Related papers: Mnesors for automatic control
Stators, which may be intuitively defined as "half states, half operators" are mathematical objects which act on two Hilbert spaces and utilize entanglement to create remote operations and exchange information between two physical systems.…
Reverse order law for the Moore-Penrose inverses of tensors are useful in the field of multilinear algebra. In this paper, we first prove some more identities involving the Moore-Penrose inverse of tensors. We then obtain a few necessary…
A new notion of controllability, eigenstate controllability, is defined for finite-dimensional bilinear quantum mechanical systems which are neither strongly completely controllably nor completely controllable. And a quantum control…
An MV-module is an MV-algebra endowed with a scalar multiplication with scalars in a PMV-algebra (i.e. an MV-algebra endowed with a binary "ring-like" product). We investigate the class of semisimple MV-modules over a semisimple and totally…
Cognitive map learners (CML) have been shown to enable hierarchical, compositional machine learning. That is, interpedently trained CML modules can be arbitrarily composed together to solve more complex problems without task-specific…
Based upon properties of ordinal length, we introduce a new class of modules, the binary modules, and study their endomorphism ring. The nilpotent endomorphisms form a two-sided ideal, and after factoring this out, we get a commutative…
Robots are often built from standardized assemblies, (e.g. arms, legs, or fingers), but each robot must be trained from scratch to control all the actuators of all the parts together. In this paper we demonstrate a new approach that takes a…
In machine learning, the use of an artificial neural network is the mainstream approach. Such a network consists of layers of neurons. These neurons are of the same type characterized by the two features: (1) an inner product of an input…
A blender is a closed convex cone of real homogeneous polynomials that is also closed under linear changes of variable. Non-trivial blenders only occur in even degree. Examples include the cones of psd forms, sos forms, convex forms and…
We study natural differential operators transforming two tensor fields into a tensor field. First, it is proved that all bilinear operators are of order one, and then we give the full classification of such operators in several concrete…
Tensors, or multi-linear forms, are important objects in a variety of areas from analytics, to combinatorics, to computational complexity theory. Notions of tensor rank aim to quantify the "complexity" of these forms, and are thus also…
Computational effects are commonly modelled by monads, but often a monad can be presented by an algebraic theory of operations and equations. This talk is about monads and algebraic theories for languages for inference, and their…
Integrating the heterogeneous controllers of a complex mechanical system, such as a mobile manipulator, within the same structure and in a modular way is still challenging. In this work we extend our framework based on Behavior Trees for…
The moment operators of a semispectral measure having the structure of the convolution of a positive measure and a semispectral measure are studied, with paying attention to the natural domains of these unbounded operators. The results are…
Multisorted modules, equivalently representations of quivers, equivalently additive functors on preadditive categories, encompass a wide variety of additive structures. In addition, every module has a natural and useful multisorted…
This paper discusses a logical operation of multi-memories that consist of coupled nonlinear micro-electro-mechanical systems (MEMS) resonators. A MEMS resonator shows two coexisting stable states when nonlinear responses appear. Previous…
The physical resources available to access and manipulate the degrees of freedom of a quantum system define the set $\cal A$ of operationally relevant observables. The algebraic structure of $\cal A$ selects a preferred tensor product…
It is known that finite crossed modules provide premodular tensor categories. These categories are in fact modularizable. We construct the modularization and show that it is equivalent to the module category of a finite Drinfeld double.
In past few decades, tensor algebra also known as multi-linear algebra has been developed and customized as a tool to be used for various engineering applications. In particular, with the help of a special form of tensor contracted product,…
This is a study of universal problems for semimodules, in particular coequalizers, coproducts, and tensor products. Furthermore the structure theory of semiideals of the semiring of natural numbers is extended.