A Quest to Unravel the Metric Structure Behind Perturbed Networks

Graphs and network data are ubiquitous across a wide spectrum of scientific and application domains. Often in practice, an input graph can be considered as an observed snapshot of a (potentially continuous) hidden domain or process. Subsequent analysis, processing, and inferences are then performed on this observed graph. In this paper we advocate the perspective that an observed graph is often a noisy version of some discretized 1-skeleton of a hidden domain, and specifically we will consider the following natural network model: We assume that there is a true graph G^* which is a certain proximity graph for points sampled from a hidden domain X; while the observed graph G is an Erdos-Renyi type perturbed version of G^*. Our network model is related to, and slightly generalizes, the much-celebrated small-world network model originally proposed by Watts and Strogatz. However, the main question we aim to answer is orthogonal to the usual studies of network models (which often focuses on characterizing / predicting behaviors and properties of real-world networks). Specifically, we aim to recover the metric structure of G^* (which reflects that of the hidden space X as we will show) from the observed graph G. Our main result is that a simple filtering process based on the Jaccard index can recover this metric within a multiplicative factor of 2 under our network model. Our work makes one step towards the general question of inferring structure of a hidden space from its observed noisy graph representation. In addition, our results also provide a theoretical understanding for Jaccard-Index-based denoising approaches

Caenorhabditis elegans as a model system for studying drug induced mitochondrial toxicity

Today HIV-1 infection is recognized as a chronic disease with obligatory lifelong treatment to keep viral titers below detectable levels. The continuous intake of antiretroviral drugs however, leads to severe and even life-threatening side effects, supposedly by the deleterious impact of nucleoside-analogue type compounds on the functioning of the mitochondrial DNA polymerase. For detailed investigation of the yet partially understood underlying mechanisms, the availability of a versatile model system is crucial. We therefore set out to develop the use of Caenorhabditis elegansto study drug induced mitochondrial toxicity. Using a combination of molecular-biological and functional assays, combined with a quantitative analysis of mitochondrial network morphology, we conclude that anti-retroviral drugs with similar working mechanisms can be classified into distinct groups based on their effects on mitochondrial morphology and biochemistry. Additionally we show that mitochondrial toxicity of antiretroviral drugs cannot be exclusively attributed to interference with the mitochondrial DNA polymerase

Explainable AI models for predicting drop coalescence in microfluidics device

In the field of chemical engineering, understanding the dynamics and probability of drop coalescence is not just an academic pursuit, but a critical requirement for advancing process design by applying energy only where it is needed to build necessary interfacial structures, increasing efficiency towards Net Zero manufacture. This research applies machine learning predictive models to unravel the sophisticated relationships embedded in the experimental data on drop coalescence in a microfluidics device. Through the deployment of SHapley Additive exPlanations values, critical features relevant to coalescence processes are consistently identified. Comprehensive feature ablation tests further delineate the robustness and susceptibility of each model. Furthermore, the incorporation of Local Interpretable Model-agnostic Explanations for local interpretability offers an elucidative perspective, clarifying the intricate decision-making mechanisms inherent to each model’s predictions. As a result, this research provides the relative importance of the features for the outcome of drop interactions. It also underscores the pivotal role of model interpretability in reinforcing confidence in machine learning predictions of complex physical phenomena that are central to chemical engineering applications

Ligand-Specific c-Fos Expression Emerges from the Spatiotemporal Control of ErbB Network Dynamics

SummaryActivation of ErbB receptors by epidermal growth factor (EGF) or heregulin (HRG) determines distinct cell-fate decisions, although signals propagate through shared pathways. Using mathematical modeling and experimental approaches, we unravel how HRG and EGF generate distinct, all-or-none responses of the phosphorylated transcription factor c-Fos. In the cytosol, EGF induces transient and HRG induces sustained ERK activation. In the nucleus, however, ERK activity and c-fos mRNA expression are transient for both ligands. Knockdown of dual-specificity phosphatases extends HRG-stimulated nuclear ERK activation, but not c-fos mRNA expression, implying the existence of a HRG-induced repressor of c-fos transcription. Further experiments confirmed that this repressor is mainly induced by HRG, but not EGF, and requires new protein synthesis. We show how a spatially distributed, signaling-transcription cascade robustly discriminates between transient and sustained ERK activities at the c-Fos system level. The proposed control mechanisms are general and operate in different cell types, stimulated by various ligands

Pure states statistical mechanics: On its foundations and applications to quantum gravity

The project concerns the interplay among quantum mechanics, statistical mechanics and thermodynamics, in isolated quantum systems. The underlying goal is to improve our understanding of the concept of thermal equilibrium in quantum systems. First, I investigated the role played by observables and measurements in the emergence of thermal behaviour. This led to a new notion of thermal equilibrium which is specific for a given observable, rather than for the whole state of the system. The equilibrium picture that emerges is a generalization of statistical mechanics in which we are not interested in the state of the system but only in the outcome of the measurement process. I investigated how this picture relates to one of the most promising approaches for the emergence of thermal behaviour in isolated quantum systems: the Eigenstate Thermalization Hypothesis. Then, I applied the results to study some equilibrium properties of many-body localised systems. Despite the localization phenomenon, which prevents thermalization of subsystems, I was able to show that we can still use the predictions of statistical mechanics to describe the equilibrium of some observables. Moreover, the intuition developed in the process led me to propose an experimentally accessible way to unravel the interacting nature of many-body localised systems. Second, I exploited the "Concentration of Measure" phenomenon to study the macroscopic properties of the basis states of Loop Quantum Gravity. These techniques were previously used to explain why the thermal behaviour in quantum systems is such an ubiquitous phenomenon, at the macroscopic scale. I focused on the local properties, their thermodynamic behaviour and interplay with the semiclassical limit. This was motivated by the necessity to understand, from a quantum gravity perspective, how and why a classical horizon exhibits thermal properties.Comment: PhD Thesis - University of Oxford - Comments and questions are welcome and encouraged

Reconstruction of random geometric graphs: breaking the Ω(r) distortion barrier

Embedding graphs in a geographical or latent space, i.e. inferring locations for vertices in Euclidean space or on a smooth manifold or submanifold, is a common task in network analysis, statistical inference, and graph visualization. We consider the classic model of random geometric graphs where n points are scattered uniformly in a square of area n, and two points have an edge between them if and only if their Euclidean distance is less than r. The reconstruction problem then consists of inferring the vertex positions, up to the symmetries of the square, given only the adjacency matrix of the resulting graph. We give an algorithm that, if r = n α for any 0 < α < 1/2, with high probability reconstructs the vertex positions with a maximum error of O(n β ) where β = 1/2−(4/3)α, until α ≥ 3/8 where β = 0 and the error becomes O( √ log n). This improves over earlier results, which were unable to reconstruct with error less than r. Our method estimates Euclidean distances using a hybrid of graph distances and short-range estimates based on the number of common neighbors. We extend our results to the surface of the sphere in R 3 and to hypercubes in any constant fixed dimension.Josep Díaz: partially supported by PID-2020-112581GB-C21 (MOTION). Cristopher Moore: partially supported by National Science Foundation grant IIS-1838251.Peer ReviewedPostprint (published version

Sources of Gravitational Waves: Theory and Observations

Gravitational-wave astronomy will soon become a new tool for observing the Universe. Detecting and interpreting gravitational waves will require deep theoretical insights into astronomical sources. The past three decades have seen remarkable progress in analytical and numerical computations of the source dynamics, development of search algorithms and analysis of data from detectors with unprecedented sensitivity. This Chapter is devoted to examine the advances and future challenges in understanding the dynamics of binary and isolated compact-object systems, expected cosmological sources, their amplitudes and rates, and highlights of results from gravitational-wave observations. All of this is a testament to the readiness of the community to open a new window for observing the cosmos, a century after gravitational waves were first predicted by Albert Einstein