Factoring Continuous Characters Defined on Subgroups of Products of Topological Groups †

This study is on the factorization properties of continuous homomorphisms defined on subgroups (or submonoids) of products of (para)topological groups (or monoids). A typical result is the following one: Let D=∏i∈IDi be a product of paratopological groups, S be a dense subgroup of D, and χ a continuous character of S. Then one can find a finite set E⊂I and continuous characters χi of Di, for i∈E, such that χ=∏i∈Eχi∘piS, where pi:D→Di is the projection.

Factoring Continuous Characters Defined on Subgroups of Products of Topological Groups

We study factorization properties of continuous homomorphisms defined on subgroups (or submonoids) of products of (para)topological groups (or monoids). A typical result is the following one: Let $D=\prod_{i\in I}D_i$ be a product of paratopological groups, $S$ be a dense subgroup of $D$, and $\chi$ a continuous character of $S$. Then one can find a finite set $E\subset I$ and continuous characters $\chi_i$ of $D_i$, for $i\in E$, such that $\chi=\big(\prod_{i\in E} \chi_i\circ p_i\big)\hs1\res\hs1 S$, where $p_i\colon D\to D_i$ is the projection.

2021 թվականի հոգեբանական աշխատանքների վերլուծությունը մարտական գործողությունների ժամանակ և հետպատերազմյան փուլում տարբեր խմբերում անձնակենտրոն ինտենսիվ ծրագրային հոգեթերապիայի շրջանակներում

The purpose of this article is to present and substantiate the effective approach of "Person-Centered Intensive Program Psychotherapy" used during the war unleashed on September 27, 2020 with the various groups involved in the hostilities. Based on the current objective, the article discussed the following issues: separately present, analyze, summarize the psychological work with wounded servicemen, their families, family members of killed servicemen, family members of missing servicemen, and returnees from captivity, make methodological-practical emphases. The article presents primary conversation algorithms, research questionnaires, methodological apparatus, which were the methodological basis of the work. As a result, it was concluded that by analyzing the four-month work, revealing the patterns from the statistical data, it is possible to give a more effective continuous character to the manners of psychological support in the above-mentioned groups within the Person-centered Intensive Psychotherapy. Proposals related to the performed preliminary psychological assessment, psychodiagnostic, psychotherapeutic work were submitted to the interested bodies in order to organize effective intensive work.

A Vision-Based Framework for Spotting and Segmentation of Gesture-Based Assamese Characters Written in the Air

The task of automatic gesture spotting and segmentation is challenging for determining the meaningful gesture patterns from continuous gesture-based character sequences. This paper proposes a vision-based automatic method that handles hand gesture spotting and segmentation of gestural characters embedded in a continuous character stream simultaneously, by employing a hybrid geometrical and statistical feature set. This framework shall form an important constituent of gesture-based character recognition (GBCR) systems, which has gained tremendous demand lately as assistive aids for overcoming the restraints faced by people with physical impairments. The performance of the proposed system is validated by taking into account the vowels and numerals of Assamese vocabulary. Another attribute to this proposed system is the implementation of an effective hand segmentation module, which enables it to tackle complex background settings.

The first dinosaur egg remains a mystery

A recent study by Norell et al. (2020) described new egg specimens for two dinosaur species, identified as the first soft-shelled dinosaur eggs. The authors used phylogenetic comparative methods to reconstruct eggshell type in a sample of reptiles, and identified the eggs of dinosaurs and archosaurs as ancestrally soft-shelled, with three independent acquisitions of a hard eggshell among dinosaurs. This result contradicts previous hypotheses of hard-shelled eggs as ancestral to archosaurs and dinosaurs. Here we estimate the ancestral condition for dinosaur and archosaur eggs by reanalyzing the original data from Norell et al. and that from a recent study on reptile eggshells (Legendre et al., 2020) with the addition of these new dinosaur specimens. We show that the recovery of dinosaur eggs as ancestrally soft-shelled is conditioned by the discretization of a continuous character (eggshell thickness), the exclusion of turtle outgroups from the original sample, and a lack of branch length information. When using a larger sample, calibrated trees, and a definition of hard-shelled eggs referencing their unique prismatic structure, we recover dinosaur and archosaur eggs as either hard-shelled or uncertain (i.e. equal probability for hard- and soft-shelled). This remaining ambiguity is due to uncertainty in the assessment of eggshell type in two dinosaur species, i.e. ∼1% of the total sample. We conclude that more reptile egg specimens and a strict comparative framework are necessary to decipher the evolution of dinosaur eggs in a phylogenetic context.

ECOLOGICAL AND GEOGRAPHICAL FEATURES OF VEGETABLE INVASIONS IN THE CONDITIONS OF THE ENTRAL RUSSIAN FOREST-STEPPE

This study discusses the ecological and geographical features of plant invasions in the Central Russian forest-steppe. The studies have been conducted since 2002. The obtained data are summarized in the context of the ecological-geographical (biogeographic) approach. The main trends of phytoinvasions in the region are identified. The invasive component of the flora is characterized by high diversity of North American elements (31 species, 40.8 %), moreover, many species formed secondary European-North American (13 species, 17.1 %), Holarctic (11 species, 14.5 %) and cosmopolitan (8 species, 10.5 %) habitats. The Asteraceae family is characterized by high variety of species (19 species (25.0 %). Groups of invasive species are almost equal by the type of drift. Thirty-two species (42.1 %) are ergasiophytes (plants deliberately introduced to a region), 36 species (47.4 %) are xenophytes (random “aliens”) and 8 species (10.5 %) have mixed type of drift (xen / ergasiophytes, ergasio/xenophytes). The invasive component of the flora of the Central Russian forest-steppe is characterized as mesophytic, forest-steppe, Eurasian-North American with a predominance of monocarpic biomorphs. The research proves high saturation of communities of broad-leaved (20 / 26.3 %), mixed (25 / 33.0 %) and pine (23 / 30.3 %) forests, meadow steppes (20 / 26.3 %), floodplain meadows (19 / 25.0 %) and coastal habitats (19 / 25.0 %) with invasive species. The analysis of the occurrence of 49 invasive species in the communities of the Central Russian forest-steppe determines the confinement of 27 species to the edge-meadow-steppe and 22 species to the edge-forest habitats. The zonal type of secondary area is characteristic for 11 species of xenophytes. Longitude (from West to East) settlement trends are recorded for 5 species. It is substantiated that the geography of the secondary range has a continuous character for 18 invasive plant species within the region. More than 20 invasive species show a tendency to uniform distribution throughout the study area.

A Bayesian Approach for Inferring the Impact of a Discrete Character on Rates of Continuous-Character Evolution in the Presence of Background-Rate Variation

Understanding how and why rates of character evolution vary across the Tree of Life is central to many evolutionary questions; for example, does the trophic apparatus (a set of continuous characters) evolve at a higher rate in fish lineages that dwell in reef versus nonreef habitats (a discrete character)? Existing approaches for inferring the relationship between a discrete character and rates of continuous-character evolution rely on comparing a null model (in which rates of continuous-character evolution are constant across lineages) to an alternative model (in which rates of continuous-character evolution depend on the state of the discrete character under consideration). However, these approaches are susceptible to a “straw-man” effect: the influence of the discrete character is inflated because the null model is extremely unrealistic. Here, we describe MuSSCRat, a Bayesian approach for inferring the impact of a discrete trait on rates of continuous-character evolution in the presence of alternative sources of rate variation (“background-rate variation”). We demonstrate by simulation that our method is able to reliably infer the degree of state-dependent rate variation, and show that ignoring background-rate variation leads to biased inferences regarding the degree of state-dependent rate variation in grunts (the fish group Haemulidae). [Bayesian phylogenetic comparative methods; continuous-character evolution; data augmentation; discrete-character evolution.]

Adapting Mussar to Develop Management Students’ Character

Management educators have been advised to cultivate their students’ character. Yet they lack the instructional resources they need to do so. We were inspired by the principles and techniques of the Jewish spiritual practice of Mussar to put students on a personalized path of continuous character improvement. According to Mussar, everyone has some measure of a given character trait and needs to calibrate it to fill in a deficiency or tone down an excess. Although correcting character deficiencies and excesses requires a commitment of effort, we can, and should, become better versions of ourselves by applying that effort—that is, engaging in reflection, setting goals, monitoring our progress, and making adjustments—to move each of our character traits ever closer to its respective virtuous mean. We have designed materials to increase students’ awareness of character and its importance in organizations, give them a vocabulary of character traits, help them identify the character traits they would like to address, and provide them with a sustainable process for self-enhancement. In this article, we introduce these materials and provide evidence of their effectiveness.

A Bayesian Approach for Inferring the Impact of a Discrete Character on Rates of Continuous-Character Evolution in the Presence of Background-Rate Variation

Understanding how and why rates of character evolution vary across the Tree of Life is central to many evolutionary questions; e.g., does the trophic apparatus (a set of continuous characters) evolve at a higher rate in fish lineages that dwell in reef versus non-reef habitats (a discrete character)? Existing approaches for inferring the relationship between a discrete character and rates of continuous-character evolution rely on comparing a null model (in which rates of continuous-character evolution are constant across lineages) to an alternative model (in which rates of continuous-character evolution depend on the state of the discrete character under consideration). However, these approaches are susceptible to a “straw-man” effect: the influence of the discrete character is inflated because the null model is extremely unrealistic. Here, we describe MuSSCRat, a Bayesian approach for inferring the impact of a discrete trait on rates of continuous-character evolution in the presence of alternative sources of rate variation (“background-rate variation”). We demonstrate by simulation that our method is able to reliably infer the degree of state-dependent rate variation, and show that ignoring background-rate variation leads to biased inferences regarding the degree of state-dependent rate variation in grunts (the fish group Haemulidae). [continuous-character evolution; discrete-character evolution; Bayesian phylogenetic comparative methods; data augmentation]

Transformation of Quotient Values for their use as Continuous Cladistic Characters

Recent advances in cladistic technology have produced novel methods for introducing morphological data into cladistic analyses, such as the landmark and continuous character functions in the software TNT and RevBayes. While these new methods begin to address the problem of representing morphology, there has been little consideration of how to transform and code the operational taxonomic units’ (OTUs) dimensions into the datamatrix. Indeed, angles, serial counts, percentages and quotient values can be used as continuous characters, but little has been said about how coding these data affect the trees discovered. Logically, counts of elements and angles measured off specimens may be coded directly into continuous character matrices but percentages and quotient values are more problematic, being transformed data. Quotient values and percentages are the simplest way of representing proportional differences between two dimensions and reducing the effect of inter-taxonomic magnitude differences. However, both are demonstrated to be problematic transformations that produce continuous characters with weighted states that are non-representative of morphological variation. Thus, two OTUs may be represented as less/more similar morphologically than other OTUs that display the same degree of morphological variation. Furthermore, the researcher’s choice of which dimension is the divisor and dividend will have a similar affect. To address this problem, a trigonometric solution and a logarithmic solution have been proposed. Another solution called linear transposition scaling (LTS) was recently presented, with the intention of best representing and coding observable morphological variation. All three methods are reviewed to establish the best way to represent and code morphology in a cladistic analysis using continuous characters.