arXiv research

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…

Proposes generating virtual data points to overcome the curse of dimensionality.

The paper confirms a conjecture and extends arrow polynomial to twisted links.

We succeed to generalize spun knots of classical 1-knots to the virtual 1-knot case by using the `spinning construction'. That, is, we prove the following: Let $Q$ be a spun knot of a virtual 1-knot $K$ by our method. The embedding type $Q$ in $S^4$ depends only on $K$. Furthermore we prove the following: The submanifo…

The paper calculates bridge numbers for knots using machine learning.

This paper gives a new interpretation of the virtual braid group in terms of a strict monoidal category SC that is freely generated by one object and three morphisms, two of the morphisms corresponding to basic pure virtual braids and one morphism corresponding to a transposition in the symmetric group. The key to this…

In this paper, we explore the virtual technique that is very useful in studying moduli problem from differential geometric point of view. We introduce a class of new objects "virtual manifolds/orbifolds", on which we develop the integration theory. In particular, the virtual localization formula is obtained.

Develops virtual Morse-Bott indices for four-manifolds, proving inequalities.

In this paper we discuss how to define a chord index via smoothing a real crossing point of a virtual knot diagram. Several polynomial invariants of virtual knots and links can be recovered from this general construction. We also explain how to extend this construction from virtual knots to flat virtual knots.

A flat virtual link is a finite collection of oriented closed curves $\mathfrak L$ on an oriented surface $M$ considered up to virtual homotopy, i.e., a composition of elementary stabilizations, destabilizations, and homotopies. Specializing to a pair of curves $(L_1,L_2)$, we show that the minimal number of intersecti…

A weak chord index $Ind'$ is constructed for self crossing points of virtual links. Then a new writhe polynomial $W$ of virtual links is defined by using $Ind'$. $W$ is a generalization of writhe polynomial defined in [6]. Based on $W$, three invariants of virtual links are constructed. These invariants can be used to …

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…

A fixed point theorem is proved for inverse transducers, leading to an automata-theoretic proof of the fixed point subgroup of an endomorphism of a finitely generated virtually free group being finitely generated. If the endomorphism is uniformly continuous for the hyperbolic metric, it is proved that the set of regula…

For ordinary knots in R3, there are no degree one Vassiliev invariants. For virtual knots, however, the space of degree one Vassiliev invariants is infinite dimensional. We introduce a sequence of three degree one Vassiliev invariants of virtual knots of increasing strength. We demonstrate that the strongest invariant …

This paper uses sheaf theory to model virtual knots geometrically.

We address the question of detecting minimal virtual diagrams with respect to the number of virtual crossings. This problem is closely connected to the problem of detecting the minimal number of additional intersection points for a generic immersion of a singular link in $R^{2}$. We tackle this problem by the so-called…

Virtual invariants defined from sheaves on surfaces.

We consider several classes of knotted objects, namely usual, virtual and welded pure braids and string links, and two equivalence relations on those objects, induced by either self-crossing changes or self-virtualizations. We provide a number of results which point out the differences between these various notions. Th…

Study improves reliability of neural models for virtual screening.

Geometrically characterizes virtual nonlinear nonholonomic constraints using symplectic methods.

We show that in the fundamental groups of closed manifolds without conjugate points centralizers of all elements virtually split.

The paper develops a multi-unit soft sensing model for virtual flow meters that improves few-shot learning.

This paper introduces a new method to create mod m almost classical links from virtual knots.

The paper extends Lipschitz metric isometries between Outer Spaces of virtually free groups.

Study on coloring virtual tangles with integer and modular arithmetic.

We consider the following properties of compact oriented irreducible graph-manifolds: to contain a $π_1$-injective surface (immersed, virtually embedded or embedded), be (virtually) fibered over $S^1$, and to carry a metric of nonpositive sectional curvature. It turns out that all these properties can be described from…

Invariants for trivalent graphs using algebraic colorings.

We study properly discontinuous and cocompact actions of a discrete subgroup $Γ$ of an algebraic group $G$ on a contractible algebraic manifold $X$. We suppose that this action comes from an algebraic action of $G$ on $X$ such that a maximal reductive subgroup of $G$ fixes a point. When the real rank of any simple subg…

We introduce the multiplexing of a crossing, replacing a classical crossing of a virtual link diagram with multiple crossings which is a mixture of classical and virtual. For integers $m_{i}$ $(i=1,\ldots,n)$ and an ordered $n$-component virtual link diagram $D$, a new virtual link diagram $D(m_{1},\ldots,m_{n})$ is ob…

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…

In this paper, we make use of the relations between the braid and mapping class groups of a compact, connected, non-orientable surface N without boundary and those of its orientable double covering S to study embeddings of these groups and their (virtual) cohomological dimensions. We first generalise results of Birman …

The paper proves that certain surface mapping class groups do not virtually surject to the integers.

We conjecture a formula for the generating function of virtual $χ_y$-genera of moduli spaces of rank 2 sheaves on arbitrary surfaces with holomorphic 2-form. Specializing the conjecture to minimal surfaces of general type and to virtual Euler characteristics, we recover (part of) a formula of C. Vafa and E. Witten. The…

We introduce the notion of ascent sliceness of virtual knots. A representative of a virtual knot is an embedding $S^1 \hookrightarrow Σ_{g} \times I$, for $Σ_g$ a closed connected oriented surface of genus $g$; the virtual knot represented is slice if there exists a pair consisting of a disc $D$ and an oriented…

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…

The article explains Rao distances and conformal mappings for 3D objects.

This is the first part of a trilogy where we apply the theory of virtual manifold/orbifolds developed by the first named author and Tian to study the Gromov-Witten moduli spaces. In this paper, we resolve the main analytic issue arising from the lack of differentiability of $PSL(2, \C)$-action on spaces of $W^{1, p}$-m…

A classical result by K.B. Lee states that every group morphism between almost crystallographic groups is induced by an affine map on the nilpotent Lie group whereon these groups by definition act. It is the main technique for studying morphisms between virtually nilpotent groups, having important applications in fixed…

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…

Deep neural network identifies potential SARS-CoV-2 inhibitors.

Enhances multi-tag classification using low-dimensional vector representations and virtual data.

In this note we point out an error in the above paper and refer to some papers where this error is corrected and a more general theorem is proved.

Study of group boundaries and subgroup properties.

Paper uses virtual big data to improve autoencoder training and address imbalanced data classification.

Novel framework for efficient Gaussian process models with monotonicity constraints.

New virtualized Δ-move simplifies virtual knots and links.

Virtual index cocycles reformulate virtual link invariants.

Estimates log-likelihood of interacting particle systems using virtual particles.