The length and depth of algebraic groups

Let G be a connected algebraic group. An unrefinable chain of G is a chain of subgroups G=G0>G1>⋯>Gt=1 , where each Gi is a maximal connected subgroup of Gi−1 . We introduce the notion of the length (respectively, depth) of G, defined as the maximal (respectively, minimal) length of such a chain. Working over an algebraically closed field, we calculate the length of a connected group G in terms of the dimension of its unipotent radical Ru(G) and the dimension of a Borel subgroup B of the reductive quotient G/Ru(G) . In particular, a simple algebraic group of rank r has length dimB+r , which gives a natural extension of a theorem of Solomon and Turull on finite quasisimple groups of Lie type. We then deduce that the length of any connected algebraic group G exceeds 12dimG . We also study the depth of simple algebraic groups. In characteristic zero, we show that the depth of such a group is at most 6 (this bound is sharp). In the positive characteristic setting, we calculate the exact depth of each exceptional algebraic group and we prove that the depth of a classical group (over a fixed algebraically closed field of positive characteristic) tends to infinity with the rank of the group. Finally we study the chain difference of an algebraic group, which is the difference between its length and its depth. In particular we prove that, for any connected algebraic group G with soluble radical R(G), the dimension of G / R(G) is bounded above in terms of the chain difference of G

On the length and depth of finite groups

An unrefinable chain of a finite group is a chain of subgroups = 0> 1>⋯> =1 , where each is a maximal subgroup of −1 . The length (respectively, depth) of is the maximal (respectively, minimal) length of such a chain. We studied the depth of finite simple groups in a previous paper, which included a classification of the simple groups of depth 3. Here, we go much further by determining the finite groups of depth 3 and 4. We also obtain several new results on the lengths of finite groups. For example, we classify the simple groups of length at most 9, which extends earlier work of Janko and Harada from the 1960s, and we use this to describe the structure of arbitrary finite groups of small length. We also present a number‐theoretic result of Heath‐Brown, which implies that there are infinitely many non‐abelian simple groups of length at most 9. Finally, we study the chain difference of (namely the length minus the depth). We obtain results on groups with chain differences 1 and 2, including a complete classification of the simple groups with chain difference 2, extending earlier work of Brewster et al. We also derive a best possible lower bound on the chain ratio (the length divided by the depth) of simple groups, which yields an explicit linear bound on the length of / ( ) in terms of the chain difference of , where ( ) is the soluble radical of

No selection on immunological markers in response to a highly virulent pathogen in an Arctic breeding bird

In natural populations, epidemics provide opportunities to look for intense natural selection on genes coding for life history and immune or other physiological traits. If the populations being considered are of management or conservation concern, then identifying the traits under selection (or ‘markers’) might provide insights into possible intervention strategies during epidemics. We assessed potential for selection on multiple immune and life history traits of Arctic breeding common eiders (Somateria mollissima) during annual avian cholera outbreaks (summers of 2006, 2007 & 2008). We measured prelaying body condition, immune traits, and subsequent reproductive investment (i.e., clutch size) and survival of female common eiders and whether they were infected with Pasteurella multocida, the causative agent of avian cholera. We found no clear and consistent evidence of directional selection on immune traits; however, infected birds had higher levels of haptoglobin than uninfected birds. Also, females that laid larger clutches had slightly lower immune responses during the prelaying period reflecting possible downregulation of the immune system to support higher costs of reproduction. This supports a recent study indicating that birds investing in larger clutches were more likely to die from avian cholera and points to a possible management option to maximize female survival during outbreaks

Sperm design and variation in the New World blackbirds (Icteridae)

Post-copulatory sexual selection (PCSS) is thought to be one of the evolutionary forces responsible for the rapid and divergent evolution of sperm design. However, whereas in some taxa particular sperm traits are positively associated with PCSS, in other taxa, these relationships are negative, and the causes of these different patterns across taxa are poorly understood. In a comparative study using New World blackbirds (Icteridae), we tested whether sperm design was influenced by the level of PCSS and found significant positive associations with the level of PCSS for all sperm components but head length. Additionally, whereas the absolute length of sperm components increased, their variation declined with the intensity of PCSS, indicating stabilizing selection around an optimal sperm design. Given the diversity of, and strong selection on, sperm design, it seems likely that sperm phenotype may influence sperm velocity within species. However, in contrast to other recent studies of passerine birds, but consistent with several other studies, we found no significant link between sperm design and velocity, using four different species that vary both in sperm design and PCSS. Potential reasons for this discrepancy between studies are discussed

Cognitive behavioural therapy for adults with dissociative seizures (CODES): a pragmatic, multicentre, randomised controlled trial.

BACKGROUND: Dissociative seizures are paroxysmal events resembling epilepsy or syncope with characteristic features that allow them to be distinguished from other medical conditions. We aimed to compare the effectiveness of cognitive behavioural therapy (CBT) plus standardised medical care with standardised medical care alone for the reduction of dissociative seizure frequency. METHODS: In this pragmatic, parallel-arm, multicentre randomised controlled trial, we initially recruited participants at 27 neurology or epilepsy services in England, Scotland, and Wales. Adults (≥18 years) who had dissociative seizures in the previous 8 weeks and no epileptic seizures in the previous 12 months were subsequently randomly assigned (1:1) from 17 liaison or neuropsychiatry services following psychiatric assessment, to receive standardised medical care or CBT plus standardised medical care, using a web-based system. Randomisation was stratified by neuropsychiatry or liaison psychiatry recruitment site. The trial manager, chief investigator, all treating clinicians, and patients were aware of treatment allocation, but outcome data collectors and trial statisticians were unaware of treatment allocation. Patients were followed up 6 months and 12 months after randomisation. The primary outcome was monthly dissociative seizure frequency (ie, frequency in the previous 4 weeks) assessed at 12 months. Secondary outcomes assessed at 12 months were: seizure severity (intensity) and bothersomeness; longest period of seizure freedom in the previous 6 months; complete seizure freedom in the previous 3 months; a greater than 50% reduction in seizure frequency relative to baseline; changes in dissociative seizures (rated by others); health-related quality of life; psychosocial functioning; psychiatric symptoms, psychological distress, and somatic symptom burden; and clinical impression of improvement and satisfaction. p values and statistical significance for outcomes were reported without correction for multiple comparisons as per our protocol. Primary and secondary outcomes were assessed in the intention-to-treat population with multiple imputation for missing observations. This trial is registered with the International Standard Randomised Controlled Trial registry, ISRCTN05681227, and ClinicalTrials.gov, NCT02325544. FINDINGS: Between Jan 16, 2015, and May 31, 2017, we randomly assigned 368 patients to receive CBT plus standardised medical care (n=186) or standardised medical care alone (n=182); of whom 313 had primary outcome data at 12 months (156 [84%] of 186 patients in the CBT plus standardised medical care group and 157 [86%] of 182 patients in the standardised medical care group). At 12 months, no significant difference in monthly dissociative seizure frequency was identified between the groups (median 4 seizures [IQR 0-20] in the CBT plus standardised medical care group vs 7 seizures [1-35] in the standardised medical care group; estimated incidence rate ratio [IRR] 0·78 [95% CI 0·56-1·09]; p=0·144). Dissociative seizures were rated as less bothersome in the CBT plus standardised medical care group than the standardised medical care group (estimated mean difference -0·53 [95% CI -0·97 to -0·08]; p=0·020). The CBT plus standardised medical care group had a longer period of dissociative seizure freedom in the previous 6 months (estimated IRR 1·64 [95% CI 1·22 to 2·20]; p=0·001), reported better health-related quality of life on the EuroQoL-5 Dimensions-5 Level Health Today visual analogue scale (estimated mean difference 6·16 [95% CI 1·48 to 10·84]; p=0·010), less impairment in psychosocial functioning on the Work and Social Adjustment Scale (estimated mean difference -4·12 [95% CI -6·35 to -1·89]; p<0·001), less overall psychological distress than the standardised medical care group on the Clinical Outcomes in Routine Evaluation-10 scale (estimated mean difference -1·65 [95% CI -2·96 to -0·35]; p=0·013), and fewer somatic symptoms on the modified Patient Health Questionnaire-15 scale (estimated mean difference -1·67 [95% CI -2·90 to -0·44]; p=0·008). Clinical improvement at 12 months was greater in the CBT plus standardised medical care group than the standardised medical care alone group as reported by patients (estimated mean difference 0·66 [95% CI 0·26 to 1·04]; p=0·001) and by clinicians (estimated mean difference 0·47 [95% CI 0·21 to 0·73]; p<0·001), and the CBT plus standardised medical care group had greater satisfaction with treatment than did the standardised medical care group (estimated mean difference 0·90 [95% CI 0·48 to 1·31]; p<0·001). No significant differences in patient-reported seizure severity (estimated mean difference -0·11 [95% CI -0·50 to 0·29]; p=0·593) or seizure freedom in the last 3 months of the study (estimated odds ratio [OR] 1·77 [95% CI 0·93 to 3·37]; p=0·083) were identified between the groups. Furthermore, no significant differences were identified in the proportion of patients who had a more than 50% reduction in dissociative seizure frequency compared with baseline (OR 1·27 [95% CI 0·80 to 2·02]; p=0·313). Additionally, the 12-item Short Form survey-version 2 scores (estimated mean difference for the Physical Component Summary score 1·78 [95% CI -0·37 to 3·92]; p=0·105; estimated mean difference for the Mental Component Summary score 2·22 [95% CI -0·30 to 4·75]; p=0·084), the Generalised Anxiety Disorder-7 scale score (estimated mean difference -1·09 [95% CI -2·27 to 0·09]; p=0·069), and the Patient Health Questionnaire-9 scale depression score (estimated mean difference -1·10 [95% CI -2·41 to 0·21]; p=0·099) did not differ significantly between groups. Changes in dissociative seizures (rated by others) could not be assessed due to insufficient data. During the 12-month period, the number of adverse events was similar between the groups: 57 (31%) of 186 participants in the CBT plus standardised medical care group reported 97 adverse events and 53 (29%) of 182 participants in the standardised medical care group reported 79 adverse events. INTERPRETATION: CBT plus standardised medical care had no statistically significant advantage compared with standardised medical care alone for the reduction of monthly seizures. However, improvements were observed in a number of clinically relevant secondary outcomes following CBT plus standardised medical care when compared with standardised medical care alone. Thus, adults with dissociative seizures might benefit from the addition of dissociative seizure-specific CBT to specialist care from neurologists and psychiatrists. Future work is needed to identify patients who would benefit most from a dissociative seizure-specific CBT approach. FUNDING: National Institute for Health Research, Health Technology Assessment programme

Vedolizumab for the Treatment of Adults with Moderate-to-Severe Active Ulcerative Colitis: An Evidence Review Group Perspective of a NICE Single Technology Appraisal.

As part of its single technology appraisal (STA) process, the National Institute for Health and Care Excellence (NICE) invited the manufacturer of vedolizumab (Takeda UK) to submit evidence of the clinical effectiveness and cost effectiveness of vedolizumab for the treatment of patients with moderate-to-severe active ulcerative colitis (UC). The Evidence Review Group (ERG) produced a critical review of the evidence for the clinical effectiveness and cost effectiveness of the technology, based upon the company's submission to NICE. The evidence was derived mainly from GEMINI 1, a Phase 3, multicentre, randomised, double-blinded, placebo-controlled study of the induction and maintenance of clinical response and remission by vedolizumab (MLN0002) in patients with moderate-to-severe active UC with an inadequate response to, loss of response to or intolerance of conventional therapy or anti-tumour necrosis factor (TNF)-α. The clinical evidence showed that vedolizumab performed significantly better than placebo in both the induction and maintenance phases. In the post hoc subgroup analyses in patients with or without prior anti-TNF-α therapy, vedolizumab performed better then placebo (p value not reported). In addition, a greater improvement in health-related quality of life was observed in patients treated with vedolizumab, and the frequency and types of adverse events were similar in the vedolizumab and placebo groups, but the evidence was limited to short-term follow-up. There were a number of limitations and uncertainties in the clinical evidence base, which warrants caution in its interpretation-in particular, the post hoc subgroup analyses and high dropout rates in the maintenance phase of GEMINI 1. The company also presented a network meta-analysis of vedolizumab versus other biologic therapies indicated for moderate-to-severe UC. However, the ERG considered that the results presented may have underestimated the uncertainty in treatment effects, since fixed-effects models were used, despite clear evidence of heterogeneity among the trials included in the network. Results from the company's economic evaluation (which included price reductions to reflect the proposed patient access scheme for vedolizumab) suggested that vedolizumab is the most effective option compared with surgery and conventional therapy in the following three populations: (1) a mixed intention-to-treat population, including patients who have previously received anti-TNF-α therapy and those who are anti-TNF-α naïve; (2) patients who are anti-TNF-α naïve only; and (3) patients who have previously failed anti-TNF-α therapy only. The ERG concluded that the results of the company's economic evaluation could not be considered robust, because of errors in model implementation, omission of relevant comparators, deviations from the NICE reference case and questionable model assumptions. The ERG amended the company's model and demonstrated that vedolizumab is expected to be dominated by surgery in all three populations

Cognitive–behavioural therapy compared with standardised medical care for adults with dissociative non-epileptic seizures: the CODES RCT

Background Dissociative (non-epileptic) seizures are potentially treatable by psychotherapeutic interventions; however, the evidence for this is limited. Objectives To evaluate the clinical effectiveness and cost-effectiveness of dissociative seizure-specific cognitive–behavioural therapy for adults with dissociative seizures. Design This was a pragmatic, multicentre, parallel-arm, mixed-methods randomised controlled trial. Setting This took place in 27 UK-based neurology/epilepsy services, 17 liaison psychiatry/neuropsychiatry services and 18 cognitive–behavioural therapy services. Participants Adults with dissociative seizures in the previous 8 weeks and no epileptic seizures in the previous year and meeting other eligibility criteria were recruited to a screening phase from neurology/epilepsy services between October 2014 and February 2017. After psychiatric assessment around 3 months later, eligible and interested participants were randomised between January 2015 and May 2017. Interventions Standardised medical care consisted of input from neurologists and psychiatrists who were given guidance regarding diagnosis delivery and management; they provided patients with information booklets. The intervention consisted of 12 dissociative seizure-specific cognitive–behavioural therapy 1-hour sessions (plus one booster session) that were delivered by trained therapists, in addition to standardised medical care. Main outcome measures The primary outcome was monthly seizure frequency at 12 months post randomisation. The secondary outcomes were aspects of seizure occurrence, quality of life, mood, anxiety, distress, symptoms, psychosocial functioning, clinical global change, satisfaction with treatment, quality-adjusted life-years, costs and cost-effectiveness. Results In total, 698 patients were screened and 368 were randomised (standardised medical care alone, n = 182; and cognitive–behavioural therapy plus standardised medical care, n = 186). Primary outcome data were obtained for 85% of participants. An intention-to-treat analysis with multivariate imputation by chained equations revealed no significant between-group difference in dissociative seizure frequency at 12 months [standardised medical care: median of seven dissociative seizures (interquartile range 1–35 dissociative seizures); cognitive–behavioural therapy and standardised medical care: median of four dissociative seizures (interquartile range 0–20 dissociative seizures); incidence rate ratio 0.78, 95% confidence interval 0.56 to 1.09; p = 0.144]. Of the 16 secondary outcomes analysed, nine were significantly better in the arm receiving cognitive–behavioural therapy at a p-value &lt; 0.05, including the following at a p-value ≤ 0.001: the longest dissociative seizure-free period in months 7–12 inclusive post randomisation (incidence rate ratio 1.64, 95% confidence interval 1.22 to 2.20; p = 0.001); better psychosocial functioning (Work and Social Adjustment Scale, standardised treatment effect –0.39, 95% confidence interval –0.61 to –0.18; p &lt; 0.001); greater self-rated and clinician-rated clinical improvement (self-rated: standardised treatment effect 0.39, 95% confidence interval 0.16 to 0.62; p = 0.001; clinician rated: standardised treatment effect 0.37, 95% confidence interval 0.17 to 0.57; p &lt; 0.001); and satisfaction with treatment (standardised treatment effect 0.50, 95% confidence interval 0.27 to 0.73; p &lt; 0.001). Rates of adverse events were similar across arms. Cognitive–behavioural therapy plus standardised medical care produced 0.0152 more quality-adjusted life-years (95% confidence interval –0.0106 to 0.0392 quality-adjusted life-years) than standardised medical care alone. The incremental cost-effectiveness ratio (cost per quality-adjusted life-year) for cognitive–behavioural therapy plus standardised medical care versus standardised medical care alone based on the EuroQol-5 Dimensions, five-level version, and imputed data was £120,658. In sensitivity analyses, incremental cost-effectiveness ratios ranged between £85,724 and £206,067. Qualitative and quantitative process evaluations highlighted useful study components, the importance of clinical experience in treating patients with dissociative seizures and potential benefits of our multidisciplinary care pathway. Limitations Unlike outcome assessors, participants and clinicians were not blinded to the interventions. Conclusions There was no significant additional benefit of dissociative seizure-specific cognitive–behavioural therapy in reducing dissociative seizure frequency, and cost-effectiveness over standardised medical care was low. However, this large, adequately powered, multicentre randomised controlled trial highlights benefits of adjunctive dissociative seizure-specific cognitive–behavioural therapy for several clinical outcomes, with no evidence of greater harm from dissociative seizure-specific cognitive–behavioural therapy. Future work Examination of moderators and mediators of outcome. Trial registration Current Controlled Trials ISRCTN05681227 and ClinicalTrials.gov NCT02325544. Funding This project was funded by the National Institute for Health Research (NIHR) Health Technology Assessment programme and will be published in full in Health Technology Assessment; Vol. 25, No. 43. See the NIHR Journals Library website for further project information

A mouse model for triple-negative breast cancer tumor-initiating cells (TNBC-TICs) exhibits similar aggressive phenotype to the human disease

<p>Abstract</p> <p>Background</p> <p>Triple-negative breast cancer (TNBC) exhibit characteristics quite distinct from other kinds of breast cancer, presenting as an aggressive disease--recurring and metastasizing more often than other kinds of breast cancer, without tumor-specific treatment options and accounts for 15% of all types of breast cancer with higher percentages in premenopausal African-American and Hispanic women. The reason for this aggressive phenotype is currently the focus of intensive research. However, progress is hampered by the lack of suitable TNBC cell model systems.</p> <p>Methods</p> <p>To understand the mechanistic basis for the aggressiveness of TNBC, we produced a stable TNBC cell line by sorting for 4T1 cells that do not express the estrogen receptor (ER), progesterone receptor (PgR) or the gene for human epidermal growth factor receptor 2 (HER2). As a control, we produced a stable triple-positive breast cancer (TPBC) cell line by transfecting 4T1 cells with rat HER2, ER and PgR genes and sorted for cells with high expression of ER and PgR by flow cytometry and high expression of the HER2 gene by Western blot analysis.</p> <p>Results</p> <p>We isolated tumor-initiating cells (TICs) by sorting for CD24⁺/CD44^high/ALDH1⁺cells from TNBC (TNBC-TICs) and TPBC (TPBC-TICs) stable cell lines. Limiting dilution transplantation experiments revealed that CD24⁺/CD44^high/ALDH1⁺cells derived from TNBC (TNBC-TICs) and TPBC (TPBC-TICs) were significantly more effective at repopulating the mammary glands of naïve female BALB/c mice than CD24^-/CD44^-/ALDH1^-cells. Implantation of the TNBC-TICs resulted in significantly larger tumors, which metastasized to the lungs to a significantly greater extent than TNBC, TPBC-TICs, TPBC or parental 4T1 cells. We further demonstrated that the increased aggressiveness of TNBC-TICs correlates with the presence of high levels of mouse twenty-five kDa heat shock protein (Hsp25/mouse HspB1) and seventy-two kDa heat shock protein (Hsp72/HspA1A).</p> <p>Conclusions</p> <p>Taken together, we have developed a TNBC-TICs model system based on the 4T1 cells which is a very useful metastasis model with the advantage of being able to be transplanted into immune competent recipients. Our data demonstrates that the TNBC-TICs model system could be a useful tool for studies on the pathogenesis and therapeutic treatment for TNBC.</p

The sperm factor: paternal impact beyond genes

The fact that sperm carry more than the paternal DNA has only been discovered just over a decade ago. With this discovery, the idea that the paternal condition may have direct implications for the fitness of the offspring had to be revisited. While this idea is still highly debated, empirical evidence for paternal effects is accumulating. Male condition not only affects male fertility but also offspring early development and performance later in life. Several factors have been identified as possible carriers of non-genetic information, but we still know little about their origin and function and even less about their causation. I consider four possible non-mutually exclusive adaptive and non-adaptive explanations for the existence of paternal effects in an evolutionary context. In addition, I provide a brief overview of the main non-genetic components found in sperm including DNA methylation, chromatin modifications, RNAs and proteins. I discuss their putative functions and present currently available examples for their role in transferring non-genetic information from the father to the offspring. Finally, I identify some of the most important open questions and present possible future research avenues

Gene expression profiles of breast biopsies from healthy women identify a group with claudin-low features

Background Increased understanding of the variability in normal breast biology will enable us to identify mechanisms of breast cancer initiation and the origin of different subtypes, and to better predict breast cancer risk. Methods Gene expression patterns in breast biopsies from 79 healthy women referred to breast diagnostic centers in Norway were explored by unsupervised hierarchical clustering and supervised analyses, such as gene set enrichment analysis and gene ontology analysis and comparison with previously published genelists and independent datasets. Results Unsupervised hierarchical clustering identified two separate clusters of normal breast tissue based on gene-expression profiling, regardless of clustering algorithm and gene filtering used. Comparison of the expression profile of the two clusters with several published gene lists describing breast cells revealed that the samples in cluster 1 share characteristics with stromal cells and stem cells, and to a certain degree with mesenchymal cells and myoepithelial cells. The samples in cluster 1 also share many features with the newly identified claudin-low breast cancer intrinsic subtype, which also shows characteristics of stromal and stem cells. More women belonging to cluster 1 have a family history of breast cancer and there is a slight overrepresentation of nulliparous women in cluster 1. Similar findings were seen in a separate dataset consisting of histologically normal tissue from both breasts harboring breast cancer and from mammoplasty reductions. Conclusion This is the first study to explore the variability of gene expression patterns in whole biopsies from normal breasts and identified distinct subtypes of normal breast tissue. Further studies are needed to determine the specific cell contribution to the variation in the biology of normal breasts, how the clusters identified relate to breast cancer risk and their possible link to the origin of the different molecular subtypes of breast cancer