Driving variable realizations and the non-negative realization problem for controllable behaviours

Non-negative linear systems, traditionally investigated within the state-space framework, have been recently analysed within the behavioural setting. In a couple of recent papers [J. W. Nieuwenhuis, “When to call a linear system nonnegative”, Linear Algebra & its Appl., 281, 1998 Nieuwenhuis, JW. 1998. “When to call a linear system non-negative”. Linear Algebra & its Appl., 281: pp. 43–58 , pp. 43–58.; M. E. Valcher, “Nonnegative linear systems in the behavioural approach: the autonomous case”, Linear Algebra and its Appl., 2000 Valcher, ME. 2000. “Nonnegative linear systems in the behavioural approach: the autonomous case”. Linear Algebra and its Appl., 319: pp. 147–162 , 319, pp. 147–162.], several definitions and results about non-negative behaviours (and, in particular, about non-negative autonomous behaviours) have been derived. Moreover, the non-negative realization problem for autonomous behaviours has been fully explored in [M. E. Valcher, “Non-negative realization of autonomous systems in the behavioral approach”, SIAM J. on Control and Opt., 2001 Valcher, ME. 2001. “Nonnegative realization of autonomous systems in the behavioural approach”. SIAM J. on Control and Opt., 40: pp. 540–556 , 40, pp. 540–556.], thus deriving an extended set of necessary and sufficient conditions for an autonomous behaviour to admit a non-negative realization. Here, we focus our attention on the non-negative realization problem for controllable behaviours. To this end, we first address the general realization problem by means of a driving variable (DV) state-space representation, and investigate under what conditions a state-space model provides a DV realization of a controllable behaviour. Based on these results, we analyse the possibility of realizing a controllable behaviour by means of a non-negative DV representation and, in particular, a reachable non-negative DV realization. Moreover, necessary and sufficient conditions for a behaviour to be the controllable part of a (complete) behaviour endowed with a non-negative realization are presented.     

Are mobile phone conversations always so annoying? The ‘need-to-listen’ effect re-visited

According to Monk et al. (2004a Monk, A.F., et al., 2004a. Why are mobile phones annoying? Behaviour & Information Technology, 23 (1), 33–42. doi: 10.1080/01449290310001638496[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]. Why are mobile phones annoying? Behaviour and Information Technology, 23 (1), 33–42), mobile phone conversations are annoying to overhear due to an involuntary need-to-listen in order to predict the inaudible half of the conversation. However, previous support for this need-to-listen explanation of annoyance has failed to consider the confound that mobile phone conversations also have less predictable acoustic patterns and has only investigated ‘neutral’ conversations. By staging mobile and face-to-face conversations in public, this study further supports the need-to-listen explanation. By removing the need-to-listen to the content of a mobile conversation through introducing foreign speech, bystanders no longer perceived the conversation as more annoying than a conversation between two co-present individuals, supporting the need-to-listen explanation over unpredictable acoustics. In two further experiments manipulating conversational content (‘neutral’ vs. ‘intriguing’), findings suggest that the need-to-listen to mobile phone conversations is not inherently annoying; it can be annoying or possibly even ‘interesting’ depending on the conversational content.     

Reasoning with Qualitative Positional Information for Domestic Domains in the Situation Calculus

In this paper, we present a thorough integration of qualitative representations and reasoning for positional information for domestic service robotics domains into our high-level robot control. In domestic settings for service robots like in the RoboCup@Home competitions, complex tasks such as “get the cup from the kitchen and bring it to the living room” or “find me this and that object in the apartment” have to be accomplished. At these competitions the robots may only be instructed by natural language. As humans use qualitative concepts such as “near” or “far”, the robot needs to cope with them, too. For our domestic robot, we use the robot programming and plan language Readylog, our variant of Golog. In previous work we extended the action language Golog, which was developed for the high-level control of agents and robots, with fuzzy set-based qualitative concepts. We now extend our framework to positional fuzzy fluents with an associated positional context called frames. With that and our underlying reasoning mechanism we can transform qualitative positional information from one context to another to account for changes in context such as the point of view or the scale. We demonstrate how qualitative positional fluents based on a fuzzy set semantics can be deployed in domestic domains and showcase how reasoning with these qualitative notions can seamlessly be applied to a fetch-and-carry task in a RoboCup@Home scenario.     

Ecosystem on the Web: non-linear mining and forecasting of co-evolving online activities

Given a large collection of co-evolving online activities, such as searches for the keywords “Xbox”, “PlayStation” and “Wii”, how can we find patterns and rules? Are these keywords related? If so, are they competing against each other? Can we forecast the volume of user activity for the coming month? We conjecture that online activities compete for user attention in the same way that species in an ecosystem compete for food. We present EcoWeb, (i.e., Ecosystem on the Web), which is an intuitive model designed as a non-linear dynamical system for mining large-scale co-evolving online activities. Our second contribution is a novel, parameter-free, and scalable fitting algorithm, EcoWeb-Fit, that estimates the parameters of EcoWeb. Extensive experiments on real data show that EcoWeb is effective, in that it can capture long-range dynamics and meaningful patterns such as seasonalities, and practical, in that it can provide accurate long-range forecasts. EcoWeb consistently outperforms existing methods in terms of both accuracy and execution speed.     

The Informational Nature of Personal Identity

In this paper, I present an informational approach to the nature of personal identity. In “Plato and the problem of the chariot”, I use Plato’s famous metaphor of the chariot to introduce a specific problem regarding the nature of the self as an informational multiagent system: what keeps the self together as a whole and coherent unity? In “Egology and its two branches” and “Egology as synchronic individualisation”, I outline two branches of the theory of the self: one concerning the individualisation of the self as an entity, the other concerning the identification of such entity. I argue that both presuppose an informational approach, defend the view that the individualisation of the self is logically prior to its identification, and suggest that such individualisation can be provided in informational terms. Hence, in “A reconciling hypothesis: the three membranes model”, I offer an informational individualisation of the self, based on a tripartite model, which can help to solve the problem of the chariot. Once this model of the self is outlined, in “ICTs as technologies of the self” I use it to show how ICTs may be interpreted as technologies of the self. In “The logic of realisation”, I introduce the concept of “realization” (Aristotle’s anagnorisis) and support the rather Spinozian view according to which, from the perspective of informational structural realism, selves are the final stage in the development of informational structures. The final “Conclusion: from the egology to the ecology of the self” briefly concludes the article with a reference to the purposeful shaping of the self, in a shift from egology to ecology.     

An approach to the DIN Kernel Lisp definition

A DIN Kernel LISP Draft (DKLisp) has been developed by DIN as Reaction to Action D1 (N79), short term goal, of ISO WG16. It defines a subset language, as compatible as possible with the ANSICommon-Lisp draft, but also with theEuLisp draft. It combines the most important LISP main stream features in a single, compact, but nevertheless complete language definition, which thereby could be well suited as basis for a short term InternationalLisp Standard. Besides the functional and knowledge processing features, the expressive power of the language is well comparable with contemporary procedural languages, as e.g. C++ (of course without libraries). Important features ofDKLisp are:

to be a “Lisp-1,” but allowing an easy “Lisp-2” transformation;

to be a simple, powerful and standardized educationalLisp;

to omit all features, which are unclean or in heavy discussion;

DKLisp programs run nearly unchanged inCommon-Lisp;

DKLisp contains a simple object and package system;

DKLisp contains those data classes and control structures also common to most modernLisp and non-Lisp languages;

DKLisp offers a simple stream I/O;

DKLisp contains a clean unified hierarchical class/type system;

DKLisp contains the typical “Lisp-features” in an orthogonal way;

DKLisp allows and encourages really small but powerful implementations;

DKLisp comes in levels, so allowing ANSICommon-Lisp to be an extension ofDKLisp level-1.

The present is the second version of the proposal, namely version 1.2, with slight differences with respect to the one sent to ISO. Sources of such changes were the remarks generously sent by many readers of the previous attempt.     

Deterministic function computation with chemical reaction networks

Chemical reaction networks (CRNs) formally model chemistry in a well-mixed solution. CRNs are widely used to describe information processing occurring in natural cellular regulatory networks, and with upcoming advances in synthetic biology, CRNs are a promising language for the design of artificial molecular control circuitry. Nonetheless, despite the widespread use of CRNs in the natural sciences, the range of computational behaviors exhibited by CRNs is not well understood. CRNs have been shown to be efficiently Turing-universal (i.e., able to simulate arbitrary algorithms) when allowing for a small probability of error. CRNs that are guaranteed to converge on a correct answer, on the other hand, have been shown to decide only the semilinear predicates (a multi-dimensional generalization of “eventually periodic” sets). We introduce the notion of function, rather than predicate, computation by representing the output of a function \({f:{\mathbb{N}}^k\to{\mathbb{N}}^l}\) by a count of some molecular species, i.e., if the CRN starts with \(x_1,\ldots,x_k\) molecules of some “input” species \(X_1,\ldots,X_k, \) the CRN is guaranteed to converge to having \(f(x_1,\ldots,x_k)\) molecules of the “output” species \(Y_1,\ldots,Y_l\) . We show that a function \({f:{\mathbb{N}}^k \to {\mathbb{N}}^l}\) is deterministically computed by a CRN if and only if its graph \({\{({\bf x, y}) \in {\mathbb{N}}^k \times {\mathbb{N}}^l | f({\bf x}) = {\bf y}\}}\) is a semilinear set. Finally, we show that each semilinear function f (a function whose graph is a semilinear set) can be computed by a CRN on input x in expected time \(O(\hbox{polylog} \|{\bf x}\|_1)\) .     

Zone analysis: a visualization framework for classification problems

There have been large attempts to adopt the bias-variance framework from the regression problems to the classification problems. However, recently, it has been shown that only non-straightforward extensions exist for classification problems. In this paper, we present an alternative visualization framework for classification problems called zone analysis. Our zone analysis framework partly extends the bias-variance idea; instead of decomposing an error into two parts, i.e. the biased and unbiased components, our framework decomposes the error into K components. While bias-variance information is still contained in our framework, our framework provides interesting observations which are not obviously seen in the previous bias-variance framework, e.g. a prejudice behavior of the bagging algorithm to various unbiased instances. Our framework is suitable for visualizing an effect of context changes on learning performance. The type of context changes which we primarily investigate in the paper is “a change from a base learner to an ensemble learner such as bagging, adaboost, arc-x4 and multi-boosting”.     

An Empirical Evaluation of the System Usability Scale

This article presents nearly 10 year's worth of System Usability Scale (SUS) data collected on numerous products in all phases of the development lifecycle. The SUS, developed by Brooke (1996) Brooke, J. 1996. “SUS: A “quick and dirty” usability scale”. In Usability evaluation in industry, Edited by: Jordan, P. W., Thomas, B. A. Weerdmeester and McClelland, I. L. 189–194. London: Taylor & Francis.  [Google Scholar], reflected a strong need in the usability community for a tool that could quickly and easily collect a user's subjective rating of a product's usability. The data in this study indicate that the SUS fulfills that need. Results from the analysis of this large number of SUS scores show that the SUS is a highly robust and versatile tool for usability professionals. The article presents these results and discusses their implications, describes nontraditional uses of the SUS, explains a proposed modification to the SUS to provide an adjective rating that correlates with a given score, and provides details of what constitutes an acceptable SUS score.     

On the relation among answer set solvers

In this paper, we study the relation among Answer Set Programming (ASP) systems from a computational point of view. We consider smodels, dlv, and cmodels ASP systems based on stable model semantics, the first two being native ASP systems and the last being a SAT-based system. We first show that smodels, dlv, and cmodels explore search trees with the same branching nodes (assuming, of course, a same branching heuristic) on the class of tight logic programs. Leveraging on the fact that SAT-based systems rely on the deeply studied Davis–Logemann–Loveland (dll) algorithm, we derive new complexity results for the ASP procedures. We also show that on nontight programs the SAT-based systems are computationally different from native procedures, and the latter have computational advantages. Moreover, we show that native procedures can guarantee the “correctness” of a reported solution when reaching the leaves of the search trees (i.e., no stability check is needed), while this is not the case for SAT-based procedures on nontight programs. A similar advantage holds for dlv in comparison with smodels if the “well-founded” operator is disabled and only Fitting’s operator is used for negative inferences. We finally study the “cost” of achieving such advantages and comment on to what extent the results presented extend to other systems.     

The Nonconvergence of h-Refinement in Prolate Elements

Prolate elements are a “plug-compatible” modification of spectral elements in which Legendre polynomials are replaced by prolate spheroidal wave functions of order zero. Prolate functions contain a“bandwidth parameter” $c \ge 0 $ c ≥ 0 whose value is crucial to numerical performance; the prolate functions reduce to Legendre polynomials for $c\,=\,0$ c = 0 . We show that the optimal bandwidth parameter $c$ c not only depends on the number of prolate modes per element $N$ N , but also on the element widths $h$ h . We prove that prolate elements lack $h$ h -convergence for fixed $c$ c in the sense that the error does not go to zero as the element size $h$ h is made smaller and smaller. Furthermore, the theoretical predictions that Chebyshev and Legendre polynomials require $\pi $ π degrees of freedom per wavelength to resolve sinusoidal functions while prolate series need only 2 degrees of freedom per wavelength are asymptotic limits as $N \rightarrow \infty $ N → ∞ ; we investigate the rather different behavior when $N \sim O(4-10)$ N ～ O ( 4 ? 10 ) as appropriate for spectral elements and prolate elements. On the other hand, our investigations show that there are certain combinations of $N,\,h$ N , h and $c>0$ c > 0 where a prolate basis clearly outperforms the Legendre polynomial approximation.     

Master Lovas–Andai and equivalent formulas verifying the $$\frac{8}{33}$$ two-qubit Hilbert–Schmidt separability probability and companion rational-valued conjectures

We begin by investigating relationships between two forms of Hilbert–Schmidt two-rebit and two-qubit “separability functions”—those recently advanced by Lovas and Andai (J Phys A Math Theor 50(29):295303, 2017), and those earlier presented by Slater (J Phys A 40(47):14279, 2007). In the Lovas–Andai framework, the independent variable \(\varepsilon \in [0,1]\) is the ratio \(\sigma (V)\) of the singular values of the \(2 \times 2\) matrix \(V=D_2^{1/2} D_1^{-1/2}\) formed from the two \(2 \times 2\) diagonal blocks (\(D_1, D_2\)) of a \(4 \times 4\) density matrix \(D= \left||\rho _{ij}\right||\). In the Slater setting, the independent variable \(\mu \) is the diagonal-entry ratio \(\sqrt{\frac{\rho _{11} \rho _ {44}}{\rho _ {22} \rho _ {33}}}\)—with, of central importance, \(\mu =\varepsilon \) or \(\mu =\frac{1}{\varepsilon }\) when both \(D_1\) and \(D_2\) are themselves diagonal. Lovas and Andai established that their two-rebit “separability function” \(\tilde{\chi }_1 (\varepsilon )\) (\(\approx \varepsilon \)) yields the previously conjectured Hilbert–Schmidt separability probability of \(\frac{29}{64}\). We are able, in the Slater framework (using cylindrical algebraic decompositions [CAD] to enforce positivity constraints), to reproduce this result. Further, we newly find its two-qubit, two-quater[nionic]-bit and “two-octo[nionic]-bit” counterparts, \(\tilde{\chi _2}(\varepsilon ) =\frac{1}{3} \varepsilon ^2 \left( 4-\varepsilon ^2\right) \), \(\tilde{\chi _4}(\varepsilon ) =\frac{1}{35} \varepsilon ^4 \left( 15 \varepsilon ^4-64 \varepsilon ^2+84\right) \) and \(\tilde{\chi _8} (\varepsilon )= \frac{1}{1287}\varepsilon ^8 \left( 1155 \varepsilon ^8-7680 \varepsilon ^6+20160 \varepsilon ^4-25088 \varepsilon ^2+12740\right) \). These immediately lead to predictions of Hilbert–Schmidt separability/PPT-probabilities of \(\frac{8}{33}\), \(\frac{26}{323}\) and \(\frac{44482}{4091349}\), in full agreement with those of the “concise formula” (Slater in J Phys A 46:445302, 2013), and, additionally, of a “specialized induced measure” formula. Then, we find a Lovas–Andai “master formula,” \(\tilde{\chi _d}(\varepsilon )= \frac{\varepsilon ^d \Gamma (d+1)^3 \, _3\tilde{F}_2\left( -\frac{d}{2},\frac{d}{2},d;\frac{d}{2}+1,\frac{3 d}{2}+1;\varepsilon ^2\right) }{\Gamma \left( \frac{d}{2}+1\right) ^2}\), encompassing both even and odd values of d. Remarkably, we are able to obtain the \(\tilde{\chi _d}(\varepsilon )\) formulas, \(d=1,2,4\), applicable to full (9-, 15-, 27-) dimensional sets of density matrices, by analyzing (6-, 9, 15-) dimensional sets, with not only diagonal \(D_1\) and \(D_2\), but also an additional pair of nullified entries. Nullification of a further pair still leads to X-matrices, for which a distinctly different, simple Dyson-index phenomenon is noted. C. Koutschan, then, using his HolonomicFunctions program, develops an order-4 recurrence satisfied by the predictions of the several formulas, establishing their equivalence. A two-qubit separability probability of \(1-\frac{256}{27 \pi ^2}\) is obtained based on the operator monotone function \(\sqrt{x}\), with the use of \(\tilde{\chi _2}(\varepsilon )\).     

Generalising Unit-Refutation Completeness and SLUR via Nested Input Resolution

The class ${\mathcal{SLUR}}$ (Single Lookahead Unit Resolution) was introduced in Schlipf et al. (Inf Process Lett 54:133–137, 1995) as an umbrella class for efficient (poly-time) SAT solving, with linear-time SAT decision, while the recognition problem was not considered. ?epek et al. (2012) and Balyo et al. (2012) extended this class in various ways to hierarchies covering all of CNF (all clause-sets). We introduce a hierarchy ${\mathcal{SLUR}}_k$ which we argue is the natural “limit” of such approaches. The second source for our investigations is the class ${\mathcal{UC}}$ of unit-refutation complete clause-sets, introduced in del Val (1994) as a target class for knowledge compilation. Via the theory of “hardness” of clause-sets as developed in Kullmann (1999), Kullmann (Ann Math Artif Intell 40(3–4):303–352, 2004) and Ansótegui et al. (2008) we obtain a natural generalisation ${\mathcal{UC}}_k$ , containing those clause-sets which are “unit-refutation complete of level k”, which is the same as having hardness at most k. Utilising the strong connections to (tree-)resolution complexity and (nested) input resolution, we develop basic methods for the determination of hardness (the level k in ${\mathcal{UC}}_k$ ). A fundamental insight now is that ${\mathcal{SLUR}}_k = {\mathcal{UC}}_k$ holds for all k. We can thus exploit both streams of intuitions and methods for the investigations of these hierarchies. As an application we can easily show that the hierarchies from ?epek et al. (2012) and Balyo et al. (2012) are strongly subsumed by ${\mathcal{SLUR}}_k$ . Finally we consider the problem of “irredundant” clause-sets in ${\mathcal{UC}}_k$ . For 2-CNF we show that strong minimisations are possible in polynomial time, while already for (very special) Horn clause-sets minimisation is NP-complete. We conclude with an extensive discussion of open problems and future directions. We envisage the concepts investigated here to be the starting point for a theory of good SAT translations, which brings together the good SAT-solving aspects from ${\mathcal{SLUR}}$ together with the knowledge-representation aspects from ${\mathcal{UC}}$ , and expands this combination via notions of “hardness”.     

A Logic for Reasoning About Knowledge of Unawareness

In the most popular logics combining knowledge and awareness, it is not possible to express statements about knowledge of unawareness such as “Ann knows that Bill is aware of something Ann is not aware of”—without using a stronger statement such as “Ann knows that Bill is aware of \(p\) and Ann is not aware of \(p\) ”, for some particular \(p\) . In Halpern and Rêgo (Proceedings of KR 2006; Games Econ Behav 67(2):503–525, 2009b) Halpern and Rêgo introduced a logic in which such statements about knowledge of unawareness can be expressed. The logic extends the traditional framework with quantification over formulae, and is thus very expressive. As a consequence, it is not decidable. In this paper we introduce a decidable logic which can be used to reason about certain types of unawareness. Our logic extends the traditional framework with an operator expressing full awareness, i.e., the fact that an agent is aware of everything, and another operator expressing relative awareness, the fact that one agent is aware of everything another agent is aware of. The logic is less expressive than Halpern’s and Rêgo’s logic. It is, however, expressive enough to express all of the motivating examples in Halpern and Rêgo (Proceedings of KR 2006; Games Econ Behav 67(2):503–525, 2009b). In addition to proving that the logic is decidable and that its satisfiability problem is PSPACE-complete, we present an axiomatisation which we show is sound and complete.     

The Trouble with Common Ground

Tenenberg, Roth and Socha (2016) documents interaction within a paired programming task. The analysis rests on a conceptualization the authors term “We-awareness.” “We-awareness”, in turn, builds on Tomasello’s notion of “shared intentionality” and through it, upon Clark’s formulation of Common Ground (CG). In this commentary I review the features of CG. I attempt to show that neither Tomasello’s (2014) notion of “shared intentionality” nor Clark’s (1996) model of CG-shared develop an adequate treatment of the sequential emergence of subjective meaning. This is a critical problem for CG and other conceptualizations that build upon it (e.g., “shared intentionality”, “We-awareness”). And it calls into question their usefulness for building an analytic apparatus for studying mutual awareness at the worksite. I suggest that Schütz’s (1953) model of “motive coordination” might serve as a better starting place.     

Valuation of R&D Investment Opportunities with the Threat of Competitors Entry in Real Option Analysis

This paper provides a real option methodology in order to value a pioneer’s R&D investment opportunity allowing for more potential competitors to enter in the market. To incorporate this competitive dimension, we assume that the pioneer may lose the “competitive dividends”   if the real option is not exercised. According to Majd and pindyck (1987) (Journal of Financial Economics 18(1):7–27), in a real options context, “dividends”   are the opportunity costs inherent in the decision to defer an investment project and so deferment implies the loss of project’s cash flows. Concerning this, Trigeorgis (1996) (Real Options: Managerial Flexibility and Strategy in Resource Allocation, The MIT Press, Cambridge, (1996) incorporates the preemption effect through the “competitive dividends”  which are the cash flows that can be eroded by anticipated competitive arrivals. In particular way, we propose the valuation of a pioneer’s R&D investment assuming that the Development cost can be spent in two moments: $t_2$ or $t_3$ . If the Development cost is realized in $t_2$ no firms enters in the market since the rivals’ R&D plan is not yet concluded otherwise, if the Development cost is delayed until time $t_3$ waiting better market conditions, other rivals may enter in the market and so the opportunity costs, namely dividends, increase. Moreover, we analyze the optimal timing to realize the Development investment, i.e. we determine the conditions for which the pioneer prefers to invest the Development cost at time $t_2$ or $t_3$ .     

CIPHER EQUIPMENT

Abstract

In this article, a simplified version of the International Data Encryption Algorithm (IDEA) is described. This simplified version, like simplified versions of DES [8-12 Schaefer , E. 1996 . “A Simplified Data Encryption Standard Algorithm,” Cryptologia , 20 ( 1 ): 77 – 84 . Schneier , B. 1996 . Applied Cryptography, , 2nd ed . Wiley , New York , NY . Schneier , B. 1999. Crypto Guru Bruce Schneier Answers. http://slashdot.org/interviews/99/10/29/0832246.shtml last accessed February 23, 2007. Shannon , C. “Communications Theory of Secrecy Systems,” Oct. 1949 . Bell Systems Technical Journal , 28 ( 4 ): 656 – 715 . Trappe , W. and L. Washington . 2006 . Introduction to Cryptography with Coding Theory, , 2nd ed. Prentice Hall , Upper Saddle River , NJ . ] and AES [6 Musa , M. , E. Shaefer , and S. Wedig . 2003 . “A Simplified AES Algorithm and its Linear and Differential Cryptanalysis,” Cryptologia , 17 ( 2 ): 148 – 177 . [Google Scholar] 7 Phan , R. 2002 . “Mini Advanced Encryption Standard (Mini-AES): A Testbed for Cryptanalysis Students,” Cryptologia , 26 ( 4 ): 283 – 306 .[Taylor &; Francis Online] , [Google Scholar]] that have appeared in print, is intended to help students understand the algorithm by providing a version that permits examples to be worked by hand. IDEA is useful teaching tool to help students bridge the gap between DES and AES.     

Local Discontinuous Galerkin Methods for One-Dimensional Second Order Fully Nonlinear Elliptic and Parabolic Equations

This paper is concerned with developing accurate and efficient nonstandard discontinuous Galerkin methods for fully nonlinear second order elliptic and parabolic partial differential equations (PDEs) in the case of one spatial dimension. The primary goal of the paper to develop a general framework for constructing high order local discontinuous Galerkin (LDG) methods for approximating viscosity solutions of these fully nonlinear PDEs which are merely continuous functions by definition. In order to capture discontinuities of the first order derivative $u_x$ of the solution $u$ , two independent functions $q^-$ and $q^+$ are introduced to approximate one-sided derivatives of $u$ . Similarly, to capture the discontinuities of the second order derivative $u_{xx}$ , four independent functions $p^{- -}, p^{- +}, p^{+ -}$ , and $p^{+ +}$ are used to approximate one-sided derivatives of $q^-$ and $q^+$ . The proposed LDG framework, which is based on a nonstandard mixed formulation of the underlying PDE, embeds a given fully nonlinear problem into a mostly linear system of equations where the given nonlinear differential operator must be replaced by a numerical operator which allows multiple value inputs of the first and second order derivatives $u_x$ and $u_{xx}$ . An easy to verify set of criteria for constructing “good” numerical operators is also proposed. It consists of consistency and generalized monotonicity. To ensure such a generalized monotonicity property, the crux of the construction is to introduce the numerical moment in the numerical operator, which plays a critical role in the proposed LDG framework. The generalized monotonicity gives the LDG methods the ability to select the viscosity solution among all possible solutions. The proposed framework extends a companion finite difference framework developed by Feng and Lewis (J Comp Appl Math 254:81–98, 2013) and allows for the approximation of fully nonlinear PDEs using high order polynomials and non-uniform meshes. Numerical experiments are also presented to demonstrate the accuracy, efficiency and utility of the proposed LDG methods.     

A general notion of global asymptotic controllability for time-varying systems and its Lyapunov characterization

A general notion of global asymptotic controllability to a given equilibrium of a time-varying system is introduced and is shown that this property is equivalent to the existence of a lower semicontinuous control Lyapunov function. The work constitutes an extension of Albertini and Sontag (1999 Albertini, F and Sontag, ED. 1999. “Continuous control-Lyapunov functions for asymptotic controllable time varying systems”. Int. J. of Control, 72: pp. 1630–1641 ) paper in same journal dealing with same subject under stricter hypotheses.     

Water film washers and mixers: their rotational modes and electro-hydrodynamical flows induced by square-wave electric fields

Our study indicates suspended water films, driven by crossed square-wave electric fields, may act as “washers”, “centrifuges” and “mixers”. Based on our recent model successfully describing experimentally observed electro-hydrodynamical flows in water films, we derive conditions for generating specific rotational flows. Our main findings, which are advantageous for microfluidic devices and basic research, are as follows: (1) the film’s rotational patterns depend on the phase difference $\Updelta\varphi$ and frequencies f of the applied fields. (2) For $\Updelta\varphi=\pi/2$ and $f\sim10^{-1}-10^{0}$  Hz, the film exhibits symmetrical reciprocating rotations, i.e. it constitutes a washer. (3) For $\Updelta\varphi=0$ and any f, it exhibits an ordinary anticlockwise (or clockwise) rotation, i.e. it constitutes a centrifuge or motor. (4) For $\Updelta\varphi$ with other values and f below 1 Hz, it exhibits asymmetrical reciprocating rotations, it constitutes an asymmetrical mixer.