1,959 research outputs found
Simulation of a Channel with Another Channel
In this paper, we study the problem of simulating a DMC channel from another
DMC channel under an average-case and an exact model. We present several
achievability and infeasibility results, with tight characterizations in
special cases. In particular for the exact model, we fully characterize when a
BSC channel can be simulated from a BEC channel when there is no shared
randomness. We also provide infeasibility and achievability results for
simulation of a binary channel from another binary channel in the case of no
shared randomness. To do this, we use properties of R\'enyi capacity of a given
order. We also introduce a notion of "channel diameter" which is shown to be
additive and satisfy a data processing inequality.Comment: 31 pages, 10 figures, and some parts of this work were published at
ITW 201
Dynamic problems for metamaterials: Review of existing models and ideas for further research
Metamaterials are materials especially engineered to have a peculiar physical behaviour, to be exploited for some well-specified technological application. In this context we focus on the conception of general micro-structured continua, with particular attention to piezoelectromechanical structures, having a strong coupling between macroscopic motion and some internal degrees of freedom, which may be electric or, more generally, related to some micro-motion. An interesting class of problems in this context regards the design of wave-guides aimed to control wave propagation. The description of the state of the art is followed by some hints addressed to describe some possible research developments and in particular to design optimal design techniques for bone reconstruction or systems which may block wave propagation in some frequency ranges, in both linear and non-linear fields. (C) 2014 Elsevier Ltd. All rights reserved
Formal Methods for Autonomous Systems
Formal methods refer to rigorous, mathematical approaches to system
development and have played a key role in establishing the correctness of
safety-critical systems. The main building blocks of formal methods are models
and specifications, which are analogous to behaviors and requirements in system
design and give us the means to verify and synthesize system behaviors with
formal guarantees.
This monograph provides a survey of the current state of the art on
applications of formal methods in the autonomous systems domain. We consider
correct-by-construction synthesis under various formulations, including closed
systems, reactive, and probabilistic settings. Beyond synthesizing systems in
known environments, we address the concept of uncertainty and bound the
behavior of systems that employ learning using formal methods. Further, we
examine the synthesis of systems with monitoring, a mitigation technique for
ensuring that once a system deviates from expected behavior, it knows a way of
returning to normalcy. We also show how to overcome some limitations of formal
methods themselves with learning. We conclude with future directions for formal
methods in reinforcement learning, uncertainty, privacy, explainability of
formal methods, and regulation and certification
Gradient and Passive Circuit Structure in a Class of Non-linear Dynamics on a Graph
We consider a class of non-linear dynamics on a graph that contains and
generalizes various models from network systems and control and study
convergence to uniform agreement states using gradient methods. In particular,
under the assumption of detailed balance, we provide a method to formulate the
governing ODE system in gradient descent form of sum-separable energy
functions, which thus represent a class of Lyapunov functions; this class
coincides with Csisz\'{a}r's information divergences. Our approach bases on a
transformation of the original problem to a mass-preserving transport problem
and it reflects a little-noticed general structure result for passive network
synthesis obtained by B.D.O. Anderson and P.J. Moylan in 1975. The proposed
gradient formulation extends known gradient results in dynamical systems
obtained recently by M. Erbar and J. Maas in the context of porous medium
equations. Furthermore, we exhibit a novel relationship between inhomogeneous
Markov chains and passive non-linear circuits through gradient systems, and
show that passivity of resistor elements is equivalent to strict convexity of
sum-separable stored energy. Eventually, we discuss our results at the
intersection of Markov chains and network systems under sinusoidal coupling
A rationale for the payback criterion
Textbooks on financial management have emphasized the shortcomings of the payback criterion for decades. However, empirical evidence suggests that in actual capital budgeting procedures the payback method is used quite regularly. Mostly, it is implemented supplementary to net present value or internal rate of return, but small companies tend to rely on payback times as single criterion. A convincing theoretical foundation for the observed use of the payback criterion is lacking. Consequently, our goal is to provide such an explanation for the payback criterionâs popularity. We demonstrate from a decision theoretical perspective how relying on payback times simplifies investment decisions in modern organizations. Gathering information from different management levels and ensuring the utilization of individual skills requires a multi-stage capital budgeting process. Accordingly, we consider fundamental organizational features of this process with respect to their impact on the payback methodâs use. For this purpose, we built upon almost stochastic dominance (ASD) as modeling device. Firstly, we show that applying his concept allows to include the risk preferences of all relevant decision makers into the analysis. Secondly, we illustrate that the criteria derived from this model help conveying these preferences to those who do the preparatory work preceding the final decision. To some extent, these new criteria are generalizations of payback times. This finding provides a potential explanation for the paybackâs persisting prominence.
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