vesicles and the release sites, and includes the induced time-dependent output current. The associated reaction dynamics are formulated by means of ordinary differential equations (ODEs), as well as via the associated stochastic jump process. While the stochastic jump model describes a single release site, the average over many release sites is close to the ODE solution and shares its periodic structure. The reason for this can be traced back to the insight that recovery dynamics of vesicles and release sites are statistically almost independent. A sensitivity analysis on the recovery rates based on the ODE formulation reveals that neither the vesicle nor the release site recovery step can be identified as the essential rate-limiting step but that the rate- limiting feature changes over the course of stimulation. Under sustained stimulation the dynamics given by the ODEs exhibit transient dynamics leading from an initial depression of the postsynaptic response to an asymptotic periodic orbit, while the individual trajectories of the stochastic jump model lack the oscillatory behavior an asymptotic periodicity of the ODE-solution