A comparison of methods for DPLL loop filter design

Four design methodologies for loop filters for a class of digital phase-locked loops (DPLLs) are presented. The first design maps an optimum analog filter into the digital domain; the second approach designs a filter that minimizes in discrete time weighted combination of the variance of the phase error due to noise and the sum square of the deterministic phase error component; the third method uses Kalman filter estimation theory to design a filter composed of a least squares fading memory estimator and a predictor. The last design relies on classical theory, including rules for the design of compensators. Linear analysis is used throughout the article to compare different designs, and includes stability, steady state performance and transient behavior of the loops. Design methodology is not critical when the loop update rate can be made high relative to loop bandwidth, as the performance approaches that of continuous time. For low update rates, however, the miminization method is significantly superior to the other methods

Effect of the Output of the System in Signal Detection

We analyze the consequences that the choice of the output of the system has in the efficiency of signal detection. It is shown that the signal and the signal-to-noise ratio (SNR), used to characterize the phenomenon of stochastic resonance, strongly depend on the form of the output. In particular, the SNR may be enhanced for an adequate output.Comment: 4 pages, RevTex, 6 PostScript figure

ASMs and Operational Algorithmic Completeness of Lambda Calculus

We show that lambda calculus is a computation model which can step by step simulate any sequential deterministic algorithm for any computable function over integers or words or any datatype. More formally, given an algorithm above a family of computable functions (taken as primitive tools, i.e., kind of oracle functions for the algorithm), for every constant K big enough, each computation step of the algorithm can be simulated by exactly K successive reductions in a natural extension of lambda calculus with constants for functions in the above considered family. The proof is based on a fixed point technique in lambda calculus and on Gurevich sequential Thesis which allows to identify sequential deterministic algorithms with Abstract State Machines. This extends to algorithms for partial computable functions in such a way that finite computations ending with exceptions are associated to finite reductions leading to terms with a particular very simple feature.Comment: 37 page

The ethical challenge of Touraine's 'living together'

In Can We Live Together? Alain Touraine combines a consummate analysis of crucial social tensions in contemporary societies with a strong normative appeal for a new emancipatory 'Subject' capable of overcoming the twin threats of atomisation or authoritarianism. He calls for a move from 'politics to ethics' and then from ethics back to politics to enable the new Subject to make a reality out of the goals of democracy and solidarity. However, he has little to say about the nature of such an ethics. This article argues that this lacuna could usefully be filled by adopting a form of radical humanism found in the work of Erich Fromm. It defies convention in the social sciences by operating from an explicit view of the 'is' and the 'ought' of common human nature, specifying reason, love and productive work as the qualities to be realised if we are to move closer to human solidarity. Although there remain significant philosophical and political differences between the two positions, particularly on the role to be played by 'the nation', their juxtaposition opens new lines of inquiry in the field of cosmopolitan ethics

Strategies used as spectroscopy of financial markets reveal new stylized facts

We propose a new set of stylized facts quantifying the structure of financial markets. The key idea is to study the combined structure of both investment strategies and prices in order to open a qualitatively new level of understanding of financial and economic markets. We study the detailed order flow on the Shenzhen Stock Exchange of China for the whole year of 2003. This enormous dataset allows us to compare (i) a closed national market (A-shares) with an international market (B-shares), (ii) individuals and institutions and (iii) real investors to random strategies with respect to timing that share otherwise all other characteristics. We find that more trading results in smaller net return due to trading frictions. We unveiled quantitative power laws with non-trivial exponents, that quantify the deterioration of performance with frequency and with holding period of the strategies used by investors. Random strategies are found to perform much better than real ones, both for winners and losers. Surprising large arbitrage opportunities exist, especially when using zero-intelligence strategies. This is a diagnostic of possible inefficiencies of these financial markets.Comment: 13 pages including 5 figures and 1 tabl

Dependency Tree Automata

Abstract. We introduce a new kind of tree automaton, a dependency tree automaton, that is suitable for deciding properties of classes of terms with binding. Two kinds of such automaton are defined, nondeterministic and alternating. We show that the nondeterministic automata have a decidable nonemptiness problem and leave as an open question whether this is true for the alternating version. The families of trees that both kinds recognise are closed under intersection and union. To illustrate the utility of the automata, we apply them to terms of simply typed lambda calculus and provide an automata-theoretic characterisation of solutions to the higher-order matching problem

Intuitionistic implication makes model checking hard

We investigate the complexity of the model checking problem for intuitionistic and modal propositional logics over transitive Kripke models. More specific, we consider intuitionistic logic IPC, basic propositional logic BPL, formal propositional logic FPL, and Jankov's logic KC. We show that the model checking problem is P-complete for the implicational fragments of all these intuitionistic logics. For BPL and FPL we reach P-hardness even on the implicational fragment with only one variable. The same hardness results are obtained for the strictly implicational fragments of their modal companions. Moreover, we investigate whether formulas with less variables and additional connectives make model checking easier. Whereas for variable free formulas outside of the implicational fragment, FPL model checking is shown to be in LOGCFL, the problem remains P-complete for BPL.Comment: 29 pages, 10 figure