## Combinatoric, mimetic and non mimetic aspects of creativity

Published in Proceedings of the National Academy of Sciences of the United States of America

In problems such as variable selection and graph estimation, models are characterized by Boolean logical structure such as the presence or absence of a variable or an edge. Consequently, false-positive error or false-negative error can be specified as the number of variables/edges that are incorrectly included or excluded in an estimated model. How...

We consider the model of random planar maps of size $n$ biased by a weight $u>0$ per $2$-connected block, and the closely related model of random planar quadrangulations of size $n$ biased by a weight $u>0$ per simple component. We exhibit a phase transition at the critical value $u_C=9/5$. If $u u_C$, the largest block is of size $\Theta(\log(n))...

A set C of vertices in a graph G = (V, E) is an identifying code if it is dominating and any two vertices of V are dominated by distinct sets of codewords. This paper presents a survey of Iiro Honkala's contributions to the study of identifying codes with respect to several aspects: complexity of computing an identifying code, combinatorics in bina...

In this paper, we propose to enumerate all different configurations belonging to a specific class of fractals: A binary initial tile is selected and a finite recursive tiling process is engaged to produce auto-similar binary patterns. For each initial tile choice the number of possible configurations is finite. This combinatorial problem recalls th...

Let N be a positive integer. For any positive integer L ≤ N and any positive divisor r of N, we enumerate the equivalence classes of dessins d’enfants with N edges, L faces and two vertices whose representatives have automorphism groups of order r. Further, for any non-negative integer h, we enumerate the equivalence classes of dessins with N edges...

Understanding the behavior of a black-box model with probabilistic inputs can be based on the decomposition of a parameter of interest (e.g., its variance) into contributions attributed to each coalition of inputs (i.e., subsets of inputs). In this paper, we produce conditions for obtaining unambiguous and interpretable decompositions of very gener...

This work aims at developing an intuitive and accessible introduction to the interesting and important area of combinatorics, focusing on permutations and combinations with and without repetition. In particular, we consider the problem of determining the number of these types of arrangements. After presenting related basic concepts including sets, ...

Blockchain applications continue to grow in popularity, but their energy costs are clearly becoming unsustainable. In most cases, the primary cost comes from the amount of energy required for proof-ofwork (PoW). Here we study the application of blockchains to the IoT, where most devices are underpowered and would not support the energy cost of proo...

Zaporedje lahko predstavimo z rodovno funkcijo, ki nam o zaporedju pove marsikaj. To nam še posebej pride prav, kadar nimamo enostavne eksplicitne formule zaporedja. Iz nekaterih lastnosti rodovne funkcije se da izpeljati asimptotske lastnosti koeficientov njenega zaporedja, kar lahko nato uporabimo za aproksimacijo koeficientov. V diplomski nalogi...