Results for “Trajectory optimization” — Page 15

DOE OSTI2016

TH-AB-BRB-03: 4n Radiotherapy

Current state-of-the art digital C-arm medical linear accelerators are capable of delivering radiation treatments with high level of automation, which affords coordinated motions of gantry, couch, and multileaf collimator (MLC) with dose rate modulations. The new machine capacity has shown the potential to bring substantially improved radiation dosimetry and/or delivery efficiency to many challenging diseases. Combining an integrated beam orientation optimization algorithm with automated machine navigation, markedly improved dose conformity has been achieved using 4ρ therapy. Trajectory modulated radiation therapy (TMAT) can be used to deliver highly conformal dose to partial breast or to carve complex dose distribution for therapy involving extended volumes such as total marrow and total lymph node treatment. Dynamic electron arc radiotherapy (DEAR) not only overcomes the deficiencies of conventional electron therapy in dose conformity and homogeneity but also achieves so without patient-specific shields. The combination of MLC and couch tracking provides improved motion management of thoracic and abdominal tumors. A substantial body of work has been done in these technological advances for clinical translation. The proposed symposium will provide a timely review of these exciting opportunities. Learning Objectives: Recognize the potential of using digitally controlled linacs for clinically significant improvements in delivered dose distributions for various treatment sites. Identify existing approaches to treatment planning, optimization and delivery for treatment techniques utilizing the advanced functions of digital linacs and venues for further development and improvement. Understand methods for testing and validating delivery system performance. Identify tools available on current delivery systems for implementation and control for such treatments. Obtain the update in clinical applications, trials and regulatory approval. K. Sheng, NIH U19AI067769, NIH R43CA183390, NIH R01CA188300, Varian Medical Systems V. Yu, Varian Medical Systems, AAPM Summer Undergraduate Fellowship, NSF graduate fellowship S. Nill, Elekta AB. Cancer Research UK under Programme C33589/A19727, NIHR Biomedical Research Centre at The Royal Marsden and The Institute of Cancer Research.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2016

TH-AB-BRB-04: Quality Assurance for Advanced Digital Linac Implementations

Current state-of-the art digital C-arm medical linear accelerators are capable of delivering radiation treatments with high level of automation, which affords coordinated motions of gantry, couch, and multileaf collimator (MLC) with dose rate modulations. The new machine capacity has shown the potential to bring substantially improved radiation dosimetry and/or delivery efficiency to many challenging diseases. Combining an integrated beam orientation optimization algorithm with automated machine navigation, markedly improved dose conformity has been achieved using 4ρ therapy. Trajectory modulated radiation therapy (TMAT) can be used to deliver highly conformal dose to partial breast or to carve complex dose distribution for therapy involving extended volumes such as total marrow and total lymph node treatment. Dynamic electron arc radiotherapy (DEAR) not only overcomes the deficiencies of conventional electron therapy in dose conformity and homogeneity but also achieves so without patient-specific shields. The combination of MLC and couch tracking provides improved motion management of thoracic and abdominal tumors. A substantial body of work has been done in these technological advances for clinical translation. The proposed symposium will provide a timely review of these exciting opportunities. Learning Objectives: Recognize the potential of using digitally controlled linacs for clinically significant improvements in delivered dose distributions for various treatment sites. Identify existing approaches to treatment planning, optimization and delivery for treatment techniques utilizing the advanced functions of digital linacs and venues for further development and improvement. Understand methods for testing and validating delivery system performance. Identify tools available on current delivery systems for implementation and control for such treatments. Obtain the update in clinical applications, trials and regulatory approval. K. Sheng, NIH U19AI067769, NIH R43CA183390, NIH R01CA188300, Varian Medical Systems V. Yu, Varian Medical Systems, AAPM Summer Undergraduate Fellowship, NSF graduate fellowship S. Nill, Elekta AB. Cancer Research UK under Programme C33589/A19727, NIHR Biomedical Research Centre at The Royal Marsden and The Institute of Cancer Research.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2016

TH-AB-BRB-05: Using a Research Real-Time Control Interface to Go Beyond Dynamic MLC Tracking

Current state-of-the art digital C-arm medical linear accelerators are capable of delivering radiation treatments with high level of automation, which affords coordinated motions of gantry, couch, and multileaf collimator (MLC) with dose rate modulations. The new machine capacity has shown the potential to bring substantially improved radiation dosimetry and/or delivery efficiency to many challenging diseases. Combining an integrated beam orientation optimization algorithm with automated machine navigation, markedly improved dose conformity has been achieved using 4ρ therapy. Trajectory modulated radiation therapy (TMAT) can be used to deliver highly conformal dose to partial breast or to carve complex dose distribution for therapy involving extended volumes such as total marrow and total lymph node treatment. Dynamic electron arc radiotherapy (DEAR) not only overcomes the deficiencies of conventional electron therapy in dose conformity and homogeneity but also achieves so without patient-specific shields. The combination of MLC and couch tracking provides improved motion management of thoracic and abdominal tumors. A substantial body of work has been done in these technological advances for clinical translation. The proposed symposium will provide a timely review of these exciting opportunities. Learning Objectives: Recognize the potential of using digitally controlled linacs for clinically significant improvements in delivered dose distributions for various treatment sites. Identify existing approaches to treatment planning, optimization and delivery for treatment techniques utilizing the advanced functions of digital linacs and venues for further development and improvement. Understand methods for testing and validating delivery system performance. Identify tools available on current delivery systems for implementation and control for such treatments. Obtain the update in clinical applications, trials and regulatory approval. K. Sheng, NIH U19AI067769, NIH R43CA183390, NIH R01CA188300, Varian Medical Systems V. Yu, Varian Medical Systems, AAPM Summer Undergraduate Fellowship, NSF graduate fellowship S. Nill, Elekta AB. Cancer Research UK under Programme C33589/A19727, NIHR Biomedical Research Centre at The Royal Marsden and The Institute of Cancer Research.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2019

Deeply Integrated Vehicle Dynamic and Powertrain Operation for Efficient Plug-in Hybrid Electric Bus

The emerging connected and automated vehicle (CAV) technology has opened the door for developing innovative applications and systems to improve vehicle energy efficiency. While most of the recent research has been focused on optimizing vehicle dynamic (VD) and powertrain (PT) operation in isolation, there exists untapped potential to further improve vehicle fuel efficiency through a co-optimization of VD&PT control. In this paper, the authors develop an eco-operation solution for a plug-in hybrid electric bus (PHEB) which seamlessly integrates state-of-the-art CAV applications with advanced powertrain optimization strategies, aiming at improving vehicle energy efficiency and reducing tailpipe emissions. The proposed eco-operation system have 6 components, including traffic/signal timing information acquirement, information integration, scenario identification, powertrain, trajectory planning and a MATLAB/Simulink model for validation and fine-tuning. A deeply integrated vehicle dynamic and powertrain control algorithm is proposed in the paper to optimize the energy-efficiency. Based on the key logic of powertrain control strategy of PHEB, the authors develop a simplified PHEB powertrain model, and put it into their graph based optimization model as the edge cost to derive the optimal speed profile, which is further fine-tuned in the Simulink model. The proposed mode is validated in multiple numerical tests under Eco-Approach and Departure, Eco-Stop and Launch and Eco-Cruise scenarios, and shows significant performance (above 20%) in energy-saving.

Hao, Peng↗

DOE OSTI2015

SU-E-T-562: Motion Tracking Optimization for Conformal Arc Radiotherapy Plans: A QUASAR Phantom Based Study

Purpose: This study is to use plan parameters optimization (Dose rate, collimator angle, couch angle, initial starting phase) to improve the performance of conformal arc radiotherapy plans with motion tracking by increasing the plan performance score (PPS). Methods: Two types of 3D conformal arc plans were created based on QUASAR respiratory motion phantom with spherical and cylindrical targets. Sinusoidal model was applied to the MLC leaves to generate motion tracking plans. A MATLAB program was developed to calculate PPS of each plan (ranges from 0–1) and optimize plan parameters. We first selected the dose rate for motion tracking plans and then used simulated annealing algorithm to search for the combination of the other parameters that resulted in the plan of the maximal PPS. The optimized motion tracking plan was delivered by Varian Truebeam Linac. In-room cameras and stopwatch were used for starting phase selection and synchronization between phantom motion and plan delivery. Gaf-EBT2 dosimetry films were used to measure the dose delivered to the target in QUASAR phantom. Dose profiles and Truebeam trajectory log files were used for plan delivery performance evaluation. Results: For spherical target, the maximal PPS (PPSsph) of the optimized plan was 0.79: (Dose rate: 500MU/min, Collimator: 90°, Couch: +10°, starting phase: 0.83π). For cylindrical target, the maximal PPScyl was 0.75 (Dose rate: 300MU/min, Collimator: 87°, starting phase: 0.97π) with couch at 0°. Differences of dose profiles between motion tracking plans (with the maximal and the minimal PPS) and 3D conformal plans were as follows: PPSsph=0.79: %ΔFWHM: 8.9%, %Dmax: 3.1%; PPSsph=0.52: %ΔFWHM: 10.4%, %Dmax: 6.1%. PPScyl=0.75: %ΔFWHM: 4.7%, %Dmax: 3.6%; PPScyl=0.42: %ΔFWHM: 12.5%, %Dmax: 9.6%. Conclusion: By achieving high plan performance score through parameters optimization, we can improve target dose conformity of motion tracking plan by decreasing total MLC leaf travel distance and leaf speed.

61 RADIATION PROTECTION AND DOSIMETRY↗

DOE OSTI2018

Self-optimized construction of transition rate matrices from accelerated atomistic simulations with Bayesian uncertainty quantification

Here, a massively parallel method to build large transition rate matrices from temperature-accelerated molecular dynamics trajectories is presented. Bayesian Markov model analysis is used to estimate the expected residence time in the known state space, providing crucial uncertainty quantification for higher-scale simulation schemes such as kinetic Monte Carlo or cluster dynamics. The estimators are additionally used to optimize where exploration is performed and the degree of temperature acceleration on the fly, giving an autonomous, optimal procedure to explore the state space of complex systems. The method is tested against exactly solvable models and used to explore the dynamics of C15 interstitial defects in iron. Our uncertainty quantification scheme allows for accurate modeling of the evolution of these defects over timescales of several seconds.

36 MATERIALS SCIENCE↗

DOE OSTI2016

A high-precision instrument for analyzing nonlinear dynamic behavior of bearing cage

The high-precision ball bearing is fundamental to the performance of complex mechanical systems. As the speed increases, the cage behavior becomes a key factor in influencing the bearing performance, especially life and reliability. This paper develops a high-precision instrument for analyzing nonlinear dynamic behavior of the bearing cage. The trajectory of the rotational center and non-repetitive run-out (NRRO) of the cage are used to evaluate the instability of cage motion. This instrument applied an aerostatic spindle to support and spin test the bearing to decrease the influence of system error. Then, a high-speed camera is used to capture images when the bearing works at high speeds. A 3D trajectory tracking software TEMA Motion is used to track the spot which marked the cage surface. Finally, by developing the MATLAB program, a Lissajous’ figure was used to evaluate the nonlinear dynamic behavior of the cage with different speeds. The trajectory of rotational center and NRRO of the cage with various speeds are analyzed. The results can be used to predict the initial failure and optimize cage structural parameters. In addition, the repeatability precision of instrument is also validated. In the future, the motorized spindle will be applied to increase testing speed and image processing algorithms will be developed to analyze the trajectory of the cage.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2023

Genetic algorithm optimization of a chemical kinetic mechanism for propane at engine relevant conditions

Propane has demonstrated significant potential for reductions in greenhouse gas and pollutant emissions in medium- and heavy-duty engine applications, but further improvements require accurate, compact, and scalable chemical kinetic mechanisms to design the next generation of propane fueled engines, particularly at the boosted operating conditions necessary to meet the power density demand of medium- and heavy-duty applications. In this work, six key chemical reactions were identified in a reduced mechanism with 70 species and 352 reactions through a sensitivity analysis performed at conditions typical of thermodynamic trajectories observed in a high compression ratio, long stroke engine operated on propane from throttled to boosted operating conditions. While the original mechanism was validated against rapid compression machine (RCM) data, it was found to overpredict experimental autoignition tendencies in 2-zone, 0-D SI engine simulations performed in Chemkin Pro. Subsequently, a genetic algorithm approach was used to optimize the six reaction rate parameters within established uncertainty bounds by performing RCM simulations and comparing to two independent sets of literature ignition delay times for propane, thus generating two new kinetic mechanisms. The first optimization achieved a mean absolute percent error (MPE) reduction in 2nd stage ignition delay of 61.4% in seven generations, while the second optimization utilized a newer experimental RCM dataset, and achieved MPE reduction of 56.7% in seven generations, and further marginal improvement to 57.8% reduction in 34 generations. Finally, the two mechanisms were then evaluated again in the 2-zone 0-D SI engine model in Chemkin Pro comparing typical mean and knocking cycle trajectories, and it was found that the second optimized mechanism provided better prediction of knock onset at the representative conditions evaluated in this work, particularly for higher load operating conditions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2019

ISiCLE: A Quantum Chemistry Pipeline for Establishing in Silico Collision Cross Section Libraries

High throughput, comprehensive, and confident identifications of metabolites and other chemicals in biological and envi-ronmental samples will revolutionize our understanding of the role of these intriguing and chemically diverse molecules in biological systems. Despite recent technological advances, a metabolomics study still results in the detection of a dispropor-tionate number of features than cannot be confidently assigned to a chemical structure. This inadequacy is driven by the sin-gle most significant limitation in metabolomics: the reliance on reference libraries constructed through the analysis of au-thentic reference chemicals and the limited commercial availability of these compounds. To this end, we have developed the in silico chemical library engine (ISiCLE), a high-performance computing-friendly cheminformatics workflow for generating chemical properties. In the instantiation described here, we predict probable three-dimensional molecular conformers (i.e. conformational isomers) using chemical identifiers as input, from which collision cross sections (CCS) are derived. The ap-proach employs state-of-the-art first-principles simulation, distinguished by use of molecular dynamics, quantum chemistry, and ion mobility calculations to generate predictions, all without training data. Importantly, optimization of ISiCLE includ-ed a refactoring of the popular MOBCAL code for trajectory-based mobility calculations, improving its computational effi-ciency by over two orders of magnitude. Calculated CCS values were validated against 1,983 experimental CCS values and compared to previously reported CCS calculation approaches. Average CCS calculation absolute error is 3.2% with standard deviation 3.1%. An online database is introduced for sharing both calculated and experimental CCS values (metabolom-ics.pnnl.gov), initially including a CCS library with over 0.8M entries. Finally, three successful applications of molecule characterization using calculated CCS are described, including the identification of an environmental degradation product, the separation of molecular isomers, and the decoding of complex blinded mixtures of exposure chemicals. This work represents a promising method to address the limitations of small molecule identification, and offers alternatives to standards-based chemical identification amenable to high-performance computation.

metabolomics, standards-free, collision cross sect↗

DOE OSTI2024

Automated experimental design of safe rampdowns via probabilistic machine learning

Abstract Typically the rampdown phase of a shot consists of a decrease in current and injected power and optionally a change in shape, but there is considerable flexibility in the rate, sequencing, and duration of these changes. On the next generation of tokamaks it is essential that this is done safely as the device could be damaged by the stored thermal and electromagnetic energy present in the plasma. This works presents a procedure for automatically choosing experimental rampdown designs to rapidly converge to an effective rampdown trajectory. This procedure uses probabilistic machine learning methods paired with acquisition functions taken from Bayesian optimization. In a set of 2022 experiments at DIII-D, the rampdown designs produced by our method maintained plasma control down to substantially lower current and energy levels than are typically observed. The actions predicted by the model significantly improved as the model was able to explore over the course of the experimental campaign.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

A Fire Community Observatory: Interdisciplinary, AI-informed Post-Fire Rapid Response for Improved Water Cycle Science at Watershed Scale

Wildfire is an ecological disturbance that disrupts the hydrological cycle. In the past few years, a record number of multiple-and-compounding fires have occurred across urban-wildland gradients in the Western United States. Changes to watershed hydrological partitioning in response to fires (infiltration, runoff, evapotranspiration) presents unprecedented challenges to “Water-in-the-West” through negative impacts to water supply and its quality, and is a direct threat to downstream communities, groundwater, and drinking water supply infrastructure. While much work is being done to advance Artificial Intelligence and Machine Learning (AI/ML) use during fires for emergency response (i.e. predict fire movement, direct evacuations), significant potential exists to use AI/ML to address three scientific grand challenges that are rarely addressed in a convergent science context: 1) how to enhance the potential resiliency of a landscape before fire(s), 2) how to cost-effectively and optimally monitor watershed changes after fires, and 3) how to predict future hydrological and biogeochemical trajectories in fire-impacted watershed given climate change. This whitepaper addresses DOE Focal Area 1: Data acquisition and assimilation enabled by machine learning, AI, and advanced methods.

58 GEOSCIENCES↗

DOE OSTI2018

ISiCLE: A Quantum Chemistry Pipeline for Establishing in Silico Collision Cross Section Libraries

High throughput, comprehensive, and confident identifications of metabolites and other chemicals in biological and envi-ronmental samples will revolutionize our understanding of the role of these intriguing and chemically diverse molecules in biological systems. Despite recent technological advances, a metabolomics study still results in the detection of a dispropor-tionate number of features than cannot be confidently assigned to a chemical structure. This inadequacy is driven by the sin-gle most significant limitation in metabolomics: the reliance on reference libraries constructed through the analysis of au-thentic reference chemicals and the limited commercial availability of these compounds. To this end, we have developed the in silico chemical library engine (ISiCLE), a high-performance computing-friendly cheminformatics workflow for generating chemical properties. In the instantiation described here, we predict probable three-dimensional molecular conformers (i.e. conformational isomers) using chemical identifiers as input, from which collision cross sections (CCS) are derived. The ap-proach employs state-of-the-art first-principles simulation, distinguished by use of molecular dynamics, quantum chemistry, and ion mobility calculations to generate predictions, all without training data. Importantly, optimization of ISiCLE includ-ed a refactoring of the popular MOBCAL code for trajectory-based mobility calculations, improving its computational effi-ciency by over two orders of magnitude. Calculated CCS values were validated against 1,983 experimental CCS values and compared to previously reported CCS calculation approaches. Average CCS calculation absolute error is 3.2% with standard deviation 3.1%. An online database is introduced for sharing both calculated and experimental CCS values (metabolom-ics.pnnl.gov), initially including a CCS library with over 0.8M entries. Finally, three successful applications of molecule characterization using calculated CCS are described, including the identification of an environmental degradation product, the separation of molecular isomers, and the decoding of complex blinded mixtures of exposure chemicals. This work represents a promising method to address the limitations of small molecule identification, and offers alternatives to standards-based chemical identification amenable to high-performance computation.

Colby, Sean M↗

DOE OSTI2021

Application of transport-based metric for continuous interpolation between cryo-EM density maps

Cryogenic electron microscopy (cryo-EM) has become widely used for the past few years in structural biology, to collect single images of macromolecules "frozen in time". As this technique facilitates the identification of multiple conformational states adopted by the same molecule, a direct product of it is a set of 3D volumes, also called EM maps. To gain more insights on the possible mechanisms that govern transitions between different states, and hence the mode of action of a molecule, we recently introduced a bioinformatic tool that interpolates and generates morphing trajectories joining two given EM maps. This tool is based on recent advances made in optimal transport, that allow efficient evaluation of Wasserstein barycenters of 3D shapes. As the overall performance of the method depends on various key parameters, including the sensitivity of the regularization parameter, we performed various numerical experiments to demonstrate how MorphOT can be applied in different contexts and settings. Finally, we discuss current limitations and further potential connections between other optimal transport theories and the conformational heterogeneity problem inherent with cryo-EM data.

3D shapes↗

DOE OSTI2018

Optimization of collision-free paths in a differential-drive robot by a smoothing piecewise-linear approach

This paper presents a methodology for optimizing pre-calculated collision-free paths of differential-drive wheeled robots. The main advantage of this methodology is that optimization is done by considering the kinematics and mechanical constraints of the mobile robot. In accordance to this proposal, the optimized path is achieved by applying recursively a local smoothing on an initial path which is originally modeled as a one-dimensional piecewise linear function. By this recursive smoothing, it can be ensured that the original piecewise linear function can be transformed into a smooth one that fulfill the constraints established by the kinematic equations of the wheeled mobile in terms of a minimum radius of curvature. As a result of this, a trajectory which guarantees lower power consumption and lower mechanical wear, is obtained. To show the better performance of the proposed approach, numerical simulation results are contrasted to those obtained from other reported methods with regards to path length, minimum radius of curvature, cross track error, continuity and resulting acceleration.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Fast dynamic aperture optimization with forward-reversal integration

A fast dynamic aperture (DA) optimization method for storage rings has been developed through the use of reversal integration. Even if dynamical systems have an exact reversal symmetry, a numerical forward integration differs from its reversal. For a chaotic trajectory, cumulative round-off errors are scaled, which results in an exponential growth on the difference. The exponential effect is a generic chaos indicator which represents the sensitivity of the chaotic motion to its initial condition. The chaos indicator of the charged particle motion can be obtained by comparing the forward integrations of particle trajectories with corresponding reversals, a.k.a. “backward integrations.” The indicator is observable even through short-term particle tracking simulations. Therefore, adopting it as an objective function could speed up optimization. Finally, the DA of the National Synchrotron Light Source II storage ring, and another test diffraction-limited light source ring, were optimized using this method for the purpose of demonstration.

43 PARTICLE ACCELERATORS↗

DOE OSTI2021

Towards increasing the performance of FTICR-MS with signal detection at frequency multiples: Signal theory and numerical study

Not Available

Wu, Qinghao (ORCID:000000031665567X)↗

DOE OSTI2018

US alternative jet fuel deployment scenario analyses identifying key drivers and geospatial patterns for the first billion gallons ,

The aviation sector's commitments to carbon-neutral growth in international aviation starting in 2020, and the desire to improve supply surety, price stability, and the environmental performance of aviation fuels, have led to broad interest in sustainable alternative jet fuels. Here, we use the system-dynamics-based biomass scenario model (BSM), focused on alternative jet fuel production capacity evolution, and the geospatially explicit Freight and Fuel Transportation Optimization Tool (FTOT), focused on optimal feedstock and fuel flows over the transportation system, to explore the incentive effects on alternative jet fuel production capacity trajectories and potential geospatial patterns of production and delivery in the USA. Scenarios presented here focus on readily available waste feedstocks (waste fats, oils and greases, municipal solid waste, and crop and forestry residues) and conversion technologies included in the ASTM D7566 synthesized aviation turbine fuels specification. The BSM modeling of possible deployment trajectories from 2015 to 2045 suggests that up to 8 billion gallons may be available by 2045 depending on the policies and incentives implemented. Both approaches suggest that 200 million to 1 billion gallons per year of alternative jet fuel production are possible in 2030 given multiple incentives and a favorable investment climate, and that capital costs and technology maturation rates will affect deployment of different fuel production technologies, and therefore the feedstocks needed. Further collaboration on these modeling approaches would reduce methodological blind spots while providing insights into future industry trajectories.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

DOE OSTI2021

Non-Adiabatic Excited State Molecular Dynamics Methodologies: comparison and convergence

Direct atomistic simulation of nonadiabatic molecular dynamics is a challenging goal that allows important insights into fundamental physical phenomena. A variety of frameworks, ranging from fully quantum treatment of nuclei to semiclassical and mixed quantum–classical approaches, were developed. These algorithms are then coupled to specific electronic structure techniques. Such diversity and lack of standardized implementation make it difficult to compare the performance of different methodologies when treating realistic systems. Here, we compare three popular methods for large chromophores: Ehrenfest, surface hopping, and multiconfigurational Ehrenfest with ab initio multiple cloning (MCE-AIMC). These approaches are implemented in the NEXMD software, which features a common computational chemistry model. The resulting comparisons reveal the method performance for population relaxation and coherent vibronic dynamics. Finally, we study the numerical convergence of MCE-AIMC algorithms by considering the number of trajectories, cloning thresholds, and Gaussian wavepacket width. Our results provide helpful reference data for selecting an optimal methodology for simulating excited-state molecular dynamics.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗