Search results for "Subspace topology"
showing 10 items of 73 documents
Communication: multireference equation of motion coupled cluster: a transform and diagonalize approach to electronic structure.
2014
The novel multireference equation-of-motion coupled-cluster (MREOM-CC) approaches provide versatile and accurate access to a large number of electronic states. The methods proceed by a sequence of many-body similarity transformations and a subsequent diagonalization of the transformed Hamiltonian over a compact subspace. The transformed Hamiltonian is a connected entity and preserves spin- and spatial symmetry properties of the original Hamiltonian, but is no longer Hermitean. The final diagonalization spaces are defined in terms of a complete active space (CAS) and limited excitations (1h, 1p, 2h, …) out of the CAS. The methods are invariant to rotations of orbitals within their respective…
Reducing the observation error in a WSN through a consensus-based subspace projection
2013
An essential process in a Wireless Sensor Network is the noise mitigation of the measured data, by exploiting their spatial correlation. A widely used technique to achieve this reduction is to project the measured data into a proper subspace. We present a low complexity and distributed algorithm to perform this projection. Unlike other algorithms existing in the literature, which require the number of connections at every node to be larger than the dimension of the involved subspace, our algorithm does not require such dense network topologies for its applicability, making it suitable for a larger number of scenarios. Our proposed algorithm is based on the execution of several consensus pro…
Variations of selective separability II: Discrete sets and the influence of convergence and maximality
2012
A space $X$ is called selectively separable(R-separable) if for every sequence of dense subspaces $(D_n : n\in\omega)$ one can pick finite (respectively, one-point) subsets $F_n\subset D_n$ such that $\bigcup_{n\in\omega}F_n$ is dense in $X$. These properties are much stronger than separability, but are equivalent to it in the presence of certain convergence properties. For example, we show that every Hausdorff separable radial space is R-separable and note that neither separable sequential nor separable Whyburn spaces have to be selectively separable. A space is called \emph{d-separable} if it has a dense $\sigma$-discrete subspace. We call a space $X$ D-separable if for every sequence of …
Distributed Pseudo-Gossip Algorithm and Finite-Length Computational Codes for Efficient In-Network Subspace Projection
2013
In this paper, we design a practical power-efficient algorithm for Wireless Sensor Networks (WSN) in order to obtain, in a distributed manner, the projection of an observed sampled spatial field on a subspace of lower dimension. This is an important problem that is motivated in various applications where there are well defined subspaces of interest (e.g., spectral maps in cognitive radios). As opposed to traditional Gossip Algorithms used for subspace projection, where separation of channel coding and computation is assumed, our algorithm combines binary finite-length Computational Coding and a novel gossip-like protocol with certain communication rules, achieving important savings in conve…
Baer cones in finite projective spaces
1987
Let R and V be two skew subspaces with dimensions r and v of P=PG(d,q). If q is a square, then there is a Baer subspace V* of V, i.e. a subspace of dimension v and order √q. We call the set C(R,V*)=\(\mathop \cup \limits_p \), where the union is taken over all PeV*, aBaer cone oftype (r,v).
Blocking sets and partial spreads in finite projective spaces
1980
A t-blocking set in the finite projective space PG(d, q) with d≥t+1 is a set $$\mathfrak{B}$$ of points such that any (d−t)-dimensional subspace is incident with a point of $$\mathfrak{B}$$ and no t-dimensional subspace is contained in $$\mathfrak{B}$$ . It is shown that | $$\mathfrak{B}$$ |≥q t +...+1+q t−1√q and the examples of minimal cardinality are characterized. Using this result it is possible to prove upper and lower bounds for the cardinality of partial t-spreads in PG(d, q). Finally, examples of blocking sets and maximal partial spreads are given.
Packing dimensions of sections of sets
1999
We obtain a formula for the essential supremum of the packing dimensions of the sections of sets parallel to a given subspace. This depends on a variant of packing dimension defined in terms of local projections of sets.
Incremental Generalized Discriminative Common Vectors for Image Classification.
2015
Subspace-based methods have become popular due to their ability to appropriately represent complex data in such a way that both dimensionality is reduced and discriminativeness is enhanced. Several recent works have concentrated on the discriminative common vector (DCV) method and other closely related algorithms also based on the concept of null space. In this paper, we present a generalized incremental formulation of the DCV methods, which allows the update of a given model by considering the addition of new examples even from unseen classes. Having efficient incremental formulations of well-behaved batch algorithms allows us to conveniently adapt previously trained classifiers without th…
Projection Clustering Unfolding: A New Algorithm for Clustering Individuals or Items in a Preference Matrix
2020
In the framework of preference rankings, the interest can lie in clustering individuals or items in order to reduce the complexity of the preference space for an easier interpretation of collected data. The last years have seen a remarkable flowering of works about the use of decision tree for clustering preference vectors. As a matter of fact, decision trees are useful and intuitive, but they are very unstable: small perturbations bring big changes. This is the reason why it could be necessary to use more stable procedures in order to clustering ranking data. In this work, a Projection Clustering Unfolding (PCU) algorithm for preference data will be proposed in order to extract useful info…
Decentralized Subspace Projection for Asymmetric Sensor Networks
2020
A large number of applications in Wireless Sensor Networks include projecting a vector of noisy observations onto a subspace dictated by prior information about the field being monitored. In general, accomplishing such a task in a centralized fashion, entails a large power consumption, congestion at certain nodes and suffers from robustness issues against possible node failures. Computing such projections in a decentralized fashion is an alternative solution that solves these issues. Recent works have shown that this task can be done via the so-called graph filters where only local inter-node communication is performed in a distributed manner using a graph shift operator. Most of the existi…