Multi-variable Polynomial Solutions to Pell's Equation and Fundamental Units in Real Quadratic Fields

For each positive integer $n$ it is shown how to construct a finite collection of multivariable polynomials $\{F_{i}:=F_{i}(t,X_{1},..., X_{\lfloor \frac{n+1}{2} \rfloor})\}$ such that each positive integer whose squareroot has a continued fraction expansion with period $n+1$ lies in the range of exactly one of these polynomials. Moreover, each of these polynomials satisfy a polynomial Pell's equation $C_{i}^{2} -F_{i}H_{i}^{2} = (-1)^{n-1}$ (where $C_{i}$ and $H_{i}$ are polynomials in the variables $t,X_{1},..., X_{\lfloor \frac{n+1}{2} \rfloor}$) and the fundamental solution can be written down. Likewise, if all the $X_{i}$'s and $t$ are non-negative then the continued fraction expansion of $\sqrt{F_{i}}$ can be written down. Furthermore, the congruence class modulo 4 of $F_{i}$ depends in a simple way on the variables $t,X_{1},..., X_{\lfloor \frac{n+1}{2} \rfloor}$ so that the fundamental unit can be written down for a large class of real quadratic fields. Along the way a complete solution is given to the problem of determining for which symmetric strings of positive integers $a_{1},..., a_{n}$ do there exist positive integers $D$ and $a_{0}$ such that $\sqrt{D} = [ a_{0};\bar{a_{1}, >..., a_{n},2a_{0}}]$.Comment: 13 page

Differential response of serum amyloid A to different therapies in early rheumatoid arthritis and its potential value as a disease activity biomarker

Background: The aim was to compare the effect of etanercept (ETN) and conventional synthetic disease-modifying anti-rheumatic drug (DMARD) therapy on serum amyloid A (SAA) levels and to determine whether SAA reflects rheumatoid arthritis (RA) disease activity better than C-reactive protein (CRP). Methods: We measured SAA and CRP at baseline, 24, 48, and 102 week follow-up visits in 594 patients participating in the Treatment of early RA (TEAR) study. We used Spearman correlation coefficients (rho) to evaluate the relationship between SAA and CRP and mixed effects models to determine whether ETN and methotrexate (MTX) treatment compared to triple DMARD therapy differentially lowered SAA. Akaike information criteria (AIC) were used to determine model fits. Results: SAA levels were only moderately correlated with CRP levels (rho = 0.58, p < 0.0001). There were significant differences in SAA by both visit (p = 0.0197) and treatment arm (p = 0.0130). RA patients treated with ETN plus MTX had a larger reduction in SAA than patients treated with traditional DMARD therapy. Similar results were found for serum CRP by visit (p = 0.0254) and by treatment (p < 0.0001), with a more pronounced difference than for SAA. Across all patients and time points, models of the disease activity score of 28 joints (DAS28)-erythrocyte sedimentation rate (ESR) using SAA levels were better than models using CRP; the ΔAIC between the SAA and CRP models was 305. Conclusions: SAA may be a better biomarker of RA disease activity than CRP, especially during treatment with tumor necrosis factor (TNF) antagonists. This warrants additional studies in other cohorts of patients on treatment for RA. Trial registration: (ClinicalTrials.gov identifier: NCT00259610 , Date of registration: 28 November 2005

Rheumatoid arthritis patients exhibit impaired Candida albicans-specific Th17 responses

Introduction: Accumulating data implicate the CD4+ T cell subset (Th17 cells) in rheumatoid arthritis (RA). IL-17 is an inflammatory cytokine that induces tumor necrosis factor (TNF)α, IL-1β and IL-6, all of which are targets of biologic therapies used to treat RA. RA patients are well documented to experience more infections than age-matched controls, and biologic therapies further increase the risk of infection. The Th17/IL-17 axis is vital for immunity to fungi, especially the commensal fungus Candida albicans. Therefore, we were prompted to examine the relationship between RA and susceptibility to C. albicans because of the increasing interest in Th17 cells and IL-17 in driving autoimmunity, and the advent of new biologics that target this pathway.Methods: We analyzed peripheral blood and saliva from 48 RA and 33 healthy control subjects. To assess C. albicans-specific Th17 responses, PBMCs were co-cultured with heat-killed C. albicans extract, and IL-17A levels in conditioned supernatants were measured by ELISA. The frequency of Th17 and Th1 cells was determined by flow cytometry. As a measure of IL-17A-mediated effector responses, we evaluated C. albicans colonization rates in the oral cavity, salivary fungicidal activity and levels of the antimicrobial peptide β-defensin 2 (BD2) in saliva.Results: Compared to controls, PBMCs from RA subjects exhibited elevated baseline production of IL-17A (P = 0.004), although they had similar capacity to produce IL-17A in response to Th17 cell differentiating cytokines (P = 0.91). However RA PBMCs secreted less IL-17A in response to C. albicans antigens (P = 0.006). Significantly more RA patients were colonized with C. albicans in the oral cavity than healthy subjects (P = 0.02). Concomitantly, RA saliva had reduced concentrations of salivary BD2 (P = 0.02). Nonetheless, salivary fungicidal activity was preserved in RA subjects (P = 0.70).Conclusions: RA subjects exhibit detectable impairments in oral immune responses to C. albicans, a strongly Th17-dependent opportunistic pathogen, despite an overall elevated baseline production of IL-17A. © 2014 Bishu et al.; licensee BioMed Central Ltd

Biologic predictors of clinical improvement in rituximab-treated refractory myositis Clinical rheumatology and osteoporosis

Background: To examine the longitudinal utility of a biomarker signature in conjunction with myositis autoantibodies (autoAbs) as predictors of disease improvement in refractory myositis patients treated with rituximab. Methods: In the RIM Trial, all subjects received rituximab on 2 consecutive weeks. Using start of treatment as baseline, serum samples (n∈=∈177) were analyzed at baseline and after rituximab with multiplexed sandwich immunoassays to quantify type-1 IFN-regulated and other pro-inflammatory chemokines and cytokines. Biomarker scores were generated for the following pathways: type-1 IFN-inducible (IFNCK), innate, Th1, Th2, Th17 and regulatory cytokines. Myositis autoAbs (anti-synthetase n∈=∈28, TIF-γ n∈=∈19, Mi-2 n∈=∈25, SRP n∈=∈21, MJ n∈=∈18, non-MAA n∈=∈24, unidentified autoantibody n∈=∈9, and no autoantibodies n∈=∈33) determined by immunoprecipitation at baseline, were correlated with outcome measures. Kruskal-Wallis rank sum tests were used for comparisons. Results: The mean (SD) values for muscle disease and physician global disease activity VAS scores (0-100 mm) were 46 (22) and 49 (19). IFNCK scores (median values) were higher at baseline in subjects with anti-synthetase (43), TIF1-γ (31) and Mi-2 (30) compared with other autoAb groups (p∈30) and autoAb group (Mi-2, non-MAA, and undefined autoantibody) demonstrated the greatest clinical improvement based on muscle VAS (muscle-interaction p∈=∈0.075). Conclusion: Biomarker signatures in conjunction with autoAbs help predict response to rituximab in refractory myositis. Biomarker and clinical responses are greatest at 16 weeks after rituximab

A Phase II Trial of Lutikizumab, an Anti–Interleukin‐1α/β Dual Variable Domain Immunoglobulin, in Knee Osteoarthritis Patients With Synovitis

Objective: To assess the efficacy and safety of the anti–interleukin‐1α/β (anti–IL‐1α/β) dual variable domain immunoglobulin lutikizumab (ABT‐981) in patients with knee osteoarthritis (OA) and evidence of synovitis. Methods: Patients (n = 350; 347 analyzed) with Kellgren/Lawrence grade 2–3 knee OA and synovitis (determined by magnetic resonance imaging [MRI] or ultrasound) were randomized to receive placebo or lutikizumab 25, 100, or 200 mg subcutaneously every 2 weeks for 50 weeks. The coprimary end points were change from baseline in Western Ontario and McMaster Universities Osteoarthritis Index (WOMAC) pain score at week 16 and change from baseline in MRI‐assessed synovitis at week 26. Results: The WOMAC pain score at week 16 had improved significantly versus placebo with lutikizumab 100 mg (P = 0.050) but not with the 25 mg or 200 mg doses. Beyond week 16, the WOMAC pain score was reduced in all groups but was not significantly different between lutikizumab‐treated and placebo‐treated patients. Changes from baseline in MRI‐assessed synovitis at week 26 and other key symptom‐ and most structure‐related end points at weeks 26 and 52 were not significantly different between the lutikizumab and placebo groups. Injection site reactions, neutropenia, and discontinuations due to neutropenia were more frequent with lutikizumab versus placebo. Reductions in neutrophil and high‐sensitivity C‐reactive protein levels plateaued with lutikizumab 100 mg, with further reductions not observed with the 200 mg dose. Immunogenic response to lutikizumab did not meaningfully affect systemic lutikizumab concentrations. Conclusion: The limited improvement in the WOMAC pain score and the lack of synovitis improvement with lutikizumab, together with published results from trials of other IL‐1 inhibitors, suggest that IL‐1 inhibition is not an effective analgesic/antiinflammatory therapy in most patients with knee OA and associated synovitis

Lateral specialization in unilateral spatial neglect : a cognitive robotics model

In this paper, we present the experimental results of an embodied cognitive robotic approach for modelling the human cognitive deficit known as unilateral spatial neglect (USN). To this end, we introduce an artificial neural network architecture designed and trained to control the spatial attentional focus of the iCub robotic platform. Like the human brain, the architecture is divided into two hemispheres and it incorporates bio-inspired plasticity mechanisms, which allow the development of the phenomenon of the specialization of the right hemisphere for spatial attention. In this study, we validate the model by replicating a previous experiment with human patients affected by the USN and numerical results show that the robot mimics the behaviours previously exhibited by humans. We also simulated recovery after the damage to compare the performance of each of the two hemispheres as additional validation of the model. Finally, we highlight some possible advantages of modelling cognitive dysfunctions of the human brain by means of robotic platforms, which can supplement traditional approaches for studying spatial impairments in humans

Persistence and selection of an expanded B-cell clone in the setting of rituximab therapy for Sjögren's syndrome

Introduction: Subjects with primary Sjögren's syndrome (SjS) have an increased risk of developing B-cell lymphoma and may harbor monoclonal B-cell expansions in the peripheral blood. Expanded B-cell clones could be pathogenic, and their persistence could exacerbate disease or predispose toward the development of lymphoma. Therapy with anti-CD20 (rituximab) has the potential to eliminate expanded B-cell clones and thereby potentially ameliorate disease. This study was undertaken to identify and track expanded B-cell clones in the blood of subjects with primary SjS who were treated with rituximab.Methods: To determine whether circulating B-cell clones in subjects with primary SjS emerge or remain after B cell-depleting therapy with rituximab, we studied the antibody heavy-chain repertoire. We performed single-memory B-cell and plasmablast sorting and antibody heavy-chain sequencing in six rituximab-treated SjS subjects over the course of a 1-year follow-up period.Results: Expanded B-cell clones were identified in four out of the six rituximab-treated SjS subjects, based upon the independent amplification of sequences with identical or highly similar VH, DH, and JH gene segments. We identified one SjS subject with a large expanded B-cell clone that was present prior to therapy and persisted after therapy. Somatic mutations in the clone were numerous but did not increase in frequency over the course of the 1-year follow-up, suggesting that the clone had been present for a long period of time. Intriguingly, a majority of the somatic mutations in the clone were silent, suggesting that the clone was under chronic negative selection.Conclusions: For some subjects with primary SjS, these data show that (a) expanded B-cell clones are readily identified in the peripheral blood, (b) some clones are not eliminated by rituximab, and (c) persistent clones may be under chronic negative selection or may not be antigen-driven. The analysis of sequence variation among members of an expanded clone may provide a novel means of measuring the chronicity and selection of expanded B-cell populations in humans. © 2014 Hershberg et al.; licensee BioMed Central Ltd

Measurement of serum total and free prostate-specific antigen in women with colorectal carcinoma

We investigated the diagnostic value and the relationship with clinicopathological features of total and free prostate-specific antigen by measuring the concentrations of these markers in the sera of 75 women with colorectal carcinoma and in 30 healthy women. Measurements were performed by immunoradiometric assay which utilizes monoclonal and polyclonal anti-prostate-specific antigen antibodies; the lowest detection level for both markers was 0.01 ng ml−1. Free prostate-specific antigen levels were significantly higher in women with colorectal carcinoma than healthy women (P=0.006). The percentage of free prostate-specific antigen predominant (free prostate-specific antigen/total prostate-specific antigen >50%) subjects was 20% in colorectal carcinoma patients and 3.3% in healthy women (P=0.035). Cut-off values were 0.34 ng ml−1 for total prostate-specific antigen and 0.01 ng ml−1 for free prostate-specific antigen. In women with colorectal carcinoma, total prostate-specific antigen positivity was 20% and free prostate-specific antigen positivity was 34.6%. When compared to negatives, total prostate-specific antigen positive patients had a lower percentage of well-differentiated (P=0.056) and early stage (stages I and II) tumours (P=0.070). However, patients with predominant free prostate-specific antigen, had a higher percentage of well-differentiated (P=0.014) and early stage tumours (P=0.090) than patients with predominant bound prostate-specific antigen. In conclusion, although the sensitivity of free prostate-specific antigen predominancy is low (20%), in distinguishing women with colorectal carcinoma than healthy women, its specificity is high (96.7%). Free prostate-specific antigen predominancy tends to be present in less aggressive tumours. These findings may indicate clinical significance of preoperative measurement of serum total and free prostate-specific antigen in women with colorectal carcinoma

Prime movers : mechanochemistry of mitotic kinesins

Mitotic spindles are self-organizing protein machines that harness teams of multiple force generators to drive chromosome segregation. Kinesins are key members of these force-generating teams. Different kinesins walk directionally along dynamic microtubules, anchor, crosslink, align and sort microtubules into polarized bundles, and influence microtubule dynamics by interacting with microtubule tips. The mechanochemical mechanisms of these kinesins are specialized to enable each type to make a specific contribution to spindle self-organization and chromosome segregation