Nonlinear Balanced Truncation: Part 1 -- Computing Energy Functions

Nonlinear balanced truncation is a model order reduction technique that reduces the dimension of nonlinear systems in a manner that accounts for either open- or closed-loop observability and controllability aspects of the system. Two computational challenges have so far prevented its deployment on large-scale systems: (a) the energy functions required for characterization of controllability and observability are solutions of high-dimensional Hamilton-Jacobi-(Bellman) equations, and (b) efficient model reduction and subsequent reduced-order model (ROM) simulation on the resulting nonlinear balanced manifolds. This work proposes a unifying and scalable approach to the challenge (a) by considering a Taylor series-based approach to solve a class of parametrized Hamilton-Jacobi-Bellman equations that are at the core of the balancing approach. The value of a formulation parameter provides either open-loop balancing or a variety of closed-loop balancing options. To solve for coefficients of the Taylor-series approximation to the energy functions, the presented method derives a linear tensor structure and heavily utilizes this to solve structured linear systems with billions of unknowns. The strength and scalability of the algorithm is demonstrated on two semi-discretized partial differential equations, namely the Burgers equation and the Kuramoto-Sivashinsky equation.Comment: 16 pages, 5 figure

Core Actuation Promotes Self-Manipulability on a Direct-Drive Quadrupedal Robot

For direct-drive legged robots operating in unstructured environments, workspace volume and force generation are competing, scarce resources. In this paper we demonstrate that introducing geared core actuation (i.e., proximal to rather than distal from the mass center) increases workspace volume and can provide a disproportionate amount of work-producing force to the mass center without affecting leg linkage transparency. These effects are analytically quantifiable up to modest assumptions, and are demonstrated empirically on a spined quadruped performing a leap both on level ground and from an isolated foothold (an archetypal feature of unstructured terrain)

An Inductive Approach for Modal Transition System Refinement

Modal Transition Systems (MTSs) provide an appropriate framework for modelling software behaviour when only a partial specification is available. A key characteristic of an MTS is that it explicitly models events that a system is required to provide and is proscribed from exhibiting, and those for which no specification is available, called maybe events. Incremental elaboration of maybe events into either required or proscribed events can be seen as a process of MTS refinement, resulting from extending a given partial specification with more information about the system behaviour. This paper focuses on providing automated support for computing strong refinements of an MTS with respect to event traces that describe required and proscribed behaviours using a non-monotonic inductive logic programming technique. A real case study is used to illustrate the practical application of the approach

Fluent temporal logic for discrete-time event-based models

Fluent model checking is an automated technique for verifying that an event-based operational model satisfies some state-based declarative properties. The link between the event-based and state-based formalisms is defined through fluents which are state predicates whose value are determined by the occurrences of initiating and terminating events that make the fluents values become true or false, respectively. The existing fluent temporal logic is convenient for reasoning about untimed event-based models but difficult to use for timed models. The paper extends fluent temporal logic with temporal operators for modelling timed properties of discrete-time event-based models. It presents two approaches that differ on whether the properties model the system state after the occurrence of each event or at a fixed time rate. Model checking of timed properties is made possible by translating them into the existing untimed framework. Copyright 2005 ACM

2018 Assessment of the Practice of Public Involvement in Florida [Summary]

FDOT BDV25-977-46University of South Florida researchers documented the state of practice of public involvement in transportation decision-making and provided an update to the 2006 report documenting public involvement in Florida

Master Grazer: Improving Grazing Management in Kentucky

The Master Grazer Educational Program is the result of funding provided by the Kentucky Agricultural Development Board to educate producers on better utilization of grazing lands to improve livestock production and the profitability of the State. County agriculture and natural resource agents, extension specialists, industry contacts and producers work together to make this program a success. The Master Grazer Educational Program began in 2006 as evening lecture sessions taking place in local extension offices. In 2008, the program grew with the addition of a field session that showcased a farm with successful grazing practices, a farm with underdeveloped grazing practices, and a final session for participants to develop their own grazing system. In 2010, the program was modified into the Applied Master Grazer Program. This program placed more emphasis on the importance of the county agriculture. The agents decided which topics would be covered and administered many areas of the program. The program now consists of a minimum of two evening field sessions in which a farm is showcased for a particular topic, as well as one impact session in which participants can interact and contribute to a producer forum. For the purpose of this article, reporting will be focused on the last two years of the Master Grazer Program. The past few years, events such as Grazing Schools, the Advanced Grazing Schools, and Pasture Walks have been held to discuss timely topics of forage and livestock management. Also, the Master Grazer Program has a newsletter, website, and DVD series

Nuances are the Key: Unlocking ChatGPT to Find Failure-Inducing Tests with Differential Prompting

Automatically detecting software failures is an important task and a longstanding challenge. It requires finding failure-inducing test cases whose test input can trigger the software's fault, and constructing an automated oracle to detect the software's incorrect behaviors. Recent advancement of large language models (LLMs) motivates us to study how far this challenge can be addressed by ChatGPT, a state-of-the-art LLM. Unfortunately, our study shows that ChatGPT has a low probability (28.8%) of finding correct failure-inducing test cases for buggy programs. A possible reason is that finding failure-inducing test cases requires analyzing the subtle code differences between a buggy program and its correct version. When these two versions have similar syntax, ChatGPT is weak at recognizing subtle code differences. Our insight is that ChatGPT's performance can be substantially enhanced when ChatGPT is guided to focus on the subtle code difference. We have an interesting observation that ChatGPT is effective in inferring the intended behaviors of a buggy program. The intended behavior can be leveraged to synthesize programs, in order to make the subtle code difference between a buggy program and its correct version (i.e., the synthesized program) explicit. Driven by this observation, we propose a novel approach that synergistically combines ChatGPT and differential testing to find failure-inducing test cases. We evaluate our approach on Quixbugs (a benchmark of buggy programs), and compare it with state-of-the-art baselines, including direct use of ChatGPT and Pynguin. The experimental result shows that our approach has a much higher probability (77.8%) of finding correct failure-inducing test cases, 2.7X as the best baseline.Comment: Accepted to the 38th IEEE/ACM International Conference on Automated Software Engineering (ASE 2023

Exact Polynomial Eigenmodes for Homogeneous Spherical 3-Manifolds

Observational data hints at a finite universe, with spherical manifolds such as the Poincare dodecahedral space tentatively providing the best fit. Simulating the physics of a model universe requires knowing the eigenmodes of the Laplace operator on the space. The present article provides explicit polynomial eigenmodes for all globally homogeneous 3-manifolds: the Poincare dodecahedral space S3/I*, the binary octahedral space S3/O*, the binary tetrahedral space S3/T*, the prism manifolds S3/D_m* and the lens spaces L(p,1).Comment: v3. Final published version. 27 pages, 1 figur

Drosophila MUS312 Interacts with the Nucleotide Excision Repair Endonuclease MEI-9 to Generate Meiotic Crossovers

AbstractMEI-9 is the Drosophila homolog of the human structure-specific DNA endonuclease XPF. Like XPF, MEI-9 functions in nucleotide excision repair and interstrand crosslink repair. MEI-9 is also required to generate meiotic crossovers, in a function thought to be associated with resolution of Holliday junction intermediates. We report here the identification of MUS312, a protein that physically interacts with MEI-9. We show that mutations in mus312 elicit a meiotic phenotype identical to that of mei-9 mutants. A missense mutation in mei-9 that disrupts the MEI-9–MUS312 interaction abolishes the meiotic function of mei-9 but does not affect the DNA repair functions of mei-9. We propose that MUS312 facilitates resolution of meiotic Holliday junction intermediates by MEI-9