Dual Formulation Research Articles

Accelerated dynamics with dry friction via time scaling and averaging of doubly nonlinear evolution equations

In a Hilbert framework, for convex differentiable optimization, we analyze the long-time behavior of inertial dynamics with dry friction. In classical approaches based on asymptotically vanishing viscous damping (in accordance with Nesterov’s method), the results are expressed in terms of rapid convergence of the values of the function to its minimum value. On the other hand, dry friction induces convergence towards an approximate minimizer, typically the system stops at x when a given threshold ‖∇f(x)‖≤r is satisfied. We obtain rapid convergence results in this direction. In our approach, we start from a doubly nonlinear first-order evolution equation involving two potentials: one is the differentiable function f to be minimized, which acts on the state of the system via its gradient, and the other is the nonsmooth potential dry friction φ(x)=r‖x‖ which acts on the velocity vector via its sub-differential. To highlight the central role played by ∇f(x), we also deal with the dual formulation of these dynamics, which have a Riemannian gradient structure. We then rely on the general acceleration method recently developed by Attouch, Boţ and Nguyen, which consists in applying the method of time scaling and then averaging to a continuous differential equation of the first order in time. We thus obtain fast convergence results for second order time-evolution systems involving dry friction, asymptotically vanishing viscous damping, and Hessian-driven damping in the implicit form.

The evolving sociotechnical futures of outer space

The anticipated futures and practices of the outer space sociotechnical system are undergoing their most significant adjustment since the Sputnik days due to the challenge posed by the vision that emphasises the interest of space for market-driven and profitable business. The theoretical notion of sociotechnical imaginaries allows to compare the traditional and commercial anticipations of space developments and their different approaches to technological progress, which are entangled with political and economic concerns. The performative power of the commerce-based imaginary is apparent in the renewed collective expectations that are shaping policy, innovation, and funding practices in the space sector. The new vision is thus contributing to transform the institutional culture that had dominated the industry, and the resulting imagination of outer space is evolving to a dual form, pragmatically alternating between the conventional and entrepreneurial representations. Yet, despite the inclusive narrative and democratisation discourse of the commercial perspective, the future-looking imaginary of outer space remains contested for economic, political, legal, and environmental reasons.

Ultrafast and facile construction of programmable, multidimensional wrinkled-patterned polyacrylamide/sodium alginate hydrogels for human skin-like tactile perception

Customizable structures and patterns are becoming powerful tools for biomimetic design and application of soft materials. The construction of long-range ordered self-wrinkled structures on multi-dimensional and complex-shaped surfaces with facile, fast and efficient strategies still faces serious challenges. During the stretch-recovery process, the carboxyl groups in the polyacrylamide/sodium alginate dual network gel form robust coordination with Fe3+ to achieve a hard shell layer, resulting in a modulus mismatch between the inner soft layer and the outer hard layer, thereby forming a wrinkled surface. This flexible strategy allows simultaneous construction of complex topologies from 1D to 3D wits well-organized microstructure and controllable dimensions. The mechanism of the influence of ion treating time and pre-stretching ratio on wrinkle wavelength was explored in detail. The finite element simulations matched well with the experimental results. Due to the unique surface and dual crosslinking network, the self-wrinkled hydrogel maintains a high sensitivity of up to 67.47 kPa−1 in 1000 compression cycles. As a high-sensitivity pressure sensor integrated into the detection system, it can be efficiently applied to the contact dynamic tactile perception and monitoring of various movement behaviors of the human body.

Influence of the dual charge compensator on solid solution of the air-sintered Ca1-xCexZrTi2-2xFexCrxO7 zirconolite

In this study, a dual charge-compensator formulation was developed for zirconolite with the nominal composition Ca1-xCexZrTi2-2xFexCrxO7 (x = 0–0.30). The design strategy here was such that trivalent Fe and Cr were both targeted to substitute across the Ti site(s) to charge balance an inventory of CeO2 included as a structural analogue for Pu. The targeted solid solution was prepared by sintering constituent oxides at 1400 °C for 10 h under an air atmosphere. By means of powder XRD refinement and selected area electron diffraction analysis, the dominant zirconolite polytype was confirmed to be 2M across the solid solution. The obtained product density was significantly increased when compared to the previously discussed Ca1-xCexZrTi2-2xCr2xO7 system, suggesting that the partial inclusion of Fe in a 1:1 molar ratio with Cr may improve sintering behaviour. The limit of solid solution was reached at approximately x = 0.30, for which the segregation of CeO2 and Cr2O3 phases was clearly evidenced. An evaluation of obtained chemical compositions and bulk oxidation states was performed to inform the solid solution mechanism of Ce, Cr and Fe within zirconolite.

Existence of Solutions on the Critical Hyperbola for a Pure Lane–Emden System with Neumann Boundary Conditions

Abstract We study the following Lane–Emden system: $$\begin{align*} & -\Delta u=|v|^{q-1}v \quad \ \textrm{in}\ \Omega, \qquad -\Delta v=|u|^{p-1}u \quad \ \textrm{in}\ \Omega, \qquad u_{\nu}=v_{\nu}=0 \quad \ \textrm{on}\ \partial \Omega, \end{align*}$$with $\Omega $ a bounded regular domain of ${\mathbb{R}}^{N}$, $N \ge 4$, and exponents $p, q$ belonging to the so-called critical hyperbola $1/(p+1)+1/(q+1)=(N-2)/N$. We show that, under suitable conditions on $p, q$, least-energy (sign-changing) solutions exist, and they are classical. In the proof we exploit a dual variational formulation, which allows to deal with the strong indefinite character of the problem. We establish a compactness condition which is based on a new Cherrier-type inequality. We then prove such condition by using as test functions the solutions to the system in the whole space and performing delicate asymptotic estimates. If $N \ge 5$, $p=1$, the system above reduces to a biharmonic equation, for which we also prove existence of least-energy solutions. Finally, we prove some partial symmetry and symmetry-breaking results in the case $\Omega $ is a ball or an annulus.

Exact chirped solutions for the NLSE having Kudryashov’s law with dual form of generalized non-local nonlinearity

This paper devotes to investigating the chirped solutions for the nonlinear Schrödinger equation with Kudryashov’s law with dual form of generalized non-local nonlinearity in optical fibers. By implementing the trial equation method and the complete discriminant system for polynomial method, we obtain nineteen exact chirped solutions, whose types include elliptic function doubly-periodic solutions, solitary wave solutions and singular solutions. After selecting specific parameters, 2D and 3D graphs of several typical solutions are drawn to demonstrate their accurate physical behaviors. These solutions recovered abundant patterns of the chirped wave propagations of the model.

Robust Z-Estimators for Semiparametric Moment Condition Models.

In the present paper, we introduce a class of robust Z-estimators for moment condition models. These new estimators can be seen as robust alternatives for the minimum empirical divergence estimators. By using the multidimensional Huber function, we first define robust estimators of the element that realizes the supremum in the dual form of the divergence. A linear relationship between the influence function of a minimum empirical divergence estimator and the influence function of the estimator of the element that realizes the supremum in the dual form of the divergence led to the idea of defining new Z-estimators for the parameter of the model, by using robust estimators in the dual form of the divergence. The asymptotic properties of the proposed estimators were proven, including here the consistency and their asymptotic normality. Then, the influence functions of the estimators were derived, and their robustness is demonstrated.

A Dual Form of Acquiring Higher Education as a Way to meet Labor Market Requirements for the Practical Training of Graduates

Based on the study of relevant regulatory and legal documents, positive foreign experience and analysis of scientific publications of recent years, the article considers the prospects of using a dual form of higher education to meet the labor market requirements for the practical training of graduates. The essence of dual education and the importance of cooperation between employers, higher education establishments and students at the institutional, personal and business levels are revealed.
 It is emphasized that due to the use of a dual form of education, a qualitatively new educational environment is created, which is favourable for combining theoretical and practical training of higher education seekers, and the implementation of the principle of student-centeredness.
 It is noted that foreign experience of acquiring higher education cannot be adjusted to the domestic practice without its proper justification, as well as organizational and educational and methodological support.
 Special attention is focused on the main stages of the pilot project (2018-2023) on the implementation of the main provisions of the Concept of training specialists in the dual form of acquiring professional pre-higher and higher education. It was concluded that, embarking on the path towards modernizing practical training of future specialists by using a dual form of education, it is necessary to take into account the interests and opportunities of higher education institutions, employers and students.

Variational Wasserstein Barycenters with C-cyclical Monotonicity Regularization

Wasserstein barycenter, built on the theory of Optimal Transport (OT), provides a powerful framework to aggregate probability distributions, and it has increasingly attracted great attention within the machine learning community. However, it is often intractable to precisely compute, especially for high dimensional and continuous settings. To alleviate this problem, we develop a novel regularization by using the fact that c-cyclical monotonicity is often necessary and sufficient conditions for optimality in OT problems, and incorporate it into the dual formulation of Wasserstein barycenters. For efficient computations, we adopt a variational distribution as the approximation of the true continuous barycenter, so as to frame the Wasserstein barycenters problem as an optimization problem with respect to variational parameters. Upon those ideas, we propose a novel end-to-end continuous approximation method, namely Variational Wasserstein Barycenters with c-Cyclical Monotonicity Regularization (VWB-CMR), given sample access to the input distributions. We show theoretical convergence analysis and demonstrate the superior performance of VWB-CMR on synthetic data and real applications of subset posterior aggregation.

A modified combined active-set Newton method for solving phase-field fracture into the monolithic limit

In this work, we examine a numerical phase-field fracture framework in which the crack irreversibility constraint is treated with a primal–dual active set method and a linearization is used in the degradation function to enhance the numerical stability. The first goal is to carefully derive from a complementarity system our primal–dual active set formulation, which has been used in the literature in numerous studies, but for phase-field fracture without its detailed mathematical derivation yet. Based on the latter, we formulate a modified combined active-set Newton approach that significantly reduces the computational cost in comparison to comparable prior algorithms for quasi-monolithic settings. For many practical problems, Newton converges fast, but active set needs many iterations, for which three different efficiency improvements are suggested in this paper. Afterwards, we design an iteration on the linearization in order to iterate the problem to the monolithic limit. Our new algorithms are implemented in the programming framework pfm-cracks from Heister and Wick (2020). In the numerical examples, we conduct performance studies and investigate efficiency enhancements. The main emphasis is on the cost complexity by keeping the accuracy of numerical solutions and goal functionals. Our algorithmic suggestions are substantiated with the help of several benchmarks in two and three spatial dimensions. Therein, predictor–corrector adaptivity and parallel performance studies are explored as well.

An implicit and explicit dual model predictive control formulation for a steel recycling process

We present a formulation for both implicit and explicit dual model predictive control for a steel recycling process. The process consists in the production of new steel by choosing a combination of several different steel scraps with unknown pollutant content. The pollutant content can only be measured after a scrap combination is molten, allowing for inference on the pollutants in the different scrap heaps. The production cost should be minimized while ensuring high quality of the product through constraining the maximum amount of pollutant. The dual control formulation allows to achieve the optimal explore-exploit trade-off between uncertainty reduction and cost minimization for the examined problem. Specifically, the dual effect is obtained by considering the dependence of the future pollutant uncertainties on the scrap selection in the predictions. The implicit formulation promotes uncertainty reduction indirectly via the impact of active constraints on the objective, while the explicit formulation adds a heuristic cost on uncertainty to encourage active exploration. We compare the formulations by numerical simulations of a simplified but representative industrial steel recycling process. The results demonstrate the superiority of the two dual formulations with respect to a robustified but non-dual formulation.

Combinatorial drug-loaded quality by design adapted transliposome gel formulation for dermal delivery: In vitro and dermatokinetic study.

Ursolic acid is a powerful drug that possesses many therapeutic properties, such as hepatoprotection, immunomodulation, anti-inflammatory, antidiabetic, antibacterial, antiviral, antiulcer, and anticancer activity. Centella asiatica (L.) Urban (Umbelliferae) contains a triterpene called asiatic acid, which has been used effectively in traditional Chinese and Indian medicine system for centuries. Anticancer, anti-inflammatory, and neuroprotective properties are only some of the many pharmacological actions previously attributed to asiatic acid . The present work developed an optimized combinatorial drug-loaded nano-formulation by Quality by design approach. The optimize transliposome for accentuated dermal delivery of dual drug. The optimization of drug-loaded transliposome was done using the "Box-Behnken design." The optimized formulation was characterized for vesicles size, entrapment efficiency (%), and in vitro drug release. Additionally, transmission electron microscopy (TEM), confocal laser scanning microscopy (CLSM), and dermatokinetic study were performed for further evaluation of drug-loaded optimized transliposome formulation. The optimized combinatorial drug-loaded transliposome formulation showed a particle size of 86.36 ± 2.54 nm, polydispersity index (PDI) 0.230 ± 0.008, and an entrapment efficiency of 87.43 ± 2.66% which depicted good entrapment efficiency. In vitro drug release of ursolic acid and asiatic acid transliposomes was found to be 85.12 ± 2.54% and 80.23 ± 3.23%, respectively, as compared to optimized ursolic acid and asiatic acid transliposome gel drug release that was 67.18 ± 2.85% and 60.28 ± 4.12%, respectively. The skin permeation study of ursolic and asiatic acid conventional formulation was only 32.48 ± 2.42%, compared with optimized combinatorial drug-loaded transliposome gel (79.83 ± 4.52%) at 12 h. After applying combinatorial drug-loaded transliposome gel, rhodamine was able to more easily cross rat skin, as observed by confocal laser scanning microscopy, in comparison with when the rhodamine control solution was used. The UA_AA-TL gel formulation absorbed more ursolic acid and asiatic acid than the UA_AA-CF gel formulation, as per dermatokinetic study. Even after being incorporated into transliposome vesicles, the antioxidant effects of ursolic and asiatic acid were still detectable. In most cases, transliposomes vesicular systems generate depots in the skin's deeper layers and gradually release the medicine over time, allowing for fewer applications. In overall our studies, it may be concluded that developed dual drug-loaded transliposomal formulation has great potential for effective topical drug delivery for skin cancer.

On the Tuning of the Parallel-T RC Network

This paper deals with two methods of tuning the parallel-T RC network. The first one is the simplest possible, in the form of a grounded resistance. The other one is a passive, rather than active, dual input form of a different kind. Neither of them have so far appeared in the literature.

Dual Quaternions Representation of Lagrange's Dynamic Equations

Abstract This paper introduces for the first time, the Lagrange's dynamic equations in dual number quaternion form. Additionally, Rayleigh's dissipation function in dual quaternion form is introduced here allowing for the accounting of dissipative (non-conservative) forces such as motion through a viscous fluid, friction, and spring damping force. As an example, dual quaternions are used here to derive the Lagrange dynamic equations of a robot manipulator.

Ranking the Importance of Variables in a Nonparametric Frontier Analysis Using Unsupervised Machine Learning Techniques

In this paper, we propose and compare new methodologies for ranking the importance of variables in productive processes via an adaptation of OneClass Support Vector Machines. In particular, we adapt two methodologies inspired by the machine learning literature: one involving the random shuffling of values of a variable and another one using the objective value of the dual formulation of the model. Additionally, we motivate the use of these type of algorithms in the production context and compare their performance via a computational experiment. We observe that the methodology based on shuffling the values of a variable outperforms the methodology based on the dual formulation. We observe that the shuffling-based methodology correctly ranks the variables in 94% of the scenarios with one relevant input and one irrelevant input. Moreover, it correctly ranks each variable in at least 65% of replications of a scenario with three relevant inputs and one irrelevant input.

Analytical Quality by Design-Driven RP-HPLC Method Conditions to Concomitantly Determine Cinnarizine and Morin Hydrate in Combined Drug Solution and Dual Drug-Loaded Formulations.

The replacement of traditional oils with a camphor and menthol-based eutectic mixture is done to prepare oil-less emulsion-like dispersions for co-delivery of cinnarizine (CNZ) and morin hydrate (MH) for managing Meniére's disease (MD). Since two drugs are loaded into the dispersions, the development of a suitable reverse phase-high performance liquid chromatography (RP-HPLC) method for their simultaneous analysis becomes inevitable. By applying the analytical quality by design (AQbD) approach, the RP-HPLC method conditions were optimized for the concomitant determination of two drugs. The systematic AQbD started with identifying critical method attributes (CMA) through an Ishikawa fishbone diagram, risk estimation matrix, and risk priority number-based failure mode effect analysis followed by screening using fractional factorial design and optimization by face-centered central composite design. The concomitant determination of two drugs by the optimized RP-HPLC method condition was substantiated via specificity checking using combined drug solution, drug entrapment efficiency, and in vitro release of the two drugs from emulsion-like dispersions. The AQbD optimized RP-HPLC method conditions revealed the retention time for CNZ and MH at 5.017 and 5.323, respectively. The studied validation parameters were found within the ICH-prescribed limits. Exposing the individual drug solutions to acidic and basic hydrolytic conditions yielded extra chromatographic peaks for MH, probably due to the degradation of MH. The DEE % values of 87.40 ± 4.70 and 74.79 ± 2.94, respectively, were noticed for CNZ and MH in emulsion-like dispersions. More than 98% CNZ and MH release was occurred from emulsion-like dispersions within 30 min post-dissolution in artificial perilymph. Overall, the AQbD approach could be helpful for systematic optimization of RP-HPLC method conditions to estimate concomitantly other therapeutic moieties. The proposed article shows the successful application of AQbD for the optimization of RP-HPLC method conditions to concomitantly estimate CNZ and MH in combined drug solution and dual-drug-loaded emulsion-like dispersions.

Neutralisation of SARS-CoV-2 by monoclonal antibody through dual targeting powder formulation.

Neutralising monoclonal antibody (mAb) is an important weapon in our arsenal for combating respiratory viral infections. However, the effectiveness of neutralising mAb has been impeded by the rapid emergence of mutant variants. Early administration of broad-spectrum mAb with improved delivery efficiency can potentially enhance efficacy and patient outcomes. WKS13 is a humanised mAb which was previously demonstrated to exhibit broad-spectrum activity against SARS-CoV-2 variants. In this study, a dual targeting formulation strategy was designed to deliver WKS13 to both the nasal cavity and lower airways, the two critical sites of infection caused by SARS-CoV-2. Dry powders of WKS13 were first prepared by spray drying, with cyclodextrin used as stabiliser excipient. Two-fluid nozzle (TFN) was used to produce particles below 5μm for lung deposition (C-TFN formulation) and ultrasonic nozzle (USN) was used to produce particles above 10μm for nasal deposition (C-USN formulation). Gel electrophoresis and size exclusion chromatography studies showed that the structural integrity of mAb was successfully preserved with no sign of aggregation after spray drying. To achieve dual targeting property, C-TFN and C-USN were mixed at various ratios. The aerosolisation property of the mixed formulations dispersed from a nasal powder device was examined using a Next Generation Impactor (NGI) coupled with a glass expansion chamber. When the ratio of C-TFN in the mixed formulation increased, the fraction of particles deposited in the lung increased proportionally while the fraction of particles deposited in the nasal cavity decreased correspondingly. A customisable aerosol deposition profile could therefore be achieved by manipulating the mixing ratio between C-TFN and C-USN. Dual administration of C-TFN and C-USN powders to the lung and nasal cavity of hamsters, respectively, was effective in offering prophylactic protection against SARS-CoV-2 Delta variant. Viral loads in both the lung tissues and nasal wash were significantly reduced, and the efficacy was comparable to systemic administration of unformulated WKS13. Overall, dual targeting powder formulation of neutralising mAb is a promising approach for prophylaxis of respiratory viral infections. The ease and non-invasive administration of dual targeting nasal powder may facilitate the widespread distribution of neutralising mAb during the early stage of unpredictable outbreaks.

Distributed Multirobot Task Assignment via Consensus ADMM

In this article, we present a distributed algorithm to solve a class of multirobot task assignment problems. We formulate task assignment as a mathematical optimization and solve for optimal solutions with a variant of the consensus alternating direction method of multipliers (C-ADMM). We provide C-ADMM-based algorithms for both the primal and dual problem formulations and show the advantages of each form depending on the problem specifics. In our algorithm, each robot solves a series of local optimization problems and communicates the results to its local neighbors, ultimately converging to an optimal task assignment in problems with linear objective functions and an optimal solution of the relaxed problem in convex problems. While many other distributed algorithms require a central station for their implementation, in our algorithm, each robot only communicates with its one-hop neighbors. In linear task assignment problems, our algorithm converges to the optimal task assignment, unlike many other distributed algorithms for this problem, which yield suboptimal solutions. We demonstrate our algorithms in task assignment problems over a variety of communication network topologies, where we show that our inexact dual algorithm is at least 60% faster than other distributed algorithms, which produce an optimal task assignment. In addition, our dual algorithm attains a 69% speedup in computation time compared to a notable distributed variant of the Hungarian method (Chopra et al., 2017). We also apply our algorithm to a multi-unmanned-aerial-vehicle persistent surveillance problem, showing its suitability for problems involving periodic task assignments.

Applications of the duality theory of convex analysis to the complete electrode model of electrical impedance tomography

The duality theory of convex analysis is applied to the complete electrode model (CEM), which is a standard model in electrical impedance tomography (EIT). This results in a dual formulation of the CEM and a general error estimate. This new formulation of the CEM is written in terms of current fields and is shown to have a unique solution. Using this formulation, the general error estimate is proved, from which two a posteriori error estimates and a well known asymptotic result on CEM solutions are obtained. The first a posteriori error estimate assesses the accuracy of solutions to approximate problems, and the second one assesses the accuracy of approximate solutions. Numerical tests to apply this second estimate are performed, employing the finite element method to obtain approximate solutions.

Universum parametric $$\nu $$-support vector regression for binary classification problems with its applications

AbstractUniversum data sets, a collection of data sets that do not belong to any specific class in a classification problem, give previous information about data in the mathematical problem under consideration to enhance the classifiers’ generalization performance. Recently, some researchers have integrated Universum data into the existing models to propose new models which result in improved classification performance. Inspired by these Universum models, an efficient parametric$$ \nu $$ν-support vector regression with Universum data ($$ {\mathfrak {U}} $$UPar-$$ \nu $$ν-SVR) is proposed in this work. This method, which finds two non-parallel hyperplanes by solving one optimization problem and considers heteroscedastic noise, overcomes some common disadvantages of the previous methods. The$$ {\mathfrak {U}} $$UPar-$$ \nu $$ν-SVR includes unlabeled samples that don’t belong to any class in the training process, which results in a quadratic programming problem. Two approaches are proposed to solve this problem. The first approach derives the dual formulation using the Lagrangian function and KKT conditions. Furthermore, a least squares parametric$$ \nu $$ν-support vector regression with Universum data (named LS-$$ {\mathfrak {U}} $$UPar-$$ \nu $$ν-SVR) is suggested to further increase the generalization performance. The LS-$$ {\mathfrak {U}} $$UPar-$$ \nu $$ν-SVR solves a single system of linear equations, instead of addressing a quadratic programming problem in the dual formulation. Numerical experiments on artificial, UCI, credit card, NDC, and handwritten digit recognition data sets show that the suggested Universum model and its solving methodologies improve prediction accuracy.