Study on groups of unrestricted virtual braids and their properties.
problem Understanding the structure and properties of virtual braids and links.
method Exploration of unrestricted virtual braids, fused links, flat virtual braids, and virtual Gauss braids.
result Definition and study of groups of flat virtual braids and virtual Gauss braids, including their linearity.
Study of unrestricted virtual braid groups and their properties.
problem Characterize and describe homomorphisms of unrestricted virtual braid groups.
method Analyzing homomorphisms to symmetric groups and finite groups, characterizing images, proving characteristic subgroups, determining automorphism groups, and studying residual properties.
result Complete description of homomorphisms from UVBn to Sn for n≥5. The paper develops a new theory for quantum link invariants using quandles and biquandles.
problem Quantum link invariants for links with SL2(C) flat connections. method Using quandles and biquandles, the paper extends Reshetikhin-Turaev functor to tangles.
result A new invariant of links with a gauge class of quandle representations.
Study on virtual singular braid groups with algebraic properties and homomorphisms.
problem Algebraic properties and homomorphisms of virtual singular braid groups.
method Numerical invariants, homomorphisms, semi-direct product decompositions, presentations, and quotients.
result Determined all group homomorphisms from VSGn to Sn and obtained corresponding semi-direct product decompositions. 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.
Adaptive algorithm generates unrestricted adversarial inputs, defeating robust classifiers.
problem Vulnerability of neural networks to unrestricted adversarial inputs.
method Adaptive algorithm for generating unrestricted adversarial inputs.
result Adversarial inputs defeat robust classifiers.
New method generates unrestricted adversarial examples from generative models.
problem Traditional defense methods are ineffective against unrestricted adversarial examples.
method Train an AC-GAN to model class-conditional distribution, then search latent space for misclassified images.
result Unrestricted adversarial examples can bypass strong defenses and fool classifiers.
Proposes a new method to generate unrestricted adversarial examples.
problem Generating unrestricted adversarial examples without norm constraints.
method Leveraging state-of-the-art generative models to manipulate image fine-grained aspects.
result Our adversarial images look indistinguishable from natural images and can bypass certified defenses.
Optimal learning procedure for arbitrary function classes.
problem Learning arbitrary function classes without structural properties.
method Unrestricted learning procedure that selects functions outside given class.
result Optimal sample complexity for arbitrary function classes.
New algorithms ensure fair selection in combinatorial semi-bandit with unrestricted delays.
problem Fair selection in stochastic combinatorial semi-bandit with delayed feedback.
method Introduced merit-based fairness constraints and new bandit algorithms for reward and fairness.
result Achieved sublinear expected reward and fairness regrets with dependence on delay distribution quantiles.
Generative models create indistinguishable adversarial objects for object detection.
problem Creating unrestricted adversarial examples for object detection.
method Search over latent space of GAN for adversarial objects.
result Generated adversarial objects are indistinguishable from non-adversarial objects and transferable.
This paper considers the optimal dividend payment problem in piecewise-deterministic compound Poisson risk models. The objective is to maximize the expected discounted dividend payout up to the time of ruin. We provide a comparative study in this general framework of both restricted and unrestricted payment schemes, wh…
New method generates unrestricted adversarial face images to bypass robust face recognition systems.
problem Vulnerability of face recognition systems to unrestricted adversarial examples.
method Image translation techniques to generate large perturbations in face images.
result Achieved high attack success rates (90% and 80%) under white- and black-box settings. New methods reduce extrapolation errors in feature importance.
problem Flawed feature importance methods using unrestricted permutations lead to extrapolation errors.
method Three new approaches: conditional model reliance, Knockoffs with Gaussian transformation, and restricted ALE plot designs.
result Theoretical and numerical results show our strategies reduce/eliminate extrapolation.
REBMIX package generates, estimates, clusters and classifies multivariate normal mixtures.
problem Generating, estimating, clustering and classifying multivariate normal mixtures with unrestricted variance-covariance matrices.
method Random generation, estimation of components, weights, and parameters, prediction of cluster and class membership.
result Demonstrates the REBMIX package's capabilities for multivariate normal mixtures.
MoMA improves model-based RL by using unrestricted policy classes.
problem Limited sample efficiency and generalizability in model-based offline RL.
method Model-based mirror ascent algorithm with general function approximations.
result Theoretical guarantees and practical implementation of MoMA.
Study compares adaptive vs fixed query learning methods.
problem Comparing adaptive and fixed query learning methods for task approximation.
method Examined in-context and agentic learning in two settings: unrestricted and realizable.
result Adaptivity does not hinder performance in unrestricted setting but can in realizable setting.
New findings on GRW space-times with constant scalar curvature.
problem Understanding GRW space-times in different subspaces.
method Analyzing orthogonal subspaces of Gray's decomposition.
result Generalized quasi-Einstein GRW space-times reduce to known types of space-times.
New method optimizes policies without assuming known link functions between preferences and rewards.
problem Policy alignment with unknown and unrestricted link functions.
method Formulates an f-divergence-constrained reward maximization problem, learning policies directly. result Induces a semiparametric single-index binary choice model for policy alignment.
New contest evaluates machine learning robustness against unrestricted adversarial examples.
problem Evaluating machine learning robustness against arbitrary adversarial inputs.
method Two-player contest with a prize pool, focusing on unconstrained adversarial examples.
result Demonstrates the need for comprehensive evaluation of machine learning models' worst-case adversarial risk.
A stochastic model helps maintain insufficiently funded pension funds.
problem Maintaining pension funds that are underfunded and require external financing.
method A time-homogeneous diffusion process with a barrier is used to model the unrestricted reserves value, and a renewal-reward process models the financing effort.
result Expected values and cost evaluations of maintenance are derived, and the approach is applied to a generalized Brownian motion process.
Study improves cryptocurrency price prediction using deep learning with trading and social media indicators.
problem Predicting price movements of cryptocurrencies using deep learning.
method Used deep learning algorithms (MLP, CNN, LSTM, ALSTM) on hourly and daily data of Bitcoin and Ethereum.
result Unrestricted model with trading and social media indicators outperforms restricted model.
ScoreAG generates unrestricted adversarial images maintaining semantic integrity.
problem Limited robustness evaluations due to ℓp-norm constraints. method Score-Based Adversarial Generation (ScoreAG) using score-based generative models.
result ScoreAG improves robustness assessments across multiple benchmarks.
Classic braids embed in virtual braids.
problem Embedding classic braids in virtual braids.
method Elementary proof using generalizations of braid groups.
result Classical braid group injects into virtual braid group.
The study extends classical results on harmonic functions to Riemannian manifolds with non-tangential boundary limits.
problem Extending classical results on harmonic functions to Riemannian manifolds with non-tangential boundary limits.
method Investigated the restricted mean-value property on Riemannian manifolds, focusing on non-tangential boundary behavior.
result Extended a classical result of Fenton to non-positively curved Harmonic manifolds of purely exponential volume growth.
The paper finds minimal generating sets and abelianizes the quasitoric braid group.
problem Understanding the structure of quasitoric braids and their subgroup properties.
method Provided two minimal generating sets and determined the abelianization.
result Minimal generating sets and abelianization of the quasitoric braid group were determined.
We study the structure of the virtual braid group. It is shown that the virtual braid group is a semi--direct product of the virtual pure braid group and the symmetric group. Also, it is shown that the virtual pure braid group is a semi--direct product of free groups. From these results we obtain a normal form of words…
Satellite links of fully positive braids are characterized.
problem Characterizing satellite links of fully positive braids.
method Analyzing fully positive braids and their satellites.
result Satellite links of fully positive braids are characterized by specific conditions.
Formula found for braid index of n-bridge braids.
problem Finding a formula for the braid index of n-bridge braids. method Elementary, effective, self-contained proof.
result Closed form formula for braid index of n-bridge braids. Most simple braids have positive topological entropy.
problem Understanding the topological entropy of simple braids.
method Reduction from simple braids to non-simple 3-strand braids.
result The proportion of simple braids with positive entropy approaches 100% as the number of strands increases.
This paper is concerned with detecting when a closed braid and its axis are 'mutually braided' in the sense of Rudolph. It deals with closed braids which are fibred links, the simplest case being closed braids which present the unknot. The geometric condition for mutual braiding refers to the existence of a close contr…
Paper proves Markov's theorem for extended welded braids and links.
problem Generalizing welded links to extended welded links and braids.
method Following Kamada's approach, proving Alexander and Markov's theorems for extended welded braids and links.
result Proves versions of Alexander and Markov's theorems for extended welded braids and links.
We show that 3-braid links with given (non-zero) Alexander or Jones polynomial are finitely many, and can be effectively determined. We classify among closed 3-braids strongly quasipositive and fibered ones, and show that 3-braid links have a unique incompressible Seifert surface. We also classify the positive braid wo…
The paper examines subgroup separability for surface and virtual braid groups.
problem Subgroup separability of surface and virtual braid groups.
method Study of subgroup separability (LERF) properties.
result Properties of subgroup separability for surface and virtual braid groups are explored.
Virtual braids are a combinatorial generalization of braids. We present abstract braids as equivalence classes of braid diagrams on a surface, joining two distinguished boundary components. They are identified up to isotopy, compatibility, stability and Reidemeister moves. We show that virtual braids are in a bijective…
Study on deformation cohomology for braided commutative structures.
problem Classifying and understanding deformations of braided commutative algebras.
method Extending Yang-Baxter Hochschild cohomology to braided commutative deformations.
result Classifies infinitesimal deformations of braided algebras that are braided commutative.
Polynomial-time algorithm for virtual braid triviality.
problem Determining if virtual braid words represent the trivial braid.
method An O(l3n)-time algorithm for VBn. result Determines triviality of virtual braid words efficiently.
This paper identifies braided 3-belts that can be written in a braid-only form.
problem Identifying braided 3-belts that can be written in a braid-only form.
method Developed an algorithm to calculate the braid word for braided 3-belts and determined the conditions for knotted boundaries.
result Identified the set of braided 3-belts that can be written in a braid-only form and derived a formula for the Jones polynomial for knotted boundaries.
Magic braids can be made with leatherworking technique.
problem Determine which braids can be made with leatherworking technique.
method Explore their relation to several braid groups.
result Magic braids can be made with leatherworking technique.
Study virtual braid groups, proving a key subgroup result.
problem Understanding congruence subgroups in virtual braid groups.
method Using an extension of the integral Burau representation.
result Proved level 2 congruence subgroup of virtual braid group is pure virtual braid group.
Machine learning classifies braids and discovers new invariants.
problem Classifying and discovering invariants of braids and flat braids.
method Supervised learning with neural networks to classify braids as trivial or non-trivial.
result Found new convenient invariants of braids, including a complete invariant of flat braids.
In the present paper we give a new method for converting virtual knots and links to virtual braids. Indeed the braiding method given in this paper is quite general, and applies to all the categories in which braiding can be accomplished. We give a unifying topological interpretation of virtuals and flats (virtual strin…
This paper extends braid lifting to coloured braid groupoids for all simple disc covers.
problem Lifting braids to homeomorphisms on branched covers of the disc.
method Defines a map from a coloured braid groupoid to a mapping class groupoid for all simple covers of the disc.
result Characterizes the lift of every coloured braid, recovering classical lifting on liftable braids.
Paper studies special braids from chromatic configuration spaces.
problem Understanding braids with crossing-changeable properties.
method Theory of chromatic configuration spaces and braids.
result Introduced braids with the ability to intersect and untangle.
The paper explores various braid-like groups and their properties.
problem Investigating the pure braid groups and their relatives.
method Examining resonance varieties, lower central series ranks, Chen ranks, residual and formality properties.
result Discussed natural homomorphisms and methods to distinguish braid-like groups.
New virtual braid group structure and presentation found.
problem Understanding the structure of virtual pure braid groups.
method Cabling construction and HNN-extension approach.
result New presentation of VP4 and P4 groups. New concept of boundary braids defined for disk configurations.
problem Defining and studying braids with points fixed on the boundary.
method Using configuration spaces and fundamental groups, defining boundary braids and analyzing their geometric properties.
result Boundary braids form a subcomplex that metrically splits into a Euclidean polyhedron and a smaller rank dual braid complex.
The notion of a braid is generalized into two and three dimensions. Two-dimensional braids are described by braid monodromies or graphics called charts. In this paper we introduce the notion of curtains, and show that three-dimensional braids are described by braid monodromies or curtains.