Related papers: Toric Fiber Products in Geometric Modeling
We generalize the tensor product theory for modules for a vertex operator algebra previously developed in a series of papers by the first two authors to suitable module categories for a ``conformal vertex algebra'' or even more generally,…
We introduce Polytopic Matrix Factorization (PMF) as a novel data decomposition approach. In this new framework, we model input data as unknown linear transformations of some latent vectors drawn from a polytope. In this sense, the article…
Category theory provides a means through which many far-ranging fields of mathematics can be related by their similar structure. In a paper by Robinson [2], this interconnectivity afforded by categorical perspectives allowed for the…
Toric varieties play an important role both in symplectic and complex geometry. In symplectic geometry, the construction of a symplectic toric manifold from a smooth polytope is due to Delzant. In algebraic geometry, there is a more general…
A statistical model is a mathematical representation of an often simplified or idealised data-generating process. In this paper, we focus on a particular type of statistical model, called linear mixed models (LMMs), that is widely used in…
Finding a common factor of two multivariate polynomials with approximate coefficients is a problem in symbolic-numeric computing. Taking a tropical view on this problem leads to efficient preprocessing techniques, applying polyhedral…
This study proposes a methodology to utilize machine learning (ML) for topology optimization of periodic lattice structures. In particular, we investigate data representation of lattice structures used as input data for ML models to improve…
The operational Chow cohomology classes of a complete toric variety are identified with certain functions, called Minkowski weights, on the corresponding fan. The natural product of Chow cohomology classes makes the Minkowski weights into a…
Collaborative filtering is one of the most popular techniques in designing recommendation systems, and its most representative model, matrix factorization, has been wildly used by researchers and the industry. However, this model suffers…
In this paper, a new class of optical fibers is studied, i.e. microstructured fibers or photonic crystal fibers (PCF). The main objective is to characterize these fibers using different dispersion diagrams and present an interface that…
We consider toric maximum likelihood estimation over the field of Puiseux series and study critical points of the likelihood function using tropical methods. This problem translates to finding the intersection points of a tropical affine…
We show for bicommutative graded connected Hopf algebras that a certain distributive (Laplace) subgroup of the convolution monoid of 2-cochains parameterizes certain well behaved Hopf algebra deformations. Using the Laplace group, or its…
Introduction: Long-term time series forecasting (LTSF) has gained significant attention in recent years. While various specialized designs exist for capturing temporal dependency, recent studies have shown that even a single linear layer…
Let $X$ be a complex manifold, $\pi: E \rightarrow X$ a locally trivial holomorphic fibration with fiber $F$, and $\mathfrak{g}$ a Lie algebra with an invariant symmetric form. We associate to this data a holomorphic prefactorization…
A blend of two Taylor series for the same smooth real- or complex-valued function of a single variable can be useful for approximation. We use an explicit formula for a two-point Hermite interpolational polynomial to construct such blends.…
The theory of topological modular forms (TMF) predicts that elliptic genera of physical theories satisfy a certain divisibility property, determined by the theory's gravitational anomaly. In this note we verify this prediction in Duncan's…
Pairwise Markov Random Fields (MRFs) or undirected graphical models are parsimonious representations of joint probability distributions. Variables correspond to nodes of a graph, with edges between nodes corresponding to conditional…
Tensor decompositions have become essential tools for feature extraction and compression of multiway data. Recent advances in tensor operators have enabled desirable properties of standard matrix algebra to be retained for multilinear…
We consider a linearly elastic composite medium, which consists of a homogeneous matrix containing a statistically homogeneous set of multimodal spherical inclusions modeling the morphology of heterogeneous solid propellants (HSP).…
These notes are based on three lectures given at the 2013 CIME/CIRM summer school. The purpose of this series of lectures is to introduce the notion of a toric fibration and to give its geometrical and combinatorial characterizations.…