Related papers: Briefly on Bottom-up
This is a short note on the log canonical inversion of adjunction.
The object of this short note is to prove a theorem and present a conjecture for the number of even entries in the character table of the symmetric group.
Investigating whether pre-trained language models (LMs) can function as knowledge bases (KBs) has raised wide research interests recently. However, existing works focus on simple, triple-based, relational KBs, but omit more sophisticated,…
A linear arrangement is a labeling or a numbering or a linear ordering of the vertices of a graph. In this paper we solve the minimum linear arrangement problem for bijective connection graphs (for short BC graphs) which include hypercubes,…
The annotation of textual information is a fundamental activity in Linguistics and Computational Linguistics. This article presents various observations on annotations. It approaches the topic from several angles including Hypertext,…
The first chapter serves as an introduction to the MSSM. I briefly review the model and explain why stops and sbottoms provide an interesting playground for exploring and testing this model. In the second chapter I discuss stop and sbottom…
We exhibit a simplified version of the construction of a field of Morley rank p with a predicate of rank p-1, extracting the main ideas for the construction from previous papers and refining the arguments. Moreover, an explicit…
We prove several inequalities on the determinants of sublattices in LLL-reduced bases. They generalize the inequalities on the length of the shortest vector proven by Lenstra, Lenstra, and Lovasz, and show that LLL-reduction finds not only…
This brief note gives a survey on results relating to existence of closed points on schemes, including an elementary topological characterization of the schemes with (at least one) closed point.
Notions of ordinal submodularity/supermodularity have been introduced and studied in the literature. We consider several classes of ordinally submodular functions defined on finite Boolean lattices and give characterizations of the set of…
We make two tiny corrections to our previous paper with the same title, and also obtain, as a bonus, something new.
In this note, we use certain sesquilinear form to realize small theta lift for even orthogonal-symplectic and unitary dual pairs over p-adic fields.
These are general notes on tensor calculus which can be used as a reference for an introductory course on tensor algebra and calculus. A basic knowledge of calculus and linear algebra with some commonly used mathematical terminology is…
Large Language Models (LLMs) possess encompassing capabilities that can process diverse language-related tasks. However, finetuning on LLMs will diminish this general skills and continual finetuning will further cause severe degradation on…
As real-world tasks grow increasingly complex, long-context reasoning has become a core capability for Large Language Models (LLMs). However, few studies explore which data types are effective for long-context reasoning and why. We find…
Recent advances in test-time scaling suggest that Large Language Models (LLMs) can gain better capabilities by generating Chain-of-Thought reasoning (analogous to human thinking) to respond a given request, and meanwhile exploring more…
In this note we answer a question concerning lineability of the set of non-absolutely summing operators.
We present an approach to minimally supervised relation extraction that combines the benefits of learned representations and structured learning, and accurately predicts sentence-level relation mentions given only proposition-level…
This paper briefly discusses some questions with analytical and topological aspects, with hopefully some useful references on both sides.
A notion of rank developed previously by the author is used to describe two correspondences which classify small unitary representations of split real forms of $E_6$ and $E_7$. The case of small principal series is studied in detail.