The paper shows how Hamiltonian diffeomorphisms and homeomorphisms can be broken down into smaller, manageable pieces.
problem Fragmenting Hamiltonian diffeomorphisms and homeomorphisms on surfaces.
method Develops a C0-fragmentation property for Hamiltonian diffeomorphisms and homeomorphisms on surfaces, proving it with a Lipschitz estimate. result Hamiltonian diffeomorphisms and homeomorphisms can be decomposed into smaller, compactly supported pieces with a Lipschitz estimate on the C0-norm. 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…
A new deep model generates molecules by fragments, improving validity and uniqueness.
problem Generating valid and unique molecules using deep learning.
method Develops a language model for molecular fragments, using frequency-based masking.
result Significantly outperforms other language model-based competitors in molecule generation.
Paper introduces a method to predict molecule properties from diverse data sources.
problem Limited ability to accommodate scarce or fragmented training data.
method Adaptive Invariance using invariant risk minimization to generalize beyond heterogeneous data.
result Predictor outperforms state-of-the-art transfer learning methods by significant margin.
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…
We present a lower bound for a fragmentation norm and construct a bi-Lipschitz embedding I:Rn→Ham(M) with respect to the fragmentation norm on the group Ham(M) of Hamiltonian diffeomorphisms of a symplectic manifold (M,ω). As an application, we provide an answer to Brandenbursk…
FluxLayer solves cross-chain liquidity fragmentation for better MEV capture.
problem Cross-chain fragmented liquidity and MEV optimization.
method Three-layer framework integrating settlement, intent, and leverage mechanisms.
result FluxLayer enhances cross-chain MEV by capturing more arbitrage opportunities.
FIRE method improves model performance in federated learning by penalizing fragmentation-induced covariate shifts.
problem Performance degradation in federated learning due to data fragmentation and covariate shift.
method FIRE method accumulates fragmentation-induced covariate shift divergences via approximate Fisher information and uses it as a per-fragment loss penalty.
result FIRE outperforms importance weighting and federated learning benchmarks by up to 5.3% on shifted validation sets.
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.
Study proves fluid limits of fragmented limit-order markets.
problem Modeling fragmented limit-order markets with small and frequent orders.
method Proved convergence of discrete system to fluid limit characterized by coupled nonlinear ODEs.
result Fluid system converges to stationary equilibrium state over time.
Paper improves Tm prediction of protein fragments using sparsity and probabilistic models.
problem Improving accuracy of melting temperature prediction for protein fragments.
method Promoting sparsity in pre-trained transformer models and adopting probabilistic frameworks.
result Mean absolute error of 0.23C for predicting melting temperature.
SILVR generates new molecules fitting protein binding sites.
problem Generating novel small molecule compounds for drug design.
method Selective Iterative Latent Variable Refinement (SILVR) for diffusion-based molecule generation.
result SILVR can generate new molecules similar in shape to original fragments without protein knowledge.
Automated rock fragmentation assessment using deep learning and spatial statistics.
problem Assessing post-blast rock fragmentation in real-time.
method Fine-tuned YOLO12l-seg model for instance segmentation, followed by spatial statistics.
result Framework accurately assesses rock fragmentation patterns in real-time.
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.
problem Efficient inference for covariance matrices in large models.
method Incorporates Inverse G-Wishart distribution for variational message passing.
result Elegant and succinct expression of variational message passing fragments.
Fragment-based autoencoder improves molecule screening with little data.
problem Limited experimental data for molecular optimization.
method Fragment-based graphical autoencoding to generate structural fingerprints.
result Fragment-based autoencoding reduces prediction error in small data.
This study aims to improve communication between fragmented blockchain systems in finance.
problem Inefficient and insecure communication in fragmented blockchain systems.
method Analysis of cross-chain interoperability protocols and their properties.
result Comparison and evaluation of cross-chain interoperability protocols.
Fragmented exchanges arise due to speed advantages in high-activity regions.
problem Fragmentation of distributed securities exchanges due to speed advantages in high-activity regions.
method Economic model and Monte Carlo simulations of a decentralized exchange with two miner clusters.
result Speed advantage increases with infrastructure asymmetry between regions.
Model shows how multiple markets can coexist or fragment based on trader behavior.
problem Understanding market competition and coexistence among multiple trading venues.
method Stylized model of traders making repeated decisions at three markets, analyzed numerically and analytically.
result Parameters like memory length and choice intensity determine whether markets coexist or fragment.
New model integrates community and link clustering for network data.
problem Lack of embedded prior information and community evolution description in MMSB.
method Fragmentation coagulation process for community and link clustering, with Gibbs sampling for inference.
result Model infers community structure and evolution, improving MMSB.
High-fee pools attract more liquidity but execute less volume; low-fee pools have more stable LPs.
problem Optimal liquidity supply and execution on decentralized exchanges with fixed gas costs.
method Analysis of Uniswap data to compare high- and low-fee pools.
result Fragmented liquidity leads to more LPs and competition, improving overall market efficiency.
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.
problem Replicating a market model with missing details and limited quantitative reporting.
method Increased simulation runs, bootstrap confidence intervals, and code analysis.
result Achieved relational equivalence for most metrics but rejected quantitative alignment.
Fragmentation methods such as the many-body expansion (MBE) are a common strategy to model large systems by partitioning energies into a hierarchy of decreasingly significant contributions. The number of fragments required for chemical accuracy is still prohibitively expensive for ab-initio MBE to compete with force fi…
The paper analyzes security issues in blockchain ecosystems with multiple SSPs and proposes two models for better stake management.
problem Security issues in blockchain ecosystems with multiple SSPs and stake fragmentation.
method Formalized the Multiple SSP Problem and analyzed two architectures: Model M and Model S through convex optimization and game-theoretic lens. result Model S achieves tighter security guarantees through single validator sets and aggregated slashing logic. Improved RL model for fragment-based molecule generation.
problem Generating molecules with high docking scores.
method Thorough reproduction, scrutiny, and improvement of the FREED model.
result The improved model produces molecules with superior docking scores.
This paper extends quasimorphism results to nonorientable surfaces.
problem Understanding quasimorphisms on nonorientable surface diffeomorphism groups.
method Constructing infinitely many quasimorphisms on the identity component of nonorientable surface diffeomorphism groups.
result The space of nontrivial quasimorphisms on the identity component of the diffeomorphism group of a closed nonorientable surface is infinite-dimensional.
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.
problem Sparse cluster loss and cluster fragmentation in density peak clustering.
method Domain-adaptive density measurement, cluster center self-identification, and cluster self-ensemble.
result DADC achieves more reasonable clustering results on data with varying density.
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…
Modof-pipe optimizes molecules by modifying a single site, outperforming state-of-the-art methods.
problem Improving drug candidates' properties through chemical modification.
method Deep generative model Modof over molecular graphs for molecule optimization.
result Modof-pipe achieves significant improvements in octanol-water partition coefficient and molecule similarity constraints.
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…
Cluster Quilting clusters fragmented data sets for neuroscience and genomics.
problem Clustering fragmented data sets in neuroscience and genomics.
method Cluster Quilting method using patch ordering, patchwise SVD, sequential linear mapping, and k-means.
result Cluster Quilting discovers more accurate clusters than other methods.
With access to large datasets, deep neural networks (DNN) have achieved human-level accuracy in image and speech recognition tasks. However, in chemistry, data is inherently small and fragmented. In this work, we develop an approach of using rule-based knowledge for training ChemNet, a transferable and generalizable de…
Study examines Bitcoin market fragmentation and price formation, revealing market leader-lagger dynamics and trading strategies.
problem Understanding price formation in fragmented Bitcoin markets at sub-second time scales.
method Utilized granular orderbook and trades data, constructed features, and trained linear models to explain market returns.
result Fee regime determines market leadership and profitability of taker strategies, maker strategies tested in real-world trading.
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…
It is shown that the compactly supported identity component of the diffeomorphism group of the 2-dimensional punctured torus Tp2 is an unbounded group. It follows that the fragmentation norm of Tp2 is unbounded.
The paper extends Thurston's method to new variants of Mather-Thurston theorem.
problem Proving new variants of Mather-Thurston theorem for PL homeomorphisms and contactomorphisms.
method Generalizing Thurston's technique to prove new variants of Mather-Thurston theorem for PL homeomorphisms and contactomorphisms.
result The paper answers questions posed by Gelfand-Fuks and Greenberg on PL foliations and Rybicki on contactomorphisms.
Measures mode separation in high-dimensional densities via a reversible diffusion process.
problem Quantifying how sharply a distribution fragments into barrier-separated clusters in high dimensions.
method A unique reversible diffusion process with f as stationary distribution, extracting SSA and DA from its autocovariance matrix.
result Empirical autocovariance spectrum and readouts (SSA, DA) quantify mode separation using only samples and pretrained score-based models.
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…
SVH-PSL uses Stein Variational Gradient Descent and Hypernetworks to improve Pareto set learning for expensive MOO.
problem Fragmented surrogate models and pseudo-local optima in expensive multi-objective optimization problems.
method SVH-PSL integrates Stein Variational Gradient Descent (SVGD) with Hypernetworks to address fragmentation and pseudo-local optima.
result SVH-PSL significantly improves the quality of the learned Pareto set, offering a promising solution for expensive MOO.
Symmetry unifies AI learning dynamics, complexity, and representation.
problem Fragmented theories of AI learning mechanisms.
method Synthesis of parameter symmetry in AI models.
result Parameter symmetry breaking and restoration unify AI learning hierarchies.
MAS scores cluster size consistency from points, robust to label changes.
problem Desired uniformity in cluster sizes, stability under label perturbations.
method Mass Agreement Score (MAS) measures point-centric cluster size consistency, robust to label changes.
result MAS yields similar scores for partitions with similar bulk structure, sensitive to genuine redistribution of cluster mass.
Optimization approach for efficient sampling in optical mapping for structural variant detection.
problem Efficient sampling strategy for structural variant detection using optical mapping.
method Developed an optimization approach using a hyper-geometric distribution and probabilistic concentration inequalities.
result Optimal sampling strategy requires sampling most chromosomal fragments to detect variants at high confidence with little biological material.