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.
Graphical notation simplifies tensor operations and decompositions.
Graphical notation simplifies complex polynomial constraints in linear models.
This tutorial introduces causal modeling methods for researchers.
Proposes a new notation for biracks to simplify rack structure analysis.
A wide class of machine learning algorithms can be reduced to variable elimination on factor graphs. While factor graphs provide a unifying notation for these algorithms, they do not provide a compact way to express repeated structure when compared to plate diagrams for directed graphical models. To exploit efficient t…
Unified notation simplifies information-theoretic concepts in machine learning.
Presentations of smooth symmetry groups of differentiable stacks are studied within the framework of the weak 2-category of Lie groupoids, smooth principal bibundles, and smooth biequivariant maps. It is shown that principality of bibundles is a categorical property which is sufficient and necessary for the existence o…
This paper presents compact notations for concentration inequalities and convenient results to streamline probabilistic analysis. The new expressions describe the typical sizes and tails of random variables, allowing for simple operations without heavy use of inessential constants. They bridge classical asymptotic nota…
Formula found for a specific knot's A-polynomial.
We construct an integer polynomial whose coefficients enumerate the Kauffman states of the two-bridge knot with Conway's notation C(n,r).
An explicit formula for the -polynomial of the knot with Conway's notation is obtained from the explicit Riley-Mednykh polynomial of it.
Tensor decomposition methods are widely used for model compression and fast inference in convolutional neural networks (CNNs). Although many decompositions are conceivable, only CP decomposition and a few others have been applied in practice, and no extensive comparisons have been made between available methods. Previo…
We describe a method of encoding various types of link diagrams, including those with classical, flat, rigid, welded, and virtual crossings. We show that this method may be used to encode link diagrams, up to equivalence, in a notation whose length is a cubic function of the number of 'riser marks'. For classical knots…
We provide a proof of backpropagation algorithm in matrix notation.
We review the actions of the supergravity theory in eleven dimensions as well as the type IIA and IIB supergravities in ten dimensions and derive the bosonic equations of motion in a coordinate-free notation. We also consider the existence of supersymmetries and the associated generalized Killing spinor equations. The …
This article contains general formulas for Tutte and Jones polynomial for families of knots and links given in Conway notation.
We calculate the Chern-Simons invariants of the hyperbolic orbifolds of the knot with Conway's notation using the Schläfli formula for the generalized Chern-Simons function on the family of cone-manifold structures. We present the concrete and explicit formula of them. We apply the general instruct…
We introduce a matrix representation of a chord on a tangle which leads us to representing tangle chord diagrams as stacks of matrices that we call books. We show that band sum moves, Reidemeister moves as well as orientation changes are implemented on \widetilde{Z}_f - a framed link invariant constructed from the Kont…
For families of knots and links given in Conway notation we compute lower maximal and upper minimal bound of hyperbolic volume by using source links and augmented links.
A new fairness metric for decision-making algorithms, conditioning on known fair variables.
This article contains general formulas for Tutte and Jones polynomials for families of knots and links given in Conway notation and "portraits of families"-- plots of zeroes of their corresponding Jones polynomials.
After defining reduced minimum braid word and criteria for a braid family representative, different braid family representatives are derived, and a correspondence between them and families of knots and links given in Conway notation is established.
In this paper, we present a new comparative study on automatic essay scoring (AES). The current state-of-the-art natural language processing (NLP) neural network architectures are used in this work to achieve above human-level accuracy on the publicly available Kaggle AES dataset. We compare two powerful language model…
Probabilistic models can handle causal inference without special tools.
This paper contains general formulae for the reduced relative Tutte, Kauffman bracket and Jones polynomials of families of virtual knots and links given in Conway notation and discussion of a counterexample to the Z-move conjecture of Fenn, Kauffman and Manturov.
Penrose's two-spinor notation for -dimensional Lorentzian manifolds can be extended to two-component notation for quaternionic manifolds, which is a very useful tool for calculation. We construct a family of quaternionic complexes over unimodular quaternionic manifolds by elementary calculation. On complex quaternio…
In this paper, we define a new special curve in Euclidean 3-space which we call {\it slant helix} and introduce some characterizations for this curve. This notation is generalization of a general helix and slant helix. Furthermore, we have given some necessary and sufficient conditions for the slant helix.
Constructing accurate and automatic solvers of math word problems has proven to be quite challenging. Prior attempts using machine learning have been trained on corpora specific to math word problems to produce arithmetic expressions in infix notation before answer computation. We find that custom-built neural networks…
We give explicit formulae for the volumes of hyperbolic cone-manifolds of double twist knots, a class of two-bridge knots which includes twist knots and two-bridge knots with Conway notation . We also study the Riley polynomial of a class of one-relator groups which includes two-bridge knot groups.
A coreset (or core-set) of an input set is its small summation, such that solving a problem on the coreset as its input, provably yields the same result as solving the same problem on the original (full) set, for a given family of problems (models, classifiers, loss functions). Over the past decade, coreset constructio…
Introduces machine learning basics and algorithms.
In mathematics, a knot is a single strand of string crossed over itself any number of times, and connected at the ends. The Reidemeister Moves have been proven to be the three core moves necessary to fully untangle a knot. Some knots can be untangled to a loop (the unknot), while others are fundamentally knotted. We de…
Graphical lasso may fail to fit models when data points are insufficient.
Study on rigidity of translating hypersurfaces not in graphical direction.
This is a short description of graphic lambda calculus, with special emphasis on a duality suggested by the two different appearances of knot diagrams, in lambda calculus and emergent algebra sectors of the graphic lambda calculus respectively. This duality leads to the introduction of the dual of the graphic beta move…
Implicit deep learning prediction rules generalize the recursive rules of feedforward neural networks. Such rules are based on the solution of a fixed-point equation involving a single vector of hidden features, which is thus only implicitly defined. The implicit framework greatly simplifies the notation of deep learni…
The concept of a symplectic structure first appeared in the works of Lagrange on the so-called "method of variation of the constants". These works are presented, together with those of Poisson, who first defined the composition law called today the "Poisson bracket". The method of variation of the constants is presente…
We consider the problem of learning high-dimensional Gaussian graphical models. The graphical lasso is one of the most popular methods for estimating Gaussian graphical models. However, it does not achieve the oracle rate of convergence. In this paper, we propose the graphical nonconvex optimization for optimal estimat…
In this paper, we discuss the region unknotting number of different classes of 2-bridge knots. In particular, we provide region unknotting number for the classes of -bridge knots whose Conway notation is and . By generalizing, we also provide a sharp up…
New method for tuning Graphical Lasso hyperparameters.
We extend some part of the unpublished paper written by Mednykh and Rasskazov. Using the approach indicated in this paper we derive the Riley-Mednykh polynomial for some family of the -bridge knot orbifolds. As a result we obtain explicit formulae for the volume of cone-manifolds and the Chern-Simons invariant of or…
In this paper, we investigate a curve whose spherical image the tangent indicatrix and binormal indicatrix is slant helix and called it as a slant helix. We obtain that the spherical images are spherical slant helices defined by [3]. This notation is a generalization of a slant helix. Furthermore, we have given some ch…
For certain problems involving vector fields, it is possible to find an associated imaginary field that, in conjunction with the first, forms a complex field for which the equation can be solved. This result is generalized to arbitrary Clifford algebras, followed by quaternionic vectors as a special case. All results a…
This paper studies the payoff amounts in simple interest loans without arbitrage.
Consider a mean curvature flow of hypersurfaces in Euclidean space, that is initially graphical inside a cylinder. There exists a period of time during which the flow is graphical inside the cylinder of half the radius. Here we prove a lower bound on this period depending on the Lipschitz-constant of the initial graphi…
Undirected graphical models, or Markov networks, are a popular class of statistical models, used in a wide variety of applications. Popular instances of this class include Gaussian graphical models and Ising models. In many settings, however, it might not be clear which subclass of graphical models to use, particularly…
Notation for spin coefficients for metrics of neutral signature in four dimensions is introduced. The utility and interpretation of spin coefficients is explored through themes in null geometry familiar from (complex) general relativity. Four-dimensional Walker geometry is exploited to provide examples and the generali…
Bayesian method for estimating functional graphical models from neuroimaging data.