A unified approximate reasoning theory suitable for both propositional calculus system \mathcal{L}^* and predicate calculus system \mathcal{K}^*

The concepts of metric R ₀-algebra and Hilbert cube of type R ₀ are introduced. A unified approximate reasoning theory in propositional caculus system $\mathcal{L}^* $ and predicate calculus system $\mathcal{K}^* $ is established semantically as well as syntactically, and a unified complete theorem is obtained.     

Branching Time Logics \mathcal {BTL}^{\mathrm {U,S}}_{\mathrm {N},\mathrm {N}^{-1}}(\mathcal {Z})_{\alpha } with Operations Until and Since Based on Bundles of Integer Numbers, Logical Consecutions, Deciding Algorithms

This paper is intended as an attempt to describe logical consequence in branching time logics. We study temporal branching time logics $\mathcal {BTL}^{\mathrm {U,S}}_{\mathrm {N},\mathrm {N}^{-1}}(\mathcal {Z})_{\alpha }$ which use the standard operations Until and Next and dual operations Since and Previous (LTL, as standard, uses only Until and Next). Temporal logics $\mathcal {BTL}^{\mathrm {U,S}}_{\mathrm {N},\mathrm {N}^{-1}}(\mathcal {Z})_{\alpha }$ are generated by semantics based on Kripke/Hinttikka structures with linear frames of integer numbers $\mathcal {Z}$ with a single node (glued zeros). For $\mathcal {BTL}^{\mathrm {U,S}}_{\mathrm {N},\mathrm {N}^{-1}}(\mathcal {Z})_{\alpha }$ , the permissible branching of the node is limited by α (where 1≤α≤ω). We prove that any logic $\mathcal {BTL}^{\mathrm {U,S}}_{\mathrm {N},\mathrm {N}^{-1}}(\mathcal {Z})_{\alpha }$ is decidable w.r.t. admissible consecutions (inference rules), i.e. we find an algorithm recognizing consecutions admissible in $\mathcal {BTL}^{\mathrm {U,S}}_{\mathrm {N},\mathrm {N}^{-1}}(\mathcal {Z})_{\alpha }$ . As a consequence, it implies that $\mathcal {BTL}^{\mathrm {U,S}}_{\mathrm {N},\mathrm {N}^{-1}}(\mathcal {Z})_{\alpha }$ itself is decidable and solves the satisfiability problem.     

The preparation of organic light-emitting diode encapsulation barrier layer by low-temperature plasma-enhanced chemical vapor deposition: a study on the $$\hbox {SiO}_\mathrm{x}\hbox {N}_\mathrm{y}$$ film parameter optimization

This study prepared \(\hbox {SiO}_\mathrm{x}\hbox {N}_\mathrm{y}\) film by using plasma-enhanced chemical vapor deposition in organic light-emitting diode (OLED) encapsulation to prevent the invasion of moisture and oxygen for longer light-emitting lifetime of OLED components. It applied high density inductively coupled plasma for the coating of film on polyethersulfone, silicon and glass substrate, and discussed the relevance between process parameters and quality characteristics including coating uniformity, coating thickness and moisture permeation. This study used Taguchi method to plan the experiment and calculated the optimal parameters of each quality, used technique for order preference by similarity to ideal solution and grey relational analysis to determine the optimal parameter of all qualities. The back-propagation neural network was combined with Levenberg–Marquardt algorithm to construct the simulation and prediction system. Based on the quality optimization design, the single layer film’s moisture permeation rate was 0.02 g/m\(^{2}\)/day, the maximum coating thickness reached 420 nm, and the fastest rate was 21 nm/min, which was higher than the industrial standard specification (10 nm/min) by 110 %.     

Asymptotic Analysis of Resource Heterogeneous QS $$ (\mathrm {MMPP}+2\mathrm {M})^{(2,\nu )}/\mathrm {GI}(2)/\infty $$ under Equivalently Increasing Service Time

Automation and Remote Control - We consider a resource heterogeneous queuing system with a flexible two-node request-response facility. Each node has a certain resource capacity for service (buffer...     

Integrated damping parameter and control design in structural systems for \bf{\mathcal{H}^2} and {\mathcal{H}^{\infty}} specifications

The paper presents a linear matrix inequality (LMI)-based approach for the simultaneous optimal design of output feedback control gains and damping parameters in structural systems with collocated actuators and sensors. The proposed integrated design is based on simplified $\mathcal{H}^2$ and $\mathcal{H}^{\infty}$ norm upper bound calculations for collocated structural systems. Using these upper bound results, the combined design of the damping parameters of the structural system and the output feedback controller to satisfy closed-loop $\mathcal{H}^2$ or $\mathcal{H}^{\infty}$ performance specifications is formulated as an LMI optimization problem with respect to the unknown damping coefficients and feedback gains. Numerical examples motivated from structural and aerospace engineering applications demonstrate the advantages and computational efficiency of the proposed technique for integrated structural and control design. The effectiveness of the proposed integrated design becomes apparent, especially in very large scale structural systems where the use of classical methods for solving Lyapunov and Riccati equations associated with $\mathcal{H}^2$ and $\mathcal{H}^{\infty}$ designs are time-consuming or intractable.     

Subspace Learning by $$\ell ^{0}$$-Induced Sparsity

Subspace clustering methods partition the data that lie in or close to a union of subspaces in accordance with the subspace structure. Such methods with sparsity prior, such as sparse subspace clustering (SSC) (Elhamifar and Vidal in IEEE Trans Pattern Anal Mach Intell 35(11):2765–2781, 2013) with the sparsity induced by the \(\ell ^{1}\)-norm, are demonstrated to be effective in subspace clustering. Most of those methods require certain assumptions, e.g. independence or disjointness, on the subspaces. However, these assumptions are not guaranteed to hold in practice and they limit the application of existing sparse subspace clustering methods. In this paper, we propose \(\ell ^{0}\)-induced sparse subspace clustering (\(\ell ^{0}\)-SSC). In contrast to the required assumptions, such as independence or disjointness, on subspaces for most existing sparse subspace clustering methods, we prove that \(\ell ^{0}\)-SSC guarantees the subspace-sparse representation, a key element in subspace clustering, for arbitrary distinct underlying subspaces almost surely under the mild i.i.d. assumption on the data generation. We also present the “no free lunch” theorem which shows that obtaining the subspace representation under our general assumptions can not be much computationally cheaper than solving the corresponding \(\ell ^{0}\) sparse representation problem of \(\ell ^{0}\)-SSC. A novel approximate algorithm named Approximate \(\ell ^{0}\)-SSC (A\(\ell ^{0}\)-SSC) is developed which employs proximal gradient descent to obtain a sub-optimal solution to the optimization problem of \(\ell ^{0}\)-SSC with theoretical guarantee. The sub-optimal solution is used to build a sparse similarity matrix upon which spectral clustering is performed for the final clustering results. Extensive experimental results on various data sets demonstrate the superiority of A\(\ell ^{0}\)-SSC compared to other competing clustering methods. Furthermore, we extend \(\ell ^{0}\)-SSC to semi-supervised learning by performing label propagation on the sparse similarity matrix learnt by A\(\ell ^{0}\)-SSC and demonstrate the effectiveness of the resultant semi-supervised learning method termed \(\ell ^{0}\)-sparse subspace label propagation (\(\ell ^{0}\)-SSLP).     

On Projection Matrices $$\mathcal{P}^k \to \mathcal{P}^2 ,k = 3,...,6, $$ and their Applications in Computer Vision

Projection matrices from projective spaces have long been used in multiple-view geometry to model the perspective projection created by the pin-hole camera. In this work we introduce higher-dimensional mappings for the representation of various applications in which the world we view is no longer rigid. We also describe the multi-view constraints from these new projection matrices (where k > 3) and methods for extracting the (non-rigid) structure and motion for each application.     

Efficient controller synthesis for a fragment of \hbox {MTL}_{0, \infty }

In this paper we offer an efficient controller synthesis algorithm for assume-guarantee specifications of the form $\varphi _1 \wedge \varphi _2 \wedge \cdots \wedge \varphi _n \rightarrow \psi _1 \wedge \psi _2 \wedge \cdots \wedge \psi _m$ . Here, $\{\varphi _i,\psi _j\}$ are all safety-MTL $_{0, \infty }$ properties, where the sub-formulas $\{\varphi _i\}$ are supposed to specify assumptions of the environment and the sub-formulas $\{\psi _j\}$ are specifying requirements to be guaranteed by the controller. Our synthesis method exploits the engine of Uppaal-Tiga and the novel translation of safety- and co-safety-MTL $_{0, \infty }$ properties into under-approximating, deterministic timed automata. Our approach avoids determinization of Büchi automata, which is the main obstacle for the practical applicability of controller synthesis for linear-time specifications. The experiments demonstrate that the chosen specification formalism is expressive enough to specify complex behaviors. The proposed approach is sound but not complete. However, it successfully produced solutions for all the experiments. Additionally we compared our tool with Acacia+ and Unbeast, state-of-the-art LTL synthesis tools; and our tool demonstrated better timing results, when we applied both tools to the analogous specifications.     

Mutually unbiased special entangled bases with Schmidt number 2 in $${\mathbb {C}}^3 \otimes {\mathbb {C}}^{4k}$$

A way of constructing special entangled basis with fixed Schmidt number 2 (SEB2) in \({\mathbb {C}}^3 \otimes {\mathbb {C}}^{4k}(k\in z^+,3\not \mid k)\) is proposed, and the conditions mutually unbiased SEB2s (MUSEB2s) satisfy are discussed. In addition, a very easy way of constructing MUSEB2s in \({\mathbb {C}}^3 \otimes {\mathbb {C}}^{4k}(k=2^l)\) is presented. We first establish the concrete construction of SEB2 and MUSEB2s in \({\mathbb {C}}^3 \otimes {\mathbb {C}}^{4}\) and \({\mathbb {C}}^3 \otimes {\mathbb {C}}^{8}\), respectively, and then generalize them into \({\mathbb {C}}^3 \otimes {\mathbb {C}}^{4k}(k\in z^+,3\not \mid k)\) and display the condition that MUSEB2s satisfy; we also give general form of two MUSEB2s as examples in \({\mathbb {C}}^3 \otimes {\mathbb {C}}^{4k}(k=2^l)\).     

Infimal Convolution Regularisation Functionals of BV and $$\varvec{\mathrm {L}}^{\varvec{p}}$$ Spaces

We study a general class of infimal convolution type regularisation functionals suitable for applications in image processing. These functionals incorporate a combination of the total variation seminorm and \(\mathrm {L}^{p}\) norms. A unified well-posedness analysis is presented and a detailed study of the one-dimensional model is performed, by computing exact solutions for the corresponding denoising problem and the case \(p=2\). Furthermore, the dependency of the regularisation properties of this infimal convolution approach to the choice of p is studied. It turns out that in the case \(p=2\) this regulariser is equivalent to the Huber-type variant of total variation regularisation. We provide numerical examples for image decomposition as well as for image denoising. We show that our model is capable of eliminating the staircasing effect, a well-known disadvantage of total variation regularisation. Moreover as p increases we obtain almost piecewise affine reconstructions, leading also to a better preservation of hat-like structures.     

PRESC ^{2}: efficient self-reconfiguration of cache strategies for elastic caching platforms

Elastic caching platforms (ECPs) play an important role in accelerating the performance of Web applications. Several cache strategies have been proposed for ECPs to manage data access and distributions while maintaining the service availability. In our earlier research, we have demonstrated that there is no “one-fits-all” strategy for heterogeneous scenarios and the selection of the optimal strategy is related with workload patterns, cluster size and the number of concurrent users. In this paper, we present a new reconfiguration framework named PRESC $^{2}$ . It applies machine learning approaches to determine an optimal cache strategy and supports online optimization of performance model through trace-driven simulation or semi-supervised classification. Besides, the authors also propose a robust cache entries synchronization algorithm and a new optimization mechanism to further lower the adaptation costs. In our experiments, we find that PRESC $^{2}$ improves the elasticity of ECPs and brings big performance gains when compared with static configurations.     

Parameterized Complexity of Satisfying Almost All Linear Equations over \mathbb{F}_{2}

The problem MaxLin2 can be stated as follows. We are given a system S of m equations in variables x ₁,…,x _n , where each equation $\sum_{i \in I_{j}}x_{i} = b_{j}$ is assigned a positive integral weight w _j and $b_{j} \in\mathbb{F}_{2}$ , I _j ?{1,2,…,n} for j=1,…,m. We are required to find an assignment of values in $\mathbb{F}_{2}$ to the variables in order to maximize the total weight of the satisfied equations. Let W be the total weight of all equations in S. We consider the following parameterized version of MaxLin2: decide whether there is an assignment satisfying equations of total weight at least W?k, where k is a nonnegative parameter. We prove that this parameterized problem is W[1]-hard even if each equation of S has exactly three variables and every variable appears in exactly three equations and, moreover, each weight w _j equals 1 and no two equations have the same left-hand side. We show the tightness of this result by proving that if each equation has at most two variables then the parameterized problem is fixed-parameter tractable. We also prove that if no variable appears in more than two equations then we can maximize the total weight of satisfied equations in polynomial time.     

A semantically complete extension sequence of the system $$\mathcal{L}^* $$

In this paper, the method of well-combined semantics and syntax proposed by Pavelka is applied to the research of the propositional calculus formal system . The partial constant values are taken as formulas, formulas are fuzzified in two manners of semantics and syntax, and inferring processes are fuzzified. A sequence of new extensions { } of the system is proposed, and the completeness of is proved.     

Phase field computations for surface diffusion and void electromigration in {mathbb{R}^3}

We consider a finite element approximation of a phase field model for the evolution of voids by surface diffusion in an electrically conducting solid. The phase field equations are given by a degenerate Cahn–Hilliard equation with an external forcing induced by the electric field. We describe the iterative scheme used to solve the resulting nonlinear discrete equations and present some numerical experiments in three space dimensions. The first author was supported by the EPSRC grant EP/C548973/1.     

Singular $$\mathcal{H}$$ 2-optimization problems for discrete-time systems

Singular ₂-optimization problems are considered for the standard discrete-time control system. Two types of singularity (type I and type II) are distinguished. A detailed treatment of problems with singularity of type II, which leads to nonuniqueness of solution, is presented. New algorithms for design of optimal controllers are presented both in frequency domain and state space, which generalize standard procedures onto the case of singular ₂-problems. A parameterization of the set of optimal controllers is given.Translated from Avtomatika i Telemekhanika, No. 3, 2005, pp. 20–33.Original Russian Text Copyright © 2005 by Polyakov.This paper was recommended for publication by B.T. Polyak, a member of the Editorial Board