We develop the notion of the good pants homology and show that it agrees with the standard homology on closed surfaces (the good pants are pairs of pants whose cuffs have the length nearly equal to some large number R). Combined with our previous wor...
We show that the set of awesome homogeneous metrics on non-compact manifolds is Ricci flow invariant. Moreover, if the universal cover of such awesome homogeneous space is not contractible the Ricci flow has finite extinction time, confirming the Dyn...
We classify six-dimensional homogeneous nearly Kähler manifolds and give a positive answer to Gray and Wolf's conjecture: every homogeneous nearly Kähler manifold is a Riemannian 3-symmetric space equipped with its canonical almost Hermitian stru...
In his paper titled "Torsion points on Fermat Jacobians, roots of circular units and relative singular homology", Anderson determines the homology of the degree $n$ Fermat curve as a Galois module for the action of the absolute Galois group $G_{\math...
Real-world graphs generally have only one kind of tendency in their connections. These connections are either homophily-prone or heterophily-prone. While graphs with homophily-prone edges tend to connect nodes with the same class (i.e., intra-class n...
We present three large families of new examples of plumbed 3-manifolds that bound rational homology 4-balls. These are constructed using two operations, also defined here, that preserve the lack of a lattice embedding obstruction to bounding rational...
We give an entirely geometric proof, without recourse to cellular homology, of the fact that $\partial^2=0$ in the chain complex defined by a handle decomposition of a given manifold. Topological invariance of the resulting `handle homology' is a con...
Racial homophily refers to the tendency of individuals to associate with others of the same racial or ethnic background. A recent study found no evidence of racial homophily in responses to mass shooting data visualizations. To increase the likelihoo...
Homogeneous countably compact spaces $X$ and $Y$ whose product $X\times Y$ is not pseudocompact are constructed. It is proved that all compact subsets of homogeneous subspaces of the third power of an extremally disconnected space are finite. Moreove...
We describe the ordering of a class of clones by minion homomorphisms, also known as minor preserving maps or height 1 clone homomorphisms. The class consists of all clones on finite sets determined by binary relations whose projections to both coord...
We argue that newly-developed large language models (LLMs), because of how they are trained and designed, are implicit computational models of humans -- a Homo silicus. LLMs can be used like economists use Homo economicus: they can be given endowment...
A simple model from game theory, which can imitate a mechanism of corruption and cooperation patterns, is proposed. The settings are divided into two studies with examples related to safety of Moldovan economy. In Homo Economicus world, players seem...
Dec 20, 2022 · Prove that $\operatorname {Hom}_A (A,M) \cong M$. I am wondering if the homomorphism that I should show is a group homomorphism or module homomorphism? Also, is my …
This paper is the extended introduction of a serie of papers about modelling T-homotopy by refinement of observation. The notion of T-homotopy equivalence is discussed. A new one is proposed and its behaviour with respect to other construction in d...
We examine how three different communication processes operating through social networks are affected by homophily -- the tendency of individuals to associate with others similar to themselves. Homophily has no effect if messages are broadcast or s...
In 1945, R. Fox introduced the so-called Fox torus homotopy groups in which the usual homotopy groups are embedded and their Whitehead products are expressed as commutators. A modern treatment of Fox torus homotopy groups and their generalization h...
We construct a homogeneous subspace of $2^ω$ whose complement is dense in $2^ω$ and rigid. Using the same method, assuming Martin's Axiom, we also construct a countable dense homogeneous subspace of $2^ω$ whose complement is dense in $2^ω$ and ri...
Sep 30, 2014 · What is the actual meaning/origin of the prefix 'homo'? I've been confused about this for a while, and here's why: 'homo', when used in such contexts as homogenous, homogeneous, and …
这其实是个蛮有意思的问题。 Homo sapiens sapiens，这个命名结构是genus species subspecies，有时候在subspecies之前会加【sp. 】或者【subsp. 】来标记亚种以免混淆。 Homo 是属（genus）名， …
In this paper, we develop a functional analytical theory for establishing that mild solutions of first-order Cauchy problems involving homogeneous operators of order zero are strong solutions; in particular, the first-order time derivative satisfies...