Related papers: On the Algebraic Structure of Linear Trellises
Natural and man-made transport webs are frequently dominated by dense sets of nested cycles. The architecture of these networks, as defined by the topology and edge weights, determines how efficiently the networks perform their function.…
In this paper, we discuss the reduction of error-trellises for tail-biting convolutional codes. In the case where some column of a parity-check matrix has a monomial factor (with indeterminate D), we show that the associated tail-biting…
This work concerns the study of properties of a group of Koszul algebras coming from the toric ideals of a chordal bipartite infinite family of graphs (alternately, these rings may be interpreted as coming from determinants of certain…
We present a braided circuit topology framework for investigating topology and structural phase transitions in aggregates of semiflexible polymers. In the conventional approach to circuit topology, which specifically applies to single…
We study an abstract notion of tree structure which lies at the common core of various tree-like discrete structures commonly used in combinatorics: trees in graphs, order trees, nested subsets of a set, tree-decompositions of graphs and…
The family of graphs that can be constructed from isolated vertices by disjoint union and graph join operations are called cographs. These graphs can be represented in a tree-like representation termed parse tree or cotree. In this paper,…
This is the first of a series of papers studying real algebraic threefolds using the minimal model program. The main results are outlined in Part II. The present part I. contains the necessary preliminary work concerning terminal…
A textile structure is a periodic arrangement of threads in the thickened plane. A topological classification of textile structures is harder than for classical knots and links that are non-periodic and restricted to a bounded region. The…
We suggest an enhancement to structural coding through the use of (a) causally bound codes, (b) basic constructs of graph theory and (c) statistics. As is the norm with structural coding, the codes are collected into categories. The…
Graph-level representations are crucial tools for characterising structural differences between graphs. However, comparing graphs with different cardinalities, even when sampled from the same underlying distribution, remains challenging.…
We study a new flexible method to extend linearly the graph of a non-linear, and usually not bijective, function so that the resulting extension is a bijection. Our motivation comes from cryptography. Examples from symmetric cryptography…
Transformer-based LLMs demonstrate strong performance on graph reasoning tasks, yet their internal mechanisms remain underexplored. To uncover these reasoning process mechanisms in a fundamental and unified view, we set the basic…
This paper proposes a new mathematical framework that can be applied to biological problems such as analysis of the structures of proteins and protein complexes. In particular, it gives a new method for encoding the three-dimensional…
This paper is concerned with the local reducibility properties of linear realizations of codes on finite graphs. Trimness and properness are dual properties of constraint codes. A linear realization is locally reducible if any constraint…
In this text we develop the formalism of products and powers of linear codes under componentwise multiplication. As an expanded version of the author's talk at AGCT-14, focus is put mostly on basic properties and descriptive statements that…
We study a general class of nonlinear iterative algorithms which includes power iteration, belief propagation and approximate message passing, and many forms of gradient descent. When the input is a random matrix with i.i.d. entries, we use…
A graph is locally chordal if each of its small-radius balls is chordal. In an earlier work [AKK25], the authors and Kobler proved that locally chordal graphs can be characterized by having chordal local covers, by forbidding short cycles…
We investigate the structure of trees that have minimal algebraic connectivity among all trees with a given degree sequence. We show that such trees are caterpillars and that the vertex degrees are non-decreasing on every path on…
The tree share structure proposed by Dockins et al. is an elegant model for tracking disjoint ownership in concurrent separation logic, but decision procedures for tree shares are hard to implement due to a lack of a systematic theoretical…
Many scientific datasets are of high dimension, and the analysis usually requires visual manipulation by retaining the most important structures of data. Principal curve is a widely used approach for this purpose. However, many existing…