Oropharyngeal Dysphagia: A Proposal for an Ecological Theoretical Model

Background: The exponential growth in epidemiological studies has been reflected in an increase in analytical studies. Thus, theoretical models are required to guide the definition of data analysis, although so far, they are seldom used in Speech, Language, and Hearing Sciences. Objective: To propose a multicausal model for oropharyngeal dysphagia using directed acyclic graphs showing mediating variables, confounding variables, and variables connected by direct causation. Design: This integrative literature review. Setting: This was carried out until January 4, 2021, and searches were performed with the MEDLINE, EMBASE,and other bases.

Path homologies of motifs and temporal network representations

Path homology is a powerful method for attaching algebraic invariants to digraphs. While there have been growing theoretical developments on the algebro-topological framework surrounding path homology, bona fide applications to the study of complex networks have remained stagnant. We address this gap by presenting an algorithm for path homology that combines efficient pruning and indexing techniques and using it to topologically analyze a variety of real-world complex temporal networks. A crucial step in our analysis is the complete characterization of path homologies of certain families of small digraphs that appear as subgraphs in these complex networks. These families include all digraphs, directed acyclic graphs, and undirected graphs up to certain numbers of vertices, as well as some specially constructed cases. Using information from this analysis, we identify small digraphs contributing to path homology in dimension two for three temporal networks in an aggregated representation and relate these digraphs to network behavior. We then investigate alternative temporal network representations and identify complementary subgraphs as well as behavior that is preserved across representations. We conclude that path homology provides insight into temporal network structure, and in turn, emergent structures in temporal networks provide us with new subgraphs having interesting path homology.

Parameterized Complexity of Directed Spanner Problems

We initiate the parameterized complexity study of minimum t-spanner problems on directed graphs. For a positive integer t, a multiplicative t-spanner of a (directed) graph G is a spanning subgraph H such that the distance between any two vertices in H is at most t times the distance between these vertices in G, that is, H keeps the distances in G up to the distortion (or stretch) factor t. An additive t-spanner is defined as a spanning subgraph that keeps the distances up to the additive distortion parameter t, that is, the distances in H and G differ by at most t. The task of Directed Multiplicative Spanner is, given a directed graph G with m arcs and positive integers t and k, decide whether G has a multiplicative t-spanner with at most $$m-k$$ m - k arcs. Similarly, Directed Additive Spanner asks whether G has an additive t-spanner with at most $$m-k$$ m - k arcs. We show that (i) Directed Multiplicative Spanner admits a polynomial kernel of size $$\mathcal {O}(k^4t^5)$$ O ( k 4 t 5 ) and can be solved in randomized $$(4t)^k\cdot n^{\mathcal {O}(1)}$$ ( 4 t ) k · n O ( 1 ) time, (ii) the weighted variant of Directed Multiplicative Spanner can be solved in $$k^{2k}\cdot n^{\mathcal {O}(1)}$$ k 2 k · n O ( 1 ) time on directed acyclic graphs, (iii) Directed Additive Spanner is $${{\,\mathrm{\mathsf{W}}\,}}[1]$$ W [ 1 ] -hard when parameterized by k for every fixed $$t\ge 1$$ t ≥ 1 even when the input graphs are restricted to be directed acyclic graphs. The latter claim contrasts with the recent result of Kobayashi from STACS 2020 that the problem for undirected graphs is $${{\,\mathrm{\mathsf{FPT}}\,}}$$ FPT when parameterized by t and k.

A Pathfinding Problem for Fork-Join Directed Acyclic Graphs with Unknown Edge Length

In a previous paper by the author, a pathfinding problem for directed trees is studied under the following situation: each edge has a nonnegative integer length, but the length is unknown in advance and should be found by a procedure whose computational cost becomes exponentially larger as the length increases. In this paper, the same problem is studied for a more general class of graphs called fork-join directed acyclic graphs. The problem for the new class of graphs contains the previous one. In addition, the optimality criterion used in this paper is stronger than that in the previous paper and is more appropriate for real applications.

Order preserving hierarchical agglomerative clustering

Partial orders and directed acyclic graphs are commonly recurring data structures that arise naturally in numerous domains and applications and are used to represent ordered relations between entities in the domains. Examples are task dependencies in a project plan, transaction order in distributed ledgers and execution sequences of tasks in computer programs, just to mention a few. We study the problem of order preserving hierarchical clustering of this kind of ordered data. That is, if we have $$a<b$$ a < b in the original data and denote their respective clusters by [a] and [b], then we shall have $$[a]<[b]$$ [ a ] < [ b ] in the produced clustering. The clustering is similarity based and uses standard linkage functions, such as single- and complete linkage, and is an extension of classical hierarchical clustering. To achieve this, we develop a novel theory that extends classical hierarchical clustering to strictly partially ordered sets. We define the output from running classical hierarchical clustering on strictly ordered data to be partial dendrograms; sub-trees of classical dendrograms with several connected components. We then construct an embedding of partial dendrograms over a set into the family of ultrametrics over the same set. An optimal hierarchical clustering is defined as the partial dendrogram corresponding to the ultrametric closest to the original dissimilarity measure, measured in the p-norm. Thus, the method is a combination of classical hierarchical clustering and ultrametric fitting. A reference implementation is employed for experiments on both synthetic random data and real world data from a database of machine parts. When compared to existing methods, the experiments show that our method excels both in cluster quality and order preservation.

Educational Expansion, Social Class, and Choosing Latin as a Strategy of Distinction

In times of educational expansion, privileged families are looking for new strategies of distinction. Referring to Pierre Bourdieu’s theory of distinction, we argue that choosing Latin at school – a language that is no longer spoken and therefore has no direct value – is one of the strategies of privileged families to set themselves apart from less privileged families. Based on two surveys we conducted at German schools, the paper analyzes the relationship between parents’ educational background and the probability that their child will learn Latin. Results indicate that historically academic families have the strongest tendency towards learning Latin, followed by new academic families, and leaving behind the non-academic families. We distinguish between four causal mechanisms that might help to explain these associations: cultural distinction, selecting a socially exclusive learning environment, beliefs in a secondary instrumental function of learning Latin, and spatial proximity between the location of humanist Gymnasiums and the residential areas of privileged families. The hypotheses are formalized by means of Directed Acyclic Graphs (DAG). Findings show that the decision to learn Latin is predominately an unintended consequence of the selection of a socially exclusive learning environment. In addition, there is evidence that especially children from historically academic families learn Latin as a strategy of cultural distinction.