arXiv research

A new approach to quantum machine learning circuits reduces training difficulties.

In this paper the multivariate fractional trading ansatz of money management from Ralph Vince (Portfolio Management Formulas: Mathematical Trading Methods for the Futures, Options, and Stock Markets, John Wiley & Sons, Inc., 1990) is discussed. In particular, we prove existence and uniqueness of an optimal f of the res…

New ansatz for generalized Kähler surfaces derived from hyperKähler ansatz.

Expressive quantum circuits are harder to train due to flatter cost landscapes.

We describe a quaternionic-based Ansatz generalizing the Gibbons-Hawking Ansatz to a class of hyperkähler metrics with hidden symmetries. We then apply it to obtain explicit expressions for gravitational instanton metrics of type $D_k$.

Deep QMC ansatzes improve variational QMC accuracy.

It was observed by Tod and later by Dunajski and Tod that the Boyer-Finley (BF) and the dispersionless Kadomtsev-Petviashvili (dKP) equations possess solutions whose level surfaces are central quadrics in the space of independent variables (the so-called central quadric ansatz). It was demonstrated that generic solutio…

A homogeneous Gibbons-Hawking ansatz is described, leading to 4-dimensional hyperkahler metrics with homotheties. In combination with Blaschke products on the unit disc in the complex plane, this ansatz allows one to construct infinite-dimensional families of such hyperkahler metrics that are, in a suitable sense, comp…

MBQC linked to CQCA, yielding efficient Ansätze.

Develops quantum circuits for faster learning with symmetry considerations.

We show that a complete simply-connected hyperkaehler 4-manifold with an isometric triholomorphic circle action is obtained from the Gibbons-Hawking ansatz with some suitable harmonic function.

Study Ricci flow on CP1-bundles over Kähler-Einstein manifolds.

Barrier methods classify minimal submanifolds in hyperkaehler spaces.

The modified J-flow with Calabi ansatz shows convergence or blow-up behavior based on topological constants.

UKM framework optimizes VQCs, showing QCL performance is bounded.

Develops methods to solve complex and real Hessian equations.

Constructs scalar-flat Kähler metrics with varying conical singularities.

We discuss the Ricci-flat `model metrics' on $\mathbb{C}^2$ with cone singularities along the conic $\{zw=1\}$ constructed by Donaldson using the Gibbons-Hawking ansatz over wedges in $\mathbb{R}^3$. In particular we describe their asymptotic behavior at infinity and compute their energies.

Invariant Kähler metrics on line bundles are derived from the Calabi ansatz.

Improved Least-Squares Monte Carlo with finite-difference ansatz.

New approach connects quantum phases to VQA trainability, enabling better scaling.

The quadric ansatz solves dKP equations in arbitrary dimensions, leading to Einstein-Weyl structures.

In this paper the fractional trading ansatz of money management is reconsidered with special attention to chance and risk parts in the goal function of the related optimization problem. By changing the goal function with due regards to other risk measures like current drawdowns, the optimal fraction solutions reflect t…

We give a dynamical description, in terms of a Weil-type zeta function, to the holomorphic torsion with coefficients for certain compact Hermitian locally symmetric manifolds, whose connected group G of isometries of the universal cover has only one conjugacy class of cuspidal maximal parabolic subgroup and satisfies a…

This article provides an explicit construction for a family of singular instantons on S^4 S^2 with arbitrary real holonomy parameter α. This family includes the original α= 1/4, c_2 = 3/2 solution discovered by P. Forgacs, Z. Horvath, and L. Palla, and our approach is modeled on that of their 1981 paper. Our primary to…

An ansatz of Calabi allows construction of Kahler metrics in an Hermitian disk bundle over a Kahler manifold. We attempt to give a definitive treatment of this ansatz, with the following results: We give curvature conditions on the disk bundle that guarantee existence of families of complete Kahler metrics of constant …

We study the convergence behavior of the general inverse $σ_k$-flow on Kähler manifolds with initial metrics satisfying the Calabi Ansatz. The limiting metrics can be either smooth or singular. In the latter case, interesting conic singularities along negatively self-intersected sub-varieties are formed as a result of …

Complete Calabi-Yau metrics on C^{N+1} are constructed.

Study complex structures of hyperkähler manifolds with infinite type.

Meta-learning algorithms prepare quantum Gibbs states efficiently for NISQ devices.

The Gibbons-Hawking ansatz provides a large family of circle-invariant hyperkaehler 4-manifolds, and thus Calabi-Yau 2-folds. In this setting, we prove versions of the Thomas conjecture on existence of special Lagrangian representatives of Hamiltonian isotopy classes of Lagrangians, and the Thomas-Yau conjecture on lon…

In this paper we apply the anholonomic frames method developed in refs. [1-4] to construct and study anisotropic vacuum field configurations in 5D gravity. Starting with an off--diagonal 5D metric, parameterized in terms of several ansatz functions, we show that using anholonomic frames greatly simplifies the resulting…

We construct geometric shrinkage priors for Kählerian signal filters. Based on the characteristics of Kähler manifolds, an efficient and robust algorithm for finding superharmonic priors which outperform the Jeffreys prior is introduced. Several ansätze for the Bayesian predictive priors are also suggested. In particul…

New steady Euler flows found on 3-sphere and Sasakian manifolds.

Derives FACT, an alternative to NFA for neural networks, explaining feature learning.

We show that the geometry of $4n$-dimensional quaternionic Kähler spaces with a locally free $\mathbb{R}^{n+1}$-action admits a Gibbons-Hawking-like description based on the Galicki-Lawson notion of quaternionic Kähler moment map. This generalizes to higher dimensions a four-dimensional construction, due to Calderbank …

Paper optimizes trading strategies by creating shadow prices for markets with transaction costs.

Study Kähler-Einstein edge metrics on Hirzebruch surfaces, verifying a conjecture and finding a rigid singularity.

We consider cones over manifolds admitting real Killing spinors and instanton equations on connections on vector bundles over these manifolds. Such cones are manifolds with special (reduced) holonomy. We generalize the scalar ansatz for a connection proposed by Harland and Nolle in such a way that instantons are parame…

[New and updated results were published in Nature Chemistry, doi:10.1038/s41557-020-0544-y.] The electronic Schrödinger equation describes fundamental properties of molecules and materials, but can only be solved analytically for the hydrogen atom. The numerically exact full configuration-interaction method is exponent…

Existence of Ricci flat metric on Kummer K3 surface proven.

The paper constructs Einstein metrics on holomorphic bundles.

We discuss the behavior of two magnitudes, physical complexity and mutual information function of the outcome of a model of heterogeneous, inductive rational agents inspired in the El Farol Bar problem and the Minority Game. The first is a measure rooted in Kolmogorov-Chaitin theory and the second one a measure related…

This paper studies Kähler-Ricci solitons on Heisenberg groups and related metrics.

Researchers describe $G_2$-structures on $7$-sphere, finding harmonic representatives.

Method identifies low-dimensional structure in high-dimensional probability measures.

Hybrid quantum-classical method optimizes financial index tracking.

Develops a method to construct entire minimal graphs of odd dimensions.