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This paper investigates the problem of correcting multiple criss-cross insertions and deletions in arrays. More precisely, we study the unique recovery of $n \times n$ arrays affected by ${t}$ -criss-cross deletions defined as any combination of ${t_{\mathrm {r}}}$ row and ${t_{\mathrm {c}}}$ column deletions such that ${t_{\mathrm {r}}}+ {t_{\mathrm {c}}}= {t}$ for a given $t$. We show an equivalence between correcting ${t}$ -criss-cross deletions and ${t}$ -criss-cross insertions and show that a code correcting ${t}$ -criss-cross insertions/deletions has redundancy at least ${t} n + {t}\log n - \log ({t}!)$. Then, we present an existential construction of a ${t}$ -criss-cross insertion/deletion correcting code with redundancy bounded from above by ${t} n + \mathcal {O}({t}^{2} \log ^{2} n)$. The main ingredients of the presented code construction are systematic binary ${t}$ -deletion correcting codes and Gabidulin codes. The first ingredient helps locating the indices of the inserted/deleted rows and columns, thus transforming the insertion/deletion-correction problem into a row/column erasure-correction problem which is then solved using the second ingredient. [ABSTRACT FROM AUTHOR]

Already in the 1960s, Levenshtein and others studied error-correcting codes that protect against synchronization errors, such as symbol insertions and deletions. However, despite significant efforts, progress on designing such codes has been lagging until recently, particularly compared to the detailed understanding of error-correcting codes for symbol substitution or erasure errors. This paper surveys the recent progress in designing efficient error-correcting codes over finite alphabets that can correct a constant fraction of worst-case insertions and deletions. Most state-of-the-art results for such codes rely on synchronization strings, simple yet powerful pseudo-random objects that have proven to be very effective solutions for coping with synchronization errors in various settings. This survey also includes an overview of what is known about synchronization strings and discusses communication settings related to error-correcting codes in which synchronization strings have been applied. [ABSTRACT FROM AUTHOR]

The number of immigrants moving to and settling in Europe has increased over the past decade, making migration one of the most topical and pressing issues in European politics. It is without a doubt that immigration has multiple impacts, in terms of economy, society and culture, on the European Union. It is fundamental to policy-makers to correctly evaluate people's attitudes towards immigration when designing integration policies. Of critical interest is to properly discriminate between subjects who are favourable towards immigration from those who are against it. Public opinions on migration are typically coded as binary responses in surveys. However, traditional methods, such as the standard logistic regression, may suffer from computational issues and are often not able to accurately model survey information. In this paper we propose an efficient Bayesian approach for modelling binary response data based on the generalized logistic regression. We show how the proposed approach provides an increased flexibility compared to traditional methods, due to its ability to capture heavy and light tails. The power of our methodology is tested through simulation studies and is illustrated using European Social Survey data on immigration collected in different European countries in 2016–2017. [ABSTRACT FROM AUTHOR]