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In this paper, we study finite dimensional Lie algebras with respect to the length of their chief series. We examine separately the semisimple, solvable, and mixed cases over fields of characteristic zero, and we establish several structural results describing Lie algebras of prescribed chief length. In the solvable and mixed settings, the problem is reduced to the study of irreducible modules arising from suitable quotient actions. In positive characteristic, we investigate semisimple Lie algebras by means of Block s structural theorem and obtain several results concerning Lie algebras of chief length two.

Clustering a group of vertices in networks facilitates applications across different domains, such as social computing and Internet of Things. However, challenges arises for clustering networks with increased scale. This paper proposes a solution which consists of two motif clustering techniques: standard acceleration CHIEF-ST and approximate acceleration CHIEF-AP. Both algorithms first find the maximal k-edge-connected subgraphs within the target networks to lower the network scale, then employ higher-order motifs in clustering. In the first procedure, we propose to lower the network scale by optimizing the network structure with maximal k-edge-connected subgraphs. For CHIEF-ST, we illustrate that all target motifs will be kept after this procedure when the minimum node degree of the target motif is equal or greater than k. For CHIEF-AP, we prove that the eigenvalues of the adjacency matrix and the Laplacian matrix are relatively stable after this step. That is, CHIEF-ST has no influence on motif clustering, whereas CHIEF-AP introduces limited yet acceptable impact. In the second procedure, we employ higher-order motifs, i.e., heterogeneous four-node motifs clustering in higher-or

The Chief Complaint (CC) is a crucial component of a patient's medical record as it describes the main reason or concern for seeking medical care. It provides critical information for healthcare providers to make informed decisions about patient care. However, documenting CCs can be time-consuming for healthcare providers, especially in busy emergency departments. To address this issue, an autocompletion tool that suggests accurate and well-formatted phrases or sentences for clinical notes can be a valuable resource for triage nurses. In this study, we utilized text generation techniques to develop machine learning models using CC data. In our proposed work, we train a Long Short-Term Memory (LSTM) model and fine-tune three different variants of Biomedical Generative Pretrained Transformers (BioGPT), namely microsoft/biogpt, microsoft/BioGPT-Large, and microsoft/BioGPT-Large-PubMedQA. Additionally, we tune a prompt by incorporating exemplar CC sentences, utilizing the OpenAI API of GPT-4. We evaluate the models' performance based on the perplexity score, modified BERTScore, and cosine similarity score. The results show that BioGPT-Large exhibits superior performance compared to the

The integration of Artificial Intelligence (AI) into corporate strategy has become critical for organizations seeking to maintain competitive advantage in the digital age. Although organizations increasingly rely on AI as a strategic and organizational resource, existing C-suite roles remain only partially equipped to govern, integrate, and leverage it coherently at the enterprise level. Organizations vary in their responses. Some create a dedicated Chief AI Officer (CAIO), others extend existing mandates into hybrid roles, and still others coordinate AI through federated structures. This paper develops a role-design theory to explain this variation. I identify three properties that distinguish AI from earlier cross-cutting enterprise technologies - distributed accountability for judgment, upstream governance, and non-stationarity - and three configurations through which organizations respond: concentrated extension, distributed extension, and role creation. The CAIO Framework links these properties to the executive design problems they generate and to the functions and capabilities required of the dedicated role. Four propositions specify when a dedicated CAIO emerges, what form a

In 'The essentially chief series of a compactly generated locally compact group', an analogue of chief series for finite groups is discovered for compactly generated locally compact groups. In the present article, we show that chief factors necessarily exist in all locally compact groups with sufficiently rich topological structure. We also show that chief factors have one of seven types, and for all but one of these types, there is a decomposition into discrete groups, compact groups, and topologically simple groups. Our results for chief factors require exploring the theory developed in 'Chief factors in Polish groups' in the setting of locally compact groups. In this context, we obtain tighter restrictions on the factorization of normal compressions and the structure of quasi-products. Consequently, both (non-)amenability and elementary decomposition rank are preserved by normal compressions.

For a group $G$, a subgroup $U \leq G$ and a group $\mathrm{Inn}(G) \leq A \leq \mathrm{Aut}(G)$, we say that $U$ is an $A$-covering group of $G$ if $G = \bigcup_{a\in A}U^a$. A theorem of Jordan (1872) implies that if $G$ is a finite group, $A = \mathrm{Inn}(G)$ and $U$ is an $A$-covering group of $G$, then $U = G$. Motivated by a question concerning Kronecker classes of field extensions, Neumann and Praeger (1988) conjectured that, more generally, there is an integer function $f$ such that if $G$ is a finite group and $U$ is an $A$-covering subgroup of $G$, then $|G:U| \leq f(|A:\mathrm{Inn}(G)|)$. A key piece of evidence for this conjecture is a theorem of Praeger (1994), which asserts that there is a two-variable integer function $g$ such that if $G$ is a finite group and $U$ is an $A$-covering subgroup of $G$, then $|G:U|\leq g(|A:\mathrm{Inn}(G)|,c)$ where $c$ is the number of $A$-chief factors of~$G$. Unfortunately, the proof of this result contains an error. In this paper, using a different argument, we give a correct proof of this theorem.

This paper is a continued investigation of the structure of Lie algebras in relation to their chief factors, using concepts that are analogous to corresponding ones in group theory. The first section investigates the structure of Lie algebras with a core-free maximal subalgebra. The results obtained are then used in section two to consider the relationship of two chief factors of L being L-connected, a weaker equivalence relation on the set of chief factors than that of being isomorphic as L-modules. A strengthened form of the Jordan-Holder Theorem in which Frattini chief factors correspond is also established for every Lie algebra. The final section introduces the concept of a crown, a notion introduced in group theory by Gaschutz, and shows that it gives much information about the chief factors

The number of Frattini chief factors or of chief factors which are complemented by a maximal subalgebra of a finite-dimensional Lie algebra $L$ is the same in every chief series for $L$, by \cite[Theorem 2.3]{[11]}. However, this is not the case for the number of chief factors which are simply complemented in $L$. In this paper we determine the possible variation in that number.

This year marks the 150th celebration of Nature. However, the understanding of the way the army of unsung editors-in-chief has strengthened and enriched the integrity and quality of the journal under the umbrella of its original mission remains nominal rather than substantial. This paper scrutinizes the chief vehicle guided by Nature's doctrine with regard to the ways it has conflicted with the advancement of both science and social progress. We first recast quantitative spatiotemporal analysis on the diachronic discourse of Nature since its debut, which promises to articulate the unfolding chronological picture of Nature on a historical time scale, and pinpoint overdue corrective to the strongly-held but flawed notions on editors-in-chief of Nature. Our findings strongly indicate that the army of editors-in-chief have never met with their fair share of identification, and they took on the challenge guided by Nature's doctrine with extraordinary polymath, unparalleled enthusiasm and diverse characters.

Automated classification of chief complaints from patient-generated text is a critical first step in developing scalable platforms to triage patients without human intervention. In this work, we evaluate several approaches to chief complaint classification using a novel Chief Complaint (CC) Dataset that contains ~200,000 patient-generated reasons-for-visit entries mapped to a set of 795 discrete chief complaints. We examine the use of several fine-tuned bidirectional transformer (BERT) models trained on both unrelated texts as well as on the CC dataset. We contrast this performance with a TF-IDF baseline. Our evaluation has three components: (1) a random test hold-out from the original dataset; (2) a "misspelling set," consisting of a hand-selected subset of the test set, where every entry has at least one misspelling; (3) a separate experimenter-generated free-text set. We find that the TF-IDF model performs significantly better than the strongest BERT-based model on the test (best BERT PR-AUC $0.3597 \pm 0.0041$ vs TF-IDF PR-AUC $0.3878 \pm 0.0148$, $p=7\cdot 10^{-5}$), and is statistically comparable to the misspelling sets (best BERT PR-AUC $0.2579 \pm 0.0079$ vs TF-IDF PR-AUC

In finite group theory, chief factors play an important and well-understood role in the structure theory. We here develop a theory of chief factors for Polish groups. In the development of this theory, we prove a version of the Schreier refinement theorem. We also prove a trichotomy for the structure of topologically characteristically simple Polish groups. The development of the theory of chief factors requires two independently interesting lines of study. First we consider injective, continuous homomorphisms with dense normal image. We show such maps admit a canonical factorization via a semidirect product, and as a consequence, these maps preserve topological simplicity up to abelian error. We then define two generalizations of direct products and use these to isolate a notion of semisimplicity for Polish groups.

Let $\mathfrak{J}$ be a class of non-abelian simple groups and $\mathfrak{X}$ be a class of groups. A chief factor $H/K$ of a group $G$ is called $\mathfrak{X}$-central in $G$ provided $(H/K)\rtimes G/C_G(H/K)\in\mathfrak{X}$. We say that $G$ is a $\mathfrak{J}cs$-$\mathfrak{X}$-\emph{group} if every chief $\mathfrak{X}$-factor of $G$ is $\mathfrak{X}$-central and other chief factors of $G$ are simple $\mathfrak{J}$-groups. We use $\mathfrak{X}_{\mathfrak{J}cs}$ to denote the class of all $\mathfrak{J}cs$-$\mathfrak{X}$-groups. A subgroup $U$ of a group $G$ is called $\mathfrak{X}$-\emph{maximal} in $G$ provided that $(a)$ $U\in\mathfrak{X}$, and $(b)$ if $U\leq V \leq G$ and $V\in\mathfrak{X}$, then $U = V$. In this paper we described the structure of $\mathfrak{J}cs$-$\mathfrak{H}$-groups for a solubly saturated formation $\mathfrak{H}$ and all hereditary saturated formations $\mathfrak{F}$ containing all nilpotent groups such that the $\mathfrak{F}_{\mathfrak{J}cs}$-hypercenter of $G$ coincides with the intersection of all $\mathfrak{F}_{\mathfrak{J}cs}$-maximal subgroups of $G$ for every group $G$.

We first obtain finiteness properties for the collection of closed normal subgroups of a compactly generated locally compact group. Via these properties, every compactly generated locally compact group admits an essentially chief series - i.e. a finite normal series in which each factor is compact, discrete, or a topological chief factor. Additionally, a Jordan-Hölder theorem holds for the `large' factors in an essentially chief series.

This paper presents the chief security officer (CSO) problem, defines its scope, and investigates several important research questions related within the scope. The CSO problem is defined based on the concept of secrecy capacity of wireless communication channels. It is also related to the chief Estimation/Executive Officer (CEO) problem that has been well studied in information theory. The CSO problem consists of a CSO, several agents capable of having two-way communication with the CSO, and a group of eavesdroppers. There are two scenarios in the CSO problem; one in which agents are not allowed to cooperate with one another and the other in which agents are allowed to cooperate with one another. While there are several research questions relevant to the CSO problem, this paper focusses on the following and provides answers: (1) How much information can be exchanged back and forth between the CSO and the agents without leaking any information to the eavesdroppers? (2) What is the power allocation strategy that the CSO needs to follow so as to maximize the secrecy capacity? (3) How can agents cooperate with one another in order to increase the overall secrecy capacity?.