Conventional harvesting problems for natural resources often assume physiological homogeneity of the body length/weight among individuals. However, such assumptions generally are not valid in real-world problems, where heterogeneity plays an essential role in the planning of biological resource harvesting. Furthermore, it is difficult to observe heterogeneity directly from the available data. This paper presents a novel optimal control framework for the cost-efficient harvesting of biological resources for application in fisheries management. The heterogeneity is incorporated into the resource dynamics, which is the population dynamics in this case, through a probability density that can be distorted from the reality. Subsequently, the distortion, which is the model uncertainty, is penalized through a divergence, leading to a non-standard dynamic differential game wherein the Hamilton-Jacobi-Bellman-Isaacs (HJBI) equation has a unique nonlinear partial differential term. Here, the existence and uniqueness results of the HJBI equation are presented along with an explicit monotone finite difference method. Finally, the proposed optimal control is applied to a harvesting problem with recreationally, economically, and ecologically important fish species using collected field data.
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The forecasting and computation of the stability of chaotic systems from partial observations are tasks for which traditional equation-based methods may not be suitable. In this computational paper, we propose data-driven methods to (i) infer the dynamics of unobserved (hidden) chaotic variables (full-state reconstruction); (ii) time forecast the evolution of the full state; and (iii) infer the stability properties of the full state. The tasks are performed with long short-term memory (LSTM) networks, which are trained with observations (data) limited to only part of the state: (i) the low-to-high resolution LSTM (LH-LSTM), which takes partial observations as training input, and requires access to the full system state when computing the loss; and (ii) the physics-informed LSTM (PI-LSTM), which is designed to combine partial observations with the integral formulation of the dynamical system's evolution equations. First, we derive the Jacobian of the LSTMs. Second, we analyse a chaotic partial differential equation, the Kuramoto-Sivashinsky (KS), and the Lorenz-96 system. We show that the proposed networks can forecast the hidden variables, both time-accurately and statistically. The Lyapunov exponents and covariant Lyapunov vectors, which characterize the stability of the chaotic attractors, are correctly inferred from partial observations. Third, the PI-LSTM outperforms the LH-LSTM by successfully reconstructing the hidden chaotic dynamics when the input dimension is smaller or similar to the Kaplan-Yorke dimension of the attractor. This work opens new opportunities for reconstructing the full state, inferring hidden variables, and computing the stability of chaotic systems from partial data.
Quantification of behavior is critical in applications ranging from neuroscience, veterinary medicine and animal conservation efforts. A common key step for behavioral analysis is first extracting relevant keypoints on animals, known as pose estimation. However, reliable inference of poses currently requires domain knowledge and manual labeling effort to build supervised models. We present a series of technical innovations that enable a new method, collectively called SuperAnimal, to develop and deploy deep learning models that require zero additional human labels and model training. SuperAnimal allows video inference on over 45 species with only two global classes of animal pose models. If the models need fine-tuning, we show SuperAnimal models are 10$\times$ more data efficient and outperform prior transfer-learning-based approaches. Moreover, we provide an unsupervised video-adaptation method to refine keypoints in videos. We illustrate the utility of our model in behavioral classification in mice and gait analysis in horses. Collectively, this presents a data-efficient solution for animal pose estimation for downstream behavioral analysis.
Biohybrid systems in which robotic lures interact with animals have become compelling tools for probing and identifying the mechanisms underlying collective animal behavior. One key challenge lies in the transfer of social interaction models from simulations to reality, using robotics to validate the modeling hypotheses. This challenge arises in bridging what we term the "biomimicry gap", which is caused by imperfect robotic replicas, communication cues and physics constrains not incorporated in the simulations that may elicit unrealistic behavioral responses in animals. In this work, we used a biomimetic lure of a rummy-nose tetra fish (Hemigrammus rhodostomus) and a neural network (NN) model for generating biomimetic social interactions. Through experiments with a biohybrid pair comprising a fish and the robotic lure, a pair of real fish, and simulations of pairs of fish, we demonstrate that our biohybrid system generates high-fidelity social interactions mirroring those of genuine fish pairs. Our analyses highlight that: 1) the lure and NN maintain minimal deviation in real-world interactions compared to simulations and fish-only experiments, 2) our NN controls the robot efficiently in real-time, and 3) a comprehensive validation is crucial to bridge the biomimicry gap, ensuring realistic biohybrid systems.
Living organisms need to acquire both cognitive maps for learning the structure of the world and planning mechanisms able to deal with the challenges of navigating ambiguous environments. Although significant progress has been made in each of these areas independently, the best way to integrate them is an open research question. In this paper, we propose the integration of a statistical model of cognitive map formation within an active inference agent that supports planning under uncertainty. Specifically, we examine the clone-structured cognitive graph (CSCG) model of cognitive map formation and compare a naive clone graph agent with an active inference-driven clone graph agent, in three spatial navigation scenarios. Our findings demonstrate that while both agents are effective in simple scenarios, the active inference agent is more effective when planning in challenging scenarios, in which sensory observations provide ambiguous information about location.
We discuss applications of exact structures and relative homological algebra to the study of invariants of multiparameter persistence modules. This paper is mostly expository, but does contain a pair of novel results. Over finite posets, classical arguments about the relative projective modules of an exact structure make use of Auslander-Reiten theory. One of our results establishes a new adjunction which allows us to "lift" these arguments to certain infinite posets over which Auslander-Reiten theory is not available. We give several examples of this lifting, in particular highlighting the non-existence and existence of resolutions by upsets when working with finitely presentable representations of the plane and of the closure of the positive quadrant, respectively. We then restrict our attention to finite posets. In this setting, we discuss the relationship between the global dimension of an exact structure and the representation dimension of the incidence algebra of the poset. We conclude with our second novel contribution. This is an explicit description of the irreducible morphisms between relative projective modules for several exact structures which have appeared previously in the literature.
We propose a generalization of nonlinear stability of numerical one-step integrators to Riemannian manifolds in the spirit of Butcher's notion of B-stability. Taking inspiration from Simpson-Porco and Bullo, we introduce non-expansive systems on such manifolds and define B-stability of integrators. In this first exposition, we provide concrete results for a geodesic version of the Implicit Euler (GIE) scheme. We prove that the GIE method is B-stable on Riemannian manifolds with non-positive sectional curvature. We show through numerical examples that the GIE method is expansive when applied to a certain non-expansive vector field on the 2-sphere, and that the GIE method does not necessarily possess a unique solution for large enough step sizes. Finally, we derive a new improved global error estimate for general Lie group integrators.
The expected Euler characteristic (EEC) method is an integral-geometric method used to approximate the tail probability of the maximum of a random field on a manifold. Noting that the largest eigenvalue of a real-symmetric or Hermitian matrix is the maximum of the quadratic form of a unit vector, we provide EEC approximation formulas for the tail probability of the largest eigenvalue of orthogonally invariant random matrices of a large class. For this purpose, we propose a version of a skew-orthogonal polynomial by adding a side condition such that it is uniquely defined, and describe the EEC formulas in terms of the (skew-)orthogonal polynomials. In addition, for the classical random matrices (Gaussian, Wishart, and multivariate beta matrices), we analyze the limiting behavior of the EEC approximation as the matrix size goes to infinity under the so-called edge-asymptotic normalization. It is shown that the limit of the EEC formula approximates well the Tracy-Widom distributions in the upper tail area, as does the EEC formula when the matrix size is finite.
Matching is a popular nonparametric covariate adjustment strategy in empirical health services research. Matching helps construct two groups comparable in many baseline covariates but different in some key aspects under investigation. In health disparities research, it is desirable to understand the contributions of various modifiable factors, like income and insurance type, to the observed disparity in access to health services between different groups. To single out the contributions from the factors of interest, we propose a statistical matching methodology that constructs nested matched comparison groups from, for instance, White men, that resemble the target group, for instance, black men, in some selected covariates while remaining identical to the white men population before matching in the remaining covariates. Using the proposed method, we investigated the disparity gaps between white men and black men in the US in prostate-specific antigen (PSA) screening based on the 2020 Behavioral Risk Factor Surveillance System (BFRSS) database. We found a widening PSA screening rate as the white matched comparison group increasingly resembles the black men group and quantified the contribution of modifiable factors like socioeconomic status. Finally, we provide code that replicates the case study and a tutorial that enables users to design customized matched comparison groups satisfying multiple criteria.
The prediction of protein 3D structure from amino acid sequence is a computational grand challenge in biophysics, and plays a key role in robust protein structure prediction algorithms, from drug discovery to genome interpretation. The advent of AI models, such as AlphaFold, is revolutionizing applications that depend on robust protein structure prediction algorithms. To maximize the impact, and ease the usability, of these novel AI tools we introduce APACE, AlphaFold2 and advanced computing as a service, a novel computational framework that effectively handles this AI model and its TB-size database to conduct accelerated protein structure prediction analyses in modern supercomputing environments. We deployed APACE in the Delta supercomputer, and quantified its performance for accurate protein structure predictions using four exemplar proteins: 6AWO, 6OAN, 7MEZ, and 6D6U. Using up to 200 ensembles, distributed across 50 nodes in Delta, equivalent to 200 A100 NVIDIA GPUs, we found that APACE is up to two orders of magnitude faster than off-the-shelf AlphaFold2 implementations, reducing time-to-solution from weeks to minutes. This computational approach may be readily linked with robotics laboratories to automate and accelerate scientific discovery.
Recent advances in 3D fully convolutional networks (FCN) have made it feasible to produce dense voxel-wise predictions of volumetric images. In this work, we show that a multi-class 3D FCN trained on manually labeled CT scans of several anatomical structures (ranging from the large organs to thin vessels) can achieve competitive segmentation results, while avoiding the need for handcrafting features or training class-specific models. To this end, we propose a two-stage, coarse-to-fine approach that will first use a 3D FCN to roughly define a candidate region, which will then be used as input to a second 3D FCN. This reduces the number of voxels the second FCN has to classify to ~10% and allows it to focus on more detailed segmentation of the organs and vessels. We utilize training and validation sets consisting of 331 clinical CT images and test our models on a completely unseen data collection acquired at a different hospital that includes 150 CT scans, targeting three anatomical organs (liver, spleen, and pancreas). In challenging organs such as the pancreas, our cascaded approach improves the mean Dice score from 68.5 to 82.2%, achieving the highest reported average score on this dataset. We compare with a 2D FCN method on a separate dataset of 240 CT scans with 18 classes and achieve a significantly higher performance in small organs and vessels. Furthermore, we explore fine-tuning our models to different datasets. Our experiments illustrate the promise and robustness of current 3D FCN based semantic segmentation of medical images, achieving state-of-the-art results. Our code and trained models are available for download: //github.com/holgerroth/3Dunet_abdomen_cascade.
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