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Domain generalization for semantic segmentation is highly demanded in real applications, where a trained model is expected to work well in previously unseen domains. One challenge lies in the lack of data which could cover the diverse…
The role of integrable systems in string theory is discussed. We remind old examples of the correspondence between stringy partition functions or effective actions and integrable equations, based on effective application of the matrix model…
We give a generalized definition of stretch that simplifies the efficient construction of low-stretch embeddings suitable for graph algorithms. The generalization, based on discounting highly stretched edges by taking their $p$-th power for…
Partition functions for non-interacting particles are known to be symmetric functions. It is shown that powerful group-theoretical techniques can be used not only to derive these relationships, but also to significantly simplify calculation…
The topological string partition function Z=exp(lambda^{2g-2} F_g) is calculated on a compact Calabi-Yau M. The F_g fulfill the holomorphic anomaly equations, which imply that Z transforms as a wave function on the symplectic space…
We define compactifications of vector spaces which are functorial with respect to certain linear maps. These "many-body" compactifications are manifolds with corners, and the linear maps lift to b-maps in the sense of Melrose. We derive a…
We study generating functions of ordinary and plane partitions coloured by the action of a finite subgroup of the corresponding special linear group. After reviewing known results for the case of ordinary partitions, we formulate a…
This paper presents a unified approach for localizing some relevant graph topological indices via majorization techniques. Through this method, old and new bounds are derived and numerical examples are provided, showing how former results…
I review type IIB string compactifications in which the three-form field strengths satisfy a self-duality condition on the internal manifold. I begin with an overview of the models, giving preliminary formulae and several points of view…
Graph clustering is a fundamental computational problem with a number of applications in algorithm design, machine learning, data mining, and analysis of social networks. Over the past decades, researchers have proposed a number of…
We study the domain wall partition function $Z_N$ for the $U_q(A_2^{(2)})$ (Izergin-Korepin) integrable $19$-vertex model on a square lattice of size $N$. $Z_N$ is a symmetric function of two sets of parameters: horizontal…
The so-called motorcycle graph has been employed in recent years for various purposes in the context of structured and aligned block decomposition of 2D shapes and 2-manifold surfaces. Applications are in the fields of surface…
We consider a class of adaptive multilevel domain decomposition-like algorithms, built from a combination of adaptive multilevel finite element, domain decomposition, and partition of unity methods. These algorithms have several interesting…
Transformations of digital spaces preserving local and global topology play an important role in thinning, skeletonization and simplification of digital images. In the present paper, we introduce and study contractions of simple pair of…
Graph embeddings have emerged as a powerful tool for representing complex network structures in a low-dimensional space, enabling the use of efficient methods that employ the metric structure in the embedding space as a proxy for the…
We show that a class of torsional compactifications of the heterotic string are dual to conventional Kahler heterotic string compactifications. This observation follows from the recently proposed analogue of the c-map for the heterotic…
This is the first of two papers on partition functions and the index theory of transversally elliptic operators. In this paper we only discuss algebraic and combinatorial issues related to partition functions. The applications to index…
We introduce a continuous domain for function spaces over topological spaces which are not core-compact. Notable examples of such topological spaces include the real line with the upper limit topology, which is used in solution of initial…
We show that string/M theory compactifications to maximally symmetric space-times using manifolds whose scalar curvature is everywhere negative, must have significant warping, large stringy corrections, or both.
This is an expositoray article on the topological string partition function promoting an extension of the partition function of open Gromov-Witten theory of CY 3-folds defined by the trace of vertex operators. We also give a brief survey of…