Related papers: Word reading is a crystal morphism
We show that a large class of formal groups can be realised functorially by even periodic ring spectra. The main advance is in the construction of morphisms, not of objects.
For a given morphism of schemes f:X->S, a sheaf F on X, a geometric point x on X, and s=f(x), the morphism f\_x : X(x) -> S(s) between the strict henselizations doesn't necessarily behave (with respect to F) like a proper morphism. However,…
Let $\psi : G\to GL(V)$ and $\varphi :G \to GL (W)$ be representations of finite group $G$. A linear map $T: V\to W$ is called a morphism from $\psi$ to $\varphi$ if it satisfys $T\psi_g= \varphi_g T$ for each $g\in G$ and let…
The Leinster matrix corresponding to a finite category has entries counting the number of morphisms between objects. A first question is to know which positive integer matrices come from at least one finite category. Here, that question…
Considering that words with different characteristic in the text have different importance for classification, grouping them together separately can strengthen the semantic expression of each part. Thus we propose a new text representation…
Given a reflection group $G$ acting on a complex vector space $V$, a reflection map is the composition of an embedding $X \hookrightarrow V$ with the orbit map $V\to\mathbb C^p$ that maps a $G$-orbit to a point. Reflection maps can be very…
We give a canonical form of matrices of a cycle of linear or semilinear mapping V_1 --- V_2 --- ... --- V_t --- V_1 in which all V_i are complex vector spaces, each line is an arrow ---> or <---, and each arrow denotes a linear or…
Almost 25 years have passed since Shechtman discovered quasicrystals, and 15 years since the Commission on Aperiodic Crystals of the International Union of Crystallography put forth a provisional definition of the term crystal to mean ``any…
A theory graph is a network of axiomatic theories connected with meaning-preserving mappings called theory morphisms. Theory graphs are well suited for organizing large bodies of mathematical knowledge. Traditional and formal proofs do not…
For every non-exceptional affine Lie algebra, we explicitly construct a positive geometric crystal associated with a fundamental representation. We also show that its ultra-discretization is isomorphic to the limit of certain perfect…
We classify affine varieties with an action of a connected, reductive algebraic group such that the group is isomorphic to an open orbit in the variety. This is accomplished by associating a set of one-parameter subgroups of the group to…
We develop the notion of crystal in the context of derived algebraic geometry, and to connect crystals to more classical objects such as D-modules.
We present a clustering-based language model using word embeddings for text readability prediction. Presumably, an Euclidean semantic space hypothesis holds true for word embeddings whose training is done by observing word co-occurrences.…
Crystallization of the amorphous phases into metastable crystals plays a fundamental role in the formation of new matter, from geological to biological processes in nature to synthesis and development of new materials in the laboratory.…
We show that the directed labelled Cayley graphs coincide with the rooted deterministic vertex-transitive simple graphs. The Cayley graphs are also the strongly connected deterministic simple graphs of which all vertices have the same cycle…
Inflection graphs are highly complex networks representing relationships between inflectional forms of words in human languages. For so-called synthetic languages, such as Latin or Polish, they have particularly interesting structure due to…
Word embeddings generated by neural network methods such as word2vec (W2V) are well known to exhibit seemingly linear behaviour, e.g. the embeddings of analogy "woman is to queen as man is to king" approximately describe a parallelogram.…
Metal oxides such as VO$_2$ undergo structural transitions to low-symmetry phases characterized by intricate crystalline order, accompanied by rich electronic behavior. We derive a minimal ionic Hamiltonian based on symmetry and local…
We adapt the classical notion of learning from text to computable structure theory. Our main result is a model-theoretic characterization of the learnability from text for classes of structures. We show that a family of structures is…
This note contributes to the structure theory of abstract rigidity matroids in general dimension. In the spirit of classical matroid theory, we prove several cryptomorphic characterizations of abstract rigidity matroids (in terms of…