Set Of Multipliers Research Articles

International Systematic Review of Utility Values Associated with Cardiovascular Disease and Reflections on Selecting Evidence for a UK Decision-Analytic Model.

Evaluating interventions for cardiovascular disease (CVD) requires estimates of its effect on utility. We aimed to 1) systematically review utility estimates for CVDs published since 2013 and 2) critically appraise UK-relevant estimates and calculate corresponding baseline utility multipliers. We searched MEDLINE and Embase (April 22, 2021) using CVD and utility terms. We screened results for primary studies reporting utility distributions for people with experience of heart failure, myocardial infarction, peripheral arterial disease, stable angina, stroke, transient ischemic attack, or unstable angina. We extracted characteristics from studies included. For UK estimates based on the EuroQoL 5-dimension (EQ-5D) measure, we assessed risk of bias and applicability to a decision-analytic model, pooled arms/time points as appropriate, and estimated baseline utility multipliers using predicted utility for age- and sex- matched populations without CVD. We sought utility sources from directly applicable studies with low risk of bias, prioritizing plausibility of severity ordering in our base-case model and highest population ascertainment in a sensitivity analysis. Most of the 403 studies identified used EQ-5D (n = 217) and most assessed Organisation for Economic Co-operation and Development populations (n = 262), although measures and countries varied widely. UK studies using EQ-5D (n = 29) produced very heterogeneous baseline utility multipliers for each type of CVD, precluding meta-analysis and implying different possible severity orderings. We could find sources that provided a plausible ordering of utilities while adequately representing health states. We cataloged international CVD utility estimates and calculated UK-relevant baseline utility multipliers. Modelers should consider unreported sources of heterogeneity, such as population differences, when selecting utility evidence from reviews. Published systematic reviews have summarized estimates of utility associated with cardiovascular disease published up to 2013.We 1) reviewed utility estimates for 7 types of cardiovascular disease published since 2013, 2) critically appraised UK-relevant studies, and 3) estimated the effect of each cardiovascular disease on baseline utility.Our review 1) recommends a consistent and reliable set of baseline utility multipliers for 7 types of cardiovascular disease and 2) provides systematically identified reference information for researchers seeking utility evidence for their own context.

Finite Horizon Worst Case Analysis of Linear Time-Varying Systems Applied to Launch Vehicle

This article presents an efficient approach to compute the worst case gain of the interconnection of a finite time horizon linear time-varying system and a perturbation. The input/output behavior of the uncertainty is described by integral quadratic constraints (IQCs). A condition for the worst case gain of such an interconnection can be formulated using dissipation theory as a parameterized Riccati differential equation, which depends on the chosen IQC multiplier. A nonlinear optimization problem is formulated to minimize the upper bound of the worst case gains over a set of admissible IQC multipliers. This problem can be efficiently solved with a custom-tailored logarithmically scaled, adaptive differential evolution algorithm. It provides a fast alternative to similar approaches based on solving semidefinite programs. The algorithm is applied to the worst case aerodynamic load analysis of an expendable launch vehicle (ELV). The worst case load of the uncertain ELV is calculated under wind turbulence during the atmospheric ascend and compared to results from nonlinear simulation.

Predicting the Spatial Distribution of Hyalomma ssp., Vector Ticks of Crimean–Congo Haemorrhagic Fever in Iraq

Crimean–Congo hemorrhagic fever (CCHF) typically spreads through ticks and is categorized as a viral hemorrhagic fever. CCHF is a fatal endemic disease in Iraq, and it has been reported sporadically since its first report in 1979. Recent outbreaks during 2021–2023 and their fatal consequences captured the interest of this study. CCHF is a tick-borne disease that represents a major challenge to the public health, social, and economic sectors. The geographical distribution of CCHF is closely linked with Hyalomma vector tick distribution. Therefore, predicting and mapping the spatial distribution of the disease vector in relation to relevant environmental factors provides invaluable information for establishing an early warning system based on which preventive measures can be taken to minimize the spread and, hence, the fatal consequences of CCHF. To achieve this, this study incorporates geospatial techniques and maximum entropy modeling (Maxent) to assess the habitat suitability of the Hyalomma vector and to identify the key environmental drivers contributing to its spatial distribution in Iraq. Utilizing the area under the ROC curve (AUC) as the performance metric, the model evaluation yielded successful results in predicting habitat suitability for Hyalomma vector ticks in Iraq. The AUC attained an average score of 0.885 with a regularization multiplier (β) set at 1. The Hyalomma ticks’ suitable habitat distribution within the study area covers a fraction of the total land, at approximately 51% (225,665 km2) of the entire 441,724 km2 region. Among these suitable areas, 41.57% (183,631 km2) were classified as lowly suitable, 8.61% (38,039 km2) as moderately suitable, and 0.9% (3994 km2) as highly suitable. Several factors have significantly influenced Hyalomma vector tick distribution in Iraq. These include land cover (accounting for 50.8%), elevation (contributing 30.4%), NDVI (5.7%), temperature seasonality (4.7%), precipitation seasonality (3.3%), sheep density (2.3%), goat density (2.2%), and the mean diurnal range (0.5%). The findings of this study could have significant implications for establishing a strategic early warning system and taking preventive measures beforehand to minimize and control Crimean–Congo haemorrhagic fever in Iraq and similar ecoregions in the Middle East. As a primary precaution, this study recommends focusing on highly suitable areas (3994 km2) in the southern part of Iraq for management and preventive actions.

A new Lagrangian-based first-order method for nonconvex constrained optimization

In this paper, we introduce a new form of Lagrangian function and propose a simple first-order primal-dual algorithm for solving nonconvex optimization with nonlinear equality constraints. We show that the algorithm generates bounded primal-dual iterates, and establish the convergence to KKT points under standard assumptions. The key features of the proposed method are: (i) it does not require boundedness assumptions on dual iterates generated by the algorithm as well as the set of multipliers; (ii) it is a single-loop algorithm that does not involve any penalty subproblems.

On the necessity and sufficiency of discrete-time O’Shea–Zames–Falb multipliers

This paper considers the robust stability of a discrete-time Lurye system consisting of the feedback interconnection between a linear system and a bounded and monotone nonlinearity. It has been conjectured that the existence of a suitable linear time-invariant (LTI) O’Shea–Zames–Falb multiplier is not only sufficient but also necessary. Roughly speaking, a successful proof of the conjecture would require: (a) a conic parameterisation of a set of multipliers that describes exactly the set of nonlinearities, (b) a lossless S-procedure to show that the non-existence of a multiplier implies that the Lurye system is not uniformly robustly stable over the set of nonlinearities, and (c) the existence of a multiplier in the set of multipliers used in (a) implies the existence of an LTI multiplier. We investigate these three steps, showing the current bottlenecks for proving this conjecture. In addition, we provide an extension of the class of multipliers which may be used to disprove the conjecture.

Advancing height growth models for the improved forest reproductive material of the main tree species in Latvia

The breeding of economically important forest tree species in the Baltic Sea region has contributed notably to the availability of quality wood for bioeconomy. Accordingly, the altered stand dynamics of improved trees should be identified and incorporated in growth models to accurately reflect these gains. Such advanced models can be used for assessment of different alternatives, e.g. strategies for increased carbon sequestration. We tested and modified dynamic forms of the King-Prodan height growth function based on the remeasured National Forest Inventory plots in Latvia to predict the growth of improved Scots pine, Norway spruce and silver birch forest reproductive material (FRM) categories ‘qualified’ and ‘tested’ using height measurements from progenies of 371, 390, and 690 open-pollinated families, respectively. Both categories had steeper growth trajectories at young age compared to an unmodified function. Growth of category ‘tested’ for pine and birch exceeded that of category ‘qualified’ across the modelled age range, while trajectories mainly overlapped for spruce on lower site indices. The functions with FRM category-specific multipliers more accurately reflect the actual growth of improved stands, advancing planning of timely management activities like thinning. The single model with category-specific set of multipliers may be easy applicable in practice or incorporated in growth simulators without increased complexity for end-users. However, the predictions are limited to the sites with medium and high site indices, where improved planting stock is typically used. Keywords: GADA approach, dynamic modelling, tree breeding, FRM categories

Weight set decomposition for weighted rank and rating aggregation: An interpretable and visual decision support tool

The problem of interpreting or aggregating multiple rankings is common to many real-world applications. Perhaps the simplest and most common approach is a weighted rank aggregation, wherein a (convex) weight is applied to each input ranking and then ordered. This paper describes a new tool for visualizing and displaying ranking information for the weighted rank aggregation method. Traditionally, the aim of rank aggregation is to summarize the information from the input rankings and provide one final ranking that hopefully represents a more accurate or truthful result than any one input ranking. While such an aggregated ranking is, and clearly has been, useful to many applications, it also obscures information. In this paper, we show the wealth of information that is available for the weighted rank aggregation problem due to its structure. We apply weight set decomposition to the set of convex multipliers, study the properties useful for understanding this decomposition, and visualize the indifference regions. This methodology reveals information–that is otherwise collapsed by the aggregated ranking–into a useful, interpretable, and intuitive decision support tool. Included are multiple illustrative examples, along with heuristic and exact algorithms for computing the weight set decomposition.

Efficient long-range convolutions for point clouds

The efficient treatment of long-range interactions (LRIs) for point clouds is a challenging problem in many scientific machine learning applications. To extract global information, one usually needs a large window size, a large number of layers, and/or a large number of channels. This can often significantly increase the computational cost. In this work, we present a novel neural network layer that directly incorporates long-range information for a point cloud. This layer, dubbed the long-range convolutional (LRC)-layer, leverages the convolutional theorem coupled with the non-uniform Fourier transform. In a nutshell, the LRC-layer mollifies the point cloud to an adequately sized regular grid, computes its Fourier transform, multiplies the result by a set of trainable Fourier multipliers, computes the inverse Fourier transform, and finally interpolates the result back to the point cloud. The resulting global all-to-all convolution operation can be performed in nearly-linear time asymptotically with respect to the number of input points. The LRC-layer is a particularly powerful tool when combined with local convolution as together they offer efficient and seamless treatment of both short- and long-range interactions. We showcase this framework by introducing a neural network architecture that combines LRC-layers with short-range convolutional layers to accurately learn the energy and force associated with a N-body potential. We also exploit the induced two-level decomposition and propose an efficient strategy to train the combined architecture with a reduced number of samples.

Localizability With Range-Difference Measurements: Numerical Computation and Error Bound Analysis

This paper studies the localization problem using noisy range-difference measurements, or equivalently time difference of arrival (TDOA) measurements. There is a reference sensor, and for each other sensor, the TDOA measurement is obtained with respect to the reference one. By minimizing the sum of squared errors, a nonconvex constrained least squares (CLS) problem is formulated. In this work, we focus on devising an algorithm to seek the global minimizer of the CLS problem, hoping that the numerical solution meets some precision requirement in terms of relative error. Based on the Lagrange multiplier method, we first branch the feasible Lagrange multiplier set into several subsets and develop a workflow in terms of if-then-else control structure to seek the global minimizer by searching for the optimal Lagrange multiplier. The execution order is carefully organized so that it is in line with the general principle of putting the flow that one normally understands to be executed first. We then dive into detailed searching methods in different cases and conduct computational error analysis, giving the error bound on the Lagrange multiplier, when we search for it, to meet the precision requirement on an approximate solution. Based on the above achievements, a programmable global minimizer seeking algorithm is proposed for the CLS problem. Simulations and experimental tests on a public dataset demonstrate the effectiveness of the proposed algorithm.

Fast and High-Accuracy Approximate MAC Unit Design for CNN Computing

Multiply and accumulate (MAC) composed of a set of multipliers and one reduction dominates the latency and power of convolutional neural network (CNN) accelerators. Existing approximate multipliers reduce latency and power at a tolerable drop in accuracy, without considering the data distribution (implicitly assuming that data are uniformly distributed). This letter discloses that practical CNNs’ activations and weights are usually Gaussian-like distributed, and the bits of quantized activations and weights are typically not with a probability of 0.5. Thus, we propose an approximate MAC unit design by taking into account the statistical features of input data, to achieve a balanced tradeoff among latency, power, and accuracy. The extensive experiments show that our proposed MAC unit design provides much higher accuracy than state-of-the-art approximate circuits, while the latency, area, and power are similar.

Global Convergence of Algorithms Under Constant Rank Conditions for Nonlinear Second-Order Cone Programming

In Andreani et al. (Weak notions of nondegeneracy in nonlinear semidefinite programming, 2020), the classical notion of nondegeneracy (or transversality) and Robinson’s constraint qualification have been revisited in the context of nonlinear semidefinite programming exploiting the structure of the problem, namely its eigendecomposition. This allows formulating the conditions equivalently in terms of (positive) linear independence of significantly smaller sets of vectors. In this paper, we extend these ideas to the context of nonlinear second-order cone programming. For instance, for an m-dimensional second-order cone, instead of stating nondegeneracy at the vertex as the linear independence of m derivative vectors, we do it in terms of several statements of linear independence of 2 derivative vectors. This allows embedding the structure of the second-order cone into the formulation of nondegeneracy and, by extension, Robinson’s constraint qualification as well. This point of view is shown to be crucial in defining significantly weaker constraint qualifications such as the constant rank constraint qualification and the constant positive linear dependence condition. Also, these conditions are shown to be sufficient for guaranteeing global convergence of several algorithms, while still implying metric subregularity and without requiring boundedness of the set of Lagrange multipliers.

Feedback tracking control of optimal reference trajectories for spacecraft relative motion

In this paper, first the optimal trajectories are defined by a fixed end-time, continuous-thrust trajectory which minimizes a terminal cost at the end of an inter-planetary trajectory by appending the multi-body dynamic equations defining the motion by a set of Lagrange multipliers or co-states. The solution of these co-states and the optimal trajectories for a fixed end-time are obtained by solving a two-point boundary value problem along with a steering control law, which is used to provide a reference trajectory. Inspired by the general expression for the gravitation potential and the Q-law, a tracking control law is designed to track the reference trajectory. As the steering controller is not a feedback controller, a feedback tracking control law is proposed to continuously correct the spacecraft's actual relative motion trajectory so it tracks the reference relative motion trajectory. The nonlinear relative motion tracking control law is reduced to a linear feedback control law, when the spacecraft is sufficiently close to the reference relative motion trajectory. The feedback laws demonstrate the feasibility of developing practical tracking laws for continuous trajectory correction manoeuvre control of spacecraft relative motion, for implementing low-thrust inter-planetary trajectory following control in electrically propelled spacecraft, in practice.

Maximum Principle and Second-Order Optimality Conditions in Control Problems with Mixed Constraints

This article concerns the optimality conditions for a smooth optimal control problem with an endpoint and mixed constraints. Under the normality assumption, which corresponds to the full-rank condition of the associated controllability matrix, a simple proof of the second-order necessary optimality conditions based on the Robinson stability theorem is derived. The main novelty of this approach compared to the known results in this area is that only a local regularity with respect to the mixed constraints, that is, a regularity in an ε-tube about the minimizer, is required instead of the conventional stronger global regularity hypothesis. This affects the maximum condition. Therefore, the normal set of Lagrange multipliers in question satisfies the maximum principle, albeit along with the modified maximum condition, in which the maximum is taken over a reduced feasible set. In the second part of this work, we address the case of abnormal minimizers, that is, when the full rank of controllability matrix condition is not valid. The same type of reduced maximum condition is obtained.

Penalty and Augmented Lagrangian Methods for Constrained DC Programming

In this paper, we consider a class of structured nonsmooth difference-of-convex (DC) constrained DC programs in which the first convex component of the objective and constraints is the sum of a smooth and a nonsmooth function, and their second convex component is the supremum of finitely many convex smooth functions. The existing methods for this problem usually have a weak convergence guarantee or require a feasible initial point. Inspired by the recent work by Pang et al. [Pang J-S, Razaviyayn M, Alvarado A (2017) Computing B-stationary points of nonsmooth DC programs. Math. Oper. Res. 42(1):95–118.], in this paper, we propose two infeasible methods with a strong convergence guarantee for the considered problem. The first one is a penalty method that consists of finding an approximate D-stationary point of a sequence of penalty subproblems. We show that any feasible accumulation point of the solution sequence generated by such a penalty method is a B-stationary point of the problem under a weakest possible assumption that it satisfies a pointwise Slater constraint qualification (PSCQ). The second one is an augmented Lagrangian (AL) method that consists of finding an approximate D-stationary point of a sequence of AL subproblems. Under the same PSCQ condition as for the penalty method, we show that any feasible accumulation point of the solution sequence generated by such an AL method is a B-stationary point of the problem, and moreover, it satisfies a Karush–Kuhn–Tucker type of optimality condition for the problem, together with any accumulation point of the sequence of a set of auxiliary Lagrangian multipliers. We also propose an efficient successive convex approximation method for computing an approximate D-stationary point of the penalty and AL subproblems. Finally, some numerical experiments are conducted to demonstrate the efficiency of our proposed methods.

Some Remarks on the Issue of Second-order Optimality Conditions in Control Problems with Mixed Constraints

A smooth optimal control problem with mixed constraints is considered. Under the normality assumption, a proof of second-order necessary optimality conditions based on the Robinson stability theorem is provided. The main feature of the obtained result is that the local regularity with respect to the mixed constraints is assumed, that is, a regularity in an ε-tube along the minimizer, but not the conventional global regularity hypothesis. This impacts the maximum condition. Therefore, the normal set of Lagrange multipliers fulfills the Legendre-Clebsch condition and the maximum principle. At the same time, the maximum condition is modified since, now, the maximum is taken over a reduced feasible set. Furthermore, the case of abnormal minimizers is considered. The same type of reduced maximum condition is obtained along with a refined Legendre-Clebsch condition which is meaningful in the abnormal case.

On constraint qualifications for second-order optimality conditions depending on a single Lagrange multiplier

We present new constraint qualifications (CQs) to ensure the validity of some well-known second-order optimality conditions. Our main interest is on second-order conditions that can be associated with numerical methods for solving constrained optimization problems. Such conditions depend on a single Lagrange multiplier, instead of the whole set of Lagrange multipliers. For each condition, we characterize the weakest CQ that guarantees its fulfillment at local minimizers, while proposing new weak conditions implying them. Relations with other CQs are discussed.

Splitting Sequences for Coding and Hybrid Incremental ARQ with Fragment Retransmission

This paper proposes a code defined on a finite ring ℤpM, where pM = 2m−1 is a Mersenne prime, and m is a binary size of ring elements. The code is based on a splitting sequence (splitting set) S, defined for the given multiplier set E=±20, ±21,…, ±2m−1. The elements of E correspond to the weights of binary error patterns that can be corrected, with the bidirectional single-bit error being the representative that occurs the most. The splitting set splits the code-word into sub-words, which inspired the name splitting code. Each sub-word, provided with auxiliary control symbols that are a byproduct of the coding procedure, corrects a single symbol error. The code can be defined, with some constraints, for general Mersenne numbers as well, while the multiplier set can be adjusted for adjacent binary errors correction. The application proposed for this code is a hybrid three-stage incremental ARQ procedure that transmits the code-word in the first stage, auxiliary control symbols in the second stage, and retransmits the sub-words detected as incorrect in the third stage. At each stage, error correction can be turned on or off, keeping both the retransmission rate and residual error rate at a low level.

The nonlocal potential transformation method and solitary wave solutions for higher dimensions in shallow water waves

In this paper, the integrable (4 + 1)-dimensional Fokas equation is investigated. Exploiting a set of non-singular local multipliers, we present a set of local conservation laws for the equation. The nonlocally related partial differential equation (PDE) systems are found. Nine nonlocally related systems are discussed reveal thirty five interesting closed form solutions of the equation. These solutions contain different types of wave solutions, double soliton, multi-solitons, kink and periodic wave solutions. Some of the resulting solutions are graphically illustrated. Furthermore, we apply the sine-cosine method to find other traveling wave solutions for this equation.

RevSCA-2.0: SCA-Based Formal Verification of Nontrivial Multipliers Using Reverse Engineering and Local Vanishing Removal

The formal verification of integer multipliers is one of the important but challenging problems in the verification community. Recently, the methods based on symbolic computer algebra (SCA) have shown very good results in comparison to all other existing proof techniques. However, when it comes to verification of huge and structurally complex multipliers, they completely fail as an explosion happens in the number of monomials. The reason for this explosion is the generation of redundant monomials known as vanishing monomials. This article introduces the SCA-based approach RevSCA-2.0 that combines reverse engineering and local vanishing removal to verify large and nontrivial multipliers. For our approach, we first come up with a theory for the origin of vanishing monomials, i.e., we prove that the gates/nodes where both outputs of half adders (HAs) converge are the origins of vanishing monomials. Then, we propose a dedicated reverse engineering technique to identify atomic blocks including HAs. The identified HAs are the basis for detecting converging cones and locally removing vanishing monomials, which finally results in a vanishing-free global backward rewriting. The efficiency of RevSCA-2.0 is demonstrated using an extensive set of multipliers with up to several million gates.

Pareto efficiency in the infinite horizon mean-field type cooperative stochastic differential game

This paper discusses the linear quadratic (LQ) mean-field type stochastic differential game with non-homogeneous terms in infinite horizon. Employing the equivalent description of Pareto efficiency, necessary conditions for the existence of Pareto solutions are presented under an assumption on the Lagrange multiplier set. Two conditions are introduced to guarantee that the assumption is established. Further, sufficient conditions for a control to be Pareto efficient are put forward in terms of the necessary conditions, the convexity condition on the homogeneous weighted sum cost functional and a transversality condition. The characterization of Pareto solutions is also studied for the homogeneous case. If the system is MF-L2-stabilizable, then the solvability of the related generalized algebraic Riccati equations (GAREs) provides a sufficient condition under which the cost functionals are convex and all Pareto efficient strategies can be obtained by the weighted sum minimization method. In addition, by introducing two algebraic Lyapunov equations (ALEs), we derive all Pareto solutions.