Bird-sized flapping-wing robots offer significant potential for agile flight in complex environments, but achieving agile and robust trajectory tracking remains a challenge due to the complex aerodynamics and highly nonlinear dynamics inherent in flapping-wing flight. In this work, a learning-based control approach is introduced to unlock the versatility and adaptiveness of flapping-wing flight. We propose a model-free reinforcement learning (RL)-based framework for a high degree-of-freedom (DoF) bird-inspired flapping-wing robot that allows for multimodal flight and agile trajectory tracking. Stability analysis was performed on the closed-loop system comprising of the flapping-wing system and the RL policy. Additionally, simulation results demonstrate that the RL-based controller can successfully learn complex wing trajectory patterns, achieve stable flight, switch between flight modes spontaneously, and track different trajectories under various aerodynamic conditions.

We present Sketch 'n Solve, an open-source Python package that implements efficient randomized numerical linear algebra (RandNLA) techniques for solving large-scale least squares problems. While sketch-and-solve algorithms have demonstrated theoretical promise, their practical adoption has been limited by the lack of robust, user-friendly implementations. Our package addresses this gap by providing an optimized implementation built on NumPy and SciPy, featuring both dense and sparse sketching operators with a clean API. Through extensive benchmarking, we demonstrate that our implementation achieves up to 50x speedup over traditional LSQR while maintaining high accuracy, even for ill-conditioned matrices. The package shows particular promise for applications in machine learning optimization, signal processing, and scientific computing.

This paper introduces the \emph{Optimist}, an autonomous system developed to advance automated conjecture generation in graph theory. Leveraging mixed-integer programming (MIP) and heuristic methods, the \emph{Optimist} generates conjectures that both rediscover established theorems and propose novel inequalities. Through a combination of memory-based computation and agent-like adaptability, the \emph{Optimist} iteratively refines its conjectures by integrating new data, enabling a feedback process with minimal human (\emph{or machine}) intervention. Initial experiments reveal the \emph{Optimist}'s potential to uncover foundational results in graph theory, as well as to produce conjectures of interest for future exploration. This work also outlines the \emph{Optimist}'s evolving integration with a counterpart agent, the \emph{Pessimist} (a human \emph{or machine} agent), to establish a dueling system that will drive fully automated graph theory research.

We consider the problem of sampling from a $d$-dimensional log-concave distribution $\pi(\theta) \propto \exp(-f(\theta))$ for $L$-Lipschitz $f$, constrained to a convex body with an efficiently computable self-concordant barrier function, contained in a ball of radius $R$ with a $w$-warm start. We propose a \emph{robust} sampling framework that computes spectral approximations to the Hessian of the barrier functions in each iteration. We prove that for polytopes that are described by $n$ hyperplanes, sampling with the Lee-Sidford barrier function mixes within $\widetilde O((d^2+dL^2R^2)\log(w/\delta))$ steps with a per step cost of $\widetilde O(nd^{\omega-1})$, where $\omega\approx 2.37$ is the fast matrix multiplication exponent. Compared to the prior work of Mangoubi and Vishnoi, our approach gives faster mixing time as we are able to design a generalized soft-threshold Dikin walk beyond log-barrier. We further extend our result to show how to sample from a $d$-dimensional spectrahedron, the constrained set of a semidefinite program, specified by the set $\{x\in \mathbb{R}^d: \sum_{i=1}^d x_i A_i \succeq C \}$ where $A_1,\ldots,A_d, C$ are $n\times n$ real symmetric matrices. We design a walk that mixes in $\widetilde O((nd+dL^2R^2)\log(w/\delta))$ steps with a per iteration cost of $\widetilde O(n^\omega+n^2d^{3\omega-5})$. We improve the mixing time bound of prior best Dikin walk due to Narayanan and Rakhlin that mixes in $\widetilde O((n^2d^3+n^2dL^2R^2)\log(w/\delta))$ steps.

Finding interpretable biomechanical models can provide insight into the functionality of organs with regard to physiology and disease. However, identifying broadly applicable dynamical models for in vivo tissue remains challenging. In this proof of concept study we propose a reconstruction framework for data-driven discovery of dynamical models from experimentally obtained undersampled MRI spectral data. The method makes use of the previously developed spectro-dynamic framework which allows for reconstruction of displacement fields at high spatial and temporal resolution required for model identification. The proposed framework combines this method with data-driven discovery of interpretable models using Sparse Identification of Non-linear Dynamics (SINDy). The design of the reconstruction algorithm is such that a symbiotic relation between the reconstruction of the displacement fields and the model identification is created. Our method does not rely on periodicity of the motion. It is successfully validated using spectral data of a dynamic phantom gathered on a clinical MRI scanner. The dynamic phantom is programmed to perform motion adhering to 5 different (non-linear) ordinary differential equations. The proposed framework performed better than a 2-step approach where the displacement fields were first reconstructed from the undersampled data without any information on the model, followed by data-driven discovery of the model using the reconstructed displacement fields. This study serves as a first step in the direction of data-driven discovery of in vivo models.

Rationing of healthcare resources is a challenging decision that policy makers and providers may be forced to make during a pandemic, natural disaster, or mass casualty event. Well-defined guidelines to triage scarce life-saving resources must be designed to promote transparency, trust, and consistency. To facilitate buy-in and use during high-stress situations, these guidelines need to be interpretable and operational. We propose a novel data-driven model to compute interpretable triage guidelines based on policies for Markov Decision Process that can be represented as simple sequences of decision trees ("tree policies"). In particular, we characterize the properties of optimal tree policies and present an algorithm based on dynamic programming recursions to compute good tree policies. We utilize this methodology to obtain simple, novel triage guidelines for ventilator allocations for COVID-19 patients, based on real patient data from Montefiore hospitals. We also compare the performance of our guidelines to the official New York State guidelines that were developed in 2015 (well before the COVID-19 pandemic). Our empirical study shows that the number of excess deaths associated with ventilator shortages could be reduced significantly using our policy. Our work highlights the limitations of the existing official triage guidelines, which need to be adapted specifically to COVID-19 before being successfully deployed.

Data is the new oil of the 21st century. The growing trend of trading data for greater welfare has led to the emergence of data markets. A data market is any mechanism whereby the exchange of data products including datasets and data derivatives takes place as a result of data buyers and data sellers being in contact with one another, either directly or through mediating agents. It serves as a coordinating mechanism by which several functions, including the pricing and the distribution of data as the most important ones, interact to make the value of data fully exploited and enhanced. In this article, we present a comprehensive survey of this important and emerging direction from the aspects of data search, data productization, data transaction, data pricing, revenue allocation as well as privacy, security, and trust issues. We also investigate the government policies and industry status of data markets across different countries and different domains. Finally, we identify the unresolved challenges and discuss possible future directions for the development of data markets.

Generalized linear mixed models (GLMMs) are a widely used tool in statistical analysis. The main bottleneck of many computational approaches lies in the inversion of the high dimensional precision matrices associated with the random effects. Such matrices are typically sparse; however, the sparsity pattern resembles a multi partite random graph, which does not lend itself well to default sparse linear algebra techniques. Notably, we show that, for typical GLMMs, the Cholesky factor is dense even when the original precision is sparse. We thus turn to approximate iterative techniques, in particular to the conjugate gradient (CG) method. We combine a detailed analysis of the spectrum of said precision matrices with results from random graph theory to show that CG-based methods applied to high-dimensional GLMMs typically achieve a fixed approximation error with a total cost that scales linearly with the number of parameters and observations. Numerical illustrations with both real and simulated data confirm the theoretical findings, while at the same time illustrating situations, such as nested structures, where CG-based methods struggle.

We present a centralized auction algorithm to solve the Multi-Depot Rural Postman Problem with Rechargeable and Reusable Vehicles (MD-RPP-RRV), focusing on rescheduling arc routing after vehicle failures. The problem involves finding heuristically obtained best feasible routes for multiple rechargeable and reusable vehicles with capacity constraints capable of performing multiple trips from multiple depots, with the possibility of vehicle failures. Our algorithm auctions the failed trips to active (non-failed) vehicles through local auctioning, modifying initial routes to handle dynamic vehicle failures efficiently. When a failure occurs, the algorithm searches for the best active vehicle to perform the failed trip and inserts the trip into that vehicle's route, which avoids a complete rescheduling and reduces the computational effort. We compare the algorithm's solutions against offline optimal solutions obtained from solving a Mixed Integer Linear Programming (MILP) formulation using the Gurobi solver; this formulation assumes that perfect information about the vehicle failures and failure times is given. The results demonstrate that the centralized auction algorithm produces solutions that are, in some cases, near optimal; moreover, the execution time for the proposed approach is much more consistent and is, for some instances, orders of magnitude less than the execution time of the Gurobi solver. The theoretical analysis provides an upper bound for the competitive ratio and computational complexity of our algorithm, offering a formal performance guarantee in dynamic failure scenarios.

Mixed-integer linear programming (MILP) is one of the most popular mathematical formulations with numerous applications. In practice, improving the performance of MILP solvers often requires a large amount of high-quality data, which can be challenging to collect. Researchers thus turn to generation techniques to generate additional MILP instances. However, existing approaches do not take into account specific block structures -- which are closely related to the problem formulations -- in the constraint coefficient matrices (CCMs) of MILPs. Consequently, they are prone to generate computationally trivial or infeasible instances due to the disruptions of block structures and thus problem formulations. To address this challenge, we propose a novel MILP generation framework, called Block Structure Decomposition (MILP-StuDio), to generate high-quality instances by preserving the block structures. Specifically, MILP-StuDio begins by identifying the blocks in CCMs and decomposing the instances into block units, which serve as the building blocks of MILP instances. We then design three operators to construct new instances by removing, substituting, and appending block units in the original instances, enabling us to generate instances with flexible sizes. An appealing feature of MILP-StuDio is its strong ability to preserve the feasibility and computational hardness of the generated instances. Experiments on the commonly-used benchmarks demonstrate that using instances generated by MILP-StuDio is able to significantly reduce over 10% of the solving time for learning-based solvers.