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If had 🙂 , , , Ts: working w/transformations in 3D can help S…
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13 days ago by tolkien
Principal Component Analysis | Hacker News
Agreed, there's something to be said for simple models that are "good enough," especially when their limitations are clear. k-NN also comes to mind.
pca  linear  algebra  toread 
16 days ago by dano
[1909.13754] Identifiability in Phylogenetics using Algebraic Matroids
"Identifiability is a crucial property for a statistical model since distributions in the model uniquely determine the parameters that produce them. In phylogenetics, the identifiability of the tree parameter is of particular interest since it means that phylogenetic models can be used to infer evolutionary histories from data. In this paper we introduce a new computational strategy for proving the identifiability of discrete parameters in algebraic statistical models that uses algebraic matroids naturally associated to the models. We then use this algorithm to prove that the tree parameters are generically identifiable for 2-tree CFN and K3P mixtures. We also show that the k-cycle phylogenetic network parameter is identifiable under the K2P and K3P models."
to:NB  identifiability  phylogenetics  algebra  statistics 
20 days ago by cshalizi
[1404.2035] Strongly continuous and locally equi-continuous semigroups on locally convex spaces
"We consider locally equi-continuous strongly continuous semigroups on locally convex spaces (X,tau). First, we show that if (X,tau) has the property that weak* compact sets of the dual are equi-continuous, then strong continuity of the semigroup is equivalent to weak continuity and local equi-continuity.
"Second, we consider locally convex spaces (X,tau) that are also equipped with a `suitable' auxiliary norm. We introduce the set N of tau continuous semi-norms that are bounded by the norm. If (X,tau) has the property that N is closed under countable convex combinations, then a number of Banach space results can be generalised in a straightforward way. Importantly, we extend the Hille-Yosida theorem.
"We apply the results to the study of transition semigroups of Markov processes on complete separable metric spaces."
to:NB  algebra  markov_models  stochastic_processes  re:almost_none 
5 weeks ago by cshalizi
Solutions to Larson Algebra 1 (9780547762883) :: Free Homework Help and Answers :: Slader
https://www.slader.com/textbook/9780547762883-larson-algebra-1-common-core-edition/ ;;;
tags: Solutions to Larson Algebra 1 (9780547762883) :: Free Homework Help and Answers :: Slader solution solutions to unsolved question questions needsEditing ;;;
Solutions  to  Larson  Algebra  1  (9780547762883)  ::  Free  Homework  Help  and  Answers  Slader  solution  unsolved  question  questions  needsEditing 
6 weeks ago by neerajsinghvns
[1907.09641] Dilated floor functions having nonnegative commutator II. Negative dilations
This paper completes the classification of the set S of all real parameter pairs (α,β) such that the dilated floor functions fα(x)=⌊αx⌋, fβ(x)=⌊βx⌋ have a nonnegative commutator, i.e. [fα,fβ](x)=⌊α⌊βx⌋⌋−⌊β⌊αx⌋⌋≥0 for all real x. It treats the negative dilation case, where both α,β<0. This result is equivalent to classifying all positive α,β satisfying ⌊α⌈βx⌉⌋−⌊β⌈αx⌉⌋≥0 for all real x. The classification analysis for negative dilations is connected with the theory of Beatty sequences and with the Diophantine Frobenius problem in two dimensions.
number-theory  constraint-satisfaction  algebra  rather-interesting  to-write-about  to-understand  elliptic-curves  consider:rediscovery  consider:genetic-programming  consider:representation-pivot 
6 weeks ago by Vaguery
[1806.00579] Dilated floor functions having nonnegative commutator I. Positive and mixed sign dilations
In this paper and its sequel we classify the set S of all real parameter pairs (α,β) such that the dilated floor functions fα(x)=⌊αx⌋ and fβ(x)=⌊βx⌋ have a nonnegative commutator, i.e. [fα,fβ](x)=⌊α⌊βx⌋⌋−⌊β⌊αx⌋⌋≥0 for all real x. The relation [fα,fβ]≥0 induces a preorder on the set of non-zero dilation factors α,β, which extends the divisibility partial order on positive integers. This paper treats the cases where at least one of the dilation parameters α or β is nonnegative. The analysis of the positive dilations case is related to the theory of Beatty sequences and to the Diophantine Frobenius problem in two generators.
number-theory  constraint-satisfaction  algebra  rather-interesting  elliptic-curves  feature-construction  to-write-about  to-understand 
6 weeks ago by Vaguery

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