Related papers: From Data to Combinatorial Multivector field Throu…

In this paper, a novel distributed optimization framework has been proposed. The key idea is to convert optimization problems into optimal control problems where the objective of each agent is to design the current control input minimizing…

In this self-contained document, we aim to present the basic theoretical building blocks to understand modeling of stellarator magnetic fields, some of the challenges associated with modeling, and optimization for designing stellarators. As…

This paper introduces the notion of upper-linearizable/quadratizable functions, a class that extends concavity and DR-submodularity in various settings, including monotone and non-monotone cases over different convex sets. A general…

This paper proposes a framework that formulates a wide range of graph combinatorial optimization problems using permutation-based representations. These problems include the travelling salesman problem, maximum independent set, maximum cut,…

This paper surveys the recent attempts at leveraging machine learning to solve constrained optimization problems. It focuses on surveying the work on integrating combinatorial solvers and optimization methods with machine learning…

We propose several techniques to construct complete permutation polynomials of finite fields by virtue of complete permutations of subfields. In some special cases, any complete permutation polynomials over a finite field can be used to…

The amount of data in the world is expanding rapidly. Every day, huge amounts of data are created by scientific experiments, companies, and end users' activities. These large data sets have been labeled as "Big Data", and their storage,…

We introduce Residue Hyperdimensional Computing, a computing framework that unifies residue number systems with an algebra defined over random, high-dimensional vectors. We show how residue numbers can be represented as high-dimensional…

With most modern visualization tools, authors need to transform their data into tidy formats to create visualizations they want. Because this requires experience with programming or separate data processing tools, data transformation…

There is a large class of problems in algebraic combinatorics which can be distilled into the same challenge: construct an explicit combinatorial bijection. Traditionally, researchers have solved challenges like these by visually inspecting…

In this paper, we consider smooth convex optimization problems with simple constraints and inexactness in the oracle information such as value, partial or directional derivatives of the objective function. We introduce a unifying framework,…

The classification of complex data usually requires the composition of processing steps. Here, a major challenge is the selection of optimal algorithms for preprocessing and classification (including parameterizations). Nowadays, parts of…

A model of multicellular systems with several types of cells is developed from the phase field model. The model is presented as a set of partial differential equations of the field variables, each of which expresses the shape of one cell.…

In this paper we propose an extension of the notion of deviation-based aggregation function tailored to aggregate multidimensional data. Our objective is both to improve the results obtained by other methods that try to select the best…

With the progress of the urbanisation process, the urban transportation system is extremely critical to the development of cities and the quality of life of the citizens. Among them, it is one of the most important tasks to judge traffic…

We develop a generic computational model that can be used effectively for establishing the existence of winning strategies for concrete finite combinatorial games. Our modelling is (equational) logic-based involving advanced techniques from…

Vector database management systems have emerged as an important component in modern data management, driven by the growing importance for the need to computationally describe rich data such as texts, images and video in various domains such…

Vectors are universal mathematical objects that can represent text, images, speech, or a mix of these data modalities. That happens regardless of whether data is represented by hand-crafted features or learnt embeddings. Collect a large…

Robust feature representation plays significant role in visual tracking. However, it remains a challenging issue, since many factors may affect the experimental performance. The existing method which combine different features by setting…

In this paper, we develop a general framework of geometric functorial field theories, meaning that all bordisms in question are endowed with geometric structures. We take particular care to establish a notion of smooth variation of such…