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At least 721 records · Page 40

Numerical study of a smoothing algorithm for the complementarity system over the second-order cone

This paper deals with the complementarity system over the second-order cone (denoted by CSSOC) which contains a wide class of problems. We extend a class of regularized Chen–Harker–Kanzow–Smale smoothing functions studied by Huang and Sun (Appl Math Optim 52:237–262, 2005) for the linear complementarity problem to the CSSOC. Based on this class of functions, we propose a smoothing algorithm for solving the CSSOC. Under weak assumptions, we prove that the proposed algorithm has global and local quadratic convergence. The proposed algorithm is different from existing smoothing algorithms for solving the CSSOC because it adopts a new nonmonotone line search rule. In addition, our algorithm solves a new equation reformulation of the CSSOC. Numerical experiments indicate that the proposed algorithm is quite effective.

97 MATHEMATICS AND COMPUTING↗

Stress-hybrid virtual element method on six-noded triangular meshes for compressible and nearly-incompressible linear elasticity

In this paper, we present a first-order Stress-Hybrid Virtual Element Method (SH-VEM) on six-noded triangular meshes for linear plane elasticity. Here, we adopt the Hellinger–Reissner variational principle to construct a weak equilibrium condition and a stress based projection operator. In each element, the stress projection operator is expressed in terms of the nodal displacements, which leads to a displacement based formulation. This stress-hybrid approach assumes a globally continuous displacement field while the stress field is discontinuous across each element. The stress field is initially represented by divergence-free tensor polynomials based on Airy stress functions, but we also present a formulation that uses a penalty term to enforce the element equilibrium conditions, referred to as the Penalty Stress-Hybrid Virtual Element Method (PSH-VEM). Numerical results are presented for PSH-VEM and SH-VEM, and we compare their convergence to the composite triangle FEM and B-bar VEM on benchmark problems in linear elasticity. The SH-VEM converges optimally in the L 2 norm of the displacement, energy seminorm, and the L 2 norm of hydrostatic stress. Furthermore, the results reveal that PSH-VEM converges in most cases at a faster rate than the expected optimal rate, but it requires the selection of a suitably chosen penalty parameter.

42 ENGINEERING↗

Data Science Meets Physical Organic Chemistry

At the heart of synthetic chemistry is the holy grail of predictable catalyst design. In particular, researchers involved in reaction development in asymmetric catalysis have pursued a variety of strategies toward this goal. This is driven by both the pragmatic need to achieve high selectivities and the inability to readily identify why a certain catalyst is effective for a given reaction. While empiricism and intuition have dominated the field of asymmetric catalysis since its inception, enantioselectivity offers a mechanistically rich platform to interrogate catalyst-structure response patterns that explain the performance of a particular catalyst or substrate. In the early stages of an asymmetric reaction development campaign, the overarching mechanism of the reaction, catalyst speciation, the turnover limiting step, and many other details are unknown or posited based on related reactions. Considering the unclear details leading to a successful reaction, initial enantioselectivity data are often used to intuitively guide the ultimate direction of optimization. However, if the conditions of the Curtin-Hammett principle are satisfied, then measured enantioselectivity can be directly connected to the ensemble of diastereomeric transition states (TSs) that lead to the enantiomeric products, and the associated free energy difference between competing TSs (ΔΔ G ‡ = - RT ln[( S )/( R )], where ( S ) and ( R ) represent the concentrations of the enantiomeric products). We, and others, speculated that this important piece of information can be leveraged to guide reaction optimization in a quantitative way. Although traditional linear free energy relationships (LFERs), such as Hammett plots, have been used to illuminate important mechanistic features, we sought to develop data science derived tools to expand the power of LFERs in order to describe complex reactions frequently encountered in modern asymmetric catalysis. Specifically, we investigated whether enantioselectivity data from a reaction can be quantitatively connected to the attributes of reaction components, such as catalyst and substrate structural features, to harness data for asymmetric catalyst design. In this context, we developed a workflow to relate computationally derived features of reaction components to enantioselectivity using data science tools. The mathematical representation of molecules can incorporate many aspects of a transformation, such as molecular features from substrate, product, catalyst, and proposed transition states. Statistical models relating these features to reaction outputs can be used for various tasks, such as performance prediction of untested molecules. Perhaps most importantly, statistical models can guide the generation of mechanistic hypotheses that are embedded within complex patterns of reaction responses. Overall, merging traditional physical organic experiments with statistical modeling techniques creates a feedback loop that enables both evaluation of multiple mechanistic hypotheses and future catalyst design. In this Account, we highlight the evolution and application of this approach in the context of a collaborative program based on chiral phosphoric acid catalysts (CPAs) in asymmetric catalysis.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Incorporation of Melittin Enhances Interfacial Fluidity of Bicontinuous Microemulsions

The effect of an antimicrobial peptide, melittin, on the long-range collective and local undulation motions of bicontinuous microemulsions (BμEs) was evaluated using dynamic light scattering (DLS) and neutron spin echo (NSE) spectroscopy. Small-angle neutron scattering (SANS) was also used to study the effect of melittin on the structure and the correlation length of BμEs. BμEs were isolated from Winsor-III systems formed by mixing aqueous melittin solutions containing sodium dodecyl sulfate with dodecane/1-pentanol mixtures at optimal salinity. An increase of melittin concentration linearly increased the diffusivity of the microemulsions (D DLS ) and decreased the bending rigidity (κ NSE ) up to an aqueous melittin concentration of 2 g/L, thus indicating an increase of interfacial fluidity. Further increase of melittin concentration above 2 g/L did not change D DLS and slightly increased κ NSE . The changes reflect differences of interaction between melittin and BμE surfactant monolayers at different melittin concentrations. At low concentrations, melittin is highly associated with the surfactant monolayers, likely ion-paired to the sulfate surfactant head groups and perhaps partially penetrating into the surfactant tail region. Above 2 g/L, an apparent saturation concentration, added melittin is less strongly associated with the monolayers. In contrast, the bare bending constant derived from SANS data (κ bare ) underwent only a minor decrease. Noting that κ bare reflects contributions from both the elasticity and saddle-splay moduli, this suggests that κ bare is not an effective indicator of dynamics for the BμEs investigated. Our study demonstrates that amphiphilic solubilizates can have a complex impact on dynamics of surfactant monolayers in microemulsions, with implications for transmembrane diffusion and the kinetics of release from the microemulsion phase, which are important characteristics for the use of BμEs as delivery vehicles and host systems for (bio)chemical reactions.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Density functional theory study of the influence of segregation of S or Fe impurities on electromigration in nano-grained copper interconnects

The reliability of the circuits in the modern microelectronic devices remains, during last decades, one of the key topics in research and gains an attention for improving the promising candidates for conductors. Improvement of materials for such applications can be obtained by both electronic and compositional optimization. Ab initio calculations using full potential linearized augmented plane wave method in density functional theory are applied to explain the reduction in electromigration effect in the vicinity of grain boundaries (GB) in nano-structured Cu due to the segregation of some additives to the GB. Several possible mechanisms are considered. It is demonstrated that S atoms segregated to GB of nano-structured Cu lead to the growth of effective mass of the electrons. This decreases the mobility of electrons in external electric field, and, correspondingly, the momentum that they may transfer to atoms in collisions. Fe atoms segregated to GB of Cu create new empty states at the top of the valance band. These non-occupied states may stimulate the current of holes when external electric field is applied to the system, creating the “hole wind” in the direction opposite to the current of electrons. Such “hole wind” will compensate the forces generated by the electron current and therefore will reduce the total momentum transfer between charge carriers and atoms. The calculated electron density maps show that S and Fe segregating to Cu GB increases the strength of covalent bonds reducing the diffusion of Cu atoms in the vicinity of GB.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Block-diagonalization as a tool for the robust diabatization of high-dimensional potential energy surfaces

Robust diabatization techniques are key for the development of high-dimensional coupled potential energy surfaces (PESs) to be used in multi-state quantum dynamics simulations. In the present study we demonstrate that, besides the actual diabatization technique, common problems with the underlying electronic structure calculations can be the reason why a diabatization fails. After giving a short review of the theoretical background of diabatization, we propose a method based on the block-diagonalization to analyse the electronic structure data. This analysis tool can be used in three different ways: First, it allows to detect issues with the ab initio reference data and is used to optimize the setup of the electronic structure calculations. Second, the data from the block-diagonalization are utilized for the development of optimal parametrized diabatic model matrices by identifying the most significant couplings. Third, the block-diagonalization data are used to fit the parameters of the diabatic model, which yields an optimal initial guess for the non-linear fitting required by standard or more advanced energy based diabatization methods. The new approach is demonstrated by the diabatization of 9 electronic states of the propargyl radical, yielding fully coupled full-dimensional (12D) PESs in closed form.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

New Effective Multithreaded Matching Algorithms

Matching is an important combinatorial problem with a number of applications in areas such as community detection, sparse linear algebra, and network alignment. Since computing optimal matchings can be very time consuming, several fast approximation algorithms, both sequential and parallel, have been suggested. Common to the algorithms giving the best solutions is that they tend to be sequential by nature, while algorithms more suitable for parallel computation give solutions of less quality. We present a new simple 1 2 -approximation algorithm for the weighted matching problem. This algorithm is both faster than any other suggested sequential 1 2 -approximation algorithm on almost all inputs and also scales better than previous multithreaded algorithms. We further extend this to a general scalable multithreaded algorithm that computes matchings of weight comparable with the best sequential algorithms. The performance of the suggested algorithms is documented through extensive experiments on different multithreaded architectures.

matching, parallel algorithms↗

Output Feedback Stabilization for a Class of Multi-Variable Bilinear Stochastic Systems with Stochastic Coupling Attenuation

In this paper, stochastic coupling attenuation is investigated for a class of multi-variable bilinear stochastic systems and a novel output feedback m-block backstepping controller with linear estimator is designed, where gradient descent optimization is used to tune the design parameters of the controller. It has been shown that the trajectories of the closed-loop stochastic systems are bounded in probability sense and the stochastic coupling of the system outputs can be effectively attenuated by the proposed control algorithm. Moreover, the stability of the stochastic systems is analyzed and the effectiveness of the proposed method has been demonstrated using a simulated example.

47 OTHER INSTRUMENTATION↗

A Probabilistic Risk Mitigation Model for Cyber-Attacks to PMU Networks

The power grid is becoming more dependent on information and communication technologies. Complex networks of advanced sensors such as phasor measurement units (PMUs) are used to collect real time data to improve the observability of the power system. Recent studies have shown that the power grid has significant cyber vulnerabilities which could increase when PMUs are used extensively. Therefore, recognizing and responding to vulnerabilities are critical to the security of the power grid. This paper proposes a risk mitigation model for optimal response to cyber-attacks to PMU networks. We model the optimal response action as a mixed integer linear programming (MILP) problem to prevent propagation of the cyber-attacks and maintain the observability of the power system.

Cyber-attack↗

An improved representation of the relationship between photosynthesis and stomatal conductance leads to more stable estimation of conductance parameters and improves the goodness-of-fit across diverse data sets

Stomata play a central role in surface-atmosphere exchange by controlling the flux of water and CO 2 between the leaf and the atmosphere. Representation of stomatal conductance (g sw ) is therefore an essential component of models that seek to simulate water and CO 2 exchange in plants and ecosystems. For given environmental conditions at the leaf surface (CO 2 concentration and vapor pressure deficit or relative humidity), models typically assume a linear relationship between g sw and photosynthetic CO 2 assimilation (A). However, measurement of leaf-level g sw response curves to changes in A are rare, particularly in the tropics, resulting in only limited data to evaluate this key assumption. Here, we measured the response of g sw and A to irradiance in six tropical species at different leaf phenological stages. We showed that the relationship between g sw and A was not linear, challenging the key assumption upon which optimality theory is based-that the marginal cost of water gain is constant. Our data showed that increasing A resulted in a small increase in g sw at low irradiance, but a much larger increase at high irradiance. We reformulated the popular Unified Stomatal Optimization (USO) model to account for this phenomenon and to enable consistent estimation of the key conductance parameters g 0 and g 1 . Our modification of the USO model improved the goodness-of-fit and reduced bias, enabling robust estimation of conductance parameters at any irradiance. In addition, our modification revealed previously undetectable relationships between the stomatal slope parameter g 1 and other leaf traits. We also observed nonlinear behavior between A and g sw in independent datasets that included data collected from attached and detached leaves, and from plants grown at elevated CO 2 concentration. We propose that this empirical modification of the USO model can improve the measurement of g sw parameters and the estimation of plant and ecosystem-scale water and CO 2 fluxes.

54 ENVIRONMENTAL SCIENCES↗

Topology Optimization for Nonlinear Transient Applications Using a Minimally Invasive Approach (LDRD Final Report)

The purpose of this project was to devise, implement, and demonstrate a method that can use Sandia's existing analysis codes (e.g., Sierra, Alegra, the CTH hydro code) with minimal modification to generate objective function gradients for optimization-based design in transient, non-linear, coupled-physics applications. The approach uses a Moving Least Squares representation of the geometry to substantially reduce the number of geometric degrees of freedom. A Multiple-Program Multiple-Data computing model is then used to compute objective gradients via finite differencing. Details of the formulation and implementation are provided, and example applications are presented that show effectiveness and scalability of the approach.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Novel Geometric Operations for Linear Programming

This report summarizes the work performed under the project "Linear Programming in Strongly Polynomial Time." Linear programming (LP) is a classic combinatorial optimization problem heavily used directly and as an enabling subroutine in integer programming (IP). Specifically IP is the same as LP except that some solution variables must take integer values (e.g. to represent yes/no decisions). Together LP and IP have many applications in resource allocation including general logistics, and infrastructure design and vulnerability analysis. The project was motivated by the PI's recent success developing methods to efficiently sample Voronoi vertices (essentially finding nearest neighbors in high-dimensional point sets) in arbitrary dimension. His method seems applicable to exploring the high-dimensional convex feasible space of an LP problem. Although the project did not provably find a strongly-polynomial algorithm, it explored multiple algorithm classes. The new medial simplex algorithms may still lead to solvers with improved provable complexity. We describe medial simplex algorithms and some relevant structural/complexity results. We also designed a novel parallel LP algorithm based on our geometric insights and implemented it in the Spoke-LP code. A major part of the computational step is many independent vector dot products. Our parallel algorithm distributes the problem constraints across processors. Current commercial and high-quality free LP solvers require all problem details to fit onto a single processor or multicore. Our new algorithm might enable the solution of problems too large for any current LP solvers. We describe our new algorithm, give preliminary proof-of-concept experiments, and describe a new generator for arbitrarily large LP instances.

97 MATHEMATICS AND COMPUTING↗

New Results on Communication- and Memory-Aware Load Balancing Model and Algorithms

While load balancing in distributed-memory computing has been well-studied, we present an innovative approach to this problem: a unified, reduced-order model that combines three key components to describe “work” in a distributed system: computation, communication, and memory. Our model enables an optimizer to explore complex tradeoffs in task placement, such as augmented parallelism, at the expense of data replication increasing memory usage. We propose a fully distributed, heuristic-based load balancing optimization algorithm, and demonstrate that it quickly finds close-to-optimal solutions. We formalize the complex optimization problem as a mixed-integer linear program, and compare it to our strategy. Finally, we show that when applied to an electromagnetics code, our approach obtains up to 2.3x speedups for the imbalanced execution.

97 MATHEMATICS AND COMPUTING↗

Multi-scale, Multi-disciplinary, and Multi-agent Explainable AI with Koopman-Undergirded Learning, Prediction, and Analysis (M3EA KULPA) (Project Closeout Report)

The goal of this project was to develop and use domain-aware machine learning formulations, based on the Koopman Operator (KO), for modelling multi-scale, multi-disciplinary (e.g., multi-physics), and/or multi-agent systems. The project developed these formulations for the following cases: • Systems with dynamics at two separate time scales, • Systems with a bi-level hierarchical control structure, • Systems with bi-level hierarchical control and dynamics at two separate time scales (the lower level controls operating at the faster time scale), and • Systems with n separate but interacting agents/disciplines (with/without control, respectively); the controls for each agent could include bi-level hierarchical control and dynamics at two separate time scales as described above. The project then defined a set of dynamical systems consisting of different nonlinear oscillators that could be used to test these different formulations and then subsequently learned the KO models for those systems. With the KO models, we were able to do the following: • Quantify system stability, including both long-term and transient behavior, • Quantify the effects of feedbacks between the different time scales and agents/disciplines in terms of those feedbacks’ effects on system stability, • Replace a standard Proportional-Integral (PI) control in the hierarchical control structure with a KO-based Linear-Quadratic Regular (LQR), a form of optimal control, • Calculate optimal supervisory control policies a) with and without time scale separated dynamics at the lower level control levels and b) with both PI and KO-based LQR lower level control policies, and • Calculate dynamic Nash equilibria for multi-agent systems where each agent makes its own control decisions.

97 MATHEMATICS AND COMPUTING↗

A new passivity-based nonlinear causal control technique for wave energy converters with finite stroke

A new technique is proposed for the design of nonlinear causal feedback controllers for wave energy converters, which explicitly protect against stroke saturation. Here, the technique is an improvement of a technique originally proposed. The primary challenge associated with the problem is the design of nonlinear controllers for which global closed-loop stability can be assured with probability 1 for stationary stochastic response, without also unduly sacrificing power generation performance. The proposed technique consists of three steps: 1) designing a linear feedback controller using multi-objective optimization techniques; 2) augmenting this design with an extra input channel that adheres to a closed-loop passivity condition; and 3) designing an outer, nonlinear passive feedback loop that controls this augmented input in such a way as to ensure stroke limits are maintained. The primary contribution of this paper is a fundamental improvement to the second of these steps, for which the previous technique was not guaranteed to return a valid solution. The proposed technique, by contrast, is shown to always produce a nonlinear controller with the desired properties, under very general modeling assumptions. The technique is illustrated on a simple heaving-buoy wave energy converter example.

16 TIDAL AND WAVE POWER↗

Third-integer Resonant Extraction Regulation System for Mu2e

A third-integer resonant slow extraction system is being developed for Fermilab's Delivery Ring to deliver protons to the upcoming Mu2e experiment. The timescale of the extraction (or spill) duration is 43 milliseconds, which is extremely short and unprecedented. Additionally, the experiment's strict and challenging requirements on the quality of the spill at this time scale has led to the development of a new Spill Regulation System (SRS) design. The SRS primarily consists of three components - slow regulation, fast regulation, and harmonic content suppressor. Contributions to the first two components of the SRS, i.e., Slow Regulation and Fast Regulation subsystems, will be presented in which new adaptive learning algorithm schemes for the slow regulation of the spill -- validated using particle tracking simulations -- shall be described. In addition to these novel methods for the enhancement of the spill regulation system, results of employing Machine Learning in enhancing the performance of the resonant extraction are also presented. At the forefront of applying ML techniques to solve non-linear accelerator control problems, this work includes optimizing the PID gains as well as the replacement of the traditional PID controller using Recurrent Neural Networks and Gated Recurrent Unit (GRU) ML models to achieve efficiencies greater than a PID controller. Cutting-edge on-going Reinforcement Learning efforts, including an actor-critic family of learning algorithms, to regulate the spill rate will be reviewed, as well as present analytical calculations pertaining the transit time of particles in a third-integer resonant extraction. Detailed numerical investigations and validations of such calculations, the model of which could be exported and reliably used in future analytical modeling of any resonant extraction, are discussed.

43 PARTICLE ACCELERATORS↗

SU-E-J-126: An Online Replanning Method for FFF Beams Without Couch Shift

Purpose: In a situation that couch shift for patient positioning is not preferred or prohibited (e.g., MR-Linac), segment aperture morphing (SAM) can address target dislocation and deformation. For IMRT/VMAT with flattening filter free (FFF) beams, however, SAM method would lead to an adverse translational dose effect due to the beam unflattening. Here we propose a new 2-step process to address both the translational effect of FFF beams and the target deformation. Methods: The replanning method consists of an offline and an online steps. The offline step is to create a series of pre-shifted plans (PSP) obtained by a so called “warm start” optimization (starting optimization from the original plan, rather from scratch) at a series of isocenter shifts with fixed distance (e.g. 2 cm, at x,y,z = 2,0,0 ; 2,2,0 ; 0,2,0; …;− 2,0,0). The PSPs all have the same number of segments with very similar shapes, since the warm-start optimization only adjusts the MLC positions instead of regenerating them. In the online step, a new plan is obtained by linearly interpolating the MLC positions and the monitor units of the closest PSPs for the shift determined from the image of the day. This two-step process is completely automated, and instantaneously fast (no optimization or dose calculation needed). The previously-developed SAM algorithm is then applied for daily deformation. We tested the method on sample prostate and pancreas cases. Results: The two-step interpolation method can account for the adverse dose effects from FFF beams, while SAM corrects for the target deformation. The whole process takes the same time as the previously reported SAM process (5–10 min). Conclusion: The new two-step method plus SAM can address both the translation effects of FFF beams and target deformation, and can be executed in full automation requiring no additional time from the SAM process. This research was supported by Elekta inc. (Crawley, UK)

60 APPLIED LIFE SCIENCES↗

Projective Integral Updates for High-Dimensional Variational Inference

Variational inference is an approximation framework for Bayesian inference that seeks to improve quantified uncertainty in predictions by optimizing a simplified distribution over parameters to stand in for the full posterior. Capturing model variations that remain consistent with training data enables more robust predictions by reducing parameter sensitivity. This work introduces a fixed-point optimization for variational inference that is applicable when every feasible log density can be expressed as a linear combination of functions from a given basis. In such cases, the optimizer becomes a fixed-point of projective integral updates. When the basis spans univariate quadratics in each parameter, the feasible distributions are Gaussian mean-fields and the projective integral updates yield quasi-Newton variational Bayes (QNVB). Other bases and updates are also possible. Since these updates require high-dimensional integration, this work begins by proposing an efficient quasirandom sequence of quadratures for mean-field distributions. Each iterate of the sequence contains two evaluation points that combine to correctly integrate all univariate quadratic functions and, if the mean-field factors are symmetric, all univariate cubics. More importantly, averaging results over short subsequences achieves periodic exactness on a much larger space of multivariate polynomials of quadratic total degree. The corresponding variational updates require four loss evaluations with standard (not second-order) backpropagation to eliminate error terms from over half of all multivariate quadratic basis functions. Furthermore, this integration technique is motivated by first proposing stochastic blocked mean-field quadratures, which may be useful in other contexts. A PyTorch implementation of QNVB allows for better control over model uncertainty during training than competing methods. Experiments demonstrate superior generalizability for multiple learning problems and architectures.

Gaussian mean-field↗