A new heap game

Given $k\ge 3$ heaps of tokens. The moves of the 2-player game introduced here are to either take a positive number of tokens from at most $k-1$ heaps, or to remove the {\sl same} positive number of tokens from all the $k$ heaps. We analyse this extension of Wythoff's game and provide a polynomial-time strategy for it.Comment: To appear in Computer Games 199

Game saturation of intersecting families

We consider the following combinatorial game: two players, Fast and Slow, claim $k$-element subsets of $[n]=\{1,2,...,n\}$ alternately, one at each turn, such that both players are allowed to pick sets that intersect all previously claimed subsets. The game ends when there does not exist any unclaimed $k$-subset that meets all already claimed sets. The score of the game is the number of sets claimed by the two players, the aim of Fast is to keep the score as low as possible, while the aim of Slow is to postpone the game's end as long as possible. The game saturation number is the score of the game when both players play according to an optimal strategy. To be precise we have to distinguish two cases depending on which player takes the first move. Let $gsat_F(\mathbb{I}_{n,k})$ and $gsat_S(\mathbb{I}_{n,k})$ denote the score of the saturation game when both players play according to an optimal strategy and the game starts with Fast's or Slow's move, respectively. We prove that $\Omega_k(n^{k/3-5}) \le gsat_F(\mathbb{I}_{n,k}),gsat_S(\mathbb{I}_{n,k}) \le O_k(n^{k-\sqrt{k}/2})$ holds

Fast Algorithm for Partial Covers in Words

A factor $u$ of a word $w$ is a cover of $w$ if every position in $w$ lies within some occurrence of $u$ in $w$. A word $w$ covered by $u$ thus generalizes the idea of a repetition, that is, a word composed of exact concatenations of $u$. In this article we introduce a new notion of $\alpha$-partial cover, which can be viewed as a relaxed variant of cover, that is, a factor covering at least $\alpha$ positions in $w$. We develop a data structure of $O(n)$ size (where $n=|w|$) that can be constructed in $O(n\log n)$ time which we apply to compute all shortest $\alpha$-partial covers for a given $\alpha$. We also employ it for an $O(n\log n)$-time algorithm computing a shortest $\alpha$-partial cover for each $\alpha=1,2,\ldots,n$

Palindromic complexity of trees

We consider finite trees with edges labeled by letters on a finite alphabet $\varSigma$. Each pair of nodes defines a unique labeled path whose trace is a word of the free monoid $\varSigma^*$. The set of all such words defines the language of the tree. In this paper, we investigate the palindromic complexity of trees and provide hints for an upper bound on the number of distinct palindromes in the language of a tree.Comment: Submitted to the conference DLT201

Predicting synthetic rescues in metabolic networks

An important goal of medical research is to develop methods to recover the loss of cellular function due to mutations and other defects. Many approaches based on gene therapy aim to repair the defective gene or to insert genes with compensatory function. Here, we propose an alternative, network-based strategy that aims to restore biological function by forcing the cell to either bypass the functions affected by the defective gene, or to compensate for the lost function. Focusing on the metabolism of single-cell organisms, we computationally study mutants that lack an essential enzyme, and thus are unable to grow or have a significantly reduced growth rate. We show that several of these mutants can be turned into viable organisms through additional gene deletions that restore their growth rate. In a rather counterintuitive fashion, this is achieved via additional damage to the metabolic network. Using flux balance-based approaches, we identify a number of synthetically viable gene pairs, in which the removal of one enzyme-encoding gene results in a nonviable phenotype, while the deletion of a second enzyme-encoding gene rescues the organism. The systematic network-based identification of compensatory rescue effects may open new avenues for genetic interventions.Comment: Supplementary Information is available at the Molecular Systems Biology website: http://www.nature.com/msb/journal/v4/n1/full/msb20081.htm

La Germania alla prova del coronavirus tra Stato di diritto e misure emergenziali

Il lavoro analizza le strategie adottate in Germania per contrastare la pandemia COVID-19. L\u2019analisi si articola su due filoni: da un lato si approfondiscono le misure per il contenimento della diffusione dei contagi, dall\u2019altro quelle volte ad arginare le ricadute economiche della pandemia. L\u2019emergenza ha rappresentato anche per la Germania un vero e proprio stress test, mettendo a dura prova sia il riparto federale delle competenze, sia le istituzioni democratiche e la salvaguardia dei diritti fondamentali come elemento qualificante dello Stato di diritto

Psychological, social and biological correlates of body perception disturbance in complex regional pain syndrome

Body Perception Disturbance (BPD) in Complex Regional Pain Syndrome (CRPS) still represents a poorly understood phenomenon. Research has shown that knowledge about changes in body perception can yield relevant information for understanding and treating the disease. This study addressed possible connections between BPD and psychological and social factors, pain intensity, and disease duration. Sixty patients with chronic CRPS Type I of the hand were recruited. Body Perception Disturbance was assessed using the Galer and Jensen Neurobehavioral Questionnaire (GJ) and the BATH CRPS Body Perception Disturbance Scale (BATH). Depression, anxiety, stress, childhood trauma and other life events were assessed using standardized and validated questionnaires. This study found that BPD in CRPS was significantly correlated with measures of depression, anxiety, current stress, quality of life, and pain intensity, but not with stress experienced in the twelve months preceding onset of illness, childhood trauma, or duration of illness. Future research needs to identify which patients are most likely to develop these psychological conditions of CRPS, so that early, preventive intervention is possible. This study establishes a relationship between depression, anxiety, current stress, quality of life, pain intensity, and BPD severity. It also supports literature suggesting that preexisting stress, childhood trauma, and disease duration have no influence on BPD. The findings suggest that there is a bidirectional influence between brain alterations, psychological symptoms, and illness severity