This paper explores Brunnian twin groups and their properties.
problem Alexander-Markov correspondence for isotopy classes of immersed circles.
method Diagrammatic representations and combinatorial structures.
result Brunnian twin groups are free groups when more than two strands are involved.
Virtual twin groups map to symmetric groups, revealing automorphism structure.
problem Understanding homomorphisms between virtual twin groups and symmetric groups.
method Using irreducible right-angled Coxeter groups and right-angled Artin groups.
result A complete description of homomorphisms between virtual twin groups and symmetric groups, including the structure of the automorphism group of VTn. The twin group Tn is a right angled Coxeter group generated by n−1 involutions and having only far commutativity relations. These groups can be thought of as planar analogues of Artin braid groups. In this note, we study some properties of twin groups whose analogues are well-known for Artin braid groups. We give…
Paper studies pure virtual twin groups and their automorphisms.
problem Understanding the structure and automorphisms of pure virtual twin groups.
method Analyzes stable isotopy classes of immersed circles on surfaces, extending classical knot theory.
result Proves PVTn is an irreducible right-angled Artin group with trivial center and gives its precise presentation. Proves Alexander and Markov theorems for higher genus virtual doodles.
problem Classifying isotopy classes of immersed circles on surfaces.
method Introduces virtual twin groups to extend twin groups and prove theorems for higher genus.
result Proves Alexander and Markov theorems for higher genus virtual doodles.
The paper characterizes crystallographic groups derived from virtual braid and twin groups.
problem Characterizing crystallographic groups from virtual braid and twin groups.
method Analyzing quotients of virtual braid and twin groups by their commutator subgroups.
result The quotients of virtual braid and twin groups by their commutator subgroups are crystallographic groups.
New groups and subgroups classified with representations and properties.
problem Classifying representations of new groups and subgroups.
method Introduced new groups and subgroups, classified representations into GL_n(C), investigated properties.
result Classified homogeneous 2-local representations of M_kVT_n into eight distinct types.
The relationship between minimal algebraic Kac-Moody groups and twin buildings is well known as is the relationship between formal completions in one direction and affine buildings. Nevertheless, as the completion of a Kac-Moody group in one direction destroys the opposite BN-pair, there exists no longer a twin buildin…
Paper defines doodles on closed surfaces, unifying classical and virtual theories.
problem Classifying doodles on closed surfaces, especially non-orientable ones.
method Introducing twisted virtual doodles, defining twin groups, and proving Alexander- and Markov-type theorems.
result Unified theory of doodles, showing trivial center and residually finite properties.
For spherical Tits buildings of the classical types there are well-known explicit descriptions as flag complexes. Similarly for affine buildings of the classical types there are explicit constructions in terms of lattices. In this article we generalize the flag complex description to twin cities, a generalization of tw…
Generators of the 4-sphere's smooth mapping class group via diffeomorphisms of Montesinos twins.
problem Understanding the smooth mapping class group of the 4-sphere.
method Homomorphism from loops of 2-spheres to smooth mapping class group, generators as twists along Montesinos twins.
result Generators of the image of the homomorphism as diffeomorphisms of Montesinos twins.
The twin group Tn is a right angled Coxeter group generated by n−1 involutions and the pure twin group PTn is the kernel of the natural surjection from Tn onto the symmetric group on n symbols. In this paper, we investigate some structural aspects of these groups. We derive a formula for the number of conj…
Alexander invariant created for doodles, vanishes on unlinked doodles.
problem Creating an Alexander type invariant for doodles.
method Deformation of Tits representation and Chebyshev polynomials of second kind.
result Invariant vanishes on unlinked doodles with more than one component.
New curves share invariant up to any fixed order.
problem Finite-order rondle invariants and lower central series.
method Formulation and construction of infinite sequences of curves.
result Infinitely many curves share invariants up to any fixed order.
Let TWn be the twin group on n arcs, n≥2. The group TWm+2 is isomorphic to Grothendieck's m-dimensional cartographical group Cm, m≥1. In this paper we give a finite presentation for the commutator subgroup TWm+2′, and prove that TWm+2′ has rank 2m−1. We derive that $TW_…
New findings about twists in 4-sphere diffeomorphisms.
problem Understanding isotopy classes of diffeomorphisms in 4-sphere.
method Using Cerf theory and twists along Montesinos twins.
result The subgroup of twists along Montesinos twins is trivial or cyclic of order two.
The paper studies congruence subgroups and crystallographic quotients of small Coxeter groups.
problem The congruence subgroup property for small Coxeter groups.
method Analyzes the properties of small Coxeter groups, proving the failure of the congruence subgroup property for certain groups.
result Proves the failure of the congruence subgroup property for infinite small Coxeter groups which are not virtually abelian.
Twinning splits data into fast, statistically similar sets.
problem Creating statistically similar data splits for Big Data.
method Twinning is a method based on SPlit for fast, model-independent dataset splitting.
result Twinning is orders of magnitude faster than SPlit.
The paper introduces twins in Kähler and Sasaki geometry, generalizing known concepts.
problem Understanding twins in Kähler and Sasaki geometry.
method Introducing weighted extremal Kähler twins and extremal Sasaki twins, studying their properties.
result Many twins appear in the Kähler setting and more than one extremal ray in the Sasaki cone.
We report some minimal surfaces that can be seen as copies of a triply periodic minimal surface (TPMS) related by reflections in parallel mirrors. We call them minimal twin surfaces for the resemblance with twin crystal. Brakke's Surface Evolver is employed to construct twinnings of various classical TPMS, including Sc…
Improved aircraft structure prediction using derivative-enhanced sparse Cholesky GP method.
problem Accurate real-time prediction of aircraft structure performance.
method Combining derivative data with a modified dynamic sparse Cholesky linear system solver.
result Improved prediction accuracy of aircraft structure performance.
We describe some buildings related to complex Kac-Moody groups. First we describe the spherical building of SLn(C) (i.e. the projective geometry PG(Cn)) and its Veronese representation. Next we recall the construction of the affine building associated to a discrete valuation on the rational function field C(z). Then …
Generative models create personalized patient health simulations.
problem Creating accurate digital twins for personalized medicine.
method Neural network architecture for conditional generative models of clinical trajectories.
result Same architecture generates accurate twins across 13 indications.
fMRI is a unique non-invasive approach for understanding the functional organization of the human brain, and task-based fMRI promotes identification of functionally relevant brain regions associated with a given task. Here, we use fMRI (using the Poffenberger Paradigm) data collected in mono- and dizygotic twin pairs t…
Smooth manifolds can be triangulated with graphs of bounded twin-width.
problem Understanding the structure of triangulations of smooth manifolds.
method Using Whitney's triangulation method and bounding the twin-width of specific graphs.
result Compact smooth manifolds have triangulations with graphs of bounded twin-width.
Digital twin reduces costs in various fields.
problem High costs in decision-making processes.
method Use of digital twin model for cost reduction.
result Digital twin acts as a cost reduction method.
Study of commutator subgroups and crystallographic quotients of virtual groups.
problem Investigate commutator subgroups and crystallographic quotients of virtual groups.
method Derived explicit finite presentations and proved crystallographic properties.
result Explicit finite presentations of commutator subgroups and crystallographic quotients.
The object of study are almost complex manifolds with a pair of Norden metrics, mutually associated by means of the almost complex structure. More precisely, a torsion-free connection and tensors with geometric interpretation are found which are invariant under the twin interchange, i.e. the swap of the counterparts of…
Proposes a probabilistic digital twin for dynamical systems using sparse Bayesian learning.
problem Creating and updating accurate digital twins for complex dynamical systems.
method Sparse Bayesian machine learning, two approaches: input-output and output-only.
result Identifies correct perturbation terms and associated parameters in dynamical systems.
Deep RL optimizes sensor placement in digital twins for dynamic data acquisition.
problem Limited applicability of traditional sensor placement techniques for online applications.
method Formulates sensor placement as a Markov decision process and uses deep reinforcement learning.
result Improves predictive accuracy and reliability of digital twins through adaptive sensor repositioning.
The object of study is almost paracomplex pseudo-Riemannian manifolds with a pair of metrics associated each other by the almost paracomplex structure. A torsion-free connection and tensors with geometric interpretation are found which are invariant under the twin interchange, i.e. the swap of the counterparts of the p…
Digital twin technology has significant promise, relevance and potential of widespread applicability in various industrial sectors such as aerospace, infrastructure and automotive. However, the adoption of this technology has been slower due to the lack of clarity for specific applications. A discrete damped dynamic sy…
Optimizes biomanufacturing processes with a new digital twin calibration method.
problem Lack of interpretability and sample efficiency in traditional DoE methods.
method Developed a computational approach to calibrate Bio-SoS digital twin model.
result Guides sample-efficient and interpretable DoEs by quantifying sub-model parameter estimation errors.
Enhanced multi-fidelity models improve digital twin accuracy and uncertainty quantification.
problem Lack of detailed application-specific data and inaccurate sensor data hinder surrogate model learning for digital twins.
method Proposes a multi-fidelity surrogate model framework integrating PCFE and GP, and deep-HPCFE with auto-regression schemes.
result Demonstrates improved accuracy and uncertainty quantification in digital twin systems.
Classifies doodles into prime and super prime types, describing them with doodle codes.
problem Classifying doodles into prime and super prime types.
method Using doodle codes to describe complementary regions and enumerate doodle diagrams.
result Super prime doodles have a Hamiltonian circuit.
The geometry of symmetric spaces, polar actions, isoparametric submanifolds and spherical buildings is governed by spherical Weyl groups and simple Lie groups. A natural generalization of semisimple Lie groups are affine Kac-Moody groups as they mirror their structure theory and have good explicitely known representati…
We show that twin building lattices have linear divergence, which implies that all asymptotic cones are without cut-points.
We introduce the category of singular 2-dimensional cobordisms and show that it admits a completely algebraic description as the free symmetric monoidal category on a twin Frobenius algebra, by providing a description of this category in terms of generators and relations. A twin Frobenius algebra (C, W, z, z^*) consist…
This paper analyzes Barlow Twins' representation efficiency using information-geometric methods.
problem Understanding and comparing the efficiency of self-supervised learning methods.
method Introduces an information-geometric framework to quantify representation efficiency and applies it to Barlow Twins.
result Proves that Barlow Twins achieves optimal representation efficiency (η=1).
Novel digital twin for complex systems improves performance.
problem Lack of practical implementation details for stochastic nonlinear MDOF systems.
method Decouples time-scales, uses physics-based model, Bayesian filtering, and machine learning.
result Excellent performance of proposed digital twin framework validated by examples.
A digital twin for multi-scale systems uses physics-based and machine learning models.
problem Lack of application-specific details in digital twin technology.
method Strategically separates into physics-based and data-driven models; uses mixture of experts with Gaussian Process.
result Robust and accurate predictions at future time-steps for multi-scale systems.
Multiple Sclerosis (MS) is a neurodegenerative disorder characterized by a complex set of clinical assessments. We use an unsupervised machine learning model called a Conditional Restricted Boltzmann Machine (CRBM) to learn the relationships between covariates commonly used to characterize subjects and their disease pr…
Paper introduces a method to learn physics between digital twins using imperfect models.
problem Learning physics from imperfect data and low-fidelity models.
method Bayesian Hierarchical modeling with physics-informed Gaussian processes.
result Models learning between digital twins are less uncertain than independent models but not over-confident.
How to price and hedge claims on nontraded assets are becoming increasingly important matters in option pricing theory today. The most common practice to deal with these issues is to use another similar or "closely related" asset or index which is traded, for hedging purposes. Implicitly, traders assume here that the h…
EHR-MPC optimizes sepsis treatment using digital twins and inference-time control.
problem Optimal sepsis treatment policies are contested and difficult to adapt during inference.
method EHR-MPC decouples learning patient dynamics from treatment optimization, enabling inference-time control over learned digital twins.
result EHR-MPC achieves comparable off-policy performance and improved simulation performance compared to RL baselines.
Study uses LLMs to create personalized treatment plans for rare gynecological tumors.
problem Suboptimal management and poor prognosis due to low incidence and heterogeneity of rare gynecological tumors.
method Developed a digital twin system using LLMs to integrate clinical and biomarker data.
result LLM-enabled digital twins efficiently model individual patient trajectories and identify potential treatment options.
A subgroup of a Kac-Moody group is called bounded if it is contained in the intersection of two finite type parabolic subgroups of opposite signs. In this paper, we study the isomorphisms between Kac-Moody groups over arbitrary fields of cardinality at least 4, which preserve the set of bounded subgroups. We show that …
A new algorithm for faster model selection in twin multi-class SVM.
problem Challenges in effective solution of multi-classification and fast model selection in twin multi-class SVM.
method Sample data set partition strategy, Lagrangian multipliers, piecewise linear update, initialization algorithm, and event-based iteration.
result Comparable classification performance achieved without solving quadratic programming problems.