A diierential algebraic (DA) formulation of a normal form theory for repetitive systems is presented. Contrary to previous approaches, no Lie algebraic tools are used. The resulting algorithm is very transparent and not restricted to the treatment of symplectic systems. In the case of symplectic systems, the normal form algorithm provides a non-linear coordinate transformation in which the moti...

Di erential privacy is a widely studied theory for analyzing sensitive data with a strong privacy guarantee— any change in an individual’s data can have only a small statistical e ect on the result—and a growing number of programming languages now support di erentially private data analysis. A common shortcoming of these languages is poor support for adaptivity. In practice, a data analyst rare...

The standard analysis of unit nonresponse in sample surveys is to assume missing at random| that is, that the probability a person responds is independent of their response to the question of interest, y, conditional on fully-observed covariates x or on sampling weights w. In this paper, we discuss weakening these assumptions without the use of additional covariates in the special case of a bin...

we give a survey of recent applications of group rings to combinatorics and tocryptography, including their use in the di erential cryptanalysis of block ciphers.

Observers are usually formulated as explicit systems of di erential equations and implemented using standard ODE solvers. In this paper, we show that there can be advantages in formulating the observer as a DAE (Di erential-Algebraic Equation). We review the general idea of DAE observer design of [10]. We give two special normal forms for which DAE observer design yields an observer with linear...

The analytic expression of the time evolution of the Reynolds stress anisotropy tensor in all planar homogeneous ows is obtained by exact integration of the modeled di erential Reynolds stress equations. The procedure is based on results of tensor representation theory, is applicable for general pressure-strain correlation tensors, and can account for any additional turbulence anisotropy e ects...

This paper is devoted to the study of periodic boundary value problems for nonlinear third order di¤erential equations subjected to impulsive e¤ects. We provide su¢ cient conditions on the nonlinearity and the impulse functions that guarantee the existence of at least one solution. Our approach is based on a priori estimates, the method of upper and lower solutions combined with an iterative te...

Stability of stochastic di#erential equations with Markovian switching has recently been discussed by many authors, for example, Basak et al. (J. Math. Anal. Appl. 202 (1996) 604), Ji and Chizeck (IEEE Trans. Automat. Control 35 (1990) 777), Mariton (Jump Linear System in Automatic Control, Marcel Dekker, New York), Mao (Stochastic Process. Appl. 79 (1999) 45), Mao et al. (Bernoulli 6 (2000) 73...

Figure 1 illustrates the interaction between a client and a database server hosting privacysensitive data, e.g., data about people’s health conditions. Di↵erential privacy prevents revealing the identity of an individual by adding noise to the query results, s.t. information about any one particular individual remain hidden. For example, a client won’t be able to tell whether Chris (or any othe...

Detecting and extracting modi cations from information sources is an integral part of data warehousing. For unsophisticated sources, in practice it is often necessary to infer modi cations by periodically comparing snapshots of data from the source. We call this problem the snapshot di erential problem. We show that this is closely related to outerjoins. In this paper we extend the traditional ...