Optimal Argument Research Articles

The best constant for inequality involving the sum of the reciprocals and product of positive numbers with unit sum

In this paper, we study a special algebraic inequality containing a parameter, the sum of reciprocals and the product of positive real numbers whose sum is 1. Using a new optimization argument the best values of the parameter are determined. In the case of three numbers the algebraic inequality has some interesting geometric applications involving a generalization of Euler’s inequality about the ratio of radii of circumscribed and inscribed circles of a triangle.

THE BEST CONSTANT FOR INEQUALITY

Abstract. In the paper we study a special parameter containing algebraic inequality involving sum of reciprocals and product of positive real numbers whose sum is 1. We determine the best values of the parameter using a new optimization argument. In the case of three numbers the algebraic inequality have some interesting geometric applications involving a generalization of Euler’s inequality about the ratio of radii of circumscribed and inscribed circles of a triangle.

Stability of hypercontractivity, the logarithmic Sobolev inequality, and Talagrand's cost inequality

We provide deficit estimates for Nelson's hypercontractivity inequality, the logarithmic Sobolev inequality, and Talagrand's transportation cost inequality under the restriction that the inputs are semi-log-subharmonic, semi-log-convex, or semi-log-concave. In particular, our result on the logarithmic Sobolev inequality complements a recently obtained result by Eldan, Lehec and Shenfeld concerning a deficit estimate for inputs with small covariance. Similarly, our result on Talagrand's transportation cost inequality complements and, for a large class of semi-log-concave inputs, improves a deficit estimate recently proved by Mikulincer. Our deficit estimates for hypercontractivity will be obtained by using a flow monotonicity scheme built on the Fokker–Planck equation, and our deficit estimates for the logarithmic Sobolev inequality will be derived as a corollary. For Talagrand's inequality, we use an optimal transportation argument. An appealing feature of our framework is robustness and this allows us to derive deficit estimates for the hypercontracivity inequality associated with the Hamilton–Jacobi equation, the Poincaré inequality, and for Beckner's inequality.

The problem of an object evaluation and optimization under several criterias

The problems of estimation and optimization of an object pursuing several goals are considered. In the estimation problem, the evaluation function is calculated with known parameters that determine the state of the object. In the optimization problem, there are optimization arguments that deliver the extremum of the objective function. Both the evaluation and objective functions are built on the basis of the concept of a nonlinear trade-off scheme, for which the principle «away from restrictions» is fulfilled. Both tasks are solved in a formalized manner, without the direct participation of the decision maker (DM). Model examples are given. The object O is considered, the state of which is determined by the set of values x1, x2,…,xn, that make up the vector x={xj}ni=1 ϵ X The object pursues several goals, the degree of achievement of each of them is expressed by the corresponding criterion yk(x), k ϵ [1,…,s]. The criteria form a vector y={yk(x)}sk=1 ϵ M. Restrictions are imposed on the criteria yk min(x)≤yk(x)≤ yk max(x). The problem of estimating the quality of the functio­ning of an object O is to determine the value of a certain function Y[y(x)] with known parameters x1, x2,…,xn. The function Y[y(x)] in this case is called the evaluation function. The optimization problem is to determine the values x1, x2,…,xn by extremizing the function Y[y(x)] In this case, the function Y[y(x)] is the objective, and the parameters are called optimization arguments. Both tasks require the function Y[y(x)]. In fact, this function is a scalar convolution of the criteria vector y(x) which reflects the utility function of the decision maker (DM) in solving a specific estimation or optimization problem. Scalar convolution is an act of composing criteria. The criterion yk(x) is a measure of the quality of the object O functioning in relation to the achievement of the k-th goal. If «more» means «better», then such a criterion should be maximized to improve the quality. Otherwise, the criterion is minimized. For definiteness, we consider the optimization problem under minimized performance criteria.

Effects of evolution on niche displacement and emergent population properties, a discussion on optimality

Understanding the effects of evolution on emergent population properties such as intrinsic growth rates, species abundances or resilience is not only a key theoretical question, but has major empirical implications, for instance in conservation, agroecology and invasion ecology. Evolution can also lead to polymorphism based on niche differentiation among different phenotypes. The present article has three aims. First, we clarify the evolutionary scenarios allowing for optimization of population growth rate and abundance. Second, we relate the eco‐evolutionary emergence of polymorphism to the niche‐overlap and fitness‐ratio sensu coexistence theory. Third, we discuss whether properties of polymorphic populations can be optimized due to niche‐displacement among phenotypes. We revisit previous theoretical results on eco‐evolutionary optimization and link them with our Lotka–Volterra framework. Depending on how the traits under selection affect species intrinsic growth rates or ecological interactions, we uncover three scenarios, ranging from the optimization of all three properties to no optimization and link evolutionary dynamics to coexistence theory. Optimization is, in general, incompatible with niche differentiation sensu coexistence theory and, therefore, with the emergence of polymorphism. Niche displacement between resident and mutant phenotypes, and potentially polymorphism, only arise when we do not expect optimality to hold. Finally, we show how our approach can be generalized to coevolutionary scenarios. In the discussion, we propose biological scenarios and traits that may fall into our three scenarios. Although it is possible to find traits for which optimality is expected, for the majority of the cases optimization arguments do not hold. We also provide practical applications of our results in conservation, agroecology, harvesting and invasion ecology.

Cell outage compensation scheme based on hybrid genetic algorithms and neural networks

In this paper, a system for LTE Cell Outage Compensation (COC) based on hybrid Genetic Algorithms (GA) and Artificial Neural Networks (ANN) has been proposed. COC aims to minimize the impact of cell outage which leads to decrease in operator revenue and/or the customer satisfaction. The proposed system adopts an optimization module to search for an optimal setting of a set of LTE operational parameters to achieve a targeted set of key performance indicators. The optimization process always leads to good enough solutions, but it also requires a huge number of trials. So, in the proposed system, a huge set of outage scenarios is collected along with their optimal argument settings that are acquired by the optimization module and they are used to train an artificial neural network (ANN) module, which acts as an expert that can optimally act on the different situations in real-time mode. Simulation environment is set to evaluate different LTE measures and Key Performance Indicators (KPIs) on different outage scenarios. Simulation results proved the capability and robustness of the proposed system to minimize the number of users experiencing outage. Simulation results also show that the proposed system achieves optimal parameter settings without violating the overall system performance and with minimal processing time, while introducing significant impact on the performance of LTE.

On the modified least action principle with dissipation

The principle of least action is a variational principle that states an object will always take the path of least action as compared to any other conceivable path. This principle can be used to derive the equations of motion of many systems, and therefore provides a unifying equation that has been applied in many fields of physics and mathematics. Hamilton’s formulation of the principle of least action typically only accounts for conservative forces, but can be reformulated to include non-conservative forces such as friction by using the approach suggested by Wang and co-workers (Lin and Wang, 2014; Wang, 2015). However, it turns out that this modified action is dependent upon the nature and amount of damping in the system and the optimality argument fails to hold for sufficiently large values of the damping coefficient. In this paper, we specifically investigate the modified action principle for the cases of a linearly and cubically damped, nonlinear pendulum.

The narrowing of dendrite branches across nodes follows a well-defined scaling law

The systematic variation of diameters in branched networks has tantalized biologists since the discovery of da Vinci's rule for trees. Da Vinci's rule can be formulated as a power law with exponent two: The square of the mother branch's diameter is equal to the sum of the squares of those of the daughters. Power laws, with different exponents, have been proposed for branching in circulatory systems (Murray's law with exponent 3) and in neurons (Rall's law with exponent 3/2). The laws have been derived theoretically, based on optimality arguments, but, for the most part, have not been tested rigorously. Using superresolution methods to measure the diameters of dendrites in highly branched Drosophila class IV sensory neurons, we have found that these types of power laws do not hold. In their place, we have discovered a different diameter-scaling law: The cross-sectional area is proportional to the number of dendrite tips supported by the branch plus a constant, corresponding to a minimum diameter of the terminal dendrites. The area proportionality accords with a requirement for microtubules to transport materials and nutrients for dendrite tip growth. The minimum diameter may be set by the force, on the order of a few piconewtons, required to bend membrane into the highly curved surfaces of terminal dendrites. Because the observed scaling differs from Rall's law, we propose that cell biological constraints, such as intracellular transport and protrusive forces generated by the cytoskeleton, are important in determining the branched morphology of these cells.

Tuning Generalized Predictive PI controllers for process control applications

Predictive PI (PPI) controllers have demonstrated to exceed traditional PID controllers when they are applied to systems with long delays. This work proposes a new controller structure and tuning that we call Generalized Predictive PI (GPPI) controller which provides greater design flexibility than PI and PPI strategies. To realize a fair comparison, the design and tuning rules for discrete PI and PPI controllers were developed using optimal arguments based on the root-locus, for critically damped response before a step change in the reference. Experimental results, using industrial equipment, have illustrated the tuning methodology and the performance of the proposed controller under real conditions. Flow and water level process in a laboratory flume were considered. For these processes, First Order Plus Time Delay (FOPTD) models are used. The GPPI control results are encouraging, reducing the settling time plus a very small overshoot before step change in the reference regarding the PI and PPI strategies, up to 41.03% for the flow control loop and up to 54.21% for the level control loop. The discrete analysis of the strategies in the Z plane was performed, allowing for a direct translation to recursive equations that can then be programmed into a Programmable Logic Controller (PLC), other industrial controllers such as Distributed Control Systems (DSC), or microcontrollers, such as Arduino, Raspberry or FPGA. This is an important result, since it demonstrates that the increased complexity of the proposed controller does not hamper its implementation in industrial controller systems. In this work, we used a Rockwell ControlLogix \\protect \\relax \\special {t4ht=®} PLC with Structured Text programming language.

Wasserstein stability estimates for covariance-preconditioned Fokker–Planck equations

We study the convergence to equilibrium of the mean field PDE associated with the derivative-free methodologies for solving inverse problems that are presented by Garbuno-Inigo et al (2020 SIAM J. Appl. Dyn. Syst. 19 412–41), Herty and Visconti (2018 arXiv:1811.09387). We show stability estimates in the Euclidean Wasserstein distance for the mean field PDE by using optimal transport arguments. As a consequence, this recovers the convergence towards equilibrium estimates by Garbuno-Inigo et al (2020 SIAM J. Appl. Dyn. Syst. 19 412–41) in the case of a linear forward model.

Impact of the compilation method on determining the accuracy of the error loss in neural network learning

In the field of NLP (Natural Language Processing) research, the use of a neural network has become important. The neural network is widely used in the semantic analysis of texts in different languages. In connection with the actualization of the processing of big data in the Kazakh language, a neural network was built for deep learning. In this study, the object is the learning process of a deep neural network, which evaluates the algorithm for constructing an LDA model. One of the most problematic places is determining the correct arguments, which, when compiling the model, will give an estimate of the algorithm’s performance. During the research, the compile () method from the Keras modular library was used, the main arguments of which are the loss function, optimizers, and metrics. The neural network is implemented in the Python programming language. The main arguments of the neural network deep learning compiler for evaluating the LDA model is the selection of arguments to obtain the correct evaluation of the algorithm of the constructed model using deep learning of the neural network. A corpus of text in the Kazakh language with no more than 8000 words is presented as learning data. Using the above methods, an experiment was carried out on the selection of arguments for the model compiler when learning a text corpus in the Kazakh language. As a result, the optimizer – SGD, the loss function – binary_crossentropy, and the estimation metric – ‘cosine_proximity’ were chosen as the optimal arguments, which, as a result of learning, showed a tendency to 0 loss (errors)=0.1984, and cosine_proximity (learning accuracy)=0.2239, which is considered acceptable learning measures. The results indicate the correct choice of compilation arguments. These arguments can be applied when conducting deep learning of a neural network, where the sample data is a pair of «topic and keywords».

Augmented Queue-Based Transmission and Transcoding Optimization for Livecast Services Based on Cloud-Edge-Crowd Integration

Nowadays, amateur broadcasters can massively generate video contents and stream them across the Internet. For this reason, crowdsourced livecast services (CLS) are attracting millions of users around the world. To provide a smooth and high-quality playback experience to viewers with diversified device configurations in dynamic network conditions, CLS providers have to find a way to deploy cost-effective transcoding operations by distributing the computation-intensive workload among Cloud, Edge, and Crowd. In addition, it is necessary to control transcoded streams from million broadcasters to worldwide viewers. To address these challenges, we propose a novel stochastic approach that jointly optimizes the usage of transmission resources ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">e.g.</i> , bandwidth), and transcoding resources ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">e.g.</i> , CPU) in CLS systems that leverage the cooperation of Cloud, Edge, and Crowd technologies. In particular, we first design an augmented queue structure that can jointly capture the dynamic features of data transmission and online transcoding, based on the virtual queue technology. Then, we formulate a joint resource allocation problem, using stochastic optimization arguments, and devise an Accelerated Gradient Optimization (AGO) algorithm to solve the optimization problem in a scalable way. Moreover, we provide four main theoretical results that characterize the algorithm’s steady-state queue-length, optimality, and fast-convergence. By conducting both numerical simulations and system-level evaluations based on our prototype, we demonstrate that our solution provides lower system costs and higher QoE performance against state-of-the-art solutions.

Arbitrage concepts under trading restrictions in discrete-time financial markets

In a discrete-time setting, we study arbitrage concepts in the presence of convex trading constraints. We show that solvability of portfolio optimization problems is equivalent to absence of arbitrage of the first kind, a condition weaker than classical absence of arbitrage opportunities. We center our analysis on this characterization of market viability and derive versions of the fundamental theorems of asset pricing based on portfolio optimization arguments. By considering specifically a discrete-time setup, we simplify existing results and proofs that rely on semimartingale theory, thus allowing for a clear understanding of the foundational economic concepts involved. We exemplify these concepts, as well as some unexpected situations, in the context of one-period factor models with arbitrage opportunities under borrowing constraints.

Sobolev inequalities with jointly concave weights on convex cones

Using optimal mass transport arguments, we prove weighted Sobolev inequalities of the form ∫ E | u ( x ) | q ω ( x ) d x 1 / q ⩽ K 0 ∫ E | ∇ u ( x ) | p σ ( x ) d x 1 / p , u ∈ C 0 ∞ ( R n ) , (WSI)where p ⩾ 1 and q > 0 is the corresponding Sobolev critical exponent. Here E ⊆ R n is an open convex cone, and ω , σ : E → ( 0 , ∞ ) are two homogeneous weights verifying a general concavity-type structural condition. The constant K 0 = K 0 ( n , p , q , ω , σ ) > 0 is given by an explicit formula. Under mild regularity assumptions on the weights, we also prove that K 0 is optimal in (WSI) if and only if ω and σ are equal up to a multiplicative factor. Several previously known results, including the cases for monomials and radial weights, are covered by our statement. Further examples and applications to partial differential equations are also provided.

A Semi-Algebraic Optimization Approach to Data-Driven Control of Continuous-Time Nonlinear Systems

This letter considers the problem of designing state feedback data-driven controllers for nonlinear continuous-time systems. Specifically, we consider a scenario where the unknown dynamics can be parametrized in terms of known basis functions and the available measurements are corrupted by unknown-but-bounded noise. The goal is to use this noisy experimental data to directly design a rational state-feedback control law guaranteed to stabilize all plants compatible with the available information. The main result of this letter shows that, by using Rantzer's Dual Lyapunov approach, combined with elements from convex analysis, the problem can be recast as an optimization over positive polynomials, which can be relaxed to a semi-definite program through the use of Sum-of-Squares and semi-algebraic optimization arguments. Three academic examples are considered to illustrate the effectiveness of the proposed method.

Mathematical models of functions of partial criteria in tasks of vectorial optimization of complex technical systems

The article is devoted to different approaches in constructing regression models of functions of partial criteria in vector optimization problems, basic requirements for models, problems that arise in the subsequent application of models and methods of their solution. Multifactor regression models for the synthesis of complex technical systems are created on the basis of experimental procedures. Models are created for each individual criterion based on the relevant experimental data. The obtained models allow to determine numerical values of partial criteria in given ranges of conceptual parameters of a complex technical system, which are used in the subsequent stages of solving the problem of vector optimization. The necessity to perform these procedures is caused by the fact that when solving an optimization task in relation to complex systems, the analytical dependencies of criteria on optimization arguments are unknown. The polynomial form of regression models is used as approximating polynomials. To ensure good conditionality of the experimental data matrix, standard transformations are performed. The polynomials of Chebyshev of the first and second order are used for this purpose. Unknown polynomial coefficients are calculated using the least squares method. In order to obtain regression models, a complex evaluation of statistical characteristics based on regression analysis results is performed. Then it is decided whether the models can be used to synthesize many alternatives of a complex technical system optimization criterion. The choice of instrumental and methodical devices for scientific and applied researches, engineering works is one problem during the solution of vector optimization problems. In the article it has been stated that nowadays there is a great number of methods and software products which provide wide opportunities for solving vector optimization problems and carrying out different types of data analysis. For example, SPSS, PS PRIAM, STATISTICA, ProSto are the most acceptable and effective, as well as the use of a large number of existing and new modules based on the integrated package of Microsoft Office. This helps to solve a wide range of problems, starting with the procedure of building a regression model of some criteria based on the data from the experiments, the calculation acceptable variants of system and ending with the choice of the residual compromise optimal solution.

Arbitrage Concepts Under Trading Restrictions in Discrete-Time Financial Markets

In a discrete-time setting, we study arbitrage concepts in the presence of convex trading constraints. We show that solvability of portfolio optimization problems is equivalent to absence of arbitrage of the first kind, a condition weaker than classical absence of arbitrage opportunities. We center our analysis on this characterization of market viability and derive versions of the fundamental theorems of asset pricing based on portfolio optimization arguments. By considering specifically a discrete-time setup, we simplify existing results and proofs that rely on semimartingale theory, thus allowing for a clear understanding of the foundational economic concepts involved. We exemplify these concepts, as well as some unexpected situations, in the context of one-period factor models with arbitrage opportunities under borrowing constraints.

Deterministic Optimality of the Steady-State Behavior of the Kalman–Bucy Filter

In this letter, we provide a deterministic characterization of optimality of the steady-state behavior of the Kalman–Bucy filter, via an inverse optimal control argument. The result is achieved in two steps, both interesting per se . First, a singular linear-quadratic (LQ) optimal control problem is formulated and solved with respect to the innovation term of a classic Luenberger observer, hence yielding a LQ optimal observer. Then, such a construction is employed to interpret the optimality of the steady-state behavior of the celebrated Kalman–Bucy filter in a purely deterministic sense.

Nonlinear and piecewise linear income taxation, and the subsidization of work-related goods

We investigate how the social welfare gain of subsidizing work-related goods depends on whether the underlying income tax system is linear, piecewise linear or fully nonlinear, focusing on child care services as a paradigmatic example of goods/services that are complements with labor supply. Our quantitative analysis employs an empirically relevant labor supply model and shows that the welfare gain of an optimally chosen subsidy is negligible when the optimal income tax is restricted to be linear but about the same as under fully nonlinear taxation when the optimal income tax is restricted to be piecewise linear. Our findings enhance the policy relevance of the optimal tax argument in favor of providing subsidies to work-related goods and also shed light on the relative welfare gains of employing piecewise linear rather than fully nonlinear income taxes.

Securitization Structures and Security Design

Securitization has been a subject of interest in the security design literature, and various models have been developed in order to explain why such transactions should produce senior securities and junior securities. However securitization structures are far more complex than a simple tranching by seniority. Using a model extending the existing literature, we derive new results by considering that interest and principal should be separately contractible, and that the senior bonds in a securitization should be par-priced, both realistic constraints. This allows us to derive optimal designs closely resembling actual securitization structures. Further, we show that the resecuritization of residuals, in the form of NIMs or reremics, is optimal through a pooling effect. We also analyze the interactions between collateral characteristics and pricing, reflecting securitization execution, and issuer structure choices. With a simple numerical application, we illustrate how important resecuritization is, and also how more attractive an excess-spread structure is relative to a more standard structure, as expected collateral losses increase. According to our analysis, the apparent complexity in excess-spread structure and in resecuritizations can be explained by a valid optimal design argument.