On the Multi-Interval Ulam-R\'enyi Game: for 3 lies 4 intervals suffice

We study the problem of identifying an initially unknown $m$-bit number by using yes-no questions when up to a fixed number $e$ of the answers can be erroneous. In the variant we consider here questions are restricted to be the union of up to a fixed number of intervals. For any $e \geq 1$ let $k_e$ be the minimum $k$ such that for all sufficiently large $m$, there exists a strategy matching the information theoretic lower bound and only using $k$-interval questions. It is known that $k_e = O(e^2)$. However, it has been conjectured that the $k_e = \Theta(e).$ This linearity conjecture is supported by the known results for small values of $e$. For $e\leq2$ we have $k_e = e.$ We extend these results to the case $e=3$. We show $k_3 \leq 4$ improving upon the previously known bound $k_3 \leq 10.$Comment: 31 pages, 5 figures, extension of the result to non-asymptotic strategie

Bubble-Flip---A New Generation Algorithm for Prefix Normal Words

We present a new recursive generation algorithm for prefix normal words. These are binary strings with the property that no substring has more 1s than the prefix of the same length. The new algorithm uses two operations on binary strings, which exploit certain properties of prefix normal words in a smart way. We introduce infinite prefix normal words and show that one of the operations used by the algorithm, if applied repeatedly to extend the string, produces an ultimately periodic infinite word, which is prefix normal. Moreover, based on the original finite word, we can predict both the length and the density of an ultimate period of this infinite word.Comment: 30 pages, 3 figures, accepted in Theoret. Comp. Sc.. This is the journal version of the paper with the same title at LATA 2018 (12th International Conference on Language and Automata Theory and Applications, Tel Aviv, April 9-11, 2018

On Infinite Prefix Normal Words

Prefix normal words are binary words that have no factor with more $1$s than the prefix of the same length. Finite prefix normal words were introduced in [Fici and Lipt\'ak, DLT 2011]. In this paper, we study infinite prefix normal words and explore their relationship to some known classes of infinite binary words. In particular, we establish a connection between prefix normal words and Sturmian words, between prefix normal words and abelian complexity, and between prefix normality and lexicographic order.Comment: 20 pages, 4 figures, accepted at SOFSEM 2019 (45th International Conference on Current Trends in Theory and Practice of Computer Science, Nov\'y Smokovec, Slovakia, January 27-30, 2019

The Anatomy of French Production Hierarchies

We use a comprehensive dataset of French manufacturing firms to study their internal organization. We first divide the employees of each firm into ‘layers’ using occupational categories. Layers are hierarchical in that the typical worker in a higher layer earns more, and the typical firm occupies less of them. In addition, the probability of adding (dropping) a layer is very positively (negatively) correlated with value added. We then explore the changes in the wages and number of employees that accompany expansions in layers, output, or markets (by becoming exporters). The empirical results indicate that reorganization, through changes in layers, is key to understand how firms expand and contract. For example, we find that firms that expand substantially add layers and pay lower average wages in all pre-existing layers. In contrast, firms that expand little and do not reorganize pay higher average wages in all pre-existing layers

Neuroprotection: The Emerging Concept of Restorative Neural Stem Cell Biology for the Treatment of Neurodegenerative Diseases

During the past decades Neural Stem Cells have been considered as an alternative source of cells to replace lost neurons and NSC transplantation has been indicated as a promising treatment for neurodegenerative disorders. Nevertheless, the current understanding of NSC biology suggests that, far from being mere spare parts for cell replacement therapies, NSCs could play a key role in the pharmacology of neuroprotection and become protagonists of innovative treatments for neurodegenerative diseases. Here, we review this new emerging concept of NSC biology