arXiv research

The study proves stabilizing of ascending chains in specific groups.

No hyperbolic group can have an infinite chain of free subgroups of fixed rank.

Generic groups satisfy a chain condition for subgroups.

The paper proves an ascending chain condition for subgroups in hyperbolic and graph 3-manifolds.

New manifolds help understand group actions on complex chains.

Positive braids minimize knot untangling steps.

Ascending numbers are determined for 64 knots with at most n=10 crossings. After proving the theorem about the signature of alternating knot families, we distinguished all families of knots obtained from generating alternating knots with at most 10 crossings, for which the unknotting number can be confirmed by using th…

Hyperbolicity proven for a specific type of group extension.

ASCEND discovers causal relationships in multi-omics data by leveraging known hierarchical structure.

We obtain several restrictions on the terms of the ascending central series of a nilpotent Lie algebra $\mathfrak g$ under the presence of a complex structure $J$. In particular, we find a bound for the dimension of the center of $\mathfrak g$ when it does not contain any non-trivial $J$-invariant ideal. Thanks to thes…

Robot untangles knots by walking and switching crossings.

Residual torsion-free nilpotence has proven to be an important property for knot groups with applications to bi-orderability and ribbon concordance. Mayland proposed a strategy to show that a two-bridge knot group has a commutator subgroup which is a union of an ascending chain of parafree groups. This paper proves May…

We introduce a new numerical invariant of knots and links from the descending diagrams. It is considered to live between the unknotting number and the bridge number.

MAGE optimizes policies using action gradients from model-based learning.

Transformers learn to integrate information from past positions incrementally, specializing heads in distinct patterns.

We give an example of a subgroup of SL(2,C) which is a strictly ascending HNN extension of a non-abelian finitely generated free group F. In particular, we exhibit a free group F in SL(2,C) of rank 6 which is conjugate to a proper subgroup of itself. This answers positively a question of Drutu and Sapir. The main ingre…

Paper solves isomorphism problem for specific Baumslag-Solitar groups.

Determinant modulo 8 classifies virtual knots based on polynomial coefficients.

Using 1-twist rim surgery, we construct infinitely many smoothly embedded, orientable surfaces in the 4-ball bounding a knot in the 3-sphere that are pairwise topologically isotopic, but not ambient diffeomorphic. We distinguish the surfaces using the maps they induce on perturbed sutured Floer homology. Along the way,…

Study improves loan default risk estimation using advanced regression models.

It seems to be a pearl of conventional wisdom that parameter learning in deep sum-product networks is surprisingly fast compared to shallow mixture models. This paper examines the effects of overparameterization in sum-product networks on the speed of parameter optimisation. Using theoretical analysis and empirical exp…

New techniques in Khovanov homology help distinguish exotic surfaces in 4-ball.

Study geometric actions of groups on horocyclic products.

Given a Kaehler group $G$ and a primitive class $φ\in H^1(G;Z)$, we show that the rank gradient of $(G;φ)$ is zero if and only if Ker $φ$ is finitely generated. Using this approach, we give a quick proof of the fact (originally due to Napier and Ramachandran) that Kaehler groups are not properly ascending or descending…

Empirical evidence is given for a significant difference in the collective trend of the share prices during the stock index rising and falling periods. Data on the Dow Jones Industrial Average and its stock components are studied between 1991 and 2008. Pearson-type correlations are computed between the stocks and avera…

Minimal crossing virtual links have minimal supporting genus.

We prove a generalized version of Kazhdan's theorem for canonical forms on Riemann surfaces. In the classical version, one starts with an ascending sequence $\{S_n \rightarrow S\}$ of finite Galois covers of a hyperbolic Riemann Surface $S$, converging to the universal cover. The theorem states that the sequence of for…

Classifies 3-braids from choreographic motions on Lissajous curves, linking them to mapping classes and geodesics.

Paper shows DMS as an EM algorithm with improved convergence.

In this article we dwell into the class of so called ill posed Linear Inverse Problems (LIP) in machine learning, which has become almost a classic in recent times. The fundamental task in an LIP is to recover the entire signal / data from its relatively few random linear measurements. Such problems arise in variety of…

The paper characterizes and examines nilpotent complex structures on stratified Lie algebras.

We solve three open problems concerning infinite-dimensional Lie groups posed in a recent survey article by K.-H. Neeb: (1) There exists a subgroup of some infinite-dimensional Lie group G which does not admit an initial Lie subgroup structure; (2) The pathology cannot occur if G is a direct limit of an ascending seque…

Develops a method to compute Morse homology for clean but not necessarily transverse intersections.

The main goal of this paper is to prove that a connected bounded geometry complete Kahler manifold which has at least 3 filtered ends admits a proper holomorphic mapping onto a Riemann surface. This also provides a different proof of the theorem of Gromov and Schoen that, for a connected compact Kahler manifold whose f…

We show that certain classes of graphs of free groups contain surface subgroups, including groups with positive $b_2$ obtained by doubling free groups along collections of subgroups, and groups obtained by "random" ascending HNN extensions of free groups. A special case is the HNN extension associated to the endomorphi…

The ability to analyze and forecast stratospheric weather conditions is fundamental to addressing climate change. However, our capacity to collect data in the stratosphere is limited by sparsely deployed weather balloons. We propose a framework to collect stratospheric data by releasing a contrail of tiny sensor device…

Study minimax estimation of stratified structure from i.i.d. samples.

Study finds on-chain data can proxy off-chain cryptocurrency pricing.

This paper examines from an experimental perspective random forests, the increasingly used statistical method for classification and regression problems introduced by Leo Breiman in 2001. It first aims at confirming, known but sparse, advice for using random forests and at proposing some complementary remarks for both …

The study connects monopole chains to Higgs bundles and classifies symmetric chains.

New proof of chain duality for simplicial complexes.

AI agents beat previous best on NetHack, but symbolic bots still outperform.

Improves multi-label classification with a new network model.

Polyak proved that the set $\{\Omega1a,\Omega1b,\Omega2a,\Omega3a\}$ is a minimal generating set of oriented Reidemeister moves. One may distinguish between forward and backward moves, obtaining $32$ different types of moves, which we call directed oriented Reidemeister moves. In this article we prove that the set of $…

Reduces identity testing of reversible Markov chains to simpler symmetric chain tests.

We present a new family of models that is based on graphs that may have undirected, directed and bidirected edges. We name these new models marginal AMP (MAMP) chain graphs because each of them is Markov equivalent to some AMP chain graph under marginalization of some of its nodes. However, MAMP chain graphs do not onl…

We introduce some chain maps between Khovanov complexes. Each of the chain maps commutes with a chain homotopy map and a retraction maps which obtain a Reidemeister invariance of Khovanov homology.

Mack's estimator improves chain ladder prediction for large exposure insurance models.