The variational formulation for Lie-transform Hamiltonian perturbation theory is presented in terms of an action functional defined on a two-dimensional parameter space. A fundamental equation in Hamiltonian perturbation theory is shown to result from the freedom of choice of the integration path for the action functional.

The apparent difficulty of finding a solution to a set of multivariate quadratic equations underlies the security of multivariate cryptography and can present an impediment to the successful application of algebraic attacks. Methods for finding such a solution are thus of considerable interest for the purposes of cryptanalysis. Several algebraic techniques for solving systems of multivariate qu...

Verifying that a concurrent program satisfies a given property, such as deadlock-freeness, is computationally difficult. Naive exploration techniques are facing the state space explosion problem: they consider an exponential number of interleavings of parallel threads (relative to the program size). Partial order reduction is a standard method to address this difficulty. It is based on the obse...

We study the estimation error of constrained M -estimators, and derive explicit upper bounds on the expected estimation error determined by the Gaussian width of the constraint set. Both of the cases where the true parameter is on the boundary of the constraint set (matched constraint), and where the true parameter is strictly in the constraint set (mismatched constraint) are considered. For bo...

We recall the basic idea of an algebraic approach to learning Bayesian network (BN) structure, namely to represent every BN structure by a certain (uniquely determined) vector, called standard imset. The main result of the paper is that the set of standard imsets is the set of vertices (= extreme points) of a certain polytope. Motivated by the geometric view, we introduce the concept of the geo...

We present a method for navigating in geometric models and enrich them with additional information. This enables us to adapt geometric models to different purposes and thus to reuse them. We offer dedicated views for the structure and context information as well as for the geometric model, develop strategies to navigate in them and focus on the tight coupling between manipulations in these view...

We are developing a geometric inference system on Internet. A rough geometric figure drawn by a student is transformed into an ideal one that satisfies the assumptions. The system extracts particular patterns in this figure and tries to connect the assumptions and the conclusion. The present paper extends the visualization of the proof by introducing a multiple view which consists of (a) senten...

This paper is largely a review of known results about various aspects of geometric logic. Following Grothendieck’s view of toposes as generalized spaces, one can take geometric morphisms as generalized continuous maps. The constructivist constraints of geometric logic guarantee the continuity of maps constructed, and can do so from two different points of view: for maps as point transformers an...

This paper is largely a review of known results about various aspects of geometric logic. Following Grothendieck’s view of toposes as generalized spaces, one can take geometric morphisms as generalized continuous maps. The constructivist constraints of geometric logic guarantee the continuity of maps constructed, and can do so from two different points of view: for maps as point transformers an...