Ward's Hierarchical Clustering Method: Clustering Criterion and Agglomerative Algorithm

The Ward error sum of squares hierarchical clustering method has been very widely used since its first description by Ward in a 1963 publication. It has also been generalized in various ways. However there are different interpretations in the literature and there are different implementations of the Ward agglomerative algorithm in commonly used software systems, including differing expressions of the agglomerative criterion. Our survey work and case studies will be useful for all those involved in developing software for data analysis using Ward's hierarchical clustering method.Comment: 20 pages, 21 citations, 4 figure

On soft singularities at three loops and beyond

We report on further progress in understanding soft singularities of massless gauge theory scattering amplitudes. Recently, a set of equations was derived based on Sudakov factorization, constraining the soft anomalous dimension matrix of multi-leg scattering amplitudes to any loop order, and relating it to the cusp anomalous dimension. The minimal solution to these equations was shown to be a sum over color dipoles. Here we explore potential contributions to the soft anomalous dimension that go beyond the sum-over-dipoles formula. Such contributions are constrained by factorization and invariance under rescaling of parton momenta to be functions of conformally invariant cross ratios. Therefore, they must correlate the color and kinematic degrees of freedom of at least four hard partons, corresponding to gluon webs that connect four eikonal lines, which first appear at three loops. We analyze potential contributions, combining all available constraints, including Bose symmetry, the expected degree of transcendentality, and the singularity structure in the limit where two hard partons become collinear. We find that if the kinematic dependence is solely through products of logarithms of cross ratios, then at three loops there is a unique function that is consistent with all available constraints. If polylogarithms are allowed to appear as well, then at least two additional structures are consistent with the available constraints.Comment: v2: revised version published in JHEP (minor corrections in Sec. 4; added discussion in Sec. 5.3; refs. added); v3: minor corrections (eqs. 5.11, 5.12 and 5.29); 38 pages, 3 figure

MaxMin Linear Initialization for Fuzzy C-Means

International audienceClustering is an extensive research area in data science. The aim of clustering is to discover groups and to identify interesting patterns in datasets. Crisp (hard) clustering considers that each data point belongs to one and only one cluster. However, it is inadequate as some data points may belong to several clusters, as is the case in text categorization. Thus, we need more flexible clustering. Fuzzy clustering methods, where each data point can belong to several clusters, are an interesting alternative. Yet, seeding iterative fuzzy algorithms to achieve high quality clustering is an issue. In this paper, we propose a new linear and efficient initialization algorithm MaxMin Linear to deal with this problem. Then, we validate our theoretical results through extensive experiments on a variety of numerical real-world and artificial datasets. We also test several validity indices, including a new validity index that we propose, Transformed Standardized Fuzzy Difference (TSFD)

Linear, Deterministic, and Order-Invariant Initialization Methods for the K-Means Clustering Algorithm

Over the past five decades, k-means has become the clustering algorithm of choice in many application domains primarily due to its simplicity, time/space efficiency, and invariance to the ordering of the data points. Unfortunately, the algorithm's sensitivity to the initial selection of the cluster centers remains to be its most serious drawback. Numerous initialization methods have been proposed to address this drawback. Many of these methods, however, have time complexity superlinear in the number of data points, which makes them impractical for large data sets. On the other hand, linear methods are often random and/or sensitive to the ordering of the data points. These methods are generally unreliable in that the quality of their results is unpredictable. Therefore, it is common practice to perform multiple runs of such methods and take the output of the run that produces the best results. Such a practice, however, greatly increases the computational requirements of the otherwise highly efficient k-means algorithm. In this chapter, we investigate the empirical performance of six linear, deterministic (non-random), and order-invariant k-means initialization methods on a large and diverse collection of data sets from the UCI Machine Learning Repository. The results demonstrate that two relatively unknown hierarchical initialization methods due to Su and Dy outperform the remaining four methods with respect to two objective effectiveness criteria. In addition, a recent method due to Erisoglu et al. performs surprisingly poorly.Comment: 21 pages, 2 figures, 5 tables, Partitional Clustering Algorithms (Springer, 2014). arXiv admin note: substantial text overlap with arXiv:1304.7465, arXiv:1209.196

Unity through truth

Renewed worries about the unity of the proposition have been taken as a crucial stumbling block for any traditional conception of propositions. These worries are often framed in terms of how entities independent of mind and language can have truth conditions: why is the proposition that Desdemona loves Cassio true if and only if she loves him? I argue that the best understanding of these worries shows that they should be solved by our theory of truth and not our theory of content. Specifically, I propose a version of the redundancy theory according to which ‘it is true that Desdemona loves Cassio’ expresses the same proposition as ‘Desdemona loves Cassio’. Surprisingly, this variant of the redundancy theory treats ‘is true’ as an ordinary predicate of the language, thereby defusing many standard criticisms of the redundancy theory

Accelarated immune ageing is associated with COVID-19 disease severity

Background: The striking increase in COVID-19 severity in older adults provides a clear example of immunesenescence, the age-related remodelling of the immune system. To better characterise the association between convalescent immunesenescence and acute disease severity, we determined the immune phenotype of COVID-19 survivors and non-infected controls. Results: We performed detailed immune phenotyping of peripheral blood mononuclear cells isolated from 103 COVID-19 survivors 3–5 months post recovery who were classified as having had severe (n = 56; age 53.12 ± 11.30 years), moderate (n = 32; age 52.28 ± 11.43 years) or mild (n = 15; age 49.67 ± 7.30 years) disease and compared with age and sex-matched healthy adults (n = 59; age 50.49 ± 10.68 years). We assessed a broad range of immune cell phenotypes to generate a composite score, IMM-AGE, to determine the degree of immune senescence. We found increased immunesenescence features in severe COVID-19 survivors compared to controls including: a reduced frequency and number of naïve CD4 and CD8 T cells (p  Conclusions: Our analyses reveal a state of enhanced immune ageing in survivors of severe COVID-19 and suggest this could be related to SARS-Cov-2 infection. Our data support the rationale for trials of anti-immune ageing interventions for improving clinical outcomes in these patients with severe disease

Microsatellite discovery in an insular amphibian (Grandisonia alternans) with comments on cross-species utility and the accuracy of locus identification from unassembled Illumina data

The Seychelles archipelago is unique among isolated oceanic islands because it features an endemic radiation of caecilian amphibians (Gymnophiona). In order to develop population genetics resources for this system, we identified microsatellite loci using unassembled Illumina MiSeq data generated from a genomic library of Grandisonia alternans, a species that occurs on multiple islands in the archipelago. Applying a recently described method (PALFINDER) we identified 8001 microsatellite loci that were potentially informative for population genetics analyses. Of these markers, we screened 60 loci using five individuals, directly sequenced several amplicons to confirm their identity, and then used eight loci to score allele sizes in 64 G. alternans individuals originating from five islands. A number of these individuals were sampled using non-lethal methods, demonstrating the efficacy of non-destructive molecular sampling in amphibian research. Although two loci satisfied our criteria as diploid, neutrally evolving loci with the statistical power to detect population structure, our success in identifying reliable loci was very low. Additionally, we discovered some issues with primer redundancy and differences between Illumina and Sanger sequences that suggest some Illumina-inferred loci are invalid. We investigated cross-species utility for eight loci and found most could be successfully amplified, sequenced and aligned across other species and genera of caecilians from the Seychelles. Thus, our study in part supported the validity of using PALFINDER with unassembled reads for microsatellite discovery within and across species, but importantly identified major limitations to applying this approach to small datasets (ca. 1 million reads) and loci with small tandem repeat sizes

Delivering an Optimised Behavioural Intervention (OBI) to people with low back pain with high psychological risk; results and lessons learnt from a feasibility randomised controlled trial of Contextual Cognitive Behavioural Therapy (CCBT) vs. Physiotherapy

Background: Low Back Pain (LBP) remains a common and costly problem. Psychological obstacles to recovery have been identified, but psychological and behavioural interventions have produced only moderate improvements. Reviews of trials have suggested that the interventions lack clear theoretical basis, are often compromised by low dose, lack of fidelity, and delivery by non-experts. In addition, interventions do not directly target known risk mechanisms. We identified a theory driven intervention (Contexual Cognitive Behavioural Therapy, CCBT) that directly targets an evidence-based risk mechanism (avoidance and ensured dose and delivery were optimised. This feasibility study was designed to test the credibility and acceptability of optimised CCBT against physiotherapy for avoidant LBP patients, and to test recruitment, delivery of the intervention and response rates prior to moving to a full definitive trial. Methods: A randomised controlled feasibility trial with patients randomised to receive CCBT or physiotherapy. CCBT was delivered by trained supervised psychologists on a one to one basis and comprised up to 8 one-hour sessions. Physiotherapy comprised back to fitness group exercises with at least 60 % of content exercise-based. Patients were eligible to take part if they had back pain for more than 3 months, and scored above a threshold indicating fear avoidance, catastrophic beliefs and distress. Results: 89 patients were recruited. Uptake rates were above those predicted. Scores for credibility and acceptability of the interventions met the set criteria. Response rates at three and six months fell short of the 75 % target. Problems associated with poor response rates were identified and successfully resolved, rates increased to 77 % at 3 months, and 68 % at 6 months. Independent ratings of treatment sessions indicated that CCBT was delivered to fidelity. Numbers were too small for formal analysis. Although average scores for acceptance were higher in the CCBT group than in the group attending physiotherapy (increase of 7.9 versus 5.1) and change in disability and pain from baseline to 6 months were greater in the CCBT group than in the physiotherapy group, these findings should be interpreted with caution. Conclusions: CCBT is a credible and acceptable intervention for LBP patients who exhibit psychological obstacles to recovery

Tension Type Headache in Adolescence and Childhood: Where Are We Now?

Tension type headache (TTH) is a primary headache disorder considered common in children and adolescents. It remains debatable whether TTH and migraine are separate biological entities. This review summarizes the most recent literature of TTH with regards to children and adolescents. Further studies of TTH are needed to develop a biologically based classification system that may be facilitated through understanding changes in the developing brain during childhood and adolescence

Intra-oral orthosis vs amitriptyline in chronic tension-type headache: a clinical and laser evoked potentials study

BACKGROUND: In the present study, we examined clinical and laser-evoked potentials (LEP) features in two groups of chronic tension-type headache (CTTH) patients treated with two different approaches: intra-oral appliance of prosthesis, aiming to reduce muscular tenderness, and 10 mg daily amitriptyline. METHODS: Eighteen patients with diagnosed CTTH participated in this open label, controlled study. A baseline evaluation was performed for clinical features, Total Tenderness Score (TTS) and a topographic analysis of LEPs obtained manually and the pericranial points stimulation in all patients vs. healthy subjects. Thereafter, patients were randomly assigned to a two-month treatment by either amitriptyline or intra-oral appliance. RESULTS AND DISCUSSION: Both the intra-oral appliance and amitriptyline significantly reduced headache frequency. The TTS was significantly reduced in the group treated with the appliance. The amplitude of P2 response elicited by stimulation of pericranial zones showed a reduction after amitriptyline treatment. Both therapies were effective in reducing headache severity, the appliance with a prevalent action on the pericranial muscular tenderness, amitriptyline reducing the activity of the central cortical structures subtending pain elaboration CONCLUSION: The results of this study may suggest that in CTTH both the interventions at the peripheral and central levels improve the outcome of headache