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At least 1,171 records · Page 65

Modbus RTU for Embedded Cyber Secure Inverter Controller

The Modbus communication protocol is a widely adopted communication standard in industrial control systems. This communication protocol is known for being reliable and straightforward to implement while being versatile in terms of its operating parameters while supporting multiple formats over various hardware infrastructures and architectures. Many intelligent devices such as Programmable Logic Controllers (PLCs), Human-Machine Interfaces (HMIs), Internet-of-Things (IoT), and various Operational Technologies (OT) utilize Modbus for their communication systems. These types of systems must communicate with each other through a standardized and central communication process. To support the integration of these modular systems, a Field-Programmable Gate Array (FPGA) can act as an embedded central routing fabric for this communication to take place. Embedded systems are versatile enough to interface with various devices and systems to accomplish various goals. Additionally, embedded systems require relatively small physical designs to minimize the required resources to facilitate the intended application by providing low-level system access. This minimization of system resources goes hand in hand with reducing the financial cost of a proposed solution or system. As remotely collaborating researchers often use FPGAs to prototype designs that are required to have a method for data transmission among systems, it is imperative to provide a baseline standard for communications among devices and systems. A typical method of implementing the Modbus RTU communication protocol in an embedded environment is using integrated logic architectures within the FPGA called “Intellectual Property (IP) cores.” IP cores can be designed using integrated logic or circuit designs to function as an embedded processor. These IP cores can then perform the required computational actions to support the Modbus RTU communication protocol by utilizing high-level programming languages such as the C programming language. The hardware description language of Very High-Speed Integrated Circuit Hardware Description Language (VHDL) allows for the control of real hardware at the logic gate and signal level. These logic gates and signals can be designed and controlled to perform desired actions based on the system design. Programming an FPGA using VHDL allows an individual to access the lowest abstraction level of the system during FPGA development. This level of abstraction is referred to as the register-transfer level (RTL), which gives access to manipulating values and variables at the register level. This register-level manipulation provides precision over creating the logical circuit within the FPGA, thus minimizing the required code to perform desired operations. The Modbus RTU communication protocol can be implemented within an FPGA using VHDL programming to establish a standardized and embedded serial communication pathway. This implementation provides a standardized communication protocol to streamline research efforts among researchers, thus increasing the efficiency of research efforts. Additionally, this Modbus RTU implementation requires fewer resources when compared to typical communication protocol implementations that utilize an IP core, reducing the hardware requirement for effective research efforts.

communication↗

Semantically-Rigorous Systems Engineering Modeling Using Sysml and OWL

The Systems Modeling Language (SysML) has found wide acceptance as a standard graphical notation for the domain of systems engineering. SysML subsets and extends the Unified Modeling Language (UML) to define conventions for expressing structural, behavioral, and analytical elements, and relationships among them. SysML-enabled modeling tools are available from multiple providers, and have been used for diverse projects in military aerospace, scientific exploration, and civil engineering. The Web Ontology Language (OWL) has found wide acceptance as a standard notation for knowledge representation. OWL-enabled modeling tools are available from multiple providers, as well as auxiliary assets such as reasoners and application programming interface libraries, etc. OWL has been applied to diverse projects in a wide array of fields. While the emphasis in SysML is on notation, SysML inherits (from UML) a semantic foundation that provides for limited reasoning and analysis. UML's partial formalization (FUML), however, does not cover the full semantics of SysML, which is a substantial impediment to developing high confidence in the soundness of any conclusions drawn therefrom. OWL, by contrast, was developed from the beginning on formal logical principles, and consequently provides strong support for verification of consistency and satisfiability, extraction of entailments, conjunctive query answering, etc. This emphasis on formal logic is counterbalanced by the absence of any graphical notation conventions in the OWL standards. Consequently, OWL has had only limited adoption in systems engineering. The complementary strengths and weaknesses of SysML and OWL motivate an interest in combining them in such a way that we can benefit from the attractive graphical notation of SysML and the formal reasoning of OWL. This paper describes an approach to achieving that combination.

Web Ontology Language (OWL)↗

Snowflake: A Lightweight Portable Stencil DSL

Stencil computations are not well optimized by general-purpose production compilers and the increased use of multicore, manycore, and accelerator-based systems makes the optimization problem even more challenging. In this paper we present Snowflake, a Domain Specific Language (DSL) for stencils that uses a 'micro-compiler' approach, i.e., small, focused, domain-specific code generators. The approach is similar to that used in image processing stencils, but Snowflake handles the much more complex stencils that arise in scientific computing, including complex boundary conditions, higher-order operators (larger stencils), higher dimensions, variable coefficients, non-unit-stride iteration spaces, and multiple input or output meshes. Snowflake is embedded in the Python language, allowing it to interoperate with popular scientific tools like SciPy and iPython; it also takes advantage of built-in Python libraries for powerful dependence analysis as part of a just-in-time compiler. We demonstrate the power of the Snowflake language and the micro-compiler approach with a complex scientific benchmark, HPGMG, that exercises the generality of stencil support in Snowflake. By generating OpenMP comparable to, and OpenCL within a factor of 2x of hand-optimized HPGMG, Snowflake demonstrates that a micro-compiler can support diverse processor architectures and is performance-competitive whilst preserving a high-level Python implementation.

97 MATHEMATICS AND COMPUTING↗

Lamellar: A Rust-based Asynchronous Tasking and PGAS Runtime for High Performance Computing

Cybersecurity is one of the largest concerns in modern computing, impacting and dictating how governments, private corporations, and individuals interact with and live in an increasingly digital world. The NSA has recently released a memo [ 1] on “Software Memory Safety” where they highlight that both Microsoft and Google have stated around 70% of software vulnerabilities were due to memory safety issues. Although languages such as C and C++ provide freedom and flexibility with memory management, guaran- teeing safety falls mostly on the developer. The NSA recommends using “memory safe” languages whenever possible. In this paper we introduce Lamellar, an asynchronous tasking and PGAS HPC runtime written in Rust, one such "memory safe" language. We describe the entire Lamellar stack, from network interfaces to high- level abstractions such as distributed LamellarArrays and Active Messages. We conclude by showing comparable performance to legacy PGAS runtimes (e.g. OpenSHMEM) on a subset of the BALE kernel suite while maintaining strong memory safety principles.

HPC Software Systems, Rust Programming Language, P↗

Verified lifting of stencil computations

This paper demonstrates a novel combination of program synthesis and verification to lift stencil computations from low-level Fortran code to a high-level summary expressed using a predicate language. The technique is sound and mostly automated, and leverages counter-example guided inductive synthesis (CEGIS) to find provably correct translations. Lifting existing code to a high-performance description language has a number of benefits, including maintainability and performance portability. For example, our experiments show that the lifted summaries can enable domain specific compilers to do a better job of parallelization as compared to an off-the-shelf compiler working on the original code, and can even support fully automatic migration to hardware accelerators such as GPUs. We have implemented verified lifting in a system called STNG and have evaluated it using microbenchmarks, mini-apps, and real-world applications. Here, we demonstrate the benefits of verified lifting by first automatically summarizing Fortran source code into a high-level predicate language, and subsequently translating the lifted summaries into Halide, with the translated code achieving median performance speedups of 4.1X and up to 24X for non-trivial stencils as compared to the original implementation.

97 MATHEMATICS AND COMPUTING↗

FRET Tutorial

In this tutorial, we present the FRET tool for writing, understanding, formalizing and analyzing requirements. In practice, requirements are typically written in natural language, which is ambiguous and consequently not amenable to formal analysis. Since formal, mathematical notations are unintuitive, requirements in FRET are entered in a restricted, natural language, called FRETish with precise unambiguous meaning. This tutorial explains how requirements can be captured in FRETish and subsequently formalized in temporal logics and in the synchronous data flow language Lustre. We show, through multiple examples, how FRET assists users in understanding FRETish requirements and clarifying subtle semantic issues through English and diagrammatic explanations as well as interactive simulation. FInally, this tutorial describes how FRET can be used to perform realizability checking for identifying conflicting requirements and the connection of FRET with (1) the CoCoSim automated analysis tool for the verification of Simulink and Stateflow models, and (2) the Copilot runtime monitoring tool for the analysis of C programs.

FRET↗

Enhancing Air Traffic Control Planning with Automatic Speech Recognition

The decisions made during the Federal Aviation Administration Air Traffic Control System Command Center's planning teleconferences hold significant sway over the National Airspace System. Held every two hours, these teleconferences convene air traffic managers and stakeholders from across the nation to discuss airspace conditions, weather, and constraints, leading to the formulation and adjustment of traffic management initiatives. Given the critical nature of these decisions, the need for accurate and efficient record-keeping is paramount. In recent years, the application of automatic speech recognition has gained popularity across diverse industries, including aviation. While traditional applications focus on transcribing air traffic control communication, this paper explores a unique application of automatic speech recognition by converting the audio from planning teleconferences into text transcriptions. This innovative approach addresses key challenges in the field, presenting potential benefits for quality assurance, real-time participation, and downstream natural language processing tasks. A notable breakthrough in the machine learning community, namely the transformer neural network architecture, forms the backbone of the proposed solution in this paper. The transformer architecture's role in this research represents a paradigm shift in the efficiency of automatic speech recognition models. By reducing the amount of in-domain training data required, this architecture allows for the fine-tuning of such models like Whisper, originally pretrained on vast English speech datasets. The adaptability of the transformer architecture proves invaluable in capturing the nuances of aviation terminology and specific language used in planning teleconferences. Leveraging the Whisper model as a baseline, our research details the fine-tuning and validation using a dataset comprising 20 hours of meticulously transcribed planning teleconferences. Notably, the baseline pretrained Whisper model exhibited a word error rate of 18.77%. Through the fine-tuning process, the model achieved a substantial improvement, demonstrating an impressive performance with a reduced word error rate of 6.82%. This substantial decrease in WER not only highlights the effectiveness of the transformer architecture but also emphasizes the practical advancements achieved through the application of automatic speech recognition in this specific domain. The utilization of automatic speech recognition in planning teleconferences in this work introduces several novelties. Firstly, the creation of text transcriptions offers a valuable tool for quality assurance and facilitates the efficient review of teleconferences. This is an important aspect of the proposed solution, given the time-sensitive and high-stakes nature of decisions made during these meetings. Furthermore, text-searchable transcriptions provide a streamlined approach for locating and validating critical information, potentially saving hours of manual effort in searching through audio recordings. Moreover, our research identifies a key use case for external facilities and stakeholders. In situations where attendance at the planning teleconference is not feasible, having access to text transcriptions in real-time or shortly after the teleconference ends, proves to be a time-saving and informative resource. This feature enhances collaboration and ensures that stakeholders can stay abreast of important discussions and decisions even in their absence. Despite the efficiency gains facilitated by the transformer architecture in automatic speech recognition technology, it is essential to acknowledge the human factors in data creation. Subject matter experts play a crucial role in accurately transcribing planning teleconferences due to the specificity and complexity of the information discussed. The research dataset, consisting of 20 hours of transcribed planning teleconferences, forms the foundation for fine-tuning and validating the Whisper model. The achieved word error rate of 6.82% demonstrates promising advancements, particularly in recognizing essential aviation terminology within the teleconferences. In conclusion, this paper presents a comprehensive exploration of the application of automatic speech recognition in Air Traffic Control System Command Center planning teleconferences, leveraging the transformer architecture for enhanced efficiency. The novel contributions lie in the improved accessibility of decision-making records, real-time participation opportunities for external stakeholders, and the potential for downstream natural language processing advancements. As the aviation industry continues to evolve, the integration of automatic speech recognition technologies holds the promise of revolutionizing decision-making processes and contributing to the overall safety and efficiency of air traffic management.

ATM↗

Logic Programming with Extensible Types

Logic programming allows structuring code in terms of predicates or relations, rather than functions. Although logic programming languages present advantages in terms of declarativeness and conciseness, the introduction of static types has not become part of most popular logic programming languages, increasing the difficulty of testing and debugging of logic programming code. This paper demonstrates how to implement logic programming in Haskell, thus empowering logic programs with types, and functional programs with relations or predicates. We do so by combining three ideas. First, we use extensible types to generalize a type by a parameter type function. Second, we use a sum type as an argument to introduce optional variables in extensible types. Third, we implement a unification algorithm capable of working with any data structure, provided that certain operations are implemented for the given type. We demonstrate our proposal via a series of increasingly complex examples inspired by educational texts in logic programming, and leverage the host language's features to make new notation convenient for users, showing that the proposed approach is not just technically possible but also practical.

logic programming↗

SMART-COM – Scalable Multi-Agent Adaptive Resolution Tools for Collaborative Outage Management

The purpose of this grant was to conduct scientific research and prototype applications to support NPP outage staff in their adaptive decision-making in efficient scheduling and resource allocation while preventing violation of safety technical specifications. The project contributed to scientific knowledge and engineering methods in (1) user interface design, (2) scheduling optimization and risk estimation, and (2) natural language processing that would benefit the nuclear power plants in minimizing schedule overruns and even unexpected shutdowns. The research team conducted site visits at a test reactor facility and an operating nuclear power plant to gather necessary information and inputs for research and development of a software application to support NPP staff in executing their outages. The final software application consisted of three modules. First, the natural language processing module supports interactive processing of technical documentation to build a database for outage staff to query non-permissible actions on system components. This module can alleviate outage staff from reviewing extensive documentation and minimize violation of technical specifications, especially in time-sensitive situations. Second, the schedule optimization module schedules outage activities and compute risk indices that outperform existing software and current practice. This module can reduce completion time of an outage that typically have too many activities for human to optimize based on current practice that does not apply the latest operations research. Finally, the visualization module presents progress and risk information of the overall outage and individual activities, as well as enabling access to the natural language processing and schedule optimization modules. This module can provide outage staff with situation awareness that are necessary to make risk-informed decisions in response to unexpected events during the execution of an outage.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Empowering Geothermal Research: The Geothermal Data Repository's New AI Research Assistant: Preprint

The Department of Energy's (DOE) Geothermal Data Repository (GDR) team has integrated a Large Language Model (LLM) with the metadata and supporting documents associated with GDR datasets to create an Artificially Intelligent (AI) research assistant. By leveraging work done to make GDR metadata machine-readable and an open-source LLM integration model called the Energy Language Model, developed by the National Renewable Energy Laboratory, AskGDR serves as a virtual research assistant to GDR users. It provides answers to a variety of user-provided questions using natural language processing and generative machine learning. Users can get answers to questions about specific datasets, including inquiries about the equipment, assumptions and methodologies used in the origination of the data; or more abstract questions, such as the applicability of data to specific research fields. AskGDR improves the discoverability of geothermal data by helping guide users to datasets beyond simple keyword searches. It enables users to find data based on properties of the data, discover information contained within supporting documents, and explore data from projects related to their research objectives.

access↗

Empowering Geothermal Research: The Geothermal Data Repository's New AI Research Assistant

The Department of Energy's (DOE) Geothermal Data Repository (GDR) team has integrated a Large Language Model (LLM) with the metadata and supporting documents associated with GDR datasets to create an Artificially Intelligent (AI) research assistant. By leveraging work done to make GDR metadata machine-readable and an open-source LLM integration model called the Energy Language Model, developed by the National Renewable Energy Laboratory, AskGDR serves as a virtual research assistant to GDR users. It provides answers to a variety of user-provided questions using natural language processing and generative machine learning. Users can get answers to questions about specific datasets, including inquiries about the equipment, assumptions and methodologies used in the origination of the data; or more abstract questions, such as the applicability of data to specific research fields. AskGDR improves the discoverability of geothermal data by helping guide users to datasets beyond simple keyword searches. It enables users to find data based on properties of the data, discover information contained within supporting documents, and explore data from projects related to their research objectives. This paper will outline the development, integration, output, and efficacy of the AskGDR LLM, including adherence to scientific rigor through improvements designed to increase the accuracy of generated answers, avoid speculation, and provide proper references for all resources used.

access↗

An overview of the evolving jurisdictional scope of the U.S. Clean Water Act for hydrologists

Abstract The Clean Water Act (CWA) is the primary federal mechanism by which the physical, chemical, and biological integrity of streams, lakes, and wetlands are protected in the United States. The CWA has evolved considerably since its initial passage in 1948, including explicit expansions and contractions of jurisdictional scope through a series of legislative actions, court decisions, and agency rules. Here, we provide a practical summary of the CWA's evolution, detailing the major updates or revisions and their circumstances. Additionally, we identify the jurisdictional scope of the law for rivers and streams, lakes, and wetlands based on the language used and implementation by the agencies during the same time period. While the rulemaking process commonly uses language that will be abstract to many hydrologists, understanding the on‐the‐ground implications, quantifying regulatory (un)certainties, and assessing the magnitude of changes through time is important to understanding the implications of environmental regulation development, litigation, and enforcement. Thus, we translate the enforcement norms and definitions into quantitative estimates for Clean Water Act scope in the Wabash River Basin (Illinois, Indiana, and Ohio, USA) as a demonstration of the spatial consequences of changing regulatory language. This article is categorized under: Engineering Water > Planning Water Human Water > Water Governance Water and Life > Conservation, Management, and Awareness

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Scheduling and Performance of Asynchronous Tasks in Fortran 2018 with FEATS

Most parallel scientific programs contain compiler directives (pragmas) such as those from OpenMP (Hermanns in Parallel programming in Fortran 95 using openMP, 2002. School of Aeronautical Engineering, Universidad Politécnica de Madrid, España, 2011), explicit calls to runtime library procedures such as those implementing the Message Passing Interface (MPI) (in A message-passing interface standard version 4.0, 2021. https://www.mpi-forum.org/docs/mpi-4.0/mpi40-report.pdf), or compiler-specific language extensions such as those provided by CUDA (Ruetsch and Fatica in CUDA Fortran for scientists and engineers: best practices for efficient CUDA Fortran programming, Elsevier, 2013). By contrast, the recent Fortran standards empower developers to express parallel algorithms without directly referencing lower-level parallel programming models (Numrich in Parallel programming with co-arrays, CRC Press, 2018, and Curcic in Modern Fortran: building efficient parallel applications, Manning Publications, 2020). Fortran’s parallel features place the language within the Partitioned Global Address Space (PGAS) class of programming models. When writing programs that exploit data parallelism, application developers often find it straightforward to develop custom parallel algorithms. Problems involving complex, heterogeneous, staged calculations, however, pose much greater challenges. Such applications require careful coordination of tasks in a manner that respects dependencies prescribed by a directed acyclic graph. When rolling one’s own solution proves difficult, extending a customizable framework becomes attractive. Further, the paper presents the design, implementation, and use of the Framework for Extensible Asynchronous Task Scheduling (FEATS), which we believe to be the first task scheduling tool written in modern Fortran. We describe the benefits and compromises associated with choosing Fortran as the implementation language, and we propose ways in which future Fortran standards can best support the use case in this paper.

97 MATHEMATICS AND COMPUTING↗

Standards, dissemination, and best practices in systems biology

In this study, the reproducibility of scientific research is crucial to the success of the scientific method. Here, we review the current best practices when publishing mechanistic models in systems biology. We recommend, where possible, to use software engineering strategies such as testing, verification, validation, documentation, versioning, iterative development, and continuous integration. In addition, adhering to the Findable, Accessible, Interoperable, and Reusable modeling principles allows other scientists to collaborate and build off of each other’s work. Existing standards such as Systems Biology Markup Language, CellML, or Simulation Experiment Description Markup Language can greatly improve the likelihood that a published model is reproducible, especially if such models are deposited in well-established model repositories. Where models are published in executable programming languages, the source code and their data should be published as open-source in public code repositories together with any documentation and testing code. For complex models, we recommend container-based solutions where any software dependencies and the run-time context can be easily replicated.

59 BASIC BIOLOGICAL SCIENCES↗

Detecting regular sound changes in linguistics as events of concerted evolution

Background: Concerted evolution is normally used to describe parallel changes at different sites in a genome, but it is also observed in languages where a specific phoneme changes to the same other phoneme in many words in the lexicon—a phenomenon known as regular sound change. We develop a general statistical model that can detect concerted changes in aligned sequence data and apply it to study regular sound changes in the Turkic language family. Results: Linguistic evolution, unlike the genetic substitutional process, is dominated by events of concerted evolutionary change. Our model identified more than 70 historical events of regular sound change that occurred throughout the evolution of the Turkic language family, while simultaneously inferring a dated phylogenetic tree. Including regular sound changes yielded an approximately 4-fold improvement in the characterization of linguistic change over a simpler model of sporadic change, improved phylogenetic inference, and returned more reliable and plausible dates for events on the phylogenies. The historical timings of the concerted changes closely follow a Poisson process model, and the sound transition networks derived from our model mirror linguistic expectations. Conclusions: We demonstrate that a model with no prior knowledge of complex concerted or regular changes can nevertheless infer the historical timings and genealogical placements of events of concerted change from the signals left in contemporary data. Our model can be applied wherever discrete elements—such as genes, words, cultural trends, technologies, or morphological traits—can change in parallel within an organism or other evolving group.

59 BASIC BIOLOGICAL SCIENCES↗

Community vulnerability is the key determinant of diverse energy burdens in the United States

Low-income households generally experience a high energy burden; however, the factors influencing energy burdens are beyond socio-economics. This study explores the relationships between the multidimensionality of community vulnerability factors and energy burden across multiple geospatial levels in the United States. Our study found the distribution of energy burden in 2020 showed a great deal of variety, ranging from a minimum of 2.93 % to a maximum of 30.45 % across 3142 counties. The results of non-spatial and spatial regressions showed that the vulnerability ranks of socioeconomic, household composition and disability, minority and language, household type and transportation, and COVID mortality rate are significant predictors of energy burdens at the national level. However, at the regional level, only socioeconomic, minority and language significantly influence energy burdens. Minority and language negatively impact energy burdens except for the South East-Central region. Additionally, our analyses highlight the need to consider community vulnerability indicators' spatial homogeneity and heterogeneity. At the national level, only the epidemiological factors index is a spatially homogeneous predictor; on the regional and state level, the spatially homogeneous predictors such as socioeconomic status, household composition and disability, and household type and transportation vary by region. Such a region-sensitive relationship between energy burden and the predictors indicates spatial heterogeneity. Here this study suggests policy recommendations through the lens of the multidimensionality of community vulnerability factors. Implementing flexible national energy policies while making particular energy assistance policies for the vulnerable population at the regional or state levels is essential.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

A tool and a methodology to use macros for abstracting variations in code for different computational demands

Scientific software used on high-performance computing platforms is in a phase of transformation because of the combined increase in the heterogeneity and complexity of models and hardware platforms. Having separate implementations for different platforms can easily lead to combinatorial explosions; therefore, the computational science community has been looking for mechanisms to express code through abstractions that can be specialized for different platforms. Most existing approaches use template meta-programming in C++, and are, therefore language specific. Here, we have developed a tool that uses customized expansion of macros to mimic some of C++ behavior in other languages. It enables unification of any code variants that may be necessary to run efficiently on different target architectures and different computational environments through use of macros with multiple alternative definitions and ability to arbitrate on definition selection for expansion. Combined with two other tools, a custom runtime, and a user specified recipe translator, our custom macroprocessor becomes a part of an overall performance portability solution that does not depend on any specific programming language. We also use macros as code-shorthand that lets code snippets become building blocks that allow variations in control flow to explore performance options. We demonstrate use of macros in Flash-X, a multiphysics multicomponent code with many Fortran legacy components derived from an earlier community code FLASH.

Heterogenous computing↗

A primer on resurgent transseries and their asymptotics

The computation of observables in general interacting theories, be them quantum mechanical, field, gauge or string theories, is a non-trivial problem which in many cases can only be addressed by resorting to perturbative methods. In most physically interesting problems these perturbative expansions result in asymptotic series with zero radius of convergence. These asymptotic series then require the use of resurgence and transseries in order for the associated observables to become nonperturbatively well-defined. Resurgence encodes the complete large-order asymptotic behaviour of the coefficients from a perturbative expansion, generically in terms of (multi) instanton sectors and for each problem in terms of its Stokes constants. Some observables arise from linear problems, and have a finite number of instanton sectors and associated Stokes constants; some other observables arise from nonlinear problems, and have an infinite number of instanton sectors and Stokes constants. By means of two very explicit examples, and with emphasis on a pedagogical style of presentation, here this work aims at serving as a primer on the aforementioned resurgent, large-order asymptotics of general perturbative expansions. This includes discussions of transseries, Stokes phenomena, generalized steepest-descent methods, Borel transforms, nonlinear resonance, and alien calculus. Furthermore, resurgent properties of transseries – usually described mathematically via alien calculus – are recast in equivalent physical languages: either a “statistical mechanical” language, as motions in chains and lattices; or a “conformal field theoretical” language, with underlying Virasoro-like algebraic structures.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗