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 …
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.
Unified model improves coherence tasks, especially local contexts.
problem Existing neural coherence models struggle with local context tasks.
method Unified neural framework integrating grammar, relations, and patterns.
result Unified model outperforms existing models significantly.
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.
Insurance surplus sharing using coherent risk measures.
problem Dividing surplus between insured and shareholders.
method Coherent risk measures and capital allocation theory.
result A method to fairly divide insurance surplus.
Method identifies coherent structures in sparse flow data.
problem Identifying coherent structures in sparse particle trajectory data.
method Spectral graph theory and hierarchical clustering.
result Algorithm successfully identifies coherent structures in various flows.
Researchers explore non-coherent banding in site-specific recombination.
problem Understanding non-coherent banding in site-specific recombination.
method Survey of recent developments in non-coherent banding on knots.
result Recent advances in non-coherent banding model for site-specific recombination.
One-relator groups with torsion are shown to be coherent.
problem One-relator groups with torsion.
method Demonstrated coherence by showing every finitely generated subgroup is finitely presented.
result One-relator groups with torsion are coherent.
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 Sg for g≥3. 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 …
New metric m-coherence measures gradient alignment during training, revealing surprising memorization patterns.
problem Measuring and understanding the alignment of per-example gradients during training.
method Introducing m-coherence as a metric to study gradient alignment, showing its advantages over existing metrics. result Training with random labels leads to high m-coherence, indicating common patterns even when generalization is not possible. 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.
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.
Extends coherence results to one-relator products of locally indicable groups.
problem Coherence in one-relator products of locally indicable groups.
method Developed new methods to extend results of Helfer, Wise, Louder, Wilton, and Brodsky.
result New proof of a theorem by Brodsky.
Method detects coherent structures from sparse flow data using graph theory.
problem Detecting coherent structures from sparse flow data.
method Graph coloring and spectral graph drawing algorithms applied to kinematic dissimilarity of trajectories.
result Robustly detects coherent structures using significantly less data than existing methods.
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-…
Morse theory extended to noncompact manifolds with complex geometric data.
problem Extending Morse theory to noncompact manifolds with intricate geometric and homotopy data.
method Defining Morse homology for pairs of manifolds and related geometric/homotopy data, constructing a homotopy coherent diagram of linear maps, and showing it computes Morse homology.
result Morse homology can be computed using a chain complex derived from a homotopy coherent diagram.
Develops non-standard analysis for coherent risk estimation.
problem Estimating coherent risk measures in financial contexts.
method Non-standard analysis, hyperfinite representations, discrete Kusuoka formulae, plug-in asymptotics.
result Uniform almost sure consistency and asymptotic normality of spectral plug-in estimators.
This paper improves facial expression recognition using CNNs and coherence constraints.
problem Facial expression recognition from static images and video sequences is challenging.
method Investigates the use of Convolutional Neural Networks (CNNs) with coherence constraints in a semi-supervised setting.
result Coherence constraints improve facial expression recognition quality, especially in the presence of occlusions.
A realization of coherent state Lie algebras by first-order differential operators with holomorphic polynomial coefficients on Kähler coherent state orbits is presented. Explicit formulas involving the Bernoulli numbers and the structure constants for the semisimple Lie groups are proved.
The MAXVAR risk measure is shown coherent and provides a formula for its risk envelope.
problem Coherency and formula for MAXVAR risk measure.
method Elementary proof of coherency, observation of convex combination, explicit formula derivation.
result MAXVAR risk measure is coherent and has an explicit risk envelope formula.
We propose a pricing technique based on coherent risk measures, which enables one to get finer price intervals than in the No Good Deals pricing. The main idea consists in splitting a liability into several parts and selling these parts to different agents. The technique is closely connected with the convolution of coh…
The coherent states are viewed as a powerful tool in differential geometry. It is shown that some objects in differential geometry can be expressed using quantities which appear in the construction of the coherent states. The following subjects are discussed via the coherent states: the geodesics, the conjugate locus a…
Paper improves video categorization using temporal coherence.
problem Video categorization in multiple modalities.
method Temporal coherence-based regularization for multimodal models.
result Models with temporal coherence outperform state-of-the-art.
CNNs improve InSAR coherence classification.
problem Improving demarcation of InSAR imagery regions based on coherence.
method Convolutional Neural Networks (CNNs) for preprocessing and classification.
result CNNs reduce misclassifications in incoherent regions and outperform established methods.
We emphasize some properties of coherent state groups, i.e. groups whose quotient with the stationary groups, are manifolds which admit a holomorphic embedding in a projective Hilbert space. We determine the differential action of the generators of the representation of coherent state groups on the symmetric Fock space…
A group is coherent if all its finitely generated subgroups are finitely presented. In this article we provide a criterion for positively determining the coherence of a group. This criterion is based upon the notion of the perimeter of a map between two finite 2-complexes which is introduced here. In the groups to whic…
For homogeneous simply connected Hodge manifolds it is proved that the set of coherent vectors orthogonal to a given one is the divisor responsible for the homogeneous holomorphic line bundle of the coherent vectors. In particular, for naturally reductive spaces, the divisor is the cut locus.
New method produces coherent forecasts for long-range data.
problem Inaccurate and non-coherent forecasts on long-horizon data.
method Probabilistic forecasting with KL-divergence for coherent aggregates.
result Improves forecast performance across base levels and aggregates.
Coherence Pursuit is a fast, simple, robust PCA algorithm.
problem Principal Component Analysis with robustness to outliers.
method Coherence Pursuit algorithm: computes Gram matrix, identifies strong coherence with rest of data.
result Outliers are distinguished from inliers by strong mutual coherence with data points.
This is a large audience version of our previous work (see math.AG/0301146) in which we prove the existence of an (exact) equivalence between the category of coherent analytic sheaves and the category of ∂ˉ-coherent sheaves. We also include here the complete proof of our main Theorem.
The study examines Kähler structures on coadjoint orbits of Lie groups using coherent and squeezed states.
problem Does the coadjoint orbits of Lie groups support a Kähler structure?
method Examined three Lie groups: Weyl-Heisenberg, SU(2), and SU(1,1). Used coherent and squeezed states to explore Kähler structures.
result Coherent states provide Kähler embeddings, while squeezed states only symplectic embeddings.
For arbitrary quantizable compact Kaehler manifolds, relations between the geometry given by the coherent states based on the manifold and the algebraic (projective) geometry realised via the coherent state mapping into projective space, are studied. Polar divisors, formulas relating the scalar products of coherent vec…
This note is mostly an exposition of an unpublished result of Deligne, which introduces an analogue of perverse t-structure on the derived category of coherent sheaves on a Noetherian scheme with a dualizing complex. Construction extends to the category of coherent sheaves equivariant under an action of an algebraic …
The intimate relationship between coherent states and geodesics is pointed out. For homogenous manifolds on which the exponential from the Lie algebra to the Lie group equals the geodesic exponential, and in particular for symmetric spaces, it is proved that the cut locus of the point 0 is equal to the set of coheren…
Develops a statistical framework for coherent risk estimation.
problem Constructing coherent risk estimators with sound financial and statistical properties.
method Inspired by axiomatic risk measure theory, defines coherent risk estimators through robust representations linked to L-estimators. result Demonstrates that coherence of a risk measure does not necessarily carry over to its estimators and shows alternative weight structures can lead to different outcomes.
Kernel methods detect coherent structures in dynamical data.
problem Detecting coherent structures in complex dynamical systems.
method Kernel-based dimensionality reduction techniques and eigendecompositions of RKHS operators.
result Coherent sets of particle trajectories can be computed by kernel CCA.
New approach uses neural networks for MIMO modulation without black-box optimization.
problem Improving MIMO modulation for non-coherent channels with short coherence windows.
method Simulation-driven optimization using neural networks for modulation and signal detection design.
result Demonstrated that neural networks can be avoided while still achieving comparable performance in MIMO communications.
Absolutely partially hyperbolic surface endomorphisms have a coherent center foliation.
problem Understanding the dynamics of absolutely partially hyperbolic surface endomorphisms.
method Showed the existence of a center foliation and leaf conjugacy to the linearization.
result Absolutely partially hyperbolic surface endomorphisms have a dynamically coherent center foliation.
End-to-end deep model for coherent probabilistic forecasts in hierarchical time series.
problem Hierarchical probabilistic forecasting for coherent predictions.
method Dirichlet proportions model for learning root and child distributions.
result Significant improvements over state-of-the-art baselines (up to 26%).
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 …
Extract coherent structures from Jupiter's clouds and snow events without flow models.
problem Finding coherent structures in fluidic systems from image data.
method Image processing with anisotropic, directed diffusion operator from a directed affinity matrix.
result Demonstrated coherence in Jupiter's clouds and snow events without flow modeling.