相关论文: A linear solution to the effective four-dimensiona…

We consider the optimization of an uncertain objective over continuous and multi-dimensional decision spaces in problems in which we are only provided with observational data. We propose a novel algorithmic framework that is tractable,…

The aim of this note is to present a construction of symplectic structures on orientable globally hyperbolic 4-dimensional lorentzian manifolds. Said structures are defined on the manifold itself, not on its cotangent bundle. It also…

Nonlinear observer design for systems whose state space evolves on Lie groups is considered. The proposed method is similar to previously developed nonlinear observers in that it involves propagating the state estimate using a process model…

The notion of multidimensional quadrilateral lattice is introduced. It is shown that such a lattice is characterized by a system of integrable discrete nonlinear equations. Different useful formulations of the system are given. The…

A simply structured distributed observer is described for estimating the state of a discrete-time, jointly observable, input-free, linear system whose sensed outputs are distributed across a time-varying network. It is explained how to…

We consider the problem of distributed state estimation of a linear time-invariant (LTI) system by a network of sensors. We develop a distributed observer that guarantees asymptotic reconstruction of the state for the most general class of…

It is shown that every scalar linear quadrilateral lattice equation lies within a family of similar equations, members of which are compatible between one another on a higher dimensional lattice. There turn out to be two such families, a…

Empirical understanding teaches us that space is three dimensional while relativity merges space with time. We tried to show that it is possible to model space as three complex coordinates. In our construction, the usual spatial coordinate…

We introduce a method of solving inverse boundary value problems for wave equations on Lorentzian manifolds, and show that zeroth order coefficients can be recovered under certain curvature bounds. The set of Lorentzian metrics satisfying…

In this short note we argue that, even if, as sometimes remarked, a Lorentzian manifold does not model correctly the structure of the spatio-temporal continuum as it is, yet a Lorentzian manifold should describe its macroscopic structure as…

The paper studies a class of quadratic optimal control problems for partially observable linear dynamical systems. In contrast to the full information case, the control is required to be adapted to the filtration generated by the…

Linear-nonlinear transforms are interesting in vision science because they are key in modeling a number of perceptual experiences such as color, motion or spatial texture. Here we first show that a number of issues in vision may be…

In this brief note I argue that putting conscious observers at the center of the considerations clarifies and strengthens the many-worlds interpretation. The basic assumption, which seems extremely plausible based on our current…

We investigate geometric properties of indecomposable but non-irreducible Lorentzian manifolds, which are total spaces of circle bundles. We investigate under which conditions these manifolds are complete and give examples which fulfill the…

For many-particle systems defined on lattices we investigate the global structure of effective Hamiltonians and observables obtained by means of a suitable basis transformation. We study transformations which lead to effective Hamiltonians…

The quantum algebra of observables of the massive closed bosonic string in 1+3 dimensions has been developed so far in the rest frame of the string. In this paper a method to write this algebra in a manifestly Lorentz covariant form is…

We study the problem of diagonalization of the metric of 3-dimensional Lorentzian manifold. Applying the technique of moving frames, we prove that every smooth Lorentzian 3-manifold admits an atlas in which the metric assumes a diagonal…

A variational principle is applied to 4D Euclidean space provided with a tensor refractive index, defining what can be seen as 4-dimensional optics (4DO). The geometry of such space is analysed, making no physical assumptions of any kind.…

Many navigation problems can be formulated as observer design on linear observed systems with a two-frame group structure, on which an invariant filter can be implemented with guaranteed consistency and stability. It's still unclear how…

The classification of 4-dimensional naturally reductive pseudo-Riemannian spaces is given. This classification comprises symmetric spaces, the product of 3-dimensional naturally reductive spaces with the real line and new families of…