**algebra**

When is proof by contradiction necessary? | Gowers's Weblog

nibble org:bleg gowers mathtariat math proofs contradiction volo-avolo structure math.CA math.NT algebra parsimony elegance simplification minimalism efficiency technical-writing necessity-sufficiency degrees-of-freedom

14 days ago by nhaliday

nibble org:bleg gowers mathtariat math proofs contradiction volo-avolo structure math.CA math.NT algebra parsimony elegance simplification minimalism efficiency technical-writing necessity-sufficiency degrees-of-freedom

14 days ago by nhaliday

Principal Component Analysis | Hacker News

16 days ago by dano

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

20 days ago by cshalizi

"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

5 weeks ago by cshalizi

"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
"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."

5 weeks ago by cshalizi

Solutions to Larson Algebra 1 (9780547762883) :: Free Homework Help and Answers :: Slader

6 weeks ago by neerajsinghvns

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
tags: Solutions to Larson Algebra 1 (9780547762883) :: Free Homework Help and Answers :: Slader solution solutions to unsolved question questions needsEditing ;;;

6 weeks ago by neerajsinghvns

[1907.09641] Dilated floor functions having nonnegative commutator II. Negative dilations

6 weeks ago by Vaguery

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

6 weeks ago by Vaguery

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