In this note we derive enumerative formulas for several types of labelled acyclic directed graphs by slight modifications of the familiar recursive formula for simple acyclic digraphs. These considerations are motivated by, and based upon, recent combinatorial results in geometric topology obtained by S.Choi, who estab…
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48 results for “Acyclic digraphs”
Directed acyclic graphs are the basic representation of the structure underlying Bayesian networks, which represent multivariate probability distributions. In many practical applications, such as the reverse engineering of gene regulatory networks, not only the estimation of model parameters but the reconstruction of t…
In the present paper we find a bijection between the set of small covers over an -cube and the set of acyclic digraphs with labeled nodes. Using this, we give a formula of the number of small covers over an -cube (generally, a product of simplices) up to Davis-Januszkiewicz equivalence classes and $\mathbf{Z}…
New algorithm improves MCMC for Bayesian network structure learning.
problem Learning the structure of Bayesian networks from data.
method Partition MCMC, employing combinatorial structure of DAGs.
result Improved convergence of the sampler compared to structure MCMC.
Develops new classifiers using proximity catch digraphs for better class imbalance handling.
problem Class imbalance in classification problems.
method Constructs semi-parametric classifiers using random geometric digraphs called proximity catch digraphs (PCDs).
result PE-PCDs find exact minimum dominating sets in polynomial time, leading to efficient classifiers.
Parameter-free clustering method using cluster catch digraphs (CCDs).
problem Finding the correct number of clusters in data without specifying a parameter.
method Hybrid of density-based and graph-based clustering methods using Ripley's K function.
result Minimum dominating sets of RK-CCDs estimate and distinguish clusters from noise.
New spectral clustering for directed graphs reveals socio-economic patterns.
problem Spectral clustering for directed graphs is unsatisfactory due to edge directionality.
method Proposes a complex-valued matrix representation and analysis for directed graphs.
result Our approach reveals socio-economic patterns in internal migration data.
Two new outlyingness scores improve outlier detection in high-dimensional data.
problem Detecting outliers in high-dimensional data with varying cluster shapes and intensities.
method Outlyingness scores (OOS and IOS) based on Cluster Catch Digraphs (CCDs).
result Both OOS and IOS outperform CCD-based methods in identifying global and local outliers, especially IOS.
A graph (digraph) with a set of terminals is called inner Eulerian if each nonterminal node has even degree (resp. the numbers of edges entering and leaving are equal). Cherkassky and Lovász showed that the maximum number of pairwise edge-disjoint -paths in an inner Eulerian graph $G…
Directed graphs can contain arbitrarily complex knots and links.
problem Proving the existence of directed graphs with arbitrarily complex knots and links.
method Proved the existence of a directed graph with an intrinsic -component link and an oriented link with specific properties.
result Directed graphs can contain arbitrarily complex knots and links, with specific properties of link components and their Conway polynomials.
New algorithms detect outliers in high-dimensional data with arbitrary shapes.
problem Challenges of high dimensionality and varying cluster shapes in traditional outlier detection methods.
method Cluster Catch Digraphs (CCDs) and their variants (U-MCCD, UN-MCCD, SU-MCCD, SUN-MCCD).
result U-MCCD efficiently identifies outliers with high true negative rates, and SU-MCCD improves handling of non-uniform clusters.
A new graph-based clustering method for moderate-dimensional data.
problem Performance degradation of existing graph-based clustering methods in high dimensions.
method Introduces UN-CCDs using NND-based MC-SRT for covering radii determination.
result UN-CCDs provide stable and competitive performance in moderate-sized datasets.
CCCDs tackle class imbalance in classification.
problem Class imbalance in statistical classification.
method Class cover catch digraphs (CCCDs) for graph theoretic solutions.
result CCCD classifiers perform well in class imbalance scenarios.
ParPIC clusters directed graphs using random walks and diffusion operators.
problem Challenges in vertex-level clustering for directed graphs due to edge directionality.
method Parametrized Power-Iteration Clustering (ParPIC) based on reversible random walks and diffusion operators.
result ParPIC achieves competitive clustering accuracy with improved scalability compared to spectral and teleportation-based methods.
We prove an explicit formula of the Berezin star product on Kaehler manifolds. The formula is expressed as a summation over certain strongly connected digraphs. The proof relies on a combinatorial interpretation of Englis' work on the asymptotic expansion of the Laplace integral.
Directed graphs can be intrinsically knotted and 4-linked.
problem Intrinsic linking and knotting in directed graphs.
method Construction of examples and operations (consistent edge contraction, H-cyclic subcontraction).
result Directed graphs can have consistently oriented knotted cycles and intrinsically 3- and 4-linked structures.
Study financial contagion and risk in sparse networks with directed edges.
problem Analyzing systemic risk in sparse financial networks with balance-sheet interactions.
method Linear fraction of institutions with zero out-degree, sender-truncated subgraph G_sh, adversarial and random systemic events, explicit fan-in accumulation bound.
result Maximal forward reachability in G_sh is O(log n) with high probability in the subcritical regime, and multi-hit defaults are negligible in the supercritical regime.
Java implementation improves nearest neighbor algorithm complexity.
problem Improving efficiency of nearest neighbor descent algorithm.
method Parallel streams implementation with statistical termination criterion.
result Complexity up to for -nearest neighbors.
GNNRank uses neural networks to learn global rankings from competition match data.
problem Learning global rankings from pairwise comparisons in directed graphs.
method Proposes GNNRank, a trainable GNN-based framework with digraph embedding and new objectives.
result GNNRank achieves competitive and superior performance compared to baselines.
We explore non-acyclic GFlowNets in discrete settings.
problem Training and understanding non-acyclic GFlowNets in discrete environments.
method Relaxing acyclicity assumption, simpler theoretical framework, novel theoretical insights, experimental validation.
result Theoretical and experimental validation of non-acyclic GFlowNets in discrete environments.
COSMO learns DAG structure without acyclicity constraints.
problem Learning DAG structure from data efficiently and without constraints.
method Differentiable approximation of smooth orientation matrix.
result COSMO converges to acyclic solutions without evaluating acyclicity.
Acyclicity proven for curve complex on surfaces.
problem Acyclicity of curve complex on surfaces.
method Analyzing homologous curves on surfaces of genus g.
result Complex is (g-3)--acyclic.
We show a relationship between the non-acyclic Reidemeister torsion and a zero of the acyclic Reidemeister torsion for a lambda-regular SU(2) or SL(2, C)-representation of a knot group. Then we give a method to calculate the non-acyclic Reidemeister torsion of a knot exterior. We calculate a new example and investigate…
New method learns DAGs from data without acyclicity constraint.
problem Learning DAGs from data without imposing acyclicity.
method Sparse matrix factorization and -penalized optimization.
result Empirical success in recovering true graphs and almost-DAG graphs.
It has been known since 1981 that if one fixes an orientable surface of genus , then there is a real number that is the dilatation of a pA diffeomorphism of , and every other pA diffeomorphism of has dilatation . We will show how a little-known theorem about digraphs gives …
It has been known since 1981 that if one fixes an orientable surface of genus , then there is a real number that is the dilatation of a pA diffeomorphism of , and every other pA diffeomorphism of has dilatation . We will show how a little-known theorem about digraphs gives …
New proof for knot state-sum formula using bijection between states.
problem Proving a knot state-sum formula for colored Jones polynomial.
method Established bijection between states on arc-graph and bichromatic digraph, used flow property of R-matrix.
result Two state models are essentially the same, extending formula to links.
ALIAS uses RL to learn DAGs without acyclicity constraints.
problem Efficiently learning DAGs from observational data without acyclicity constraints.
method ALIAS employs RL to generate DAGs in a single step with optimal complexity, bypassing acyclicity constraints.
result ALIAS outperforms state-of-the-art methods in causal discovery.
Develops a new method for learning non-parametric DAGs using RKHS.
problem Challenges of learning non-parametric causal models with large combinatorial search space.
method Uses reproducing kernel Hilbert spaces (RKHS) and sparsity-inducing regularization terms based on partial derivatives to enforce acyclicity.
result Shows improved performance through simulations and data analyses.
We give a geometric proof of the following result of Juhasz. \emph{Let be the leading coefficient of the Alexander polynomial of an alternating knot . If then has a unique minimal genus Seifert surface.} In doing so, we are able to generalise the result, replacing `minimal genus' with `incompress…
The acyclic group dichotomymath.GR
Two extremal classes of acyclic groups are discussed. For an arbitrary group G, there is always a homomorphism from an acyclic group of cohomological dimension 2 onto the maximum perfect subgroup of G, and there is always an embedding of G in a binate (hence acyclic) group. In the other direction, there are no nontrivi…
ENCOD learns causal graphs efficiently without acyclicity constraints.
problem Learning causal graphical models from observational and interventional data.
method ENCOD uses optimization of edge likelihoods with separate orientation parameters.
result ENCOD efficiently recovers large graphs (hundreds of nodes) without acyclicity constraints.
Deep Q-learning generates directed acyclic graphs.
problem Generating DAGs with specified structures.
method Deep reinforcement learning, specifically deep Q-learning.
result Demonstrated capability of generating DAGs in sparse reward environments.
We give a Dehn-Nielsen type theorem for the homology cobordism group of homology cylinders by considering its action on the acyclic closure, which was defined by Levine, of a free group. Then we construct an additive invariant of those homology cylinders which act on the acyclic closure trivially. We also describe some…
New results on relative simplicial volume using bounded acyclicity.
problem Understanding relative simplicial volume in bounded cohomology.
method Equivariant nerve pairs, relative classifying spaces, and small relative amenable category.
result Vanishing results for -Betti numbers and mapping degrees.
Proves condition for 4-manifolds with sphere boundary to be standard.
problem Determining when acyclic 4-manifolds with sphere boundary are standard.
method Uses Turaev's shadows to provide a sufficient condition for diffeomorphism to the standard 4-ball.
result If a compact, smooth, acyclic 4-manifold with sphere boundary has shadow-complexity at most 2, it is diffeomorphic to the standard 4-ball.
The paper explores conditions for homology spheres to bound acyclic smooth manifolds and symplectic fillings.
problem Conditions for integral homology 3-spheres to bound acyclic smooth 4-manifolds and their symplectic fillings.
method Structural results and analysis of smooth embeddings of lens spaces in .
result Smooth embeddings of connected sums of lens spaces in cannot be upgraded to Stein embeddings.
Proposes an approach to ensure acyclic graphs in Bayesian structure learning.
problem Ensuring acyclic graphs in Bayesian structure learning.
method Integration of knowledge from topological orderings to constrain acyclicty.
result Outperforms related Bayesian score-based approaches in experiments.
We consider finite groups which admit a faithful, smooth action on an acyclic manifold of dimension three, four or five (e.g. euclidean space). Our first main result states that a finite group acting on an acyclic 3- or 4-manifold is isomorphic to a subgroup of the orthogonal group O(3) or O(4), respectively. The analo…
We determine which 3-manifolds admit a unitary representation such that the corresponding twisted chain complex is acyclic.
Proposes an evolutionary approach to fitting acyclic VAR models.
problem Cycles in multivariate time series systems obscure hierarchical analysis.
method Evolutionary approach to fitting acyclic VAR processes with hierarchical representation.
result Outperforms unconstrained models and captures key structural properties.
Solves linearity problem for acyclic groups, bounds Cheeger-Gromov ρ-invariants.
problem Linearity problem for acyclic groups and Cheeger-Gromov ρ-invariants.
method Quantitative algebraic and geometric techniques over simplicial classifying spaces.
result Universal linear bound for Cheeger-Gromov ρ-invariants of PL (4k-1)-manifolds.
J. Przytycki has established a connection between the Hochschild homology of an algebra and the chromatic graph homology of a polygon graph with coefficients in . In general the chromatic graph homology is not defined in the case where the coefficient ring is a non-commutative algebra. In this paper we define a …
DAGMA learns DAGs faster and more accurately using log-determinant acyclicity.
problem Learning directed acyclic graphs from data efficiently and accurately.
method DAGMA uses M-matrices and log-determinant acyclicity to optimize DAG learning.
result DAGMA achieves faster and more accurate DAG learning compared to existing methods.
Smooth actions on certain 3-spheres can't extend to acyclic 4-manifolds.
problem Smooth actions on Brieskorn homology 3-spheres that bound acyclic 4-manifolds.
method Equivariant Yang-Mills moduli spaces
result No smooth extensions of actions to acyclic 4-manifolds.
What discuss the problem of obtaining new manifold invariants via different analogues of 6j-symbols and the torsion of acyclic complexes.
The paper tackles learning varying DAG structures based on contextual features.
problem Learning a single DAG for the entire population from observational data.
method A neural network that maps contextual features to a weighted adjacency matrix of a DAG, with a projection layer to ensure acyclicity.
result The new approach can recover context-specific DAGs where existing methods fail.
Rational acyclic resolutionsmath.GT
Let X be a compactum such that dim_Q X < n+1, n>1. We prove that there is a Q-acyclic resolution r: Z-->X from a compactum Z of dim < n+1. This allows us to give a complete description of all the cases when for a compactum X and an abelian group G such that dim_G X < n+1, n>1 there is a G-acyclic resolution r: Z-->X fr…