Search results for "REPRESENTATION"

Pseudo-bosons and Riesz Bi-coherent States

2016

After a brief review on D-pseudo-bosons we introduce what we call Riesz bi-coherent states, which are pairs of states sharing with ordinary coherent states most of their features. In particular, they produce a resolution of the identity and they are eigenstates of two different annihilation operators which obey pseudo-bosonic commutation rules.

Commensurability classification of a family of right-angled Coxeter groups

2008

We classify the members of an infinite family of right-angled Coxeter groups up to abstract commensurability.

1986

An osmotic pressure equation proposed over 50 years ago is found to be consistent with the des Cloizeaux scaling relation for semi-dilute polymer solutions in good solvents. With a physically plausible modification, the equation can also give a satisfactory representation of dilute solutions and of the cross-over to the semi-dilute regime.

Multiscale Information Storage of Linear Long-Range Correlated Stochastic Processes

2019

Information storage, reflecting the capability of a dynamical system to keep predictable information during its evolution over time, is a key element of intrinsic distributed computation, useful for the description of the dynamical complexity of several physical and biological processes. Here we introduce a parametric approach which allows one to compute information storage across multiple timescales in stochastic processes displaying both short-term dynamics and long-range correlations (LRC). Our analysis is performed in the popular framework of multiscale entropy, whereby a time series is first "coarse grained" at the chosen timescale through low-pass filtering and downsampling, and then …

Some remarks on unconditionally convergent multipliers

2017

We present some results concerning the representation of unconditionally convergent multipliers, including a reformulation of a conjecture of Balazs and Stoeva.

Generalized twisted cubics on a cubic fourfold as a moduli space of stable objects

2016

We revisit the work of Lehn-Lehn-Sorger-van Straten on twisted cubic curves in a cubic fourfold not containing a plane in terms of moduli spaces. We show that the blow-up $Z'$ along the cubic of the irreducible holomorphic symplectic eightfold $Z$, described by the four authors, is isomorphic to an irreducible component of a moduli space of Gieseker stable torsion sheaves or rank three torsion free sheaves. For a very general such cubic fourfold, we show that $Z$ is isomorphic to a connected component of a moduli space of tilt-stable objects in the derived category and to a moduli space of Bridgeland stable objects in the Kuznetsov component. Moreover, the contraction between $Z'$ and $Z$ i…

Two-view “cylindrical decomposition” of binary images

2001

This paper describes the discrete cylindrical algebraic decomposition (DCAD) construction along two orthogonal views of binary images. The combination of two information is used to avoid ambiguities for image recognition purposes. This algorithm associates an object connectivity graph to each connected component, allowing a complete description of the structuring information. Moreover, an easy and compact representation of the scene is achieved by using strings in a five letter alphabet. Examples on complex digital images are also provided. © 2001 Elsevier Science Inc.

Representing 2D Digital Objects

2000

The paper describes the combination a multi-views approach to represent connected components of 2D binary images. The approach is based on the Object Connectivity Graph (OCG), which is a sub-graph of the connectivity graph generated by the Discrete Cylindrical Algebraic Decomposition(DCAD) performed in the 2D discrete space. This construction allows us to find the number of connected components, to determine their connectivity degree, and to solve visibility problem. We show that the CAD construction, when performed on two orthogonal views, supply information to avoid ambiguities in the interpretation of each image component. The implementation of the algorithm is outlined and the computati…

The self-organizing consciousness

2003

We propose that the isomorphism generally observed between the representations composing our momentary phenomenal experience and the structure of the world is the end-product of a progressive organization that emerges thanks to elementary associative processes that take our conscious representations themselves as the stuff on which they operate, a thesis that we summarize in the concept of Self-Organizing Consciousness (SOC).

The emergence of a shared action ontology: building blocks for a theory.

2003

To have an ontology is to interpret a world. In this paper we argue that the brain, viewed as a representational system aimed at interpreting our world, possesses an ontology too. It creates primitives and makes existence assumptions. It decomposes target space in a way that exhibits a certain invariance, which in turn is functionally significant. We will investigate which are the functional regularities guiding this decomposition process, by answering to the following questions: What are the explicit and implicit assumptions about the structure of reality, which at the same time shape the causal profile of the brain's motor output and its representational deep structure, in particular of t…