Study on random Coxeter groups, extending Erdös-Rényi model.
problem Understanding random Coxeter groups and their properties.
method Extended Erdös-Rényi model to study random general Coxeter groups.
result Results on homology of nerve and hyperbolicity of random Coxeter groups.
Graphs of certain groups are Helly, leading to geometric and combinatorial properties.
problem Characterizing Helly property in certain groups and its geometric implications.
method Introducing cell Helly complexes and proving Helly property for weak Garside and Artin groups.
result Weak Garside and Artin groups act geometrically on Helly graphs with nonpositive curvature-like structures.
We give a conjectural classification of virtually cocompactly cubulated Artin-Tits groups (i.e. having a finite index subgroup acting geometrically on a CAT(0) cube complex), which we prove for all Artin-Tits groups of spherical type, FC type or two-dimensional type. A particular case is that for n≥4, the n-st…
We construct a family of morphisms between Artin-Tits groups which generalise the ones constructed by J. Crisp in [Injective maps between Artin groups, Proceedings of the Special Year in Geometric Group Theory, Berlin, (1999), 119 -- 138]. We show that their restrictions to the positive Artin monoids respect normal for…
The paper introduces a Deligne complex for Artin monoids and studies its properties.
problem Understanding geometric structures associated with Artin monoids.
method Constructing a Deligne complex for Artin monoids and analyzing its properties.
result The Deligne complex for Artin monoids is contractible and can be embedded into the Deligne complex for the corresponding Artin group.
The paper proves that certain spaces are injective and Helly graphs.
problem Understanding the structure of certain geometric and algebraic spaces.
method Building Helly graphs and injective metric spaces from lattices.
result The natural piecewise ℓ∞ metric on Euclidean buildings and Deligne complexes is injective. Groups with Property (T) have fiber products with Property (T).
problem When does the fiber product of groups with Property (T) have Property (T)?
method Analyzing fiber products of groups with Property (T).
result Fiber products of groups with Property (T) also have Property (T).
We prove recognition theorems for codimension one manifold factors of dimension n≥4. In particular, we formalize topographical methods and introduce three ribbons properties: the crinkled ribbons property, the twisted crinkled ribbons property, and the fuzzy ribbons property. We show that X×R i…
The study shows that several properties are not profinite invariants.
problem Determining which properties are profinite invariants.
method Combining Rips constructions and iterated group-theoretic Dehn filling on hyperbolic virtually special groups.
result Several properties (stable commutator length, quasimorphisms, property NL, property FW∞, property FA, and non-abelian free subgroups) are not profinite invariants. We show that all finite-dimensional resolvable generalized manifolds with the piecewise disjoint arc-disk property are codimension one manifold factors. We then show how the piecewise disjoint arc-disk property and other general position properties that detect codimension one manifold factors are related. We also note …
New complexity notion connects finite decomposition and asymptotic property C.
problem Understanding and connecting different properties in metric spaces.
method Introducing finite APC-decomposition complexity and proving its implications.
result Finite APC-decomposition complexity implies property A for metric spaces.
Extended Tetrahedral Property to non-Euclidean spaces.
problem Prove Tetrahedral Property in non-Euclidean spaces.
method Extend Tetrahedral Property to less restrictive definition and prove its properties.
result Generalized Tetrahedral Property retains original properties and leads to convergence results.
Investigates stability properties of Haezendonck-Goovaerts premium principles in Orlicz spaces.
problem Stability properties of Haezendonck-Goovaerts premium principles in various Orlicz spaces.
method Analysis of stability properties including Fatou and Lebesgue properties, and continuity with respect to Φ-weak convergence. result Haezendonck-Goovaerts principles satisfy the Fatou property and Lebesgue property under certain conditions.
The paper explores higher property T in lattices and its connections to geometric phenomena.
problem Understanding higher property T in lattices and related geometric phenomena.
method Operator-algebraic characterizations of higher property T and connections to lattice geometry.
result Unified framework for understanding higher property T and related geometric phenomena.
Asymptotic property C was introduced by Dranishnikov to study spaces with infinite asymptotic dimension. We show that asymptotic property C is preserved by infinite products. We also show that countable restricted direct products of countable groups with finite asymptotic dimension have asymptotic property C. Then we i…
Groups of importance in group theory have flexible stability properties.
problem Stability and flexibility of groups in geometric and combinatorial group theory.
method Establishing Kirchberg's Local Lifting Property and Lubotzky--Shalom's Property FD for specific groups.
result Groups like 3-manifold groups, limit groups, and certain one-relator groups are very flexibly stable. This paper generalizes property (QT) to a broader class of groups.
problem Proving property (QT) for a wider range of groups.
method Using projection complex machinery and hierarchical hyperbolic groups.
result Established sufficient conditions for groups to have property (QT).
Proves a vanishing property for symplectic manifold cohomology.
problem Generalizing complex geometry results to symplectic geometry.
method Based on Tseng and Zhou's vanishing property under symplectic flatness.
result Establishes necessity of symplectic flatness for certain results.
Survey shows degenerate elliptic equations have analytic properties despite low regularity.
problem Understanding analytic properties of degenerate elliptic equations.
method Explains why solutions of a specific degenerate elliptic equation are analytic.
result Solutions of a specific degenerate elliptic equation are analytic despite low regularity.
Unified approach amplifies data for distribution property estimation.
problem Estimating properties of discrete distributions efficiently.
method Unified, linear-time, competitive estimator using just 2n samples.
result Achieves performance of empirical estimator with n√log n samples using only 2n samples.
Survey on foliations and diffeomorphism groups.
problem Relationship between algebraic and homotopical properties.
method Survey and analysis of existing literature.
result Explains the connection between diffeomorphism groups and foliations.
Paper explores limits of graph property testing in Ising models.
problem Understanding information-theoretic limits of graph property testing in Ising models.
method Combinatorial constructs and correlation-based tests.
result Property testing is more challenging for general Ising models than ferromagnets.
We prove extension theorems for several geometric properties such as asymptotic property C (APC), finite decomposition complexity (FDC), strict finite decomposition complexity (sFDC) which are weakenings of Gromov's finite asymptotic dimension (FAD). The context of all theorems is a finitely generated group G with a …
Study generalizes property elicitation to imprecise probabilities.
problem Minimizing risk over imprecise probability distributions.
method Maximin risk minimization over a set of imprecise probabilities.
result Conditions for elicitability of IP-properties.
Introduces bounded scale measure and generalizes property A.
problem Defining property A for large scale spaces with bounded geometry.
method Introduces bounded scale measure, shows its coarse invariance, and generalizes property A.
result Definition of property A for large scale spaces with bounded scale measure is a coarse invariant.
Model predicts price polarity of real estate properties using website information.
problem Predicting price polarity of real estate properties.
method Uses doc2vec and xgboost to learn correlations between price and text descriptions of properties.
result Text descriptions provide slightly higher accuracy than features alone.
Study cohomological and metric properties of non-Kähler complex manifolds.
problem Understanding cohomological invariants and metrics of non-Kähler complex manifolds.
method Partial account of problems through cohomological and metric properties.
result Partial insights into cohomological and metric properties of non-Kähler manifolds.
The paper explores the twisted Rokhlin property in mapping class groups of surfaces.
problem Classifying surfaces whose mapping class groups have the twisted Rokhlin property.
method Generalizing the Rokhlin property to the twisted version, the authors classify surfaces based on their mapping class groups' properties.
result The mapping class groups of connected orientable infinite-type surfaces without boundaries have the twisted Rokhlin property, while those of other surfaces do not.
Study shows space of persistence diagrams doesn't have Yu's property A.
problem Failure of property A in the space of persistence diagrams.
method Introduced k-prisms to prove failure of property A.
result Space of persistence diagrams fails to have Yu's property A in a Wasserstein metric.
The balance property is crucial for insurance pricing, ensuring total actuarial price equals loss. Maximum likelihood GLMs fulfill it, but Lindholm-Wüthrich suggests three methods, with constrained GLM being superior.
problem Ensuring the balance property in insurance pricing models
method Using constrained GLM fitting
result Constrained GLM fitting is superior to the two previously discussed balance correction methods
We prove some general results about quasi-actions on trees and define Property (QFA), which is analogous to Serre's Property (FA), but in the coarse setting. This property is shown to hold for a class of groups, including SL(n,Z) for n≥3. We also give a way of thinking about Property (QFA) by breaking it down …
Study Finsler metric measure manifolds' concentration properties.
problem Understanding concentration properties in Finsler metric measure manifolds.
method Established relationships with observable diameter, isoperimetric inequalities, and first eigenvalue.
result Derived a Cheng type upper bound estimate for the first closed eigenvalue.
Hybrid clustering combines partitional and hierarchical clustering for computational effectiveness and versatility in cluster shape. In such clustering, a dissimilarity measure plays a crucial role in the hierarchical merging. The dissimilarity measure has great impact on the final clustering, and data-independent prop…
Paper proves naturally reductive property is inaudible for certain manifolds.
problem Proving naturally reductive property is inaudible for specific manifolds.
method Using a pair of non-compact 11-dimensional generalized Heisenberg groups, the paper proves the naturally reductive property is inaudible.
result The naturally reductive property is inaudible for certain manifolds.
The paper examines curvature properties of twistor spaces.
problem None explicitly stated in the abstract.
method Review of Riemannian and almost Hermitian geometry of twistor spaces.
result Curvature properties of twistor spaces are explored.
3-manifold groups have a property that allows them to act on quasi-trees.
problem Proving property (QT) for 3-manifold groups.
method Analyzing the geometry of 3-manifolds and using quasi-trees.
result Compact, orientable 3-manifold groups have property (QT) if they don't support Sol or Nil geometry.
Unified method for estimating properties of large domain distributions efficiently.
problem Estimating properties of distributions over large domains efficiently.
method Piecewise-polynomial approximation technique for constructing sample- and time-efficient estimators.
result Near-linear-time computable estimators with optimal and highly-concentrated approximation values.
The average shadowing property is considered for set-valued dynamical systems, generated by parameterized IFS, which are uniformly contracting, or conjugacy, or products of such ones. We also prove that if a continuous surjective IFS F on a compact metric space X has the aver- age shadowing property, then every point x…
A property, or statistical functional, is said to be elicitable if it minimizes expected loss for some loss function. The study of which properties are elicitable sheds light on the capabilities and limitations of point estimation and empirical risk minimization. While recent work asks which properties are elicitable, …
Simplicial spheres have a weak Lefschetz property in characteristic 2.
problem Proving the weak Lefschetz property for simplicial spheres.
method Using bistellar moves to show the property is preserved.
result The weak Lefschetz property is preserved by bistellar moves for PL-spheres.
Paper proposes a method to design molecules with specific properties.
problem Designing molecules with desired chemical and biological properties.
method Energy-based model in latent space, SGDS algorithm for gradual distribution shifting.
result Method achieves strong performances on various molecule design tasks.
In this article, we survey recent developments in defining the quasi-local mass in general relativity. We discuss various approaches and the properties and applications of the different definitions. Among the expected properties, we focus on the rigidity property: for a surface in the Minkowski spacetime, one expects t…
Groups with hyperbolic properties don't have strong Property (T).
problem Proving groups with hyperbolic properties don't have strong Property (T).
method Constructing an unbounded affine representation with polynomial growth.
result Groups with hyperbolic properties do not have strong Property (T).
The paper tests properties of trees in graphical models using covariance queries.
problem Testing properties of trees in graphical models.
method Covariance queries model, randomized tests for tree properties.
result Efficient testing of global tree properties using sub-quadratic number of queries.
The strong Fatou property is crucial for risk measures' dual representations.
problem Ensuring nice dual representations of risk measures.
method Exploring Fatou-type properties and inf-convolutions of law-invariant or surplus-invariant risk measures.
result Every quasiconvex law-invariant functional on a rearrangement invariant space with the strong Fatou property is σ(X, L∞)-lower semicontinuous.
Discussing rigidity properties of conics, inspired by billiards in ellipses.
problem Rigidity properties of conics and billiards in ellipses.
method Analog of polar duality and circle map properties.
result Two rigidity properties of conics.
Paper offers a framework for estimating symmetric properties efficiently.
problem Estimating symmetric properties of distributions from samples.
method General framework using profile maximum likelihood (PML) distribution.
result Optimal sample complexity for many properties, practical algorithms.
Proposes a new prior for deep generative models to capture latent properties.
problem Complex non-linear relationships between data and latent properties.
method Factorial mixture prior with Gaussian mixture models for quantization.
result Empirically evaluated method for learning discrete properties in unsupervised or semi-supervised settings.