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In this paper, we show that there exists a balanced linear threshold function (LTF) which is unique games hard to approximate, refuting a conjecture of Austrin, Benabbas, and Magen. We also show that the almost monarchy predicate on k…
We present a regularity lemma for Boolean functions $f:\{-1,1\}^n \to \{-1,1\}$ based on noisy influence, a measure of how locally correlated $f$ is with each input bit. We provide an application of the regularity lemma to weaken the…
Linear structural equation models postulate noisy linear relationships between variables of interest. Each model corresponds to a path diagram, which is a mixed graph with directed edges that encode the domains of the linear functions and…
The topic of this manuscript is the stability analysis of continuous-time switched nonlinear systems with constraints on the admissible switching signals. Our particular focus lies in considering signals characterized by upper and lower…
We consider a nonlinear polynomial regression model in which we wish to test the null hypothesis of structural stability in the regression parameters against the alternative of a break at an unknown time. We derive the extreme value…
We present a systematic study of moment evolution in multidimensional stochastic difference systems, focusing on characterizing systems whose low-order moments diverge in the neighborhood of a stable fixed point. We consider systems with a…
This article provides a characterization of stability for switched nonlinear systems under average dwell-time constraints, in terms of necessary and sufficient conditions involving multiple Lyapunov functions. Earlier converse results focus…
We discuss the equilibrium of a single collective variable characterizing a finite set of coupled, noisy, bistable systems as the noise strength, the size and the coupling parameter are varied. We identify distinct regions in parameter…
The issue addressed in this paper is that of testing for common breaks across or within equations of a multivariate system. Our framework is very general and allows integrated regressors and trends as well as stationary regressors. The null…
A nonlinear parabolic differential equation is presented which has at least one equilibrium. This equilibrium is shown to have a negative definite linearization, but a spectrum which includes zero. An elementary construction shows that the…
We study the stability of an equilibrium point in a conservative Hamiltonian system in the case that equilibrium is not a minimum of the potential energy and this fact is shown by a jet of this function. Thanks to a modification of a result…
In this paper, a technique on constructing nonlinear resilient Boolean functions is described. By using several sets of disjoint spectra functions on a small number of variables, an almost optimal resilient function on a large even number…
We address the stability problem for linear switching systems with mode-dependent restrictions on the switching intervals. Their lengths can be bounded as from below (the guaranteed dwell-time) as from above. The upper bounds make this…
The principle of linearized stability and instability is established for a classical model describing the spatial movement of an age-structured population with nonlinear vital rates. It is shown that the real parts of the eigenvalues of the…
We survey the design of elections that are resilient to attempted interference by third parties. For example, suppose votes have been cast in an election between two candidates, and then each vote is randomly changed with a small…
Estimation of structure, such as in variable selection, graphical modelling or cluster analysis is notoriously difficult, especially for high-dimensional data. We introduce stability selection. It is based on subsampling in combination with…
This report investigates the dynamical stability conjectures of Palis and Smale, and Pugh and Shub from the standpoint of numerical observation and lays the foundation for a stability conjecture. As the dimension of a dissipative dynamical…
We consider the design of a linear sensing system with a fixed energy budget assuming that the sampling noise is the dominant noise source. The energy constraint implies that the signal energy per measurement decreases linearly with the…
Recently, many regularized procedures have been proposed for variable selection in linear regression, but their performance depends on the tuning parameter selection. Here a criterion for the tuning parameter selection is proposed, which…
In this note we study the numerical stability problem that may take place when calculating the cumulative distribution function of the {\it Hypoexponential} random variable. This computation is extensively used during the execution of Monte…