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Structured adaptive grid generation using algebraic methods

The accuracy of the numerical algorithm depends not only on the formal order of approximation but also on the distribution of grid points in the computational domain. Grid adaptation is a procedure which allows optimal grid redistribution as the solution progresses. It offers the prospect of accurate flow field simulations without the use of an excessively timely, computationally expensive, grid. Grid adaptive schemes are divided into two basic categories: differential and algebraic. The differential method is based on a variational approach where a function which contains a measure of grid smoothness, orthogonality and volume variation is minimized by using a variational principle. This approach provided a solid mathematical basis for the adaptive method, but the Euler-Lagrange equations must be solved in addition to the original governing equations. On the other hand, the algebraic method requires much less computational effort, but the grid may not be smooth. The algebraic techniques are based on devising an algorithm where the grid movement is governed by estimates of the local error in the numerical solution. This is achieved by requiring the points in the large error regions to attract other points and points in the low error region to repel other points. The development of a fast, efficient, and robust algebraic adaptive algorithm for structured flow simulation applications is presented. This development is accomplished in a three step process. The first step is to define an adaptive weighting mesh (distribution mesh) on the basis of the equidistribution law applied to the flow field solution. The second, and probably the most crucial step, is to redistribute grid points in the computational domain according to the aforementioned weighting mesh. The third and the last step is to reevaluate the flow property by an appropriate search/interpolate scheme at the new grid locations. The adaptive weighting mesh provides the information on the desired concentration of points to the grid redistribution scheme. The evaluation of the weighting mesh is accomplished by utilizing the weight function representing the solution variation and the equidistribution law. The selection of the weight function plays a key role in grid adaptation. A new weight function utilizing a properly weighted boolean sum of various flowfield characteristics is defined. The redistribution scheme is developed utilizing Non-Uniform Rational B-Splines (NURBS) representation. The application of NURBS representation results in a well distributed smooth grid by maintaining the fidelity of the geometry associated with boundary curves. Several algebraic methods are applied to smooth and/or nearly orthogonalize the grid lines. An elliptic solver is utilized to smooth the grid lines if there are grid crossings. Various computational examples of practical interest are presented to demonstrate the success of these methods.

Yang, Jiann-Cherng

Boolean integral calculus

The concept of Boolean integration is developed, and different Boolean integral operators are introduced. Given the changes in a desired function in terms of the changes in its arguments, the ways of 'integrating' (i.e. realizing) such a function, if it exists, are presented. The necessary and sufficient conditions for integrating, in different senses, the expression specifying the changes are obtained. Boolean calculus has applications in the design of logic circuits and in fault analysis.

Tucker, Jerry H.

Verification of VLSI designs

In this paper we explore the specification and verification of VLSI designs. The paper focuses on abstract specification and verification of functionality using mathematical logic as opposed to low-level boolean equivalence verification such as that done using BDD's and Model Checking. Specification and verification, sometimes called formal methods, is one tool for increasing computer dependability in the face of an exponentially increasing testing effort.

Windley, P. J.

Circuit complexity and functionality: A statistical thermodynamics perspective

Circuit complexity, defined as the minimum circuit size required for implementing a particular Boolean computation, is a foundational concept in computer science. Determining circuit complexity is believed to be a hard computational problem. Recently, in the context of black holes, circuit complexity has been promoted to a physical property, wherein the growth of complexity is reflected in the time evolution of the Einstein-Rosen bridge (“wormhole”) connecting the two sides of an anti-de Sitter “eternal” black hole. Here, we are motivated by an independent set of considerations and explore links between complexity and thermodynamics for functionally equivalent circuits, making the physics-inspired approach relevant to real computational problems, for which functionality is the key element of interest. In particular, our thermodynamic framework provides an alternative perspective on the obfuscation of programs of arbitrary length—an important problem in cryptography—as thermalization through recursive mixing of neighboring sections of a circuit, which can be viewed as the mixing of two containers with “gases of gates.” This recursive process equilibrates the average complexity and leads to the saturation of the circuit entropy, while preserving functionality of the overall circuit. The thermodynamic arguments hinge on ergodicity in the space of circuits which we conjecture is limited to disconnected ergodic sectors due to fragmentation. The notion of fragmentation has important implications for the problem of circuit obfuscation as it implies that there are circuits of same size and functionality that cannot be connected via a polynomial number of local moves. Furthermore, we argue that fragmentation is unavoidable unless the complexity classes NP and coNP coincide, a statement that implies the collapse of the polynomial hierarchy of computational complexity theory to its first level.

Science & Technology - Other Topics

Orion Script Generator

NASA Engineering's Orion Script Generator (OSG) is a program designed to run on Exploration Flight Test One Software. The script generator creates a SuperScript file that, when run, accepts the filename for a listing of Compact Unique Identifiers (CUIs). These CUIs will correspond to different variables on the Orion spacecraft, such as the temperature of a component X, the active or inactive status of another component Y, and so on. OSG will use a linked database to retrieve the value for each CUI, such as "100 05," "True," and so on. Finally, OSG writes SuperScript code to display each of these variables before outputting the ssi file that allows recipients to view a graphical representation of Orion Flight Test One's status through these variables. This project's main challenge was creating flexible software that accepts and transfers many types of data, from Boolean (true or false) values to "Unsigned Long Long'' values (any number from 0 to 18,446,744,073,709,551,615). We also needed to allow bit manipulation for each variable, requiring us to program functions that could convert any of the multiple types of data into binary code. Throughout the project, we explored different methods to optimize the speed of working with the CUI database and long binary numbers. For example, the program handled extended binary numbers much more efficiently when we stored them as collections of Boolean values (true or false representing 1 or 0) instead of as collections of character strings or numbers. We also strove to make OSG as user-friendly and accommodating of different needs as possible its default behavior is to display a current CUI's maximum value and minimum value with three to five intermediate values in between, all in descending order. Fortunately, users can also add other input on the same lines as each CUI name to request different high values, low values, display options (ascending, sine, and so on), and interval sizes for generating intermediate values. Developing input validation took up quite a bit of time, but OSG's flexibility in the end was worth it.

Dooling, Robert J.

Software Development: 3D Animations and Creating User Interfaces for Realistic Simulations

My fall 2015 semester was spent at the Lyndon B. Johnson Space Center working in the Integrated Graphics, Operations, and Analysis Laboratory (IGOAL). My first project was to create a video animation that could tell the story of OMICS. OMICS is a term being used in the field of biomedical science to describe the collective technologies that study biological systems, such as what makes up a cell and how it functions with other systems. In the IGOAL I used a large 23 inch Wacom monitor to draw storyboards, graphics, and line art animations. I used Blender as the 3D environment to sculpt, shape, cut or modify the several scenes and models for the video. A challenge creating this video was to take a term used in biomedical science and describe it in such a way that an 8th grade student can understand. I used a line art style because it would visually set the tone for what we thought was an educational style. In order to get a handle on the perspective and overall feel for the animation without overloading my workspace, I split up the 2 minute animation into several scenes. I used Blender's python scripting capabilities which allowed for the addition of plugins to add or modify tools. The scripts can also directly interact with the objects to create naturalistic patterns or movements. After collecting the rendered scenes, I used Blender's built-in video editing workspace to output the animation. My second project was to write software that emulates a physical system's interface. The interface was to simulate a boat, ROV, and winch system. Simulations are a time and cost effective way to test complicated data and provide training for operators without having to use expensive hardware. We created the virtual controls with 3-D Blender models and 2-D graphics, and then add functionality in C# using the Unity game engine. The Unity engine provides several essential behaviors of a simulator, such as the start and update functions. A framework for Unity, which was developed in the lab, provided a way to place the different widgets on the virtual console dock and have them resize correctly based on the window dimensions.. My task in this project was to create the controls and visualizations for the data coming in from the simulator for the boat portion of the project. I wrote a class for each control window to handle the functionality of that widget. I implemented 11 widgets that make up the ship portion of the simulator. The members of the lab were each masters of their craft and I'm glad I had the opportunity to learn from them. I learned to plan strategically so I could finish this project on time. I allotted time for storyboarding, development, and refinement. In regards to animating I learned to use modifiers like lattice, boolean and build deformers. I also learned how to animate with drivers, how to use the dope sheet, and how to use the graph editor. In coding I learned to limit the chances for bugs by privatizing functions that should be exclusive to their class. I learned how to use the GIT repository to commit, stash and pull the latest build. I learned a bit of everything because I had the chance to see the entire application development process from the artwork, to the implementation.

Gordillo, Orlando Enrique

Measuring Questions: Relevance and its Relation to Entropy

The Boolean lattice of logical statements induces the free distributive lattice of questions. Inclusion on this lattice is based on whether one question answers another. Generalizing the zeta function of the question lattice leads to a valuation called relevance or bearing, which is a measure of the degree to which one question answers another. Richard Cox conjectured that this degree can be expressed as a generalized entropy. With the assistance of yet another important result from Janos Acz6l, I show that this is indeed the case; and that the resulting inquiry calculus is a natural generalization of information theory. This approach provides a new perspective of the Principle of Maximum Entropy.

Knuth, Kevin H.

When Gravity Fails: Local Search Topology

Local search algorithms for combinatorial search problems frequently encounter a sequence of states in which it is impossible to improve the value of the objective function; moves through these regions, called {\em plateau moves), dominate the time spent in local search. We analyze and characterize {\em plateaus) for three different classes of randomly generated Boolean Satisfiability problems. We identify several interesting features of plateaus that impact the performance of local search algorithms. We show that local minima tend to be small but occasionally may be very large. We also show that local minima can be escaped without unsatisfying a large number of clauses, but that systematically searching for an escape route may be computationally expensive if the local minimum is large. We show that plateaus with exits, called benches, tend to be much larger than minima, and that some benches have very few exit states which local search can use to escape. We show that the solutions (i.e. global minima) of randomly generated problem instances form clusters, which behave similarly to local minima. We revisit several enhancements of local search algorithms and explain their performance in light of our results. Finally we discuss strategies for creating the next generation of local search algorithms.

Frank, Jeremy

An operator calculus for surface and volume modeling

The mathematical techniques which form the foundation for most of the surface and volume modeling techniques used in practice are briefly described. An outline of what may be termed an operator calculus for the approximation and interpolation of functions of more than one independent variable is presented. By considering the linear operators associated with bivariate and multivariate interpolation/approximation schemes, it is shown how they can be compounded by operator multiplication and Boolean addition to obtain a distributive lattice of approximation operators. It is then demonstrated via specific examples how this operator calculus leads to practical techniques for sculptured surface and volume modeling.

Gordon, W. J.

A procedure concept for local reflex control of grasping

An architecture is proposed for the control of robotic devices, and in particular of anthropomorphic hands, characterized by a hierarchical structure in which every level of the architecture contains data and control function with varying degree of abstraction. Bottom levels of the hierarchy interface directly with sensors and actuators, and process raw data and motor commands. Higher levels perform more symbolic types of tasks, such as application of boolean rules and general planning operations. Layers implementation has to be consistent with the type of operation and its requirements for real time control. It is proposed to implement the rule level with a Boolean Artificial Neural Network characterized by a response time sufficient for producing reflex corrective action at the actuator level.

Fiorini, Paolo

Autonomous organization of grasping tasks

This paper describes an architecture for the control of robotic devices, and in particular of anthropomorphic hands, characterized by a hierarchical structure in which every level of the architecture contains data and control function with varying degree of abstraction. Bottom levels of the hierarchy interface directly with sensors and actuators, and process raw data and motor commands. Higher levels perform more symbolic types of tasks, such as application of Boolean rules and general planning operations. The implementation of the layer has to be consistent with the type of operation and its requirements for real time control. One implementation of the rule level, with a Boolean artificial neural network which would have a response time sufficient for producing reflex corrective action at the actuator level is presented.

Fiorini, Paolo

Shape-dependent control of cell growth, differentiation, and apoptosis: switching between attractors in cell regulatory networks

Development of characteristic tissue patterns requires that individual cells be switched locally between different phenotypes or "fates;" while one cell may proliferate, its neighbors may differentiate or die. Recent studies have revealed that local switching between these different gene programs is controlled through interplay between soluble growth factors, insoluble extracellular matrix molecules, and mechanical forces which produce cell shape distortion. Although the precise molecular basis remains unknown, shape-dependent control of cell growth and function appears to be mediated by tension-dependent changes in the actin cytoskeleton. However, the question remains: how can a generalized physical stimulus, such as cell distortion, activate the same set of genes and signaling proteins that are triggered by molecules which bind to specific cell surface receptors. In this article, we use computer simulations based on dynamic Boolean networks to show that the different cell fates that a particular cell can exhibit may represent a preprogrammed set of common end programs or "attractors" which self-organize within the cell's regulatory networks. In this type of dynamic network model of information processing, generalized stimuli (e.g., mechanical forces) and specific molecular cues elicit signals which follow different trajectories, but eventually converge onto one of a small set of common end programs (growth, quiescence, differentiation, apoptosis, etc.). In other words, if cells use this type of information processing system, then control of cell function would involve selection of preexisting (latent) behavioral modes of the cell, rather than instruction by specific binding molecules. Importantly, the results of the computer simulation closely mimic experimental data obtained with living endothelial cells. The major implication of this finding is that current methods used for analysis of cell function that rely on characterization of linear signaling pathways or clusters of genes with common activity profiles may overlook the most critical features of cellular information processing which normally determine how signal specificity is established and maintained in living cells. Copyright 2000 Academic Press.

Review

Expressions Module for the Satellite Orbit Analysis Program

The Expressions Module is a software module that has been incorporated into the Satellite Orbit Analysis Program (SOAP). The module includes an expressions- parser submodule built on top of an analytical system, enabling the user to define logical and numerical variables and constants. The variables can capture output from SOAP orbital-prediction and geometric-engine computations. The module can combine variables and constants with built-in logical operators (such as Boolean AND, OR, and NOT), relational operators (such as >, <, or =), and mathematical operators (such as addition, subtraction, multiplication, division, modulus, exponentiation, differentiation, and integration). Parentheses can be used to specify precedence of operations. The module contains a library of mathematical functions and operations, including logarithms, trigonometric functions, Bessel functions, minimum/ maximum operations, and floating- point-to-integer conversions. The module supports combinations of time, distance, and angular units and has a dimensional- analysis component that checks for correct usage of units. A parser based on the Flex language and the Bison program looks for and indicates errors in syntax. SOAP expressions can be built using other expressions as arguments, thus enabling the user to build analytical trees. A graphical user interface facilitates use.

Edmonds, Karina

Reveal, A General Reverse Engineering Algorithm for Inference of Genetic Network Architectures

Given the immanent gene expression mapping covering whole genomes during development, health and disease, we seek computational methods to maximize functional inference from such large data sets. Is it possible, in principle, to completely infer a complex regulatory network architecture from input/output patterns of its variables? We investigated this possibility using binary models of genetic networks. Trajectories, or state transition tables of Boolean nets, resemble time series of gene expression. By systematically analyzing the mutual information between input states and output states, one is able to infer the sets of input elements controlling each element or gene in the network. This process is unequivocal and exact for complete state transition tables. We implemented this REVerse Engineering ALgorithm (REVEAL) in a C program, and found the problem to be tractable within the conditions tested so far. For n = 50 (elements) and k = 3 (inputs per element), the analysis of incomplete state transition tables (100 state transition pairs out of a possible 10(exp 15)) reliably produced the original rule and wiring sets. While this study is limited to synchronous Boolean networks, the algorithm is generalizable to include multi-state models, essentially allowing direct application to realistic biological data sets. The ability to adequately solve the inverse problem may enable in-depth analysis of complex dynamic systems in biology and other fields.

Liang, Shoudan

Juvenile Salmon and Their Habitats in the Columbia River Estuary: A Review and Synthesis of Knowledge Development 2000–2025

[This is a 90% discussion draft.] This is the third Synthesis Memorandum funded by the U.S. Army Corps of Engineers and developed for the Columbia Estuary Ecosystem Restoration Program (CEERP) on the topic of habitat restoration in the Columbia River Estuary (CRE) from Bonneville Dam to the river mouth. While the first two were developed by PNNL and NOAA without the benefit of stakeholder participation, for the current memo, two key activities were initiated: (1) review, by the Expert Regional Technical Group (ERTG), of status and trends monitoring and action effectiveness monitoring funded by CEERP, and (2) a workshop including representatives of the Bonneville Power Administration and the U.S. Army Corps of Engineers (the action agencies [AAs]), the National Oceanic and Atmospheric Administration (NOAA), major research agencies contributing to CEERP, and sponsors who implement CEERP restoration actions. A systematic literature review was conducted using ClarivateTM Web of ScienceTM database. The topics of interest for CRE relevant research included salmon ecology, physical processes, and wetland habitats, and therefore required the use of broad search terms. Our final search criteria included a combination of Boolean operators and an approach to combine different sets of search terms. The final search result yielded 669 records. The records were classified by groups and assigned to the relevant disciplinary expert for review. The review identified substantive advances in understanding the provision of salmon habitat functions through spatiotemporally dynamic physical and ecological processes, and the use of CRE habitats by numerous stocks of juvenile salmon. It also uncovered heretofore unincorporated historical documentation of riparian habitats across the CRE. The characterization of the structural components of floodplain habitat including plant associations and channel networks has advanced considerably, together with the understanding of seasonal changes and long-term trends. The relative influence of salmon-habitat location in the CRE as compared with temporal factors, mainly season, has been well described, which affects the prioritization of restoration. Stressors on the ecosystem and fish, and the drivers of these stressors, have been more carefully elucidated and predictive models are in various stages of development. The vision, aims, and design of restoration projects have advanced together with methods of data collection, analysis, and modeling that have seen substantial improvements. Experiments intended to inform the design of restoration projects are underway or have been completed. An important outstanding area of research that has lagged behind the advances in fundamental understanding of the ecosystem and salmon habitat functions remains the peer-reviewed documentation of the outcomes of restoration for both habitats and fish functions.

estuary

NLR HPC Kestrel Jobs Data

Overview: Anonymized job-level records from the Kestrel HPC system at the National Laboratory of the Rockies (NLR). Each record represents a Slurm batch job with scheduling metadata, resource requests, utilization, energy estimates, and efficiency metrics. Sensitive fields (user, account, job name, submit line, working directory, submit script, and job type) are replaced with 7-character cryptographic hashes. System & Timeframe: Kestrel is located at the NLR campus. Standard compute nodes have 104 cores and 256 GB RAM; bigmem nodes have 2,000 GB. GPU nodes (gpu-h100 partition) use NVIDIA H100 GPUs. Data covers jobs submitted August 2023 through December 2025. Funding provided by the U.S. Department of Energy, EERE. Files: esif.hpc.kestrel.job-anon.zip — Anonymized job records (Hive-partitioned Parquet) datacard.md — Full dataset documentation ~11 million rows, 50 variables. Readable with PyArrow, pandas, DuckDB, Apache Spark, or any Parquet-compatible tool. Data Collection: Jobs collected via sacct with timezone-aware export (SLURM_TIME_FORMAT="%Y-%m-%dT%H:%M:%S%z"), loaded into PostgreSQL. Calculated columns updated via database triggers and batch functions. All timestamps use timestamptz and correctly handle DST transitions. Preprocessing: Anonymization of name, user, account, submit_line, work_dir, submit_script, and job_type via 7-char hex hashes Derived columns: queue_wait, cpu_eff, max/min/avg_mem_eff, energy estimates Simplified job state mapping (e.g., "CANCELLED by 132357" → "CANCELLED") Boolean flags: python_job, reframe_job Temporal decomposition: year, month, day, day_of_week, hour, minute from submit_time Shared node tracking: shared_job_count, nodes_shared, jobs_shared Key Variables: Scheduling: job_id, partition, state_simple, submit_time, start_time, end_time, queue_wait Resources: nodes_req/used, processors_req/used, memory_req, wallclock_req/used, gpus_requested Efficiency: cpu_eff, max/min/avg_mem_eff Energy: cpu_energy_tdp_estimated_max/used_watt_hours, consumed_energy_raw_joules, consumed_energy_raw_watt_hours Sharing: shared_job_count, nodes_shared, jobs_shared Partitions: short, standard, debug, gpu-h100 Job States: CANCELLED, COMPLETED, FAILED, PENDING, RUNNING QoS Levels: normal, high Important Notes: Timestamps include timezone offsets; DST transitions are handled correctly, though adding intervals across DST boundaries requires offset adjustment shared_job_count reflects physical node co-residency, not use of the shared partition Job step records and raw Slurm JSONB fields are excluded Do not attempt to re-identify individuals from hashed fields

97 MATHEMATICS AND COMPUTING

An Abstract Interpretation Framework for the Round-Off Error Analysis of Floating-Point Programs

This paper presents an abstract interpretation framework for the round-off error analysis of floating-point programs. This framework defines a parametric abstract analysis that computes, for each combination of ideal and floating-point execution path of the program, a sound over-approximation of the accumulated floating-point round-off error that may occur. In addition, a Boolean expression that characterizes the input values leading to the computed error approximation is also computed. An abstraction on the control flow of the program is proposed to mitigate the explosion of the number of elements generated by the analysis. Additionally, a widening operator is defined to ensure the convergence of recursive functions and loops. An instantiation of this framework is implemented in the prototype tool PRECiSA that generates formal proof certificates stating the correctness of the computed round-off errors.

Titolo, Laura

Genetic Network Inference: From Co-Expression Clustering to Reverse Engineering

Advances in molecular biological, analytical, and computational technologies are enabling us to systematically investigate the complex molecular processes underlying biological systems. In particular, using high-throughput gene expression assays, we are able to measure the output of the gene regulatory network. We aim here to review datamining and modeling approaches for conceptualizing and unraveling the functional relationships implicit in these datasets. Clustering of co-expression profiles allows us to infer shared regulatory inputs and functional pathways. We discuss various aspects of clustering, ranging from distance measures to clustering algorithms and multiple-duster memberships. More advanced analysis aims to infer causal connections between genes directly, i.e., who is regulating whom and how. We discuss several approaches to the problem of reverse engineering of genetic networks, from discrete Boolean networks, to continuous linear and non-linear models. We conclude that the combination of predictive modeling with systematic experimental verification will be required to gain a deeper insight into living organisms, therapeutic targeting, and bioengineering.

Dhaeseleer, Patrik