In a typical online learning scenario, a learner is required to process a large data stream using a small memory buffer. Such a requirement is usually in conflict with a learner's primary pursuit of prediction accuracy. To address this dilemma, we introduce a novel Bayesian online classi cation algorithm, called the Vi…
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48 results for “virtual data”
Invariants for trivalent graphs using algebraic colorings.
problem Creating an invariant for virtual trivalent spatial graphs.
method Colorings by virtual Niebrzydowski algebras.
result Generalization and computational implementation of invariants.
Modern computer vision algorithms typically require expensive data acquisition and accurate manual labeling. In this work, we instead leverage the recent progress in computer graphics to generate fully labeled, dynamic, and photo-realistic proxy virtual worlds. We propose an efficient real-to-virtual world cloning meth…
Hyperinflation and price volatility in virtual economies has the potential to reduce player satisfaction and decrease developer revenue. This paper describes intuitive analytical methods for monitoring volatility and inflation in virtual economies, with worked examples on the increasingly popular multiplayer game Old S…
This paper describes a polynomial invariant of virtual knots that is defined in terms of an integer labeling of the virtual knot diagram. This labeling is seen to derive from an essentially unique structure of affine flat biquandle for flat virtual diagrams. The invariant is discussed in detail with many examples,inclu…
Enhances multi-tag classification using low-dimensional vector representations and virtual data.
problem Improving the performance of multi-tag classifiers.
method Embedding raw data into a low-dimensional feature space, then generating virtual data from linear operations on these vectors, to train multi-tag classifiers.
result Significant improvement in F1 scores (up to 224%) compared to training directly with raw data.
Paper uses virtual big data to improve autoencoder training and address imbalanced data classification.
problem Imbalanced data classification and autoencoder over-fitting.
method Cross-concatenation using Virtual Big Data.
result Cross-concatenation method effectively balances imbalanced class distributions.
New virtualized Δ-move simplifies virtual knots and links.
problem Simplifying virtual knots and links.
method Introducing a new local deformation called the virtualized Δ-move.
result Virtualized Δ-move is an unknotting operation for virtual knots.
The paper calculates bridge numbers for knots using machine learning.
problem Determining the bridge number for virtual knots with multiple definitions.
method Employed computational techniques and machine learning models to classify knots based on their bridge numbers.
result Demonstrated that the bridge number for virtual knots can differ significantly.
Virtual index cocycles reformulate virtual link invariants.
problem No specific problem stated; focuses on reformulation.
method Using virtual index cocycles to reformulate invariants.
result Unified reformulation of virtual link invariants.
The paper studies strict equivalence in multi-virtual linkoids with new invariants.
problem Understanding strict equivalence in multi-virtual linkoids.
method Utilizing multi-virtual knot theory, defining strict virtual linkoids, and studying invariants.
result New invariants for strict virtual linkoids are defined.
The study enumerates virtual quandles up to isomorphism.
problem Classifying virtual quandles up to isomorphism.
method Computer search and classification based on conjugacy class structures of rack automorphism groups.
result Classifications of virtual racks and quandles up to order 8.
Virtual Thompson's groupmath.GT
New virtual version of Thompson's group created to handle virtual knots.
problem Creating a mathematical framework for virtual knots.
method Defining a virtual version of Thompson's group and proving its properties.
result Any virtual link can be constructed from an element of the new virtual Thompson's group.
CF-moves for virtual linksmath.GT
The paper extends CF-moves to classify virtual links of any number of components.
problem Classifying virtual links using CF-moves.
method Extending CF-moves to classify virtual links of arbitrary number of components using the virtual linking number and invariants.
result Classification of 3-component even virtual links up to CF-moves.
Refines virtual link equality criterion for diagrams with one virtual crossing.
problem Determining when a virtual link diagram represents a properly virtual link.
method Refines the Kauffman-Murasugi-Thislethwaite type inequality for virtual links.
result Criterion for virtual link diagrams with exactly one virtual crossing to represent a properly virtual link.
Extend writhe polynomial from virtual knots to multi-virtual knots
problem Extend writhe polynomial from virtual knots to multi-virtual knots
method Extend writhe polynomial from virtual knots to multi-virtual knots
result Several questions asked in [16] have been answered
New invariants for virtual knots and links defined via quiver representations.
problem Defining new invariants for virtual knots and links.
method Quiver representations associated to virtual biquandles and rings.
result New polynomial invariants for virtual knots and links.
Study virtualized Delta, Sharp, and Pass moves for oriented virtual knots and links.
problem Conditions for unknotting oriented virtual knots and links.
method Local moves (Delta, Sharp, Pass) for oriented virtual links.
result Lower bounds for the unknotting numbers are proven and shown to be best possible.
The virtual unknotting number of a virtual knot is the minimal number of crossing changes that makes the virtual knot to be the unknot, which is defined only for virtual knots virtually homotopic to the unknot. We focus on the virtual knot obtained from the standard (p,q)-torus knot diagram by replacing all crossings o…
This paper connects virtual biquandles to biquandles for virtual link colorings.
problem Extending invariants from biquandles to virtual biquandles.
method Establishing equivalence between two representations of virtual braid groups and introducing new labeling rules.
result The number of colorings of a virtual link by virtual biquandles can be recovered from colorings by biquandles.
Virtual knots and links get multicrossings and petal diagrams.
problem Defining multicrossings for virtual knots and links.
method Extending multicrossings to virtual knots and links, showing petal diagrams exist.
result Petal diagrams exist for all virtual knots.
A virtual string can be defined as an equivalence class of planar diagrams under certain kinds of diagrammatic moves. Virtual strings are related to virtual knots in that a simple operation on a virtual knot diagram produces a diagram for a virtual string. In this paper we consider three operations on a virtual string …
Study uses sentiment analysis to predict cryptocurrency token returns in virtual reality.
problem Predicting cryptocurrency token returns in virtual reality economies.
method Used BERT for sentiment analysis and developed LSTM models integrating multi-modal features.
result Multi-modal model significantly outperforms price-only baseline in prediction accuracy.
Multistring based matricesmath.GT
A virtual -string is a chord diagram with core circles and a collection of arrows between core circles. We consider virtual -strings up to virtual homotopy, compositions of flat virtual Reidemeister moves on chord diagrams. Given a virtual 1-string , Turaev associated a based matrix that encodes invariants…
Given a virtual knot , we construct a group called the virtual knot group, and we use the elementary ideals of to define invariants of called the virtual Alexander invariants. For instance, associated to the ideal is a polynomial in three variables which we call the virtual Alexa…
A virtual link diagram is called normal if the associated abstract link diagram is checkerboard colorable, and a virtual link is normal if it has a normal diagram as a representative. Normal virtual links have some properties similar to classical links.In this paper, we introduce a method of converting a virtual link d…
Virtual reality (VR) offers immersive visualization and intuitive interaction. We leverage VR to enable any biomedical professional to deploy a deep learning (DL) model for image classification. While DL models can be powerful tools for data analysis, they are also challenging to understand and develop. To make deep le…
New polynomial invariants for virtual links are stronger than F-polynomials.
problem Defining new invariants for virtual links.
method Introducing weight functions and a recurrent construction for new invariants.
result New polynomial invariants are stronger than F-polynomials.
Virtual singular braids are generalizations of singular braids and virtual braids. We define the virtual singular braid monoid via generators and relations, and prove Alexander- and Markov-type theorems for virtual singular links. We also show that the virtual singular braid monoid has another presentation with fewer g…
Virtual Adversarial Training: A Regularization Method for Supervised and Semi-Supervised Learningstat.ML
We propose a new regularization method based on virtual adversarial loss: a new measure of local smoothness of the conditional label distribution given input. Virtual adversarial loss is defined as the robustness of the conditional label distribution around each input data point against local perturbation. Unlike adver…
Study algebraic invariants of multi-virtual links.
problem Algebraic invariants of multi-virtual links.
method Determining moves, introducing operator quandles, constructing invariants.
result Established new invariants for multi-virtual links.
The aim of the present paper is to prove that the minimal number of virtual crossings for some families of virtual knots grows quadratically with respect to the minimal number of classical crossings. All previously known estimates for virtual crossing number were principally no more than linear in the number of classic…
Virtual knot theory, introduced by Kauffman, is a generalization of classical knot theory of interest because its finite-type invariant theory is potentially a topological interpretation of Etingof and Kazhdan's theory of quantization of Lie bi-algebras. Classical knots inject into virtual knots, and flat virtual knots…
A 3-manifold is Haken if it contains a topologically essential surface. The Virtual Haken Conjecture says that every irreducible 3-manifold with infinite fundamental group has a finite cover which is Haken. Here, we discuss two interrelated topics concerning this conjecture. First, we describe computer experiments whic…
A virtual link can be understood as a link in a trivial I-bundle over an orientable compact surface with genus. A twisted virtual link is a link in a trivial I-bundle over a not-necessarily orientable compact surface. A twisted virtual birack is an algebraic structure with axioms derived from the twisted virtual Reidem…
We introduce a theory of virtual Legendrian knots. A virtual Legendrian knot is a cooriented wavefront on an oriented surface up to Legendrian isotopy of its lift to the unit cotangent bundle and stabilization and destablization of the surface away from the wavefront. We show that the groups of Vassiliev invariants of …
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.
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.
We generalize unoriented handlebody-links to the twisted virtual case, obtaining Reidemeister moves for handlebody-links in ambient spaces of the form for a compact closed 2-manifold up to stable equivalence. We introduce a related algebraic structure known as twisted virtual bikeigebras whose axiom…
Study Vassiliev invariants for virtual knots, expanding quantum theory.
problem Understanding Vassiliev invariants for virtual knots.
method Define chord diagrams, weight systems, and Lie algebra weight systems for rotational virtual knots.
result Extended quantum invariants capture more information than standard invariants.
Paper introduces a new skein relation for multivariable polynomials of virtual links.
problem Understanding properties of virtual links through polynomial invariants.
method Developed a virtual skein relation for multivariable polynomials of virtual links.
result New skein relation for multivariable polynomials of virtual links.
Virtual stringsmath.GT
A virtual string is a scheme of self-intersections of a closed curve on a surface. We introduce virtual strings and study their geometric properties and homotopy invariants. We also discuss connections between virtual strings, Gauss words, and virtual knots.
Virtual Mosaic Knot Theorymath.GT
This paper studies virtual knots using mosaic diagrams.
problem Understanding virtual knots through mosaic diagrams.
method Developed moves to preserve knot type and showed all virtual knots can be represented.
result Any virtual knot can be represented as a virtual mosaic.
Proposes generating virtual data points to overcome the curse of dimensionality.
problem Increased intrinsic dimensionality requires large data sets for local sampling.
method Manifold embedding motivated super sampling (MESS) framework.
result Generates virtual data points that faithfully represent the manifold.
A comprehensive study on the prediction reliability of graph neural networks for virtual screeningcs.LG
Study improves reliability of neural models for virtual screening.
problem Reliability issues in neural models for molecular property prediction.
method Investigated model architectures, regularization, and loss functions.
result Correct choice of regularization and inference methods improves reliability.
A virtual link diagram is called normal if the associated abstract link diagram is checkerboard colorable, and a virtual link is normal if it has a normal diagram as a representative.In this paper, we introduce a method of converting a virtual link diagram to a normal virtual link diagram by use of the double covering …
In 2002, D. Hrencecin and L.H. Kauffman defined a filamentation invariant on oriented chord diagrams that may determine whether the corresponding flat virtual knot diagrams are non-trivial. A virtual knot diagram is non-classical if its related flat virtual knot diagram is non-trivial. Hence filamentations can be used …
Study links' flat-virtual diagrams to create link invariants.
problem Equivalence and invariants of flat-virtual diagrams.
method Maps from links in thickened surfaces to flat-virtual links.
result Investigation of flat-virtual diagrams' equivalence and invariants.