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

Recently, an infinite class of holographic generalized complexities was proposed. These gravitational observables display the behavior required to be duals of complexity, in particular, linear growth at late times and switchback effect. In…

Current theories of perception suggest that the brain represents features of the world as probability distributions, but can such uncertain foundations provide the basis for everyday vision? Perceiving objects and scenes requires knowing…

Problems in optimization and geometric probability are discussed, all connected with angles subtended at an observer's eye by an object at a distance. Several of these remain unsolved.

A final-state observability result in the Banach space setting for non-autonomous observation problems is obtained that covers and extends all previously known results in this context, while providing a streamlined proof that follows the…

Capabilities and the number of vision-based models are increasing rapidly. And these vision models are now able to do more tasks like object detection, image classification, instance segmentation etc. with great accuracy. But models which…

A (M4 x M4) x Z4 model, describing an extended particle composed of two local modes and represented by a field psi(x, xi ;z), is formulated in its most general form (x, xi ; z) belong to (M4 x M4) x Z4. The 'z' argument specifies whether…

A dominant paradigm in visual intelligence treats semantics as a static property of latent representations, assuming that meaning can be discovered through geometric proximity in high dimensional embedding spaces. In this work, we argue…

The existence of a positive solution for a class of asymptotically lin- ear problems in exterior domains is established via a linking argument on the Nehari manifold and by means of a barycenter function.

We address the observability problem for ensembles that are described by probability distributions. The problem is to reconstruct a probability distribution of the initial state from the time-evolution of the probability distribution of the…

In this paper, we consider a model of classical linear logic based on coherence spaces endowed with a notion of totality. If we restrict ourselves to total objects, each coherence space can be regarded as a uniform space and each linear map…

Infinite-dimensional control systems with outputs are considered in the Hamiltonian formulation with generalized coordinates. An explicit scheme for constructing a dynamic observer for this class of systems is proposed with arbitrary gain…

Physical theories must stem from observation. The possibility that perceived events are simulated, not real, raises a crucial dilemma about the credibility of known physics, known as the simulation hypothesis. To analyze this hypothesis in…

A simple visual representation of Minkowski spacetime appropriate for a student with a background in geometry and algebra is presented. Minkowski spacetime can be modeled with a Euclidean 4-space to yield accurate visualizations as…

Shapes do not define a linear space. This paper explores the linear structure of deformations as a representation of shapes. This transforms shape optimization to a variant of optimal control. The numerical challenges of this point of view…

A study is made of 4-dimensional Lorentz manifolds which are projectively related, that is, whose Levi-Civita connections give rise to the same (unparameterised) geodesics. A brief review of some relevant recent work is provided and a list…

Surprisingly, the issue of events localization in spacetime is poorly understood and a fortiori realized even in the context of Einstein's relativity. Accordingly, a comparison between observational data and theoretical expectations might…

We study state estimation for nonlinear differential-algebraic systems, where the nonlinearity satisfies a Lipschitz condition or a generalized monotonicity condition or a combination of these. The presented observer design unifies earlier…

Introductory state-space linear control courses focus on linear, time-invariant systems and spend intense efforts by introducing system realizations that allow the student to grasp fundamental concepts, among which controllability,…

The concept of {\em complexity} (as a quantity) has been plagued by numerous contradictory and confusing definitions. By explicitly recognising a role for the observer of a system, an observer that attaches meaning to data about the system,…

Nonlinear dimensionality reduction methods provide a valuable means to visualize and interpret high-dimensional data. However, many popular methods can fail dramatically, even on simple two-dimensional manifolds, due to problems such as…