Develops a new framework for causal models on cyclic graphs, solving unique solvability issues.
problem Challenges in specifying unique probability distributions for cyclic functional causal models.
method Introduces a new probability rule and graph-separation property (p-separation) for cyclic fCMs.
result Proves p-separation is sound and complete for all consistent cyclic fCMs, recovering d-separation for DAGs.
Cycles in causal learning cause feedback loops under intervention.
problem Cyclic causal structures lead to feedback loops in causal inference.
method Theoretical observations about self-referential distributions and their factorizations.
result Cyclic causal dependence can exist even when observational data suggest independence.
Study counterfactuals in cyclic systems with shifts and scales.
problem Counterfactual inference in cyclic systems with shifts and scales.
method Shift-scale interventions in cyclic SCMs.
result Valid inference in cyclic systems with shifts and scales.
Solves Nekhoroshev's problem on invariant tori for Hamiltonian systems with cyclic variables.
problem Finding invariant isotropic tori under Hamiltonian phases flows with involution Hamilton functions.
method Constructs monodromy operator and provides conditions for existence and uniqueness of complex germ without simple spectrum condition.
result Full solution to Nekhoroshev's problem, including Hamiltonian systems with cyclic variables.
Causal processes in nature may contain cycles, and real datasets may violate causal sufficiency as well as contain selection bias. No constraint-based causal discovery algorithm can currently handle cycles, latent variables and selection bias (CLS) simultaneously. I therefore introduce an algorithm called Cyclic Causal…
Geometric phases describe how in a continuous-time dynamical system the displacement of a variable (called phase variable) can be related to other variables (shape variables) undergoing a cyclic motion, according to an area rule. The aim of this paper is to show that geometric phases can exist also for discrete-time sy…
We solve structure learning for cyclic linear causal models using observational data.
problem Learning the structure of cyclic linear causal models from observational data.
method Assuming simple graphs, we use a criterion for distributional equivalence and implement a greedy search method.
result We show that simple cyclic models are of expected dimension and justify score-based methods for structure learning.
Recent techniques built on Generative Adversarial Networks (GANs), such as Cycle-Consistent GANs, are able to learn mappings among different domains built from unpaired datasets, through min-max optimization games between generators and discriminators. However, it remains challenging to stabilize the training process a…
New method tackles complex systems with hidden confounders and feedback loops.
problem Understanding complex systems with hidden confounders and feedback loops.
method Robust Causal Analysis of Linear Cyclic Systems with Hidden Confounders (LLC)
result LLC method can robustly analyze cyclic systems with hidden confounders.
DCCD-CONF discovers causal graphs with unmeasured confounders.
problem Discovering causal relationships in systems with unmeasured confounders.
method Differentiable learning of nonlinear cyclic causal graphs using interventional data.
result DCCD-CONF outperforms state-of-the-art methods in causal graph recovery and confounder identification.
Develop a variational framework for statistical inference on cyclic interactions.
problem Estimating and comparing large-scale recurrent organization in directed interactions.
method Represent directed interactions as edge flows on a simplicial complex and evolve under an energy-minimizing dynamical system.
result Separate transient interaction components from persistent harmonic flows, yielding a low-dimensional cycle space.
Two criteria for a closed connected definite 4-manifold with infinite cyclic fundamental group to be TOP-split are given. One criterion extends a sufficient condition made in a previous paper. The result is equivalent to a purely algebraic result on the question asking when a positive definite Hermitian form over the r…
Clusterpath estimator simplifies graphical model interpretation for large datasets.
problem Difficulty in interpreting graphical models with many variables.
method Clusterpath estimator that groups variables for block-structured precision matrix.
result CGGM outperforms other methods in variable clustering and practical applications.
New framework learns nonlinear cyclic causal models from data.
problem Challenges in learning causal relationships from real-world, cyclic systems.
method NODAGS-Flow: a novel framework using residual normalizing flows for likelihood estimation.
result Significant performance improvements in structure recovery and predictive performance compared to state-of-the-art methods.
New Alexander invariant classes computed for knot group representations.
problem Computing Alexander invariants for knot group representations.
method Introducing a new K1-class and comparing it with existing classes. result Showed a relation to Reidemeister torsions and reciprocity.
The Trek Separation Theorem (Sullivant et al. 2010) states necessary and sufficient conditions for a linear directed acyclic graphical model to entail for all possible values of its linear coefficients that the rank of various sub-matrices of the covariance matrix is less than or equal to n, for any given n. In this pa…
We characterize distributional equivalence in latent-variable models with cycles.
problem Lack of an equivalence characterization for latent-variable causal models with cycles.
method Established graphical criterion for distributional equivalence and developed edge rank constraints.
result First equivalence characterization without structural assumptions for latent-variable models with cycles.
RECLAIM discovers causal graphs in cyclic, noisy systems.
problem Discovering causal relationships in cyclic, noisy systems.
method RECLAIM uses EM with residual normalizing flows to handle cycles and noise.
result RECLAIM effectively discovers causal graphs in both synthetic and real-world datasets.
Wavelet analysis reveals non-linear dynamics in cryptocurrency prices.
problem Understanding non-linear dynamics in high-frequency cryptocurrency prices.
method Wavelet analysis of frequency and time variables.
result Cyclical persistence at different frequencies in cryptocurrency prices.
In this survey, a short introduction in the recent discovery of log-normally distributed market-technical trend data will be given. The results of the statistical evaluation of typical market-technical trend variables will be presented. It will be shown that the log-normal assumption fits better to empirical trend data…
This work constructs a finite-dimensional projective representation for a quantum Teichmüller model.
problem Quantum Teichmüller theory and its finite-dimensional representation.
method Explicit construction using cyclic quantum dilogarithm and mutations of coefficients.
result Reconstruction of quantum Teichmüller space with explicit intertwiners.
Develops a model for causal discovery in path spaces.
problem Discover causal relationships in path spaces using asymmetric independence.
method Theory linking E-separation in DMGs to conditional independence in SDEs, proving global Markov property, characterizing equivalence classes of graphs.
result Each equivalence class of graphs has a greatest element as a parsimonious representation, which can be identified from data.
This paper introduces 'General Cyclical Training' for neural networks.
problem Improving training efficiency and performance of neural networks.
method Cyclical training phases with varying hyperparameters, batch sizes, loss functions, and data augmentation.
result Cyclical weight decay, softmax temperature, and gradient clipping enhance model accuracy.
A new method learns DAGs from Gaussian data without verifying acyclicity.
problem Learning DAGs from Gaussian data without verifying acyclicity.
method Relaxation technique for permutation matrix estimation and cyclic coordinatewise descent for sparse Cholesky factor estimation.
result The method recovers DAGs without verifying acyclicity constraints.
The paper generalizes cyclic metrics in homogeneous Finsler geometry.
problem Understanding cyclic metrics in homogeneous Finsler spaces.
method Generalization of cyclic metrics, proving conditions for symmetry, and constructing cyclic metrics.
result A Finsler cyclic Lie group with an Abelian Lie algebra.
Characterizes non-degenerate cyclic metric Lie algebras.
problem Understanding the structure of non-solvable cyclic metric Lie algebras.
method Using sufficient conditions, cyclic quadruples, and double extension method.
result Complete characterization of non-degenerate cyclic metric Lie algebras.
In this paper we study the connections between cyclic presentations of groups and branched cyclic coverings of (1,1)-knots. In particular, we prove that every n-fold strongly-cyclic branched covering of a (1,1)-knot admits a cyclic presentation for the fundamental group encoded by a Heegaard diagram of genus n.
New method selects direct causal parents from large sets of variables.
problem Inferring direct causal parents from many variables, especially nonlinear and cyclic.
method One-vs.-the-rest feature selection approach with theoretical guarantees.
result Significant improvements over existing methods.
The study classifies and explores SU(2)-cyclic and SU(2)-abelian 3-manifolds.
problem Classifying SU(2)-cyclic and SU(2)-abelian 3-manifolds. method Analysis of geometric 3-manifolds and representation theory of fundamental groups.
result Examples of hyperbolic 3-manifolds with specific properties.
Proves almost profinite rigidity for certain free-by-cyclic groups.
problem Profinite rigidity of free-by-cyclic groups.
method Analyzes ranks of fibres, characteristic polynomials, and stretch factors of monodromies.
result Generic free-by-cyclic groups are almost profinitely rigid.
We study the connections among the mapping class group of the twice punctured torus, the cyclic branched coverings of (1,1)-knots and the cyclic presentations of groups. We give the necessary and sufficient conditions for the existence and uniqueness of the n-fold strongly-cyclic branched coverings of (1,1)-knots, thro…
New cyclicity measures defined in weighted Besov spaces, with stability and geometric analysis.
problem Characterizing cyclicity in weighted Besov spaces.
method Defining cyclicity indices based on potential theory and capacity, studying stability under perturbations, and linking zero set structure to cyclicity.
result Novel invariants and conditions for cyclicity in various function spaces.
We refine the cyclic cohomological apparatus for computing the Hopf cyclic cohomology of the Hopf algebras associated to infinite primitive Cartan-Lie pseudogroups, and for the transfer of their characteristic classes to foliations. The main novel feature is the precise identification as a Hopf cyclic complex of the im…
We propose a simple method to learn linear causal cyclic models in the presence of latent variables. The method relies on equilibrium data of the model recorded under a specific kind of interventions ("shift interventions"). The location and strength of these interventions do not have to be known and can be estimated f…
Complex systems can be modelled at various levels of detail. Ideally, causal models of the same system should be consistent with one another in the sense that they agree in their predictions of the effects of interventions. We formalise this notion of consistency in the case of Structural Equation Models (SEMs) by intr…
In this paper, we study quandles of cyclic type, which form a particular subclass of finite quandles. The main result of this paper describes the set of isomorphism classes of quandles of cyclic type in terms of certain cyclic permutations. By using our description, we give a direct classification of quandles of cyclic…
Study compares causal discovery methods for cyclic models with hidden confounders.
problem Detect causal directions in cyclic systems with hidden confounders.
method Comprehensive comparison of four causal discovery techniques.
result Performance varies across different experimental setups and dataset sizes.
Cyclical learning rates improve DRL performance without manual tuning.
problem Manual hyperparameter tuning in DRL is time-consuming and error-prone.
method Proposes cyclical learning rates for DRL problems.
result Cyclical learning achieves similar or better results than fixed learning rates.
The paper investigates cyclic arbitrage opportunities in decentralized exchanges.
problem Price discrepancies in decentralized exchanges lead to arbitrage opportunities.
method Theoretical framework and analysis of transaction-level data.
result Traders have executed over 292,606 cyclic arbitrages over eleven months, exploiting more than 138 million USD in revenue.
Unified rigidity theorem for cyclic and alternating surfaces.
problem Infinitesimal rigidity of equivariant minimal maps.
method Unified Lie-theoretic framework connecting cyclic surfaces and cyclic harmonic bundles.
result Infinitesimal rigidity for irreducible cyclic surfaces under various variations.
This paper tackles causal interactions in mixtures of DAGs using interventions.
problem Learning causal interactions among variables governed by a mixture of causal systems.
method Establishes necessary and sufficient conditions for intervention size, designs an adaptive algorithm.
result Identifies true edges in a mixture of DAGs using optimal or near-optimal interventions.
In spin geometry, traceless cyclic homogeneous Riemannian manifolds equipped with a homogeneous spin structure can be viewed as the simplest manifolds after Riemannian symmetric spin spaces. In this paper, we give some characterizations and properties of cyclic and traceless cyclic homogeneous Riemannian manifolds and …
This paper characterizes the equilibrium in a continuous time financial market populated by heterogeneous agents who differ in their rate of relative risk aversion and face convex portfolio constraints. The model is studied in an application to margin constraints and found to match real world observations about financi…
The abstract introduces a new cyclic structure for surfaces.
problem Defining a cyclic structure for surfaces.
method Endowing surfaces with a structure of a (co)cyclic object in 3D cobordisms.
result 3D TQFTs induce (co)cyclic modules, which are computed algebraically.
Study integrable discretizations of cyclic systems with circular coordinate lines.
problem Integrable discretizations of 3D cyclic systems with circular coordinate lines.
method Investigate circle congruences and flat connections in the context of discrete cyclic systems.
result Characterization of circle congruences and existence of certain flat connections.
We give a construction of cyclic cocycles representing the equivariant characteristic classes of equivariant bundles. Our formulas generalize Connes' Godbillon-Vey cyclic cocycle. An essential tool of our construction is Connes-Moscovici's theory of cyclic cohomology of Hopf algebras.
Proved Farrell-Jones conjecture for free-by-cyclic groups.
problem Proving the Farrell-Jones conjecture for a specific class of groups.
method Geometric methods for establishing the Farrell-Jones Conjecture.
result Proved the Farrell-Jones conjecture for free-by-cyclic groups.
A surgery on a knot in 3-sphere is called SU(2)-cyclic if it gives a manifold whose fundamental group has no non-cyclic SU(2) representations. Using holonomy perturbations on the Chern-Simons functional, we prove that the distance of two SU(2)-cyclic surgery coefficients is bounded by the sum of the absolute values of …