On minimal critical exponent of balanced sequences

We study the threshold between avoidable and unavoidable repetitions in infinite balanced sequences over finite alphabets. The conjecture stated by Rampersad, Shallit and Vandomme says that the minimal critical exponent of balanced sequences over the alphabet of size d≥5 equals [Formula presented]. This conjecture is known to hold for d∈{5,6,7,8,9,10}. We refute this conjecture by showing that the picture is different for bigger alphabets. We prove that critical exponents of balanced sequences over an alphabet of size d≥11 are lower bounded by [Formula presented] and this bound is attained for all even numbers d≥12. According to this result, we conjecture that the least critical exponent of a balanced sequence over d letters is [Formula presented] for all d≥11. © 2022075-02-2021-1387, 075-02-2022-877; České Vysoké Učení Technické v Praze, ČVUT: SGS20/183/OHK4/3T/14; Ministerstvo Školství, Mládeže a Tělovýchovy, MŠMT: CZ.02.1.01/0.0/0.0/16_019/0000778; Ministry of Education and Science of the Russian Federation, MinobrnaukaThe second author was supported by Czech Technical University in Prague , through the project SGS20/183/OHK4/3T/14 . The first and the third authors were supported by The Ministry of Education, Youth and Sports of the Czech Republic through the project CZ.02.1.01/0.0/0.0/16_019/0000778 . The fourth author acknowledges the support by the Ministry of Science and Higher Education of the Russian Federation (Ural Mathematical Center project No. 075-02-2021-1387 ) and by Ural Mathematical Center , project No. 075-02-2022-877

Diagnosis of neuronal ceroid lipofuscinosis type 2 (CLN2 disease): Expert recommendations for early detection and laboratory diagnosis

Neuronal ceroid lipofuscinoses (NCLs) are a heterogeneous group of lysosomal storage disorders. NCLs include the rare autosomal recessive neurodegenerative disorder neuronal ceroid lipofuscinosis type 2 (CLN2) disease, caused by mutations in the tripeptidyl peptidase 1 (TPP1)/CLN2 gene and the resulting TPP1 enzyme deficiency. CLN2 disease most commonly presents with seizures and/or ataxia in the late-infantile period (ages 2-4), often in combination with a history of language delay, followed by progressive childhood dementia, motor and visual deterioration, and early death. Atypical phenotypes are characterized by later onset and, in some instances, longer life expectancies. Early diagnosis is important to optimize clinical care and improve outcomes; however, currently, delays in diagnosis are common due to low disease awareness, nonspecific clinical presentation, and limited access to diagnostic testing in some regions. In May 2015, international experts met to recommend best laboratory practices for early diagnosis of CLN2 disease. When clinical signs suggest an NCL, TPP1 enzyme activity should be among the first tests performed (together with the palmitoyl-protein thioesterase enzyme activity assay to rule out CLN1 disease). However, reaching an initial suspicion of an NCL or CLN2 disease can be challenging; thus, use of an epilepsy gene panel for investigation of unexplained seizures in the late-infantile/childhood ages is encouraged. To confirm clinical suspicion of CLN2 disease, the recommended gold standard for laboratory diagnosis is demonstration of deficient TPP1 enzyme activity (in leukocytes, fibroblasts, or dried blood spots) and the identification of causative mutations in each allele of the TPP1/CLN2 gene. When it is not possible to perform both analyses, either demonstration of a) deficient TPP1 enzyme activity in leukocytes or fibroblasts, or b) detection of two pathogenic mutations in trans is diagnostic for CLN2 disease

Global Analysis of Proline-Rich Tandem Repeat Proteins Reveals Broad Phylogenetic Diversity in Plant Secretomes

Cell walls, constructed by precisely choreographed changes in the plant secretome, play critical roles in plant cell physiology and development. Along with structural polysaccharides, secreted proline-rich Tandem Repeat Proteins (TRPs) are important for cell wall function, yet the evolutionary diversity of these structural TRPs remains virtually unexplored. Using a systems-level computational approach to analyze taxonomically diverse plant sequence data, we identified 31 distinct Pro-rich TRP classes targeted for secretion. This analysis expands upon the known phylogenetic diversity of extensins, the most widely studied class of wall structural proteins, and demonstrates that extensins evolved before plant vascularization. Our results also show that most Pro-rich TRP classes have unexpectedly restricted evolutionary distributions, revealing considerable differences in plant secretome signatures that define unexplored diversity

Ultramafic vegetation and soils in the circumboreal region of the Northern Hemisphere

The paper summarizes literature on climate, soil chemistry, vegetation and metal accumulation by plants found on ultramafic substrata in the circumboreal zone (sensu Takhtajan, Floristic regions of the world, 1986) of the Northern Hemisphere. We present a list of 50 endemic species and 18 ecotypes obligate to ultramafic soils from the circumboreal region of Holarctic, as well as 30 and 2 species of Ni and Zn hyperaccumulators, respectively. The number of both endemics and hyperaccumulators are markedly lower compared to that of the Mediterranean and tropical regions. The diversity of plant communities on ultramafics soils of the circumboral region is also described. The underlying causes for the differences of ultramafic flora between arctic, cold, cool temperate and Mediterranean and tropical regions are also discussed. © 2018, The Ecological Society of Japan

Size-distribution analysis in the study of urban systems: Evidence from Greece

This paper examines empirically the utility of size-distribution analysis in the study of urban systems, on data referring to every urban settlement recorded in 2011 national census of Greece. The study lowers the scale of the size-distribution analysis to the regional, instead of the national level, where is commonly being applied, examining two aspects of size-distributions, the rank-size and the city-size-distribution, in comparison with three well-established statistical dispersion indices, the coefficient of variation, the Theil index and the Gini coefficient. The major research question is to detect how capable are the size-distribution exponents to operate as measures of statistical dispersion and to include socioeconomic information. Overall, the analysis concludes that the size-distribution assessment is useful for the initialisation of the study of urban systems, where the available information is restricted to population size, and is capable to provide structural information of an urban system and its socioeconomic framework, but not more effective than other measures of statistical dispersion. Copyright © 2021 Inderscience Enterprises Ltd

Automatic Streaming Processing of XSLT Transformations Based on Tree Transducers

Streaming processing of XML transformations is practically needed especially when large XML documents or XML data streams are to be transformed. In this paper, the design of an automatic streaming processor for XSLT transformations is presented. Unlike other similar systems, our processor guarantees bounds on the resource usage for the processing of a particular type of transformation. This feature is achieved by employing tree transducers as the underlying formal base. The processor includes a set of streaming algorithms, each of them is associated with a tree transducer with specific resource usage (memory, number of passes), and thus captures different transformation subclass. The input XSLT stylesheet is analyzed in order to identify the transformation subclass to which it belongs. Then the lowest resourceconsuming streaming algorithm capturing this subclass is applied