Related papers: Let's reinvent subtraction
One of the most fundamental questions in Biology or Artificial Intelligence is how the human brain performs mathematical functions. How does a neural architecture that may organise itself mostly through statistics, know what to do? One…
A new summation method is introduced to convert a relatively wide family of infinite sums and local expansions into integrals. The integral representations yield global information such as analytic continuability, position of singularities,…
We investigate the definability (reducts) lattice of the order of integers and describe a sublattice generated by relations 'between', 'cycle', 'separation', 'neighbor', '1-codirection', 'order' and equality'. Some open questions are…
Tandem duplication is an evolutionary process whereby a segment of DNA is replicated and proximally inserted. The different configurations that can arise from this process give rise to some interesting combinatorial questions. Firstly, we…
We study the termination problem for probabilistic term rewrite systems. We prove that the interpretation method is sound and complete for a strengthening of positive almost sure termination, when abstract reduction systems and term rewrite…
We present a novel freehand sketch beautification method, which takes as input a freely drawn sketch of a man-made object and automatically beautifies it both geometrically and structurally. Beautifying a sketch is challenging because of…
We prove a gluing theorem which allows to construct an ample divisor on a rational surface from two given ample divisors on simpler surfaces. This theorem combined with the Cremona action on the ample cone gives rise to an algorithm for…
Detecting objects of interest in images was always a compelling task to automate. In recent years this task was more and more explored using deep learning techniques, mostly using region-based convolutional networks. In this project we…
A vocabulary is a list of words designating subsets from a grand set X. We model a vocabulary as a partition of X and study the aggregation of individual vocabularies into a collective one. We characterize aggregation rules when X is…
This paper introduces a new equation for rewriting two unit fractions to another two unit fractions. This equation is useful for optimizing the elements of an Egyptian Fraction. Parity of the elements of the Egyptian Fractions are also…
Distillation is the task of replacing a complicated machine learning model with a simpler model that approximates the original [BCNM06,HVD15]. Despite many practical applications, basic questions about the extent to which models can be…
We introduce a new method for studying the Baum-Connes conjecture, which we call the direct splitting method. The method can simplify and clarify proofs of some of the known cases of the conjecture. In a separate paper, with J. Brodzki, E.…
Repetition, a basic form of artistic creation, appears in most musical works and delivers enthralling aesthetic experiences.
Computational approaches in historical linguistics have been increasingly applied during the past decade and many new methods that implement parts of the traditional comparative method have been proposed. Despite these increased efforts,…
We study word reconstruction problems. Improving a previous result by P. Fleischmann, M. Lejeune, F. Manea, D. Nowotka and M. Rigo, we prove that, for any unknown word $w$ of length $n$ over an alphabet of cardinality $k$, $w$ can be…
Chinese poetry is an important part of worldwide culture, and classical and modern sub-branches are quite different. The former is a unique genre and has strict constraints, while the latter is very flexible in length, optional to have…
We present an unusual algorithm involving classification trees where two trees are grown in opposite directions so that they are matched at their leaves. This approach finds application in a new data mining task we formulate, called…
Divisibility tests are algorithms that can quickly decide if one integer is divisible by another. There are many tests but most are either of the trimming or summing variety. Our goals are to present Zbikowski's family of trimming tests as…
An technically interesting proof of a known theorem.
Knowledge reduction, includes attribute reduction and value reduction, is an important topic in rough set literature. It is also closely relevant to other fields, such as machine learning and data mining. In this paper, an algorithm called…