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.
New modularity function improves clustering of spatially embedded networks.
The paper develops a method to discover causal relations and predict material laws with uncertainty quantification.
For every strong coarse homology theory we construct a coarse assembly map as a natural transformation between coarse homology theories. We provide various conditions implying that this assembly map is an equivalence. These results generalize known results for the analytic coarse assembly map for K-homology to general …
Model predicts composite structures assembly quality with input uncertainty.
Survey on metrics and assembly maps in positive scalar curvature.
If a Lie algebra structures $\gG$ on a vector space is the sum of a family of mutually compatible Lie algebra structures $\gG_i$, we say that $\gG$ is \emph{simply assembled} from $\gG_s$'s. By repeating this procedure several times one gets a family of Lie algebras \emph{assembled} from $\gG_s$'s. The central result o…
We construct the geometric Baum-Connes assembly map for twisted Lie groupoids, that means for Lie groupoids together with a given groupoid equivariant principle bundle. The construction is based on the use of geometric deformation groupoids, these objects allow in particular to give a geometric construction of …
We study in this paper the maximal version of the coarse Baum-Connes assembly map for families of expanding graphs arising from residually finite groups. Unlike for the usual Roe algebra, we show that this assembly map is closely related to the (maximal) Baum-Connes assembly map for the group and is an isomorphism for …
Realistic evolutionary fitness landscapes are notoriously difficult to construct. A recent cutting-edge model of virus assembly consists of a dodecahedral capsid with corresponding packaging signals in three affinity bands. This whole genome/phenotype space consisting of genomes has been explored via comp…
GBOC detects anomalies in time series data using granular-ball vectors.
Controlled -theory is used to show that algebraic -theory of virtually abelian groups is described by an assembly map defined using possibly-infinite hyperelementary subgroups. The Farrell-Jones summand (coming from infinite subgroups) is parameterized by the rational projective space of the group, and a reduced …
Higher granularity in MoE models boosts expressivity exponentially.
If a Lie algebra structure g on a vector space is the sum of a family of mutually compatible Lie algebra structures g_i's, we say that g is simply assembled from the g_i's. Repeating this procedure with a number of Lie algebras, themselves simply assembled from the g_i's, one obtains a Lie algebra assembled in two step…
We use assembly maps to study , the topological cyclic homology at a prime of the group algebra of a discrete group with coefficients in a connective ring spectrum . For any finite group, we prove that the assembly map for the family of cyclic subgroups is an isomorphis…
A framework for generating 3D shapes by sequentially assembling primitives.
In this article, we introduce the notion of a functor on coarse spaces being coarsely excisive- a coarse analogue of the notion of a functor on topological spaces being excisive. Further, taking cones, a coarsely excisive functor yields a topologically excisive functor, and for coarse topological spaces there is an ass…
Defines and computes geometric pairings for discrete groups using Baum-Connes assembly map.
GACAN combines multi-granularity time series for traffic forecasting.
Currently, the diagnosis of Autism Spectrum Disorder (ASD) is dependent upon a subjective, time-consuming evaluation of behavioral tests by an expert clinician. Non-invasive functional MRI (fMRI) characterizes brain connectivity and may be used to inform diagnoses and democratize medicine. However, successful construct…
Chaos in cerebellar cells enhances complexity of neural patterns.
New method detects anomalies in computing centers' logs.
Model for assembly map of bordism-invariant functors.
We analyze linear independence of rank one tensors produced by tensor powers of randomly perturbed vectors. This enables efficient decomposition of sums of high-order tensors. Our analysis builds upon [BCMV14] but allows for a wider range of perturbation models, including discrete ones. We give an application to recove…
We construct a higher Whitehead torsion map, using algebraic K-theory of spaces, and show that it satisfies the usual properties of the classical Whitehead torsion. This is used to describe a "geometric assembly map" defined on stabilized structure spaces in purely homotopy theoretic terms.
Model detects patterns in noisy binary data, explaining neuron activity in terms of cell assemblies.
In this paper, we propose a semi-supervised deep learning method for detecting the specific types of reads that impede the de novo genome assembly process. Instead of dealing directly with sequenced reads, we analyze their coverage graphs converted to 1D-signals. We noticed that specific signal patterns occur in each r…
Machine learning uncovers hidden correlations in granular material behavior.
Easy-to-assemble 3D model of Boy's surface.
In this paper we introduce a homotopy theoretic technique for proving that the -theoretic assembly map is an equivalence. It is an extension of the methods used to prove split injectivity of the assembly and applies to any geometrically finite group. Our result is that there are two requirements which need to hold. …
Bayesian calibration for BCP self-assembly models using image data and measure transport.
We introduce a microscopic model for the dynamics of the order book to study how the lack of liquidity influences price fluctuations. We use the average density of the stored orders (granularity ) as a proxy for liquidity. This leads to a Price Impact Surface which depends on both volume and . The dependence …
INGB improves oversampling for noisy imbalanced datasets.
Between the category of exact metric spaces with bounded geometry (about which much is known) and the larger category of arbitrary exact metric spaces (about which little is known) lies the intermediate category of asymptotically exact metric spaces. We show that the coarse Baum-Connes assembly map is naturally split s…
We propose a probabilistic model for refining coarse-grained spatial data by utilizing auxiliary spatial data sets. Existing methods require that the spatial granularities of the auxiliary data sets are the same as the desired granularity of target data. The proposed model can effectively make use of auxiliary data set…
Revisits granular models explaining firm growth rates and sizes.
We introduce a hierarchical architecture for video understanding that exploits the structure of real world actions by capturing targets at different levels of granularity. We design the model such that it first learns simpler coarse-grained tasks, and then moves on to learn more fine-grained targets. The model is train…
Graph Neural Networks model 3D granular flow simulations.
New method predicts bankruptcy by imputing missing data with granular semantics.
Motivated by the practical demands for simplification of data towards being consistent with human thinking and problem solving as well as tolerance of uncertainty, information granules are becoming important entities in data processing at different levels of data abstraction. This paper proposes a method to construct c…
Tree++ graph kernel captures similarities at multiple granularities.
Deep neural networks (DNNs) are known for extracting useful information from large amounts of data. However, the representations learned in DNNs are typically hard to interpret, especially in dense layers. One crucial issue of the classical DNN model such as multilayer perceptron (MLP) is that neurons in the same layer…
Network analysis reveals distinct financial relationships among Euro Area banks.
Study uses trajectory embedding to measure place function similarity at fine spatial granularity.
In this paper, the first of a series of two, we continue the study of higher index theory for expanders. We prove that if a sequence of graphs is an expander and the girth of the graphs tends to infinity, then the coarse Baum-Connes assembly map is injective, but not surjective, for the associated metric space . Exp…
The clustering ensemble technique aims to combine multiple clusterings into a probably better and more robust clustering and has been receiving an increasing attention in recent years. There are mainly two aspects of limitations in the existing clustering ensemble approaches. Firstly, many approaches lack the ability t…
Paper tackles cross-granularity few-shot learning with meta-embedder.
This paper provides a full controlled version of algebraic -theory. This includes a rich array of assembly maps; the controlled assembly isomorphism theorem identifying the controlled group with homology; and the stability theorem describing the behavior of the inverse limit as the control parameter goes to 0. There…
Develops MgCSL for discovering causal structures in high-dimensional data.