arXiv research

A deep model learns to infer fluorescence labels from unlabeled microscopy images.

Histopathology tissue samples are widely available in two states: paraffin-embedded unstained and non-paraffin-embedded stained whole slide RGB images (WSRI). Hematoxylin and eosin stain (H&E) is one of the principal stains in histology but suffers from several shortcomings related to tissue preparation, staining proto…

An important part of Digital Pathology is the analysis of multiple digitised whole slide images from differently stained tissue sections. It is common practice to mount consecutive sections containing corresponding microscopic structures on glass slides, and to stain them differently to highlight specific tissue compon…

Stem uses diffusion models to infer gene expression from H&E images.

Study proposes deep learning techniques to diagnose and differentiate Celiac Disease and Environmental Enteropathy from biopsy images.

Determining the localization of specific protein in human cells is important for understanding cellular functions and biological processes of underlying diseases. Among imaging techniques, high-throughput fluorescence microscopy imaging is an efficient biotechnology to stain the protein of interest in a cell. In this w…

A novel approach for augmenting histopathological images by blending Gaussian-Laplacian pyramids.

Automatization of the diagnosis of any kind of disease is of great importance and it's gaining speed as more and more deep learning solutions are applied to different problems. One of such computer aided systems could be a decision support too able to accurately differentiate between different types of breast cancer hi…

New virtualized Δ-move simplifies virtual knots and links.

Virtual index cocycles reformulate virtual link invariants.

The paper studies strict equivalence in multi-virtual linkoids with new invariants.

The study enumerates virtual quandles up to isomorphism.

New virtual version of Thompson's group created to handle virtual knots.

The paper extends CF-moves to classify virtual links of any number of components.

Refines virtual link equality criterion for diagrams with one virtual crossing.

Extend writhe polynomial from virtual knots to multi-virtual knots

New invariants for virtual knots and links defined via quiver representations.

Study virtualized Delta, Sharp, and Pass moves for oriented virtual knots and links.

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.

Virtual knots and links get multicrossings and petal diagrams.

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 …

A virtual $n$-string is a chord diagram with $n$ core circles and a collection of arrows between core circles. We consider virtual $n$-strings up to virtual homotopy, compositions of flat virtual Reidemeister moves on chord diagrams. Given a virtual 1-string $α$, Turaev associated a based matrix that encodes invariants…

New invariant for virtual n-links defined and studied.

Given a virtual knot $K$, we construct a group $VG_K$ called the virtual knot group, and we use the elementary ideals of $VG_K$ to define invariants of $K$ called the virtual Alexander invariants. For instance, associated to the $k=0$ ideal is a polynomial $H_K(s,t,q)$ 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…

New polynomial invariants for virtual links 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…

Paper detects checkerboard colorability of virtual links using odd writhe and arrow polynomial.

Study algebraic invariants of multi-virtual links.

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…

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…

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.

The paper characterizes crystallographic groups derived from virtual braid and twin groups.

We generalize unoriented handlebody-links to the twisted virtual case, obtaining Reidemeister moves for handlebody-links in ambient spaces of the form $Σ\times [0,1]$ for $Σ$ a compact closed 2-manifold up to stable equivalence. We introduce a related algebraic structure known as twisted virtual bikeigebras whose axiom…

Invariants for trivalent graphs using algebraic colorings.

Study Vassiliev invariants for virtual knots, expanding quantum theory.

Paper introduces a new skein relation for multivariable polynomials of virtual links.

This paper studies virtual knots using mosaic diagrams.

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.

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…

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.

Virtual knot theory is a generalization (discovered by the author in 1996) of knot theory to the study of all oriented Gauss codes. (Classical knot theory is a study of planar Gauss codes.) Graph theory studies non-planar graphs via graphical diagrams with virtual crossings. Virtual knot theory studies non-planar Gauss…

Graphoids are topological invariants of virtual graph diagrams.