We study the space of linear difference equations with periodic coefficients and (anti)periodic solutions. We show that this space is isomorphic to the space of tame frieze patterns and closely related to the moduli space of configurations of points in the projective space. We define the notion of combinatorial Gale tr…
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48 results for “different spaces”
What does it mean for an algorithm to be fair? Different papers use different notions of algorithmic fairness, and although these appear internally consistent, they also seem mutually incompatible. We present a mathematical setting in which the distinctions in previous papers can be made formal. In addition to characte…
Examines different approaches to Poisson structures in Banach spaces.
problem Exploring various definitions of Poisson structures in Banach spaces.
method Presenting and comparing different definitions of Poisson structures.
result Illustrates differences between existing definitions with examples.
Study shows mapping class groups differ for -cobordant manifolds.
problem Mapping class groups are invariant under -cobordism.
method Introduced moduli spaces of -block bundles to distinguish manifolds.
result Mapping class groups of -cobordant manifolds can differ.
We give the complete classification of all sub-Riemannian model spaces with both step and rank three. They will be divided into three families based on their nilpotentization. Each family will depend on a different number of parameters, making the result crucially different from the known case of step two model spaces.…
We discuss two different in general natural approaches to the ideal closure and ideal boundary of Busemann nonpositively curved metric space. It is shown that the identity map of the space admits surjective continuation from its coarse ideal closure to the weak one. We consider some situations when these closures coinc…
Some moduli spaces of irregular connections on the trivial bundle over the Riemann sphere will be identified with Nakajima quiver varieties. In particular this enables us to associate a Kac-Moody root system to such connections (yielding many isomorphisms between such moduli spaces, via the reflection functors for the …
This work proposes a new method to match distributions across different spaces using cycle-consistent maps.
problem Matching distributions across different spaces with consistent bidirectional maps.
method A novel unbalanced Monge optimal transport formulation for matching distributions on different spaces, employing cycle-consistent maps.
result The proposed discrepancy captures the cycle-consistent GAN framework and provides theoretical support.
We describe our language-independent unsupervised word sense induction system. This system only uses topic features to cluster different word senses in their global context topic space. Using unlabeled data, this system trains a latent Dirichlet allocation (LDA) topic model then uses it to infer the topics distribution…
Research connects Lie algebras to configuration space (co)homology.
problem Understanding the (co)homology of configuration spaces.
method Identifying Lie algebra (co)homology as a counterpart to configuration space (co)homology.
result Lie algebras and configuration spaces have a deep mathematical relationship.
In a paper (math.DG/0403528) we obtained explicit examples of Moishezon twistor spaces of some compact self-dual four-manifolds admitting a non-trivial Killing field, and also determined their moduli space. In this note we investigate minitwistor spaces associated to these twistor spaces. We determine their structure, …
The role of feature space in atomistic learningphysics.comp-ph
A framework to compare atomistic descriptors and their transformations.
problem Comparing and understanding different atomistic descriptors and their transformations.
method Introducing a framework to compare different sets of descriptors and their transformations by metrics and kernels.
result Diagnostic tools to determine equivalent information and distorted common information between feature spaces.
It is known that connected sums of positive torus knots are not concordant to -space knots. Here we consider differences of torus knots. The main result states that the subgroup of the concordance group generated by two positive torus knots contains no nontrivial -space knots other than the torus knots themselves…
We study the space of "link maps": the space of maps of a disjoint union of compact, closed manifolds P_1, . . ., P_k into a manifold N whose images are pairwise disjoint. We apply the manifold calculus of functors developed by Goodwillie and Weiss to study the difference between it and its linear and quadratic approxi…
New examples show nonnegatively curved metrics with same soul but different moduli space components.
problem Finding nonnegatively curved metrics with same soul but different moduli space components.
method Examples of open manifolds with infinitely many metrics of nonnegative sectional curvature.
result Found open manifolds with souls of codimensions 3 and 2, showing different moduli space components.
Four-dimensional quaternion-Kahler metrics, or equivalently self-dual Einstein spaces M, are known to be encoded locally into one real function h subject to Przanowski's Heavenly equation. We elucidate the relation between this description and the usual twistor description for quaternion-Kahler spaces. In particular, w…
Index difference on surfaces of genus at least 3 is non-trivial.
problem Index difference on surfaces of genus at least 3
method Show that the index difference is non-trivial
result Index difference is non-trivial
Study on uniqueness of hypersurfaces in hyperbolic space with constant mean curvature.
problem Uniqueness of hypersurfaces with constant higher order mean curvature in hyperbolic space.
method Generalization of Bernstein theorem and proof of Bernstein type results for immersed hypersurfaces.
result Rigidity of horospheres and equidistant spheres in terms of their higher order mean curvatures.
Doppler shift in semi-Riemannian signature and the non-uniqueness of the Krein space of spinorsmath.DG
We give examples illustrating the fact that the different space/time splittings of the tangent bundle of a semi-Riemannian spin manifold give rise to non-equivalent norms on the space of compactly supported sections of the spinor bundle, and as a result, to different completions. We give a necessary and sufficient cond…
We give two examples of metric measure spaces satisfying the measure contraction property MCP(K,N) but having different topological dimensions at different regions of the space. The first one satisfies MCP(0,3) and contains a subset isometric to , but does not topologically split. The second space satisfies…
Improved detection of burnt areas in satellite images using evolved hyper-features.
problem Radiometric variations across satellite images and different datasets.
method Understanding feature spaces, training on multi-image datasets, evolving hyper-features, and optimizing for different classifiers.
result Training on multi-image datasets improves model generalization, and evolved hyper-features enhance classifier performance.
Geometrically transforms word embeddings into a common space for better comparison.
problem Comparing embeddings from different sources is challenging.
method Applies orthogonal rotations and Mahalanobis scaling to transform embeddings into a shared latent space.
result The method improves word similarity and analogy tasks.
New proof shows how to fill a square with Fibonacci curve.
problem How to fill a square with a space-filling curve.
method Used Cartesian product of Fibonacci substitution with itself.
result Different proof of space-filling curve construction.
Multi-View Fuzzy Clustering with The Alternative Learning between Shared Hidden Space and Partitioncs.LG
As the multi-view data grows in the real world, multi-view clus-tering has become a prominent technique in data mining, pattern recognition, and machine learning. How to exploit the relation-ship between different views effectively using the characteristic of multi-view data has become a crucial challenge. Aiming at th…
A new method improves semi-supervised learning by handling tasks with different attribute spaces.
problem Existing methods assume tasks share the same attribute space, limiting their applicability.
method Meta-learning approach that embeds labeled and unlabeled data in task-specific spaces using neural networks.
result Improves test performance on tasks with small labeled data using unlabeled and various task data.
Weyl and Cartan proposed different but related ways to handle infinitesimal geometry in the early 1920s.
problem How to apply transformation groups in differential geometry.
method Both used connections and parallel transfer, with Cartan aiming for a more general framework.
result They reached an agreement on handling Cartan's infinitesimal geometric structures by the 1930s.
Synthetic Ricci flows defined for metric measure spaces.
problem Characterizing Ricci flows for non-smooth spaces.
method Heat flow, optimal transport, volume asymptotics.
result Equivalent characterizations of weighted Ricci flow.
Quantum methods model uncertain volatility in financial markets.
problem Modeling financial asset prices with uncertain volatility.
method Quantum stochastic calculus with unitary and non-unitary time evolution.
result Different volatility levels encoded in quantum states, leading to varied market price evolutions.
The article proves a Hineva inequality for various submanifolds in Quaternionic Space forms.
problem Proving a Hineva inequality for submanifolds in Quaternionic Space forms.
method Establishing the Hineva inequality for different types of submanifolds.
result A Hineva inequality has been proven for various submanifolds in Quaternionic Space forms.
We define a new homology theory we call symbol homology by using decorated moduli spaces of Whitney polygons. By decorating different types of moduli spaces we obtain different flavors of this homology theory together with morphisms between them. Each of these flavors encodes the properties of a different type of Heega…
We show that any equation from the Davey--Stewartson hierarchy induces an infinite family of geometrically different deformations of tori in preserving the Willmore functional. We expose a derivation of the Weierstrass representation for surfaces in the four-space which is not unique in difference from the case …
Geometric approach finds correspondences between different conditions.
problem Integrating multiple biological datasets.
method Fibered latent space with pull-back metric, diffeomorphism flows.
result Minimizing energy functional yields diffeomorphism flows.
Develops new synthetic Ricci flow concepts for metric measure spaces.
problem No specific problem stated; focuses on new mathematical concepts.
method Formulated in terms of dynamic convexity and local concavity of entropy, and global/short-time asymptotic transport cost estimates.
result Shows these properties characterise smooth (weighted) Ricci flows.
We derive a necessary and sufficient condition for the existence of symmetric space structures on quotients of Banach symmetric spaces. Along the way, we investigate the different kinds of reflection subspaces and their Lie triple systems.
Marginalized particle Gibbs for multiple state-space models coupled through shared parametersstat.ME
New PG samplers improve inference in coupled state-space models.
problem Bayesian inference from multiple time series with shared parameters.
method Marginalized Particle Gibbs samplers for coupled state-space models.
result Improved parameter inference through shared information.
In this paper we investigate a link between state- space models and Gaussian Processes (GP) for time series modeling and forecasting. In particular, several widely used state- space models are transformed into continuous time form and corresponding Gaussian Process kernels are derived. Experimen- tal results demonstrat…
Most of the 50-year history of the study of the set of knot concordance classes, C, has focused on its structure as an abelian group. Here we take a different approach, namely we study C as a metric space admitting many natural geometric operators, especially satellite operators. We consider several knot concordance sp…
A complete classification is obtained of continuous, translation invariant, Minkowski valuations on an m-dimensional complex vector space which are covariant under the complex special linear group.
Proposes a new metric space example showing non-constant topological dimension.
problem Non-constant topological dimension in metric measure spaces.
method Refines Ketterer and Rajala's example to satisfy CD(0,∞) condition.
result Shows non-constancy of topological dimension for CD spaces.
Generalizes neural networks for infinite-dimensional mappings, including PDE solutions.
problem Learning mappings between infinite-dimensional spaces and finite-dimensional approximations.
method Graph kernel network architecture with message passing for kernel integration.
result Competitive performance compared to state-of-the-art solvers for PDEs.
Characterizes deep neural network weight space for adversarial attacks.
problem Poor performance of deep learning models in adversarial examples.
method Characterizes deep neural network solution space using two paradigms.
result Adversarial attacks are less successful against Associative Memory Models.
We review part of the classical theory of curves and surfaces in -dimensional Lorentz-Minkowski space. We focus in spacelike surfaces with constant mean curvature pointing the differences and similarities with the Euclidean space.
ADS explains object differences by quantifying and removing underlying properties.
problem Explaining differences between two object images.
method Align-Deform-Subtract (ADS) framework that uses semantic alignments and iterative quantification/removal of differences.
result ADS provides disentangled error measures explaining object differences in terms of underlying properties.
In this paper, we consider holomorphic mappings between real hypersurfaces in different dimensional complex spaces. We give a number of conditions that imply that such mappings are transversal to the target hypersurface at most points.
Proposes GDTW for aligning time series on different, incomparable spaces.
problem Dynamic time warping requires comparable spaces, but time series can live on different, incomparable spaces.
method Gromov dynamic time warping (GDTW) considers intra-relational geometry to avoid comparability requirements.
result Demonstrates effectiveness of GDTW in aligning, combining, and comparing time series on incomparable spaces.
We study two aspects of the loop group formulation for isometric immersions with flat normal bundle of space forms. The first aspect is to examine the loop group maps along different ranges of the loop parameter. This leads to various equivalences between global isometric immersion problems among different space forms …
Relation extraction aims to extract relational facts from sentences. Previous models mainly rely on manually labeled datasets, seed instances or human-crafted patterns, and distant supervision. However, the human annotation is expensive, while human-crafted patterns suffer from semantic drift and distant supervision sa…
CW-EDMD improves prediction accuracy by learning local Koopman models for different state-space regions.
problem Inefficient global Koopman operator approximation for distinct local dynamics.
method Cluster-Weighted EDMD (CW-EDMD) learns a soft phase-space partition and per-cluster EDMD operators using EM objective.
result CW-EDMD significantly reduces prediction errors across various systems and configurations.