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.
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…
A new method uses coherent structure coloring to estimate model parameters more accurately than traditional methods.
We present a frame-invariant method for detecting coherent structures from Lagrangian flow trajectories that can be sparse in number, as is the case in many fluid mechanics applications of practical interest. The method, based on principles used in graph coloring and spectral graph drawing algorithms, examines a measur…
The clustering of data into physically meaningful subsets often requires assumptions regarding the number, size, or shape of the subgroups. Here, we present a new method, simultaneous coherent structure coloring (sCSC), which accomplishes the task of unsupervised clustering without a priori guidance regarding the under…
Study on colored Jones polynomial and link complements.
Study shows colored Jones invariants limit to link volumes.
Enhances quandle and biquandle colorings using biquandle structures.
The paper introduces new structures for colored HOMFLY-PT invariants using skein theory.
A virtual link diagram is called normal if the associated abstract link diagram is checkerboard colorable, and a virtual link is normal if it has a normal diagram as a representative. Normal virtual links have some properties similar to classical links.In this paper, we introduce a method of converting a virtual link d…
The study examines Kähler structures on coadjoint orbits of Lie groups using coherent and squeezed states.
The study characterizes torus links' coloring quivers using dihedral quandles.
Model criticism tool evaluates text coherence and structure in generated long-form text.
Paper constructs super integrable systems on color Lie algebra.
We introduce two kinds of structures, called v-structures and t-structures, on biquandles. These structures are used for colorings of diagrams of virtual links and twisted links such that the numbers of colorings are invariants. Given a biquandle or a quandle, we give a method of constructing a biquandle with these str…
Study on quandle coloring quivers for (p, 2)-torus knots and links.
We study the structural properties of colored Kauffman homologies of knots. Quadruple-gradings play an essential role in revealing the differential structure of colored Kauffman homology. Using the differential structure, the Kauffman homologies carrying the symmetric tensor products of the vector representation for th…
We consider a quiver structure on the set of quandle colorings of an oriented knot or link diagram. This structure contains a wealth of knot and link invariants and provides a categorification of the quandle counting invariant in the most literal sense, i.e., giving the set of quandle colorings the structure of a small…
The paper studies coherent sheaves on subvarieties of Hopf manifolds.
We generalize results of Lee, Gornik and Wu on the structure of deformed colored sl(N) link homologies to the case of non-generic deformations. To this end, we use foam technology to give a completely combinatorial construction of Wu's deformed colored sl(N) link homologies. By studying the underlying deformed higher r…
Solves division problem for L. Hörmander's systems.
We conjecture the existence of four independent gradings in the colored HOMFLY homology. We describe these gradings explicitly for the rectangular colored homology of torus knots and make qualitative predictions of various interesting structures and symmetries in the colored homology of general knots. We also give a si…
The ability to characterize the color content of natural imagery is an important application of image processing. The pixel by pixel coloring of images may be viewed naturally as points in color space, and the inherent structure and distribution of these points affords a quantization, through clustering, of the color i…
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.
New knot homology invariant grows exponentially with color.
Kernel methods detect coherent structures in dynamical data.
Diabetic eye disease is one of the fastest growing causes of preventable blindness. With the advent of anti-VEGF (vascular endothelial growth factor) therapies, it has become increasingly important to detect center-involved diabetic macular edema (ci-DME). However, center-involved diabetic macular edema is diagnosed us…
We define reduced colored sl(N) link homologies and use deformation spectral sequences to characterize their dependence on color and rank. We then define reduced colored HOMFLY-PT homologies and prove that they arise as large N limits of sl(N) homologies. Together, these results allow proofs of many aspects of the phys…
New colored knot Floer homology defined using infinite full twists.
Let M be a K3 surface or an even-dimensional compact torus. We show that the category of coherent sheaves on M is independent from the choice of the complex structure, if this complex structure is generic.
We illustrate from the viewpoint of braiding operations on WZNW conformal blocks how colored HOMFLY polynomials with multiplicity structure can detect mutations. As an example, we explicitly evaluate the (2,1)-colored HOMFLY polynomials that distinguish a famous mutant pair, Kinoshita-Terasaka and Conway knot.
Clarifies how knot homset invariants relate to diagram colorings.
It is shown that the heat operator in the Hall coherent state transform for a compact Lie group is related with a Hermitian connection associated to a natural one-parameter family of complex structures on . The unitary parallel transport of this connection establishes the equivalence of (geometric) quantizati…
Introduces multi-tribrackets for knot and link coloring.
Rapid overlay of chemical structures (ROCS) is a standard tool for the calculation of 3D shape and chemical ("color") similarity. ROCS uses unweighted sums to combine many aspects of similarity, yielding parameter-free models for virtual screening. In this report, we decompose the ROCS color force field into "color com…
An invariant for knots with colored bonds respects HOMFLYPT relation.
The paper connects GL-racks to knot coloring invariants.
We introduce length dilatation structures on metric spaces, tempered dilatation structures and coherent projections and explore the relations between these objects and the Radon-Nikodym property and Gamma-convergence of length functionals. Then we show that the main properties of sub-riemannian spaces can be obtained f…
Novel symmetry found in colored HOMFLY polynomials from superalgebras.
New method calculates bridge indices of spatial graphs using diagram colorings and Wirtinger number.
Text documents are structured on multiple levels of detail: individual words are related by syntax, but larger units of text are related by discourse structure. Existing language models generally fail to account for discourse structure, but it is crucial if we are to have language models that reward coherence and gener…
Colored HOMFLY-PT invariant, the generalization of the colored Jones polynomial, is one of the most important quantum invariants of links. This paper is devoted to investigating the basic structures of the colored HOMFLY-PT invariants of links. By using the HOMFLY-PT skein theory, firstly, we show that the (reformulate…
This note is mostly an exposition of an unpublished result of Deligne, which introduces an analogue of perverse -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 …
We formulate a conjecture (already proven by A. Kricker) about the structure of Kontsevich integral of a knot. We describe its value in terms of the generating functions for the numbers of external edges attached to closed 3-valent diagrams. We conjecture that these functions are rational functions of the exponentials …
This paper explores neural networks for colorizing grayscale images.
New dataset and models generate piano music with coherent structure across multiple timescales.
We formulate a stability conjecture for the coefficients of the colored Jones polynomial of a knot, colored by irreducible representations in a fixed ray of a simple Lie algebra, and verify it for all torus knots and all simple Lie algebras of rank . Our conjecture is motivated by a structure theorem for the degree …
Viewing a data set such as the clouds of Jupiter, coherence is readily apparent to human observers, especially the Great Red Spot, but also other great storms and persistent structures. There are now many different definitions and perspectives mathematically describing coherent structures, but we will take an image pro…
New symmetry found in colored Alexander polynomial.