Information-Preserving Markov Aggregation

We present a sufficient condition for a non-injective function of a Markov chain to be a second-order Markov chain with the same entropy rate as the original chain. This permits an information-preserving state space reduction by merging states or, equivalently, lossless compression of a Markov source on a sample-by-sample basis. The cardinality of the reduced state space is bounded from below by the node degrees of the transition graph associated with the original Markov chain. We also present an algorithm listing all possible information-preserving state space reductions, for a given transition graph. We illustrate our results by applying the algorithm to a bi-gram letter model of an English text.Comment: 7 pages, 3 figures, 2 table

K1K_1-groups via binary complexes of fixed length

We modify Grayson's model of $K_1$ of an exact category to give a presentation whose generators are binary acyclic complexes of length at most $k$ for any given $k \ge 2$. As a corollary, we obtain another, very short proof of the identification of Nenashev's and Grayson's presentations.Comment: 10 pages, minor changes following a referee report, to appear in HH

Atomistic-to-continuum coupling approximation of a one-dimensional toy model for density functional theory

We consider an atomistic model defined through an interaction field satisfying a variational principle and which can therefore be considered a toy model of (orbital-free) density functional theory. We investigate atomistic-to-continuum coupling mechanisms for this atomistic model, paying special attention to the dependence of the atomistic subproblem on the atomistic region boundary and the boundary conditions. We rigorously prove first-order error estimates for two related coupling mechanisms

Optimal Lower Bounds for Projective List Update Algorithms

The list update problem is a classical online problem, with an optimal competitive ratio that is still open, known to be somewhere between 1.5 and 1.6. An algorithm with competitive ratio 1.6, the smallest known to date, is COMB, a randomized combination of BIT and the TIMESTAMP algorithm TS. This and almost all other list update algorithms, like MTF, are projective in the sense that they can be defined by looking only at any pair of list items at a time. Projectivity (also known as "list factoring") simplifies both the description of the algorithm and its analysis, and so far seems to be the only way to define a good online algorithm for lists of arbitrary length. In this paper we characterize all projective list update algorithms and show that their competitive ratio is never smaller than 1.6 in the partial cost model. Therefore, COMB is a best possible projective algorithm in this model.Comment: Version 3 same as version 2, but date in LaTeX \today macro replaced by March 8, 201

The impact of managerial ownership, monitoring and accounting standard choice on accrual mispricing

We analyse to what extent the accrual anomaly is related to the choice of the accounting system as well as firm-level heterogeneity in corporate governance mechanisms. Using a unique dataset of listed German firms over the period 1995 to 2005 we first corroborate former results indicating that the accrual anomaly is also present in Germany. However, this anomaly seems to be driven mainly by firms with managerial ownership. In a second step, we test how different corporate governance mechanisms affect the anomaly. For the German experiment on voluntary adoption of IFRS our results confirm previous findings that the anomaly is less likely to be present under a conservative accounting system. While creditor monitoring is able to reduce the accrual anomaly, shareholder monitoring is not. Apart from offering evidence related to the cross-sectional difference in the degree of accrual mispricing, our results give also some insights related to the cross-country variation of this phenomenon. --Accrual Anomaly,Earnings Quality,Corporate Governance,Managerial Ownership,Capital Market Efficiency,Accounting Standard,Shareholder Monitoring,Creditor Monitoring