A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
A-Ward p{eta} improves hierarchical clustering with faster convergence and better recovery.
The Ward error sum of squares hierarchical clustering method has been very widely used since its first description by Ward in a 1963 publication. It has also been generalized in various ways. However there are different interpretations in the literature and there are different implementations of the Ward agglomerative …
The Ward equation, also called the modified 2+1 chiral model, is obtained by a dimension reduction and a gauge fixing from the self-dual Yang-Mills field equation on . It has a Lax pair and is an integrable system. Ward constructed solitons whose extended solutions have distinct simple poles. He also used a li…
Conditions for Penrose-Ward transformation on specific manifolds.
The moduli space of static finite energy solutions to Ward's integrable chiral model is the space of based rational maps from $\CP^1$ to itself with degree . The Lagrangian of Ward's model gives rise to a Kähler metric and a magnetic vector potential on this space. However, the magnetic field strength vanishes…
Using the `Riemann Problem with zeros' method, Ward has constructed exact solutions to a (2+1)-dimensional integrable Chiral Model, which exhibit solitons with nontrivial scattering. We give a correspondence between what we conjecture to be all pure soliton solutions and certain holomorphic vector bundles on a compact …
We show that, in quaternionic geometry, the Ward transform is a manifestation of the functoriality of the basic correspondence between the -quaternionic manifolds and their twistor spaces. We apply this fact, together with the Penrose transform, to obtain existence results for hypercomplex manifolds and for harmonic…
Graphical estimation of count time series dependencies.
The space-time monopole equation is obtained from a dimension reduction of the anti-self dual Yang-Mills equation on . A family of Ward equations is obtained by gauge fixing from the monopole equation. In this paper, we give an introduction and a survey of the space-time monopole equation. Included are altern…
The conformal invariance and universality results of Chelkak-Smirnov on the two-dimensional Ising model hold for isoradial planar graphs with critical weights. Motivated by the problem of extending these results to a wider class of graphs, we define a generalized notion of s-holomorphicity for functions on arbitrary we…
The Kac-Ward formula allows to compute the Ising partition function on a planar graph G with straight edges from the determinant of a matrix of size 2N, where N denotes the number of edges of G. In this paper, we extend this formula to any finite graph: the partition function can be written as an alternating sum of the…
We use the compactified twistor correspondence for the (2+1)-dimensional integrable chiral model to prove a conjecture of Ward. In particular, we construct the correspondence space of a compactified twistor fibration and use it to prove that the second Chern numbers of the holomorphic vector bundles, corresponding to t…
Derives stress-energy identities in Liouville theory on compact surfaces.
Improves hierarchical clustering in Euclidean space using autoencoders.
ClustGeo uses Ward-like clustering with spatial constraints in R.
New framework estimates staged tree models using hierarchical clustering on the probability simplex.
Method clusters molecular systems based on dynamics or structure similarity.
Ward2ICU dataset protects patient privacy while generating synthetic ICU transitions data.
The Kac-Ward formula allows to compute the Ising partition function on any finite graph G from the determinant of 2^{2g} matrices, where g is the genus of a surface in which G embeds. We show that in the case of isoradially embedded graphs with critical weights, these determinants have quite remarkable properties. Firs…
Survey on -Hitchin equations and Higgs bundles from geometric perspective.
Simplified geometric derivation of quantum A-polynomials for knots.
Geometric method captures rare topics and temporal alignment in co-author networks.
The paper defines ASD connections and constructs families over a 5D Heisenberg group.
Study on type-D metrics aligned with Einstein-Maxwell equations, deriving solutions.
Probabilistic Boolean tensor decomposition improves accuracy and scalability.
We show that a twistor construction of Hitchin and Ward can be adapted to study unitons (harmonic spheres in a unitary group). Specifically, we show that unitons are equivalent to holomorphic bundles with extra structure over a rational ruled surface with energy given by Chern class. This equivalence allows us to confi…
Study on type-D Ricci-flat metrics with Killing spinors and Killing vectors.
We establish a Penrose-Ward transform yielding a bijection between holomorphic principal 2-bundles over a twistor space and non-Abelian self-dual tensor fields on six-dimensional flat space-time. Extending the twistor space to supertwistor space, we derive sets of manifestly N=(1,0) and N=(2,0) supersymmetric non-Abeli…
The Lax formulation of the hyper-Hermiticity condition in four dimensions is used to derive a potential that generalises Plebanski's second heavenly equation for hyper-Kahler 4-manifolds. A class of examples of hyper-Hermitian metrics which depend on two arbitrary functions of two complex variables is given. The twisto…
Revisits twistorial structures with new geometric proofs.
I show that solutions of the SU(infinity) Toda field equation generating a fixed Einstein-Weyl space are governed by a linear equation on the Einstein-Weyl space. From this, obstructions to the existence of Toda solutions generating a given Einstein-Weyl space are found. I also give a classification of Einstein-Weyl sp…
Let l be a link of d components. For every finite-index lattice in Z^d there is an associated finite abelian cover of S^3 branched over l. We show that the order of the torsion subgroup of the first homology of these covers has exponential growth rate equal to the logarithmic Mahler measure of the Alexander polynomial …
We construct a Teichmueller curve uniformized by the Fuchsian triangle group (m,n,\infty) for every m<n. Our construction includes the Teichmueller curves constructed by Veech and Ward as special cases. The construction essentially relies on properties of hypergeometric differential operators. For small m, we find Bill…
Paper addresses limitations of traditional hierarchical clustering methods.
New equations define frustrated conformal transformations generating maps on ambitwistor space.
The two-sphere valued wave map flow on a Lorentzian domain R x Sigma, where Sigma is any flat two-torus, is studied. The Cauchy problem with initial data tangent to the moduli space of holomorphic maps Sigma -> S^2 is considered, in the limit of small initial velocity. It is proved that wave maps, in this limit, conver…
Develops twistorial approach to define monopoles on R^5.
We formulate and solve the analog of the universal Conformal Ward Identity for the stress-energy tensor on a compact Riemann surface of genus , and present a rigorous invariant formulation of the chiral sector in the induced two-dimensional gravity on higher genus Riemann surfaces. Our construction of the action f…
We construct manifestly superconformal field theories in six dimensions which contain a non-Abelian tensor multiplet. In particular, we show how principal 3-bundles over a suitable twistor space encode solutions to these self-dual tensor field theories via a Penrose-Ward transform. The resulting higher or categorified …
Machine learning improves early detection of patient deterioration in Brazilian hospitals.
In recent years, a rapidly growing literature has focussed on the construction of wavelet systems to analyze functions defined on the sphere. Our purpose in this paper is to generalize these constructions to situations where sections of line bundles, rather than ordinary scalar-valued functions, are considered. In part…
The variational calculus for the Faddeev-Hopf model on a general Riemannian domain, with general Kaehler target space, is studied in the strong coupling limit. In this limit, the model has key similarities with pure Yang-Mills theory, namely conformal invariance in dimension 4 and an infinite dimensional symmetry group…
In the first part of this paper we provide a short introduction to the AdS/CFT correspondence and to holographic renormalization. We discuss how QFT correlation functions, Ward identities and anomalies are encoded in the bulk geometry. In the second part we develop a Hamiltonian approach to the method of holographic re…
We study finite-dimensional integrals in a way that elucidates the mathematical meaning behind the formal manipulations of path integrals occurring in quantum field theory. This involves a proper understanding of how Wick's theorem allows one to evaluate integrals perturbatively, i.e., as a series expansion in a formal…
Study the geometry of twistor spaces with rotating circle action.
Defines non-Abelian gerbes with connections for physical applications.
We formulate a 4-dimensional higher gauge theoretic Chern-Simons theory. Its symmetry is encoded in a semistrict Lie 2-algebra equipped with an invariant non singular bilinear form. We analyze the gauge invariance of the theory and show that action is invariant under a higher gauge transformation up to a higher winding…
New clustering method recovers hidden tree structure from data.