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.
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. 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 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. 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. 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.
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…
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. 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.
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 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.
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.
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.
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.
The object of the present paper is to study invariant submanifolds of (LCS)n-manifolds with respect to quarter symmetric metric connection. It is shown that the mean curvature of an invariant submanifold of (LCS)n-manifold with respect to quarter symmetric metric connection and Levi-Civita connection are equal. An exam…
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.
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.
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…
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…
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.
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.
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.
Study on RCD(0,N) spaces with small linear diameter growth.
problem Understanding structure properties of RCD(0,N) spaces.
method Analyzing the (revised) fundamental group of RCD(0,N) spaces.
result Proved that the revised fundamental group is finitely generated for RCD(0,N) spaces with small linear diameter growth.
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.
Since non-compact RCD(0, N) spaces have at least linear volume growth, we study noncompact RCD(0, N) spaces with linear volume growth in this paper. One of the main results is that the diameter of level sets of a Busemann function grow at most linearly on a noncompact RCD(0, N) space satisfying the linear volume growth…
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.
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…
Paper proves almost rigidity theorem and applies it to study RCD(0,N) spaces.
problem Understanding the structure of noncompact RCD(0,N) spaces with linear volume growth.
method Developed an almost rigidity theorem and applied it to study RCD(0, N) spaces.
result Obtained sublinear growth of diameter of geodesic spheres and non-existence of harmonic functions with polynomial growth.
Study on topological properties and boundaries of RCD(K,N) spaces.
problem Understanding the topology and boundaries of non-collapsed RCD(K,N) spaces.
method Established topological regularity and stability, introduced boundary concept.
result Properties of boundaries and behavior under convergence studied.
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.
Study spacelike loxodromes on helicoidal surfaces in Lorentzian n-space.
problem Characterize spacelike loxodromes on helicoidal surfaces in Lorentzian n-space.
method Find parametrizations of spacelike loxodromes on both spacelike and timelike helicoidal surfaces.
result Classification of spacelike loxodromes on helicoidal surfaces in Lorentzian n-space.
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.
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.
The paper generalizes rectifying and normal curves in Lorentzian n-space.
problem Characterizing and classifying g−rectifying and g−normal curves in Lorentzian n-space. method Introducing a g−position vector field and defining g−rectifying and g−normal curves based on this field. result Comprehensive characterization and classification of g−rectifying and g−normal curves. The study presents examples of CD(0,N) spaces with varying dimensions and discusses the limitations of the CD(0,N) condition.
problem Exploring the properties and limitations of CD(0,N) spaces with varying dimensions. method Generalizing results from previous work, presenting examples and analyzing the conditions under which the CD(0,N) condition fails. result The CD(0,N) condition is not stable under measured Gromov-Hausdorff convergence and may fail in various ways. We show that the constant mean curvature hypersurfaces in the hyperbolic n-space spanning the boundary of a star shaped C^{1,1} domain in the asymptotic sphere give a foliation of the hyperbolic n-space. We also show that if C is a closed codimension-1 C^{2,a} submanifold in the asymptotic sphere bounding a unique cons…
In this paper, we investigate the similarity transformations in the Minkowski-n space. We study the geometric invariants of non-null curves under the similarity transformations. Besides, we extend the fundamental theorem for a non-null curve according to a similarity motion. We determine all non-null self-similar curve…
Study heat content on RCD(K,N) spaces with specific boundary conditions.
problem Analyzing heat content in RCD(K,N) spaces with irregular boundaries.
method Proved first-order asymptotics using measured interior geodesic condition.
result Established first-order heat content asymptotics on RCD(K,N) spaces.
Extends Margulis Lemma to RCD(K,N) spaces.
problem Applying Margulis Lemma to new geometric structures.
method Improved Regularity Estimates for Regular Langrangian Flows.
result Margulis Lemma extended to RCD(K,N) spaces.