Search results for "Discrete set"
showing 10 items of 12 documents
Automatic Location of Sources of Electrical Activation from Electroanatomical Maps
2016
Electro-anatomical mapping is a widely used technique used by electrophysiologists to understand patient's activation pattern. The system measures activation time at different locations but does not provide information on underlying electrical pathways or triggering points, such as Purkinje-myocardial junctions or ectopic foci. We present a method to estimate the locations of Purkinje-myocardial junctions from a discrete set of endocardial samples. Using less than 1000 endocardial samples it can recover locations and activation times of the most influencing Purkinje myocardial junctions from Purkinje trees of up to 500 junctions. A simulation study revealed that using the estimated Purkinje…
Increasing chains and discrete reflection of cardinality
2013
Combining ideas from two of our previous papers, we refine Arhangel'skii Theorem by proving a cardinal inequality of which this is a special case: any increasing union of strongly discretely Lindelof spaces with countable free sequences and countable pseudocharacter has cardinality at most continuum. We then give a partial positive answer to a problem of Alan Dow on reflection of cardinality by closures of discrete sets.
On closures of discrete sets
2018
The depth of a topological space $X$ ($g(X)$) is defined as the supremum of the cardinalities of closures of discrete subsets of $X$. Solving a problem of Mart\'inez-Ruiz, Ram\'irez-P\'aramo and Romero-Morales, we prove that the cardinal inequality $|X| \leq g(X)^{L(X) \cdot F(X)}$ holds for every Hausdorff space $X$, where $L(X)$ is the Lindel\"of number of $X$ and $F(X)$ is the supremum of the cardinalities of the free sequences in $X$.
Reference point approach for multiple decision makers
2005
We consider multiple criteria decision-making problems where a group of decision-makers wants to find the most preferred solution from a discrete set of alternatives. We develop a method that uses achievement functions for charting subsets of reference points that would support a certain alternative to be the most preferred one. The resulting descriptive information is provided to the decision-makers in the form of reference acceptability indices and central reference points for each decision alternative. Then, the decision-makers can compare this information with their own preferences. We demonstrate the use of the method using a strategic multiple criteria decision model for an electricit…
On the cardinality of almost discretely Lindelof spaces
2016
A space is said to be almost discretely Lindelof if every discrete subset can be covered by a Lindelof subspace. Juhasz et al. (Weakly linearly Lindelof monotonically normal spaces are Lindelof, preprint, arXiv:1610.04506 ) asked whether every almost discretely Lindelof first-countable Hausdorff space has cardinality at most continuum. We prove that this is the case under $$2^{<{\mathfrak {c}}}={\mathfrak {c}}$$ (which is a consequence of Martin’s Axiom, for example) and for Urysohn spaces in ZFC, thus improving a result by Juhasz et al. (First-countable and almost discretely Lindelof $$T_3$$ spaces have cardinality at most continuum, preprint, arXiv:1612.06651 ). We conclude with a few rel…
Discrete frequency models for inventory management – an introduction
2001
Abstract The paper deals with the problem of devising a periodic replenishment policy when orders must be periodic, but only a given, discrete set of order frequencies can be used. The multi-item, instantaneous replenishment case with known demand is studied. In particular, staggering policies somehow arranging replenishments not to come at the same time instants are considered. The paper is composed of three parts: first, a taxonomy of several versions of the discrete frequency problem is proposed, according to different elements; in the second part, a general mixed integer programming model is proposed which is able to capture the peculiarities of the whole spectrum of this kind of proble…
Covering by discrete and closed discrete sets.
2008
Say that a cardinal number $\kappa$ is \emph{small} relative to the space $X$ if $\kappa <\Delta(X)$, where $\Delta(X)$ is the least cardinality of a non-empty open set in $X$. We prove that no Baire metric space can be covered by a small number of discrete sets, and give some generalizations. We show a ZFC example of a regular Baire $\sigma$-space and a consistent example of a normal Baire Moore space which can be covered by a small number of discrete sets. We finish with some remarks on linearly ordered spaces.
kq-Representation for pseudo-bosons, and completeness of bi-coherent states
2017
We show how the Zak $kq$-representation can be adapted to deal with pseudo-bosons, and under which conditions. Then we use this representation to prove completeness of a discrete set of bi-coherent states constructed by means of pseudo-bosonic operators. The case of Riesz bi-coherent states is analyzed in detail.
A note on discrete sets
2009
We give several partial positive answers to a question of Juhasz and Szentmiklossy regarding the minimum number of discrete sets required to cover a compact space. We study the relationship between the size of discrete sets, free sequences and their closures with the cardinality of a Hausdorff space, improving known results in the literature.
Discrete cortical representations and their stability in the presence of synaptic turnover
2015
Population imaging in mouse auditory cortex revealed clustering of neural responses to brief complex sounds: the activity of a local population typically falls close to one out of a small number of observed states [1]. These clusters appear to group sets of auditory stimuli into a discrete set of activity patterns and could thereby form the basis for representations of sound categories. However, to be useful for the brain, such representations should be robust against fluctuations in the underlying circuitry, which are significant even in the absences of any explicit learning paradigm [2]. Here we introduce a novel firing rate based circuit model of mouse auditory cortex to study the emerge…