Complementary Formulations Research Articles

Efficient Ensemble Refinement by Reweighting.

Ensemble refinement produces structural ensembles of flexible and dynamic biomolecules by integrating experimental data and molecular simulations. Here we present two efficient numerical methods to solve the computationally challenging maximum-entropy problem arising from a Bayesian formulation of ensemble refinement. Recasting the resulting constrained weight optimization problem into an unconstrained form enables the use of gradient-based algorithms. In two complementary formulations that differ in their dimensionality, we optimize either the log-weights directly or the generalized forces appearing in the explicit analytical form of the solution. We first demonstrate the robustness, accuracy, and efficiency of the two methods using synthetic data. We then use NMR J-couplings to reweight an all-atom molecular dynamics simulation ensemble of the disordered peptide Ala-5 simulated with the AMBER99SB*-ildn-q force field. After reweighting, we find a consistent increase in the population of the polyproline-II conformations and a decrease of α-helical-like conformations. Ensemble refinement makes it possible to infer detailed structural models for biomolecules exhibiting significant dynamics, such as intrinsically disordered proteins, by combining input from experiment and simulation in a balanced manner.

A New Voltage Sensitivity Analysis Method for Medium-Voltage Distribution Systems Incorporating Power Losses Impact

—In this paper, a novel voltage sensitivity analysis method is proposed. It presents a complementary formulation of the direct sensitivity analysis approach which has been previously developed based on the topological structure of the network. The proposed method named improved direct sensitivity analysis (IDSA) incorporates variations of power losses in the system branches due to the nodal power changes and their eventual impacts on the node voltages. Effectiveness of the IDSA in voltage estimation is investigated and compared with the voltage results obtained by the direct, Jacobian-based, as well as the perturb-and-observe sensitivity analysis methods. To this end, firstly, the introduced sensitivity analysis methods are tested when active or reactive power is changed at the selected nodes of the studied test systems. Accuracy of voltage responses obtained by each of the considered sensitivity analysis methods is evaluated with respect to the exact voltage value obtained from the load flow study. Moreover, performance of the introduced sensitivity analysis methods is examined when they are separately embedded in a multi-step voltage control algorithm which manages active and reactive powers of distributed generation units in order to keep the system voltages within the permitted voltage limits. Simulation results confirm that when the power losses impact is considerable, the IDSA outperforms the direct, perturb-and-observe, and Jacobian-based sensitivity analysis methods in terms of accuracy of the voltage estimation.

An RBF–FD method for pricing American options under jump–diffusion models

American option prices under jump–diffusion models are determined as solutions to partial integro-differential equations (PIDE). In this paper a new combination of a time and spatial discretization applied to a linear complementary formulation (LCP) of the free boundary PIDE is proposed. First a coordinate stretching transformation is performed to the asset price so that the computation of the prices can be focused on regions of real interest instead of on the whole solution domain. An implicit–explicit time discretization applied to the reformulated LCP on a uniform temporal grid is followed by a spatial discretization to get a fully discrete system. The radial basis function (RBF) finite difference method is a local method resulting in a sparse linear system in contrast to global RBF-methods which lead to ill-conditioned dense matrix systems. For the corresponding European option we prove consistency, stability and second-order convergence in a discrete L2-norm. We derive mild conditions for the model parameters under which these results hold. Numerical experiments are performed with European and American options, and a comparison with numerical results available in the literature illustrates the accuracy and efficiency of the proposed algorithm.

Hypernuclear no-core shell model

We extend the No-Core Shell Model (NCSM) methodology to incorporate strangeness degrees of freedom and apply it to single-$\Lambda$ hypernuclei. After discussing the transformation of the hyperon-nucleon (YN) interaction into Harmonic-Oscillator (HO) basis and the Similarity Renormalization Group transformation applied to it to improve model-space convergence, we present two complementary formulations of the NCSM, one that uses relative Jacobi coordinates and symmetry-adapted basis states to fully exploit the symmetries of the hypernuclear Hamiltonian, and one working in a Slater determinant basis of HO states where antisymmetrization and computation of matrix elements is simple and to which an importance-truncation scheme can be applied. For the Jacobi-coordinate formulation, we give an iterative procedure for the construction of the antisymmetric basis for arbitrary particle number and present the formulae used to embed two- and three-baryon interactions into the many-body space. For the Slater-determinant formulation, we discuss the conversion of the YN interaction matrix elements from relative to single-particle coordinates, the importance-truncation scheme that tailors the model space to the description of the low-lying spectrum, and the role of the redundant center-of-mass degrees of freedom. We conclude with a validation of both formulations in the four-body system, giving converged ground-state energies for a chiral Hamiltonian, and present a short survey of the $A\le7$ hyper-helium isotopes.

On connections between Rényi entropy Principal Component Analysis, kernel learning and graph embedding

In this paper, we study the connections between Rényi entropy PCA, kernel learning and graph embedding. A natural complementary formulation of maximum entropy PCA, namely minimum error entropy PCA, is presented. These two formulations can be combined together to give a two-fold understanding of Rényi entropy PCA. Further, we establish connections between Rényi entropy PCA, kernel learning and graph embedding, and propose a generalized graph embedding framework that unifies a variety of existing algorithms. This proposed framework essentially covers previous graph embedding framework, and partially answers the problem of how to make use of high order statistics of data in dimensionality reduction. The theoretic development enables a close relationship between information theoretic learning, kernel learning and graph embedding.

Analysis of the retrodirective mechanism of a flattened dihedral

In this journal, an explicit analysis of the retrodirective mechanism of a flattened dihedral using periodic arrays is proposed. Once flattened , a corner dihedral requires a phasing mechanism to restore its retrodirective behavior. This can be achieved by equipping each of the panels with passive phase-shifting cells that obey a global retrodirective phase law. The challenge is to have a trade-off between two steering mechanisms on each side such that this global phase law is achieved. In this work, an analytical study of the reflection phenomenon between the two panels is presented and sufficient information are provided to predict the retrodirective performance affected by the dihedral geometrical configuration itself. The analytical formulation of the global phase law is thus defined along with other complementary formulations to provide a better understanding of the reflection phenomenon involved. Based on these analysis and comprehension, guidelines are suggested in terms of the cell design and the dihedral geometrical configuration so that to efficiently engineer the retrodirective profile of the dihedral. A simple method utilizing these guidelines is proposed to enhance the flattened dihedral performances. And an experimental validation of this design is finally proposed at 24 GHz.

Knot invariants and M-theory: Proofs and derivations

We construct two distinct yet related M-theory models that provide suitable frameworks for the study of knot invariants. We then focus on the four-dimensional gauge theory that follows from appropriately compactifying one of these M-theory models. We show that this theory has indeed all required properties to host knots. Our analysis provides a unifying picture of the various recent works that attempt an understanding of knot invariants using techniques of four-dimensional physics. This is a companion paper to arXiv:1608.05128, covering all but section 3.3. It presents a detailed mathematical derivation of the main results there, as well as additional material. Among the new insights, those related to supersymmetry and the topological twist are highlighted. This paper offers an alternative, complementary formulation of the contents in~\cite{Dasgupta:2016rhc}, but is self-contained and can be read independently.

Modeling and simulation of longitudinal dynamics coupled with clutch engagement dynamics for ground vehicles

During the engagement of the dry clutch in automotive transmissions, clutch judder may occur. Vehicle suspension and engine mounts couple the torsional and longitudinal models, leading to oscillations of the vehicle body that are perceived by the driver as poor driving quality. This paper presents an effective formulation for the modeling and simulation of longitudinal dynamics and powertrain torsional dynamics of the vehicle based on non-smooth dynamics of multibody systems. In doing so friction forces between wheels and the road surface are modeled along with friction torque in the clutch using Coulomb’s friction law. First, bilateral constraint equations of the system are derived in Cartesian coordinates and the dynamical equations of the system are developed using the Lagrange multiplier technique. Complementary formulations are proposed to determine the state transitions from stick to slip between wheels and road surface and from the clutch. An event-driven scheme is used to represent state transition problem, which is solved as a linear complementarity problem (LCP), with Baumgarte’s stabilization method applied to reduce constraint drift. Finally, the numerical results demonstrate that the modeling technique is effective in simulating the vehicle dynamics. Using this method stick-slip transitions between driving wheel and the road surface and from the clutch, as a form of clutch judder, are demonstrated to occur periodically for certain values of the parameters of input torque from engine, and static and dynamic friction characteristics of tire/ground contact patch and clutch discs.

Biofortification of maize flour with grain amaranth for improved nutrition

Food insecurity and malnutrition remain two major problems in Kenya that cause undernutrition (protein-energy malnutrition) and nutrient deficiencies. In a bid to combat the problem, the government has targeted increased production of the micronutrient (minerals, vitamins) fortified maize flour. This is mostly based on chemical fortificants, which is a short-term measure that targets reducing the level of malnutrition while creating better livelihoods. However, there is need to think about long- term and sustainable strategies. Among the causes that have led to food and nutrition insecurity in the country is the over reliance on maize as the staple food. Other staples in Kenya are sorghum, rice and millet. This study aimed at providing a better and more sustainable approach by fortifying maize based diets with grain amaranth. Maize was procured from National Cereals and Produce Board and processed to refined flour, while amaranth grain that had been toasted at 100oC for 5 minutes and milled into flour was obtained from Annicos Limited Company, Nairobi. Complementary formulations were then prepared by blending the flours. The refined maize flour was mixed with varying ratios of 0, 20, 30 and 40% of the grain amaranth flour. The proximate composition, mineral content and microbiological analysis of the raw materials and the blends were determined using recognized standard methods, while protein digestibility was determined after enzyme digestion. Nutritional composition of grain amaranth flour differed significantly (p≤0.05) as compared to refined maize flour; amaranth flour was found to be superior in proteins (15.82%), lipids (7.61%), ash (2.54%) and fibre (4.39%), as compared to proteins (6.29%), lipids (1.92%), ash (0.55%) and fibre (0.76%) in refined maize flour. Adding grain amaranth flour to refined maize flour at the different ratios increased the nutrient density significantly (p≤0.05), particularly protein, iron, calcium and zinc. However, it decreased the digestibility of protein significantly (p≤0.05). The results indicate that although adding 40% grain amaranth gave the best results, the most acceptable blend was the 20% grain amaranth addition. They also indicate that “food to food” fortification can be an approach that can be adapted towards meeting the nutrition requirements of the society. Keywords: Nutrition security, biofortification, amaranth flour, maize flour, optimal blend

Radial Basis Functions with Partition of Unity Method for American Options with Stochastic Volatility

In this article, we price American options under Heston’s stochastic volatility model using a radial basis function (RBF) with partition of unity method (PUM) applied to a linear complementary formulation of the free boundary partial differential equation problem. RBF-PUMs are local meshfree methods that are accurate and flexible with respect to the problem geometry and that produce algebraic problems with sparse matrices which have a moderate condition number. Next, a Crank–Nicolson time discretisation is combined with the operator splitting method to get a fully discrete problem. To better control the computational cost and the accuracy, adaptivity is used in the spatial discretisation. Numerical experiments illustrate the accuracy and efficiency of the proposed algorithm.

On the Displacement of a Two-Dimensional Eshelby Inclusion of Elliptic Cylindrical Shape

In a companion paper, we have obtained the closed-form solutions to the stress and strain fields of a two-dimensional Eshelby inclusion. The current work is concerned with the complementary formulation of the displacement. All the formulae are derived in explicit closed-form, based on the degenerate case of a three-dimensional (3D) ellipsoidal inclusion. A benchmark example is provided to validate the present analytical solutions. In conjunction with our previous study, a complete elasticity solution to the classical elliptic cylindrical inclusion is hence documented in Cartesian coordinates for the convenience of engineering applications.

Method of images applied to driven solid-state emitters

Increasing the collection efficiency from solid-state emitters is an important step towards achieving robust single photon sources, as well as optically connecting different nodes of quantum hardware. A metallic substrate may be the most basic method of improving the collection of photons from quantum dots, with predicted collection efficiency increases of up to 50%. The established 'method-of-images' approach models the effects of a reflective surface for atomic and molecular emitters by replacing the metal surface with a second fictitious emitter which ensures appropriate electromagnetic boundary conditions. Here, we extend the approach to the case of driven solid-state emitters, where exciton-phonon interactions play a key role in determining the optical properties of the system. We derive an intuitive polaron master equation and demonstrate its agreement with the complementary half-sided cavity formulation of the same problem. Our extended image approach offers a straightforward route towards studying the dynamics of multiple solid-state emitters near a metallic surface.

The impact of a predator on the outcome of competition in the three-trophic food web

We study the effects of predation on the competition of prey populations for two resources in a chemostat. We investigate a variety of small food web compositions: the bi-trophic food web (two resources—two competing prey) and the three-trophic food web (two resources—two prey—generalist predator) comparing different model formulations: substitutable resources and essential resources, namely Liebig's minimum law model (perfect essential resources) and complementary resources formulations. The prediction of the outcome of competition is solely based on bifurcation analysis in which the inflow of resources into the chemostat is used as the bifurcation parameter. We show that the results for different bi-trophic food webs are very similar, as only equilibria are involved in the long-term dynamics. In the three-trophic food web, the outcome of competition is manifested largely by non-equilibrium dynamics, i.e., in oscillatory behavior. The emergence of predator–prey cycles leads to strong deviations between the predictions of the outcome of competition based on Liebig's minimum law and the complementary resources. We show that the complementary resources formulation yields a stabilization of the three-trophic food web by decreasing the existence interval of oscillations. Furthermore, we find an exchange of a region of oscillatory co-existence of all three species in Liebig's formulation by a region of bistability of two limit cycles containing only one prey and the predator in the complementary formulation.

Complementary Discrete Geometric <inline-formula> <tex-math notation="LaTeX">$h$ </tex-math> </inline-formula>-Field Formulation for Wave Propagation Problems

An electromagnetic wave propagation problem can be formulated according to a pair of complementary formulations, called the ${e}$ -formulation and the ${h}$ -formulation. The two formulations are linked to each other by Maxwell’s curl equations, and, in the continuous setting, they are perfectly equivalent in describing the wave propagation phenomenon. However, this is not true in the discrete setting, where the two formulations, in general, give different solutions. In the past decades, complementary formulations were widely studied for static problems and eddy-current problems, where they were exploited as error estimators for adaptive refinement schemes. Moreover, the so-called bilateral energy bounds arise for some problems whether theoretically or at least numerically. However, to the best of our knowledge, little attention has been given to complementarity in the wave propagation problems. In this paper, we propose an adaptive refinement scheme using the constitutive error as an estimator, and then, we investigate the behavior in terms of bilateral energy bounds.

Lean Complementarity for Poisson Problems

We introduce a novel technique—lean complementarity—that attempts to eliminate any waste of computational resources occurring during the pursuing of complementarity. First, contrarily to the widely used practice of solving the problem two times with a pair of complementary or complementary-dual formulations, lean complementarity requires just one solution with the computationally cheap formulation based on the scalar potential. This result is enabled by a novel and explicit flux equilibration technique that produces tight bounds and is computationally inexpensive, because no system has to be solved. Second, the systems arising during the adaptive mesh refinement procedure are solved inexactly on purpose, by stopping the iterations of the iterative solver when the algebraic error gets negligible with respect to the discretization error. The discretization error is bounded with complementarity, whereas the algebraic error is computed very accurately with a novel and cheap technique.

Phytochemicals as Complementary and Alternative Therapeutic Formulations with Potential pro-Apoptotic Effects on Various Cancerous Cell Lines: A Literature Survey

Cancer is characterized as one of the deadliest diseases and claims millions of lives every year with higher proportion of causalities in developing countries as compared to the developed ones. Though there exist a number of treatment technologies against cancer including chemotherapies, radiotherapies, surgeries etc. But people are now turning towards plant derived herbal therapies for treatment of cancerous diseases due to ill-effects associated with allopathic treatments. These plant derived bioactive compounds may target fast dividing cells by impairing mitosis or cause target cells to undergo apoptosis without affecting normal cells. This manuscript is concerned about current scenario of epidemiological prevalence of various cancer lines, the pharmacological applications of various plant derived bioactive compounds with potential competency as anticancer therapeutic agents and delineation of probable effects of these compounds on cellular targets and their mechanisms of action.

Complementary formulation of the TFA for the elasto-plastic analysis of composites

In this paper, a new mixed nonuniform Transformation Field Analysis (TFA) homogenization technique for deriving the overall mechanical response of heterogeneous materials is proposed. The new TFA approach is based on a mixed stress variational formulation of the elasto-plasticity theory, assuming stresses and plastic multiplier as independent variables. The case of periodic composites is considered, so that the homogenization is performed on a repetitive unit cell that plays the equivalent role of representative volume element for random media. The unit cell of the material is divided into subsets and in each subset the weak form of the compatibility condition and of the consistency condition are enforced, leading to a simultaneous evaluation of the stress and of the plastic strain field. It is assumed that the stress field satisfies a priori the equilibrium equations while the inelastic strain distribution is evaluated as function of the assumed stress resulting nonuniform in each subset.Some numerical examples are performed in the framework of plane stress plasticity in order to assess the effectiveness of the proposed technique. In particular, the homogenization results are compared with the ones carried out by micromechanical nonlinear finite element analyses.

Multi-field Dual-Mixed Variational Principles Using Non-symmetric Stress Field in Linear Elastodynamics

Three types of multi-field dual-mixed variational principles using a priori non-symmetric stress field will be derived for dynamic problems of linearly elastic solids. Starting from the functional of complementary Hamilton’s principle it is shown how this variational formulation is modified with applying the Lagrange multiplier technique, to obtain a new four-field dual-mixed functional. The independent fields of this functional will be the displacement vector, the non-symmetric stress tensor, the skew-symmetric rotation tensor and the momentum vector. Then we present how to treat appropriately the six different types of initial conditions in a weak and/or strong sense by adding a new integral expression to the four-field functional. Modifying this functional through a Legendre transformation results in a new complementary energy-based five-field dual-mixed functional which allows the momentum- and velocity vectors to be independently approximated. A complementary energy-based three-field dual-mixed variational formulation is obtained by eliminating the momentum- and velocity fields through the strong enforcement of the kinematic equation and the impulse-velocity relation from the five-field principle.

Simultaneous Optimization of Heat-Integrated Water Allocation Networks Using the Mathematical Model with Equilibrium Constraints Strategy

A general optimization model is proposed for the simultaneous optimization of integrated water allocation and heat exchanger networks (WAHEN). An improved superstructure and mathematical model for the WAHEN problem is presented. Complementary formulations are applied to model the discrete decisions, and a mathematical model with equilibrium constraints (MPEC) is formulated. Both the MINLP model and the MPEC model are developed and solved for the problem. The effectiveness of the proposed model is illustrated with two case studies. A comparison between the results obtained by the proposed model and those obtained from the model in the literature is carried out. Case studies show that the proposed simultaneous methodology performs well and is efficient.

Optimization of thin noise barrier designs using Evolutionary Algorithms and a Dual BEM Formulation

This work aims at assessing the acoustic efficiency of different thin noise barrier models. These designs frequently feature complex profiles and their implementation in shape optimization processes may not always be easy in terms of determining their topological feasibility. A methodology to conduct both overall shape and top edge optimizations of thin cross section acoustic barriers by idealizing them as profiles with null boundary thickness is proposed. This procedure is based on the maximization of the insertion loss of candidate profiles proposed by an evolutionary algorithm. The special nature of these sorts of barriers makes necessary the implementation of a complementary formulation to the classical Boundary Element Method (BEM). Numerical simulations of the barriers׳ performance are conducted by using a 2D Dual BEM code in eight different barrier configurations (covering overall shaped and top edge configurations; spline curved and polynomial shaped based designs; rigid and noise absorbing boundaries materials). While results are achieved by using a specific receivers' scheme, the influence of the receivers' location on the acoustic performance is previously addressed. With the purpose of testing the methodology here presented, a numerical model validation on the basis of experimental results from a scale model test [34] is conducted. Results obtained show the usefulness of representing complex thin barrier configurations as null boundary thickness-like models.