Constrained Domain Research Articles

Probability Bracket Notation for Probability Modeling

Following Dirac’s notation in Quantum Mechanics (QM), we propose the Probability Bracket Notation (PBN), by defining a probability-bra (P-bra), P-ket, P-bracket, P-identity, etc. Using the PBN, many formulae, such as normalizations and expectations in systems of one or more random variables, can now be written in abstract basis-independent expressions, which are easy to expand by inserting a proper P-identity. The time evolution of homogeneous Markov processes can also be formatted in such a way. Our system P-kets are identified with probability vectors and our P-bra system is comparable with Doi’s state function or Peliti’s standard bra. In the Heisenberg picture of the PBN, a random variable becomes a stochastic process, and the Chapman–Kolmogorov equations are obtained by inserting a time-dependent P-identity. Also, some QM expressions in Dirac notation are naturally transformed to probability expressions in PBN by a special Wick rotation. Potential applications show the usefulness of the PBN beyond the constrained domain and range of Hermitian operators on Hilbert Spaces in QM all the way to IT.

Method for solving state‐path constrained optimal control problems using adaptive Radau collocation

AbstractA new method is developed for accurately approximating the solution to state‐variable inequality path constrained optimal control problems using a multiple‐domain adaptive Legendre–Gauss–Radau collocation method. The method consists of the following parts. First, a structure detection method is developed to estimate switch times in the activation and deactivation of state‐variable inequality path constraints. Second, using the detected structure, the domain is partitioned into multiple‐domains where each domain corresponds to either a constrained or an unconstrained segment. Furthermore, additional decision variables are introduced in the multiple‐domain formulation, where these additional decision variables represent the switch times of the detected active state‐variable inequality path constraints. Within a constrained domain, the path constraint is differentiated with respect to the independent variable until the control appears explicitly, and this derivative is set to zero along the constrained arc while all preceding derivatives are set to zero at the start of the constrained arc. The time derivatives of the active state‐variable inequality path constraints are computed using automatic differentiation and the properties of the chain rule. The method is demonstrated on two problems, the first being a benchmark optimal control problem which has a known analytical solution and the second being a challenging problem from the field of aerospace engineering in which there is no known analytical solution. When compared against previously developed adaptive Legendre–Gauss–Radau methods, the results show that the method developed in this paper is capable of computing accurate solutions to problems whose solution contain active state‐variable inequality path constraints.

Modeling, testing, and optimization of novel lattice structures for enhanced mechanical performance

Cellular materials have drawn increasing interest in numerous applications due to their promising specific stiffness, strength and energy absorption capacity. In this work, a variety of rather novel lattice topologies pertinent to additive manufacturing are derived and examined. A number of these are derived by free-domain and constrained domain topology optimization procedures, while others are inspired by the triply periodic minimum surface (TPMS) sheet-based topologies. The topology optimization module utilized a single objective function of minimizing strain energy under linear elastic conditions. A total of fifteen different lattice topologies are investigated numerically, including both novel and conventional topologies (e.g. strut-based lattices) and their effective elastic properties are determined with respect to relative density through finite element analysis (FEA). Based on the preliminary FEA results, a number of these topologies are selected of which tessellated lattice structures are fabricated through laser powder bed fusion (LPBF) additive manufacturing technique out of Nylon thermoplastic material. The tessellated lattice structures are experimentally tested in compression and their mechanical performance, including uniaxial modulus, yield strength, and energy absorption capacity (EAC), is assessed. FEA simulations have been conducted using an elastic-plastic constitutive model for the Nylon base material. Both the experimental and numerical results reveal that the mechanical performance of the novel tube-based TPMS lattice P-100 and the combined loading (CL) topology derived through free-domain topology optimization surpasses all other topologies. P-100 uses a primitive TPMS with equal-length tubular connections in each direction, where the tubular length percentage compared to the primitive lattice size is 100%, while CL lattice topology is a free domain topology optimized under compressive loads on the centers of faces, edges, and vertices toward the center. The innovative lattice topologies proposed in the current study, particularly the P-100 and CL topologies, can become crucial in applications where it is necessary to improve the energy absorption capacity, such as sandwich panel cores, supports, and infills for 3D printed components.

Börjeson–Forssman–Lehmann syndrome: delineating the clinical and allelic spectrum in 14 new families

Börjeson-Forssman-Lehmann syndrome (BFLS) is an X-linked intellectual disability syndrome caused by variants in the PHF6 gene. We ascertained 19 individuals from 15 families with likely pathogenic or pathogenic PHF6 variants (11 males and 8 females). One family had previously been reported. Six variants were novel. We analysed the clinical and genetic findings in our series and compared them with reported BFLS patients. Affected males had classic features of BFLS including intellectual disability, distinctive facies, large ears, gynaecomastia, hypogonadism and truncal obesity. Carrier female relatives of affected males were unaffected or had only mild symptoms. The phenotype of affected females with de novo variants overlapped with the males but included linear skin hyperpigmentation and a higher frequency of dental, retinal and cortical brain anomalies. Complications observed in our series included keloid scarring, digital fibromas, absent vaginal orifice, neuropathy, umbilical hernias, and talipes. Our analysis highlighted sex-specific differences in PHF6 variant types and locations. Affected males often have missense variants or small in-frame deletions while affected females tend to have truncating variants or large deletions/duplications. Missense variants were found in a minority of affected females and clustered in the highly constrained PHD2 domain of PHF6. We propose recommendations for the evaluation and management of BFLS patients. These results further delineate and extend the genetic and phenotypic spectrum of BFLS.

How Does a Stone Carver Create? A Participatory Case Study

ABSTRACTArt and design involve divergent creative processes. Design is a more constrained domain than art. While creativity in some specific domains, such as painting, sculpture, and music, has been widely studied, some have as yet been little explored. One example is stone carving. What characterizes stone carving, as a creative occupation? What is a stone carver's creative process? We set out to answer these questions by interviewing a stone carver about his profession, his process, his productions, and his place in society. In this case study, we examined the stone carver's discourse using a combination of three content analysis software tools. Taken together, the results highlight and detail 3 of the 7 Cs of creativity: the stone carver as creator, his creating (creative process), and his creations (productions) on which the interview focuses. The results of this participatory case study were validated by the stone carver himself. They reveal that stone carving sits at the intersection between handicraft, design, and art.

Epistasis reduces fitness costs of influenza A virus escape from stem-binding antibodies

The hemagglutinin (HA) stem region is a major target of universal influenza vaccine efforts owing to the presence of highly conserved epitopes across multiple influenza A virus (IAV) strains and subtypes. To explore the potential impact of vaccine-induced immunity targeting the HA stem, we examined the fitness effects of viral escape from stem-binding broadly neutralizing antibodies (stem-bnAbs). Recombinant viruses containing each individual antibody escape substitution showed diminished replication compared to wild-type virus, indicating that stem-bnAb escape incurred fitness costs. A second-site mutation in the HA head domain (N129D; H1 numbering) reduced the fitness effects observed in primary cell cultures and likely enabled the selection of escape mutations. Functionally, this putative permissive mutation increased HA avidity for its receptor. These results suggest a mechanism of epistasis in IAV, wherein modulating the efficiency of attachment eases evolutionary constraints imposed by the requirement for membrane fusion. Taken together, the data indicate that viral escape from stem-bnAbs is costly but highlights the potential for epistatic interactions to enable evolution within the functionally constrained HA stem domain.

Dimensionality-reduced antenna modeling with stochastically established constrained domain

Over the recent years, surrogate modeling methods have become increasingly widespread in the design of contemporary antenna systems. On the one hand, it is associated with a growing awareness of numerical optimization, instrumental in achieving high-performance structures. On the other hand, considerable computational expenses incurred by massive full-wave electromagnetic (EM) analyses, routinely employed as a major design tool, foster the development of novel design techniques that exhibit practically acceptable costs while ensuring reliability. In this context, substituting EM simulations by fast surrogates is a profitable solution. Data-driven modeling is arguably the most popular approach owing to its versatility and the abundance of specific methods. Yet, a construction of approximation surrogates is severely encumbered by the curse of dimensionality, and even more so by the broad ranges of material and geometry parameters the model should cover to be applicable for solving practical design tasks. The recently reported performance-driven modeling paradigm offers workaround these obstacles by restricting the surrogate rendition to a small section of the parameter space, containing designs of sufficiently high quality according to performance requirements imposed on the system under study. Nevertheless, identification of this region is based on database designs that have to be pre-optimized, which is associated with significant CPU expenses. The usage of the reference designs can be replaced by stochastic domain identification, leading to considerable computational savings. This paper introduces a further advancement, where the metamodel domain is outlined based on the spectral analysis of the random observables pre-selected using an automated decision-making process. Our procedure retains the benefits of the prior techniques but also reduces the domain dimensionality, which translates into additional cost reduction of training data acquisition. These have been conclusively demonstrated through numerical validation involving three microstrip antennas and comprehensive comparisons with six state-of-the-art benchmark techniques.

A novel method for rotor fault diagnosis based on deep transfer learning with simulated samples

For solving the problem of data without failure samples, a novel transfer unsupervised learning method called classifier constrained domain adaptation network (CCDAN) is proposed for extracting transfer characteristics from simulated samples by theory model for experimental rotor fault diagnosis. Firstly, a dynamical model of Jeffcott rotor with crack fault is established and the achieved vibration responses of the system are used as generated simulation samples. Then, the multilayer convolutional network and multiple-kernel maximum mean discrepancy (MK-MMD) are adopted to extract similar characteristics between source and target domains. Finally, two independent classifiers are designed to constrain the features which have fallen near the decision boundary in network learning, which could effectively increase the accuracy and promote the fault identifying generalization. The proposed CCDAN method is verified through two unsupervised transfer tasks of crack rotor fault datasets. The comprehensive experiment analyses conclude the proposed method can learn the transferable characteristics of rotor crack fault diagnosis and its classification accuracy is superior to the existing intelligent transfer network of fault diagnosis.

Memory-efficient emulation of physical tabular data using quadtree decomposition

Computationally expensive functions are sometimes replaced in simulations with an emulator that approximates the true function (e.g., equations of state, wavelength-dependent opacity, or composition-dependent materials properties). For functions that have a constrained domain of interest, this can be done by discretizing the domain and performing a local interpolation on the tabulated function values of each local domain. For these so-called tabular data methods, the method of discretizing the domain and mapping the input space to each subdomain can drastically influence the memory and computational costs of the emulator. This is especially true for functions that vary drastically in different regions. We present a method for domain discretization and mapping that utilizes quadtrees, which results in significant reductions in the size of the emulator with minimal increases to computational costs or loss of global accuracy. We apply our method to the electron–positron Helmholtz free energy equation of state and show over an order of magnitude reduction in memory costs for reasonable levels of numerical accuracy.

DeepRide: Dashcam Video Description Dataset for Autonomous Vehicle Location-Aware Trip Description

Video description is one of the most challenging task in the combined domain of computer vision and natural language processing. Captions for various open and constrained domain videos have been generated in the recent past but descriptions for driving dashcam videos have never been explored to the best of our knowledge. With the aim to explore dashcam video description generation for autonomous driving, this study presents DeepRide: a large-scale dashcam driving video description dataset for location-aware dense video description generation. The human-described dataset comprises visual scenes and actions with diverse weather, people, objects, and geographical paradigms. It bridges the autonomous driving domain with video description by textual description generation of the visual information as seen by a dashcam. We describe 16,000 videos (40 seconds each) in English employing 2,700 man-hours by two highly qualified teams with domain knowledge. The descriptions consist of eight to ten sentences covering each dashcam video’s global features and event features in 60 to 90 words. The dataset consists of more than 130K sentences, totaling approximately one million words. We evaluate the dataset by employing location aware vision-language recurrent transformer framework to elaborate on the efficacy and significance of the visio-linguistics research for autonomous vehicles. We provided base line results to evaluate the dataset by employing three existing state-of-the-art recurrent models. The memory augmented transformer performed superior due to its highly summarized memory state for visual information and the sentence history while generating the trip description. Our proposed dataset opens a new dimension of diverse and exciting applications, such as self-driving vehicle reporting, driver and vehicle safety, inter-vehicle road intelligence sharing, and travel occurrence reports.

Low-Cost Modeling of Microwave Components by Means of Two-Stage Inverse/Forward Surrogates and Domain Confinement

Full-wave electromagnetic (EM) analysis is one of the most important tools in the design of modern microwave components and systems. EM simulation permits reliable evaluation of circuits at the presence of cross-coupling effects or substrate anisotropy, as well as for accounting for interactions with the immediate environment. However, repetitive analyses required by EM-driven procedures, such as parametric optimization or statistical analysis, may entail considerable computational expenditures, often prohibitive. Tackling the high-cost issue fostered the shift toward the incorporation of fast replacement models, including both physics-based surrogates and data-driven ones. While the latter is more popular and versatile, the construction of reliable approximation metamodels for microwave components is hindered by the curse of dimensionality and nonlinearity of system responses. The recent performance-driven modeling methodologies are capable of alleviating these difficulties by confining the surrogate domain to a vicinity of the optimum design manifold (i.e., the region that contains high-quality designs rather than the entire parameter space). Although setting up the model in a constrained domain requires small amounts of training data, domain definition itself requires a set of preoptimized reference designs, acquisition of which is an expensive endeavor. This work proposes a novel approach, which replaces the reference designs with a small set of random observables, thereby considerably reducing the overall cost of the model setup. Comprehensive verification involving several miniaturized microstrip structures demonstrates that our methodology is competitive to performance-driven frameworks both in terms of modeling accuracy and computational efficiency with an average savings of around 80%.

Soft congestion approximation to the one-dimensional constrained Euler equations

This article is concerned with the analysis of the one-dimensional compressible Euler equations with a singular pressure law, the so-called hard sphere equation of state. We provide a detailed description of the effect of the singular pressure on the breakdown of the smooth solutions. Moreover, we rigorously justify the singular limit for smooth solutions towards the free-congested Euler equations, where the compressible (free) dynamics is coupled with the incompressible one in the constrained (i.e. congested) domain.

Chance-constrained controller state and reference governor

The controller state and reference governor (CSRG) is an add-on scheme for nominal closed-loop systems with dynamic controllers which supervises the controller internal state and the reference input to the closed-loop system to enforce pointwise-in-time constraints. By admitting both controller state and reference modifications, the CSRG can achieve an enlarged constrained domain of attraction compared to conventional reference governor schemes where only reference modification is permitted. This paper studies the CSRG for systems subject to stochastic disturbances and chance constraints. We describe the CSRG algorithm in such a stochastic setting and analyze its theoretical properties, including chance-constraint enforcement, finite-time reference convergence, and closed-loop stability. We also present examples illustrating the application of CSRG to constrained aircraft flight control.

Expedited Acquisition of Database Designs for Reduced-Cost Performance-Driven Modeling and Rapid Dimension Scaling of Antenna Structures

Fast replacement models have been playing an increasing role in high-frequency electronics, including the design of antenna structures. Their role is to improve the computational efficiency of the procedures that normally entail large numbers of expensive full-wave electromagnetic (EM) simulations, e.g., parametric optimization or uncertainty quantification. Recently introduced performance-driven modeling methods, such as the nested kriging framework, alleviate some of the common difficulties pertinent to conventional modeling methods. These include the curse of dimensionality but also the need for rendering models to be valid for broad ranges of antenna parameters and operating conditions, as dictated by the design utility of the surrogates. The keystone of performance-driven methods is an appropriate confinement of the model domain so that the training data are only acquired in the regions containing high-quality designs. Identification of such regions is realized using a set of so-called reference designs preoptimized for selected ensembles of performance requirements. The CPU cost of generating the reference points may be considerable and compromise the savings obtained by operating in a constrained domain. In this article, a technique for automated, reliable and low-cost acquisition of the reference designs is proposed. Our methodology involves inverse sensitivities, iterative correction procedures, and accelerated feature-based gradient search with sparse Jacobian updates. It is validated using three microstrip antenna examples and demonstrated as an efficient tool for lowering the cost of building surrogate models within the nested kriging framework. The intended use of our approach is expedited construction of database designs for constrained modeling frameworks, construction of inverse surrogates, as well as procedures for rapid redesign and dimension scaling of antenna structures.

Constrained Domain Adaptation for Image Segmentation.

Domain Adaption tasks have recently attracted substantial attention in computer vision as they improve the transferability of deep network models from a source to a target domain with different characteristics. A large body of state-of-the-art domain-adaptation methods was developed for image classification purposes, which may be inadequate for segmentation tasks. We propose to adapt segmentation networks with a constrained formulation, which embeds domain-invariant prior knowledge about the segmentation regions. Such knowledge may take the form of anatomical information, for instance, structure size or shape, which can be known a priori or learned from the source samples via an auxiliary task. Our general formulation imposes inequality constraints on the network predictions of unlabeled or weakly labeled target samples, thereby matching implicitly the prediction statistics of the target and source domains, with permitted uncertainty of prior knowledge. Furthermore, our inequality constraints easily integrate weak annotations of the target data, such as image-level tags. We address the ensuing constrained optimization problem with differentiable penalties, fully suited for conventional stochastic gradient descent approaches. Unlike common two-step adversarial training, our formulation is based on a single segmentation network, which simplifies adaptation, while improving training quality. Comparison with state-of-the-art adaptation methods reveals considerably better performance of our model on two challenging tasks. Particularly, it consistently yields a performance gain of 1-4% Dice across architectures and datasets. Our results also show robustness to imprecision in the prior knowledge. The versatility of our novel approach can be readily used in various segmentation problems, with code available publicly.

The optimized memristor performance by utilizing the constrained domain wall motion in Pt/Co–Tb/Ta structure

Spintronic devices can realize multilevel state storage and mimic the properties of the synapse, which enables their potential application in the field of artificial neural networks. In this paper, we demonstrate the existence of a large intermediate transition zone in current-induced magnetization switching curves of Pt/Co–Tb/Ta structures, and the number of states in the transition zone that can be manipulated by changing the Co content. The magneto-optical Kerr microscope imaging indicates that this property is related to the constrained domain wall motion in the Co–Tb films with large Co content. We also demonstrate the multilevel state storage properties of the sample by applying a sequence of current pulses. The synaptic plasticity behaviors were mimicked in these samples through regulating the value of Hall resistance by current pulses. The constrained domain wall motion supplies a simple but effective way to achieve multilevel state storage and show potential applications in neuromorphic computing.

Design optimization of a rocket engine’s inner liner with improved response surface methodology

This article presents the optimization of the design of a subscale effusion-cooled rocket engine inner liner made of porous composite material, with the aim of improving the ability of the coolant film to protect the combustion chamber wall from thermochemical attacks. The optimization problem is defined as a global minimization problem and solved using response surface methodology (RSM). Recommendations to construct an efficient D-optimal design in a constrained design domain using design of experiments theory are provided. Computational fluid dynamics simulations are carried out to provide measurements of the response. The iteratively reweighted least squares method is used in the fit of the regression models to improve the efficiency of RSM with no additional cost. Enhanced coolant film properties for the optimal design show that the optimization problem was properly solved and the inner liner design was successfully optimized. These results demonstrate the efficiency of the optimization method.

Design and analysis method of nonlinear helical springs using a combining technique: Finite element analysis, constrained Latin hypercube sampling and genetic programming

Helical springs have been widely used in various engineering applications for centuries. For many years, there is no significant development in the design methods of helical springs. Recently, a renewed interest is raised from the industry in exploring new designs for the helical springs with novel configurations due to the requirements of customised properties, such as specific spring stiffness and natural frequency for better performance of valve train systems. In this paper, an innovative method which combines the techniques of Finite Element Analysis (FEA), constrained Latin Hypercube sampling (cLHS) and Genetic Programming (GP) is developed to design and analyse helical springs with arbitrary shapes. cLHS method is applied to generate 300 sets of spring samples within a constrained design domain, and FE analysis is conducted on these spring samples. Two meta-models are developed from the 300 sets of FE results by using GP. They successfully describe the relationships between the design parameters and the overall mechanical performances including compression force and fundamental natural frequency of helical springs. The results show that the developed models have robust abilities on designing helical springs with arbitrary shapes, which significantly expands the design domain of the engineering design methods and potential for precise optimization of helical springs.

Improved variance estimation for inequality-constrained domain mean estimators using survey data

In survey domain estimation, a priori information can often be imposed in the form of linear inequality constraints on the domain estimators. Wu et al. (2016) formulated the isotonic domain mean estimator, for the simple order restriction, and methods for more general constraints were proposed in Oliva-Avilés et al. (2020). When the assumptions are valid, imposing restrictions on the estimators will ensure that the a priori information is respected, and in addition allows information to be pooled across domains, resulting in estimators with smaller variance. Here, we propose a method to further improve the estimation of the covariance matrix for these constrained domain estimators, using a mixture of possible covariance matrices obtained from the inequality constraints. We prove consistency of the improved variance estimator, and simulations demonstrate that the new estimator results in improved coverage probabilities for domain mean confidence intervals, while retaining the smaller confidence interval lengths.

Improved Modeling of Microwave Structures Using Performance-Driven Fully-Connected Regression Surrogate

Fast replacement models (or surrogates) have been widely applied in the recent years to accelerate simulation-driven design procedures in microwave engineering. The fundamental reason is a considerable—and often prohibitive—CPU cost of massive full-wave electromagnetic (EM) analyses related to solving common tasks such as parametric optimization or uncertainty quantification. The most popular class of surrogates are data-driven models, which are fast to evaluate, versatile, and easy to handle. Notwithstanding, the curse of dimensionality as well as the utility demands (e.g., so that the model covers sufficiently broad ranges of the system operating conditions), limit the applicability of conventional methods. A performance-driven modeling paradigm allows for mitigating these issue by focusing the surrogate setup process in a constrained domain encapsulating designs being of high quality w.r.t. the assumed figures of interest. The nested kriging framework capitalizing on this idea, renders the constrained surrogate using kriging interpolation, and has been shown to surpass traditional approaches. In pursuit of further accuracy improvements, this work incorporates the performance-driven concept into the fully-connected regression model (FRCM). The latter has been recently introduced in the context of frequency selective surfaces, and combined deep neural networks with Bayesian optimization, the latter employed to determine the network architecture and hyper-parameters. Using two examples of miniaturized microstrip couplers, our methodology is demonstrated to outperform both conventional modeling techniques and nested kriging, with reliable models constructed over multi-dimensional parameters spaces using just a few hundreds of samples.