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.
For surface-knots, branched covers with degree 3 have simplifying numbers <3.
In this paper we describe a procedure to simplify any given triangulation of the 3-sphere using Pachner moves. We obtain an explicit exponential-type bound on the number of Pachner moves needed for this process. This leads to a new recognition algorithm for the 3-sphere.
RL pipeline simplifies knot diagrams, including very hard unknots.
We consider a Black-Scholes market in which a number of stocks and an index are traded. The simplified Capital Asset Pricing Model is the conjunction of the usual Capital Asset Pricing Model, or CAPM, and the statement that the appreciation rate of the index is equal to its squared volatility plus the interest rate. (T…
Simplified DGPs training by fixing inducing inputs to subset of data.
Lower bound on BART's mixing time increases with data points.
Muon optimizer simplifies matrix optimization with spectral orthogonalization.
We compare two different bilateral counterparty valuation adjustment (BVA) formulas. The first formula is an approximation and is based on subtracting the two unilateral Credit Valuation Adjustment (CVA)'s formulas as seen from the two different parties in the transaction. This formula is only a simplified representati…
Complex neural networks simplify to a mean field model as the number of neurons increases.
In this paper we continue our systematic analysis of the operatorial approach previously proposed in an economical context and we discuss a {\em mixed} toy model of a simplified stock market, i.e. a model in which the price of the shares is given as an input. We deduce the time evolution of the portfolio of the various…
In this paper we look for closed expressions to calculate the number of colourings of prime knots for given linear Alexander quandles. For this purpose the colouring matrices are simplified to a triangular form, when possible. The operations used to perform this triangularization preserve the property that the entries …
Simplified proof of cosmic singularity theorem using new mathematical techniques.
New method for simplifying knots with specific properties.
We give a locally minimal, but not globally minimal bridge position of a knot, that is, an unstabilized, nonminimal bridge position of a knot. It implies that a bridge position cannot always be simplified so that the bridge number monotonically decreases to the minimal.
Simplified A-polynomial calculation for twisted knots.
Paper studies simplified trisections and their equivalence classes.
We refine Osserman's argument on the exceptional values of the Gauss map of algebraic minimal surfaces. This gives an effective estimate for the number of exceptional values and the totally ramified value number for a wider class of complete minimal surfaces that includes algebraic minimal surfaces. It also provides a …
Improved model for multivariate time series prediction with simpler architecture.
Paper introduces simplified formulas for Milnor's triple linking number.
A branched covering surface-knot is a surface-knot in the form of a branched covering over an oriented surface-knot , where we include the case when the covering has no branch points. A branched covering surface-knot is presented by a graph called a chart on a surface diagram of . We can simplify a branched cover…
Tensor approach simplifies Euclidean space descriptions.
A new algorithm simplifies number theory and geometry problems.
Calibration of simplified vine copulas using noise contrastive estimation
The linking integral is an invariant of the link-type of two manifolds immersed in a Euclidean space. It is shown that the ordinary Gauss integral in three dimensions may be simplified to a winding number integral in two dimensions. This result is then generalized to show that in certain circumstances the linking integ…
Maryam Mirzakhani (in her doctoral dissertation) has proved the author's conjecture that the number of simple curves of length bounded by L on a hyperbolic surface S is assymptotic to a constant times L to the power d, where d is the dimension of the Teichmuller space of S. In this note we clarify and simplify Mirzakha…
We construct a completed version C(Gamma) of the configuration space of a linkage Gamma in R^3 which takes into account the ways one link can touch another. We also describe a simplified version of C(Gamma) which is a blow-up of the space of immersions of Gamma in R^3 A number of simple detailed examples are given.
A simplified trisection is a trisection map on a 4-manifold such that, in its critical value set, there is no double point and cusps only appear in triples on innermost fold circles. We give a necessary and sufficient condition for a 3-tuple of systems of simple closed curves in a surface to be a diagram of a simplifie…
Simplified proof for Cheeger's isoperimetric constant.
Classifies 3-manifolds from simplified (2,0)-trisections of 4-manifolds.
We give an explicit algorithm and source code for computing optimal weights for combining a large number N of alphas. This algorithm does not cost O(N^3) or even O(N^2) operations but is much cheaper, in fact, the number of required operations scales linearly with N. We discuss how in the absence of binary or quasi-bin…
We define transit clusters to simplify causal diagrams and preserve their essential properties.
The paper simplifies knot and link diagrams with triple-crossings.
Shapes of four dimensional spaces can be studied effectively via maps to standard surfaces. We explain, and illustrate by quintessential examples, how to simplify such generic maps on 4-manifolds topologically, in order to derive simple decompositions into much better understood manifold pieces. Our methods not only al…
PixelCNNs are a recently proposed class of powerful generative models with tractable likelihood. Here we discuss our implementation of PixelCNNs which we make available at https://github.com/openai/pixel-cnn. Our implementation contains a number of modifications to the original model that both simplify its structure an…
We introduce fully scalable Gaussian processes, an implementation scheme that tackles the problem of treating a high number of training instances together with high dimensional input data. Our key idea is a representation trick over the inducing variables called subspace inducing inputs. This is combined with certain m…
Simplified proof of Honda-Huang's contact convexity result.
Simplified speaker verification backend improves calibration across varying conditions.
This research simplifies computation of feature attribution methods under certain conditions.
This paper defines RII number for knot projections and shows it can be any nonnegative number.
Recurrent neural networks with various types of hidden units have been used to solve a diverse range of problems involving sequence data. Two of the most recent proposals, gated recurrent units (GRU) and minimal gated units (MGU), have shown comparable promising results on example public datasets. In this paper, we int…
Study on nonorientable 4-manifolds using simplified fibrations and trisections.
Proposes simplified SHAP for faster black-box model explanations.
With the advent of Big Data era, data reduction methods are highly demanded given its ability to simplify huge data, and ease complex learning processes. Concretely, algorithms that are able to filter relevant dimensions from a set of millions are of huge importance. Although effective, these techniques suffer from the…
We simplify Khovanov homology for torus braids using Gaussian elimination.
Simplified argument for second order estimate in quaternionic Calabi-Yau problem.
Develops exact convex optimization formulations for neural networks.
We present a simplified formulation of open intersection numbers, as an alternative to the theory initiated by Pandharipande, Solomon and Tessler. The relevant moduli spaces consist of Riemann surfaces (either with or without boundary) with only interior marked points. These spaces have a combinatorial description usin…
Proves a conjecture about the maximum tet-volume of triangulations of a 2-sphere.