Miracle-dz/UniFAR-FTUs huggingface dataset:
Adaptive Voronoi-based Column Selection Methods for Interpretable Dimensionality Reduction

In data analysis, there continues to be a need for interpretable dimensionality reduction methods whereby instrinic meaning associated with the data is retained in the reduced space. Standard approaches such as Principal Component Analysis (PCA) and the Singular Value Decomposition (SVD) fail at this task. A popular alternative is the CUR decomposition. In an SVD-like manner, the CUR decomposition approximates a matrix $A \in \mathbb{R}^{m \times n}$ as $A \approx CUR$, where $C$ and $R$ are matrices whose columns and rows are selected from the original matrix \cite{goreinov1997theory}, \cite{mahoney2009cur}. The difficulty in constructing a CUR decomposition is in determining which columns and rows to select when forming $C$ and $R$. Current column/row selection algorithms, particularly those that rely on an SVD, become infeasible as the size of the data becomes large \cite{dong2021simpler}. We address this problem by reducing the column/row selection problem to a collection of smaller sub-problems. The basic idea is to first partition the rows/columns of a matrix, and then apply an existing selection algorithm on each piece; for illustration purposes we use the Discrete Empirical Interpolation Method (\textsf{DEIM}) \cite{sorensen2016deim}. For the first task, we consider two existing algorithms that construct a Voronoi Tessellation (VT) of the rows and columns of a given matrix. We then extend these methods to automatically adapt to the data. The result is four data-driven row/column selection methods that are well-suited for parallelization, and compatible with nearly any existing column/row selection strategy. Theory and numerical examples show the design to be competitive with the original \textsf{DEIM} routine.
Cost-Efficient and Storm Surge-sensitive Bridge Design for Coastal Maine

Climatic variation felt through changing weather patterns is having increasingly acute effects on Maine’s transportation infrastructure. Acute risk occurs as a result of events, such as storms and flooding, while chronic risk surrounds longer range changes due to climate over time. It is acute risk that results in an increased need for disaster designation and response, increased risk of collateral property damage, and threats to safety of the traveling public. This type of risk can be mitigated by early preparation. Because of uncertainty about the future of climate and weather variability, chronic risk is much harder to gauge. This uncertainty can create paralysis in an agency charged with making and justifying long-term, fiscally-responsible decisions around the safety and efficiency of public travel. But long life cycles of most transportation infrastructure demand adaptation via early preparation to protect significant taxpayer investments into the reasonably foreseeable future. This research effort builds on cost modeling developed to estimate fiscal impacts of related state legislation and develops an approach to estimate acute and chronic cost/risk tradeoffs for a subset of transportation project needs along the Maine coast. The general goal is to address cost and risk issues associated with projected sea level rise (SLR) and threats to state infrastructure elements that are also designed to pass freshwater streams and rivers. More specifically, this project aims to help develop storm surge-sensitive design standards and approaches for large, tidally influenced transportation structures along the Maine coast. For each of the two major tidal regimes along the coast, the project aims to 1) obtain and analyze surge frequency from an existing tide gauge; 2) obtain and analyze flood flows from the corresponding stream flow gauge at the site (if none available, use regional hydrologic analysis to develop) and develop a joint probability distribution with coastal storm surges; 3) focus on one type of structure (bridges); and 4) identify installation costs versus damage risk-tradeoffs under different SLR, storm surge, and river flood scenarios extending out over the useful life of the asset.
Dimension of equilibrium measures for complex maps

For certain families of complex maps, we give a formula for the Hausdorff dimension of the equilibrium measure. In particular, given an endomorphism $f$ of $\mathbb C\mathbb P^k$ of algebraic degree $d \ge2$, and given the equilibrium measure $\mu$ with Lyapunov exponents $\chi_1\geq \ldots\geq \chi_k$, we show $\dim_\mathrm{H}(\mu) = \log d\sum_{i\leq k}\frac{1}{\chi_i}$ where $\dim_\mathrm{H}(\mu)$ is the Hausdorff dimension of the measure $\mu$. This gives an answer to the question of Forn{\ae}ss and Sibony, and proves the Binder-DeMarco Conjecture.
NavFormer: A Transformer Architecture for Robot Target-Driven Navigation in Unknown and Dynamic Environments

In unknown cluttered and dynamic environments such as disaster scenes, mobile robots need to perform target-driven navigation in order to find people or objects of interest, while being solely guided by images of the targets. In this paper, we introduce NavFormer, a novel end-to-end transformer architecture developed for robot target-driven navigation in unknown and dynamic environments. NavFormer leverages the strengths of both 1) transformers for sequential data processing and 2) self-supervised learning (SSL) for visual representation to reason about spatial layouts and to perform collision-avoidance in dynamic settings. The architecture uniquely combines dual-visual encoders consisting of a static encoder for extracting invariant environment features for spatial reasoning, and a general encoder for dynamic obstacle avoidance. The primary robot navigation task is decomposed into two sub-tasks for training: single robot exploration and multi-robot collision avoidance. We perform cross-task training to enable the transfer of learned skills to the complex primary navigation task without the need for task-specific fine-tuning. Simulated experiments demonstrate that NavFormer can effectively navigate a mobile robot in diverse unknown environments, outperforming existing state-of-the-art methods in terms of success rate and success weighted by (normalized inverse) path length. Furthermore, a comprehensive ablation study is performed to evaluate the impact of the main design choices of the structure and training of NavFormer, further validating their effectiveness in the overall system.
Roots of Alexander polynomials of random positive 3-braids

Motivated by an observation of Dehornoy, we study the roots of Alexander polynomials of knots and links that are closures of positive 3-strand braids. We give experimental data on random such braids and find that the roots exhibit marked patterns, which we refine into precise conjectures. We then prove several results along those lines, for example that generically at least 69% of the roots are on the unit circle, which appears to be sharp. We also show there is a large root-free region near the origin. We further study the equidistribution properties of such roots by introducing a Lyapunov exponent of the Burau representation of random positive braids, and a corresponding bifurcation measure. In the spirit of Deroin and Dujardin, we conjecture that the bifurcation measure gives the limiting measure for such roots, and prove this on a region with positive limiting mass. We use tools including work of Gambaudo and Ghys on the signature function of links, for which we prove a central limit theorem.
The Implicit Bias of Gradient Noise: A Symmetry Perspective

We characterize the learning dynamics of stochastic gradient descent (SGD) when continuous symmetry exists in the loss function, where the divergence between SGD and gradient descent is dramatic. We show that depending on how the symmetry affects the learning dynamics, we can divide a family of symmetry into two classes. For one class of symmetry, SGD naturally converges to solutions that have a balanced and aligned gradient noise. For the other class of symmetry, SGD will almost always diverge. Then, we show that our result remains applicable and can help us understand the training dynamics even when the symmetry is not present in the loss function. Our main result is universal in the sense that it only depends on the existence of the symmetry and is independent of the details of the loss function. We demonstrate that the proposed theory offers an explanation of progressive sharpening and flattening and can be applied to common practical problems such as representation normalization, matrix factorization, and the use of warmup.
The Relevance Feature and Vector Machine for health applications

This paper presents the Relevance Feature and Vector Machine (RFVM), a novel model that addresses the challenges of the fat-data problem when dealing with clinical prospective studies. The fat-data problem refers to the limitations of Machine Learning (ML) algorithms when working with databases in which the number of features is much larger than the number of samples (a common scenario in certain medical fields). To overcome such limitations, the RFVM incorporates different characteristics: (1) A Bayesian formulation which enables the model to infer its parameters without overfitting thanks to the Bayesian model averaging. (2) A joint optimisation that overcomes the limitations arising from the fat-data characteristic by simultaneously including the variables that define the primal space (features) and those that define the dual space (observations). (3) An integrated prunning that removes the irrelevant features and samples during the training iterative optimization. Also, this last point turns out crucial when performing medical prospective studies, enabling researchers to exclude unnecessary medical tests, reducing costs and inconvenience for patients, and identifying the critical patients/subjects that characterize the disorder and, subsequently, optimize the patient recruitment process that leads to a balanced cohort. The model capabilities are tested against state-of-the-art models in several medical datasets with fat-data problems. These experimental works show that RFVM is capable of achieving competitive classification accuracies while providing the most compact subset of data (in both terms of features and samples). Moreover, the selected features (medical tests) seem to be aligned with the existing medical literature.
Adapting to loss: A normative account of grief

Grief is a reaction to loss that is observed across human cultures and even in other species. While the particular expressions of grief vary significantly, universal aspects include experiences of emotional pain and frequent remembering of what was lost. Despite its prevalence, and its obvious nature, the normative value of grief is puzzling: Why do we grieve? Why is it painful? And why is it sometimes prolonged enough to be clinically impairing? Using the framework of reinforcement learning with memory replay, we offer answers to these questions and suggest that grief may have normative value with respect to reward maximization.
Old, broad-leaved stands support both high biodiversity and carbon storage in German forests

Ecosystems worldwide face threats related to human-driven degradation, climate change, and biodiversity loss. Addressing these challenges requires management strategies that combine biodiversity conservation with climate change mitigation. Here, we aimed to identify local-scale management actions that promote biodiversity at multiple trophic levels while also promoting carbon storage and sequestration. We combined data on the diversity of nine taxonomic groups (plants, birds, moths, Mollusca, soil fungi, active soil bacteria, Cercozoan and Endomyxan soil protists, Oomycotan soil protists, and nematodes), with above- and belowground carbon storage in 150 temperate forest plots in three regions of Germany. These were dominated by European beech, pine, spruce and oak. We investigated the relationships between multiple forest structure and management variables, biodiversity and carbon storage and sequestration in forest plots with different management types. Carbon storage was 32% higher in uneven-aged than even-aged forests and increased with mean tree diameter, while carbon sequestration in trees was 15% higher in even-aged than uneven-aged stands. Mean tree diameter was positively related to overall biodiversity, especially bird species richness and the richness of forest specialist birds. Oak and beech-dominated stands harboured higher biodiversity than stands dominated by conifers (especially Pine). One exception to this was the richness of plant species and forest specialist plants, which were highest in spruce plantations. Surprisingly, deadwood input did not significantly affect the diversity of any taxonomic group in this study. By showing that older forests with a high proportion of uneven-aged broad-leafed trees, or oak-dominated forests, can promote both biodiversity and carbon storage, our results could help inform sustainable local-scale forest management in Central Europe that promotes both biodiversity conservation and carbon storage. These findings can form the basis of further larger-scale studies investigating such relations at larger spatial scales to inform landscape-level recommendations for sustainable multifunctional forest management.
Gene regulatory network landscape of Group 3/4 medulloblastoma

Resolving the molecular mechanisms driving childhood brain tumors will uncover tumor-specific vulnerabilities and advance mechanism-of-action-based therapies. Here we describe a continuum of cell-states in Group 3/4 medulloblastomas, the most frequent and fatal cerebellar embryonal tumor subgroups, based on the differential activity of transcription-factor-driven gene networks derived using a comprehensive single-nucleus multi-omic medulloblastoma atlas. We show that Group 3/4 tumor diversity stems from enriched cell-states along four molecular identity axes: photoreceptor, MYC, precursor, and unipolar brush cell-like. We identified a potential role of PAX6 in driving dual Group 3- and Group 4-like tumor trajectories in subtype VII tumors. Our study demonstrates how oncogenic events together with lineage determinants drive Group 3/4 tumor identity away from their original source in the cerebellar unipolar brush cell lineage.
An integrated biogeographic assessment of reef fish populations and fisheries in Dry Tortugas : effects of no-take reserves

The Tortugas Integrated Biogeographic Assessment presents a unique analysis of demographic changes in living resource populations, as well as societal and socioeconomic benefits that resulted from the Tortugas Ecological Reserves during the first five years after their implementation. In 2001, state and federal agencies established two no-take reserves within the region as part of the Florida Keys National Marine Sanctuary. The northern reserve (Tortugas Ecological Reserve North) was established adjacent to the Dry Tortugas National Park, which was first declared a national monument in 1935. The reserves were designed to protect a healthy coral reef ecosystem that supports diverse faunal assemblages and fisheries, serves as important spawning grounds for groupers and snappers, and includes essential feeding and breeding habitats for seabirds. The unique ecological qualities of the Tortugas region were recognized as far back as 1850, and it remains an important ecosystem and research area today. The two main goals of the Tortugas Ecological Reserve Integrated Ecological Assessment were: 1) to determine if demographic changes such as increases in abundance, average size and spawning potential of exploited populations occurred in the Tortugas region after reserve implementation; and 2) whether short-term economic losses occurred to fishers displaced by the reserve. This project utilized a biogeographic approach in which information on the physical features (i.e., habitat) and oceanographic patterns were first used to determine the spatial distribution of selected fish populations within and outside the Tortugas Ecological Reserve. Before-and-after reserve implementation comparisons of selected fish populations were then conducted to determine if demographic changes occurred in reef fish assemblages. These comparisons were done for the Tortugas region and also for a subset of available habitats within the Tortugas Ecological Reserve Study Area. Social and economic impacts of the reserves were determined through: 1) analyses of commercial landings and revenues from fishers, operating in the Tortugas region before and after reserve implementation and 2) surveys of recreational tour guides. Analyses of the commercial landings and revenues excluded areas inside Dry Tortugas National Park because commercial fishing has been prohibited within park boundaries since 1992. Key findings and outcomes of this integrated ecological assessment are organized by chapter and listed below.
An iPSC-derived bio-inspired scaffold modelling the structure and the effects of extracellular matrix in cardiac fibrosis

Cardiac fibrosis occurs following insults to the myocardium and is characterized by the abnormal accumulation of non-compliant extracellular matrix (ECM), which compromises cardiomyocyte contractile activity and eventually leads to heart failure. This phenomenon is driven by the differentiation of cardiac fibroblasts (cFbs) into myofibroblasts and results in changes in ECM biochemical, structural and mechanical properties. The lack of predictive in vitro models of heart fibrosis has so far hampered the search for innovative treatments. Here, we devised a single-step decellularization protocol to obtain and thoroughly characterize the biochemical and micro-mechanical properties of the ECM secreted by activated cFbs differentiated from human induced pluripotent stem cells (iPSCs). We activated iPSC-derived cFbs to the myofibroblast phenotype by tuning basic fibroblast growth factor (bFGF) and transforming growth factor beta 1 (TGF-β1) signalling and confirmed that activated cells acquired key features of myofibroblast phenotype, like SMAD2/3 nuclear shuttling, the formation of aligned alpha-smooth muscle actin (α−SMA)-rich stress fibres and increased focal adhesions (FAs) assembly. Next, we used Mass Spectrometry, nanoindentation, scanning electron and confocal microscopy to unveil the characteristic composition and the visco-elastic properties of the abundant, collagen-rich ECM deposited by cardiac myofibroblasts in vitro. Finally, we demonstrated that the fibrotic ECM activates mechanosensitive pathways in iPSC-derived cardiomyocytes, impacting on their shape, sarcomere alignment, phenotype, and calcium handling properties. We thus propose human bio-inspired decellularized matrices as animal-free, isogenic cardiomyocyte culture substrates recapitulating key pathophysiological changes occurring at the cellular level during cardiac fibrosis.
Interpretable Drug Response Prediction through Molecule Structure-aware and Knowledge-Guided Visible Neural Network

Precise prediction of anti-cancer drug responses has become a crucial obstruction in anti-cancer drug design and clinical applications. In recent years, various deep learning methods have been applied to drug response prediction and become more accurate. However, they are still criticized as being non-transparent. To offer reliable drug response prediction in real-world applications, there is still a pressing demand to develop a model with high predictive performance as well as interpretability. In this study, we propose DrugVNN, an end-to-end interpretable drug response prediction framework, which extracts gene features of cell lines through a knowledge-guided visible neural network (VNN), and learns drug representation through a node-edge communicative message passing network (CMPNN). Additionally, between these two networks, a novel drug-aware gene attention gate is designed to direct the drug representation to VNN to simulate the effects of drugs. By evaluating on the GDSC dataset, DrugVNN achieved state-of-the-art performance. Moreover, DrugVNN can identify active genes and relevant signaling pathways for specific drug-cell line pairs with supporting evidence in the literature, implying the interpretability of our model.
Structures of the Foamy virus fusion protein reveal an unexpected link with the F protein of paramyxo- and pneumoviruses

Foamy viruses (FVs) constitute a subfamily of retroviruses. Their envelope glycoprotein (Env) drives the merger of viral and cellular membranes during entry into cells. The only available structures of retroviral Envs are those from human and simian immunodeficiency viruses from the subfamily of orthoretroviruses, which are only distantly related to the FVs. We report here the cryo-EM structures of the FV Env ectodomain in the pre- and post-fusion states, which demonstrate structural similarity with the fusion protein (F) of paramyxo- and pneumoviruses, implying an evolutionary link between the two viral fusogens. Based on the structural information on the FV Env in two states, we propose a mechanistic model for its conformational change, highlighting how the interplay of its structural elements could drive the structural rearrangement. The structural knowledge on the FV Env now provides a framework for functional investigations such as the FV cell tropism and molecular features controlling the Env fusogenicity, which can benefit the design of FV Env variants with improved features for use as gene therapy vectors.
Multi-model investigations of the biogeophysical effects of historical and future land-cover changes on climate

Vegetation plays an important role in the climate system by determining the biogeophysical properties of the land surface, such as its albedo, emissivity, evapotranspiration rate and roughness length. Since these properties depend on the plant type, their modifications through human-induced land-cover changes (LCC) affect the surface energy budget and the water cycle, and can therefore lead to changes in climate conditions. However, some questions are still unresolved regarding the overall biogeophysical effect of LCC on climate, due to the many mechanisms at play and their geographically-varying nature. This explains for example the high uncertainties regarding the climatic effect of the expansion of agricultural areas which occurred at the expense of forests over the northern mid-latitudes during the industrial period, or of the deforestation that is projected to occur in the future over tropical areas, especially in the Amazon Basin. The aim of this thesis is thus to reduce these uncertainties. To achieve this goal, I primarily base my analyses on simulations run by recent climate models, which include state-of-the-art land surface models representing the energy and water fluxes at the land-atmosphere interface. Emphasis is put on comparing the results from multiple models, so as to assess the robustness of their overall conclusions. Moreover, I also confront these model findings with observational evidence of the effect of deforestation on climate in order to identify their most realistic aspects. In Chapters 2 and 3 of this thesis, I look at how the LCC that have occurred during the industrial period over the northern mid-latitudes (mainly North America, northern Eurasia and South Asia) have locally modified surface air temperature. To do so, I adapt a recently introduced statistical method which aims to extract the climate impact from the LCC forcing in simulations where other climate forcings are also imposed. In Chapter 2, I first demonstrate the suitability of this reconstruction method to study the local impacts of LCC on albedo, the latent heat flux and surface air temper-