Neural network residuals isolate and locate unknown faults.
problem Locating unknown faults in industrial systems.
method Neural network-based residuals combining physical insights and machine learning.
result Neural network residuals can isolate and locate unknown faults.
Survey uses Milnor fibrations to classify first integrals of differential systems.
problem Classifying first integrals of differential systems using geometric-topological methods.
method Utilizing Milnor fibrations and connections with harmonic morphisms to provide topological and geometric descriptions.
result Geometric-topological classifications of first integrals for both isolated and non-isolated singularities.
Study limits of quasi-local angular momentum at infinity of gravitating systems.
problem Understanding limits of quasi-local angular momentum at infinity of gravitating systems.
method Based on optimal isometric embedding and quasilocal mass theory, the study defines and analyzes the limits of quasi-local angular momentum at spatial and null infinity.
result Limits of quasi-local angular momentum are discussed at spatial and null infinity of an isolated gravitating system.
New foliation method for isolated systems in General Relativity.
problem Defining a robust center of mass for isolated systems in GR.
method Foliation by constant spacetime mean curvature (STCMC) 2-spheres.
result Unique STCMC-foliation exists near infinity of any asymptotically Euclidean initial data set.
RAID algorithm detects anomalies in real-time IoT systems.
problem Anomaly detection limitations in multivariate dynamic processes.
method Adapts to non-stationary effects and handles data drift.
result Improved detection accuracy and root cause isolation.
Study confirms financial bubbles' common patterns in isolated markets.
problem Testing universal dynamics of financial bubbles in isolated markets.
method Log-Periodic Power Law Singularity (LPPLS) model analysis of two major bubble episodes.
result Tehran Stock Exchange shows clear LPPLS hallmarks, supporting bubble universality.
Algorithmic fairness, and in particular the fairness of scoring and classification algorithms, has become a topic of increasing social concern and has recently witnessed an explosion of research in theoretical computer science, machine learning, statistics, the social sciences, and law. Much of the literature considers…
We consider in this paper the regularity problem for time-optimal trajectories of a single-input control-affine system on a n-dimensional manifold. We prove that, under generic conditions on the drift and the controlled vector field, any control u associated with an optimal trajectory is smooth out of a countable set o…
Proposes methods to improve interpretability of Isolation Forest for anomaly detection.
problem Lack of interpretability in Isolation Forest.
method Defines feature importance scores and unsupervised feature selection methods.
result Improves interpretability of Isolation Forest for anomaly detection.
New energy measure for isolated systems in general relativity.
problem Quantifying energy in isolated systems in general relativity.
method Optimal isometric embedding and conformal Killing fields.
result Finite quasi-local energies for asymptotically flat spacetimes.
This paper constructs metrics with constant fractional higher order curvature on punctured spheres.
problem Constructing complete metrics with constant fractional higher order curvature on punctured spheres.
method The approach involves constructing singular solutions for a conformally invariant integro-differential equation, reducing the problem to solving an infinite-dimensional Toda-type system.
result Unified approach for fractional and higher order cases, proving Fredholm properties for the linearized operator.
Enhanced Extended Isolation Forest (EIF+) improves anomaly detection and provides interpretable explanations.
problem Detecting anomalies in complex datasets and explaining model predictions.
method Extended Isolation Forest (EIF) and Extended Isolation Forest Feature Importance (ExIFFI) methods.
result EIF+ outperforms EIF in detecting unseen anomalies and provides better generalization.
Algorithmic fairness is a field of study that addresses the systematic disadvantage of marginalized groups in machine learning systems.
problem Modern machine learning systems increasingly determine access to economic and social opportunities, leading to structural inequalities and prejudices.
method Statistical and structural approaches to algorithmic fairness.
result The field of algorithmic fairness emerged to address the systematic disadvantage of marginalized groups in machine learning systems.
Study of singular solutions to a fourth order system in a ball with a singularity.
problem Asymptotic behavior of singular solutions to a conformally invariant fourth order system.
method Spectral analysis and a priori estimates for Jacobi fields.
result Solutions near the singularity behave like Emden--Fowler solutions.
The paper identifies all link projections with isolate-region number one.
problem Determining link projections with a specific isolate-region number.
method Analyzing link projections to find isolated regions and their cardinality.
result All link projections with isolate-region number one are identified.
FLBench automates federated learning benchmarking.
problem Manual dataset partitioning fails to simulate real-world isolated data islands.
method Develops a federated learning benchmark suite with three domains.
result Automates evaluation of federated learning systems and algorithms.
Study shows market volatility affects optimal communication design for trading strategies.
problem Investigating how communication impacts trading strategy performance in multi-agent systems.
method 5-agent LLM-based trading systems across 450 experiments spanning 21 months, comparing 5 organizational structures.
result Communication improves performance but depends on market characteristics, with competitive conversation excelling in volatile tech stocks.
New method separates sounds with weak labels in noisy environments.
problem Training audio source separation systems with limited labeled data.
method Proposes objective functions and network architectures for weakly labeled training.
result Achieves significant SI-SDR improvement in noisy scenarios.
Extends IF to detect anomalies in functional data.
problem Anomaly detection in complex infrastructures with unlabeled multivariate functional data.
method Develops a variant of the Isolation Forest algorithm for functional data, addressing topological and pattern variety.
result Demonstrates the accuracy of the extended IF algorithm through numerical experiments.
Floer constructs homology from flow lines in generalized dynamical systems and combinatorial vector fields.
problem Computing homology in discrete and smooth dynamical systems.
method Counting flow lines between orbits and critical points.
result Directly recovers Z2 homology from flow lines. TIME network simplifies complex physical processes with interpretable models.
problem Challenges in learning coupled dynamic processes from multiple observations.
method Fully convolutional architecture capturing invariant domain structure.
result Robust and transparent in capturing process kernels and anomalies.
Study finds all local models for flat metrics with isolated singularities.
problem Understanding isolated singularities in flat metrics on Riemann surfaces.
method Complex Analysis to find local models and polynomial growth conditions.
result An isolated singularity of a flat metric with finite area is a conical one.
This paper improves t-SNE using Isolation kernel for better data representation and efficiency.
problem Misrepresentation of data structures and high computational cost in t-SNE.
method Replacing Gaussian kernel with Isolation kernel in t-SNE.
result Isolation kernel improves t-SNE's accuracy and efficiency without sacrificing quality.
Study of G2-structures with isolated singularities and bounded torsion.
problem Understanding G2-structures with special torsion and isolated singularities. method Revisiting known examples, describing symmetries, and analyzing collapsing of circle fibres.
result Collapsing circle fibres at isolated points cannot produce G2-structures with bounded torsion. The paper proves local isometric embeddings for singular metrics near a point.
problem Existence of local isometric embeddings for singular Riemannian metrics.
method Ramified local isometric embeddings using Leray's ramified Cauchy-Kovalevskaya Theorem.
result Existence of local analytic isometric embeddings into Euclidean space.
New stability and isolation results for Einstein manifolds.
problem Stability and isolation of Einstein manifolds.
method Conditions on Weyl tensor for AH and ALE manifolds, Bochner tensor for Kähler and Sasaki manifolds.
result Established new stability criteria and isolation results for various types of Einstein manifolds.
Study extends Gai-Kapadia framework to assess systemic risk in global equity markets.
problem Systemic risk and default cascades in global equity markets.
method Network analysis, threshold filtering, Monte Carlo simulations, tail risk assessment.
result System exhibits strong global resilience with negligible probability of large-scale failure.
Map quandle orders to actions, characterize isolated orders, and prove no isolated right orders.
problem Characterizing isolated orders on quandles and proving the absence of certain orders.
method Construct a continuous map from orders to actions, use strong rigidity, and analyze specific cases.
result No isolated right orders on free quandles, except for specific cases.
Maps don't exist for certain CAT(0) groups with isolated flats.
problem Existence of Cannon--Thurston maps for specific CAT(0) groups with isolated flats.
method Analyzing normal subgroups and visual boundaries of CAT(0) groups with isolated flats.
result Cannon--Thurston maps do not exist for certain CAT(0) groups with isolated flats.
This research proposes a new distance metric using Isolation Forests.
problem Approximating spatial distance between data points.
method Isolation Forests for outlier detection, transforming separation depth into a distance metric.
result The method produces a distance metric invariant to variable scales and capable of handling non-linear relationships.
Constructs a Dolbeault-Hilbert complex for spaces with isolated singular points.
problem Cohomology of spaces with isolated singular points.
method Constructs a Dolbeault-type Hilbert complex.
result Cohomology of the complex is isomorphic to the structure sheaf cohomology.
Defines Perelman's functionals on manifolds with non-isolated conical singularities.
problem Defining functionals on manifolds with non-isolated conical singularities.
method Starting from a spectral point of view for the Perelman's λ-functional, defining the spectrum of Schrödinger operator and proving the existence of discrete eigenvalues.
result Proves the existence of the infimum of W-functional and obtains asymptotic behavior of eigenfunctions.
DBSCAN clustering improved by using nearest neighbour-induced Isolation Similarity.
problem Improving clustering performance of DBSCAN.
method Proposed nearest neighbour method to implement Isolation Similarity.
result DBSCAN clustering performance surpassed by DP algorithm.
iMondrian forest combines isolation forest and Mondrian forest for better anomaly detection.
problem Anomaly detection in batch and online settings.
method Hybrid of isolation forest and Mondrian forest, using depth in Mondrian forest structure.
result iMondrian forest outperforms existing methods in batch and online settings.
We investigate the face numbers of simplicial complexes with Buchsbaum vertex links, especially pseudomanifolds with isolated singularities. This includes deriving Dehn-Sommerville relations for pseudomanifolds with isolated singularities and establishing lower bound theorems when the singularities are also homological…
Local bifurcation theory typically deals with the response of a degenerate but isolated equilibrium state or periodic orbit of a dynamical system to perturbations controlled by one or more independent parameters, and characteristically uses tools from singularity theory. There are many situations, however, in which the…
We explore the geometry of nonpositively curved spaces with isolated flats, and its consequences for groups that act properly discontinuously, cocompactly, and isometrically on such spaces. We prove that the geometric boundary of the space is an invariant of the group up to equivariant homeomorphism. We also prove that…
The Poincaré-Hopf theorem is extended to projective varieties with isolated singularities.
problem Extending the Poincaré-Hopf theorem to varieties with isolated singularities.
method Using generalizations of the Poincaré-Hopf index.
result A Poincaré-Hopf type theorem for projective varieties with isolated singularities.
Quantifies how geodesic planes isolate in hyperbolic 3-manifolds.
problem Understanding isolation properties of geodesic planes in hyperbolic 3-manifolds.
method Quantitative estimates of geodesic planes in frame bundles, using tight areas and densities.
result Polynomial estimates of isolation properties with degree given by modified critical exponents.
We propose a definition of center of mass for asymptotically flat manifolds satisfying Regge-Teitelboim condition at infinity. This definition has a coordinate-free expression and natural properties. Furthermore, we prove that our definition is consistent both with the one proposed by Corvino and Schoen and another by …
Given a smooth closed manifold M, the Morse-Witten complex associated to a Morse function f and a Riemannian metric g on M consists of chain groups generated by the critical points of f and a boundary operator counting isolated flow lines of the negative gradient flow. Its homology reproduces singular homology of M. Th…
Proves conditions for positive scalar curvature on certain manifolds with conical singularities.
problem Conditions for positive scalar curvature on manifolds with isolated conical singularities.
method Analyzes isolated conical singularities and uses Geroch type results.
result No metric with positive scalar curvature on X#Tn with isolated conical singularity. Study reveals GAGA phenomenon in Poisson cohomology for plane structures with isolated singularities.
problem Understanding Poisson cohomology for plane structures with isolated singularities.
method Determined Gerstenhaber algebra structure over Poisson cohomology groups.
result GAGA type phenomenon observed in Poisson cohomology.
We define two types of local indices of a vector field at an isolated zero on the boundary, and prove Poincare-Hopf-type index theorems for certain vector fields on a compact smooth manifold which have only isolated zeros.
This paper introduces a model of environmental acoustic scenes which adopts a morphological approach by ab-stracting temporal structures of acoustic scenes. To demonstrate its potential, this model is employed to evaluate the performance of a large set of acoustic events detection systems. This model allows us to expli…
We study the Euler obstruction of essentially isolated determinantal singularities (EIDS). The EIDS were defined by W. Ebeling and S. Gusein-Zade, as a generalization of isolated singularity. We obtain some formulas to calculate the Euler obstruction for the determinantal varieties with singular set an ICIS.
The paper builds complex hyperbolic 2-manifolds with isolated singularities.
problem Finding compact complex hyperbolic 2-manifolds with non-free actions and isolated fixed points.
method Constructs specific examples for each prime p with Z/pZ action. result General examples for p=2 related to complex hyperbolic lattices conjugacy separability. The Poincaré-Hopf theorem is extended to projective varieties with isolated singularities.
problem Extending the Poincaré-Hopf theorem to projective varieties with isolated singularities.
method Using generalized Poincaré-Hopf indices for a projective variety with isolated determinantal singularities.
result A Poincaré-Hopf type theorem is proven for projective varieties with isolated singularities.