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Chaotic roots of the modular multiplication dynamical system in Shor's algorithm

Shor's factoring algorithm, believed to provide an exponential speedup over classical computation, relies on finding the period of an exactly periodic quantum modular multiplication operator. This exact periodicity is the hallmark of an integrable system, which is paradoxical from the viewpoint of quantum chaos, given that the classical limit of the modular multiplication operator is a highly chaotic system that occupies the “maximally random” Bernoulli level of the classical ergodic hierarchy. In this work, we approach this apparent paradox from a quantum dynamical systems viewpoint, and consider whether signatures of ergodicity and chaos may indeed be encoded in such an “integrable” quantization of a chaotic system. We show that Shor's modular multiplication operator, in specific cases, can be written as a superposition of quantized 𝐴-baker's maps exhibiting more typical signatures of quantum chaos and ergodicity. This work suggests that the integrability of Shor's modular multiplication operator may stem from the interference of other “chaotic” quantizations of the same family of maps, and paves the way for deeper studies on the interplay of integrability, ergodicity, and chaos in and via quantum algorithms.

Dynamical systems

Modular Autonomous Experimentation for Biological Applications (Full Report)

The Modular Autonomous Research System (MARS) was developed to address the pressing need for faster, more reliable, and more adaptable scientific discovery. Traditional experimentation is limited by manual labor, long cycle times, and fragmented data streams, which constrain the ability to explore complex chemical and materials design spaces. To overcome these limitations, we created an integrated, modular platform that combines laboratory robotics, diverse measurement instruments, and a central data infrastructure with artificial intelligence–driven decision-making. The system links liquid handling robots, robotic arms, and optical plate readers into a closed loop where experiments are executed automatically, data is analyzed in real time, and subsequent experimental conditions are adaptively chosen to maximize information gain. Over the course of the project, MARS was validated on two primary test cases—spectroscopic metal–ligand binding assays and peptide-directed mineralization—which highlighted the system’s ability to handle uncertainty and variability in experimental measurements. To further demonstrate modularity and extensibility, we also established additional testbeds in electrochemistry for catalyst discovery and electrolyte formulation for advanced batteries. The results show that MARS can reliably conduct autonomous campaigns with minimal human intervention, adapt to distinct scientific domains, and provide a scalable model for future self-driving laboratories. This work establishes new capabilities for modular, uncertainty-aware automation and directly supports the need for advanced, data-driven research platforms capable of accelerating discovery across a wide range of scientific and national security missions.

59 BASIC BIOLOGICAL SCIENCES

Modularity in robotic systems

Most robotic systems today are designed one at a time, at a high cost of time and money. This wasteful approach has been necessary because the industry has not established a foundation for the continued evolution of intelligent machines. The next generation of robots will have to be generic, versatile machines capable of absorbing new technology rapidly and economically. This approach is demonstrated in the success of the personal computer, which can be upgraded or expanded with new software and hardware at virtually every level. Modularity is perceived as a major opportunity to reduce the 6 to 7 year design cycle time now required for new robotic manipulators, greatly increasing the breadth and speed of diffusion of robotic systems in manufacturing. Modularity and its crucial role in the next generation of intelligent machines are the focus of interest. The main advantages that modularity provides are examined; types of modules needed to create a generic robot are discussed. Structural modules designed by the robotics group at the University of Texas at Austin are examined to demonstrate the advantages of modular design.

Tesar, Delbert

Space biology initiative program definition review. Trade study 4: Design modularity and commonality

The relative cost impacts (up or down) of developing Space Biology hardware using design modularity and commonality is studied. Recommendations for how the hardware development should be accomplished to meet optimum design modularity requirements for Life Science investigation hardware will be provided. In addition, the relative cost impacts of implementing commonality of hardware for all Space Biology hardware are defined. Cost analysis and supporting recommendations for levels of modularity and commonality are presented. A mathematical or statistical cost analysis method with the capability to support development of production design modularity and commonality impacts to parametric cost analysis is provided.

Jackson, L. Neal

Modular Rocket Engine Control Software (MRECS)

The Modular Rocket Engine Control Software (MRECS) Program is a technology demonstration effort designed to advance the state-of-the-art in launch vehicle propulsion systems. Its emphasis is on developing and demonstrating a modular software architecture for advanced engine control systems that will result in lower software maintenance (operations) costs. It effectively accommodates software requirement changes that occur due to hardware technology upgrades and engine development testing. Ground rules directed by MSFC were to optimize modularity and implement the software in the Ada programming language. MRECS system software and the software development environment utilize Commercial-Off-the-Shelf (COTS) products. This paper presents the objectives, benefits, and status of the program. The software architecture, design, and development environment are described. MRECS tasks are defined and timing relationships given. Major accomplishments are listed. MRECS offers benefits to a wide variety of advanced technology programs in the areas of modular software architecture, reuse software, and reduced software reverification time related to software changes. MRECS was recently modified to support a Space Shuttle Main Engine (SSME) hot-fire test. Cold Flow and Flight Readiness Testing were completed before the test was cancelled. Currently, the program is focused on supporting NASA MSFC in accomplishing development testing of the Fastrac Engine, part of NASA's Low Cost Technologies (LCT) Program. MRECS will be used for all engine development testing.

Tarrant, C.

Modular Rocket Engine Control Software (MRECS)

The Modular Rocket Engine Control Software (MRECS) Program is a technology demonstration effort designed to advance the state-of-the-art in launch vehicle propulsion systems. Its emphasis is on developing and demonstrating a modular software architecture for a generic, advanced engine control system that will result in lower software maintenance (operations) costs. It effectively accommodates software requirements changes that occur due to hardware. technology upgrades and engine development testing. Ground rules directed by MSFC were to optimize modularity and implement the software in the Ada programming language. MRECS system software and the software development environment utilize Commercial-Off-the-Shelf (COTS) products. This paper presents the objectives and benefits of the program. The software architecture, design, and development environment are described. MRECS tasks are defined and timing relationships given. Major accomplishment are listed. MRECS offers benefits to a wide variety of advanced technology programs in the areas of modular software, architecture, reuse software, and reduced software reverification time related to software changes. Currently, the program is focused on supporting MSFC in accomplishing a Space Shuttle Main Engine (SSME) hot-fire test at Stennis Space Center and the Low Cost Boost Technology (LCBT) Program.

Tarrant, Charlie

Analysis of In-Space Assembly of Modular Systems

Early system-level life cycle assessments facilitate cost effective optimization of system architectures to enable implementation of both modularity and in-space assembly, two key Exploration Systems Research & Technology (ESR&T) Strategic Challenges. Experiences with the International Space Station (ISS) demonstrate that the absence of this rigorous analysis can result in increased cost and operational risk. An effort is underway, called Analysis of In-Space Assembly of Modular Systems, to produce an innovative analytical methodology, including an evolved analysis toolset and proven processes in a collaborative engineering environment, to support the design and evaluation of proposed concepts. The unique aspect of this work is that it will produce the toolset, techniques and initial products to analyze and compare the detailed, life cycle costs and performance of different implementations of modularity for in-space assembly. A multi-Center team consisting of experienced personnel from the Langley Research Center, Johnson Space Center, Kennedy Space Center, and the Goddard Space Flight Center has been formed to bring their resources and experience to this development. At the end of this 30-month effort, the toolset will be ready to support the Exploration Program with an integrated assessment strategy that embodies all life-cycle aspects of the mission from design and manufacturing through operations to enable early and timely selection of an optimum solution among many competing alternatives. Already there are many different designs for crewed missions to the Moon that present competing views of modularity requiring some in-space assembly. The purpose of this paper is to highlight the approach for scoring competing designs.

Moses, Robert W.

Modular, Adaptive, Reconfigurable Systems: Technology for Sustainable, Reliable, Effective, and Affordable Space Exploration

In order to execute the Vision for Space Exploration, we must find ways to reduce cost, system complexity, design, build, and test times, and at the same time increase flexibility to satisfy multiple functions. Modular, Adaptive, Reconfigurable System (MARS) technologies promise to set the stage for the delivery of system elements that form the building blocks of increasingly ambitious missions involving humans and robots. Today, space systems are largely specialized and built on a case-by-case basis. The notion of modularity however, is nothing new to NASA. The 1970's saw the development of the Multi-Mission Modular spacecraft (MMS). From 1980 to 1992 at least six satellites were built under this paradigm, and included such Goddard Space Flight Center missions as SSM, EUVE, UARS, and Landsat 4 and 5. Earlier versions consisted of standard subsystem "module" or "box" components that could be replaced within a structure based on predefined form factors. Although the primary motivation for MMS was faster/cheaper integration and test, standardization of interfaces, and ease of incorporating new subsystem technology, it lacked the technology maturity and programmatic "upgrade infrastructure" needed to satisfy varied mission requirements, and ultimately it lacked user buy-in. Consequently, it never evolved and was phased out. Such concepts as the Rapid Spacecraft Development Office (RSDO) with its regularly updated catalogue of prequalified busses became the preferred method for acquiring satellites. Notwithstanding, over the past 30 years since MMS inception, technology has advanced considerably and now modularity can be extended beyond the traditional MMS module or box to cover levels of integration, from the chip, card, box, subsystem, to the space system and to the system-of-systems. This paper will present the MARS architecture, cast within the historical context of MMS. Its application will be highlighted by comparing a state-of-the-art point design vs. a MARS-enabled lunar mission, as a representative robotic case design.

Esper, Jaime

Modular, Intelligent Power Systems for Space Exploration

NASA's new Space Exploration Initiative demands that vehicles, habitats, and rovers achieve unprecedented levels of reliability, safety, effectiveness, and affordability. Modular and intelligent electrical power systems are critical to achieving those goals. Modular electrical power systems naturally increase reliability and safety through built-in fault tolerance. These modular systems also enable standardization across a multitude of systems, thereby greatly increasing affordability of the programs. Various technologies being developed to support this new paradigm for space power systems will be presented. Examples include the use of digital control in power electronics to enable better performance and advanced modularity functions such as distributed, master-less control and series input power conversion. Also, digital control and robust communication enables new levels of power system control, stability, fault detection, and health management. Summary results from recent development efforts are presented along with expected future technology development needs required to support NASA's ambitious space exploration goals.

Button, Robert

Modular Apparatus and Method for Attaching Multiple Devices

A modular apparatus for attaching sensors and electronics is disclosed. The modular apparatus includes a square recess including a plurality of cavities and a reference cavity such that a pressure sensor can be connected to the modular apparatus. The modular apparatus also includes at least one voltage input hole and at least one voltage output hole operably connected to each of the plurality of cavities such that voltage can be applied to the pressure sensor and received from the pressure sensor.

Okojie, Robert S

Modular Fixturing System

The modular fixturing system of the present invention is modular, reusable and capable of significant customization, both in terms of system radius and system height, allowing it to be arranged and rearranged in numerous unique configurations. The system includes multiple modular stanchions having stanchion shafts and stanchion feet that removably attach to apertures in a table. Angle brackets attached to the modular stanchions support shelves. These shelves in turn provide support to work pieces during fabrication processes such as welding.

Littell, Justin Anderson

Modular Apparatus and Method for Attaching Multiple Devices

A modular apparatus for attaching sensors and electronics is disclosed. The modular apparatus includes a square recess including a plurality of cavities and a reference cavity such that a pressure sensor can be connected to the modular apparatus. The modular apparatus also includes at least one voltage input hole and at least one voltage output hole operably connected to each of the plurality of cavities such that voltage can be applied to the pressure sensor and received from the pressure sensor.

Okojie, Robert S.

Electra: A Modular-Based Expansion of NASA's Supercomputing Capability

NASA has increasingly relied on high-performance computing (HPC) re- sources for computational modeling, simulation, and data analysis to meet the science and engineering goals of its missions in space exploration, aeronautics, and Earth and space science. The NASA Advanced Supercomputing (NAS) Division at Ames Research Center in Silicon Valley, Calif., hosts NASA’s premier supercomputing resources, integral to achieving and enhancing the success of the agency’s missions. NAS provides a balanced environment, funded under the High-End Computing Capability (HECC) project, comprised of world-class supercomputers, including its flagship distributed-memory cluster, Pleiades; high-speed networking; and massive data storage facilities, along with multi-disciplinary support teams for user support, code porting and optimization, and large-scale data analysis and scientific visualization. However, as scientists have increased the fidelity of their simulations and engineers are conducting larger parameter-space studies, the requirements for supercomputing resources have been growing by leaps and bounds. With the facility housing the HECC systems reaching its power and cooling capacity, NAS undertook a prototype project to investigate an alternative approach for housing supercomputers. Modular supercomputing, or container-based computing, is an innovative concept for expanding NASA’s HPC capabilities. With modular supercomputing, additional containers—similar to portable storage pods—can be connected together as needed to accommodate the agency’s ever-increasing demand for computing resources. In addition, taking advantage of the local weather permits the use of cooling technologies that would additionally save energy and reduce annual water usage. The first stage of NASA’s Modular Supercomputing Facility (MSF) prototype, which resulted in a 1,000 square-foot module on a concrete pad with room for 16 compute racks, was completed in Fall 2016 and an SGI (now HPE) computer system, named Electra, was deployed there in early 2017. Cooling is performed via an evaporative system built into the module, and preliminary experience shows a Power Usage Effectiveness (PUE) measurement of 1.03. Electra achieved over a petaflop on the LINPACK benchmark, sufficient to rank number 96 on the November 2016 TOP500 list [14]. The system consists of 1,152 InfiniBand-connected Intel Xeon Broadwell-based nodes. Its users access their files on a facility-wide file system shared by all HECC compute assets via Mellanox MetroX InfiniBand extenders, which connect the Electra fabric to Lustre routers in the primary facility over fiber-optic links about 900 feet long. The MSF prototype has exceeded expectations and is serving as a blueprint for future expansions. In the remainder of this chapter, we detail how modular data center technology can be used to expand an existing compute resource. We begin by describing NASA’s requirements for supercomputing and how resources were provided prior to the integration of the Electra module-based system.

Biswas, Rupak

Progress on Modular Unmanned Aircraft Technology

Modular unmanned aerial systems (UAS) are a new development in UAS architecture that holds promise for reusable, reconfigurable hosts for science and autonomy payloads. Modularity of airframe subcomponents lowers costs, facilitates rapid field repair, permits holistic optimization, and enables mass-customization of bespoke platforms customizing the aircraft around a given payload or payloads. Without modular UAS, sensors and instruments often must be designed to fit in a non-modifiable airframe. This talk will present how the nexus of modularity, rapid prototyping and design reuse opens up new tradeoffs, and discuss the envisioned benefits, price paid, and enhanced missions made possible by this new approach to aircraft development.

Dahlgren, Robert P.

Benefits Of Automated Construction And Energy Efficiency Measures In Modular Homes

This article builds on and adds to a Buildings XV publication that introduced the Transformative Efficiency and Automation in Modular Homes (TEAMH) project. The TEAMH project sought to develop a scalable solution for producing modular homes with 20-50% energy savings and similar cost relative to site-fabricated single-family home construction. A key aspect of the project was assessing the potential for labor cost reductions through automation-assisted construction using light gauge steel (LGS). To quantify the advantages of this approach, side-by-side comparisons were made between traditional wood-framed construction and automation-assisted LGS construction. This demonstration involved constructing one wood-framed wall and several LGS test walls, accompanied by a time-and-motion study. The results indicated that automation assistance could decrease construction time and associated labor costs by as much as 46%. High-performance envelope technologies for exterior insulation and air sealing were evaluated to compare modular homes with site-built homes that meet the International Energy Conservation Code (IECC). A key technology considered was vacuum insulation panels (VIPs) with fiberglass cores. Guarded hot box testing of multiple full-scale wall assemblies containing different combinations of exterior continuous insulation systems containing phenolic foam and VIPs. Testing on various full-scale wall assemblies revealed that, with LGS construction, cavity insulation had minimal impact on exterior wall performance. Omitting cavity insulation can reduce labor and material costs while streamlining manufacturing, as its installation is labor-intensive and not easily automated due to the need for precise placement around wiring and other internal components. Guarded hot box tests of multiple LGS test walls with foam and VIP-based exterior insulation systems achieved R-values of up to 31 hr-ft2-°F/Btu. Finally, building energy modeling of multiple modular home designs indicated that the upgraded envelope assemblies can yield heating energy savings of up to 50% and cooling energy savings of up to 30% compared to IECC 2018 standards.

Shrestha, Som [ORNL] (ORCID:0000000183993797)

Modular Assembled Radiators for Nuclear Electric Propulsion (NEP) VehicLes (MARVL) Project Thermal Technology Development

Nuclear Electric Propulsion (NEP) has been considered for crew and cargo class missions to Mars for more than six decades. The Primary Heat Rejection Subsystem (PHRS) of an NEP vehicle expels the megawatts of waste heat generated by the Power Conversion Subsystem (PCS). In previous studies, integrating the majority of the NEP vehicle within a single launch fairing required the use of complex deployable elements and resulted in reduced PCS efficiency. To achieve the necessary radiating area, past design studies have utilized massive multi-wing folding radiators resulting in conceptual PHRS designs that have been widely acknowledged as non-optimal. The Modular Assembled Radiators for NEP VehicLes (MARVL) project is incorporating in-Space Assembly (iSA) into the design process to realize lightweight, modular, and more capable PHRS radiators. Since the project’s Authority to Proceed (ATP) date of October 2024, the project team has been developing a modular design for the PHRS radiators that will be suitable for both the Mars mission environments and iSA commissioning operations. This document captures the current progress of the incremental technology development for the thermal components of the MARVL System of Interest (SOI).

Modular Radiator

Advanced Polymer Characterization: Modular Operations for Spectral Alignment by Iterative Compression (MOSAIC)

Matrix-assisted laser desorption/ionization (MALDI) mass spectrometry encodes structural information across diverse homo- and copolymer ensembles, yet decrypting these spectra requires a systematic analytical approach. We introduce Modular Operations for Spectral Alignment by Iterative Compression (MOSAIC)─a general cipher algorithm that applies modular arithmetic to filter monomer-derived mass contributions and cluster MALDI peaks by nonconstitutional repeating units (non-CRUs). MOSAIC performs sequential modular operations using monomer mass differences as base units to compress complex spectral data, revealing end-group distributions and comonomer incorporation. As a demonstration, we applied MOSAIC to five copolymers formed by two different polymerization mechanisms. Furthermore, the resulting remainder–mass plots clearly resolve polymer homologs with distinct non-CRUs into visually apparent clusters, enabling intuitive assignment of mass spectral features.

Wang, Hanlin M. [University of Illinois at Urbana−

A modular and extensible CHARMM-compatible model for all-atom simulation of polypeptoids

Peptoids (N-substituted glycines) are a class of sequence-defined synthetic peptidomimetic polymers with applications including drug delivery, catalysis, and biomimicry. Classical molecular simulations have been used to predict and understand the conformational dynamics of single chains and their self-assembly into morphologies including sheets, tubes, spheres, and fibrils. The CGenFF-NTOID model based on the CHARMM General Force Field has demonstrated success in accurate all-atom molecular modeling of peptoid structure and thermodynamics. Extension of this force field to new peptoid side chains has historically required reparameterization of side chain bonded interactions against ab initio data. This fitting protocol improves the accuracy of the force field but is also burdensome and precludes modular extensibility of the model to arbitrary peptoid sequences. In this work, we develop and demonstrate a Modular Side Chain CGenFF-NTOID (MoSiC-CGenFF-NTOID) as an extension of CGenFF-NTOID employing a modular decomposition of the peptoid backbone and side chain parameterizations, wherein arbitrary side chains within the large family of substituted methyl groups (i.e., –CH 3 , –CH 2 R, –CHRR', and –CRR'R") are directly ported from CGenFF. We validate this approach against ab initio calculations and experimental data to develop a MoSiC-CGenFF-NTOID model for all 20 natural amino acid side chains along with 13 commonly used synthetic side chains and present an extensible paradigm to efficiently determine whether a novel side chain can be directly incorporated into the model or whether refitting of the CGenFF parameters is warranted. We make the model freely available to the community along with a tool to perform automated initial structure generation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH