arXiv research

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.

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 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…

The study examines Kähler structures on coadjoint orbits of Lie groups using coherent and squeezed states.

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…

The paper defines and analyzes coherent and squeezed states on manifolds and their quantization.

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…

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…

The study bounds entanglement entropy for coherent states on Kähler manifolds.

On certain manifolds, the phase which appears in the scalar product of two coherent state vectors is twice the symplectic area of the geodesic triangle determined by the corresponding points on the manifold and the origin of the system of coordinates. This result is proved for compact Hermitian symmetric spaces using t…

Recently, neural approaches to coherence modeling have achieved state-of-the-art results in several evaluation tasks. However, we show that most of these models often fail on harder tasks with more realistic application scenarios. In particular, the existing models underperform on tasks that require the model to be sen…

It is shown that the heat operator in the Hall coherent state transform for a compact Lie group $K$ is related with a Hermitian connection associated to a natural one-parameter family of complex structures on $T^*K$. The unitary parallel transport of this connection establishes the equivalence of (geometric) quantizati…

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.

It is shown how the coherent states permit to find different geometrical objects as the geodesics, the conjugate locus, the cut locus, the Calabi's diastasis and its domain of definition, the Euler-Poincaré characteristic, the number of Borel-Morse cells, the Kodaira embedding theorem.

Defines coherent manifolds and their quantum applications.

Representations of coherent state Lie algebras on coherent state manifolds as first order differential operators are presented. The explicit expressions of the differential action of the generators of semisimple Lie groups determine for linear Hamiltonians in the generators of the groups first order differential equati…

The coherent state representation of the Jacobi group $G^J_1$ is indexed with two parameters, $μ(=\frac{1}{\hbar})$, describing the part coming from the Heisenberg group, and $k$, characterizing the positive discrete series representation of $\text{SU}(1,1)$. The Ricci form, the scalar curvature and the geodesics of th…

Paper improves video categorization using temporal coherence.

Different topics on the differential geometry of the complex Grassmann manifold are surveyed in relation to the coherent states. A calculation of the tangent conjugate locus and conjugate locus in the complex Grassmann manifold is presented. The proofs use the Jordan's stationary angles. Also various formulas for the d…

CoRe method improves time series forecasting coherency without strict constraints.

The consequences for Berezin's quantization on symmetric spaces of the identity of the set of coherent vectors orthogonal to a fixed one with the cut locus are stated precisely. It is shown that functions expressing the coherent states, the covariant symbols of operators, the diastasis function, the characteristic and …

New method produces coherent forecasts for long-range data.

Generates coherent storybooks from plain text using diffusion models.

We extend the coherent state transform (CST) of Hall to the context of the moduli spaces of semistable holomorphic vector bundles with fixed determinant over elliptic curves. We show that by applying the CST to appropriate distributions, we obtain the space of level k, rank n and genus one non-abelian theta functions w…

End-to-end deep model for coherent probabilistic forecasts in hierarchical time series.

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 …

Adler had shown in 1979 that the Toda system can be given a coad- joint orbit description. We quantize the Toda system by viewing it as a single orbit of a multiplicative group of lower triangular matrices of determinant one with pos- itive diagonal entries. We get a unitary representation of the group with square inte…

Recurrent neural networks' hidden state can be reconstructed from its past, providing a theoretical framework for stability and tracking.

Enhances neural forecasting for hierarchically organized time series data.

Quantum reservoir computing needs coherence influx for effective information processing.

C-HMCNN(h) improves HMC classification by leveraging class hierarchy.

This paper presents a remarkably simple, yet powerful, algorithm termed Coherence Pursuit (CoP) to robust Principal Component Analysis (PCA). As inliers lie in a low dimensional subspace and are mostly correlated, an inlier is likely to have strong mutual coherence with a large number of data points. By contrast, outli…

A membrane technique, in which the symplectic and Ricci forms are integrated over surfaces in a complexification of the phase space, as well a ``creation" connection with zero curvature over lagrangian submanifolds, is used to obtain a unified quantization including a noncommutative algebra of functions, its representa…

Recognizing facial expressions from static images or video sequences is a widely studied but still challenging problem. The recent progresses obtained by deep neural architectures, or by ensembles of heterogeneous models, have shown that integrating multiple input representations leads to state-of-the-art results. In p…

The abstract explores a new wave equation linking quantum mechanics and complex adaptive systems.

TOAD-GAN generates coherent game levels from a single example.

The paper studies gauge fields on coherent sheaves and their Yang-Mills properties.

CMC method detects causal relationships in time series data.

Optimal hashing embeddings reduce linear least squares solving time.

In emerging Internet-of-Nano-Thing (IoNT), information will be embedded and conveyed in the form of molecules through complex and diffusive medias. One main challenge lies in the long-tail nature of the channel response causing inter-symbol-interference (ISI), which deteriorates the detection performance. If the channe…

The paper addresses speckle noise in coherent imaging systems.

Paper explores PG for MCR, finding suboptimal policies but providing bounds.

A new framework for robust and coherent counterfactual transports.

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 neural topic model using optimal transport improves document representation and topic coherence.

Coherent Multiplex analyzes real-time wavelet coherence among multiple signals.

Top-H decoding improves text generation by balancing creativity and coherence.

In this article, we study the convergence of Mirror Descent (MD) and Optimistic Mirror Descent (OMD) for saddle point problems satisfying the notion of coherence as proposed in Mertikopoulos et al. We prove convergence of OMD with exact gradients for coherent saddle point problems, and show that monotone convergence on…