Stability of iterative processes with errors for a system of nonlinear -accretive variational inclusions in Banach spaces

In this paper, by using the concept of (A,η)-accretive mappings and the new resolvent operator technique associated with (A,η)-accretive mappings, we introduce and study a system of general mixed quasivariational inclusions involving (A,η)-accretive mappings in Banach spaces, and construct a new perturbed iterative algorithm with mixed errors for this system of nonlinear (A,η)-accretive variational inclusions in q-uniformly smooth Banach spaces. Our results improve and generalize the corresponding results of recent works.     

Controller synthesis with guaranteed closed-loop phase constraints

In this paper, we present an analysis and synthesis approach for guaranteeing that the phase of a single-input, single-output closed-loop transfer function is contained in the interval [−α,α] for a given α>0 at all frequencies. Specifically, we first derive a sufficient condition involving a frequency domain inequality for guaranteeing a given phase constraint. Next, we use the Kalman–Yakubovich–Popov theorem to derive an equivalent time domain condition. In the case where , we show that frequency and time domain sufficient conditions specialize to the positivity theorem. Furthermore, using linear matrix inequalities, we develop a controller synthesis approach for guaranteeing a phase constraint on the closed-loop transfer function. Finally, we extend this synthesis approach to address mixed gain and phase constraints on the closed-loop transfer function.     

Controller certification

A modern problem from aerospace control involves the certification of a large set of potential controllers with either a single plant or a fleet of potential plant systems, with both plants and controllers being MIMO and, for the moment, linear. Experiments on a limited number of controller/plant pairs should establish the stability and a certain level of margin of the complete set. We consider this certification problem for a set of controllers and provide algorithms for selecting an efficient subset for testing. This is done for a finite set of candidate controllers and, at least for SISO plants, for compact infinite set. In doing this, the ν-gap metric will be the main tool. Computational examples are given, including one of certification of an aircraft engine controller. The overarching aim is to introduce truly MIMO margin calculations and to understand their efficacy in certifying stability over a set of controllers and in replacing legacy single-loop gain and phase margin calculations.     

A -based optimal finite-word-length controller design

A novel optimal Finite Word Length (FWL) controller design is proposed in the framework of μ theory. A computationally tractable close-loop stability measure with FWL implementation considerations of the controller is derived based on the μ theory, and the optimal FWL controller realizations are obtained by solving the resulting optimal FWL realization problem using linear matrix inequality techniques.     

Parameterized complexity of control problems in Maximin election

Elections are a central model in a variety of areas. This paper studies parameterized computational complexity of five control problems in the Maximin election. We obtain the following results: constructive control by adding candidates is W[2]-hard with respect to the parameter “number of added candidates”; both constructive and destructive control by adding/deleting voters are W[1]-hard with respect to the parameter “number of added/deleted voters”.     

A class of aggregation functions encompassing two-dimensional OWA operators

In this paper we prove that, under suitable conditions, Atanassov’s K_α operators, which act on intervals, provide the same numerical results as OWA operators of dimension two. On one hand, this allows us to recover OWA operators from K_α operators. On the other hand, by analyzing the properties of Atanassov’s operators, we can generalize them. In this way, we introduce a class of aggregation functions - the generalized Atanassov operators - that, in particular, include two-dimensional OWA operators. We investigate under which conditions these generalized Atanassov operators satisfy some properties usually required for aggregation functions, such as bisymmetry, strictness, monotonicity, etc. We also show that if we apply these aggregation functions to interval-valued fuzzy sets, we obtain an ordered family of fuzzy sets.     

Embedding HMMs-based models in a Euclidean space: the topological hidden Markov models

Current extensions of hidden Markov models such as structural, hierarchical, coupled, and others have the power to classify complex and highly organized patterns. However, one of their major limitations is the inability to cope with topology: When applied to a visible observation (VO) sequence, the traditional HMM-based techniques have difficulty predicting the n-dimensional shape formed by the symbols of the VO sequence. To fulfill this need, we propose a novel paradigm named “topological hidden Markov models” (THMMs) that classifies VO sequences by embedding the nodes of an HMM state transition graph in a Euclidean space. This is achieved by modeling the noise embedded in the shape generated by the VO sequence. We cover the first and second level topological HMMs. We describe five basic problems that are assigned to a second level topological hidden Markov model: (1) sequence probability evaluation, (2) statistical decoding, (3) structural decoding, (4) topological decoding, and (5) learning. To show the significance of this research, we have applied the concept of THMMs to: (i) predict the ASCII class assigned to a handwritten numeral, and (ii) map protein primary structures to their 3D folds. The results show that the second level THMMs outperform the SHMMs and the multi-class SVM classifiers significantly.     

A high quality and small shadow size visual secret sharing scheme based on hybrid strategy for grayscale images

Many secret sharing schemes for digital images have been developed in recent decades. Traditional schemes typically must deal with the problem of computational complexity, and other visual secret sharing schemes come with a higher transmission cost and storage cost; that is, each shadow size is m times as big as the original secret image. The new (2,n) secret sharing scheme for grayscale images proposed in this paper is based a combination of acceptable image quality using block truncation coding (BTC), high compression ratio discrete wavelet transform (DWT) and good subjective performance of the vector quantization (VQ) technique. Experimental results confirm that our proposed scheme not only generates a high quality reconstructed original image but also generates small, random-like grayscale shadows.     

A goodness-of-fit test for Archimedean copula models in the presence of right censoring

A goodness-of-fit testing procedure for Archimedean copula (AC) models is developed based on right-censored data. The proposed approach extends an existing method, which is suitable for the Clayton model, to general AC models. Asymptotic properties of the proposed test statistics under the true model assumption are derived. Simulation analysis shows that the proposed test has reasonable performance. Finally, two real data examples are analyzed for illustrative purposes.     

Robust model selection with flexible trimming

The forward search provides data-driven flexible trimming of a C_p statistic for the choice of regression models that reveals the effect of outliers on model selection. An informed robust model choice follows. Even in small samples, the statistic has a null distribution indistinguishable from an F distribution. Limits on acceptable values of the C_p statistic follow. Two examples of widely differing size are discussed. A powerful graphical tool is the generalized candlestick plot, which summarizes the information on all forward searches and on the choice of models. A comparison is made with the use of M-estimation in robust model choice.