Questions tagged [classification]
Classification of various mathematical structures. For classification in the sense of statistics / machine learning, use [tag:statistical-classification].
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Can one formalize the prevalence of the Big Five systems of reverse math?
Simpson's systems of second order arithmetic turn out to be five in
number; to simplify notation let's denote them A, B, C, D, E. What
seems to be an empirical observation is that most theorems in
...
- 15.8k
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1
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Bayes classifiers with cost of misclassification
A minimum ECM classifier disciminate the features $\underline{x}$ to belong to class $t$ ($\delta(\underline{x}) = t$) if $\forall j \ne t$:
$$\sum_{k\ne t} c(t|k) f_k(\underline{x})p_k \le \sum_{k\ne ...
- 11
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Classification of all connected simple real Lie groups?
Is there an explicit(!) classification of all(!) connected real simple Lie groups up to isomorphism? Not just simply connected or adjoint, but all of them?
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Almost simple groups and their involutions without CFSG
Suppose $A$ is a finite almost simple group (meaning, by definition, that there exists a finite simple group $P$ such that $P \leq A \leq \mathrm{Aut}(P)$). Suppose furthermore that $A$ acts $2$-...
- 4,503
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Finding inverses of certain elements in the set of normal invariants of a smooth manifold
Let, $V$ denote the Stiefel manifold of 2-frames $V_{10,2}$ . Consider the the map $S_\text{diff} (V) \xrightarrow{\eta} N_\text{diff} (V) $ in the surgery exact sequence of a smooth manifold. . ...
- 141
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CFSG-free proof for classifying simple $K_3$-group
Let $G$ be a finite nonabelian simple group.
We call $G$ a $K_3$-group if $|G|=p^aq^br^c$ where $p,q,r$ are distinct primes and $a,b,c$ are positive integers.
My question is: Is there a CFSG-free ...
- 603
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Understanding segments in Bernstein-Zelevinsky Classification
All reps shall be admissible in what follows.
Let $k$ be a non-arch. field, $n = a\cdot b$ natural numbers and $P = M \cdot N \subset \mathrm{GL}_n(k)$ the standard parabolic subgroup with
$$
M = \...
- 748
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Perceptron / logistic regression accuracy on the n-bit parity problem
$\DeclareMathOperator{\sgn}{sign}$The perceptron (similarly, logistic regression) of the form $y=\sgn(w^T \cdot x+b)$ is famously known for its inability to solve the XOR problem, meaning it can get ...
- 141
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Counting degrees of freedom in Lie algebra structure constants (aka why are there any nontrivial Lie algebras of dim >5?)
This is a question about the true number of constraints imposed by the Jacobi identity on the structure constants of a Lie algebra.
For an $n$-dimensional Lie algebra, there are $\frac{n^2(n-1)}{2}$ ...
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Classification results
A typical classification result for a class $C$ of objects looks like that:
Theorem. Each object of $C$ is isomorphic to one object of the following list: [insert list here].
Examples are the ...
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Wild classification problems and Borel reducibility
My question is whether the archetype of 'wild' problems in algebra, namely classifying pairs of square matrices up to similarity, is 'non-smooth' in the sense of Borel reducibility.
This was ...
- 21.8k
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Centralizers of automorphisms in finite simple groups (reference request)
I would like to have a precise version of the following statement and, if possible, a reference to such a statement in some standard book.
Claim 1: Let $G$ be a finite simple non abelian group with ...
- 167
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Twisted root subgroups in twisted Chevalley groups (reference request)
I am trying to find a standard reference for the natural analogue of root subgroups (and their properties) in twisted Chevalley groups.
Let me first recall the classical set-up. According to Steinberg'...
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Is there a classification of the first geodesic nets?
A geodesic net is an embedding of a multigraph $(V,E)$ into a Riemannian manifold $(M,g)$, so that the vertices are mapped to points of $M$ and the edges to geodesics connecting them. Additionally, ...
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Classification of octonionic reflection groups
I know that there exist classification theorems for real, complex, and quaternionic, reflection groups.
There are presentations for the real reflection groups, as well as further presentations for the ...
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