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.
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.
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.
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.
New framework for cyclic quantum causal models with graph separation property.
problem Understanding causal relationships in feedback processes and exotic scenarios.
method Introducing a robust probability rule and a novel graph-separation property, p-separation.
result Established graph-separation properties for all consistent cyclic causal models.
In the first part, we give a self contained introduction to the theory of cyclic systems in n-dimensional space which can be considered as immersions into certain Grassmannians. We show how the (metric) geometries on spaces of constant curvature arise as subgeometries of Moebius geometry which provides a slightly new v…
The paper solves the conjugacy problem in a specific braid group quotient and finds infinite virtually cyclic subgroups.
problem Solving the conjugacy problem in the Artin braid group quotient Bn/[Pn,Pn]. method Using systems of equations over the integers derived from the action of Bn/[Pn,Pn] on the abelianization of Pn/[Pn,Pn]. Also, explicitly realizing infinite virtually cyclic subgroups. result Explicitly realized infinite virtually cyclic subgroups in Bn/[Pn,Pn]. 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.
The virtually cyclic dimension of Out(F_N) is finite and related properties are established.
problem Understanding the virtually cyclic dimension of Out(F_N) and related properties.
method Proving properties of finite index congruence subgroups and using exact sequences.
result The virtually cyclic dimension of Out(F_N) is finite.
A new framework learns cyclic causal graphs from incomplete data.
problem Learning causal models in systems with feedback loops and missing data.
method MissNODAGS framework, alternating imputation and likelihood maximization.
result Improved performance compared to imputation followed by causal learning.
In this paper, we derive a maximum principle for a type of elliptic systems and apply it to analyze the Hitchin equation for cyclic Higgs bundles. We show several domination results on the pullback metric of the (possibly branched) minimal immersion f associated to cyclic Higgs bundles. Also, we obtain a lower and up…
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.
MissNODAG learns cyclic causal graphs from incomplete data.
problem Causal discovery in systems with feedback loops and missing data.
method Differentiable framework integrating additive noise model and expectation-maximization.
result MissNODAG uncovers cyclic structures and missingness mechanisms from partially observed data.
This paper provides a construction of a quantum statistical mechanical system associated to knots in the 3-sphere and cyclic branched coverings of the 3-sphere, which is an analog, in the sense of arithmetic topology, of the Bost-Connes system, with knots replacing primes, and cyclic branched coverings of the 3-sphere …
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.
Algorithm classifies saddle-focus singularities in Hamiltonian systems.
problem Classifying nondegenerate saddle-focus singularities in integrable Hamiltonian systems.
method Developed an algorithm based on semi-local equivalence to represent singularities as almost direct products.
result Obtained complete lists of saddle-focus singularities of complexities 1, 2, and 3.
We study the monodromy of meromorphic cyclic SL(n,C)-opers on the Riemann sphere with a single pole. We prove that the monodromy map, sending such an oper to its Stokes data, is an immersion in the case where the order of the pole is a multiple of n. To do this, we develop a method based on the wo…
Paper examines Go AI robustness against adversarial attacks.
problem Superhuman Go AIs are vulnerable to simple adversarial strategies.
method Three defenses tested: adversarial training, iterated adversarial training, and changing network architecture.
result No defense is robust against newly trained adversaries, and attacks are similar to cyclic attacks.
In addition to constraining bilateral exposures of financial institutions, there are essentially two options for future financial regulation of systemic risk (SR): First, financial regulation could attempt to reduce the financial fragility of global or domestic systemically important financial institutions (G-SIBs or D…
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…
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.
Paper studies Frobenius manifolds and quantum differential equations, proving Dubrovin Conjecture for Hirzebruch surfaces.
problem Quantum differential equations and their solutions in Gromov-Witten theory.
method Introduces cyclic strata, Borel-Laplace multitransforms, and integral representations.
result Proof of Dubrovin Conjecture for Hirzebruch surfaces.
The study explores autonomous systems and their connections to contact geometry and Frobenius manifolds.
problem Understanding the connections between autonomous systems and geometric structures.
method Investigation of the Darboux-Halphen-Ramanujan system, contact geometry, and Frobenius manifolds.
result Highlighting the role of contact geometry in autonomous systems.
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.
We consider a generalization of the notion of a natural mechanical system to the case of additional forces of gyroscopic type. Such forces appear, for example, as a result of global reduction of a natural system with symmetry. We study symmetries in the systems with gyroscopic forces to find out when these systems admi…
A contractible simplicial complex is constructed that parametrizes different ways of representing a fixed one-dimensional homology class in a closed orientable surface by isotopy classes of systems of disjoint oriented simple closed curves. This is a variant on an earlier construction of Bestvina-Bux-Margalit.
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.
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.
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 develop a structural default model for interconnected financial institutions in a probabilistic framework. For all possible network structures we characterize the joint default distribution of the system using Bayesian network methodologies. Particular emphasis is given to the treatment and consequences of cyclic fi…
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…
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.
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…
We establish causal semantics for SDEs and develop methods to reason about them.
problem Understanding causal relationships in systems modeled by stochastic differential equations.
method We introduce a causal graph framework, Markov properties, and do-calculus for SDEs.
result We prove the σ-separation Markov property and do-calculus for causal SDEs. 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.
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 …
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.
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.
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 …
New definite 4-manifolds found with non-cyclic groups.
problem Finding exotic smooth structures on 4-manifolds with specific fundamental groups.
method Constructing infinitely many non-diffeomorphic structures.
result Infinitely many pairwise non-diffeomorphic definite 4-manifolds with Z/2imesZ/2 fundamental group. We classify SU(2)-cyclic and SU(2)-abelian 3-manifolds, for which every representation of the fundamental group into SU(2) has cyclic or abelian image respectively, among geometric 3-manifolds which are not hyperbolic. As an application, we give examples of hyperbolic 3-manifolds which do not admit degree-1 maps …
Cyclic projections in Hadamard spaces can be irregular, unlike in Hilbert spaces.
problem Understanding the behavior of cyclic projections in Hadamard spaces compared to Hilbert spaces.
method Constructing an example of convex subsets in a Hadamard space.
result Cyclic product of projections is not asymptotically regular in Hadamard spaces.
Cyclic covers of knots uniquely determine the original knot.
problem Determining knots from their branched covers.
method Examining n-fold cyclic branched covers of alternating prime knots.
result The n-fold cyclic cover of an alternating prime knot uniquely determines the original knot.
New Heegaard Floer homology for orbifolds with cyclic singularities.
problem Defining Heegaard Floer homology for orbifolds with arbitrary cyclic singularities.
method Generalizing recent work by defining Heegaard Floer homology for orbifolds with arbitrary cyclic singularities.
result Defined a new Heegaard Floer homology for orbifolds with arbitrary cyclic singularities.