General Constraints Research Articles

Nonreciprocal radiative heat transfer between two planar bodies

We develop an analytical framework for nonreciprocal radiative heat transfer in two-body planar systems. Based on our formalism, we identify effects that are uniquely nonreciprocal in near-field heat transfer in planar systems. We further introduce a general thermodynamic constraint that is applicable for both reciprocal and nonreciprocal planar systems, in agreement with the second law of thermodynamics. We numerically demonstrate our findings in an example system consisting of magneto-optical materials. Our formalism applies to both near- and far-field regimes, opening opportunities for exploiting nonreciprocity in two-body radiative heat transfer systems.

The Boundaries of KKLT

AbstractWe consider the conundrum of generating de Sitter space from higher‐dimensional geometry, with particular attention to KKLT‐type constructions[3] and their 5d implications. We show that even in the probe approximation with small , a consistent higher‐dimensional solution requires a deformation of a modulus field playing the role of a Goldberger‐Wise stabilizing field in Randall‐Sundrum type geometries that occurs through a shift in a the throat length. We identify the light radion field that sets the length of the throat, whose origin is the dynamical conifold deformation parameter. By analyzing the theory as a 5d model of mismatched branes in AdS5 space with a GW stabilization mechanism, we show how energy (and supersymmetry breaking) is transferred to both the IR and UV regions of the throat to generate a consistent 4d de Sitter sliced geometry. This should help resolve some of the recent apparent paradoxes in explicit higher‐dimensional constructions. Moreover, the radion gives insight into the potential for the previously identified “conifold instability”. We argue that this instability would be a destabilization of the potential for the radion in KKLT, which can occur when the perturbation is too large. If indeed is too small, the radion would enter on its runaway direction and the conifold deformation would shrink to zero size. It is difficult to satisfy the required bound and a) maintain a hierarchy in the simpler CY manifolds and b) complete the cosmological phase transition into the stabilized throat, We also discuss the implications of this type of setup for supersymmetry breaking, and how multiple throats can introduce hierarchies of supersymmetry breaking masses, even in an anomaly‐mediated scenario. In an appendix we consider general compactification constraints.

The Multivariate Linear Prediction Problem: Model-Based and Direct Filtering Solutions

Numerous contexts in macroeconomics, finance, and quality control require real-time estimation of trends, turning points, and anomalies. The real-time signal extraction problem is formulated as a multivariate linear prediction problem, the optimal solution is presented in terms of a known model, and multivariate direct filter analysis is proposed to address the more typical situation where the process’ model is unknown. It is shown how general constraints – such as level and time shift constraints – can be imposed on a concurrent filter in order to guarantee that real-time estimates have requisite properties. The methodology is applied to petroleum and construction data.

Coordinating questions: The scope puzzle

This paper introduces a new puzzle concerning the interaction between questions on the one hand, and conjunction and disjunction on the other. It shows that a conjunction of two polar interrogative clauses is interpreted so that each conjunct involves a polar question operator and the conjunction takes scope over these, whereas a disjunction of two polar interrogative clauses can only be interpreted as involving a single polar question operator scoping over the disjunction. In other words, two full-fledged polar questions each including their own question operator can be conjoined, but cannot be disjoined. We argue that the source of this contrast is semantic (rather than syntactic, pragmatic, or other), and we formulate two general constraints on question meanings which can each account for it. The first, based on Fox (2018), requires that the resolutions of a question are related in a particular way to the cells of the partition that the question induces on the context set. The second requires that the exhaustive interpretation of a consistent resolution of the question is never inconsistent. We leave open which of these two constraints is to be preferred.

An Image Clustering Auto-Encoder Based on Predefined Evenly-Distributed Class Centroids and MMD Distance

In this paper, we propose a novel, effective and simpler end-to-end image clustering auto-encoder algorithm: ICAE. The algorithm uses PEDCC (Predefined Evenly-Distributed Class Centroids) as the clustering centers, which ensures the inter-class distance of latent features is maximal, and adds data distribution constraint, data augmentation constraint, auto-encoder reconstruction constraint and Sobel smooth constraint to improve the clustering performance. Specifically, we perform one-to-one data augmentation to learn the more effective features. The data and the augmented data are simultaneously input into the autoencoder to obtain latent features and the augmented latent features whose similarity are constrained by an augmentation loss. Then, making use of the maximum mean discrepancy distance (MMD), we combine the latent features and augmented latent features to make their distribution close to the PEDCC distribution (uniform distribution between classes, Dirac distribution within the class) to further learn clustering-oriented features. At the same time, the MSE of the original input image and reconstructed image is used as reconstruction constraint, and the Sobel smooth loss to build generalization constraint to improve the generalization ability. Finally, extensive experiments on three common datasets MNIST, Fashion-MNIST, COIL20 are conducted. The experimental results show that the algorithm has achieved the best clustering results so far. In addition, we can use the predefined PEDCC class centers, and the decoder to clearly generate the samples of each class. The code can be downloaded at https://github.com/zyWang-Power/Clustering!

Optimizing Information Freshness in Wireless Networks Under General Interference Constraints

Age of information (AoI) is a recently proposed metric for measuring information freshness. AoI measures the time that elapsed since the last received update was generated. We consider the problem of minimizing average and peak AoI in a wireless networks, consisting of a set of source-destination links, under general interference constraints. When fresh information is always available for transmission, we show that a stationary scheduling policy is peak age optimal. We also prove that this policy achieves average age that is within a factor of two of the optimal average age. In the case where fresh information is not always available, and packet/information generation rate has to be controlled along with scheduling links for transmission, we prove an important separation principle: the optimal scheduling policy can be designed assuming fresh information, and independently, the packet generation rate control can be done by ignoring interference. Peak and average AoI for discrete time G/Ber/1 queue is analyzed for the first time, which may be of independent interest.

Coalition Formation of Microgrids with Distributed Energy Resources and Energy Storage in Energy Market

In recent years, significant efforts for improving the technical and the economic performance of smart grids have been applied with the presence of different players making decisions in these grids. This paper proposes a bi-level hierarchical structure for designing and planning distributed energy resources in home microgrids (H-MGs). Such a small-scale grid inside the market environment permits energy exchange among distributed energy resources and home microgrids through a pool market. In this paper, each home microgrid's planner maximizes the performance of distributed energy resources while exchanging energy with other H-MGs. The problem is formulated as a high-level problem decomposed into a set of low-level market clearing problems. The global optimal performance in terms of energy cost is met for a market structure (H-MGs, consumers, and retailers) at a Nash optimum point for the formulated scheduling game considering local and general constraints on the spot market. In general, the upper-level structure is based on H-MG generation competition for maximizing their individual and/or group income in the process of forming coalition with other H-MGs. In addition, the functionality of the lower-level of the hierarchical structure is governed by a market clearing based on the price response method by all the DERs enabling H-MGs to change the spot market strategic behavior. Prices are obtained as dual variables of power balance equations. This paper will investigate a set of bilevel games, including nonlinear programming problems solved through a complementary problem method. Using the binary theory, the bilevel hierarchical structure will be replanned using a nonlinear problem. Results prove that the proposed structure can increase the players's profit.

On the ensemble‐based linearization of numerical models

AbstractCurrent parallelization trends in computer technology facilitates development of the algorithms that retrieve linear approximations of the model operators and their adjoints from ensembles of model simulations. In this study we address the problem of obtaining exact linearizations in the presence of semi‐implicit numerics of the parent model under realistic constraints on the ensemble size. The method is based on factorization of the model into a sequence of local and non‐local linear operators and employs prior information on the structure of the respective sparse matrices. The performance of the method is tested using 28 perturbed solutions of the shallow‐water equations with a moderate size () state vector. Numerical experiments have shown feasibility of the approach under relatively general constraints on the structure of the parent model. Because of the substantial expense of the ensemble‐based linearization, special focus is made on the assessment of the optimal frequency of such computations within the time intervals between data injections in typical operational systems.

Scheduling Extra Train Paths Into Cyclic Timetable Based on the Genetic Algorithm

In order to support the process of scheduling a hybrid cyclic timetable, this paper is devoted to inserting additional non-cyclic train paths into existing cyclic timetable. The adding train paths problem is an integration of timetable scheduling and rescheduling problem. The train dispatcher can not only modify the given timetable to manage the interruptions in existing operations, but also establish schedules for additional trains. A multi-objective model minimizing both the travel time of additional trains and the variation of existing trains is proposed in this paper. In addition, we consider both general constraints and some additional practical constraints, such as the overtaking priority constraint, reasonable adjustment of initial schedules and the scheduled connections. This problem is very difficult and must be solved in practice. A heuristic algorithm is introduced to find high-quality solutions for large-scale cases within reasonable computing time. Based on high-speed railway line in China, the case studies illustrate the methodology and compare the performance of trains. Numerical experiments indicate that the proposed solution approach to the adding train paths problem is promising.

Strategic Approach to Implementation and Integration of Routing-Based Tasks in Warehouse Management Information Systems

One of the frequently occurring tasks during the development of warehouse management systems is the implementation of routing algorithms of some kind. Whether it is for routing workers during order picking, delivery vehicles or company representatives, this task has proven to be challenging in the technical as well as the social sense. In other words, the task is heavily dependent on various general and company-specific constraints and it directly dictates the way employees should do their job. This paper describes a strategic approach to the development and gradual integration of such algorithms which makes sure that all constraints are satisfied and, more importantly, ensures that route suggestions are viewed by the employees as a helpful tool rather than a threat to their job. In the first part of this paper, the approach is described and evaluated on a warehouse representative routing problem through a real-world case study in a medium-to-large warehouse. In the second part, the same approach is adapted to a delivery vehicle routing problem for a smaller retailer company. In both cases, routing efficiency almost doubled in comparison to previous approaches used by the companies. The most important factors of the implementation and integration stages as well as the impact of the changes on employee satisfaction are aggregated, analysed in detail, and discussed throughout different stages of development.

Sharp Worst-Case Evaluation Complexity Bounds for Arbitrary-Order Nonconvex Optimization with Inexpensive Constraints

We provide sharp worst-case evaluation complexity bounds for nonconvex minimization problems with general inexpensive constraints, i.e., problems where the cost of evaluating/enforcing of the (poss...

Production scheduling considering dynamic electricity price in energy-efficient factories

Factories account for more than 42% of global energy consumption. In order to contribute to reduce carbon footprint and increase energy efficiency, it is important to optimize the tasks and time of product manufacturing according to the renewable generation and lower prices of the grid but without compromising production quality and output. This paper aims to develop flexible optimization platform for industrial production processes. The proposed production scheduling model is formulated as a 15-minute interval of one week time-span adopting mixed-integer linear optimization model and solved in TOMLAB. The model considers general production constraints for different products and takes into account with the photovoltaic generation of the factory as well as the dynamic price of the grid. The results are compared with a reference case without photovoltaic and where the dynamic price is not considered. The energy cost savings can amount up to 29% or 100 € in the considered example.

Set-Membership Filtering for Nonlinear Dynamic Systems With Quadratic Inequality Constraints

The present study investigates the problem of set-membership filtering for nonlinear dynamic systems with general nonconvex inhomogeneous quadratic inequality constraints. The investigators propose an ellipsoidal state bounding estimation in the setting of unknown but bounded noise. In order to guarantee the on-line usage, the nonlinear function is linearized by Taylor expansion at each time step, where the bounding ellipsoid of the remainder is updated on-line based on the current state bounding ellipsoid. Furthermore, based on the remainder bounds and the constraints, both the state prediction and measurement update of the filtering can be transformed into a semidefinite programming problem that can be efficiently solved. In order to further reduce the computational complexity, a part-analytical formula of the shape matrix and the center of the bounding ellipsoid is derived using a decoupled technique, which is also helpful to clarify how these constraints affect the state estimation. Finally, typical numerical examples demonstrate the effectiveness of this filtering.

MIMO Radar Waveform Optimization in Clutter Under General Power Constraints

In this paper, we investigate a novel framework on the waveform optimization for multiple-input multiple-output (MIMO) radar systems under assumptions of statistical information of scattering matrices and colored noise. Different from most of traditional designs under total power constraint, in our framework, a general power constraint named as multiple weighted power constraints is provided, which includes total power constraint, per-antenna power constraints as its special cases. In the framework, the transmit and receive correlations of parameter matrix to estimate and the spatial and time correlations of noise matrix are all taken into account. Moreover, the signal-dependent interference is also taken into account, which can be considered as a self-interference noise. Based on the available statistics of scattering matrices and colored noise, two kinds of estimation schemes are proposed in this paper, which can realize different trade-offs between complexity and performance. Finally, some numerical results are given to demonstrate the performance advantages of the proposed radar waveform designs.

Recovering Structured Data From Superimposed Non-Linear Measurements

This work deals with the problem of distributed data acquisition under non-linear communication constraints. More specifically, we consider a model setup where $M$ distributed nodes take individual measurements of an unknown structured source vector $x_0 \in \mathbb{R}^n$, communicating their readings simultaneously to a central receiver. Since this procedure involves collisions and is usually imperfect, the receiver measures a superposition of non-linearly distorted signals. In a first step, we will show that an $s$-sparse vector $x_0$ can be successfully recovered from $O(s \cdot\log(2n/s))$ of such superimposed measurements, using a traditional Lasso estimator that does not rely on any knowledge about the non-linear corruptions. This direct method however fails to work for several "uncalibrated" system configurations. These blind reconstruction tasks can be easily handled with the $\ell^{1,2}$-Group-Lasso, but coming along with an increased sampling rate of $O(s\cdot \max\{M, \log(2n/s) \})$ observations - in fact, the purpose of this lifting strategy is to extend a certain class of bilinear inverse problems to non-linear acquisition. Our two algorithmic approaches are a special instance of a more abstract framework which includes sub-Gaussian measurement designs as well as general (convex) structural constraints. These results are of independent interest for various recovery and learning tasks, as they apply to arbitrary non-linear observation models. Finally, to illustrate the practical scope of our theoretical findings, an application to wireless sensor networks is discussed, which actually serves as the prototypical example of our methodology.

A Computation-Efficient Decentralized Algorithm for Composite Constrained Optimization

This paper focuses on solving the problem of composite constrained convex optimization with a sum of smooth convex functions and non-smooth regularization terms (ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> norm) subject to locally general constraints. Motivated by the modern large-scale information processing problems in machine learning (the samples of a training dataset are randomly decentralized across multiple computing nodes), each of the smooth objective functions is further considered as the average of several constituent functions. To address the problem in a decentralized fashion, we propose a novel computation-efficient decentralized stochastic gradient algorithm, which leverages the variance reduction technique and the decentralized stochastic gradient projection method with constant step-size. Theoretical analysis indicates that if the constant step-size is less than an explicitly estimated upper bound, the proposed algorithm can find the exact optimal solution in expectation when each constituent function (smooth) is strongly convex. Concerning the existing decentralized schemes, the proposed algorithm not only is suitable for solving the general constrained optimization problems but also possesses low computation cost in terms of the total number of local gradient evaluations. Furthermore, the proposed algorithm via differential privacy strategy can effectively mask the privacy of each constituent function, which is more practical in applications involving sensitive messages, such as military affairs or medical treatment. Finally, numerical evidence is provided to demonstrate the appealing performance of the proposed algorithm.

Upper and Lower Bounds of Average Elastic Constants of an Anisotropic Polycrystalline Medium: Calculations and A Priori Estimates

Abstract —A general procedure is suggested for calculating the upper (Voigt) and lower (Reuss) bounds of the average elastic constants of an anisotropic medium from crystallographic directions. The elastic tensors of Hooke’s law can be expanded into irreducible representations of the rotation group. The Voigt/Reuss-averaged elastic constants depend on the second and fourth moments of the distribution function rather than on the entire function used for the averaging. In this case, the distribution function depends on one angle, while the elastic constants depend on two variables. The limitations imposed by the probability theory on the moment values are investigated and used to derive general constraints on the Voigt (Reuss) bounds of elastic constants.

Null controllability for distributed systems with time-varying constraint and applications to parabolic-like equations

<p style='text-indent:20px;'>We consider the null controllability problem fo linear systems of the form <inline-formula><tex-math id="M1">\begin{document}$ y'(t) = Ay(t)+Bu(t) $\end{document}</tex-math></inline-formula> on a Hilbert space <inline-formula><tex-math id="M2">\begin{document}$ Y $\end{document}</tex-math></inline-formula>. We suppose that the control operator <inline-formula><tex-math id="M3">\begin{document}$ B $\end{document}</tex-math></inline-formula> is bounded from the control space <inline-formula><tex-math id="M4">\begin{document}$ U $\end{document}</tex-math></inline-formula> to a larger extrapolation space containing <inline-formula><tex-math id="M5">\begin{document}$ Y $\end{document}</tex-math></inline-formula>. The control <inline-formula><tex-math id="M6">\begin{document}$ u $\end{document}</tex-math></inline-formula> is constrained to lie in a time-varying bounded subset <inline-formula><tex-math id="M7">\begin{document}$ \Gamma(t) \subset U $\end{document}</tex-math></inline-formula>. From a general existence result based on a selection theorem, we obtain various properties on local and global constrained null controllability. The existence of the time optimal control is established in a general framework. When the constraint set <inline-formula><tex-math id="M8">\begin{document}$ \Gamma (t) $\end{document}</tex-math></inline-formula> contains the origin in its interior at each <inline-formula><tex-math id="M9">\begin{document}$ t&gt;0 $\end{document}</tex-math></inline-formula>, the local constrained property turns out to be equivalent to a weighted dual observability inequality of <inline-formula><tex-math id="M10">\begin{document}$ L^{1} $\end{document}</tex-math></inline-formula> type with respect to the time variable. We treat also the problem of determining a steering control for general constraint sets <inline-formula><tex-math id="M11">\begin{document}$ \Gamma (t) $\end{document}</tex-math></inline-formula> in nonsmooth convex analysis context. Applications to the heat equation are treated for distributed and boundary controls under the assumptions that <inline-formula><tex-math id="M12">\begin{document}$ \Gamma (t) $\end{document}</tex-math></inline-formula> is a closed ball centered at the origin and its radius is time-varying.

Constraint polynomial approach: an alternative to the functional Bethe Ansatz method?

Recently developed general constraint polynomial approach is shown to replace a set of algebraic equations of the functional Bethe Ansatz method by a single polynomial constraint. As the proof of principle, the usefulness of the method is demonstrated for a number of quasi-exactly solvable (QES) potentials of the Schr\"odinger equation, such as two different sets of modified Manning potentials with three parameters, an electron in Coulomb and magnetic fields and relative motion of two electrons in an external oscillator potential, the hyperbolic Razavy potential, and a (perturbed) double sinh-Gordon system. The approach enables one to straightforwardly determine eigenvalues and wave functions. Odd parity solutions for the modified Manning potentials are also determined. For the QES examples considered here, constraint polynomials terminate a finite chain of orthogonal polynomials in an independent variable that need not to be necessarily energy. In the majority of cases the finite chain of orthogonal polynomials is characterized by a positive-definite moment functional ${\cal L}$, implying that a corresponding constraint polynomial has only real and simple zeros. Constraint polynomials are shown to be different from the weak orthogonal Bender-Dunne polynomials. At the same time the QES examples considered elucidate essential difference with various generalizations of the Rabi model. Whereas in the former case there are $n+1$ polynomial solutions at each point of a $n$th baseline, in the latter case there are at most $n+1$ polynomial solutions on entire $n$th baseline.

Метод анализа экономических процессов в условиях нестабильности (на примере анализа динамики выручки российских компаний)

New methods are proposed that allow using the properties of nonlinear dynamics models to analyze the dynamics of real socio-economic processes. For this, a complex of models has been developed in the form of connected nonlinear one-dimensional and multidimensional map pings that meet the general laws of socio-economic processes - development in a rapidly changing environment under resource constraints. The proposed set of models allows you to analyze the dynamics of processes under the assumptions of both their independence and interconnection with each other. The definition of interrelated processes is introduced as processes developing under conditions of general constraints. Three criteria are proposed for identifying interrelated processes based on empirical data. In the case of interrelation of processes, the parameters of one-dimensional and multidimensional models are also interrelated, which allows a deeper analysis of the situations under consideration. The use of the proposed method is demonstrated by the example of analyzing the dynamics of revenue of Russian companies in the pe­riod from 2006 to 2015 (38 thousand companies in total). All companies were divided into four groups, depending on the rate of revenue growth from 2010 to 2015. The hypothesis of a possible relationship between the decline of one and the parallel strengthening of another group of Russian firms after the crisis of 2008-2009 is investigated and rejected. Innovative firms that boosted their revenue growth potential after the crisis were targeting markets other than con ser­vative firms whose revenue growth potential was exhausted after the crisis. The peculiarities of the dynamics of revenue of groups of companies are visually presented in the form of normalized values, when the median estimates of each of the groups in 2007 are taken as a unit.