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Determining the crossing numbers of Cartesian products of small graphs with arbitrarily large paths has been an ongoing topic of research since the 1970s. Doing so requires the establishment of coincident upper and lower bounds; the former…
Graph theory provides fundamental concepts for many fields of science like statistical physics, network analysis and theoretical computer science. Here we give a pedagogical introduction to graph theory, divided into three sections. In the…
Learning DAG structures from purely observational data remains a long-standing challenge across scientific domains. An emerging line of research leverages the score of the data distribution to initially identify a topological order of the…
Thousands of experiments are analyzed and papers are published each year involving the statistical analysis of grouped data. While this area of statistics is often perceived -- somewhat naively -- as saturated, several misconceptions still…
This paper studies recommender systems with knowledge graphs, which can effectively address the problems of data sparsity and cold start. Recently, a variety of methods have been developed for this problem, which generally try to learn…
Sequential testing problems involve a complex system with several components, each of which is "working" with some independent probability. The outcome of each component can be determined by performing a test, which incurs some cost. The…
Sorting is one of the most used and well investigated algorithmic problem [1]. Traditional postulation supposes the sorting data archived, and the elementary operation as comparisons of two numbers. In a view of appearance of new processors…
Searching for papers from different academic databases is the most commonly used method by research beginners to obtain cross-domain technical solutions. However, it is usually inefficient and sometimes even useless because traditional…
Research shows that expert-like approaches to problem-solving can be promoted by encouraging students to explicate their thought processes and follow a prescribed problem-solving strategy. Since grading communicates instructors'…
Statistics has moved beyond the frequentist-Bayesian controversies of the past. Where does this leave our ability to interpret results? I suggest that a philosophy compatible with statistical practice, labeled here statistical pragmatism,…
The complexity class NP of decision problems that can be solved nondeterministically in polynomial time is of great theoretical and practical importance where the notion of polynomial-time reductions between NP-problems is a key concept for…
In a series of well-known papers, Chi and Slotta (Chi, 1992; Chi & Slotta, 1993; Chi, Slotta & de Leeuw, 1994; Slotta, Chi & Joram, 1995; Chi, 2005; Slotta & Chi, 2006) have contended that a reason for students' difficulties in learning…
Inferring cause-effect relationships from observational data has gained significant attention in recent years, but most methods are limited to scalar random variables. In many important domains, including neuroscience, psychology, social…
Fractional scoring has been proposed to avoid inconsistencies in the attribution of publications to percentile rank classes. Uncertainties and ambiguities in the evaluation of percentile ranks can be demonstrated most easily with small…
Machine learning is more and more applied in critical application areas like health and driver assistance. To minimize the risk of wrong decisions, in such applications it is necessary to consider the certainty of a classification to reject…
Being able to learn from small amounts of data is a key characteristic of human intelligence, but exactly {\em how} small? In this paper, we introduce a novel experimental paradigm that allows us to examine classification in an extremely…
Intuitively, unfamiliarity should lead to lack of confidence. In reality, current algorithms often make highly confident yet wrong predictions when faced with relevant but unfamiliar examples. A classifier we trained to recognize gender is…
In this methodological article on experimental-yet-rigorous enumerative combinatorics, we use two instructive case studies, to show that often, just like Alexander the Great before us, the simple, "cheating" solution to a hard problem is…
We consider the problem of estimating a signal corrupted by independent interference with the assistance of a cost-constrained helper who knows the interference causally or noncausally. When the interference is known causally, we…
The paper focuses on sequential experiments for categorical responses in which whether or not a further observation is made depends on the outcome of a previous experiment. Examples include subsequent medical interventions being performed…