Study on disk configurations in strips shows stability patterns.
problem Understanding stability patterns in disk configurations in strips.
method Finite presentation of rational homology groups, representation stability.
result Disk configuration space exhibits first-order representation stability.
Study handles in 3D shapes, applies to material patterns.
problem Understanding 3D shapes through handlebody decompositions.
method Introduced handlebody decompositions, showed stability, applied to materials.
result Stable equivalence of handlebody decompositions in 3-manifolds.
Study of embeddings avoiding certain tangent patterns using polynomial spaces.
problem Classifying embeddings avoiding specific tangent patterns.
method Introduce equivalence relation (quasitopy) and use spaces of polynomials as Grassmannians.
result Quasitopy classes of Θ-constrained embeddings stabilize as degree increases.
This paper introduces TDA and TSI for better business analytics.
problem Nonlinear, multi-scale business datasets under-represented by traditional tools.
method Topological Data Analysis (TDA) and Topological Stability Index (TSI).
result TSI reveals structural variability in business data.
The paper tackles entry prediction in row/column-exchangeable matrices with arbitrary missing data.
problem Prediction in matrices with arbitrary missing data.
method Proposes two practical algorithms: one for fast emulation and another for acceleration using algorithmic stability.
result Demonstrates superior performance in synthetic and real-world data sets.
We introduce the idea of *representation stability* (and several variations) for a sequence of representations V_n of groups G_n. A central application of the new viewpoint we introduce here is the importation of representation theory into the study of homological stability. This makes it possible to extend classical t…
A novel framework interprets driving patterns using Action phases clustering.
problem Challenges in comprehending driving heterogeneity from underlying behavior mechanisms.
method Resampling and Downsampling Method (RDM) followed by iterative clustering calibration.
result Six driving patterns identified in real-world datasets, revealing dynamic nature of driving.
Empirical study on UEEs reveals liquidity's role and universal recovery patterns.
problem Understanding and stabilizing financial markets affected by UEEs.
method Comparative analysis of UEEs over different years in US stock market.
result Liquidity is dominant in UEEs emergence and recovery patterns are universal.
The recently introduced Tsetlin Machine (TM) has provided competitive pattern classification accuracy in several benchmarks, composing patterns with easy-to-interpret conjunctive clauses in propositional logic. In this paper, we go beyond pattern classification by introducing a new type of TMs, namely, the Regression T…
FinCast is a foundation model for financial time-series forecasting that outperforms existing methods.
problem Challenges in financial time-series forecasting due to temporal non-stationarity, multi-domain diversity, and varying temporal resolutions.
method FinCast is a foundation model specifically designed for financial time-series forecasting, trained on large-scale financial datasets.
result FinCast exhibits robust zero-shot performance, effectively capturing diverse patterns without domain-specific fine-tuning.
New learning methods for open systems with variable agents.
problem Learning in open systems with dynamic agent arrivals and departures.
method Formulated a unified open-system bandit problem with general dynamics, introducing new concepts like pre-training degree and stability.
result Certified global-UCB learning methodologies with provable guarantees, revealing dependencies between entry uncertainty, stability, and agent patterns.
Here are studied pairs of transversal foliations with singularities, defined on the Elliptic region (where the Gaussian curvature K is positive) of an oriented surface immersed in R3. The leaves of the foliations are the lines of geometric mean curvature, along which the normal curvature is given …
Associated to oriented surfaces immersed in R^3 here are studied pairs of transversal foliations with singularities, defined on the Elliptic region, where the Gaussian curvature K, given by the product of the principal curvatures k_1, k_2 of the immersion, is positive. The leaves of the foliations are the lines of M- m…
CSTs improve stability in covariance spectrum analysis without training.
problem Stability and expressiveness in covariance spectrum analysis.
method Sequential application of covariance wavelet filters to input data.
result Stable and expressive hierarchical representations in low-data settings.
Databases of electronic health records (EHRs) are increasingly used to inform clinical decisions. Machine learning methods can find patterns in EHRs that are predictive of future adverse outcomes. However, statistical models may be built upon patterns of health-seeking behavior that vary across patient subpopulations, …
Android and Facebook provide third-party applications with access to users' private data and the ability to perform potentially sensitive operations (e.g., post to a user's wall or place phone calls). As a security measure, these platforms restrict applications' privileges with permission systems: users must approve th…
The global financial crisis in 2007-2009 demonstrated that systemic risk can spread all over the world through a complex web of financial linkages, yet we still lack fundamental knowledge about the evolution of the financial web. In particular, interbank credit networks shape the core of the financial system, in which …
This paper introduces Non-Autonomous Input-Output Stable Network(NAIS-Net), a very deep architecture where each stacked processing block is derived from a time-invariant non-autonomous dynamical system. Non-autonomy is implemented by skip connections from the block input to each of the unrolled processing stages and al…
A streaming GNN model tackles continual learning for updating node representations in real-time.
problem Learning new patterns in streaming graph data while maintaining existing patterns.
method Designing an approximation algorithm for pattern detection, combining data replaying and model regularization.
result Our model efficiently updates model parameters and achieves comparable performance to model retraining.
Ensemble learning that can be used to combine the predictions from multiple learners has been widely applied in pattern recognition, and has been reported to be more robust and accurate than the individual learners. This ensemble logic has recently also been more applied in feature selection. There are basically two st…
Optimizes dividends with stability for risky businesses.
problem Maximizing dividends with stability in risky businesses.
method Linear-quadratic optimization for a general Lévy process.
result Derives optimal affine dividend strategies with stability.
Persistent homology analysis provides means to capture the connectivity structure of data sets in various dimensions. On the mathematical level, by defining a metric between the objects that persistence attaches to data sets, we can stabilize invariants characterizing these objects. We outline how so called contour fun…
Randomized hierarchical clustering tests for stability and detects clusters.
problem Greedy hierarchical clustering's sensitivity to data perturbations.
method Randomization scheme and p-values at each node.
result Valid hypothesis testing procedures for clustering results.
Geometrically classifies total stability spaces for Dynkin diagrams.
problem Classifying total stability spaces for triangulated categories.
method Constructing a geometric model of root categories as hQ-gons and proving isomorphisms. result Total stability spaces ToStDb(Q)/[2] are isomorphic to moduli spaces of stable hQ-gons. Recurrent neural networks trained on regular languages exhibit stable states that can recover from noise.
problem Stability of internal states in recurrent neural networks trained on regular languages.
method Empirical study with analysis of network activation and transitions between states.
result Recurrent neural networks trained on regular languages can recover from random perturbations and maintain stable states.
The paper models financial markets and real economy interactions using a large agent framework.
problem Understanding capital allocation and accumulation in financial markets and real economy interactions.
method Developed a field-formalism model to analyze interactions between financial markets and real economy with a large number of heterogeneous agents.
result The number of firms in each sector depends on the aggregate financial capital invested and expected long-term returns.
Study reveals LLM personality patterns but lacks behavioral consistency.
problem Understanding and validating personality traits in LLMs.
method Characterized LLM personality across three dimensions: training dynamics, self-report validity, and intervention effects.
result Self-reported traits do not reliably predict behavior, and instructional alignment affects trait expression but not behavior.
An image pattern can be represented by a probability distribution whose density is concentrated on different low-dimensional subspaces in the high-dimensional image space. Such probability densities have an astronomical number of local modes corresponding to typical pattern appearances. Related groups of modes can join…
FredNormer improves time series forecasting by adapting to frequency domain patterns.
problem Current normalization methods struggle with non-stationary time series due to their time-domain approach.
method FredNormer analyzes frequency components, adapts weights, and improves robustness.
result FredNormer boosts forecasting accuracy by 33.3% on ETTm2 dataset.
We consider the matrix completion problem with a deterministic pattern of observed entries. In this setting, we aim to answer the question: under what condition there will be (at least locally) unique solution to the matrix completion problem, i.e., the underlying true matrix is identifiable. We answer the question fro…
New method connects knot Floer homology with bordered Floer homology.
problem Computing involutive knot Floer homology of satellites.
method Invariant splitting principles for knot Floer complexes and bordered Floer homology.
result Involutive knot Floer homology of satellites can be computed from their companions.
The study explores vector flows on manifolds, focusing on polynomial constraints and equivalence relations.
problem Understanding vector flows on compact manifolds with constraints on tangency patterns.
method Introduces equivalence relations (quasitopy) and computes spaces of polynomials with constrained divisors.
result Quasitopy classes stabilize as the degree of polynomials increases.
Consider oriented surfaces immersed in R3. Associated to them, here are studied pairs of transversal foliations with singularities, defined on the Elliptic region, where the Gaussian curvature K, given by the product of the principal curvatures k1,k2 is positive. The leaves of the foliations …
Enhanced CNN for financial data improves predictive accuracy and stability.
problem Complexity and variability in financial data.
method Normalization and Gradient Reduction Architecture.
result Improvement in model accuracy and stability.
The efficient market hypothesis has far-reaching implications for financial trading and market stability. Whether or not cryptocurrencies are informationally efficient has therefore been the subject of intense recent investigation. Here, we use permutation entropy and statistical complexity over sliding time-windows of…
SentARL uses sentiment features to improve trading profits.
problem Improving profit stability in single-asset trading.
method Sentiment-Aware Reinforcement Learning (SentARL) system.
result SentARL consistently outperforms baselines across multiple assets and conditions.
Study analyzes price change patterns across different market capitalizations using Markov chains.
problem Understanding price dynamics in limit order markets across various market capitalizations.
method Discrete-time Markov chain analysis of intraday price changes in NASDAQ100 tick data.
result Systematic patterns in price inertia and stability across market capitalizations are identified.
Study clusters Kenyan medical insurance companies based on financial performance and reporting consistency.
problem Identifying financial health and reporting consistency in Kenyan medical insurance companies.
method Advanced clustering techniques (KMeans, DTW) on financial ratios and time series data.
result Four distinct clusters identified, each representing different financial performance and reporting consistency combinations.
New algorithm improves GAN stability and quality.
problem Training GANs is unstable and computationally expensive.
method Inspired by host-pathogen co-evolution, proposes a new algorithm.
result Increased stability and better image generation with less computing.
New algorithm improves fraud detection by analyzing financial account relationships.
problem High false positive rates and missed detections in conventional fraud detection systems.
method Personalized PageRank (PPR) algorithm to capture social dynamics of fraud.
result Integrating PPR enhances fraud detection model's predictive power.
Many new models for measuring financial contagion have been presented recently. While these models have not been specified for investment funds directly, there are many similarities that could be explored to extend the models. In this work we explore ideas developed about financial contagion to create a network of inve…
Framework detects covert financial market manipulation using LOB representations.
problem Detecting covert financial market manipulation (spoofing) from complex anomaly patterns in multilevel prices.
method Cascaded contrastive representation learning of LOB data.
result Transformer-based architectures achieve state-of-the-art results in detection performance.
The paper explores how data geometry influences generalization in neural networks.
problem Understanding generalization in overparameterized neural networks.
method Theoretical exploration of overparametrized two-layer ReLU networks trained below the edge of stability.
result Generalization bounds adapt to the intrinsic dimension of data distributions and deteriorate as data concentrates towards the unit sphere.
We say that a collection Gamma of geodesics in the hyperbolic plane H^2 is a modular pattern if Gamma is invariant under the modular group PSL_2(Z), if there are only finitely many PSL_2(Z)-equivalence classes of geodesics in Gamma, and if each geodesic in Gamma is stabilized by an infinite order subgroup of PSL_2(Z). …
Paper develops a framework for hyperbolic Monge-Ampère equation on strips, proving well-posedness and stability.
problem Addressing the rigidity-flexibility dichotomy for wrinkled patterns in thin elastic sheets.
method Develops hodograph transformation and parametrix-corrector decomposition to handle corner singularities and prove well-posedness.
result Proves existence and uniqueness of hodograph weak solutions and derives energy estimates for stability.
We derive optimal statistical and computational complexity bounds for exp-concave stochastic minimization in terms of the effective dimension. For common eigendecay patterns of the population covariance matrix, this quantity is significantly smaller than the ambient dimension. Our results reveal interesting connections…
New control theory shows neural networks can be sparsely active over time.
problem Optimizing neural networks for long-time control with sparsity constraints.
method Proving optimal controls vanish after a positive time and providing a stability estimate.
result Optimal controls for ℓ1-penalized neural ODEs are sparsely active over time. node2coords learns interpretable graph node representations robust to graph perturbations.
problem Need representations that capture graph structure and are robust to perturbations.
method Proposes a graph representation learning algorithm using Wasserstein barycenters.
result Learned representations are interpretable and stable to graph perturbations.