Surrogate-based branch-and-bound algorithms for simulation-based black-box optimization
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Bounding the Failure Probability Range of Polynomial Systems Subject to P-box Uncertainties
This paper proposes a reliability analysis framework for systems subject to multiple design requirements that depend polynomially on the uncertainty. Uncertainty is prescribed by probability boxes, also known as p-boxes, whose distribution functions have free or fixed functional forms. An approach based on the Bernstein expansion of polynomials and optimization is proposed. In particular, we search for the elements of a multi-dimensional p-box that minimize (i.e., the best-case) and maximize (i.e., the worst-case) the probability of inner and outer bounding sets of the failure domain. This technique yields intervals that bound the range of failure probabilities. The offset between this bounding interval and the actual failure probability range can be made arbitrarily tight with additional computational effort.
Crespo, Luis G.↗
Molecular Mechanisms Regulating Muscle Fiber Composition Under Microgravity
The overall goal of this project is to reveal the molecular mechanisms underlying the selective and debilitating atrophy of specific skeletal muscle fiber types that accompanies sustained conditions of microgravity. Since little is currently known about the regulation of fiber-specific gene expression programs in mammalian muscle, elucidation of the basic mechanisms of fiber diversification is a necessary prerequisite to the generation of therapeutic strategies for attenuation of muscle atrophy on earth or in space. Vertebrate skeletal muscle development involves the fusion of undifferentiated mononucleated myoblasts to form multinucleated myofibers, with a concomitant activation of muscle-specific genes encoding proteins that form the force-generating contractile apparatus. The regulatory circuitry controlling skeletal muscle gene expression has been well studied in a number of vertebrate animal systems. The goal of this project has been to achieve a similar level of understanding of the mechanisms underlying the further specification of muscles into different fiber types, and the role played by innervation and physical activity in the maintenance and adaptation of different fiber phenotypes into adulthood. Our recent research on the genetic basis of fiber specificity has focused on the emergence of mature fiber types and have implicated a group of transcriptional regulatory proteins, known as E proteins, in the control of fiber specificity. The restriction of E proteins to selected muscle fiber types is an attractive hypothetical mechanism for the generation of muscle fiber-specific patterns of gene expression. To date our results support a model wherein different E proteins are selectively expressed in muscle cells to determine fiber-restricted gene expression. These studies are a first step to define the molecular mechanisms responsible for the shifts in fiber type under conditions of microgravity, and to determine the potential importance of E proteins as upstream targets for the effects of weightlessness. In the past year we have determined that the expression of E Proteins is restricted to specific fiber types by post-transcriptional mechanisms. By far, the most prevalent mechanism of cellular control for achieving post-transcriptional regulation of gene expression is selective proteolysis -through the ubiquitin -proteasome pathway. Steady-state levels of HEB message are similar in all fast and slow skeletal muscle fiber types, yet the protein is restricted to Type IIX fibers. HEB appears to be a nodal point for regulating fiber-specific transcription, as expression of the transcription factor is regulated at the post-transcriptional level. It is not clear at present whether the regulation is at the level of protein synthesis or degradation. We are now poised to evaluate the biological role of ubiquitination in fiber specific-gene expression by controlling the post-transcriptional expression of E Proteins. The use of metabolic labelling and pharmacological inhibitors of the ubiquitin pathway will be used to identify the mode of regulation of the Type IIX expression pattern. The potential role of specific kinases in effecting the restriction of HEB expression will be examined by using both inhibitors and activators. The results of these studies will provide the necessary information to evaluate the biological role of E proteins in controlling fiber type transitions, and in potentially attenuating the atrophic effects of microgravity conditions. We have also recently shown that ectopic expression of the HEB protein transactivates the Type IIX-specific skeletal a-actin reporter. The 218 bp skeletal a-actin promoter drives transgene expression solely in mature Type IIX fibers. A mouse also carrying the transgene MLCI/HEB (which ectopically expresses the E Protein HEB in Type IIB fibers) forces expression of the skeletal a-actin reporter gene in Type IIB fibers. We can now dissect the composition of this fiber-specific cis-element. The skeletal a-actin promoter is quite compact and has been extensively characterized in vitro for activity and binding factors. The single E box may act as a binding target of myogenic factor/HEB heterodimer to allow for IIX expression. The HEB transcription factor may recognize either the precise flanking sequences of the E Box, or perhaps interacting with other proteins bound nearby, and activating expression in Type IIX fibers. This E box will be both ablated, and alternatively, as ablation may well destroy any muscle-specific transcriptional activity, flanking sequences substituted with those surrounding the E box (El) of the myogenin promoter. Modification of fiber-specific transgene expression will be tested in transgenic mice. The results of these studies will provide basic information on the regulatory circuitry underlying fiber specificity, and will form the basis for building appropriate transgenic regulatory cassettes to effect fiber transitions in subsequent experimental manipulations on unweighted muscles.
Rosenthal, Nadia A.↗
Hybrid Decompositional Verification for Discovering Failures in Adaptive Flight Control Systems
Adaptive flight control systems hold tremendous promise for maintaining the safety of a damaged aircraft and its passengers. However, most currently proposed adaptive control methodologies rely on online learning neural networks (OLNNs), which necessarily have the property that the controller is changing during the flight. These changes tend to be highly nonlinear, and difficult or impossible to analyze using standard techniques. In this paper, we approach the problem with a variant of compositional verification. The overall system is broken into components. Undesirable behavior is fed backwards through the system. Components which can be solved using formal methods techniques explicitly for the ranges of safe and unsafe input bounds are treated as white box components. The remaining black box components are analyzed with heuristic techniques that try to predict a range of component inputs that may lead to unsafe behavior. The composition of these component inputs throughout the system leads to overall system test vectors that may elucidate the undesirable behavior
Thompson, Sarah↗
Modeling the Impact of the Organic Aerosol Phase State on Multiphase OH Reactive Uptake Kinetics and the Resultant Heterogeneous Oxidation Timescale of Organic Aerosol in the Amazon Rainforest
Accurate predictions of chemical lifetime, i.e., oxidation timescale and change in the mass of organic aerosols (OAs) in atmospheric models, are critical to quantify the impacts of OA on aerosol–cloud interactions, radiative forcing, and air quality. The heterogeneous oxidation of OA by hydroxyl (OH) radicals is a key process governing OA mass changes during their oxidation. Recently, laboratory observations of the OH uptake coefficient (γ OH ) and heterogeneous reaction rate (k het,OH ) for different OA systems with varying phase states have been combined to develop a new parameterization of γ OH and k het,OH as a function of the OA phase state, i.e., viscosity (η OA ). Here, in this work, we use a recently published viscosity prediction framework to analyze the new γ OH and k het,OH parameterization with a box model. Subsequently, we implement this box model to predict γ OH and k het,OH over the Amazon rainforest in the dry-to-wet transition season with both significant biomass burning and biogenic influences. Relevant parameters within our box model are specified based on detailed regional model simulations over the Amazon using the Weather Research and Forecasting model coupled with Chemistry (WRF-Chem). η OA is predicted as a function of species volatility, OA composition (including water uptake) along with ambient relative humidity (RH), and temperature. Based on ambient conditions simulated by WRF-Chem over the entire atmospheric column, we use the box model to predict the upper bounds of the heterogeneous oxidation timescale of OA. Based on previous laboratory measurements, we assume that this heterogeneous OH oxidation causes fragmentation (carbon loss) of OA, followed by the evaporation of the fragmented molecules that results in the exponential decay of OA. We predict that the oxidation timescale of OA is ~1 month near the Earth’s surface in the pristine Amazonian background because of low OH concentrations. But OA is oxidized more rapidly within urban and wildfire plumes near the Earth’s surface with an order of magnitude higher OH concentrations compared to the pristine background, causing the simulated oxidation timescale of OA to be much shorter, ~3–4 days. At 3–5 km altitudes where biomass burning OA is predicted to be semisolid, the heterogeneous oxidation timescale is estimated as ~6 days to 3 weeks and decreases with increasing OH concentrations within plumes. We show that the simulated mass loss of OA is strongly size-dependent, where smaller particles oxidize more rapidly compared to larger particles due to their greater per-particle surface area-to-volume ratio. Increasing urbanization and deforestation in the Amazon in the future might increase OH concentrations in the background Amazon, causing faster oxidation of OA. At higher altitudes above liquid clouds, especially in the upper troposphere where temperatures approach ~250 K, future measurements are needed to reduce the uncertainties related to the mass loss of OA at colder temperatures and low relative humidity conditions due to its heterogeneous OH oxidation.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Energy spectrum of two-particle scattering in a periodic box
We aim to compute the discrete energy spectrum for two-body scattering in a three-dimensional box under periodic boundary conditions. The spectrum in the center of mass is obtained by solving the Schödinger equation in a test potential using the Fourier basis. The focus is on how to project the spectrum into the various irreducible representations of the symmetry groups of the box. Four examples are given to show how the infinite-volume spectrum (including both bound and scattering states) is resolved in cubic or elongated boxes, and in systems with integer or half-integer total spin. Such a demonstration is a crucial step in relating the discrete spectrum in the box to the infinite-volume scattering phaseshifts via the Lüscher method.
Computer Science↗
Empirical Bounding Analysis and User Recommendations for a Neutron Multiplicity Detector
Neutron multiplicity detectors are useful for a variety of applications including nuclear emergency response, nuclear nonproliferation, safeguards, and criticality safety. When measuring black-box problems (i.e., when the system being measured is completely unknown) with systems that have relatively low detection efficiency, expert analysis is frequently required to determine appropriate bounds for system parameters such as neutron multiplication and neutron leakage. This is because the detection efficiency can vary wildly, which also means that the resulting system parameters can have large variations. This work applies an empirical approach to provide bounds on system parameters (such as system multiplication, neutron leakage, and detector efficiency). The results of this bounding analysis are then used as inputs to provide recommendations to users regarding criticality safety. In addition to describing the method used, this work provides sample results from a measurement campaign performed at the National Criticality Experiments Research Center (NCERC).
46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
Modeling of SRS Aluminum-clad Spent Nuclear Fuel in Standard DOE Sealed Canisters
At the Savannah River Site (SRS), approximately 7 MTHM of aluminum-clad spent nuclear fuel is currently in wet storage at L-basin. A significant portion of this fuel is slated to be dried and sealed in DOE standard canisters for long-term storage. This report will focus on a few fuel types, which should bound all other fuel stored at SRS. These consist of the reference fuel assembly, the MURR fuel and the HFIR fuel. These bound a hypothetical maximum scenario for MTR box fuel, a maximum for decay heat in an assembly, and a maximum for the aluminum surface area, respectively. The geometry for the packages were created from DOE specifications for storage of each of the fuels. As long as the minimum time from reactor discharge to sealed storage is 3 years, then the highest temperatures which occur within the sealed canisters do not exceed 100° C for all scenarios considered here. In the geometry considered, while the HFIR fuel has a large surface area, the packaging configuration leaves large void areas, such that the aluminum surface to free volume ratio is about 30% less than an ATR or MURR packaging configuration.
11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
Broken Ergodicity in MHD Turbulence
Ideal magnetohydrodynamic (MHD) turbulence may be represented by finite Fourier series, where the inherent periodic box serves as a surrogate for a bounded astrophysical plasma. Independent Fourier coefficients form a canonical ensemble described by a Gaussian probability density function containing a Hermitian covariance matrix with positive eigenvalues. The eigenvalues at lowest wave number can be very small, resulting in a large-scale coherent structure: a turbulent dynamo. This is seen in computations and a theoretical explanation in terms of 'broken ergodicity' contains Taylor s theory of force-free states. An important problem for future work is the case of real, i.e., dissipative flows. In real flows, broken ergodicity and coherent structure are still expected to occur in MHD turbulence at the largest scale, as suggested by low resolution simulations. One challenge is to incorporate coherent structure at the largest scale into the theory of turbulent fluctuations at smaller scales.
Shebalin, John V.↗
An aspect ration bound for triangulating a d-grid cut by a hyperplane
We consider the problem of triangulating a d-dimensional uniform grid of d-cubes that is cut by a k-dimensional affine subspace. The goal is to obtain a triangulation with bounded aspect ratio. To achieve this goal, we allow some of the box faces near the affine subspace to be displaced. This problem has applications to finite element mesh generation. For general d and k, the bound on aspect ratio that we attain is double-exponential in d. For the important special case of d = 3, the aspect ratio bound is small enough that the technique is useful in practice.
Mitchell, Scott A.↗
A Hybrid Gradient Method to Designing Bayesian Experiments for Implicit Models
Bayesian experimental design (BED) aims at designing an experiment to maximize the information gathering from the collected data. The optimal design is usually achieved by maximizing the mutual information (MI) between the data and the model parameters. When the analytical expression of the MI is unavailable, e.g.,having implicit models with intractable data distributions, a neural network-based lower bound of the MI was recently proposed and a gradient ascent method was used to maximize the lower bound [1]. However, the approach in [1] requires a pathwise sampling path to compute the gradient of the MI lower bound with respect to the design variables, and such a pathwise sampling path is usually inaccessible for implicit models. In this work, we propose a hybrid gradient approach that leverages recent advances in variational MI estimator and evolution strategies (ES)combined with black-box stochastic gradient ascent (SGA) to maximize the MI lower bound. This allows the design process to be achieved through a unified scalable procedure for implicit models without sampling path gradients. Several experiments demonstrate that our approach significantly improves the scalability of BED for implicit models in high-dimensional design space.
Zhang, Jiaxin↗
Theoretical constraints on oxygen and carbon dixoide concentrations in the Precambrian atmosphere
Theoretical arguments which bear on the time histories of atmospheric oxygen and carbon dioxide during the Precambrian are reviewed and extended. It is shown that reasonably tight constraints can be placed on atmospheric pCO2 during the early and late Proterozoic, based on the observation that parts of the earth were glaciated at those times. It is demonstrated that an upper bound on early Proterozoic pO2 can be derived from a simple box model of the atmosphere-ocean system.
Kasting, James F.↗
A new algorithm for constrained nonlinear least-squares problems, part 1
A Gauss-Newton algorithm is presented for solving nonlinear least squares problems. The problem statement may include simple bounds or more general constraints on the unknowns. The algorithm uses a trust region that allows the objective function to increase with logic for retreating to best values. The computations for the linear problem are done using a least squares system solver that allows for simple bounds and linear constraints. The trust region limits are defined by a box around the current point. In its current form the algorithm is effective only for problems with small residuals, linear constraints and dense Jacobian matrices. Results on a set of test problems are encouraging.
Hanson, R. J.↗
Probabilistic error estimation for non-intrusive reduced models learned from data of systems governed by linear parabolic partial differential equations
This work derives a residual-based a posteriori error estimator for reduced models learned with non-intrusive model reduction from data of high-dimensional systems governed by linear parabolic partial differential equations with control inputs. It is shown that quantities that are necessary for the error estimator can be either obtained exactly as the solutions of least-squares problems in a non-intrusive way from data such as initial conditions, control inputs, and high-dimensional solution trajectories or bounded in a probabilistic sense. Here, the computational procedure follows an offline/online decomposition. In the offline (training) phase, the high-dimensional system is judiciously solved in a black-box fashion to generate data and to set up the error estimator. In the online phase, the estimator is used to bound the error of the reduced-model predictions for new initial conditions and new control inputs without recourse to the high-dimensional system. Numerical results demonstrate the workflow of the proposed approach from data to reduced models to certified predictions.
97 MATHEMATICS AND COMPUTING↗
Library Screening, In Vivo Confirmation, and Structural and Bioinformatic Analysis of Pentapeptide Sequences as Substrates for Protein Farnesyltransferase
Protein farnesylation is a post-translational modification where a 15-carbon farnesyl isoprenoid is appended to the C-terminal end of a protein by farnesyltransferase (FTase). This process often causes proteins to associate with the membrane and participate in signal transduction pathways. The most common substrates of FTase are proteins that have C-terminal tetrapeptide CaaX box sequences where the cysteine is the site of modification. However, recent work has shown that five amino acid sequences can also be recognized, including the pentapeptides CMIIM and CSLMQ. In this work, peptide libraries were initially used to systematically vary the residues in those two parental sequences using an assay based on Matrix Assisted Laser Desorption Ionization–Mass Spectrometry (MALDI-MS). In addition, 192 pentapeptide sequences from the human proteome were screened using that assay to discover additional extended CaaaX-box motifs. Selected hits from that screening effort were rescreened using an in vivo yeast reporter protein assay. The X-ray crystal structure of CMIIM bound to FTase was also solved, showing that the C-terminal tripeptide of that sequence interacted with the enzyme in a similar manner as the C-terminal tripeptide of CVVM, suggesting that the tripeptide comprises a common structural element for substrate recognition in both tetrapeptide and pentapeptide sequences. Molecular dynamics simulation of CMIIM bound to FTase further shed light on the molecular interactions involved, showing that a putative catalytically competent Zn(II)-thiolate species was able to form. Bioinformatic predictions of tetrapeptide (CaaX-box) reactivity correlated well with the reactivity of pentapeptides obtained from in vivo analysis, reinforcing the importance of the C-terminal tripeptide motif. This analysis provides a structural framework for understanding the reactivity of extended CaaaX-box motifs and a method that may be useful for predicting the reactivity of additional FTase substrates bearing CaaaX-box sequences.
59 BASIC BIOLOGICAL SCIENCES↗
Finding inputs that trigger floating-point exceptions in heterogeneous computing via Bayesian optimization
Testing code for floating-point exceptions is crucial as exceptions can quickly propagate and produce unreliable numerical answers. The state-of-the-art to test for floating-point exceptions in heterogeneous systems is quite limited and solutions require the application’s source code, which precludes their use in accelerated libraries where the source is not publicly available. We present an approach to find inputs that trigger floating-point exceptions in black-box CPU or GPU functions, i.e., functions where the source code and information about input bounds are unavailable. Our approach is the first to use Bayesian optimization (BO) to identify such inputs and uses novel strategies to overcome the challenges that arise in applying BO to this problem. Here, we implement our approach in the XSCOPE framework and demonstrate it on 58 functions from the CUDA Math Library and 81 functions from the Intel Math Library. XSCOPE is able to identify inputs that trigger exceptions in about 73% of the tested functions.
97 MATHEMATICS AND COMPUTING↗
Few-Body Bound States and Resonances in Finite Volume
Since the pioneering work of Lüscher in the 1980s it is well known that considering quantum systems in finite volume, specifically, finite periodic boxes, can be used as a powerful computational tool to extract physical observables. While this formalism has been worked out in great detail in the two-body sector, much effort is currently being invested into deriving analogous relations for systems with more constituents. This work is relevant not only for nuclear physics, where lattice methods are now able to calculate few- and many-nucleon states, but also for other fields such as simulations of cold atoms. This article discusses recent progress regarding the extraction of few-body bound-state and resonance properties from finite-volume calculations of systems with an arbitrary number of constituents.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Diesel Generator Model Parameterization for Microgrid Simulation Using Hybrid Box-Constrained Levenberg-Marquardt Algorithm
Existing generator parameterization methods, typically developed for large turbine generator units, are difficult to apply to small kW-level diesel generators in microgrid applications. Here, this article presents a model parameterization method that estimates a complete set of kW-level diesel generator parameters simultaneously using only load-step-change tests with limited measurement points. This method provides a more cost-efficient and robust approach to achieve high-fidelity modeling of diesel generators for microgrid dynamic simulation. A two-stage hybrid box-constrained Levenberg-Marquardt (H-BCLM) algorithm is developed to search the optimal parameter set given the parameter bounds. A heuristic algorithm, namely Generalized Opposition-based Learning Genetic Algorithm (GOL-GA), is applied to identify proper initial estimates at the first stage, followed by a modified Levenberg-Marquardt algorithm designed to fine tune the solution based on the first-stage result. The proposed method is validated against dynamic simulation of a diesel generator model and field measurements from a 16kW diesel generator unit.
42 ENGINEERING↗