arXiv research

We present a lower bound for a fragmentation norm and construct a bi-Lipschitz embedding $I\colon \mathbb{R}^n\to\mathrm{Ham}(M)$ with respect to the fragmentation norm on the group $\mathrm{Ham}(M)$ of Hamiltonian diffeomorphisms of a symplectic manifold $(M,ω)$. As an application, we provide an answer to Brandenbursk…

We prove that manifolds with complicated enough fundamental group admit measure-preserving homeomorphisms which have positive stable fragmentation norm with respect to balls of bounded measure.

The paper shows how Hamiltonian diffeomorphisms and homeomorphisms can be broken down into smaller, manageable pieces.

We relate generalized Lebesgue decompositions of measures in terms of curve fragments (Alberti representations) and Weaver derivations. This correspondence leads to a geometric characterization of the local norm on the Weaver cotangent bundle of a metric measure space $(X,μ)$: the local norm of a form $df$ sees how fas…

Diffeomorphisms of surfaces have many unbounded quasi-morphisms.

It is shown that the compactly supported identity component of the diffeomorphism group of the 2-dimensional punctured torus $\mathbb T^2_p$ is an unbounded group. It follows that the fragmentation norm of $\mathbb T^2_p$ is unbounded.

A new deep model generates molecules by fragments, improving validity and uniqueness.

This paper introduces a new approach for the automated reconstruction - reassembly of fragmented objects having one surface near to plane, on the basis of the 3D representation of their constituent fragments. The whole process starts by 3D scanning of the available fragments. The obtained representations are properly p…

FluxLayer solves cross-chain liquidity fragmentation for better MEV capture.

Technological progress is leading to proliferation and diversification of trading venues, thus increasing the relevance of the long-standing question of market fragmentation versus consolidation. To address this issue quantitatively, we analyse systems of adaptive traders that choose where to trade based on their previ…

FIRE method improves model performance in federated learning by penalizing fragmentation-induced covariate shifts.

It is shown that certain diffeomorphism or homeomorphism groups with no restriction on support of an open manifold with finite number of ends are bounded. It follows that these groups are uniformly perfect. In order to characterize the boundedness several conditions on automorphism groups of an open manifold are introd…

Study proves fluid limits of fragmented limit-order markets.

SILVR generates new molecules fitting protein binding sites.

Automated rock fragmentation assessment using deep learning and spatial statistics.

Tree structures are ubiquitous in data across many domains, and many datasets are naturally modelled by unobserved tree structures. In this paper, first we review the theory of random fragmentation processes [Bertoin, 2006], and a number of existing methods for modelling trees, including the popular nested Chinese rest…

Generating music medleys is about finding an optimal permutation of a given set of music clips. Toward this goal, we propose a self-supervised learning task, called the music puzzle game, to train neural network models to learn the sequential patterns in music. In essence, such a game requires machines to correctly sor…

New distribution simplifies covariance matrix inference.

Fragment-based autoencoder improves molecule screening with little data.

Fragmented exchanges arise due to speed advantages in high-activity regions.

The paper examines boundedness of diffeomorphism groups of manifold pairs, focusing on the circle case.

Model shows how multiple markets can coexist or fragment based on trader behavior.

New model integrates community and link clustering for network data.

High-fee pools attract more liquidity but execute less volume; low-fee pools have more stable LPs.

Microbial clades modeling is a challenging problem in biology based on microarray genome sequences, especially in new species gene isolates discovery and category. Marker family genome sequences play important roles in describing specific microbial clades within species, a framework of support vector machine (SVM) base…

Study replicates market model, finds replication hindered by missing details.

The paper analyzes security issues in blockchain ecosystems with multiple SSPs and proposes two models for better stake management.

Improved RL model for fragment-based molecule generation.

This paper extends quasimorphism results to nonorientable surfaces.

Paper introduces a method to predict molecule properties from diverse data sources.

In this work, a method of random parameters generation for randomized learning of a single-hidden-layer feedforward neural network is proposed. The method firstly, randomly selects the slope angles of the hidden neurons activation functions from an interval adjusted to the target function, then randomly rotates the act…

Pareto law, which states that wealth distribution in societies have a power-law tail, has been a subject of intensive investigations in statistical physics community. Several models have been employed to explain this behavior. However, most of the agent based models assume the conservation of number of agents and wealt…

DADC algorithm improves clustering for data with varying density.

Archaeologists are in dire need of automated object reconstruction methods. Fragments reassembly is close to puzzle problems, which may be solved by computer vision algorithms. As they are often beaten on most image related tasks by deep learning algorithms, we study a classification method that can solve jigsaw puzzle…

Study examines Bitcoin market fragmentation and price formation, revealing market leader-lagger dynamics and trading strategies.

We suggest an analytical approach for Pareto-Zipf law, where we assume random multiplicative noise and fragmentation processes for the growth of the number of citizens of each city and the number of the cities, respectively.

A big challenge in algorithmic composition is to devise a model that is both easily trainable and able to reproduce the long-range temporal dependencies typical of music. Here we investigate how artificial neural networks can be trained on a large corpus of melodies and turned into automated music composers able to gen…

The paper extends Thurston's method to new variants of Mather-Thurston theorem.

With a compact PL manifold X we associate a category T(X). The objects of T(X) are all combinatorial manifolds of type X, and morphisms are combinatorial assemblies. We prove that the homotopy equivalence BT (X) \approx BPL(X) holds, where PL(X) is the simplicial group of PL-homeomorphisms. Thus the space BT(X) is a ca…

Using the most comprehensive source of commercially available data on the US National Market System, we analyze all quotes and trades associated with Dow 30 stocks in 2016 from the vantage point of a single and fixed frame of reference. We find that inefficiencies created in part by the fragmentation of the equity mark…

This study aims to improve communication between fragmented blockchain systems in finance.

Paper improves Tm prediction of protein fragments using sparsity and probabilistic models.

SVH-PSL uses Stein Variational Gradient Descent and Hypernetworks to improve Pareto set learning for expensive MOO.

Symmetry unifies AI learning dynamics, complexity, and representation.

MAS scores cluster size consistency from points, robust to label changes.

Optimization approach for efficient sampling in optical mapping for structural variant detection.

Regression is widely used by practioners across many disciplines. We reformulate the underlying optimisation problem as a second-order conic program providing the flexibility often needed in applications. Using examples from portfolio management and quantitative trading we solve regression problems with and without con…

We define an integer-valued non-degenerate bi-invariant metric (the discriminant metric) on the universal cover of the identity component of the contactomorphism group of any contact manifold. This metric has a very simple geometric definition, based on the notion of discriminant points of contactomorphisms. Using gene…