Search

The goal of this paper is to construct a Frobenius splitting on $G/U$ via the Poisson geometry of $(G/U,\pi _{{{\scriptscriptstyle G}}/{{\scriptscriptstyle U}}})$, where $G$ is a simply connected semi-simple algebraic group defined over an algebraically closed field of characteristic $p> 3$, $U$ is the uniradical of a Borel subgroup of $G$, and $\pi _{{{\scriptscriptstyle G}}/{{\scriptscriptstyle U}}}$ is the standard Poisson structure on $G/U$. We first study the Poisson geometry of $(G/U,\pi _{{{\scriptscriptstyle G}}/{{\scriptscriptstyle U}}})$. Then we develop a general theory for Frobenius splittings on $\mathbb{T}$-Poisson varieties, where $\mathbb{T}$ is an algebraic torus. In particular, we prove that compatibly split subvarieties of Frobenius splittings constructed in this way must be $\mathbb{T}$-Poisson subvarieties. Lastly, we apply our general theory to construct a Frobenius splitting on $G/U$.

Let G be a connected and simply connected complex semisimple Lie group. For a collection of homogeneous G-spaces G/Q, we construct a finite atlas $${{\mathcal {A}}}_{{\scriptscriptstyle BS}}(G/Q)$$ on G/Q, called the Bott–Samelson atlas, and we prove that all of its coordinate functions are positive with respect to the Lusztig positive structure on G/Q. We also show that the standard Poisson structure $$\pi _{{\scriptscriptstyle G}/{\scriptscriptstyle Q}}$$ on G/Q is presented, in each of the coordinate charts of $${{\mathcal {A}}}_{{\scriptscriptstyle BS}}(G/Q)$$ , as a symmetric Poisson CGL extension (or a certain localization thereof) in the sense of Goodearl–Yakimov, making $$(G/Q, \pi _{{\scriptscriptstyle G}/{\scriptscriptstyle Q}}, {{\mathcal {A}}}_{{\scriptscriptstyle BS}}(G/Q))$$ into a Poisson–Ore variety. In addition, all coordinate functions in the Bott–Samelson atlas are shown to have complete Hamiltonian flows with respect to the Poisson structure $$\pi _{{\scriptscriptstyle G}/{\scriptscriptstyle Q}}$$ . Examples of G/Q include G itself, G/T, G/B, and G/N, where $$T \subset G$$ is a maximal torus, $$B \subset G$$ a Borel subgroup, and N the uniradical of B.

We present a novel, logic-based solution to the challenge of reconciling the meanings of taxonomic names across multiple biological taxonomies. The challenge arises due to limitations inherent in using type-anchored taxonomic names as identifiers of granular semantic similarities and differences being expressed in original and revised taxonomic classifications. We address this challenge through: (1) the use of taxonomic concept labels - thereby individuating name usages according to particular sources and allowing each taxonomy to be recognized separately; (2) sets of user-provided Region Connection Calculus articulations among concepts (RCC-5: congruence, proper inclusion, inverse proper inclusion, overlap, exclusion); and (3) the use of an Answer Set Programming-based reasoning toolkit that ingests these constraints to infer and visualize consistent multi-taxonomy alignments. The feasibility of this approach is demonstrated with a use case involving pairwise alignments of 11 non-congruent classifications of Eastern United States grass entities variously assigned to the Andropogon glomeratus- virginicus 'complex' over an interval of 126 years. Analyses of name:meaning identity reveal that, on average, taxonomic names are reliable identifiers of taxonomic non-/congruence for approximately 60% of the 127 merge regions obtained in 12 pairwise alignments. The name:meaning cardinality over the entire time interval ranges from 1:6 to 4:1, with only 1:36 names attaining the semantically ideal 1:1 ratio. We discuss the applicability of the RCC-5 alignment approach in the context of achieving logic-based integration of non-/congruent taxonomic concept hierarchies in dynamic biodiversity data environments.

Classifications and phylogenies of perceived natural entities change in the light of new evidence. Taxonomic changes, translated into Code-compliant names, frequently lead to name:meaning dissociations across succeeding treatments. Classification standards such as the Mammal Species of the World (MSW) may experience significant levels of taxonomic change from one edition to the next, with potential costs to long-term, large-scale information integration. This circumstance challenges the biodiversity and phylogenetic data communities to express taxonomic congruence and incongruence in ways that both humans and machines can process, that is, to logically represent taxonomic alignments across multiple classifications. We demonstrate that such alignments are feasible for two classifications of primates corresponding to the second and third MSW editions. Our approach has three main components: (i) use of taxonomic concept labels, that is name sec. author (where sec. means according to), to assemble each concept hierarchy separately via parent/child relationships; (ii) articulation of select concepts across the two hierarchies with user-provided Region Connection Calculus (RCC-5) relationships; and (iii) the use of an Answer Set Programming toolkit to infer and visualize logically consistent alignments of these input constraints. Our use case entails the Primates sec. Groves (1993; MSW2-317 taxonomic concepts; 233 at the species level) and Primates sec. Groves (2005; MSW3-483 taxonomic concepts; 376 at the species level). Using 402 RCC-5 input articulations, the reasoning process yields a single, consistent alignment and 153,111 Maximally Informative Relations that constitute a comprehensive meaning resolution map for every concept pair in the Primates sec. MSW2/MSW3. The complete alignment, and various partitions thereof, facilitate quantitative analyses of name:meaning dissociation, revealing that nearly one in three taxonomic names are not reliable across treatments-in the sense of the same name identifying congruent taxonomic meanings. The RCC-5 alignment approach is potentially widely applicable in systematics and can achieve scalable, precise resolution of semantically evolving name usages in synthetic, next-generation biodiversity, and phylogeny data platforms.

Phylogenomic research is accelerating the publication of landmark studies that aim to resolve deep divergences of major organismal groups. Meanwhile, systems for identifying and integrating the products of phylogenomic inference–such as newly supported clade concepts–have not kept pace. However, the ability to verbalize node concept congruence and conflict across multiple, in effect simultaneously endorsed phylogenomic hypotheses, is a prerequisite for building synthetic data environments for biological systematics and other domains impacted by these conflicting inferences. Here we develop a novel solution to the conflict verbalization challenge, based on a logic representation and reasoning approach that utilizes the language of Region Connection Calculus (RCC–5) to produce consistent alignments of node concepts endorsed by incongruent phylogenomic studies. The approach employs clade concept labels to individuate concepts used by each source, even if these carry identical names. Indirect RCC–5 modeling of intensional (property-based) node concept definitions, facilitated by the local relaxation of coverage constraints, allows parent concepts to attain congruence in spite of their differentially sampled children. To demonstrate the feasibility of this approach, we align two recent phylogenomic reconstructions of higher-level avian groups that entail strong conflict in the "neoavian explosion" region. According to our representations, this conflict is constituted by 26 instances of input "whole concept" overlap. These instances are further resolvable in the output labeling schemes and visualizations as "split concepts", which provide the labels and relations needed to build truly synthetic phylogenomic data environments. Because the RCC–5 alignments fundamentally reflect the trained, logic-enabled judgments of systematic experts, future designs for such environments need to promote a culture where experts routinely assess the intensionalities of node concepts published by our peers–even and especially when we are not in agreement with each other., Author summary Synthetic platforms for phylogenomic knowledge tend to manage conflict between different evolutionary reconstructions in the following way: "If we do not agree, then it is either our view over yours, or we just collapse all conflicting node concepts into polytomies". We argue that this is not an equitable way to realize synthesis in this domain. For instance, it would not be an adequate solution for building a unified data environment where authors can endorse and yet also reconcile their diverging perspectives, side by side. Hence, we develop a novel system for verbalizing–i.e., consistently identifying and aligning–incongruent node concepts that reflects a more forward-looking attitude: "We may not agree with you, but nevertheless we understand your phylogenomic inference well enough to express our disagreements in a logic-compatible syntax. We can therefore maximize the translatability of data linked to our diverging phylogenomic hypotheses". We show that achieving phylogenomic synthesis fundamentally depends on the application of trained expert judgment to assert parent node congruence in spite of incongruently sampled children.

The efficiency of post-quake emergency management depends heavily on the speed of seismic damage assessment software, which depends on the evaluation algorithm essentially. Traditional seismic damage assessment models based on sequence algorithms usually need tens of minutes to get visualized results. More efficient computing models for seismic damage assessment are demanded urgently. General parallel evaluation algorithm based on GPU computing framework was investigated by the authors, and an improved seismic damage assessment model for buildings was proposed in this paper. We designed a three-level parallel scheme to accelerate the computing and visualization. At the top level, the earthquake area is divided into smaller regions, such as cities or counties. At the middle level, fundamental geographic data for each region is split into layers by features. At the bottom level, buildings are grouped into several types, which can be processed by GPU cores simultaneously. The developed model can estimate and analyze the seismic damage of buildings and the spatial distribution of victims in earthquake region more rapidly than traditional models.

Derivations and proofs are a form of provenance in automated deduction that can assist users in understanding how reasoners derive logical consequences from premises. However, system-generated proofs are often overly complex or detailed, and making sense of them is non-trivial. Conversely, without any form of provenance, it is just as hard to know why a certain fact was derived.

We study model-based diagnosis and propose a new approach of hybrid diagnosis combining black-box and white-box reasoning. We implemented and compared different diagnosis approaches including the standard hitting set algorithm and new approaches using answer set programming engines (DLV, Potassco) in the application of Euler/X toolkit, a logic-based toolkit for alignment of multiple biological taxonomies. Our benchmarks show that the new hybrid diagnosis approach runs about twice fast as the black-box diagnosis approach of the hitting set algorithm.