We study Morse theory on noncompact manifolds equipped with exhaustions by compact pieces, defining the Morse homology of a pair which consists of the manifold and related geometric/homotopy data. We construct a collection of Morse data parametrized by cubes of arbitrary dimensions. From this collection, we obtain a fa…
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48 results for “coherent collections”
Financial markets have been extensively studied as highly complex evolving systems. In this paper, we quantify financial price fluctuations through a coupled dynamical system composed of phase oscillators. We find a Financial Coherence and Incoherence (FCI) coexistence collective behavior emerges as the system evolves …
In this paper we introduce a new coherent cumulative risk measure on , the space of càdlàg processes having Laplace transform. This new coherent risk measure turns out to be tractable enough within a class of models where the aggregate claims is driven by a spectrally positive Lévy process. Moreover, w…
Enhances neural forecasting for hierarchically organized time series data.
problem Probabilistic coherent forecasting of time series data across different levels of aggregation.
method Proposes a coherent multivariate mixture output for neural forecasting architectures, optimizing with a composite likelihood objective.
result 13.2% average accuracy improvements on most datasets compared to state-of-the-art baselines.
A tutorial on dynamic Laplacian for time-evolving data clusters.
problem Handling data with a time component and lying on a time-evolving manifold.
method Dynamic generalization of the Laplacian, SEBA algorithm for feature separation.
result Clusters correspond to long-lived coherent collections in time-evolving data.
HierarchicalForecast provides a Python framework for coherent hierarchical forecasting.
problem Ensuring forecasts at disaggregate levels add up to aggregate forecasts.
method Preprocessed datasets, evaluation metrics, and statistical baseline models.
result Python-based reference framework for statistical and ML forecasting.
Origami edge-paths connect coherent curves on surfaces.
problem Understanding coherent curves on surfaces.
method Origami structure and edge-paths.
result Existence of origami edge-paths connecting coherent curves.
Optimal hashing embeddings reduce linear least squares solving time.
problem Efficiently solving large-scale linear least squares problems.
method Optimal hashing sketching matrices for linear least squares.
result Ski-LLS outperforms state-of-the-art solvers on various problem types.
We compare correlations and coherent structures in nuclei and financial markets. In the nuclear physics part we review giant resonances which can be interpreted as a coherent structure embedded in chaos. With similar methods we investigate the financial empirical correlation matrix of the DAX and Dow Jones. We will sho…
The study finds an upper limit for the number of minimal origami pairs on a surface.
problem Counting the minimal origami pairs on a surface of genus g.
method Algorithm to count minimal origami pairs and using Ménage Problem to establish an upper bound.
result Established a new upper bound for the count of minimal origami pairs.
We provide a dual characterisation of the weak-closure of a finite sum of cones in adapted to a discrete time filtration : the cone in the sum contains bounded random variables that are -measurable. Hence we obtain a generalisation of Delbaen's m-stability condition…
Coherent Patterns in Nuclei and in Financial Marketsphysics.data-an
In the area of traditional physics the atomic nucleus belongs to the most complex systems. It involves essentially all elements that characterize complexity including the most distinctive one whose essence is a permanent coexistence of coherent patterns and of randomness. From a more interdisciplinary perspective, thes…
Measures collectivity in financial covariances and correlations to reveal trends and precursors.
problem Capturing collective motion in financial markets to predict trends and precursors.
method Measures collectivity using the largest eigenvalue and average sector collectivity.
result Identifies collective signals around major financial events and captures trends in covariances and correlations.
Topic Extraction of Crawled Documents Collection using Correlated Topic Model in MapReduce Frameworkcs.IR
The tremendous increase in the amount of available research documents impels researchers to propose topic models to extract the latent semantic themes of a documents collection. However, how to extract the hidden topics of the documents collection has become a crucial task for many topic model applications. Moreover, c…
AOBTM adapts online topic modeling for short app reviews, revealing coherent topics over time.
problem Challenges in inferring latent topics from short, dynamic app reviews over multiple versions.
method Adaptive Online Biterm Topic Model (AOBTM) that addresses sparsity and considers statistical data from previous versions.
result AOBTM finds more coherent topics and outperforms state-of-the-art baselines.
Financial market is an example of complex system, which is characterized by a highly intricate organization and the emergence of collective behavior. In this paper, we quantify this emergent dynamics in the financial market by using concepts of network synchronization. We consider networks constructed by the correlatio…
Set-valued risk measures on with for conical market models are defined, primal and dual representation results are given. The collection of initial endowments which allow to super-hedge a multivariate claim are shown to form the values of a set-valued sublinear (coherent) risk measure. Sc…
Despite significant advances in artificial intelligence (AI) for computer vision, its application in medical imaging has been limited by the burden and limits of expert-generated labels. We used images from optical coherence tomography angiography (OCTA), a relatively new imaging modality that measures perfusion of the…
Selecting an optimal set of icons is a crucial step in the pipeline of visual design to structure and navigate through content. However, designing the icons sets is usually a difficult task for which expert knowledge is required. In this work, to ease the process of icon set selection to the users, we propose a similar…
ISOKANN learns collective variables and effective dynamics for metastable transitions.
problem Understanding metastable transitions in complex molecular systems.
method Integrates Koopman operators with neural networks to extract CVs and effective dynamics.
result Reconstructs coarse-grained kinetics and reproduces transition times across barriers.
This paper extends some results of Hatcher and Quinn beyond the metastable range. We give a bordism theoretic obstruction to deforming a map between manifolds simultaneously off of a collection of pairwise disjoint submanifolds under the assumption that it can be deformed off of any proper subcollection in a homotopy c…
Emergence of frustration signals systemic riskphysics.soc-ph
We show that the emergence of systemic risk in complex systems can be understood from the evolution of functional networks representing interactions inferred from fluctuation correlations between macroscopic observables. Specifically, we analyze the long-term collective dynamics of the New York Stock Exchange between 1…
We propose a robust risk measurement approach that minimizes the expectation of overestimation plus underestimation costs. We consider uncertainty by taking the supremum over a collection of probability measures, relating our approach to dual sets in the representation of coherent risk measures. We provide results that…
The paper tackles the problem of deriving a topological structure among stock prices from high frequency historical values. Similar studies using low frequency data have already provided valuable insights. However, in those cases data need to be collected for a longer period and then they have to be detrended. An effec…
Risk-averse model uncertainty framework for safe reinforcement learning.
problem Safe decision making in uncertain environments.
method Risk-averse perspective towards model uncertainty using coherent distortion risk measures; equivalent to distributionally robust safe reinforcement learning problems; efficient, model-free implementation.
result Demonstrates robust performance and safety across perturbed test environments.
Coherent manifoldsmath-ph
Defines coherent manifolds and their quantum applications.
problem Understanding quantum spaces and coherent states.
method Generalizes quantum field theory and Schrödinger equation solutions.
result Solves Schrödinger equation on coherent manifolds.
CoRe method improves time series forecasting coherency without strict constraints.
problem Noisy hierarchical time series data that doesn't perfectly adhere to aggregation constraints.
method Coherency Regularization using neural networks.
result Improved forecast accuracy and coherence, especially in noisy data scenarios.
In this paper we present a theoretical framework for studying coherent acceptability indices in a dynamic setup. We study dynamic coherent acceptability indices and dynamic coherent risk measures, and we establish a duality between them. We derive a representation theorem for dynamic coherent risk measures in terms of …
A new video prediction model treats videos as continuous processes, reducing sampling steps and improving efficiency.
problem Efficiency and temporal coherence in video prediction models.
method Treats videos as a continuous multi-dimensional process, reducing sampling steps.
result Reduction of 75% sampling steps, state-of-the-art performance on benchmark datasets.
Coherent Multiplex analyzes real-time wavelet coherence among multiple signals.
problem Identifying and visualizing coherence among multiple time series.
method Fast spectral similarity based on cosine similarity metrics of Fourier-transformed signals and sparse time-frequency wavelet coherence.
result Scalable real-time system for low-latency inference and monitoring of inter-signal relationships.
Twitmo analyzes geo-tagged Twitter data for topic modeling and visualization.
problem Analyzing public discourse on Twitter for various topics, parties, or individuals.
method Collects and preprocesses geo-tagged Tweets, applies LDA, CTM, STM, and visualizes results.
result Automatic pooling of Tweets into pseudo-documents improves topic coherence.
Study financial markets using synchronization measures and clustering algorithms.
problem Analyze high-frequency trading dynamics and market states.
method Ordinal pattern series, information-theoretic synchronization measure, clustering algorithms, Markov model.
result Identify two coherent seasons of centralized and decentralized synchronicity.
The transition amplitudes between coherent states on a coherent state manifold are expressed in terms of the embedding of the coherent state manifold into a projective Hilbert space. Consequences for the dimension of projective Hilbert space and a simple geometric interpretation of Calabi's diastasis follows.
We use mathematical induction to prove that the horizontal composition in the class of coherently diagonal complexes is indeed a binary operation. That is to say, the embedding of two coherently diagonal complexes in an alternating planar diagram produces a coherently diagonal complex.
Equation Embeddingsstat.ML
We present an unsupervised approach for discovering semantic representations of mathematical equations. Equations are challenging to analyze because each is unique, or nearly unique. Our method, which we call equation embeddings, finds good representations of equations by using the representations of their surrounding …
BBM models short texts using biterms to improve coherence.
problem Challenges in analyzing short texts from social media.
method Bag of Biterms (BoB) for document representation and simple statistical models.
result BBM enhances coherence and performance over traditional models.
The study of topological groups with compact open subgroups and their geometric properties.
problem Characterizing and understanding topological groups with compact open subgroups.
method Geometric techniques, discrete actions on complexes, quasi-isometry invariance, and hyperbolic fine graphs.
result Generalizations of discrete group results to topological groups with compact open subgroups.
Paper constructs Chern character for coherent sheaves.
problem Chern character for coherent sheaves with values in Bott-Chern cohomology.
method Based on Block's fundamental construction, constructs Chern character.
result Proves Riemann-Roch-Grothendieck formula for coherent sheaves.
The paper constructs minimal coherent filling pairs on surfaces.
problem Finding minimal intersecting coherent filling pairs on surfaces.
method Geometric procedure starting from a torus filling pair.
result Construction of minimal intersecting coherent filling pairs on for .
Sparse coding in learned dictionaries has been established as a successful approach for signal denoising, source separation and solving inverse problems in general. A dictionary learning method adapts an initial dictionary to a particular signal class by iteratively computing an approximate factorization of a training …
Paper defines dynamical coherence for flows and proves it under specific conditions.
problem Understanding the dynamics of partially hyperbolic flows.
method Introduces dynamical coherence and proves it for flows with a specific foliation.
result Dynamical coherence proved for flows with a particular foliation.
Develops equivariant Chern characters for coherent sheaves with group actions.
problem Computing Chern characters for coherent sheaves on manifolds with group actions.
method Introduces equivariant Chern characters and proves Riemann-Roch-Grothendieck theorem in Bott-Chern cohomology.
result Establishes a Riemann-Roch-Grothendieck theorem for coherent sheaves with finite group actions.
New metric -coherence measures gradient alignment during training, revealing surprising memorization patterns.
problem Measuring and understanding the alignment of per-example gradients during training.
method Introducing -coherence as a metric to study gradient alignment, showing its advantages over existing metrics.
result Training with random labels leads to high -coherence, indicating common patterns even when generalization is not possible.
Topic modeling analyzes documents to learn meaningful patterns of words. For documents collected in sequence, dynamic topic models capture how these patterns vary over time. We develop the dynamic embedded topic model (D-ETM), a generative model of documents that combines dynamic latent Dirichlet allocation (D-LDA) and…
Identification of individual coherent sets associated with flow trajectories using Coherent Structure Coloringphysics.flu-dyn
We present a method for identifying the coherent structures associated with individual Lagrangian flow trajectories even where only sparse particle trajectory data is available. The method, based on techniques in spectral graph theory, uses the Coherent Structure Coloring vector and associated eigenvectors to analyze t…
We study a space of coherent risk measures M_phi obtained as certain expansions of coherent elementary basis measures. In this space, the concept of ``Risk Aversion Function'' phi naturally arises as the spectral representation of each risk measure in a space of functions of confidence level probabilities. We give nece…
Generates coherent storybooks from plain text using diffusion models.
problem Ensuring coherency in a sequence of images for storytelling applications.
method Combines pre-trained LLM and text-guided Latent Diffusion Model for zero-shot generation.
result Outperforms state-of-the-art image editing baselines in generating coherent storybooks.
Low-rank matrix approximations are often used to help scale standard machine learning algorithms to large-scale problems. Recently, matrix coherence has been used to characterize the ability to extract global information from a subset of matrix entries in the context of these low-rank approximations and other sampling-…