arXiv research

TrajectoryNet models dynamic cellular trajectories using optimal transport.

In the present work we introduce a stochastic cellular automata model in order to simulate the dynamics of the stock market. A direct percolation method is used to create a hierarchy of clusters of active traders on a two dimensional grid. Active traders are characterised by the decision to buy, (+1), or sell, (-1), a …

Optimizes natural frequencies of cellular composites with various microstructures.

New method learns cell trajectories and network interactions from single-cell data.

We present a machine learning framework for modeling protein dynamics. Our approach uses L1-regularized, reversible hidden Markov models to understand large protein datasets generated via molecular dynamics simulations. Our model is motivated by three design principles: (1) the requirement of massive scalability; (2) t…

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…

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…

Until recently, transcriptomics was limited to bulk RNA sequencing, obscuring the underlying expression patterns of individual cells in favor of a global average. Thanks to technological advances, we can now profile gene expression across thousands or millions of individual cells in parallel. This new type of data has …

Method learns cell interaction rules from individual trajectories.

The study classifies cellular pseudomanifolds and their properties.

The paper studies Morse theory on manifolds with boundaries, constructing cellular structures and estimating critical points.

Quantum cellular automata form a homology theory.

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…

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.

Animals excel at adapting their intentions, attention, and actions to the environment, making them remarkably efficient at interacting with a rich, unpredictable and ever-changing external world, a property that intelligent machines currently lack. Such an adaptation property relies heavily on cellular neuromodulation,…

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

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.

ChemCPA predicts cellular responses to novel drugs using transfer learning.

In this paper, we introduce a novel method to interpret recurrent neural networks (RNNs), particularly long short-term memory networks (LSTMs) at the cellular level. We propose a systematic pipeline for interpreting individual hidden state dynamics within the network using response characterization methods. The ranked …

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.

Solves challenges of drone communication in cellular networks.

We aim to jointly optimize antenna tilt angle, and vertical and horizontal half-power beamwidths of the macrocells in a heterogeneous cellular network (HetNet). The interactions between the cells, most notably due to their coupled interference render this optimization prohibitively complex. Utilizing a single agent rei…

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.

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

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…

We discuss algorithms for estimating the Shannon entropy h of finite symbol sequences with long range correlations. In particular, we consider algorithms which estimate h from the code lengths produced by some compression algorithm. Our interest is in describing their convergence with sequence length, assuming no limit…

Designs a Cellular Automata rule for forming touching loop patterns.

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…

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…

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…

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.

A novel method for efficient CDRL over wireless networks.