Feedback affinization of nonlinear control systems

In this paper conditions for the nonlinear control system

to have a nonlinear feedback control

u=(x,v), vΩ′R^m′, m′m, 0Ω′

such that the nonlinear system takes a form of an affine system

are presented. All results require algebraic operations and differentiation of functions only.     

Simple adaptive stabilization of high-gain stabilizable systems

It is shown that the simple adaptive feedback strategy

Full-size image

is a universal adaptive stabilizer for the class of single-input, single-output, finite-dimensional, linear systems which are stabilizable by either negative or positive high-gain feedback.     

On the impact of size to the understanding of UML diagrams

Background

Practical experience suggests that usage and understanding of UML diagrams is greatly affected by the quality of their layout. While existing research failed to provide conclusive and comprehensive evidence in support of this hypothesis, our own previous work provided substantial evidence to this effect, also suggesting diagram size as a relevant factor, for a range of diagram types and layouts.

Aims

Since there is no generally accepted precise notion of “diagram size,” we first need to operationalize this concept, analyze its impact on diagram understanding, and derive practical advice from our findings.

Method

We define three alternative, plausible metrics. Since they are all highly correlated on a large sample of UML diagrams, we opt for the simplest one. We use it to re-analyze existing experimental data on diagram understanding.

Results

We find a strong negative correlation between diagram size and modeler performance. Our results are statistically highly significant and exhibit a very large degree of validity. We utilize these results to derive a recommendation on diagram sizes that are, on average, optimal for model understanding. These recommendations are implemented in a plug-in to a widely used modeling tool, providing continuous feedback about diagram size to modelers.

Conclusions

The effect sizes are varying, but generally suggest that the impact of size matches or exceeds that of other factors in diagram understanding. With the guideline and tool, modelers are steered toward avoiding too large diagrams.

     

Explaining Computation Without Semantics: Keeping it Simple

This paper deals with the question: how is computation best individuated?

1. 1.
   The semantic view of computation: computation is best individuated by its semantic properties.
    
2. 2.
   The causal view of computation: computation is best individuated by its causal properties.
    
3. 3.
   The functional view of computation: computation is best individuated by its functional properties.
    

Some scientific theories explain the capacities of brains by appealing to computations that they supposedly perform. The reason for that is usually that computation is individuated semantically. I criticize the reasons in support of this view and its presupposition of representation and semantics. Furthermore, I argue that the only justified appeal to a representational individuation of computation might be that it is partly individuated by implicit intrinsic representations.

     

Global stability for separable nonlinear delay differential equations

Consider the following separable nonlinear delay differential equation

, where we assume that, there is a strictly monotone increasing function f(x) on (−∞, +∞) such that

In this paper, to the above separable nonlinear delay differential equation, we establish conditions of global asymptotic stability for the zero solution. In particular, for a special wide class of f(x) which contains a case of f(x) = e^x−1, we give more explicit conditions. Applying these, we offer conditions of global asymptotic stability for solutions of nonautonomous logistic equations with delays.     

Miniversal deformations of linear systems under the full group action

We consider the equivalence relation in the space of time-invariant linear dynamical systems of the form

under the full group action of state feedback/output injection transformations. As in the case of the reduction of a matrix to its Jordan canonical form, the reduction of a quadruple (A,B,C,D) defining a system as above to its canonical reduced form is an unstable operation. Following V.I. Arnold’s techniques, the starting point for the study of local perturbations is to obtain a miniversal deformation of a differentiable family of quadruples. In this paper, a “real” miniversal deformation and some applications are shown.     

Supporting the notion of context within a database environment for intelligent reporting and query optimisation

Information used for decision-making is often semi-quantitative, rather than quantitative in nature. For example, knowing that a student received the top mark in an examination may be more useful than knowing the precise mark achieved; similarly, to be given the information that a company has low market penetration in a given census district might be more important than to be given a numerical value derived from (say) sales divided by average take home pay. The purpose of this paper is to examine how database semantics can be enhanced to provide support for the interpretation of raw data, in order that the significance of the data can be understood. The significance of a reported result is usually dependent on its context, that is, the domain in which it appears, so it is clear that the notion of context must be supported. This paper describes extensions to the object-oriented model which involve equipping it with the means to handle contextual knowledge relating to the patterns of data values, and the means to perform analyses on the data held within the system. We hope to make good use of these extensions in two ways.

1. i)
   As data is retrieved from the database it can be placed in context, that is, some measure of the significance of reported values can be given.
    
2. ii)
   This new knowledge can be used as a guide to query optimisation, since it allows the optimiser to determine, with greater accuracy, the expected size of the intermediate stages when performing a search operation.
    

This paper concentrates on the rules necessary for the reporting of significance information, along with a control strategy for firing the rules, and a mechanism for the inheritance of significance data.     

Oscillations and nonoscillations of half-linear difference equations generated by deviating arguments

For the half-linear difference equation

where α > 0, we shall offer sufficient conditions for the oscillation of all solutions, as well as necessary and sufficient conditions for the existence of both bounded and unbounded nonoscillatory solutions. Several examples which dwell upon the importance of our results are also included.     

Unprovable Security of Perfect NIZK and Non-interactive Non-malleable Commitments

We present barriers to provable security of two important cryptographic primitives, perfect non-interactive zero knowledge (NIZK) and non-interactive non-alleable commitments:

1. ○
   Black-box reductions cannot be used to demonstrate adaptive soundness (i.e., that soundness holds even if the statement to be proven is chosen as a function of the common reference string) of any statistical NIZK for NP based on any “standard” intractability assumptions.
    
2. ○
   Black-box reductions cannot be used to demonstrate non-malleability of non-interactive, or even 2-message, commitment schemes based on any “standard” intractability assumptions.
    

We emphasize that the above separations apply even if the construction of the considered primitives makes a non-black-box use of the underlying assumption.

As an independent contribution, we suggest a taxonomy of game-based intractability assumptions.     

Tau method treatment of a delayed negative feedback equation

The step-by-step Tau method is applied to find polynomial approximations to the solution of the nonlinear functional equation,

, which arises in population dynamics. The behavior of the approximate solutions is consistent with the theoretical results obtained elsewhere.     

The Complexity of König Subgraph Problems and Above-Guarantee Vertex Cover

A graph is König-Egerváry if the size of a minimum vertex cover equals that of a maximum matching in the graph. These graphs have been studied extensively from a graph-theoretic point of view. In this paper, we introduce and study the algorithmic complexity of finding König-Egerváry subgraphs of a given graph. In particular, given a graph G and a nonnegative integer k, we are interested in the following questions:

1. 1.
   does there exist a set of k vertices (edges) whose deletion makes the graph König-Egerváry?
    
2. 2.
   does there exist a set of k vertices (edges) that induce a König-Egerváry subgraph?
    

We show that these problems are NP-complete and study their complexity from the points of view of approximation and parameterized complexity. Towards this end, we first study the algorithmic complexity of Above Guarantee Vertex Cover, where one is interested in minimizing the additional number of vertices needed beyond the maximum matching size for the vertex cover. Further, while studying the parameterized complexity of the problem of deleting k vertices to obtain a König-Egerváry graph, we show a number of interesting structural results on matchings and vertex covers which could be useful in other contexts.