New connection found between cluster algebras and knot theory.
problem Connecting cluster algebras to knot theory and Jones polynomials.
method Using continued fractions and snake graphs.
result Direct formula for the Jones polynomial of 2-bridge links.
Snake solves large graph optimization problems with fast proximal steps.
problem Optimization over large unstructured graphs with graph-specific regularization.
method Snake algorithm using random simple paths for proximal gradient steps.
result Convergence proven for the Snake algorithm.
Study reveals CR structure of snake robot's geometry.
problem Understanding the kinematics and geometry of a snake robot.
method Analysis of (2,3,5) distributions and solving Cartan equivalence problem.
result Discovery of a CR structure with CR dimension 1 and real codimension 3.
Paper studies geometric and combinatorial properties of circular snakes.
problem Exploring geometric and combinatorial properties of circular snakes.
method Definition and investigation of outer Lipschitz geometry, decomposition of Valette link, construction of combinatorial objects, weakly outer Lipschitz classification.
result Existence of canonical decomposition and necessary/sufficient criteria for removing segments or Hölder triangles.
This paper generalizes knot polynomials to include the HOMFLY polynomial.
problem Generalizing knot polynomials to include the HOMFLY polynomial.
method Using path posets to directly generalize the construction of the Jones and Alexander polynomials to the HOMFLY polynomial.
result The HOMFLY polynomial is obtained by specializing path posets.
Lecture notes on Teichmüller spaces with boundary examples.
problem Understanding higher Teichmüller spaces of Riemann surfaces with boundaries.
method Explicit and computationally tractable examples, chewing-gum move, snake calculus.
result The chewing-gum move is the inverse of amalgamation in bordered cusped Teichmüller space.
Infinite rank surface cluster algebras extend traditional concepts to surfaces with accumulation points.
problem Extending surface cluster algebras to infinite surfaces with accumulation points.
method Consider infinite mutation sequences and hyperbolic structures to define cluster variables as lambda lengths of arcs.
result Established transitivity of infinite mutation sequences on triangulations of infinite surfaces and provided expansion formulas for cluster variables.
New q-deformed integers help compute Jones polynomials efficiently.
problem Computing Jones polynomials of rational links efficiently.
method Defining q-deformed integers from pairs of coprime integers and using them to compute Jones polynomials.
result Efficient algorithm for computing Jones polynomials of rational links.
The snake charmer algorithm permits us to deform a piecewise smooth curve starting from the origin in R^d, so that its end follows a given path. When this path is a loop, a holonomy phenomenon occurs. We prove that the holonomy orbits are closed manifolds diffeomorphic to real Stiefel manifolds. A survey of the snake c…
The purpose of this paper is to give a simpler proof to the problem of controllability of a Hilbert snake \cite{PeSa}. Using the action of the Möbius group of the unit sphere on the configuration space, in the context of a separable Hilbert space. We give a generalization of the Theorem of accessibility contained in \c…
A new snake model improves segmentation of SEM images.
problem Efficiently segmenting overlapping electronic structures in SEM images.
method Geodesic tracking on projective line bundle with a geometric criterion for switching between fast spatial snakes and minimizing geodesics.
result Improved robust and automatic segmentation of overlapping electronic structures in SEM images.
Quantum trace map connects Teichmüller theory and quantum groups.
problem Connecting quantum groups to Teichmüller theory for knots.
method Quantum snakes technology to relate Fock-Goncharov monodromy matrices to quantum SL_n.
result Quantized Fock-Goncharov matrices satisfy quantum SL_n relations.
Animal vision surpasses human tech, but we can't replicate their abilities.
problem Can we replicate animal vision capabilities?
method Comparing animal vision systems to human technological achievements.
result Human tech can't match animal vision capabilities.
Link Floer homology is split into snake complexes and local systems.
problem Classifying link Floer complexes over specific rings.
method Classifying isomorphism and chain homotopy equivalence classes of free chain complexes over a specific ring, then applying these results to link Floer complexes.
result Link Floer complexes split uniquely into snake complexes and local systems.
We show that the Snake on a square SC(S1) is homotopy equivalent to the space AC(S1) which was investigated in the previous work by Eda, Karimov and Repov\vs. We also introduce related constructions CSC(−) and CAC(−) and investigate homotopical differences between these four constructions. Finally, we explici…
We construct a privileged system of coordinates with respect to the controlling distribution of a trident snake robot and, furthermore, we construct a nilpotent approximation with respect to the given filtration. Note that all constructions are local in the neighbourhood of a particular point. We compare the motions co…
The paper examines addictive behaviors in RL agents using a modified Snake game.
problem The emergence of addictive behaviors in reinforcement learning agents.
method A modified Snake game was used to model addictive policies in Q-learning agents, and sufficient parametric conditions were derived for the emergence of addictive behaviors.
result The feasibility of addictive wireheading in RL agents was demonstrated, providing venues for further research.
Framework for multi-agent RL with human feedback in a Snake game.
problem Improving multi-agent reinforcement learning with human feedback.
method Developed a simulated game environment for offline model training and online competitions. Introduced HILL methods and reward manipulation heuristics.
result Agents with HILL methods outperform those without in online competitions.
Under appropriate assumptions, we generalize the concept of linear almost Poisson struc- tures, almost Lie algebroids, almost differentials in the framework of Banach anchored bundles and the relation between these objects. We then obtain an adapted formalism for mechanical systems which is illustrated by the evolution…
The paper encodes local shapes of polynomial curves using permutations.
problem Measuring non-convexity of real algebraic plane curves.
method Generic projections avoiding specific tangencies.
result Local shapes of curves can be encoded in alternating permutations.
Paper tackles CC generation for metrics in GR.
problem Finding CC for metrics in GR.
method Homological snake lemma approach.
result Link between CC, formal exactness, and FI.
This paper was motivated by work of Arnold where he explains how to count "snakes", i.e. Morse functions on the real axis with prescribed behavior at infinity. This leads immediately to a count of excellent Morse functions on the circle, where following Thom's terminology, excellent means that no two critical points li…
TAMIS improves MIA on synthetic data, reducing cost and requiring less knowledge.
problem Empirical assessment of privacy in machine learning algorithms.
method Improves MAMA-MIA by recovering graphical model from synthetic data and introducing a more accurate attack score.
result TAMIS achieves better or similar performance to MAMA-MIA on synthetic data challenges.
The paper explores infinite-dimensional nonholonomic and vakonomic systems.
problem Understanding dynamics of infinite-dimensional systems with constraints.
method Visualizing and revisiting classical and new examples of nonholonomic and vakonomic systems.
result Infinite-dimensional systems exhibit both nonholonomic and vakonomic dynamics.
Study of electronic corn futures trading shows discrete price changes and non-Gaussian distributions.
problem Discrepancy between theoretical continuous price models and actual intra-day trading data.
method Analysis of discrete price increments, volume, and profit strategies using statistical distributions and probability theory.
result Kumaraswamy distribution better fits waiting times than Weibull, and price jumps resemble branching reactions.
Line graph transformation aids graph isomorphism tests by excluding challenging graph properties.
problem Limited theoretical understanding of line graph transformation's impact on GNN models.
method Examined CFI and strongly regular graphs, showing line graph transformation helps WL tests distinguish these graphs.
result Line graph transformation aids WL tests in distinguishing challenging graph properties.
Proposes MGMN for end-to-end graph similarity learning.
problem Lack of cross-level interactions in graph similarity learning.
method Multi-level graph matching network (MGMN) combining node-graph matching and siamese graph neural networks.
result MGMN outperforms state-of-the-art models on graph-graph classification and regression tasks.
GWNN uses graph wavelets for efficient graph CNNs.
problem Spectral graph CNNs' high computational cost and lack of interpretability.
method Graph wavelet transform for efficient graph convolution.
result GWNN significantly outperforms spectral graph CNNs.
The paper explores graphons of line graphs from sparse finite graphs.
problem Estimating graph limits from sparse finite graphs.
method Mapping finite graphs to their line graphs and analyzing graphs with the square-degree property.
result Graphons of line graphs can distinguish between sparse graphs like star graphs and superlinear preferential attachment graphs.
edGNN improves graph embeddings for directed labeled graphs.
problem Improving node and graph embeddings for directed labeled graphs.
method edGNN is a GNN designed for directed labeled graphs, leveraging both topology and labels.
result edGNN is as powerful as the Weisfeiler-Lehman algorithm for graph isomorphism.
Graph CNNs adapt to varying graph structures for better performance.
problem Fixed graph structures limit the performance of Graph CNNs on real data.
method Adaptive graph learning and distance metric learning for efficient graph construction.
result Adaptive Graph CNNs improve convergence speed and predictive accuracy on various graph datasets.
MxPool learns graph features from diverse graphs using a hierarchical structure.
problem Learning graph features from diverse graphs with varying properties and sizes.
method MxPool uses a multiplex structure with multiple graph convolution/pooling networks in a hierarchical learning structure.
result MxPool outperforms state-of-the-art methods on graph classification benchmarks.
Study the geometry of graph product extension graphs.
problem Properties of graph products.
method Introduce and study the extension graph of graph products of groups.
result Extension graph is isomorphic to crossing graph of a quasi-median graph and exhibits asymptotic dimension similar to quasi-trees.
Graph neural network learns graph distances effectively.
problem Maintaining graph distance metric properties.
method GRAPH-BERT based semi-supervised distance metric learning.
result GB-DISTANCE outperforms existing methods.
UGRAPHEMB embeds graphs into vectors preserving their proximity, achieving competitive results.
problem Graph-level representation learning in an unsupervised and inductive manner.
method UGRAPHEMB uses graph-graph proximity to embed graphs into a vector space. MSNA generates multi-scale node attention for graph-level embedding.
result UGRAPHEMB achieves competitive accuracy in graph classification, similarity ranking, and visualization tasks.
Quasi-transitive graphs quasi-isometric to planar graphs can be upgraded to Cayley graphs.
problem Quasi-transitive graphs quasi-isometric to planar graphs need to be upgraded to Cayley graphs.
method Upgrading a planar graph to a Cayley graph.
result Quasi-transitive graphs quasi-isometric to planar graphs can be upgraded to Cayley graphs.
Deep Divergence Graph Kernels learn graph representations without supervision.
problem Learning graph representations without feature engineering or labeled graphs.
method Unsupervised method using cross-graph attention networks and divergence scores.
result Learned representations achieve competitive results on graph classification tasks.
Paper proposes a new graph embedding framework to improve graph analytics.
problem Graph embedding often fails to capture the distribution of latent codes.
method Adversarial graph autoencoder framework that combines topological structure and node content.
result ARGA and ARVGA outperform baselines in link prediction, clustering, and visualization.
GRAPH-BERT uses only attention for graph representation learning.
problem Graph neural networks over-rely on graph links and suffer from performance issues.
method GRAPH-BERT uses only attention mechanism without graph convolution or aggregation, trained on sampled subgraphs.
result GRAPH-BERT outperforms existing GNNs in learning effectiveness and efficiency.
Customized-GNN generates model-specific for each graph.
problem Graphs in the same dataset have distinct structures.
method Proposes Customized-GNN framework to generate model-specific for each graph.
result Demonstrates effectiveness on various graph classification benchmarks.
Graph embedding leaks sensitive graph properties and subgraphs.
problem Privacy risks in graph embedding sharing.
method Three inference attacks and a defense mechanism.
result High accuracy in inferring graph properties and subgraphs.
Graph ConvNets outperform RNNs in graph learning tasks.
problem Designing neural networks for graphs with variable length.
method Compare graph RNN and ConvNet architectures, propose extensions, and conduct controlled experiments.
result Graph ConvNets are more accurate and faster than graph RNNs.
Characterizes graphs with leveled embeddings and introduces new graph invariants.
problem Understanding the properties of leveled embeddings in spatial graphs.
method Characterization of graphs with leveled embeddings, introduction of new invariants.
result Characterization of graphs with low level number and determination of specific invariants for complete graphs and complete bipartite graphs.
HGP-SL pools and learns graph structure for hierarchical representation learning.
problem Graph pooling is overlooked in GNN models, limiting hierarchical representation learning.
method Integrates graph pooling and structure learning into a unified module.
result HGP-SL improves graph classification performance on benchmarks.
The paper shows conflict graphs of Petersen family graphs are mostly unbalanced.
problem Understanding the balance of conflict graphs in Petersen family graphs.
method Analyzing maximally planar subgraphs and their conflict graphs.
result All but three strong conflict graphs from Petersen Family Graphs are unbalanced.
Two new methods improve graph embedding without needing a complete graph structure.
problem Graph autoencoders' performance depends on the adjacency matrix quality.
method BAGE and VBAGE: unsupervised graph embedding via adaptive graph learning.
result The methods expand GAEs' applicability to datasets without graph structure.
GSimCNN predicts graph similarity using CNNs, outperforming existing methods.
problem Challenging pairwise graph similarity computation due to NP-hardness.
method Graph Edit Distance (GED) as core metric, GSimCNN (Convolutional Neural Networks).
result State-of-the-art performance on graph similarity search.
We define a pseudo-inverse for line graphs using linear integer programming.
problem Not all graphs have a corresponding root graph, making the line graph operation non-invertible.
method Propose a linear integer program to edit the smallest number of edges in the line graph to recover a root graph.
result The pseudo-inverse operation is well-behaved and works in practice as shown by empirical experiments.