Coalgebraic Semantics for Timed Processes

We give a coalgebraic formulation of timed processes and their operational semantics. We model time by a monoid called a “time domain”, and we model processes by “timed transition systems”, which amount to partial monoid actions of the time domain or, equivalently, coalgebras for an “evolution comonad ” generated by the time domain. All our examples of time domains satisfy a partial closure property, yielding a distributive law of a monad for total monoid actions over the evolution comonad, and hence a distributive law of the evolution comonad over a dual comonad for total monoid actions. We show that the induced coalgebras are exactly timed transition systems with delay operators. We then integrate our coalgebraic formulation of time qua timed transition systems into Turi and Plotkin’s formulation of structural operational semantics in terms of distributive laws. We combine timing with action via the more general study of the combination of two arbitrary sorts of behaviour whose operational semantics may interact. We give a modular account of the operational semantics for a combination induced by that of each of its components. Our study necessitates the investigation of products of comonads. In particular, we characterise when a monad lifts to the category of coalgebras for a product comonad, providing constructions with which one can readily calculate. Key words: time domains, timed transition systems, evolution comonads, delay operators, structural operational semantics, modularity, distributive laws

On the intersection conjecture for infinite trees of matroids

Using a new technique, we prove a rich family of special cases of the matroid intersection conjecture. Roughly, we prove the conjecture for pairs of tame matroids which have a common decomposition by 2-separations into finite parts

Lipschitz and uniformly continuous reducibilities on ultrametric Polish spaces

We analyze the reducibilities induced by, respectively, uniformly continuous, Lipschitz, and nonexpansive functions on arbitrary ultrametric Polish spaces, and determine whether under suitable set-theoretical assumptions the induced degree-structures are well-behaved.Comment: 37 pages, 2 figures, revised version, accepted for publication in the Festschrift that will be published on the occasion of Victor Selivanov's 60th birthday by Ontos-Verlag. A mistake has been corrected in Section

Regularity of Pure Strategy Equilibrium Points in a Class of Bargaining Games

For a class of n-player (n ? 2) sequential bargaining games with probabilistic recognition and general agreement rules, we characterize pure strategy Stationary Subgame Perfect (PSSP) equilibria via a finite number of equalities and inequalities. We use this characterization and the degree theory of Shannon, 1994, to show that when utility over agreements has negative definite second (contingent) derivative, there is a finite number of PSSP equilibrium points for almost all discount factors. If in addition the space of agreements is one-dimensional, the theorem applies for all SSP equilibria. And for oligarchic voting rules (which include unanimity) with agreement spaces of arbitrary finite dimension, the number of SSP equilibria is odd and the equilibrium correspondence is lower-hemicontinuous for almost all discount factors. Finally, we provide a sufficient condition for uniqueness of SSP equilibrium in oligarchic games.Local Uniqueness of Equilibrium, Regularity, Sequential Bargaining.

Bayesian analysis of DSGE models

This paper reviews Bayesian methods that have been developed in recent years to estimate and evaluate dynamic stochastic general equilibrium (DSGE) models. We consider the estimation of linearized DSGE models, the evaluation of models based on Bayesian model checking, posterior odds comparisons, and comparisons to vector autoregressions, as well as the nonlinear estimation based on a second-order accurate model solution. These methods are applied to data generated from correctly specified and misspecified linearized DSGE models, and a DSGE model that was solved with a second-order perturbation method.Macroeconomics ; Vector autoregression

Subspaces with equal closure

We take a unifying and new approach toward polynomial and trigonometric approximation in an arbitrary number of variables, resulting in a precise and general ready-to-use tool that anyone can easily apply in new situations of interest. The key idea is to show, in considerable generality, that a module, which is generated over the polynomials or trigonometric functions by some set, necessarily has the same closure as the module which is generated by this same set, but now over the compactly supported smooth functions. The particular properties of the ambient space or generating set are to a large degree irrelevant. This translation -- which goes in fact beyond modules -- allows us, by what is now essentially a straightforward check of a few properties, to replace many classical results by more general and stronger statements of a hitherto unknown type. As a side result, we also obtain a new integral criterion for multidimensional measures to be determinate. At the technical level, we use quasi-analytic classes in several variables and we show that two well-known families of one-dimensional weights are essentially equal. The method can be formulated for Lie groups and this interpretation shows that many classical approximation theorems are "actually" theorems on the unitary dual of n-dimensional real space. Polynomials then correspond to the universal enveloping algebra.Comment: 61 pages, LaTeX 2e, no figures. Second and final version, with minor changes in presentation. Mathematically identical to the first version. Accepted by Constructive Approximatio

Monetary Policy, Determinacy, and the Natural Rate Hypothesis

Imposing the natural rate hypothesis (NRH) can dramatically alter the determinacy bounds on monetary policy by closing the output gap in the long run. I show that the hypothesis eliminates any role for the output gap in determinacy and renders the conditions for determinacy identical for all conforming supply equations. Specializing further to IS demand, determinacy depends only on the parameters in the interest rate rule and a pure forward or backward-looking inflation target is inconsistent with determinacy. Monetary policy that embodies the Taylor principle with respect to contemporaneous inflation delivers a determinate equilibrium in all models that satisfy the NRH.Time Series,Natural rate hypothesis; Phillips curve; Taylor Principle

Pointwise adaptive estimation for quantile regression

A nonparametric procedure for quantile regression, or more generally nonparametric M-estimation, is proposed which is completely data-driven and adapts locally to the regularity of the regression function. This is achieved by considering in each point M-estimators over different local neighbourhoods and by a local model selection procedure based on sequential testing. Non-asymptotic risk bounds are obtained, which yield rate-optimality for large sample asymptotics under weak conditions. Simulations for different univariate median regression models show good finite sample properties, also in comparison to traditional methods. The approach is the basis for denoising CT scans in cancer research.M-estimation, median regression, robust estimation, local model selection, unsupervised learning, local bandwidth selection, median filter, Lepski procedure, minimax rate, image denoising