New model identifies patient-specific disease root causes.
problem Identifying root causes of complex diseases varying between patients.
method Generalized Root Causal Inference (GRCI) algorithm for heteroscedastic noise model.
result GRCI accurately extracts patient-specific root causes.
A new method simulates square-root processes efficiently.
problem Simulating square-root processes accurately and efficiently.
method Simulate the integrated square-root process instead of the square-root process itself.
result High precision with low number of time steps, and exact limiting Inverse Gaussian distributions.
Identifies patient-specific root causes of disease using structural equation models.
problem Detecting significant variables in complex diseases that differ between patients.
method Defining patient-specific root causes as exogenous errors in a structural equation model, quantifying predictivity using Shapley values, and developing a fast algorithm called Root Causal Inference.
result Significant improvements in accuracy by uncovering root causes with large effect sizes at the individual level but clinically insignificant effect sizes at the group level.
A new probability distribution on full rooted trees helps in model selection.
problem Model selection for full rooted trees is problematic due to their hierarchical structure.
method Assume a prior distribution on full rooted trees, using Bayes decision theory.
result The proposed distribution enables optimal model selection and prevents overfitting.
Study finds root vertex in large networks with high probability.
problem Finding the root vertex in large growing networks.
method Constructs confidence sets for the root vertex in various random network models.
result Confidence sets of size independent of the number of vertices contain the root vertex with high probability.
Paper simplifies calculating causation probabilities and ranks root causes.
problem Computational challenges in assessing causal relationships.
method Algorithmic simplifications and novel methodological framework for Root Cause Analysis.
result Significantly reduces computational complexity for calculating causation probabilities.
New method identifies root causes in presence of latent confounding.
problem Identifying root causes in the presence of latent variables.
method Extract Errors with Latents (EEL) procedure for inferring root causes.
result Superior accuracy and robustness compared to previous methods.
The paper proposes a new probability distribution for rooted trees.
problem Overfitting in tree selection for statistical models.
method Bayesian approach with a generalized probability distribution for rooted trees.
result Recursive methods to evaluate the probability distribution without approximations.
Two-root Riemannian manifolds have no odd-dimensional examples.
problem Characterizing Riemannian manifolds with specific eigenvalues of the Jacobi operator.
method Investigation of k-root manifolds, focusing on one-root and two-root cases. result There are no two-root Riemannian manifolds of odd dimension.
New framework for root-cause analysis in complex CPSs using spatiotemporal graphical modeling.
problem Anomaly detection and root-cause analysis in complex cyber-physical systems (CPSs).
method Spatiotemporal graphical modeling based on symbolic dynamics.
result Approaches S3 and A3 achieve high accuracy in root-cause analysis under various fault scenarios. In this paper, we characterize locally dually flat generalized m-th root Finsler metrics. Then we find a condition under which a generalized m-th root metric is projectively related to a m-th root metric. Finally, we prove that if a generalized m-th root metric is conformal to a m-th root metric, then both of them redu…
New definition of patient-specific root causes of disease using counterfactuals.
problem Lack of rigorous mathematical formulation for automatic detection of root causes.
method Proposes a counterfactual definition matching clinical intuition and uses Shapley values for causal contribution scores.
result Adapts to disease prevalence, accounts for noisy labels, and admits fast computation.
We investigate the behavior of the Shanghai Stock Exchange Composite (SSEC) index for the period from 1990:12 to 2007:06 using an unconstrained two-regime threshold autoregressive (TAR) model with an unit root developed by Caner and Hansen. The method allows us to simultaneously consider non-stationarity and nonlineari…
Study on roots of Dehn twists on nonorientable surfaces.
problem Investigate roots of Dehn twists on nonorientable surfaces.
method Explore existence, conjugacy classes, and maximal degree roots of Dehn twists.
result Prove existence of roots of degree n for sufficiently large g.
Uniqueness of quasi-roots explored in right-angled Artin groups.
problem Uniqueness of quasi-roots in right-angled Artin groups.
method Introducing quasi-roots and studying their uniqueness.
result Uniqueness of quasi-roots established in right-angled Artin groups.
New method estimates root-directed tree from extreme data.
problem Discovering causality in river networks from extreme flow data.
method Qualitative max-linear Bayesian network approach to estimate bivariate scores and root-directed spanning tree.
result The new estimator is consistent under max-linear Bayesian network model with noise.
Study differential properties of matrix square roots in specific cases.
problem Understanding matrix square roots in semi-simple, symmetric, and orthogonal cases.
method Analysis of differential and metric structures of real square roots of matrices under specific conditions.
result Differential properties of matrix square roots in semi-simple, symmetric, and orthogonal cases.
Note on special curvature properties of m-th root metrics.
problem Characterizing m-th root metrics with specific curvature properties.
method Analyzing isotropic Landsberg curvature and almost vanishing H-curvature.
result m-th root metrics with isotropic Landsberg curvature reduce to Landsberg metrics.
Identifies root causes of outliers in unknown cyclic graphs.
problem Outliers in unknown cyclic graphs with linear structural equations.
method Identifies a short list of potential root causes based on strong perturbation and structural equations.
result The shortlist includes true root causes and their parents on the cycle.
The paper explores conditions for projective and dually flat metrics in Finsler spaces with Kropina changes of mth-root metrics.
problem Conditions for projective and dually flat metrics in Finsler spaces with Kropina changes of mth-root metrics.
method Analyzes conditions for projective and dually flat metrics in Finsler spaces with Kropina changes of mth-root metrics.
result Conditions for projective and dually flat metrics in Finsler spaces with Kropina changes of mth-root metrics are identified.
Study Liouville currents for Hitchin representations using root flows.
problem Understanding Liouville currents in Hitchin representations.
method Investigate simple root flows and Liouville currents.
result Derive a Liouville volume rigidity result and construct a Liouville pressure metric.
D. Margalit and S. Schleimer found examples of roots of the Dehn twist about a nonseparating curve in a closed orientable surface, that is, homeomorphisms whose nth power is isotopic to the Dehn twist. Our main theorem gives elementary number-theoretic conditions that describe the values of n for which an nth root exis…
Root Laplacian Eigenmaps help in spectral embedding of graphs.
problem Efficient spectral embedding of graphs.
method Square root of graph-Laplacian operator.
result Improved spectral embedding techniques.
Spatial metamodels improve root finding in uncertain oracle responses.
problem Finding roots in noisy, location-dependent oracle responses.
method Propose spatial metamodels to infer oracle distribution and update Bayesian knowledge.
result Spatial PBA algorithm outperforms earlier models in synthetic and real-world problems.
CROC identifies the earliest-changing stream as the root cause in multi-stream data.
problem Distribution-free root cause analysis in multi-stream data with unknown distributional changes.
method Conformal p-values and finite-sample valid confidence sets.
result CROC efficiently isolates the root cause under minimal assumptions.
The paper explores curvature properties of specific metric spaces.
problem Investigating curvature properties of Cartan spaces with mth root metrics.
method Analyzing isotropic mean Berwald and Landsberg curvatures, and examining conformal β-changes.
result Conditions for conformal β-change of m-th root metrics to be locally dually flat and locally Minkowskian.
We apply an asymmetric version of Kirman's herding model to volatile financial markets. In the relation between returns and agent concentration we use the square root law proposed by Zhang. This can be derived by extending the idea of a critical mean field theory suggested by Plerou et al. We show that this model is eq…
Enhanced ROOT-SGD optimizes stochastic optimization with diminishing stepsizes.
problem Improving statistical efficiency in stochastic optimization.
method Integrates a diminishing stepsize strategy into ROOT-SGD.
result Achieves optimal convergence rates with improved stability and precision.
The study of random positive 3-strand braids reveals patterns in the roots of their Alexander polynomials.
problem Investigating the roots of Alexander polynomials of random positive 3-strand braids.
method Experimental data analysis, conjectures refinement, and proof of results using tools like the signature function of links and Lyapunov exponent of the Burau representation.
result Generically, at least 69% of the roots of Alexander polynomials are on the unit circle, with a large root-free region near the origin.
Geometric models for Lie algebras from simple singularities.
problem Classifying simply-laced simple Lie algebras.
method Using polygonal wheels derived from Milnor fibers of simple singularities.
result Geometric root systems are isomorphic to Lie algebras.
Recent work of Dupire and Carr and Lee has highlighted the importance of understanding the Skorokhod embedding originally proposed by Root for the model-independent hedging of variance options. Root's work shows that there exists a barrier from which one may define a stopping time which solves the Skorokhod embedding p…
Characterizes and simplifies m-th root Finsler metrics.
problem Understanding and simplifying m-th root Finsler metrics. method Characterization and reduction of m-th root Finsler metrics. result Every isotropic mean Berwald curvature m-th root Finsler metric reduces to a weakly Berwald metric. Automorphisms of Lie algebras and their root systems are fully lifted.
problem Understanding automorphisms of real semisimple Lie algebras and their root systems.
method Proving every automorphism of the restricted root system can be lifted to a Lie algebra automorphism.
result Automorphisms of restricted root systems can be fully lifted to Lie algebras.
Margalit and Schleimer constructed nontrivial roots of the Dehn twist about a nonseparating curve. We prove that the conjugacy classes of roots of the Dehn twist about a nonseparating curve correspond to the conjugacy classes of periodic maps with certain conditions. Futhermore, we give data set which determine the con…
GRM models k-way dependencies in univariate exponential families.
problem Modeling dependencies between variable sets of size k > 2.
method Taking k-th root of sufficient statistics for univariate exponential families.
result GRM models for Poisson and exponential families have no and only slight restrictions on parameters, respectively.
Develops a model to explain price dynamics under predictable market flow.
problem Diffusive price dynamics paradox under predictable market-order flow.
method Integrates square-root price-impact law into Lillo--Mike--Farmer model.
result Price dynamics are diffusive at long times under predictable market-order flow.
Root's barrier is continuous and finite under certain conditions.
problem Continuity of the root barrier function.
method Analyzing Skorokhod embedding problem and properties of target measures.
result The barrier function is continuous and finite under specified conditions.
Square-root impact law confirmed for option trades.
problem Is market impact similar for stocks and options?
method Analyzed proprietary data of option trades.
result Square-root law holds for option markets.
In this paper, we consider Kropina change of m-th root Finsler metrics. We find necessary and sufficient condition under which the Kropina change of an m-th root Finsler metric be locally dually flat. Then we prove that the Kropina change of an m-th root Finsler metric is locally projectively flat if and only if …
Defines a generalized string concept for abstract root systems.
problem Generalizing the concept of strings to abstract root systems.
method Introduces a new definition for Φ-strings in abstract root systems. result Defines a new set of elements in Σ based on a given λ and subset Φ of simple roots. Continuity of roots of hyperbolic polynomials with smooth coefficients.
problem Continuity of the solution map for hyperbolic polynomials.
method Proving continuity of the solution map from hyperbolic polynomials of degree d with C^d coefficients to their increasingly ordered roots.
result Continuity of the solution map for hyperbolic polynomials with C^d coefficients.
Polynomials' roots count tied to surface umbilics.
problem Relating roots of polynomials to umbilics on surfaces.
method Constructing a convex surface from a polynomial, determining umbilic index, and applying Hamburger's bound.
result Bounding the number of roots inside the unit circle for polynomials with self-inversive second derivatives.
Study shows dense roots of Yamada polynomial for certain graphs.
problem Understanding the roots of Yamada polynomials for spatial graphs.
method Construction and analysis of Yamada polynomial for spatial graphs.
result Found an infinite family of graphs with dense roots of Yamada polynomials.
The notion of limit roots of a Coxeter group W was recently introduced (see arXiv:1112.5415 and arXiv:1303.6710): they are the accumulation points of directions of roots of a root system for W. In the case where the root system lives in a Lorentzian space W admits a faithful representation as a discrete reflection grou…
Jones polynomials have infinitely many roots of unity as zeros.
problem Finding roots of unity as zeros of Jones polynomials.
method Constructing families of prime knots with specific Jones polynomials.
result Infinitely many roots of unity are zeros of some Jones polynomials.
Improved root-finding method for smooth functions.
problem Finding roots of smooth functions efficiently and reliably.
method A new improvement over Newton's method for doubly differentiable functions.
result Faster and more reliable convergence compared to Newton's method.
The study explores knot invariants using roots of unity.
problem Understanding knot invariants at roots of unity.
method Using Reshetikhin-Turaev method and generalizing ADO invariants.
result Clarified definitions and connections between different invariants.
TPSQRs model longitudinal event data, detecting ADRs from EHRs.
problem Detecting adverse drug reactions from longitudinal event data.
method Learned by estimating a collection of interrelated PSQRs, using Poisson pseudo-likelihood for estimation.
result TPSQRs effectively and efficiently recover ADR signals from EHRs.