Candida Bowtell, Alice Devillers, André Kündgen
et al.
A Latin hypercuboid of order $n$ is a $d$-dimensional matrix of dimensions $n\times n\times\cdots\times n\times k$, with symbols from a set of cardinality $n$ such that each symbol occurs at most once in each axis-parallel line. If $k=n$ the hypercuboid is a Latin hypercube. The Latin hypercuboid is \emph{completable} if it is contained in a Latin hypercube of the same order and dimension. It is \emph{extendible} if it can have one extra layer added. In this note we consider which Latin hypercuboids are completable/extendible. We also consider a generalisation that involves multidimensional arrays of sets that satisfy certain balance properties. The extendibility problem corresponds to choosing representatives from the sets in a way that is analogous to a choice of a Hall system of distinct representatives, but in higher dimensions. The completability problem corresponds to partitioning the sets into such SDRs. We provide a construction for such an array of sets that does not have the property analogous to completability. A related concept was introduced by Häggkvist under the name $(m,m,m)$-array. We generalise a construction of $(m,m,m)$-arrays credited to Pebody, but show that it cannot be used to build the arrays that we need.
The opening of Marrakech to the world, its dual UNESCO listing, and the development of its tourism have transformed the old medina. Since the late 1980s, it has become a tourist destination marked by urban beautification and aesthetic-architectural improvement. The attraction of foreigners to old houses (dars, riads, and ancient palaces) plays a key role in the spread of tourism, offering an immersion into the socio-spatial universe of historically rich intramural neighborhoods.What are the underlying logics of the spread of tourism in the medina of Marrakech? And how has the appropriation of its houses by foreign residents redefined the relationship with space within its neighborhoods? In this article, we will first study the mechanisms of the spread of tourism and the proliferation of riad-guesthouses (RGHs) within the medina, highlighting their correlation with the way domestic space and ancestral neighborhoods are appropriated by and for visitors. Secondly, we will examine the transformation of the socio-spatial landscape of the medina since the 1990s and the new socio-economic modalities of the relationship with domestic space and old neighborhoods.
A Latin square is an $n$ by $n$ grid filled with $n$ symbols so that each symbol appears exactly once in each row and each column. A transversal in a Latin square is a collection of cells which do not share any row, column, or symbol. This survey will focus on results from the last decade which have continued the long history of the study of transversals in Latin squares.
Yadir Garnica, América Morales, Carlos A. Vaquera-Araujo
We propose a $U(1)_{B-L}$ gauge extension to the SM, in which the dark sector is stabilized through a matter parity symmetry preserved after spontaneous symmetry breaking. The fermion spectrum includes three neutral right-handed fields with $B-L$ charges $(-4,-4, 5)$, that make the model free of gauge anomalies. Two of these neutral fermion fields serve as mediators in a scotogenic mechanism for light-active Majorana neutrino masses. The corresponding neutrino mass matrix has rank 2, predicting a massless state and a lower bound for neutrinoless double beta decay. Regions in the parameter space consistent with dark matter relic abundance are accomplished by the lightest neutral mediator.
Anthony Bonato, Caleb Jones, Trent G. Marbach
et al.
We investigate the lazy burning process for Latin squares by studying their associated hypergraphs. In lazy burning, a set of vertices in a hypergraph is initially burned, and that burning spreads to neighboring vertices over time via a specified propagation rule. The lazy burning number is the minimum number of initially burned vertices that eventually burns all vertices. The hypergraphs associated with Latin squares include the $n$-uniform hypergraph, whose vertices and hyperedges correspond to the entries and lines (that is, sets of rows, columns, or symbols) of the Latin square, respectively, and the $3$-uniform hypergraph, which has vertices corresponding to the lines of the Latin square and hyperedges induced by its entries. Using sequences of vertices that together form a vertex cover, we show that for a Latin square of order $n$, the lazy burning number of its $n$-uniform hypergraph is bounded below by $n^2-3n+3$ and above by $n^2-3n+2 + \lfloor \log_2 n \rfloor.$ These bounds are shown to be tight using cyclic Latin squares and powers of intercalates. For the $3$-uniform hypergraph case, we show that the lazy burning number of Latin squares is one plus its shortest connected chain of subsquares. We determine the lazy burning number of Latin square hypergraphs derived from finitely generated groups. We finish with open problems.
Social conflicts stemming from industrial mining projects in Peru have increasingly been fought in court cases in recent years. This article analyzes the dark side of this judicialization of mining conflicts, a process through which state authorities criminalize participation in social protests and attempt to prevent the mobilization of social movements. This use of the law by public authorities is an example of the so-called shrinking space in which the scope of action of civil society actors is increasingly restricted and constrained worldwide. This article presents an in-depth analysis of a specific court case against a group of mining opponents in the Cajamarca region of Peru. Based on ethnographic field research conducted in Peru, the article discusses three different modalities of the law’s domination, exploring the various ways the law rules those who oppose large-scale extractive projects.
A transversal in an $n \times n$ latin square is a collection of $n$ entries not repeating any row, column, or symbol. Kwan showed that almost every $n \times n$ latin square has $\bigl((1 + o(1)) n / e^2\bigr)^n$ transversals as $n \to \infty$. Using a loose variant of the circle method we sharpen this to $(e^{-1/2} + o(1)) n!^2 / n^n$. Our method works for all latin squares satisfying a certain quasirandomness condition, which includes both random latin squares with high probability as well as multiplication tables of quasirandom groups.
A Latin square has six conjugate Latin squares obtained by uniformly permuting its (row, column, symbol) triples. We say that a Latin square has conjugate symmetry if at least two of its six conjugates are equal. We enumerate Latin squares with conjugate symmetry and classify them according to several common notions of equivalence. We also do similar enumerations under additional hypotheses, such as assuming the Latin square is reduced, diagonal, idempotent or unipotent. Our data corrected an error in earlier literature and suggested several patterns that we then found proofs for, including (1) The number of isomorphism classes of semisymmetric idempotent Latin squares of order $n$ equals the number of isomorphism classes of semisymmetric unipotent Latin squares of order $n+1$, and (2) Suppose $A$ and $B$ are totally symmetric Latin squares of order $n\not\equiv0\bmod3$. If $A$ and $B$ are paratopic then $A$ and $B$ are isomorphic.
Asier Gutiérrez-Fandiño, Jordi Armengol-Estapé, Marc Pàmies
et al.
This work presents MarIA, a family of Spanish language models and associated resources made available to the industry and the research community. Currently, MarIA includes RoBERTa-base, RoBERTa-large, GPT2 and GPT2-large Spanish language models, which can arguably be presented as the largest and most proficient language models in Spanish. The models were pretrained using a massive corpus of 570GB of clean and deduplicated texts with 135 billion words extracted from the Spanish Web Archive crawled by the National Library of Spain between 2009 and 2019. We assessed the performance of the models with nine existing evaluation datasets and with a novel extractive Question Answering dataset created ex novo. Overall, MarIA models outperform the existing Spanish models across a variety of NLU tasks and training settings.
In this article we study, from a historical and sociocultural perspective, a set of suicide cases that occurred in the city of Buenos Aires between 1859 and 1888 to analyze the letters left by those who committed suicide. We understand these writings as communicative actions that had different meanings, and transmitted messages to the members of the deceased's social network. Also, one of our specific objectives is to explore the circumstances, concerns and conflicts that were part of the context in which these texts were produced. In other words, we seek to answer the following question: in which situations did suicide notes appear more frequently? Based on the evidence from the the judicial summaries, in this paper we show that letters appeared more frequently in files that narrated a series of particular events. Likewise, we argue that these plausible explanations of suicidal acts, and the notes associated with them, were stated based on the expectations of men and women from Buenos Aires during the last third of the 19th century.
O presente artigo pretende construir uma leitura crítica do racismo nas relações de trabalho escravo contemporâneo pensado sob a ótica da hierarquização e a superexploração da mão-de-obra negra. A investigação trata-se com base em pesquisa bibliográfica, tendo como aporte teórico os estudos de Costa (2018), Rodrigues (2016), Fanon (1968), Oliva (2007), Harvey (2001), etc.. Temos como objetivo refletir sobre a questão racial no contexto histórico e social da reprodução do trabalho escravo na sociedade atual, bem como, problematizar suas interfaces na produção da desigualdade social, emergida com os “novos” processos de modernização em múltiplas dimensões.
Palavras-chave: Racismo. Hierarquização. Superexploração. Trabalho Escravo Contemporâneo.
The present article intends to build a critical reading of racism in the relations of contemporany slave labor thourght from the perspective of hierarchization of black labor.The investigation is based on bibliographic research, having as theoretical contribution the studies of Costa (2018), Rodrigues (2016), Fanon (1968), Oliva (2007), Harvey (2001), etc.. We ain to reflecton the racial inssue in the historical and social context of the reproduction of slave labor in today's society, as well as to problematize its interfaces in the “new” moderniztion processes in multiple dimensionis.
Keywords: Racism. Hierarchy. Overexploitation. Contemporany Slave Labor.
Le présent article entend construire une lecture critique du racisme dansles relations de travail contemporaines entre esclaves pensé dans la perspective de la hiérarchie et de la surexploitation du travail noir. L'enquête et basée sur la recherche bibliographique, ayant pour contribution thé o rique les études de Costa (2018), Rodrigues (2016), Fanon (1968), Oliva (2007), Harvey (2001), etc.. Nous cherchons à réfléchir sur la question raciale dans le contexte historique et social de la reproduction du travail esclave dans la société d'aujourd'hui, ainsi qu'á problématiser ses interfaces dans la production des inégualités sociales, qui ont émergé avec les nouveaux processus de modernisation dans de multiples dimensionis.
Mosts-clés: Racisme; Hiérarchie. Surexploitation. Travail Esclave Contemporain.
El artículo procura reconstruir las modalidades a través de las cuales algunos de los museos que funcionaban en Buenos Aires durante la primera mitad de la década de 1940 se relacionaban con su público: concretamente se tratará de precisar cuánta gente concurría a los museos de carácter histórico e indagar acerca de los motivos por los cuales lo hacía. El recorte espacio-temporal responde a la necesidad de efectuar un análisis comparativo sobre los modos de funcionamiento de cuatro museos históricos relativamente cercanos, entre los años 1938 y 1946, en momentos en los cuáles la recién instalada Comisión Nacional de Museos y de Monumentos y Lugares Históricos estuvo presidida por el historiador Ricardo Levene.
In this paper, we first present the relation between a transversal in a Latin square with some concepts in its Latin square graph, and give an equivalent condition for a Latin square has an orthogonal mate. The most famous open problem involving Combinatorics is to find maximum number of disjoint transversals in a Latin square. So finding some family of decomposable Latin squares into disjoint transversals is our next aim. In the next section, we give an equivalent statement of a conjecture which has been attributed to Brualdi, Stein and Ryser by the concept of quasi-transversal. Finally, we prove the truth of the Rodney's conjecture for a family of graphs.
Choi Seok-Jeong studied Latin squares at least 60 years earlier than Euler although this was less known. He introduced a pair of orthogonal Latin squares of order 9 in his book. Interestingly, his two orthogonal non-double-diagonal Latin squares produce a magic square of order 9, whose theoretical reason was not studied. There have been a few studies on Choi's Latin squares of order 9. The most recent one is Ko-Wei Lih's construction of Choi's Latin squares of order 9 based on the two $3 \times 3$ orthogonal Latin squares. In this paper, we give a new generalization of Choi's orthogonal Latin squares of order 9 to orthogonal Latin squares of size $n^2$ using the Kronecker product including Lih's construction. We find a geometric description of Choi's orthogonal Latin squares of order 9 using the dihedral group $D_8$. We also give a new way to construct magic squares from two orthogonal non-double-diagonal Latin squares, which explains why Choi's Latin squares produce a magic square of order 9.
Este artículo presenta los alcances de una experiencia docente sobre la enseñanza de la historia y la memroia con estudiantes del grado quinto de básica primaria. En la primera parte, abordo el lugar de la experiencia, la cual movilizó el quehacer docente hacia nuevas búsquedas y diálogos entre saberes, sujetos y realidades. En la segunda parte, se analiza la enseñanza de la historia y la memoria. La primera aún cautiva de su herencia, a partir de la recordación de ciertos hechos y personajes, con recientes transformaciones en su didáctica y legislación escolar; por su parte, la enseñanza de la memoria, de ingreso más reciente en la escuela, asume la temporalidad a través de la palabra, el sentir y la corporeidad del otro, cuyas versiones pueden ser oiciales, polémicas u omitidas. En la última parte, se narra la experiencia docente cuyo eje articulador fue el 9 de abril de 1948 y la toma y retoma al Palacio de Justicia, proponiendo desde la sistematización de experiencias, la memoria de las vivencias, para la construcción de conocimientos compartidos a través de una lectura relexiva y sensible de lo acontecido.
History (General) and history of Europe, Latin America. Spanish America
Founded in Iquitos by the school teacher and writer Francisco Izquierdo Ríos, Trocha was the “monthly press organ of schoolteachers in Bajo Amazonas” between 1941 and 1944. This article postulates that the journal was also a laboratory for the establishment of a group of intellectuals in Peruvian Amazonia aiming to spread Amazonian culture as a means of integrating the national production.
Latin America. Spanish America, French literature - Italian literature - Spanish literature - Portuguese literature