The Maslov index of a symplectic path, under a certain transversality assumption, is given by an algebraic count of the intersections of the path with a subvariety of the Lagrangian Grassmannian called the Maslov cycle. In these notes we use the notion of generalized signatures at a singularity of a smooth curve of symmetric bilinear forms to determine a formula for the computation of the Maslo...

The Maslov index of a Lagrangian path, under a certain transversality assumption, is given by an algebraic count of the intersections of the path with a subvariety of the Lagrangian Grassmannian called the Maslov cycle. In these notes we use the notion of generalized signatures at a singularity of a smooth curve of symmetric bilinear forms to determine a formula for the computation of the Maslo...

In this paper, we show that the Chapman-Kolmogorov formula could be used as a recursive formula for computing the m-step-ahead conditional density of a Markov bilinear model. The stationary marginal probability density function of the model may be approximated by the m-step-ahead conditional density for sufficiently large m.

We describe an algorithm for learning bilinear SVMs. Bilinear classifiers are a discriminative variant of bilinear models, which capture the dependence of data on multiple factors. Such models are particularly appropriate for visual data that is better represented as a matrix or tensor, rather than a vector. Matrix encodings allow for more natural regularization through rank restriction. For ex...

1. introduction the effect of climate of the earth's surface is the result of interaction of different levels of atmosphere and lithosphere. one of the factors which influences that interaction is the way the system pressure transcends it. in this way, the system pressure changes and can be changed and eventually may become an environmental hazard and geomorphodynamic phenomenon. hazards are an...

In this paper, we focus on model reduction of large-scale bilinear systems. The main contributions are threefold. First, we introduce a new framework for interpolatory model reduction of bilinear systems. In contrast to the existing methods where interpolation is forced on some of the leading subsystem transfer functions, the new framework shows how to enforce multipoint interpolation of the un...

In this paper we will prove several weighted estimates for bilinear fractional integral operators and their commutators with BMO functions. We also prove maximal function control theorem for these operators, that is, we prove the weighted Lp norm is bounded by the weighted Lp norm of a natural maximal operator when the weight belongs to A∞. As a corollary we are able to obtain new weighted esti...

We explore when Hirota bilinear equations possess linear subspaces of solutions. First, we establish a sufficient and necessary criterion for the existence of linear subspaces of exponential traveling wave solutions to Hirota bilinear equations. Second, we show that multivariate polynomials whose zeros form a vector space can generate the desired Hirota bilinear equations with given linear subs...

When excited by an input consisting of a number of discrete levels, a bilinear system becomes a linear time-varying system whose dynamics switches from one linear subsystem to another depending on the input level. This paper describes an identification method that uses the concept of a superstate of a linear switching system as a superstate of the bilinear system. In a superspace method, these ...

A new generalized predictive control algorithm for a kind of input-output bilinear system is proposed in the paper (BGPC). The algorithm combines bilinear and linear terms of I/O bilinear system, and constitutes an ARIMA model analogous to linear systems. Using optimization predictive information fully, the algorithm carries out multi-step predictions by recursive approximation. The heavy compu...