We introduce a basis of the Orlik-Solomon algebra labeled by chambers, so called chamber basis. We consider structure constants of the Orlik-Solomon algebra with respect to the chamber basis and prove that these structure constants recover D. Cohen's minimal complex from the Aomoto complex.
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48 results for “chambers”
The paper explores genericity of triples of antipodal chambers in affine buildings.
problem Investigating genericity of triples of antipodal ideal chambers in locally finite affine buildings.
method Defined ideal-genericity and affine-genericity at the ideal boundary and within the affine building, respectively. Established a barycenter map and showed its continuity.
result Affine-genericity implies ideal-genericity, but the latter is more suitable for constructing a barycenter map.
Developed causal chambers for AI validation, providing real-world data.
problem Limited real-world datasets for AI method validation.
method Created computer-controlled physical systems (causal chambers) to generate datasets.
result Demonstrated applications in various AI fields, validated causal models.
The paper studies the geometric structure of modular curves using meromorphic differentials.
problem Understanding the topological complexity of modular curves .
method Using the walls-and-chambers structure of strata of meromorphic differentials.
result Formulas for the number of chambers and effective means to draw the incidence graph of .
The paper studies chambered invariants of real Cauchy-Riemann operators on Riemann surfaces.
problem Counting pseudo-holomorphic curves in symplectic Calabi-Yau 3-folds.
method Constructs three chambered invariants: , , , defined by counting solutions to ADHM vortex equations and pseudo-holomorphic sections of bundles.
result Conjectures a relationship between and and symplectic invariants.
The paper analyzes feedback loops in recommender systems causing echo chambers and filter bubbles.
problem Feedback loops in recommender systems leading to echo chambers and filter bubbles.
method Theoretical analysis of user dynamics and recommender system behavior.
result Solutions to slow down system degeneracy and understanding echo chambers and filter bubbles.
Properly discontinuous actions, growth indicators, and conformal measures for transverse subgroupsmath.DS
The paper studies proper discontinuity of actions on Weyl chamber flow spaces.
problem Properly discontinuous actions on Weyl chamber flow spaces for transverse subgroups.
method Analyzes limit sets and quotient spaces, introduces growth indicators and conformal measures.
result Establishes ergodic dichotomy for Weyl chamber flow and introduces new measures.
Structure of chambers cut out by Veronese arrangements of hyperplanes in the real projective spacesmath.GT
Research examines arrangements of hyperplanes in real projective spaces, focusing on specific cases.
problem Analyzing the structure of hyperplane arrangements in real projective spaces.
method Investigates arrangements of hyperplanes in the -dimensional real projective space, with a focus on and or .
result Provides insights into the structure of chambers cut out by these specific hyperplane arrangements.
The real spectrum compactification of character varieties: characterizations and applicationsmath.GT
New compactification for character varieties with good topological properties.
problem Compactification of character varieties with good topological properties.
method Announced a new compactification with interpretations of ideal points.
result Relates to Weyl chamber length compactification and applies to maximal and Hitchin representations.
In this paper we set up the family Seiberg-Witten theory. It can be applied to the counting of nodal pseudo-holomorphic curves in a symplectic 4-manifold (especially a Kahler surface). A new feature in this theory is that the chamber structure plays a more prominent role. We derive some wall crossing formulas measuring…
We investigate the geometry in a real Euclidean building X of type A2 of some simple configurations in the associated projective plane at infinity P, seen as ideal configurations in X, and relate it with the projective invariants (from the cross ratio on P). In particular we establish a geometric classification of gene…
We study the space $\nua{m}{d}$ of clouds in $\bbr^d$ (ordered sets of points modulo the action of the group of affine isometries). We show that $\nua{m}{d}$ is a smooth space, stratified over a certain hyperplane arrangement in $\bbr^m$. We give an algorithm to list all the chambers and other strata (this is indep…
The radius of the star-shaped set need not have been continuous.
Planar Soap Bubblesmath.MG
The generalized soap bubble problem seeks the least perimeter way to enclose and separate n given volumes in R^m. We study the possible configurations for perimeter minimizing bubble complexes enclosing more than two regions. We prove that perimeter minimizing planar bubble complexes with equal pressure regions and wit…
Automatic trajectory recognition in Active Target Time Projection Chambers data by means of hierarchical clusteringphysics.ins-det
New algorithm clusters particle tracks for better trajectory recognition in noisy data.
problem Challenging automatic reconstruction of particle tracks from Active Target Time Projection Chambers data.
method Non-parametric algorithm based on hierarchical clustering of point triplets.
result Algorithm identifies and isolates non-analytical particle tracks with high recall and precision.
The paper proves an infinite double bubble theorem in higher dimensions.
problem Characterizing minimizing partitions of infinite and finite volumes in .
method Proves a variant of the double bubble theorem for configurations with infinite and finite chambers.
result Locally minimizing -clusters are unique in for and under certain conditions.
The paper characterizes when numerical criteria for PDE solvability fail and provides effective criteria for existence.
problem Characterizing when numerical criteria for PDE solvability fail.
method Finite number of subvarieties violating Nakai type criterion, and their rigidity.
result Finite number of subvarieties violating the Nakai type criterion, and these subvarieties are rigid.
We investigate discrete groups of isometries of a complete connected Riemannian manifold which are generated by reflections, in particular those generated by disecting reflections. We show that these are Coxeter groups, and that the the orbit space is isometric to a Weyl chamber which is a Riemannian …
The paper studies HYM connections on stable vector bundles over Kähler manifolds.
problem Analyzing stability and convergence of Hermitian Yang-Mills connections.
method Semialgebraic decomposition of the Kähler cone into stability chambers.
result HYM connections converge to a stable HYM connection as polarisation converges.
New techniques simplify computing geometric index of links in solid tori.
problem Computing the geometric index of links in solid tori.
method Introducing geometric index for solid chambers and proving its computation under specific conditions.
result Simplified computation of geometric index for new examples.
In this paper we present a topological way of building a compactification of a symmetric space from a compactification of a Weyl Chamber.
New framework models echo chamber learning, proving tight bounds on algorithm performance.
problem Echo chambers in machine learning where systems learn from self-annotated data.
method Online Learning in the Replay Setting, Extended Threshold dimension, closure-based learner.
result Proves tight bounds on algorithm performance against replay adversaries.
Explicitly constructs moduli spaces of stable parabolic bundles.
problem Understanding moduli spaces of stable parabolic bundles over the Riemann sphere.
method Explicit construction and quotient of stable parabolic structures by bundle automorphisms.
result Explicit models of moduli spaces as smooth, compact complex manifolds.
Fast 2D Bicephalous Convolutional Autoencoder for Compressing 3D Time Projection Chamber Datastat.ML
BCAE-2D compresses 3D data from a time projection chamber at high speed.
problem Compressing high-speed, sparse 3D data from a time projection chamber.
method 2D Bicephalous Convolutional Autoencoder (BCAE-2D) approach.
result 3x speedup in compression throughput with improved reconstruction accuracy.
New resonance theory for Anosov flows connects spectral properties to mixing measures.
problem Defining and analyzing Ruelle-Taylor resonances for Anosov actions.
method Combining microlocal methods and J. Taylor's cohomological theory, defining Ruelle-Taylor resonances and proving Fredholm theory.
result Ruelle-Taylor resonances form a discrete subset of with being a leading resonance.
We consider the family of harmonic measures on a lamination of a compact space by locally symmetric spaces of noncompact type, i.e. . We establish a natural bijection between these measures and the measures on an associated lamination foliated by -orbits, $\hat{\mathc…
Characterizes solutions to Z-critical equations on surfaces using effective conditions.
problem Characterizing solutions to Z-critical equations on compact Kähler surfaces.
method Uses effective conditions and Picard number bounds to characterize solutions.
result Characterizes optimally destabilizing curves for Donaldson's J-equation and deformed Hermitian Yang-Mills equation.
New topological invariant distinguishes real line arrangements with same combinatorics.
problem Determining topological properties from combinatorial data of real line arrangements.
method Introducing chamber weight invariant based on dual configuration points in real projective plane.
result New Zariski pairs of 13, 15, and 17 lines with different topological embeddings.
Study convex hulls of orbits for compact groups, defining new invariants related to polynomial degrees.
problem Understanding properties of convex hulls of coadjoint orbits of compact groups.
method Introduce partial convex hulls and use them to define numerical invariants.
result Orbits with new invariants form rational convex polyhedral cones related to Littlewood-Richardson cones.
We present the Bayesian Echo Chamber, a new Bayesian generative model for social interaction data. By modeling the evolution of people's language usage over time, this model discovers latent influence relationships between them. Unlike previous work on inferring influence, which has primarily focused on simple temporal…
Model financial markets with social media influences using hierarchical networks.
problem Understanding social media's impact on financial markets.
method Agent-based model with hierarchical influence network.
result Model accurately simulates real-world financial market behaviors.
Survey on hyperplane arrangements and their topology.
problem Topology of hyperplane arrangements.
method Focus on the relationship between topology and real structure.
result Relationship between topology and real structure of hyperplane arrangements.
There is a well known link between (maximal) polar representations and isotropy representations of symmetric spaces provided by Dadok. Moreover, the theory by Tits and Burns-Spatzier provides a link between irreducible symmetric spaces of non-compact type of rank at least three and irreducible topological spherical bui…
Closed geodesics found on specific non-compact manifolds.
problem Existence of closed geodesics on non-compact Riemannian manifolds.
method Conditions on the manifold and its boundary to ensure the existence of closed geodesics.
result Existence of non-trivial closed geodesics on the manifold.
We compute the Moore-Witten regularized u-plane integral on CP^1 x CP^1 directly in a chamber where the elliptic unfolding technique fails to work. This allows us to determine explicit formulas for its SU(2) and SO(3)-Donaldson invariants in terms of Mock modular forms.
Symmetrizes 4d and 3d BPS quivers for Argyres-Douglas theories.
problem Understanding the relationship between 4d and 3d BPS quivers.
method Analyzes geometric backgrounds and uses skein modules to derive quiver partition functions.
result Proves isomorphism between 4d wall-crossing and unlinking of symmetric quivers.
Model clusters authors and topics in short texts like social media posts.
problem Analysis of short texts is difficult due to brevity and lack of context.
method Expands Latent Dirichlet Allocation to model word dependencies and cluster users.
result Improves topic and user clustering, outperforming traditional methods.
New method constructs multi-monopoles on mapping tori.
problem Understanding wall-crossing in multi-monopole counts.
method Adiabatic limit theorem to construct multi-monopoles.
result First explicit constructions of multi-monopoles in various chambers.
The purpose of this paper is applying minimality of hyperplane arrangements to local system cohomology groups. It is well known that twisted cohomology groups with coefficients in a generic rank one local system vanish except in the top degree, and bounded chambers form a basis of the remaining cohomology group. We det…
In this paper we describe the Seiberg-Witten invariants, which have been introduced by Witten, for manifolds with . In this case the invariants depend on a chamber structure, and there exists a universal wall crossing formula. For every Kähler surface with and =0, these invariants are non-trivial for …
Study geodesic currents on surfaces, proving new properties of character varieties.
problem Characterizing discontinuity sets in Hitchin and maximal character varieties.
method Decompose geodesic currents into measured laminations or positive systole components.
result Bi-Lipschitz equivalence of intersection functions to length functions for currents with positive systole.
We study Milnor fibers of complexified real line arrangements. We give a new algorithm computing monodromy eigenspaces of the first cohomology. The algorithm is based on the description of minimal CW-complexes homotopic to the complements, and uses the real figure, that is, the adjacency relations of chambers. It enabl…
In this paper we describe the Seiberg-Witten invariants, which have been introduced by Witten, for manifolds with . In this case the invariants depend on a chamber structure, and there exists a universal wall crossing formula. We take into account the contribution of the 1-homology of the base-manifold. For ever…
Machine Learning Accelerated Likelihood-Free Event Reconstruction in Dark Matter Direct Detectionastro-ph.IM
New algorithm improves Dark Matter detection accuracy.
problem Reconstructing Dark Matter interactions with high precision.
method Likelihood-free framework with Bayesian Optimization for Likelihood-Free Inference (BOLFI).
result BOLFI improved reconstruction accuracy by up to 15%.
Flat surfaces that correspond to meromorphic -forms or to meromorphic quadratic differentials containing poles of order two and higher are surfaces of infinite area. We classify groups that appear as Veech groups of translation surfaces with poles. We characterize those surfaces such that their $GL^{+}(2,\mathbb{R})…
In a symmetric space of noncompact type X = G/K oriented geodesic segments correspond to points in the Euclidean Weyl chamber. We can hence assign vector-valued side-lengths to segments. Our main result is a system of homogeneous linear inequalities describing the restrictions on the side -lengths of closed polygons. T…
Study Poisson boundaries of building lattices and generalize rigidity results.
problem Understanding Poisson boundaries of building lattices and their rigidity properties.
method Proved Poisson boundaries and used them to generalize rigidity results.
result Generalized rigidity results for morphisms and cocycles from lattices in buildings to groups with negative curvature.
Real spectrum compactification of Hitchin components, Weyl chamber valued lengths, and dual spacesmath.GT
This paper connects real closed fields to Hitchin representations and their properties.
problem Understanding representations of surface groups over real closed fields.
method Tarski-Seidenberg transfer principle and multiplicative Bonahon-Dreyer coordinates.
result Hitchin representations correspond to -positive representations over real closed fields.