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.
Paper proves hardness of learning various complex models under local pseudorandom generators.
Generation of pseudorandom numbers from different probability distributions has been studied extensively in the Monte Carlo simulation literature. Two standard generation techniques are the acceptance-rejection and inverse transformation methods. An alternative approach to Monte Carlo simulation is the quasi-Monte Carl…
New framework improves text watermark detection under imperfect pseudorandomness.
Quantum speedup for Monte Carlo integration reduces integrand calls.
Arora, Barak, Brunnermeier, and Ge showed that taking computational complexity into account, a dishonest seller could strategically place lemons in financial derivatives to make them substantially less valuable to buyers. We show that if the seller is required to construct derivatives of a certain form, then this pheno…
Power laws detected in financial data, modeled with random multipliers.
We consider the problem of simulating loss probabilities and conditional excesses for linear asset portfolios under the t-copula model. Although in the literature on market risk management there are papers proposing efficient variance reduction methods for Monte Carlo simulation of portfolio market risk, there is no pa…
Paper proves first non-trivial PTF testing lower bounds for NGCA.
New findings show learning deeper neural networks is hard even with Gaussian inputs and non-degenerate weights.
The paper shows how shared random seeds can reduce variance in machine learning evaluations.
A new watermarking method corrects bias in language models using maximal coupling.
Next-gen reservoir computing models dynamical systems from time-series data.
New concept of epiplexity quantifies useful information from data.
Estimates proportions of LLM-generated text in mixed documents.
New findings suggest minimax optimality doesn't guarantee distribution learning for GANs.
Study on estimating Gumbel--Max watermark proportions in edited documents.
New framework to understand and exploit curvature in deep learning loss landscapes.
We define and compare several natural ways to compute the bridge number of a knot diagram. We study bridge numbers of crossing number minimizing diagrams, as well as the behavior of diagrammatic bridge numbers under the connected sum operation. For each notion of diagrammatic bridge number considered, we find crossing …
Spatial embeddings of planar graphs can have higher unknotting numbers than crossing numbers.
The unknotting number of a knot is the minimum number of crossings one must change to turn that knot into the unknot. The algebraic unknotting number is the minimum number of crossing changes needed to transform a knot into an Alexander polynomial-one knot. We work with a generalization of unknotting number due to Math…
The paper bounds the handle number of sutured manifolds using Morse-Novikov numbers and tunnel numbers.
New measure shows how links can be untangled as twists increase.
New number bounds knot complexity, including unknotting and crosscap numbers.
We give an upper bound for the dealternating number of a closed 3-braid. As applications, we determine the dealternating numbers, the alternation numbers and the Turaev genera of some closed positive 3-braids. We also show that there exist infinitely many positive knots with any dealternating number (or any alternation…
Paper shows that for torus knots, the pinch number equals the unoriented band unknotting number.
Delta-unlinking number measures how to unlink algebraically split links.
Study on knot properties, showing relation between unknotting and crossing numbers.
Odd crossing numbers and even rotation numbers for cycles in plane immersions.
Study computability of real numbers from group properties.
We define the basket number, the flat plumbing number and the flat plumbing basket number of a link. Then we provide some upperbounds for these plumbing numbers by using Seifert's algorithm. We study the relation between these plumbing numbers and the genera of links.
The aim of the present paper is to prove that the minimal number of virtual crossings for some families of virtual knots grows quadratically with respect to the minimal number of classical crossings. All previously known estimates for virtual crossing number were principally no more than linear in the number of classic…
This paper calculates stick numbers for rail arcs and knot classes.
The (ordinary) unknotting-number of 1-dimensional knots, which is defined by using the crossing-change, is a very basic and important invariant. It is very natural to consider the `unknotting-number' associated with other local-moves on n-dimensional knots, where n is a natural number. In this paper we prove the follow…
In this paper we investigate the unlinking numbers of 10-crossing links. We make use of various link invariants and explore their behaviour when crossings are changed. The methods we describe have been used previously to compute unlinking numbers of links with crossing number at most 9. Ultimately, we find the unlinkin…
This paper is about the clock number of a knot. First we define the clock number by using states of a knot defined by Kauffman. Next we show that if K is a prime knot, its clock number is greater than or equal to its crossing number. Finally we prove that its clock number is equal to its crossing number if and only if …
We study three knot invariants related to smoothly immersed disks in the four-ball. These are the four-ball crossing number, which is the minimal number of normal double points of such a disk bounded by a given knot; the slicing number, which is the minimal number of crossing changes to a slice knot; and the concordanc…
For a knot the cube number is a knot invariant defined to be the smallest for which there is a cube diagram of size for . There is also a Legendrian version of this invariant called the \emph{Legendrian cube number}. We will show that the Legendrian cube number distinguishes the Legendrian left hand toru…
Jablan and Radović originally defined two invariants called the Meander number and OGC number of knots for certain classes of knots. We generalize these definitions to all knots and name the straight number and contained straight number of a knot, respectively, and prove they are well defined. We answer two questions a…
New insights into knot fusion numbers via cabling.
Links with minimum tunnel number have one less component than their number of parts.
New bounds and examples for sphere unknotting numbers.
A rational linear combination of Chern numbers is an oriented diffeomorphism invariant of smooth complex projective varieties if and only if it is a linear combination of the Euler and Pontryagin numbers. In dimension at least three only multiples of the top Chern number, which is the Euler characteristic, are invarian…
We give lower bounds for the tunnel number of knots and handlebody-knots. We also give a lower bound for the cutting number, which is a "dual" notion to the tunnel number in the handlebody-knot theory. We provide necessary conditions for constituent handlebody-knots by using -family of quandles colorings. The above …
An -crossing is a point in the projection of a knot where strands cross so that each strand bisects the crossing. An übercrossing projection has a single -crossing and a petal projection has a single -crossing such that there are no loops nested within others. The übercrossing number, , is the…
Connected sum and trivalent vertex sum are natural operations on genus 2 spatial graphs and, as with knots, tunnel number behaves in interesting ways under these operations. We prove sharp Scharlemann-Schultens type bounds for the tunnel number of a composite genus 2 spatial graph. For the tunnel number of a composite …
The paper tabulates and computes the number of alternating pretzel links up to a given crossing number.
In the 1950's Milnor defined a family of higher order invariants generalizing the linking number. Even the first of these new invariants, the triple linking number, has received and fruitful study since its inception. In the case that has vanishing pairwise linking numbers, this triple linking number gives an integ…
New method to untangle knots using null-homologous twists.