arXiv research

Optimizes natural frequencies of cellular composites with various microstructures.

We present a construction of cellular BF theory (in both abelian and non-abelian variants) on cobordisms equipped with cellular decompositions. Partition functions of this theory are invariant under subdivisions, satisfy a version of the quantum master equation, and satisfy Atiyah-Segal-type gluing formula with respect…

We construct a small regular cellular decomposition of the Fulton MacPherson operad $FM_2$ that is compatible with the operad composition. The cells are indexed by trees with edges of two colors and vertices labelled by cells of the cacti operad. We compute the generating functions counting the cells, that are algebrai…

DCMIX learns channel importance for high content imaging.

A new framework for knowledge graph embedding using sheaves.

In this paper we generalize cellular algebras by allowing different partial orderings relative to fixed idempotents. For these relative cellular algebras we classify and construct simple modules, and we obtain other characterizations in analogy to cellular algebras. We also give several examples of algebras that are re…

We develop functoriality for Morse theory, namely, to a pair of Morse-Smale systems and a generic smooth map between the underlying manifolds we associate a chain map between the corresponding Morse complexes, which descends to the correct map on homology. This association does not in general respect composition. We gi…

This article introduces descriptive cellular homology on cell complexes, which is an extension of J.H.C. Whitehead's CW topology. A main result is that a descriptive cellular complex is a topology on fibres in a fibre bundle. An application of two forms of cellular homology is given in terms of the persistence of shape…

The study classifies cellular pseudomanifolds and their properties.

Quantum cellular automata form a homology theory.

Defines a simplicial operad related to Fulton-MacPherson.

For leveled spatial graphs, we find a surface embedding that allows cellular embedding.

We give examples of harmonic cellular maps between negatively curved manifolds which are not diffeomorphisms but are homotopic to diffeomorphisms.

The notion of cellular stratified spaces was introduced in a joint work of the author with Basabe, González, and Rudyak [1009.1851] with the aim of constructing a cellular model of the configuration space of a sphere. In particular, it was shown that the classifying space (order complex) of the face poset of a totally …

Study immersions of punctured 4-manifolds for quantum automata applications.

Main subject of the paper is a (strong) Morse function on a compact manifold with boundary. We construct a cellular structure and discuss its algebraic properties in this paper. Also we get an estimation on Arnold's question on a number of critical points of a Morse function with given boundary condition.

In this work we develop a cellular equivariant homology functor and apply it to prove an equivariant Euler-Poincare formula and an equivariant Lefschetz theorem.

The paper extends Gaussian processes to model complex interactions in cellular complexes.

ChemCPA predicts cellular responses to novel drugs using transfer learning.

Machine learning algorithms can be fooled by small well-designed adversarial perturbations. This is reminiscent of cellular decision-making where ligands (called antagonists) prevent correct signalling, like in early immune recognition. We draw a formal analogy between neural networks used in machine learning and model…

New findings on hyperbolicity of augmented links in thickened surfaces.

TrajectoryNet models dynamic cellular trajectories using optimal transport.

CURIE uses cellular automata to detect concept drift in data streams.

Electron Cryo-Tomography (ECT) allows 3D visualization of subcellular structures at the submolecular resolution in close to the native state. However, due to the high degree of structural complexity and imaging limits, the automatic segmentation of cellular components from ECT images is very difficult. To complement an…

Classifies fake surfaces up to complexity 5.

Paper proposes kernel-based tests for model misspecification.

New tool lassos connects virtual and surface link diagrams, changing primeness rules.

The paper optimizes UAV path and power for QoS in cellular networks.

New model identifies cell-specific genes for cancer prognosis.

Motivation: Understanding functions of proteins in specific human tissues is essential for insights into disease diagnostics and therapeutics, yet prediction of tissue-specific cellular function remains a critical challenge for biomedicine. Results: Here we present OhmNet, a hierarchy-aware unsupervised node feature le…

We show that tree almost automorphism groups, including Neretin groups, satisfy the analogue of the $F_\infty$-finiteness condition in the world of totally disconnected groups: They possess a cellular action on a contractible cellular complex such that the stabilizers are open and compact and the restriction of the act…

In this brief sequel to a previous article, we recall the notion of a cut cellular surface (CCS), being a surface with boundary, which is cut in a specified way to be represented in the plane, and is composed of 0-, 1- and 2-cells. We obtain invariants of CCS's under Pachner-like moves on the cellular structure, by cou…

Designs a Cellular Automata rule for forming touching loop patterns.

Recently V. Krushkal and D. Renardy generalized the Tutte polynomial from graphs to cell complexes. We show that evaluating this polynomial at the origin gives the number of cellular spanning trees in the sense of A. Duval, C. Klivans, and J. Martin. Moreover, after a slight modification, the Tutte-Krushkal-Renardy pol…

Multicomponent bilayer structures arise as the ubiquitous plasma membrane in cellular biology and as blends of amphiphilic copolymers used in electrolyte membranes, drug delivery, and emulsion stabilization within the context of synthetic chemistry. We develop the multicomponent functionalized Cahn-Hilliard (mFCH) free…

Tuning cellular network performance against always occurring wireless impairments can dramatically improve reliability to end users. In this paper, we formulate cellular network performance tuning as a reinforcement learning (RL) problem and provide a solution to improve the performance for indoor and outdoor environme…

LUNAR uses cellular automata for real-time data classification in fast streams.

We introduce the notion of a cut cellular surface (CCS), being a surface with boundary, which is cut in a specified way to be represented in the plane, and is composed of 0-, 1- and 2-cells. We obtain invariants of CCS's under Pachner-like moves on the cellular structure, by counting colourings of the 1-cells with elem…

The paper solves curvature problems on infinite hyperbolic surfaces.

Let $\mathbb{F}_{Θ}=G/P_{Θ}$ be a generalized flag manifold, where $G$ is a real noncompact semi-simple Lie group and $P_{Θ}$ a parabolic subgroup. A classical result says the Schubert cells, which are the closure of the Bruhat cells, endow $\mathbb{F}_Θ$ with a cellular CW structure. In this paper we exhibit explicit …

We give an explicit graded cellular basis of the $\mathfrak{sl}_3$-web algebra $K_S$. In order to do this, we identify Kuperberg's basis for the $\mathfrak{sl}_3$-web space $W_S$ with a version of Leclerc-Toffin's intermediate crystal basis and we identify Brundan, Kleshchev and Wang's degree of tableaux with the weigh…

Enabling cellular connectivity for drones introduces a wide set of challenges and opportunities. Communication of cellular-connected drones is influenced by 3-dimensional mobility and line-of-sight channel characteristics which results in higher number of handovers with increasing altitude. Our cell planning simulation…

Geometrically interprets a duality theorem linking cochain and chain complexes.

We propose an algorithm to automate fault management in an outdoor cellular network using deep reinforcement learning (RL) against wireless impairments. This algorithm enables the cellular network cluster to self-heal by allowing RL to learn how to improve the downlink signal to interference plus noise ratio through ex…

New stability theorem for nonorientable surfaces mapping class groups.

The paper explores handlebody versions of various diagram algebras.

This paper detects anomalies in cellular network traffic using hybrid methods.

Optimizes antenna tilt for better QoS in cellular networks.