The paper extends cellular algebras with relative orderings and explores their properties.
problem Generalizing cellular algebras with different partial orderings.
method Classification and construction of simple modules, characterizations, and examples.
result Examples of relative cellular algebras that are not cellular.
Extends CW topology to describe cellular homology on cell complexes.
problem Describing topological properties of cell complexes.
method Introduces descriptive cellular homology on cell complexes, extending Whitehead's CW topology.
result Descriptive cellular complex is a topology on fibres in a fibre bundle.
A theory for cellular BF models on decomposed spaces.
problem Constructing invariant partition functions for cellular BF models.
method Construction of cellular BF theory on cobordisms with cellular decompositions.
result Invariants under subdivisions and gluing formulas.
The study classifies cellular pseudomanifolds and their properties.
problem Understanding the structure of cellular pseudomanifolds.
method Analyzing the combinatorial and geometric properties of cellular pseudomanifolds.
result Complete classification of cellular pseudomanifolds with excess < 2, and progress towards excess 2.
The paper studies Morse theory on manifolds with boundaries, constructing cellular structures and estimating critical points.
problem Understanding Morse functions on manifolds with boundaries.
method Constructing a cellular structure and analyzing its algebraic properties.
result Estimation of the number of critical points of a Morse function with boundary conditions.
Quantum cellular automata form a homology theory.
problem Understanding the topological structure of quantum cellular automata.
method Formal properties of coarse homology theories.
result Quantum cellular automata naturally form the degree-zero part of a coarse homology theory.
Tree almost automorphism groups have a cellular action on a contractible complex.
problem Understanding the structure of tree almost automorphism groups.
method Showed cellular action on a contractible complex with specific stabilizers.
result Tree almost automorphism groups satisfy the F∞-finiteness condition. Optimizes natural frequencies of cellular composites with various microstructures.
problem Designing cellular composites with diverse microstructures for maximizing natural frequencies.
method Data-driven topology optimization with a latent-variable Gaussian process model.
result Cellular designs with multiclass microstructures achieve higher natural frequencies.
Machine learning attacks mimic cellular decision-making, revealing new defense mechanisms.
problem Adversarial perturbations fool machine learning models, similar to how ligands prevent correct signaling in cells.
method Formal analogy between neural networks and cellular decision-making models, applying machine learning techniques to study cellular processes.
result Found two regimes in cellular decision-making models, each with a critical point that shapes the loss landscape and defense mechanisms.
For leveled spatial graphs, we find a surface embedding that allows cellular embedding.
problem Finding a surface embedding for general spatial graphs is not always possible.
method Define leveled property, decompose graph into subgraphs, and construct surface.
result For leveled spatial graphs with a small number of levels, a surface can always be found.
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 …
We give examples of harmonic cellular maps between negatively curved manifolds which are not diffeomorphisms but are homotopic to diffeomorphisms.
Study immersions of punctured 4-manifolds for quantum automata applications.
problem Existence of immersions between specific 4-manifolds.
method Analyzing immersions of punctured 4-manifolds to establish a partial order.
result Established a partial order on closed 4-manifolds via immersions.
The paper extends Gaussian processes to model complex interactions in cellular complexes.
problem Capturing topological inductive biases in machine learning models.
method Proposes Gaussian processes on cellular complexes, introducing novel kernels.
result Derives two novel kernels for modeling interactions between cells.
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.
A saliency detection method for ECT images segments cellular components without supervision.
problem Automatic segmentation of cellular components from ECT images is difficult due to structural complexity and imaging limits.
method Supervoxel over-segmentation, feature extraction, feature matrix decomposition, and computation of saliency.
result The method successfully labels most salient regions detected by a human observer and filters out background regions.
Invariants derived from finite group colorings of cut cellular surfaces.
problem Counting colorings of 1-cells to define invariants of cut cellular surfaces.
method Counting colorings of 1-cells with elements of a finite group, subject to a flatness condition.
result Derived invariants of cut cellular surfaces under Pachner-like moves.
Predicts cellular functions in human tissues using multi-layer networks.
problem Challenges in predicting tissue-specific cellular function.
method Hierarchy-aware unsupervised node feature learning for multi-layer networks.
result Improves prediction accuracy of cellular functions in 48 tissues.
The paper computes the cellular homology of real flag manifolds.
problem Computing the cellular homology of real flag manifolds.
method Explicit parametrizations of Schubert cells by closed balls (cubes) in R^n, using them to compute the boundary operator.
result Explicit formula for the boundary operator with refined coefficients.
Deep RL improves cellular network fault management and performance.
problem Fault management and radio performance improvement in outdoor cellular networks.
method Deep Q-Learning for self-organizing networks fault management.
result The proposed algorithm learns to clear alarms and improve radio performance better than existing methods.
ChemCPA predicts cellular responses to novel drugs using transfer learning.
problem Scaling high-throughput screens to measure cellular responses for many drugs is costly and challenging.
method ChemCPA, a new encoder-decoder architecture combined with transfer learning.
result Training on existing bulk RNA HTS datasets improves generalization performance, reducing the need for extensive single-cell screens.
Paper proposes RL algorithms for optimizing cellular network performance.
problem Improving cellular network performance against wireless impairments.
method Formulated as a reinforcement learning problem and developed two algorithms: PC and SON.
result RL algorithms outperform industry standards in simulated environments.
New findings on hyperbolicity of augmented links in thickened surfaces.
problem Proving hyperbolicity of links in thickened surfaces.
method Extending hyperbolicity results to generalized augmented cellular alternating links.
result Generalized augmented cellular alternating links in thickened surfaces are hyperbolic.
Solves challenges of drone communication in cellular networks.
problem Interference from drones to base stations in cellular networks.
method Derived analytical models, formulated optimization problem, transformed into machine learning problem, solved using deep reinforcement learning.
result Optimal handover and resource management policies for drones in cellular networks.
TrajectoryNet models dynamic cellular trajectories using optimal transport.
problem Modeling continuous and non-linear paths in dynamic processes.
method Continuous normalizing flows linked to dynamic optimal transport.
result TrajectoryNet improves interpolation of cellular distributions.
Kernel-based algorithm optimizes cellular network configuration through multi-task learning.
problem Optimizing network configuration based on field experience and minimizing exploration cost.
method Kernel-based multi-BS contextual bandit algorithm leveraging conditional kernel embedding for multi-task learning.
result The proposed algorithm reduces exploration cost and improves network performance.
CURIE uses cellular automata to detect concept drift in data streams.
problem Detecting changes in data distribution (concept drift) in data streams.
method CURIE represents data stream distribution in a cellular automata grid and uses its neighborhood rule to detect changes.
result CURIE, when hybridized with base learners, performs competitively in detection metrics and classification accuracy.
Invariants for surfaces with 0-, 1-, and 2-cells are derived from finite 2-groups.
problem Counting colorings of 1- and 2-cells in a surface to define invariants.
method Counting colorings of 1- and 2-cells with elements of a finite 2-group, subject to a fake flatness condition.
result Invariants of cut cellular surfaces extend Yetter's invariants to this class of surfaces.
Classifies fake surfaces up to complexity 5.
problem Classifying fake surfaces for low-dimensional topology.
method Derived properties of fake surfaces, classified up to complexity 5.
result Proved conjectures about fake surfaces up to complexity 5.
The paper optimizes UAV path and power for QoS in cellular networks.
problem Optimizing UAV path and power for QoS in cellular networks.
method Apprenticeship learning via deep inverse reinforcement learning (IRL) combined with Q-learning and DRL.
result The proposed method achieves expert-level performance and maintains performance in unseen situations.
Designs a Cellular Automata rule for forming touching loop patterns.
problem Forming stable touching loop patterns in a 2D grid.
method Developed a Cellular Automata rule that uses templates to cover the space and match patterns.
result The rule successfully evolves stable touching loop patterns in a 2D grid.
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…
Machine learning aids self-healing in cellular networks, tackling data imbalance and cost sensitivity.
problem Challenges in applying machine learning for self-healing in cellular networks.
method Data-driven machine learning techniques addressing data imbalance, insufficiency, and cost sensitivity.
result Feasibility and effectiveness of cost-sensitive fault detection with imbalanced data.
LUNAR uses cellular automata for real-time data classification in fast streams.
problem Real-time machine learning challenges with fast data streams and concept drift.
method Streamified cellular automata approach for incremental learning and adaptation.
result Competitive performance in classification compared to established online learning methods.
The paper solves curvature problems on infinite hyperbolic surfaces.
problem Prescribed curvature flow on hyperbolic surfaces with infinite topological type.
method Introduced a prescribed curvature flow adapted to infinite cellular decompositions.
result Established well-posedness of the flow and proved convergence under certain conditions.
We give an explicit graded cellular basis of the sl3-web algebra KS. In order to do this, we identify Kuperberg's basis for the sl3-web space WS 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.
problem Understanding a complex duality theorem in geometric terms.
method Introduces a chain isomorphism involving simplicial and cellular complexes.
result Establishes a geometric interpretation of Ranicki duality.
New stability theorem for nonorientable surfaces mapping class groups.
problem Stability of homology groups of mapping class groups of nonorientable surfaces.
method Galatius--Kupers--Randal-Williams framework of cellular E2-algebras. result New best known stability range for homology of nonorientable surfaces.
The paper explores handlebody versions of various diagram algebras.
problem None explicitly stated, but related to algebraic structures.
method Study of handlebody versions of classical diagram algebras and reformulation of cellular algebras.
result All mentioned algebras are part of the reformulated cellular algebra theory.
This paper detects anomalies in cellular network traffic using hybrid methods.
problem Detecting anomalies in network traffic for security and analysis.
method Hybrid method combining GARCH, K-means, and Neural Network.
result Anomaly detection in cellular network traffic successfully achieved.
Optimizes antenna tilt for better QoS in cellular networks.
problem Hard to learn optimal antenna tilt policies in real networks due to risk and simulation gap.
method Uses off-policy Contextual Multi-Armed-Bandit (CMAB) techniques to learn from existing data.
result Trained policies show consistent improvements over existing logging policies.
IH-GAN models cellular structures accurately and improves structural performance.
problem Optimizing variable-density cellular structures with multiscale design challenges.
method Conditional deep generative model (IH-GAN) for property-to-geometry mapping using implicit function parameterization.
result Generates unit cells with high accuracy and improves structural performance.
Optimizes antenna settings in heterogeneous cellular networks using RL.
problem Complex interactions between cells cause optimization challenges.
method Two-step approach: offline multi-agent mean field RL, online single-agent deep RL.
result Approaches multi-agent RL performance with fewer trials.
The main results of this paper are: (1) If a space X can be embedded as a cellular subspace of Rn then X admits arbitrary fine open coverings whose nerves are homeomorphic to the n-dimensional cube Dn; (2) Every n-dimensional cell-like compactum can be embedded into (2n+1)-dimensional …
Hierarchical FL reduces latency in HCNs by sharing model updates.
problem Latency and privacy issues in federated learning across heterogeneous cellular networks.
method Hierarchical federated learning, gradient sparsification, periodic averaging.
result Significant reduction in communication latency without compromising model accuracy.
The study embeds graphs on translation surfaces, proving essential-systolic embeddings and estimating surface genera.
problem Embedding graphs on translation surfaces with specific properties.
method Proving essential-systolic embeddings and estimating surface genera.
result Finite graphs admit essential-systolic embeddings on translation surfaces with estimated genera.
CT improves neural network performance on cell complex data.
problem Improving predictive performance of neural networks on complex data.
method Introducing the Cellular Transformer (CT) that generalizes graph-based transformers to cell complexes.
result CT achieves state-of-the-art performance on cell complex datasets without complex enhancements.
PerturBench benchmarks ML models for cellular perturbation analysis.
problem Standardizing benchmarking in modeling single cell transcriptomic responses to perturbations.
method Modular platform, diverse datasets, metrics, extensive evaluation, rank metrics.
result Simpler models are competitive and scale well with larger datasets.