Article constructs jet-structures in homotopy type theory.
problem Formalizing jet-structures in homotopy type theory.
method Constructs moduli stack of torsionfree jet-structures in homotopy type theory with one monadic modality.
result Formalization yields construction of moduli stack for any ∞-topos with stable factorization systems.
A new nonparametric approach for system identification has been recently proposed where the impulse response is seen as the realization of a zero--mean Gaussian process whose covariance, the so--called stable spline kernel, guarantees that the impulse response is almost surely stable. Maximum entropy properties of the …
The OLS estimator optimally identifies stable linear systems with a finite number of samples.
problem Identifying stable linear systems with a finite number of samples.
method Finite-time analysis of the Ordinary Least Squares (OLS) estimator for stable linear systems.
result The OLS estimator achieves optimal sample complexity for stable systems, matching existing lower bounds up to universal factors.
The paper analyzes market risk factors for a mining company using a VAR model with stable distribution.
problem Understanding mid- and long-term dynamics of market risk factors for a mining company.
method Two-dimensional vector autoregressive (VAR) model with α-stable distribution, identifying two regimes.
result Derives dynamics of copper price in PLN, crucial for company risk exposure.
New bounds show current methods overestimate system parameter errors.
problem Current bounds overestimate parameter errors in system identification.
method Utilized asymptotic normality and second-order decomposition.
result Obtained finite-sample bounds matching optimal rates up to constants.
New algorithm extends Greville's method for partitioned matrices efficiently and stably.
problem Efficiently compute pseudoinverse of partitioned matrices without retraining.
method Incorporates inverse Cholesky factorization to reduce computational complexity and improve stability.
result 1 iteration to compute pseudoinverse of whole matrix from first part, addressing all cases.
The paper refines 2-factor homology to a stable homotopy type for planar trivalent graphs with perfect matchings.
problem Developing a stable homotopy type for planar trivalent graphs with perfect matchings.
method Defining a cover functor from the 2-factor flow category to the cube flow category, realizing the 2-factor spectrum, and showing it's an invariant.
result The stable homotopy type of the 2-factor spectrum is an invariant of planar trivalent graphs with perfect matchings.
The fields of compressed sensing (CS) and matrix completion have shown that high-dimensional signals with sparse or low-rank structure can be effectively projected into a low-dimensional space (for efficient acquisition or processing) when the projection operator achieves a stable embedding of the data by satisfying th…
Effective rank rigidity proved for cubulated groups with factor systems.
problem Rank rigidity in cubulated groups with factor systems.
method Exhibiting special pairs of hyperplanes and curtains for skewering.
result Effective form of rank rigidity proved for cubulated groups.
Studied stable solutions for symmetric systems with hypoelliptic operators.
problem Analyzing stable solutions for symmetric systems with hypoelliptic operators.
method Examined stable solutions for symmetric systems with hypoelliptic operators.
result Identified stable solutions for symmetric systems with hypoelliptic operators.
We give an algorithm to compute stable commutator length in free products of cyclic groups which is polynomial time in the length of the input, the number of factors, and the orders of the finite factors. We also describe some experimental and theoretical applications of this algorithm.
New invariant measures loop iterations in algebraic structures.
problem Measuring the asymptotic behavior of loop iterations in algebraic structures.
method Introduced sign stability and cluster stretch factor to measure loops.
result Cluster algebraic entropies match cluster stretch factor.
Two new ridge solutions improve BLS on added nodes, achieving better accuracy.
problem Improving the Broad Learning System (BLS) for new nodes.
method Proposed two ridge solutions for BLS output weights, updating efficiently.
result Proposed ridge solutions achieve better testing accuracy than original BLS.
The paper examines the stability of Fama-French multi-factor models over time.
problem Stability of Fama-French multi-factor models over time.
method Rolling window method, Fama and MacBeth's two-step estimation, generalized GRS statistics.
result The effectiveness of Fama-French factors is not stable over time in all countries.
Model-based collaborative filtering analyzes user-item interactions to infer latent factors that represent user preferences and item characteristics in order to predict future interactions. Most collaborative filtering algorithms assume that these latent factors are static, although it has been shown that user preferen…
Study on numerical analysis for corporate bonds using a unified 2 factor model.
problem Develop a numerical method to solve a unified 2 factor model for corporate bonds with fixed discrete coupons.
method Used explicit finite difference scheme to analyze stability and compute bond prices.
result Found conditions for the explicit finite difference scheme to be stable and computed bond prices, credit spread, and duration.
The paper tackles long-context linear system identification with improved sample complexity bounds.
problem Identifying dynamical systems with long dependencies over fixed context windows.
method Established sample complexity bounds for systems with linear dependencies over a context window of length p.
result The learning process is not hindered by slow mixing properties in extended context windows.
A network-based approach identifies financial factors from asset interactions, explaining market dynamics.
problem Characterizing joint financial asset behavior through underlying drivers.
method Modeling market as coupled iterated maps, where asset returns depend on past returns and interactions.
result Stable patterns of co-movement (financial factors) emerge from asset interactions, explaining asset variance.
New mathematical foundations for stable RKHSs improve system identification.
problem Improving stability tests and modeling of impulse responses.
method Providing new structural properties and stability conditions for stable RKHSs.
result Any stable kernel admits feature maps induced by orthogonal eigenvectors in l2.
AI system synthesizes chemical plant operation procedures for efficiency and stability.
problem Developing efficient and stable operation procedures for complex chemical plants.
method Integrates automated reasoning, deep reinforcement learning, and dynamic simulation with external knowledge.
result Synthesized procedure achieves faster recovery from malfunctions compared to standard PID control.
We introduce large scale analogues of topological monotone and light maps, which we call coarsely monotone and coarsely light maps respectively. We show that these two classes of maps constitute a factorization system on the coarse category. We also show how coarsely monotone maps arise from a reflection in a similar w…
The paper addresses online prediction in marginally stable systems with bounded perturbations.
problem Online prediction in marginally stable linear dynamical systems with adversarial or stochastic perturbations.
method The online least-squares algorithm is used to achieve sublinear regret, with a refined regret analysis and a structural lemma.
result The online least-squares algorithm achieves sublinear regret, with polynomial dependence on the system's parameters.
Study examines crypto-backed stable derivatives in DeFi, focusing on DAI.
problem Stability of crypto-backed stablecoins in DeFi.
method Introduced a belief parameter to simulate DAI, proposed a mathematical model, analyzed risk factors.
result Belief parameter improves simulation of DAI price stability.
Algorithm learns dynamics from past observations.
problem Learning a nonlinear dynamical system.
method Spectral filtering, online convex optimization.
result Vanishing prediction error for marginally stable systems.
Study identifies stable configurations of intertwined threads with repulsive interactions.
problem Stable configurations of entangled systems with repulsive interactions.
method Analysis of steepest descent flow of an energy functional.
result Existence and uniqueness of stable configuration of two layers drifting apart at t1/3 rate. Statistic dynamics of financial systems is investigated, basing on a model of randomly coupled equation system driven by stochastic Langevin force. It is found that in stable regime the noise power spectrum of the system is of 1/f^alpha form, with the exponent alpha=3/2 in case of Hermitian coupling matrices, or slight…
Style Miner generates stable and significant style factors for time series analysis.
problem Finding significant and stable explanatory factors in high-dimensional time series data.
method Proposes a reinforcement learning method to balance explanatory power and stability constraints.
result Outperforms existing methods by a large margin and achieves a 10% gain in R-squared explanatory power.
The paper proves stability of certain singularities in integrable systems.
problem Stability of singularities in integrable systems under perturbations.
method Analytic and smooth perturbations of completely integrable systems, connectedness condition.
result Non-degenerate singular fibers are structurally stable under small perturbations.
This work extracts stochastic dynamical systems with α-stable Lévy noise.
problem Extracting data-driven governing laws of dynamical systems with non-Gaussian noise.
method End-to-end deep learning approach for learning drift and diffusion coefficients for α-stable Lévy noise. result Effectiveness of the method confirmed by numerical experiments.
We establish sufficient conditions for existence of curves minimizing length as measured with respect to a degenerate metric on the plane while enclosing a specified amount of Euclidean area. Non-existence of minimizers can occur and examples are provided. This continues the investigation begun in [ABCDS] where the met…
Turaev's shadow can be seen locally as the Stein factorization of a stable map. In this paper, we define the notion of stable map complexity for a compact orientable 3-manifold bounded by (possibly empty) tori counting, with some weights, the minimal number of singular fibers of codimension 2 of stable maps into the re…
Stable deep models learn dynamical systems with formal stability guarantees.
problem Difficulties in making formal claims about stability of deep network dynamics models.
method Jointly learning a dynamics model and Lyapunov function to ensure non-expansiveness.
result Proposes an approach for stable deep learning of dynamical systems.
The paper studies surface bundles and Dehn twists, providing new bounds and factorizations.
problem Understanding stable commutator lengths of Dehn twists and their gaps in mapping class groups.
method Examples of surface bundles, factorizations of Dehn twists, and asymptotic bounds.
result Improved upper bounds for stable commutator lengths and a gap in mapping class groups.
We define the representation ring of a saturated fusion system F as the Grothendieck ring of the semiring of F-stable representations, and study the dimension functions of F-stable representations using the transfer map induced by the characteristic idempotent of F. We find a…
We show that stable commutator length is rational on free products of free Abelian groups amalgamated over Zk, a class of groups containing the fundamental groups of all torus knot complements. We consider a geometric model for these groups and parameterize all surfaces with specified boundary mapping to th…
Spaces of polynomials are shown to be Euclidean balls.
problem Understanding the geometry of Lorentzian and real stable polynomials.
method Refined connection between symmetric exclusion process and polynomial geometry.
result Spaces of Lorentzian and real stable polynomials are homeomorphic to closed Euclidean balls.
We examine stable solutions of the following symmetric system on a complete, connected, smooth Riemannian manifold M without boundary, \begin{equation*} -Δ_g u_i = H_i(u_1,\cdots,u_m) \ \ \text{on} \ \ \mathbb{M}, \end{equation*} when Δg stands for the Laplace-Beltrami operator, $u_i:\mathbb{M}\to \mathbb…
New algorithm learns stable LDSs with lower error and better control performance.
problem Learning stable LDSs from data with minimal reconstruction error and stability constraints.
method Proposes an optimization method using a recent characterization of stable matrices, iteratively improving reconstruction error and ensuring stability.
result Achieves orders-of-magnitude improvement in reconstruction error compared to existing methods.
Machine learning clusters mutations in cancer exomes, improving diagnostic speed and cost.
problem Extracting stable mutation structures from cancer exome data for early diagnostics.
method Statistically deterministic machine learning algorithm *K-means applied to exome samples.
result Majority of cancer types exhibit stable mutation clustering, while NMF methods are unstable.
CausalKinetiX identifies stable kinetic models from noisy data.
problem Learning stable and predictive kinetic models from noisy data.
method CausalKinetiX framework for identifying structure from discrete time, noisy observations.
result Causal approach improves generalization and prediction in kinetic systems.
This paper applies reactor theory to supply chain management.
problem Maintaining optimal item delivery and collection ratios in supply chains.
method Translating neutron transport and diffusion theory to supply chain management, introducing analogy factors and interactors.
result A deterministic model for supply chain optimization.
Model shows cities can grow superexponentially but also stabilize due to economic factors.
problem Understanding and controlling population growth in cities.
method Generalized population dynamics model and algorithm for regime shifts.
result Cities can stabilize economically and grow again through algorithmic intervention.
Proposes neural delay differential equations for stable system identification with partially observed states.
problem Learning stable models for systems with partial or delayed observations.
method Augments states with history, uses neural delay differential equations, and ensures stability through time delay analysis.
result The approach ensures stability of learned models for partially observed systems.
CVF learns stable dynamical systems from trajectories.
problem Stable dynamical systems from sampled trajectories.
method Constructs vector fields with controlled contraction and curvature using convex optimization.
result CVF learns stable dynamical systems explicitly controlled by curvature and contraction.
Study on hyperparameter optimization for smartphone-based HAR.
problem Maintaining stable classification accuracy in HAR systems with mobile devices.
method Semi-supervised classifier and study on hyperparameter configuration.
result Adjusting hyperparameters can maintain classification accuracy.
Stabilizes complex systems using diffusion models trained on Lyapunov functions.
problem Generating stabilizing controllers for complex dynamical systems.
method Trains a diffusion model on pairs of asymptotically stable vector fields and their Lyapunov functions to identify the closest stable field and adjust control functions.
result Efficient and rapid stabilization of unseen systems, showcasing generalizability.
Proposes a method to learn stable invariant sets in dynamical systems.
problem Learning stable invariant sets in general dynamical systems.
method Generalizes Manek and Kolter's approach by introducing projection onto latent space shapes and using invertible neural networks.
result Validates the method and shows its usefulness for long-term prediction.
The paper establishes a correspondence between Higgs torsors and connections on curves.
problem Establishing a correspondence between Higgs torsors and connections on curves.
method Introduced a stability condition on filtered Stokes local systems and used it to prove a one-to-one correspondence.
result One-to-one correspondence between stable meromorphic parahoric Higgs torsors and stable meromorphic parahoric connections.