Related papers: A note on the state-space realizations equivalence
The goal of this paper is to clarify when a stochastic partial differential equation with an affine realization admits affine state processes. This includes a characterization of the set of initial points of the realization. Several…
A phase space mathematical formulation of quantum mechanical processes accompanied by and ontological interpretation is presented in an axiomatic form. The problem of quantum measurement, including that of quantum state filtering, is…
Two possible realizations of the formal neuron are considered as quantum system. The first type complies with classical system. The second type vastly increases the possible problems.
A prevalent problem in general state space models is the approximation of the smoothing distribution of a state conditional on the observations from the past, the present, and the future. The aim of this paper is to provide a rigorous…
Shedding a new light in the coarse-graining scenario, in this contribution we came up with different necessary and sufficient conditions for the existence of a well-defined coarse-grained state. For doing so, we had to break apart with the…
In this paper, we consider formal series associated with events, profiles derived from events, and statistical models that make predictions about events. We prove theorems about realizations for these formal series using the language and…
This note comprises a synthesis of certain results in the theory of exact interpolation between Hilbert spaces. In particular, we examine various characterizations of interpolation spaces and their relations to a number of results in…
The purpose of this note is to give a number of open problems on matching theory and their relation to the well-known results in this area. We also give a linear analogue of the acyclic matchings.
In this paper we introduce a natural model for the realization space of a polytope up to projective equivalence which we call the slack realization space of the polytope. The model arises from the positive part of an algebraic variety…
By parametrizing input and state trajectories with basis functions different approximations to the constrained linear quadratic regulator problem are obtained. These notes present and discuss technical results that are intended to…
A new characterization of conformal transformations is given. By use of this, the general form of conformal transformation on two-dimensional Minkowski space is given and its conformal structure is analyzed.
The invariant subspace problem is solved correcting my earlier attempts [6]-[12].
Both constrained and unconstrained optimization problems regularly appear in recursive tracking problems engineers currently address -- however, constraints are rarely exploited for these applications. We define the Kalman Filter and…
Coherence distillation is one of the central problems in the resource theory of coherence. In this Letter, we complete the deterministic distillation of quantum coherence for a finite number of coherent states under strictly incoherent…
In this short note, we try to provide the reader with a brief pedagogical account of some similarities and differences between stochastic and deterministic processes. A short presentation of some basic notions related to the mathematical…
A new understanding of the notion of regularizer is proposed. It is argued that this new notion is more realistic than the old one and better fits the practical computational needs. An example of the regularizer in the new sense is given. A…
We define two versions of compositions of matrix-valued rational functions of appropriate sizes and whenever analytic at infinity, offer a set of formulas for the corresponding state-space realization, in terms of the realizations of the…
Tabular reinforcement learning methods cannot operate directly on continuous state spaces. One solution for this problem is to partition the state space. A good partitioning enables generalization during learning and more efficient…
We propose a model theoretic interpretation of the theorems about the equivalence between mixed characteristic perfectoid spaces and their tilts.
A standard approach to approximate inference in state-space models isto apply a particle filter, e.g., the Condensation Algorithm.However, the performance of particle filters often varies significantlydue to their stochastic nature.We…