The paper explores properties of special manifolds related to Yamabe solitons.
problem Characterizing and studying (LCS)n-manifolds with Yamabe solitons. method Analyzing curvature conditions and constructing specific manifolds.
result Characterizations and constructions of (LCS)n-manifolds with Yamabe solitons. The paper examines Ricci solitons on specific types of (LCS)n-manifolds.
problem Investigating Ricci solitons on (LCS)n-manifolds. method Analyzing various types of Ricci pseudosymmetric (LCS)n-manifolds. result Conditions for Ricci solitons on specific (LCS)n-manifolds. Durhuus and Jonsson (1995) introduced the class of "locally constructible" (LC) triangulated manifolds and showed that all the LC 2- and 3-manifolds are spheres. We show here that for each d>3 some LC d-manifolds are not spheres. We prove this result by studying how to collapse products of manifolds with exactly one fa…
Study bounds Ricci curvature in (LCS)n-manifolds with almost η-Ricci solitons.
problem Bounding Ricci curvature in (LCS)n-manifolds with specific solitons. method Provided lower and upper bounds for Ricci curvature, derived a Bochner-type formula.
result Derived bounds and consequences for (LCS)n-manifolds with almost η-Ricci solitons. Study on totally real submanifolds in (LCS)n-manifolds.
problem Characterizing properties of totally real submanifolds in (LCS)n-manifolds. method Analysis of submanifolds with respect to Levi-Civita and quarter symmetric metric connections.
result Scalar curvature of C-totally real submanifolds is same for both connections.
New t-LC triangulated manifolds are exponentially many.
problem Counting t-LC triangulated manifolds. method Introducing t-LC triangulated manifolds and proving their exponential growth. result There are at most $2^{ rac{d^3}{2}N}$ triangulated 2-LC d-manifolds with N facets. The paper characterizes warped product submanifolds in LCS-manifolds.
problem Characterizing warped product submanifolds in LCS-manifolds.
method Analyzing contact CR-warped product and pseudo-slant submanifolds, and constructing examples.
result There do not exist any proper warped product bi-slant submanifolds of LCS-manifolds.
Study invariant submanifolds in (LCS)n-manifolds with quarter symmetric metric connection.
problem Characterize invariant submanifolds in (LCS)n-manifolds.
method Investigate invariant submanifolds with respect to quarter symmetric metric connection.
result Mean curvature of invariant submanifold is equal to the mean curvature with Levi-Civita connection.
Examines special manifolds with specific properties.
problem Analyzing properties of (LCS)n-manifolds.
method Investigates semi-generalized recurrent, semi-generalized Ricci recurrent, and conformal Ricci soliton properties.
result Discovers new insights into the structure of (LCS)n-manifolds.
Study of Ricci solitons on specific submanifolds.
problem Understanding Ricci solitons on invariant and anti-invariant submanifolds.
method Investigation of Ricci solitons on invariant and anti-invariant submanifolds of (LCS)n-manifolds with respect to both Riemannian and quarter symmetric metric connections. result Characterization of Ricci solitons on these submanifolds.
New metrics found on toric LCS manifolds.
problem Finding compatible complex structures on toric LCS manifolds.
method Proved a bijective correspondence between toric LCS manifolds and pairs (C,a). result Compact toric LCS manifolds have a positive potential.
New methods prove non-squeezing in locally conformal symplectic geometry.
problem Non-squeezing theorem in locally conformal symplectic geometry.
method Generating functions and spectral selectors for lcs Hamiltonian diffeomorphisms.
result Proves a non-squeezing theorem in S1imesR2nimesS1. Study LCS structures of the second kind on Lie algebras.
problem Characterize and construct LCS Lie algebras.
method Construct new examples using representations and characterize existing ones.
result Characterize all LCS Lie algebras obtained with the construction.
Constructs symplectic structures on product manifolds from LCS structures.
problem Understanding symplectic structures on product manifolds from LCS structures.
method Constructs a R+-torsor of LCS structures on a covering space. result Bounds the number of fixed points of a Hamiltonian isotopy.
We initiate here the study of Gromov-Witten theory of locally conformally symplectic manifolds or $\lcs$ manifolds, $\lcsm$'s for short, which are a natural generalization of both contact and symplectic manifolds. We find that the main new phenomenon (relative to the symplectic case) is the potential existence of holom…
Lorentzian LCS spaces are equivalent to Generalized Robertson-Walker spaces.
problem Identifying equivalent space-time structures.
method Direct demonstration of equivalence between LCS and GRW spaces.
result Lorentzian LCS spaces are equivalent to Generalized Robertson-Walker spaces.
Study invariants of elliptic curves in LCS manifolds, leading to new phenomena in Riemann-Finsler geometry.
problem Defining and studying invariants of elliptic curves in locally conformally symplectic manifolds.
method Using J-holomorphic curves and Gromov-Witten theory to define and study invariants. result Found new phenomena in Riemann-Finsler geometry and an analogue of the Weinstein conjecture.
A locally conformally symplectic (LCS) form is an almost symplectic form ω such that a closed one-form θ exists with dω=θ∧ω. We present a version of the well-known result of Darboux and Weinstein in the LCS setting and give an application concerning Lagrangian submanifolds.
The study explores properties of homologically locally connected spaces and their connections to other topological concepts.
problem Characterizing and understanding homologically locally connected spaces.
method Investigates properties and characterizations of homologically UVn-maps and lcGn-spaces, comparing them to existing concepts. result Identifies similarities and parallels between homologically locally connected spaces and other topological concepts.
A locally conformally symplectic (LCS) form is an almost symplectic form ω such that a closed one-form θ exists with dω=θ∧ω. A fiber bundle with LCS fiber (F,ω,θ) is called LCS if the transition maps are diffeomorphisms of F preserving ω (and hence θ). In this paper, we find conditions for the total…
The Weinstein conjecture is extended to a new class of manifolds.
problem Existence of Reeb 2-curves in locally conformally symplectic manifolds.
method Extended Gromov-Witten theory and elliptic curve counts.
result Partial verification of the conjecture in higher dimensions.
Reduces LCS manifolds with symplectic actions, preserving conformal structure.
problem Reduction of LCS manifolds with symplectic actions.
method Locally conformally symplectic reduction procedure.
result Compatibility with locally conformally Kähler structure and contact reduction.
The abstract investigates convexity in locally conformally symplectic geometry.
problem Characterizing and proving convexity in locally conformally symplectic manifolds.
method Geometric characterization and proof of convexity theorems for twisted and symplectic moment maps.
result Established an analog of the symplectic convexity theorem for locally conformally symplectic manifolds.
We present a formulation of general nonlinear LC circuits within the framework of Birkhoffian dynamical systems on manifolds. We develop a systematic procedure which allows, under rather mild non-degeneracy conditions, to write the governing equations for the mathematical description of the dynamics of an LC circuit as…
Study on deformations of LC Spin(7) instantons simplifies the problem.
problem Deformation theory of instantons on locally conformal Spin(7) manifolds.
method Reformulated linearized deformation equations using a t-parameter family of Dirac operators, demonstrating cancellation of torsion terms.
result The deformation space H^1 is governed by Levi-Civita geometry, reducing the problem to a torsion-free setting.
Paper proposes LC-Checkpoint for efficient deep learning model checkpoints.
problem Efficient construction of checkpoints for deep learning models.
method Lossy compression scheme using quantization and priority promotion with Huffman coding.
result LC-Checkpoint achieves up to 28x compression and 5.77x speedup over SCAR.
Study LCS structures on Lie algebras of type I, proving trivial Morse-Novikov cohomology and constructing solvmanifolds.
problem Locally conformal symplectic structures on Lie algebras of type I.
method Analyzing Lie algebras of type I, proving trivial Morse-Novikov cohomology, and constructing solvmanifolds.
result LCS structures on Lie algebras of type I are of the first kind and can be used to construct compact solvmanifolds.
Study various series of groups and their Lie algebras in split extensions.
problem Understanding different series of groups and their Lie algebras in split extensions.
method General construction of N-series, semi-direct products, and monodromy action.
result Generalize the well-known theorem of Falk-Randell to other versions of the LCS.
In n-dimensional Euclidean space E^n, harmonic curvatures of a non-degenerate curve defined by Özdamar and Hacisalihoğlu [4]. In this paper, We define a new type of curves called LC helix when the angle between tangent of this curve and LC parallel vector field in space form is constant. Furthermore, several characteri…
Logit correction improves model performance by correcting spurious correlations.
problem Spurious correlations lead to poor model performance during inference.
method Proposes logit correction (LC) loss to mitigate spurious correlations.
result LC loss outperforms state-of-the-art solutions by 5.5% absolute improvement.
In this article we construct a canonical Kähler-Einstein current on a LC (log canonical) pairs of log general type as the limit of a sequence of canonical Kähler-Einstein currents on KLT(Kawamata log terminal) pairs of log general type. We call the volume form associated with the canonical Kähler-Einstein current the c…
This paper compares machine learning methods for recognizing lane change intentions from vehicle trajectories.
problem Accurately detecting and predicting lane change processes in autonomous vehicles.
method Comparison of different machine learning methods on high-dimensional time series data.
result Ensemble methods reduce Type II and Type III classification errors, while LightGBM outperforms XGBoost in training efficiency.
Study of CR-submanifolds in various Lorentzian manifolds.
problem Exploring CR-submanifolds in different Lorentzian structures.
method Analyzing properties and results of CR-submanifolds in LCS, LP-cosymplectic, S, and GKM manifolds.
result Obtained results on totally umbilical and geodesic CR-submanifolds.
LC-SAC tackles non-stationary dynamics in reinforcement learning.
problem Degradation of deep RL methods in non-stationary environments.
method LC-SAC uses latent context encoders and contrastive loss for dynamic information capture.
result LC-SAC outperforms SAC on environments with drastic dynamics changes.
LC-GNN improves GNNs for node classification by incorporating label consistency.
problem Limited performance of GNNs due to label consistency assumption not always holding.
method LC-GNN uses node pairs with the same label but unconnected to expand GNN's receptive field.
result LC-GNN outperforms traditional GNNs in semi-supervised node classification.
LC-CRFs are equivalent to HMMs, and MPM/MAP classifiers can be reformulated as CRFs.
problem Comparing and reformulating HMMs and CRFs.
method Demonstrating equivalence and reformulation of classifiers.
result LC-CRFs are equivalent to HMMs, and MPM/MAP classifiers can be reformulated as CRFs.
The paper classifies submanifolds in a specific Lorentz-Minkowski space.
problem Characterizing submanifolds in a Lorentz-Minkowski space.
method Constructing a global frame field and analyzing extrinsic invariants.
result Local classification theorems for specific submanifold classes.
This study evaluates Lx-norm penalties for resolving complex LC-MS data.
problem Resolving complex LC-MS data with rotational ambiguity.
method Simulated LC-MS data and grid search strategy to compare L0-, L1-, and L2-norm penalties.
result L1-norm penalty (Lasso) provides more sparse solutions and reduces rotational ambiguity.
LC-FL uses generative models to reduce communication costs in federated learning.
problem High communication costs and strict model homogeneity in federated learning.
method LC-FL employs generative models to transmit data and aggregate models.
result LC-FL reduces communication costs and supports heterogeneous models.
Flexible framework compresses models using LC algorithm.
problem Efficiently compressing neural networks for resource constraints.
method Decouples learning and compression steps with alternating L and C phases.
result Compressed models maintain performance and accuracy.
In this paper, the concepts and the direct theorems of stability in the sense of Liapunov, within the framework of Birkhoffian dynamical systems on manifolds, are considered. The Liapunov-type functions are constructed for linear and nonlinear LC and RLC electrical networks, to prove stability under certain conditions.
LC-PFN predicts learning curve performance more accurately and faster than MCMC.
problem Bayesian extrapolation of learning curves is computationally expensive and overly restrictive.
method Prior-Data Fitted Neural Networks (PFNs) for approximate Bayesian inference.
result LC-PFN outperforms MCMC in accuracy and is significantly faster.
Extends Gromov non-squeezing to locally conformally symplectic structures.
problem Generalizing Gromov non-squeezing to new geometric structures.
method Deformation theory applied to locally conformally symplectic structures.
result Proves a new extension of the Gromov non-squeezing phenomenon.
Let π:X∗→B∗ be an algebraic family of compact Kähler manifolds of complex dimension n with negative first Chern class over a punctured disc B∗∈C. Let gt be the unique Kähler-Einstein metric on Xt=π−1(t). We show that as t→0, $(\mathcal{X}_t, g…
We study the Morse-Novikov cohomology and its almost-symplectic counterpart on manifolds admitting locally conformally symplectic structures. More precisely, we introduce lcs cohomologies and we study elliptic Hodge theory, dualities, Hard Lefschetz Condition. We consider solvmanifolds and Oeljeklaus-Toma manifolds. In…
Model complexity is an important factor to consider when selecting among graphical models. When all variables are observed, the complexity of a model can be measured by its standard dimension, i.e. the number of independent parameters. When hidden variables are present, however, standard dimension might no longer be ap…
Our aim is to determine the lower central series (LCS) and derived series (DS) for the braid groups of the sphere and of the finitely-punctured sphere. We show that for all n (resp. all n\geq 5), the LCS (resp. DS) of the n-string braid group B\_n(S^2) is constant from the commutator subgroup onwards, and that Γ\_2(B\_…
A new graph kernel uses LCS and Wasserstein distance for better graph comparisons.
problem Graph learning methods can be limited by information from distant vertices and path length constraints.
method Proposes a Graph Kernel based on LCS similarity and Wasserstein distance in a novel metric space.
result The new kernel emphasizes comparisons between similar paths and reduces information loss.