Related papers: Sudoku Associated Two Dimensional Bijections for I…

Motivated by the bijection between Schnyder labelings of a plane triangulation and partitions of its inner edges into three trees, we look for binary labelings for quadrangulations (whose edges can be partitioned into two trees). Our…

This paper addresses the search for a fast and meaningful image segmentation in the context of $k$-means clustering. The proposed method builds on a widely-used local version of Lloyd's algorithm, called Simple Linear Iterative Clustering…

This paper presents a comparative analysis of Sudoku-solving strategies, focusing on recursive backtracking and a heuristic-based constraint propagation method. Using a dataset of 500 puzzles across five difficulty levels (Beginner to…

In this paper, we propose two new algorithms for transduction with Matrix Completion (MC) problem. The joint MC and prediction tasks are addressed simultaneously to enhance the accuracy, i.e., the label matrix is concatenated to the data…

Typical graph embeddings may not capture type-specific bipartite graph features that arise in such areas as recommender systems, data visualization, and drug discovery. Machine learning methods utilized in these applications would be better…

Recall the classical 15-puzzle, consisting of 15 sliding blocks in a $4\times 4$ grid. Famously, the configuration space of this puzzle consists of two connected components, corresponding to the odd and even permutations of the symmetric…

We study two-dimensional, two-piece, piecewise-linear maps having two saddle fixed points. Such maps reduce to a four-parameter family and are well known to have a chaotic attractor throughout open regions of parameter space. The purpose of…

A division sudoku is a latin square whose all six conjugates are sudoku squares. We enumerate division sudokus up to a suitable equivalence, introduce powerful invariants of division sudokus, and also study latin squares that are division…

We introduce a new stereo formulation which does not use pixel and disparity models. Many problems in vision are treated as assigning each pixel a label. Disparities are labels for stereo. Such pixel-labeling problems are naturally…

Embeddings mapping high-dimensional discrete input to lower-dimensional continuous vector spaces have been widely adopted in machine learning applications as a way to capture domain semantics. Interviewing 13 embedding users across…

Research in Simultaneous Localization And Mapping (SLAM) is increasingly moving towards richer world representations involving objects and high level features that enable a semantic model of the world for robots, potentially leading to a…

We present a non-commutative algorithm for the multiplication of a 2 x 2 block-matrix by its adjoint, defined by a matrix ring anti-homomorphism. This algorithm uses 5 block products (3 recursive calls and 2 general products)over C or in…

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…

The Rubix Cube is a 3-dimensional single-player combination puzzle attracting attention in the reinforcement learning community. A Rubix Cube has six faces and twelve possible actions, leading to a small and unconstrained action space and a…

We describe a combinatorial approach for investigating properties of rational numbers. The overall approach rests on structural bijections between rational numbers and familiar combinatorial objects, namely rooted trees. We emphasize that…

Rectangular standard Young tableaux with 2 or 3 rows are in bijection with $U_q(\mathfrak{sl}_2)$-webs and $U_q(\mathfrak{sl}_3)$-webs respectively. When $W$ is a web with a reflection symmetry, the corresponding tableau $T_W$ has a…

Cross-modal image-text retrieval is challenging because of the diverse possible associations between content from different modalities. Traditional methods learn a single-vector embedding to represent semantics of each sample, but struggle…

We propose a novel probabilistic dimensionality reduction framework that can naturally integrate the generative model and the locality information of data. Based on this framework, we present a new model, which is able to learn a smooth…

In this paper, a robust visual tracking approach via mixed model based convolutional neural networks (SDT) is developed. In order to handle abrupt or fast motion, a prior map is generated to facilitate the localization of region of interest…

To represent anything from mathematical concepts to real-world objects, we have to resort to an encoding. Encodings, such as written language, usually assume a decoder that understands a rich shared code. A semantic embedding is a form of…