This note constructs complex structures on specific isoparametric hypersurfaces.
problem Building complex structures on isoparametric hypersurfaces.
method Constructing almost or complex structures on isoparametric hypersurfaces in unit spheres.
result Complex structures on S1imesS7imesS6 and S1imesS3imesS2 are built. Improved time complexity for parallel stochastic optimization in heterogeneous systems.
problem Time complexity in parallel stochastic optimization for large-scale machine learning models.
method Proposes Rennala MVR, a variance-reduced extension of Rennala SGD based on momentum-based variance reduction.
result Variance reduction improves time complexity in relevant parameter regimes for parallel stochastic optimization in heterogeneous systems.
Study compares Bitcoin, gold, and gas price complexity using multifractal and multiscale entropy methods.
problem Quantifying complexity of financial time series for market analysis.
method Employed MF-DFA and RCMSE to analyze Bitcoin, GBP/USD, gold, and natural gas price log-return time series.
result Bitcoin shows higher complexity compared to other markets, linked to higher nonlinear correlations.
Ringmaster ASGD improves Asynchronous SGD's efficiency under varying worker times.
problem Suboptimal performance of Asynchronous SGD under heterogeneous worker computation times.
method Ringmaster ASGD, a novel Asynchronous SGD method with optimal time complexity.
result Ringmaster ASGD achieves optimal time complexity under arbitrary worker heterogeneity.
In this paper almost complex surfaces of the nearly Kähler S3×S3 are studied in a systematic way. We show that on such a surface it is possible to define a global holomorphic differential, which is induced by an almost product structure on the nearly Kähler S3×S3. We also find a correspondence betwe…
We describe and extract time-ordered multibody interactions from complex systems.
problem Complex systems with temporal and multibody dependencies.
method Decompose multivariate Markov chains into time-ordered multibody interactions. Algorithm to extract interactions from data. Measure complexity of interaction ensembles.
result Robust and efficient algorithm to infer time-ordered multibody interactions from data.
The paper proves complex geometry results for manifolds of the form X × R², answering a 1994 conjecture.
problem Proving complex geometry results for manifolds of the form X × R².
method Using Riemannian and complex geometry techniques, the authors show the existence of metrics with positive scalar curvature.
result The paper answers a 1994 Rosenberg-Stolz conjecture for X × R², extending results to noncompact manifolds.
This paper introduces intrinsic time, a new measure of time for complex systems.
problem Traditional time measures fail to capture the dynamic nature of real-world phenomena.
method Intrinsic time uses an event-based, algorithmic framework to analyze time series data.
result Intrinsic time reveals novel structures and regularities in financial markets.
Cryptocurrency time-series predictability is low, resembling Brownian noise.
problem Low predictability of cryptocurrency exchange rates.
method Complexity and model predictions of Litecoin, Binance Coin, Bitcoin, Ethereum, and XRP exchange rates.
result Simpler models outperform complex ones in cryptocurrency forecasting.
Examines predictability and complexity of economic time series using symbolic dynamics and entropy.
problem Understanding the predictability and complexity of economic time series.
method Symbolic dynamics and Information theory (entropy and uncertainty).
result Economic time series are complex and can be expressed in terms of information production.
Efficient algorithms improve learning of large-margin halfspaces.
problem Learning large-margin halfspaces efficiently and reproducibly.
method Design of efficient, dimension-independent, polynomial-time algorithms; SGD-based approach; DP-to-Replicability reduction.
result Improved sample complexity compared to previous algorithms, with optimal sample complexity for one algorithm.
We study the geometry of Engel structures, which are 2-plane fields on 4-manifolds satisfying a generic condition, that are compatible with other geometric structures. A complex Engel structure is an Engel 2-plane field on a complex surface for which the 2-planes are complex lines. We solve the equivalence problems for…
We give an algorithm to decide which elements of pi_2(S^2\times S^1#...#S^2\times S^1) can be represented by embedded spheres. Such spheres correspond to splittings of the free group on k generators. Equivalently our algorithm decides whether, for a handlebody N, an element in pi_2(N,\partial N) can be represented by a…
Polynomial-time DP algorithm for learning Gaussians with matching sample complexity.
problem Learning Gaussian distributions while maintaining privacy.
method General framework for reducing DP estimation to non-private, polynomial-time algorithm for Gaussian learning.
result Matching sample complexity to information-theoretic upper bound for Gaussian learning.
Special shadow-complexity equals k+1 for k copies of S1×S3.
problem Calculating the special shadow-complexity of a specific 4-manifold.
method Defined by Costantino using Turaev's shadows, proved for connected sums of S1×S3.
result The special shadow-complexity of k copies of S1×S3 is k+1.
Study models Ricci flow on complex surfaces, showing mixed behavior.
problem Understanding long-time behavior of Ricci flow on complex surfaces.
method BiLipschitz models for 4-manifolds (minimal surfaces of general type).
result Exhibits a combination of expanding and static behavior.
New algorithms improve agnostic learning for triangles and polygons, reducing time complexity.
problem Efficient agnostic learning for geometric concept classes.
method Data structures and algorithms from computational geometry, probabilistic combinatorics.
result Optimal time complexity improvements for agnostic learning of triangles and polygons.
This paper improves entropy bounds for ranking time-series complexity.
problem Ranking the complexity of time series processes.
method Building on information theoretic bounds, the paper improves the upper bound of conditional differential entropy using Hadamard's inequality and covariance matrix properties.
result The improved bounds can be used to rank the complexity of time series processes.
This paper establishes for the first time the predictive performance of speed priors and their computational complexity. A speed prior is essentially a probability distribution that puts low probability on strings that are not efficiently computable. We propose a variant to the original speed prior (Schmidhuber, 2002),…
We show that the genus problem for alternating knots with n crossings has linear time complexity and is in Logspace(n). Almost all alternating knots of given genus possess additional combinatorial structure, we call them standard. We show that the genus problem for these knots belongs to TC0 circuit complexity c…
Improved sample and time complexity for identifying mixtures of product distributions.
problem Identifying a mixture of k product distributions from statistics. method Combining robust tensor decomposition and Hadamard extensions to bound the condition number of key matrices.
result Achieved sample complexity and run-time complexity of (1/ζ)O(k) for n≥2k−1. New insights into training ReLU networks, especially as data dimensionality increases.
problem Understanding computational complexity of training ReLU networks with varying data dimensions.
method Analyzed the parameterized complexity of two-layer ReLU networks with respect to various loss functions, focusing on the influence of data dimensionality.
result Running time lower bounds and optimal brute-force strategies for training ReLU networks, extending previous results to broader loss functions.
Flexible Cox model for time-dependent covariates with complex sparsity patterns.
problem Lack of flexibility in enforcing specific sparsity patterns in time-dependent Cox models.
method Proposes a flexible framework for variable selection in time-dependent Cox models, accommodating complex selection rules.
result Achieves accurate estimation with low false alarm rates for complex covariate structures.
Study of metrics on spheres and their complex structure properties.
problem Identifying metrics on spheres and their complex structure properties.
method Identify metrics via Nash isometric embeddings, use isotopic extension theorem, and analyze extrinsic quantities.
result No sphere of dimensions 6 or higher can be diffeomorphic to a complex manifold.
ALT improves TSC by capturing complex patterns in time series data.
problem Challenges in traditional TSC methods with time series complexity and variability.
method ALT incorporates variable-length shifted time windows to enhance LLT for better feature representation.
result ALT achieves state-of-the-art performance with few hyperparameters.
This work analyzes actor-critic methods for faster convergence.
problem Finite-time analysis and sample complexity of two-time-scale actor-critic methods.
method Non-asymptotic analysis under non-i.i.d. setting, proving convergence to first-order stationary point.
result Actor-critic method finds a first-order stationary point with ildeO(ε−2.5) sample complexity. BASS efficiently learns time-varying graphs with low complexity and automatic tuning.
problem Estimating time-varying graphical models with efficient and automatic parameter tuning.
method BASS uses temporally-dependent spike-and-slab priors and variational inference to learn graph structures efficiently.
result BASS outperforms existing methods in recovering true graphs, especially for high-dimensional cases.
New solutions found for complex structures on specific manifolds.
problem Constructing smooth solutions to the Hull-Strominger system.
method Using fibrations over K3 orbisurfaces.
result Proved existence of solutions for certain manifolds.
In the research area of time series classification, the ensemble shapelet transform algorithm is one of state-of-the-art algorithms for classification. However, its high time complexity is an issue to hinder its application since its base classifier shapelet transform includes a high time complexity of a distance calcu…
The anomaly flow on a complex 3-fold is studied with integral Shi-type estimates and long-time existence conditions.
problem Long-time existence of the anomaly flow on a compact complex 3-fold.
method Integral Shi-type estimates adapted from integration-by-parts arguments, with a smallness condition on the slope parameter.
result Long-time existence of the anomaly flow on a compact complex 3-fold under a smallness condition on the slope parameter.
Improved NODEs for long-term time series forecasting.
problem Dealing with complex, multi-frequency data.
method Progressive learning paradigm with curriculum learning.
result Performance improved by over 64%.
Proves smooth solution uniqueness and long-term existence for a parabolic equation on a complex manifold.
problem Existence and uniqueness of solutions to a parabolic equation on compact complex manifolds.
method Uses parabolic Donaldson's equation to prove existence and uniqueness of smooth solutions.
result Smooth solutions to the parabolic Donaldson's equation on compact complex manifolds exist and are unique for all time.
In this paper, we present an online adaptive PCA algorithm that is able to compute the full dimensional eigenspace per new time-step of sequential data. The algorithm is based on a one-step update rule that considers all second order correlations between previous samples and the new time-step. Our algorithm has O(n) co…
Revisits Koiso's rigid metrics on complex projective spaces.
problem Computing obstructions to integrability of deformations.
method Elementary complex differential geometry.
result Computes Koiso's obstruction on CPnimesCP1. We consider different levels of complexity which are observed in the empirical investigation of financial time series. We discuss recent empirical and theoretical work showing that statistical properties of financial time series are rather complex under several ways. Specifically, they are complex with respect to their…
Algorithm classifies surface homeomorphisms with polynomial time complexity.
problem Classifying surface homeomorphisms with polynomial time complexity.
method Algorithm to compute curve distances and decide Nielsen-Thurston types.
result Polynomial time classification of surface homeomorphisms.
Global models outperform univariate benchmarks in complex time series forecasting.
problem Comparing global forecasting models to univariate benchmarks in various challenging scenarios.
method Simulated datasets with controlled characteristics, including homogeneity, complexity, and series lengths. Global forecasting models (RNN, LGBM) compared to univariate techniques.
result Global models like RNN and LGBM are competitive in complex scenarios with short series lengths and heterogeneous data.
Enhances understanding of Kähler-Ricci flow singularities.
problem Understanding singularities in Kähler-Ricci flow.
method Relates to classic Kähler-Ricci flow and degenerate complex Monge-Ampère equation.
result Improves understanding of finite and infinite time singularities.
There exist non-degenerate 3-form dωI, ωI(X,Y)=g(IX,Y), for each leftinvariant almost Hermitian structure (g,I), where g is Killing-Cartan metric on the M=S3×S3=SU(2)×SU(2). Known \cite{H1}, that arbitrary non-degenerate 3-form on the 6-dimensional manifold, with some additional properties def…
Linformer reduces transformer complexity to linear, improving efficiency.
problem High cost of training and deploying large transformer models for long sequences.
method Approximates self-attention with low-rank matrix, proposing Linformer with O(n) complexity. result Linformer performs similarly to standard transformers but is more memory- and time-efficient.
MTHetGNN models complex relations in multivariate time series forecasting.
problem Complex relations among variables in multivariate time series forecasting.
method Designs a relation embedding module and a temporal embedding module, using graph neural networks and CNNs.
result Achieves state-of-the-art results in multivariate time series forecasting.
We study the Hermitian curvature flow of locally homogeneous non-Kähler metrics on compact complex surfaces. In particular, we characterize the long-time behavior of the solutions to the flow. We also provide the first example of a compact complex non-Kähler manifold admitting a finite time singularity for the Hermitia…
We prove that the tangent bundle of an inner symmetric space M of compact type is weakly complex if and only if M is a Riemannian product M1×...×Mk, each Mi being an even-dimensional round sphere or Hermitian symmetric.
New Spencer complexes for Lie groupoids developed.
problem Developing Spencer complexes for Lie groupoids.
method Extending Malgrange's diagonal calculus to IimesG. result Construction of non-linear and linear Spencer complexes.
Study on complex hyperbolic bidisk isometries and their Dirichlet domains.
problem Investigating isometries and Dirichlet domains in the complex hyperbolic bidisk.
method Examined the isometries of the complex hyperbolic bidisk and the Dirichlet domain formed by a cyclic subgroup action.
result Proved that the Dirichlet domain has two sides.
A manifold which admits a reducible genus-2 Heegaard splitting is one of the 3-sphere, S2×S1, lens spaces or their connected sums. For each of those splittings, the complex of Haken spheres is defined. When the manifold is the 3-sphere, S2×S1 or the connected sum whose summands are lens spac…
Consider a circle action on an 8-dimensional compact almost complex manifold with 4 fixed points. To the author's knowledge, S2×S6 is the only known example of such a manifold. In this paper, we prove that if the circle acts on an 8-dimensional compact almost complex manifold M with 4 fixed points, all the…
Paper accelerates nonlinear mapping in online systems with lower time complexity.
problem Speeding up nonlinear mapping in online systems.
method Integrates an acceleration module into Dendrite Net (DD) to reduce time complexity.
result DD with AC has lower time complexity while maintaining nonlinear mapping and system identification properties.