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The Middeck Active Control Experiment (MACE)

The Middeck Active Control Experiment (MACE) is a NASA In-Step and Control Structure Interaction (CSI) Office funded Shuttle middeck experiment. The objective is to investigate the extent to which closed-loop behavior of flexible spacecraft in zero-gravity (0-g) can be predicted. This prediction becomes particularly difficult when dynamic behavior during ground testing exhibits extensive suspension and direct gravity coupling. On-orbit system identification and control reconfiguration is investigated to improve performance which would otherwise be limited due to errors in prediction. The program is presently in its preliminary design phase with launch expected in the summer of 1994. The MACE test article consists of three attitude control torque wheels, a two axis gimballing payload, inertial sensors and a flexible support structure. With the acquisition of a second payload, this will represent a multiple payload platform with significant structural flexibility. This paper presents on-going work in the areas of modelling and control of the MACE test article in the zero and one-gravity environments. Finite element models, which include suspension and gravity effects, and measurement models, derived from experimental data, are used as the basis for Linear Quadratic Gaussian controller designs. Finite element based controllers are analytically used to study the differences in closed-loop performance as the test article transitions between the 0-g and 1-g environments. Measurement based controllers are experimentally applied to the MACE test article in the 1-g environment and achieve over an order of magnitude improvement in payload pointing accuracy when disturbed by a broadband torque disturbance. The various aspects of the flight portion of the experiment are also discussed.

Miller, David W.↗

Primate translational vestibuloocular reflexes. II. Version and vergence responses to fore-aft motion

To maintain binocular fixation on near targets during fore-aft translational disturbances, largely disjunctive eye movements are elicited the amplitude and direction of which should be tuned to the horizontal and vertical eccentricities of the target. The eye movements generated during this task have been investigated here as trained rhesus monkeys fixated isovergence targets at different horizontal and vertical eccentricities during 10 Hz fore-aft oscillations. The elicited eye movements complied with the geometric requirements for binocular fixation, although not ideally. First, the corresponding vergence angle for which the movement of each eye would be compensatory was consistently less than that dictated by the actual fixation parameters. Second, the eye position with zero sensitivity to translation was not straight ahead, as geometrically required, but rather exhibited a systematic dependence on viewing distance and vergence angle. Third, responses were asymmetric, with gains being larger for abducting and downward compared with adducting and upward gaze directions, respectively. As frequency was varied between 4 and 12 Hz, responses exhibited high-pass filter properties with significant differences between abduction and adduction responses. As a result of these differences, vergence sensitivity increased as a function of frequency with a steeper slope than that of version. Despite largely undercompensatory version responses, vergence sensitivity was closer to ideal. Moreover, the observed dependence of vergence sensitivity on vergence angle, which was varied between 2.5 and 10 MA, was largely linear rather than quadratic (as geometrically predicted). We conclude that the spatial tuning of eye velocity sensitivity as a function of gaze and viewing distance follows the general geometric dependencies required for the maintenance of foveal visual acuity. However, systematic deviations from ideal behavior exist that might reflect asymmetric processing of abduction/adduction responses perhaps because of different functional dependencies of version and vergence eye movement components during translation.

NASA Program Biomedical Research and Countermeasur↗

An optimized index of human cardiovascular adaptation to simulated weightlessness

Prolonged exposure to weightlessness is known to produce a variety of cardiovascular changes, some of which may influence the astronaut's performance during a mission. In order to find a reliable indicator of cardiovascular adaptation to weightlessness, we analyzed data from nine male subjects after a 24-hour period of normal activity and after a period of simulated weightlessness produced by two hours in a launch position followed by 20 hours of 6 degrees head-down tilt plus pharmacologically induced diuresis (furosemide). Heart rate, arterial pressure, thoracic fluid index, and radial flow were analyzed. Autoregressive spectral estimation and decomposition were used to obtain the spectral components of each variable from the subjects in the supine position during pre- and post-simulated weightlessness. We found a significant decrease in heart rate power and an increase in thoracic fluid index power in the high frequency region (0.2-0.45 Hz) and significant increases in radial flow and arterial pressure powers in the low frequency region (<0.2 Hz) in response to simulated weightlessness. However, due to the variability among subjects, any single variable appeared limited as a dependable index of cardiovascular adaptation to weightlessness. The backward elimination algorithm was then used to select the best discriminatory features from these spectral components. Fisher's linear discriminant and Bayes' quadratic discriminant were used to combine the selected features to obtain an optimal index of adaptation to simulated weightlessness. Results showed that both techniques provided improved discriminant performance over any single variable and thus have the potential for use as an index to track adaptation and prescribe countermeasures to the effects of weightlessness.

NASA Discipline Number 14-10↗

Superconvergence of Online Optimization for Model Predictive Control

We develop a one-Newton-step-per-horizon, online, lag-L, model predictive control (MPC) algorithm for solving discrete-time, equality-constrained, nonlinear dynamic programs. Based on recent sensitivity analysis results for the target problems class, we prove that the approach exhibits a behavior that we call superconvergence; that is, the tracking error with respect to the full horizon solution is not only stable for successive horizon shifts, but also decreases with increasing shift order to a minimum value that decays exponentially in the length of the receding horizon. The key analytical step is the decomposition of the one-step error recursion of our algorithm into algorithmic error and perturbation error. We show that the perturbation error decays exponentially with the lag between two consecutive receding horizons, while the algorithmic error, determined by Newton’s method, achieves quadratic convergence instead. Overall this approach induces our local exponential convergence result in terms of the receding horizon length for suitable values of L. In conclusion, numerical experiments validate our theoretical findings.

97 MATHEMATICS AND COMPUTING↗

Integration of Libration Point Orbit Dynamics into a Universal 3-D Autonomous Formation Flying Algorithm

The autonomous formation flying control algorithm developed by the Goddard Space Flight Center (GSFC) for the New Millennium Program (NMP) Earth Observing-1 (EO-1) mission is investigated for applicability to libration point orbit formations. In the EO-1 formation-flying algorithm, control is accomplished via linearization about a reference transfer orbit with a state transition matrix (STM) computed from state inputs. The effect of libration point orbit dynamics on this algorithm architecture is explored via computation of STMs using the flight proven code, a monodromy matrix developed from a N-body model of a libration orbit, and a standard STM developed from the gravitational and coriolis effects as measured at the libration point. A comparison of formation flying Delta-Vs calculated from these methods is made to a standard linear quadratic regulator (LQR) method. The universal 3-D approach is optimal in the sense that it can be accommodated as an open-loop or closed-loop control using only state information.

Folta, David↗

QSPIN: A High Level Java API for Quantum Computing Experimentation

QSPIN is a high level Java language API for experimentation in QC models used in the calculation of Ising spin glass ground states and related quadratic unconstrained binary optimization (QUBO) problems. The Java API is intended to facilitate research in advanced QC algorithms such as hybrid quantum-classical solvers, automatic selection of constraint and optimization parameters, and techniques for the correction and mitigation of model and solution errors. QSPIN includes high level solver objects tailored to the D-Wave quantum annealing architecture that implement hybrid quantum-classical algorithms [Booth et al.] for solving large problems on small quantum devices, elimination of variables via roof duality, and classical computing optimization methods such as GPU accelerated simulated annealing and tabu search for comparison. A test suite of documented NP-complete applications ranging from graph coloring, covering, and partitioning to integer programming and scheduling are provided to demonstrate current capabilities.

Quantu↗

Exploring MPI Communication Models for Graph Applications Using Graph Matching as a Case Study

Traditional implementations of parallel graph operations on distributed memory platforms are written using Message Passing Interface (MPI) point to point communication primitives such as Send-Recv (blocking and nonblocking). Apart from this classical model, the MPI community has over the years added other communication models; however, their suitability for handling the irregular traffic workloads typical of graph operations remain comparatively less explored. Our aim in this paper is to study these relatively underutilized communication models of MPI for graph applications. More specifically, we evaluate MPI’s one-sided programming, or Remote Memory Access (RMA), and nearest neighborhood collectives using a process graph topology. There are features in these newer models that are intended to better map to irregular communication patterns, as exemplified in graph algorithms. As a concrete application for our case study, we use distributed memory implementations of a weighted graph matching algorithm to investigate performances of MPI-3 RMA and neighborhood collective operations compared to nonblocking Send- Recv. A matching in a graph is a subset of edges such that no two matched edges are incident on the same vertex. A maximum weight matching is a matching of maximum weight computed as the sum of the weights of matched edges. Algorithms for optimal matching have quadratic complexity and are difficult to parallelize. More importantly, execution of graph matching is dominated by high volume of irregular memory accesses, making it an ideal candidate for studying the effects of various MPI communication models on graph applications at scale. Our neighborhood collectives and RMA implementations yields up to 6× speedup over traditional optimized nonblocking Send-Recv implementations, on thousands of cores of the NERSC Cori supercomputer. We believe the lessons learned from this case study can be adopted to benefit a wider range of graph application codes.

Ghosh, Sayan↗

Investigation of Nonlinear Difference-Frequency Wave Excitation on a Semisubmersible Offshore-Wind Platform with Bichromatic-Wave CFD Simulations: Preprint

The natural surge and pitch frequencies of semisubmersible offshore wind platforms are typically designed to be below the wave frequencies to avoid direct excitation. However, surge or pitch resonance can be excited by the nonlinear low-frequency loads generated by irregular incident waves. Second-order potential-flow models with added Morison drag have been found to underpredict this low-frequency excitation and response. As part of the OC6 project, Computational Fluid Dynamics (CFD) simulations were performed to enable a better understanding of the low-frequency loads and the limitations of lower-fidelity models. The focus of the current paper is to set up a computationally cost-effective CFD simulation of a fixed semisubmersible platform to investigate nonlinear difference-frequency loads and establish the corresponding uncertainty in the results. Due to the high computing cost, CFD simulations of irregular waves can be challenging. Instead, simulations were performed with bichromatic waves having a shorter repeat period. A preliminary comparison with Quadratic Transfer Functions from second-order potential-flow theory shows that CFD models consistently predict higher nonlinear wave loads at the difference frequency, likely due to flow separation and viscous drag not accounted for in potential-flow theory.

2nd order↗

3D numerical simulation of the long range propagation of acoustical shock waves through a heterogeneous and moving medium

Many situations involve the propagation of acoustical shock waves through flows. Natural sources such as lightning, volcano explosions, or meteoroid atmospheric entries, emit loud, low frequency, and impulsive sound that is influenced by atmospheric wind and turbulence. The sonic boom produced by a supersonic aircraft and explosion noises are examples of intense anthropogenic sources in the atmosphere. The Buzz-Saw-Noise produced by turbo-engine fan blades rotating at supersonic speed also propagates in a fast flow within the engine nacelle. Simulating these situations is challenging, given the 3D nature of the problem, the long range propagation distances relative to the central wavelength, the strongly nonlinear behavior of shocks associated to a wide-band spectrum, and finally the key role of the flow motion. With this in view, the so-called FLHOWARD (acronym for FLow and Heterogeneous One-Way Approximation for Resolution of Diffraction) method is presented with three-dimensional applications. A scalar nonlinear wave equation is established in the framework of atmospheric applications, assuming weak heterogeneities and a slow wind. It takes into account diffraction, absorption and relaxation properties of the atmosphere, quadratic nonlinearities including weak shock waves, heterogeneities of the medium in sound speed and density, and presence of a flow (assuming a mean stratified wind and 3D turbulent ? flow fluctuations of smaller amplitude). This equation is solved in the framework of the one-way method. A split-step technique allows the splitting of the non-linear wave equation into simpler equations, each corresponding to a physical effect. Each sub-equation is solved using an analytical method if possible, and finite-differences otherwise. Nonlinear effects are solved in the time domain, and others in the frequency domain. Homogeneous diffraction is handled by means of the angular spectrum method. Ground is assumed perfectly flat and rigid. Due to the 3D aspect, the code was massively parallelized using the single program, multiple data paradigm with the Message Passing Interfaces (MPI) for distributed memory architectures. This allows us to handle problems in the order of a thousand billion mesh points in the four dimensions (3 dimensions of space plus time). The validity of the method has been thoroughly evaluated on many cases with known solutions: linear piston, scattering of plane wave by a heterogeneous sphere, propagation in a waveguide with a shear flow, scattering by a finite amplitude vortex and nonlinear propagation in a thermoviscous medium. This validation process allows for a detailed assessment of the advantages and limitations of the method. Finally, applications to atmospheric propagation of shock waves will be presented.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

The design of a turboshaft speed governor using modern control techniques

The objectives of this program were: to verify the model of off schedule compressor variable geometry in the T700 turboshaft engine nonlinear model; to evaluate the use of the pseudo-random binary noise (PRBN) technique for obtaining engine frequency response data; and to design a high performance power turbine speed governor using modern control methods. Reduction of T700 engine test data generated at NASA-Lewis indicated that the off schedule variable geometry effects were accurate as modeled. Analysis also showed that the PRBN technique combined with the maximum likelihood model identification method produced a Bode frequency response that was as accurate as the response obtained from standard sinewave testing methods. The frequency response verified the accuracy of linear models consisting of engine partial derivatives and used for design. A power turbine governor was designed using the Linear Quadratic Regulator (LQR) method of full state feedback control. A Kalman filter observer was used to estimate helicopter main rotor blade velocity. Compared to the baseline T700 power turbine speed governor, the LQR governor reduced droop up to 25 percent for a 490 shaft horsepower transient in 0.1 sec simulating a wind gust, and up to 85 percent for a 700 shaft horsepower transient in 0.5 sec simulating a large collective pitch angle transient.

Delosreyes, G.↗

ARTSN: An Automated Real-Time Spacecraft Navigation System

As part of the Deep Space Network (DSN) advanced technology program an effort is underway to design a filter to automate the deep space navigation process.The automated real-time spacecraft navigation (ARTSN) filter task is based on a prototype consisting of a FORTRAN77 package operating on an HP-9000/700 workstation running HP-UX 9.05. This will be converted to C, and maintained as the operational version. The processing tasks required are: (1) read a measurement, (2) integrate the spacecraft state to the current measurement time, (3) compute the observable based on the integrated state, and (4) incorporate the measurement information into the state using an extended Kalman filter. This filter processes radiometric data collected by the DSN. The dynamic (force) models currently include point mass gravitational terms for all planets, the Sun and Moon, solar radiation pressure, finite maneuvers, and attitude maintenance activity modeled quadratically. In addition, observable errors due to troposphere are included. Further data types, force and observable models will be ncluded to enhance the accuracy of the models and the capability of the package. The heart of the ARSTSN is a currently available continuous-discrete extended Kalman filter. Simulated data used to test the implementation at various stages of development and the results from processing actual mission data are presented.

Burkhart, P. Daniel↗

Short-Depth QAOA circuits and Quantum Annealing on Higher-Order Ising Models (Rev.2)

The Quantum Alternating Operator Ansatz (QAOA) and Quantum Annealing (QA) are quantum algorithms that are both based on the adiabatic theorem and both have the goal of sampling the optimal solution(s) of combinatorial optimization problems. Quantum annealing has been physically instantiated on D-Wave devices using superconducting flux qubits, and QAOA can be programmed on digital gate-model quantum computers such as the programmable superconducting transmon qubits devices of the IBMQ series, for instance ibm washington. QAOA and QA address the same types of problems, but it is unclear how they will scale to large problem sizes and to larger and higher-fidelity quantum computers. In this article, we present a direct comparison between QAOA, one and two rounds, run on all 127 qubits of ibm washington and QA run on D-Wave Advantage system4.1 and Advantage system6.1. The problems which allow for this comparison are random Ising model problems whose connectivity matches the heavy hexagonal lattice topology of ibm washington and the Pegasus graph connectivity of the two D-Wave devices. We create two classes of problem instances for this comparison: one with higher order terms (ZZZ variable interactions), linear terms, and quadratic terms, and a separate problem type with only linear and quadratic terms. Our QAOA circuits are novel and extremely short depth, with a CNOT depth of 6 per round, which allows whole chip usage of ibm washington’s heavy hexagonal lattice and can be applied to future heavy-hex chips. We also test the effectiveness of the error suppression technique digital dynamical decoupling on the QAOA circuits. The QAOA circuits compiled to ibm washington are composed of several thousand circuit instructions, approximately 3, 000 depending on the details of the circuit, making these some the largest quantum circuits ever executed on a digital quantum processor. QAOA and QA are compared against the classical heuristic algorithm of simulated annealing and all problem instances are exactly solved using CPLEX in order to evaluate which samplers, if any, correctly found the ground state solution(s) of the problem instances. We find that (i) QA outperforms QAOA on all problem instances, (ii) QAOA samples the problems better than random sampling, and (iii) QAOA angle computation exhibits clear parameter concentration across the ensemble of Ising models.

127 Qubits↗

Privacy-Preserving Aggregation of Controllable Loads to Compensate Fluctuations in Solar Power

Cybersecurity and privacy are of the utmost importance for safe, reliable operation of the electric grid. It is well known that the increased connectivity/interoperability between all stakeholders (e.g., utilities, suppliers, and consumers) will enable personal information collection. Significant advanced metering infrastructure (AMI) deployment and demand response (DR) programs across the country, while enable enhanced automation, also generate energy data on individual consumers that can potentially be used for exploiting privacy. Inspired by existing works which consider DR, battery-based perturbation, and differential privacy noise adding, we novelly consider the aggregator (cluster) level privacy issue in the DR framework of solar photovoltaic (PV) generation following. Different from most of the existing works which mainly rely on the charging/discharging scheduling of rechargeable batteries, we utilize controllable building loads to serve as virtual storage devices to absorb a large portion of the PV genertaion while delicately keeping desired noisy terms to satisfy the differential privacy for the raw load profiles at the aggregator level. This not only ensures differential privacy, but also improves the DR efficiency in load following since part of the noisy signal in solar PV generation has been filtered out. In particular, a mixed integer quadratic optimization problem is formulated to optimally dispatch a population of on/off controllable loads to achieve this privacy-preserving DR service.

Dong, Jin↗

Velocity-pressure integrated versus penalty finite element methods for high Reynolds number flows

Velocity-pressure integrated and consistent penalty finite element computations of high Reynolds number, laminar flows are presented. In both of the methods, the pressure has been interpolated using linear shape functions for a triangular element. The triangular element is contained inside the bi-quadratic isoparametric element. It has been reported previously that the pressure interpolation method, when used in the velocity-pressure integrated method, yielded accurate computational results for high Reynolds number flows. It is shown that use of the same pressure interpolation method in the consistent penalty finite element method yielded accurate velocity and pressure fields which were comparable to those obtained using the velocity-pressure integrated method. Accuracy of the two finite element methods has been demonstrated by comparing the computational results with available experimental data and/or fine-grid finite difference computational results. Advantages and disadvantages of the two methods are discussed on the basis of accuracy and convergence nature. Example problems considered include a lid-driven cavity flow for Reynolds number of 10,000, a laminar backward-facing step flow, a laminar flow through a nest of cylinders, and a channel flow with an internal blockage. A finite element computer program (NSFLOW/P) for the 2-D, incompressible Navier-Stokes equations is also presented.

Kim, Sang-Wook↗

Colorless top partners, a 125 GeV Higgs boson, and the limits on naturalness

Theories of physics beyond the Standard Model that address the hierarchy problem generally involve top partners, new particles that cancel the quadratic divergences associated with the Yukawa coupling of the Higgs to the top quark. With extensions of the Standard Model that involve new colored particles coming under strain from collider searches, scenarios in which the top partners carry no charge under the strong interactions have become increasingly compelling. Although elusive for direct searches, these theories predict modified couplings of the Higgs boson to the Standard Model particles. This results in corrections to the Higgs production and decay rates that can be detected at the Large Hadron Collider (LHC) provided the top partners are sufficiently light, and the theory correspondingly natural. In this paper we consider three theories that address the little hierarchy problem and involve colorless top partners, specifically the Mirror Twin Higgs, Folded Supersymmetry, and the Quirky Little Higgs. For each model we investigate the current and future bounds on the top partners, and the corresponding limits on naturalness, that can be obtained from the Higgs program at the LHC. Here, we conclude that the LHC will not be able to strongly disfavor naturalness, with mild tuning at the level of about one part in ten remaining allowed even with 3000 fb$^{-1}$ of data at 14 TeV.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

SU-E-T-502: Initial Results of a Comparison of Treatment Plans Produced From Automated Prioritized Planning Method and a Commercial Treatment Planning System

Purpose We developed an automated treatment planning system based on a hierarchical goal programming approach. To demonstrate the feasibility of our method, we report the comparison of prostate treatment plans produced from the automated treatment planning system with those produced by a commercial treatment planning system. Methods In our approach, we prioritized the goals of the optimization, and solved one goal at a time. The purpose of prioritization is to ensure that higher priority dose-volume planning goals are not sacrificed to improve lower priority goals. The algorithm has four steps. The first step optimizes dose to the target structures, while sparing key sensitive organs from radiation. In the second step, the algorithm finds the best beamlet weight to reduce toxicity risks to normal tissue while holding the objective function achieved in the first step as a constraint, with a small amount of allowed slip. Likewise, the third and fourth steps introduce lower priority normal tissue goals and beam smoothing. We compared with prostate treatment plans from Memorial Sloan Kettering Cancer Center developed using Eclipse, with a prescription dose of 72 Gy. A combination of liear, quadratic, and gEUD objective functions were used with a modified open source solver code (IPOPT). Results Initial plan results on 3 different cases show that the automated planning system is capable of competing or improving on expert-driven eclipse plans. Compared to the Eclipse planning system, the automated system produced up to 26% less mean dose to rectum and 24% less mean dose to bladder while having the same D95 (after matching) to the target. Conclusion We have demonstrated that Pareto optimal treatment plans can be generated automatically without a trial-and-error process. The solver finds an optimal plan for the given patient, as opposed to database-driven approaches that set parameters based on geometry and population modeling.

60 APPLIED LIFE SCIENCES↗

Re-evaluation of ortho-para- dependence of self pressure-broadening in the ν 1 + ν 3 band of acetylene

Optical frequency comb-referenced measurements of self pressure-broadened line profiles of the R(8) to R(13) lines in the ν 1 + ν 3 combination band of acetylene near 1.52 µ m are reported. The analysis of the data found no evidence for a previously reported systematic alternation in self pressure-broadened line widths with the nuclear spin state of the molecule. This work brought out the need for the use of an accurate line profile model and careful accounting for weak background absorptions due to hot band and lower abundance isotopomer lines. The data were adequately fit using the quadratic speed-dependent Voigt profile model, neglecting the small speed-dependent shift. Parameters describing the most probable and speed-dependent pressure-broadening, most probable shift, and the line strength were determined for each line. Detailed modeling of the results of Iwakuni et al. showed that their neglect of collisional narrowing due to the speed-dependent broadening term combined with the strongly absorbing data recorded and analyzed in transmission mode were the reasons for their results.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Final technical report: From colliders to cosmology in the LHC era

Now that the Higgs boson has been discovered, the question is: why is it so light when its mass is expected to blow up to the highest mass scale of the particles to which it couples? Supersymmetry tames these quadratic divergences, yet there is as yet no sign of superparticles at LHC. Sparticle mass limits and the Higgs mass suggest sparticles which reside in the multi-TeV range if at all. This situation heightens the Little Hierarchy or SUSY naturalness question: why the mass gap between weak scale and sparticle mass scale? In the past several years, our group has been highly focused on understanding the naturalness question (H. Baer). During this period, we have made some major clarifications in naturalness, showing how conventional measures overestimate fine-tuning and showing that ``natural SUSY'' requires light higgsino states-- with mass the closer to the 100 GeV scale the better. Such an inverted electroweakino spectrum leads to new, distinctive signatures at LHC (e.g. same-sign diboson production) while the ILC is expected to be a higgsino factory. We have found a deep connection between naturalness and the Peccei-Quinn scale. Dark matter is expected to occur as a higgsino-like WIMP plus axion admixture and detection of both is ultimately expected. Additional objectives of our research program are making more precise predictions for the production and decay rates of new particles, developing techniques and computer codes to discover these particles and to measure their properties, and searching for new phenomena and new interactions at present and future colliders. In addition, we will investigate direct and indirect searches for supersymmetric dark matter: both WIMPs and axions. % To carry out these studies, we will calculate production rates for SUSY particles, other new particles in various extensions to the Standard Model and physics backgrounds, as well as evaluate QCD and electroweak radiative corrections. Since the cross sections of most signals are expected to be small relative to those of the backgrounds, we plan on developing analysis techniques suitable for extracting small signals. In this project, we propose continuing along these productive investigation lines so as to facilitate discoveries which can be made at LHC, ILC and at various dark matter detectors. These projects facilitate the DoE goals at the Energy and Cosmic Frontiers.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗