The paper studies deformations of cohesive modules on complex manifolds.
problem Deformation theory of cohesive modules on compact complex manifolds.
method Development of Kuranishi maps and obstructions for deformations of cohesive modules.
result Generalization of deformation theory for holomorphic vector bundles and coherent sheaves.
The paper develops residue currents for cohesive modules and proves a generalized Poincaré-Lelong formula.
problem Analyzing coherent sheaves on complex manifolds using global analytic methods.
method Developing residue currents for cohesive modules and proving their properties.
result Proves a generalized Poincaré-Lelong formula for cohesive modules.
The paper generalizes current constructions to cohesive modules and characteristic forms.
problem Constructing currents for characteristic forms of cohesive modules.
method Generalized construction of pseudomeromorphic currents for de-Rham characteristic classes and characteristic forms of cohesive modules.
result Currents representing characteristic forms can be constructed using the degree-0 and degree-1 parts of the superconnection.
Using the concept of a cohesive module defined by Block, we use the theory of superconnections in the sense of Quillen to construct natural superconnections on Hermitian cohesive modules. By the Chern-Weil construction, we obtain characteristic classes with values in Bott-Chern cohomology which refines the usual deRham…
Policy-gradient method controls multiple non-cohesive targets.
problem Controlling multiple non-cohesive targets in a decentralized manner.
method Proximal Policy Optimization for target selection and driving.
result Effective control of non-cohesive targets without prior dynamics knowledge.
Motivated by recent financial crises significant research efforts have been put into studying contagion effects and herding behaviour in financial markets. Much less has been said about influence of financial news on financial markets. We propose a novel measure of collective behaviour in financial news on the Web, New…
We formulate differential cohomology and Chern-Weil theory -- the theory of connections on fiber bundles and of gauge fields -- abstractly in the context of a certain class of higher toposes that we call "cohesive". Cocycles in this differential cohomology classify higher principal bundles equipped with cohesive struct…
Study examines how business units can benefit from group cohesion under regulatory constraints.
problem Regulatory constraints limit business units' ability to form a single cohesive group.
method Defined and analyzed cohesive risk measures to minimize capital costs.
result Cohesive risk measures allow groups to achieve minimal capital costs without altering individual liabilities.
A new method improves graph node embeddings by considering both nearby and distant node similarities.
problem Improving graph node embeddings by considering both nearby and distant node similarities.
method Distance-aware Negative Sampling (DNS) which maximizes cohesion at nearby node-pairs and separation at distant node-pairs.
result DNS outperforms baseline methods in downstream node classification tasks on various datasets and GRL algorithms.
Cyclification of orbifolds explained in cohesive higher topos theory.
problem Understanding cyclification of orbifolds in geometric and algebraic contexts.
method Cohesive higher topos theory and transgression of cohomological charges.
result Cyclification of orbifolds is a fundamental base-change construction.
Generalizes Riemann-Hilbert correspondence for curved local systems.
problem Higher Riemann-Hilbert correspondence with scalar curvature.
method Equivalence of dg-categories of curved local systems, graded vector bundles, and representations.
result Equivalence of dg-enhancements of twisted sheaves categories.
Higher gauge theory via differential nonabelian cohomology
problem Global infrared completion of higher gauge fields
method Maxwell-type higher gauge fields
result Electromagnetic flux quantization
Enhances kernel regression with network data for better predictions.
problem Improving predictive power in high-dimensional data.
method Combines kernel regression with network cohesion data to model nonlinearities.
result Significantly better predictive performances in high-dimensional data.
Unified classification of equivariant principal bundles using higher homotopy theory.
problem Unified classification of equivariant principal bundles.
method Smooth Oka principle, singular-cohesive homotopy theory, internally describing principal bundles.
result Unified classification results for equivariant principal bundles.
Intuitive clustering algorithm balances cluster size and cohesion.
problem Cluster definition and selection in data analysis.
method Nearest neighbours equilibrium condition for clustering.
result High-quality clustering solutions compared to benchmarks.
Discriminative clustering uses mutual information to cluster data.
problem Clustering data into cohesive groups.
method Discriminative clustering using mutual information.
result Mutual information has been a cornerstone of discriminative clustering.
Cohesion uses deep Koopman operators to generate long-range forecasts of chaotic dynamics.
problem Challenges in data-driven emulation of chaotic dynamics, especially long-range skill decay.
method Generative modeling with coherent priors estimated using reduced-order models.
result Superior long-range forecasting skill on chaotic systems, including climate dynamics.
New bounds improve linkage methods for clustering, distinguishing complete-link from single-link.
problem Improving bounds on linkage methods for clustering quality.
method Developed new bounds for complete-link and average-link methods in agglomeration clustering.
result Separated complete-link from single-link in terms of approximation for diameter.
Introduces a new geometric framework for non-perturbative BV-theory.
problem Non-perturbative generalization of BV-theory in infinite-dimensional spaces.
method Derived differential geometry and homotopical algebraic geometry.
result Concrete model of derived smooth stacks for encoding non-perturbative BV-theory.
Online PaLD extends PaLD for semi-supervised online applications.
problem Scalability of unsupervised clustering algorithms for large datasets.
method Adapted partitioned local depth algorithm for online semi-supervised prediction.
result Online PaLD extends cohesion network to new data points efficiently.
This is a survey of motivations, constructions and applications of higher prequantum geometry. In section 1 we highlight the open problem of prequantizing local field theory in a local and gauge invariant way, and we survey how a solution to this problem exists in higher differential geometry. In section 2 we survey ex…
Protein interactions constitute the fundamental building block of almost every life activity. Identifying protein communities from Protein-Protein Interaction (PPI) networks is essential to understand the principles of cellular organization and explore the causes of various diseases. It is critical to integrate multipl…
This work investigates fundamental questions related to learning features in convolutional neural networks (CNN). Empirical findings across multiple architectures such as VGG, ResNet, Inception, DenseNet and MobileNet indicate that weights near the center of a filter are larger than weights on the outside. Current regu…
Study derived Lie ∞-groupoids and algebroids in higher differential geometry.
problem Addressing problems in higher differential geometry using derived Lie ∞-groupoids and algebroids.
method Construct CFO structures, study L∞-algebroids, homotopical algebras, and homotopy-coherent representations.
result Construct Atiyah classes for L∞-algebroids pairs and study singular foliations and their holonomies.
We introduce a method to predict which correlation matrix coefficients are likely to change their signs in the future in the high-dimensional regime, i.e. when the number of features is larger than the number of samples per feature. The stability of correlation signs, two-by-two relationships, is found to depend on thr…
This paper argues that the fundamental principle of contemporary financial economics is balanced reciprocity, not the principle of utility maximisation that is important in economics more generally. The argument is developed by analysing the mathematical Fundamental Theory of Asset Pricing with reference to the emergen…
Examines multiagent systems for complex learning tasks.
problem Achieving cohesive learning behavior in multiagent networks.
method General formulation for multiagent dynamics and conditions for learning.
result Conditions for achieving cohesive learning behavior in multiagent networks.
Extends partitioned local depth concept with probabilistic considerations.
problem Uncertain, variable, and conflicting information in data.
method Partitioned local depth with probabilistic concepts of local relevance and support division.
result Extends original ideas to handle uncertain data.
The paper explains the importance of diffeological groupoids in modern geometry and physics.
problem None explicitly stated, focuses on the concept and applications.
method Expository review of the development and applications of diffeological groupoids.
result The diffeological groupoid serves as a powerful tool in various areas of modern geometry and physics.
Classifies modules of surface-knots in terms of their properties.
problem Characterizing modules of surface-knots in terms of their properties.
method Using homology and covering spaces, the reduced first module is characterized.
result The reduced first module for every genus g is characterized in terms of properties of a finitely generated module.
This paper presents a simple agent-based model of an economic system, populated by agents playing different games according to their different view about social cohesion and tax payment. After a first set of simulations, correctly replicating results of existing literature, a wider analysis is presented in order to stu…
Proves finiteness and holonomicity of skein modules for 3-manifolds.
problem Finiteness and holonomicity of skein modules for 3-manifolds.
method Defining skein transfer bimodules and using q-analogues of D-module theory.
result Internal skein modules are holonomic modules over the internal skein algebra of the boundary.
Defines super projective modules and explores their properties.
problem Exploring the geometric-algebraic link in super geometry.
method Defined and explored super projective modules over supersmooth functions.
result Module of vector fields over a supersphere is a super projective module.
Synthetic theory defines orbifolds as microlinear types with finite identifications.
problem Defining orbifolds in traditional set-level foundations with internal symmetries.
method Synthetic differential cohesive homotopy type theory, microlinearity, finite identifications.
result Proper étale groupoids are orbifolds in synthetic theory.
We introduce higher skein modules of links generalizing the Conway skein module. We show that these modules are closely connected to the HOMFLY polynomial.
A new method to derive presentations of skein modules is developed. For the case of homotopy skein modules it will be shown how the topology of a 3-manifold is reflected in the structure of the module. The freeness problem for q-homotopy skein modules is solved, and a natural skein module related to linking numbers is …
Neural Module Networks, originally proposed for the task of visual question answering, are a class of neural network architectures that involve human-specified neural modules, each designed for a specific form of reasoning. In current formulations of such networks only the parameters of the neural modules and/or the or…
Paper compares skein modules to Kauffman bracket modules.
problem Comparing skein modules to Kauffman bracket modules.
method Using skein relations and Reshetikhin-Turaev model.
result Resolved the problem of comparing skein modules to Kauffman bracket modules.
Skein modules are the main objects of an algebraic topology based on knots (or position). In the same spirit as Leibniz we would call our approach "algebra situs." When looking at the panorama of skein modules we see, past the rolling hills of homologies and homotopies, distant mountains - the Kauffman bracket skein mo…
The paper explores how to fairly share longevity risk among participants of tontine schemes.
problem Fair distribution of longevity risk among participants with varying wealth and health.
method Develops a modeling framework for sharing benefits among survivors in tontine schemes.
result There are multiple ways to share longevity risk, depending on social cohesion.
Generalized Steinberg module presentation for Gaussian and Eisenstein integers.
problem Presenting Steinberg modules for specific number rings.
method Generalization of Bykovskii's presentation to Gaussian and Eisenstein integers.
result Generalization does not yield a presentation for all Euclidean number rings.
Enhanced Alexander module detects linking numbers in links.
problem Detecting linking numbers in links using Alexander modules.
method Defining and singling out meridians and longitudes in reduced Alexander modules.
result The enhanced Alexander module determines all linking numbers.
We define 2-crossed module bundle 2-gerbes related to general Lie 2-crossed modules and discuss their properties. A 2-crossed module bundle 2-gerbe over a manifold is defined in terms of a so called 2-crossed module bundle gerbe, which is a crossed module bundle gerbe equipped with an extra sructure. It is shown that s…
Combinatorial approach to compute satellite knot invariants using graph theory.
problem Computing knot invariants for satellite knots using bordered Heegaard Floer homology.
method Construct weighted A∞-modules using decorated planar graphs and prove their isomorphism. result Combinatorial proof of A∞ structure relations for the constructed modules. Data stream classification methods demonstrate promising performance on a single data stream by exploring the cohesion in the data stream. However, multiple data streams that involve several correlated data streams are common in many practical scenarios, which can be viewed as multi-task data streams. Instead of handli…
New sl(2) action defined on a mathematical module.
problem No specific problem stated; focuses on mathematical construction.
method Construction of sl(2)-action on equivariant skein lasagna module.
result Infinitesimal sl(2)-symmetries constructed.
Introduces admissible skein modules for non-semisimple categories.
problem No specific problem stated; generalization of Kauffman skein algebra.
method Introduces admissible skein modules associated to ideals in pivotal categories.
result These modules generalize Kauffman skein algebra and relate to quantum invariants.
Studies modules over a category of Jacobi diagrams in handlebodies.
problem Understanding modules over a specific category of Jacobi diagrams.
method Generalizes adjunctions and studies subquotient modules.
result Generalizes adjunctions between modules and Casimir Lie algebra modules.