Condensation of the roots of real random polynomials on the real axis

We introduce a family of real random polynomials of degree n whose coefficients a_k are symmetric independent Gaussian variables with variance = e^{-k^\alpha}, indexed by a real \alpha \geq 0. We compute exactly the mean number of real roots for large n. As \alpha is varied, one finds three different phases. First, for 0 \leq \alpha \sim (\frac{2}{\pi}) \log{n}. For 1 < \alpha < 2, there is an intermediate phase where grows algebraically with a continuously varying exponent, \sim \frac{2}{\pi} \sqrt{\frac{\alpha-1}{\alpha}} n^{\alpha/2}. And finally for \alpha > 2, one finds a third phase where \sim n. This family of real random polynomials thus exhibits a condensation of their roots on the real line in the sense that, for large n, a finite fraction of their roots /n are real. This condensation occurs via a localization of the real roots around the values \pm \exp{[\frac{\alpha}{2}(k+{1/2})^{\alpha-1} ]}, 1 \ll k \leq n.Comment: 13 pages, 2 figure

Design of a single chamber air cathode microbial fuel cell using a stainless steel spiral anode and 3D printing techniques for continuous flow dye decolourisation

Microbial fuel cells (MFC) offer a novel solution in wastewater treatment systems. Their capacity for COD removal and concomitant electricity generation are highly attractive properties for reducing costs & environmental impacts in industry. MFCs require expensive membranes & catalysts such as Nafion and platinum respectively to achieve increased power output, but the cost of these materials is prohibitive for real world applications. An air breathing, 1 litre-scale spiral anode MFC was designed (Fig. 1) to provide a high electrode surface area to reactor volume ratio using commonly and cheaply available materials such as stainless steel and activated carbon. Non-platinum group metal catalysts (FeAAPyr family) were integrated into a PVDF cathode fabricated using single step phase inversion to improve rate of the oxygen reduction reaction. Anode surface area was maximized by concertina folding and spiral arrangement and its surface was modified using sulphuric acid, heat treatment & carbon black adsorption to provide a more biocompatible surface for biofilms. The performance characteristics of the designed MFC are currently being investigated. Decolourisation of Acid orange-7 azo dye & COD removal were initially investigated in recirculating batch mode followed by continuous flow configuration with a hydraulic retention time of 36 hours. Optimisation of hydraulic retention times, cathode construction & anode surface modification will present a feasible system for the scale up of microbial fuel cells for industrial use, maximizing COD removal & electricity production

Tracking Target Signal Strengths on a Grid using Sparsity

Multi-target tracking is mainly challenged by the nonlinearity present in the measurement equation, and the difficulty in fast and accurate data association. To overcome these challenges, the present paper introduces a grid-based model in which the state captures target signal strengths on a known spatial grid (TSSG). This model leads to \emph{linear} state and measurement equations, which bypass data association and can afford state estimation via sparsity-aware Kalman filtering (KF). Leveraging the grid-induced sparsity of the novel model, two types of sparsity-cognizant TSSG-KF trackers are developed: one effects sparsity through $\ell_1$-norm regularization, and the other invokes sparsity as an extra measurement. Iterative extended KF and Gauss-Newton algorithms are developed for reduced-complexity tracking, along with accurate error covariance updates for assessing performance of the resultant sparsity-aware state estimators. Based on TSSG state estimates, more informative target position and track estimates can be obtained in a follow-up step, ensuring that track association and position estimation errors do not propagate back into TSSG state estimates. The novel TSSG trackers do not require knowing the number of targets or their signal strengths, and exhibit considerably lower complexity than the benchmark hidden Markov model filter, especially for a large number of targets. Numerical simulations demonstrate that sparsity-cognizant trackers enjoy improved root mean-square error performance at reduced complexity when compared to their sparsity-agnostic counterparts.Comment: Submitted to IEEE Trans. on Signal Processin

Degradation of azo dyes (Acid orange 7) in a microbial fuel cell: comparison between anodic microbial-mediated reduction and cathodic laccase-mediated oxidation

Microbial fuel cells (MFCs) are a promising technology for the simultaneous treatment of wastewater and electricity production. With regard to azo-dye containing wastewater (e.g. from textile manufacturing), the dyes may be fed via the anode chamber containing electrochemically active bacteria or via the cathode chamber containing laccase enzyme as catalyst for oxygen reduction. This study investigated which of the two approaches is the best with regard to rate of decolourisation of the dye (Acid orange 7), COD reduction and electricity production. The power density was higher for the MFCdye at cathode (25 mW/m2, COD reduction 80%) compared with 18 mW/m2 (COD reduction 69%) for MFCdye at anode (Shewanella oneidensis as catalyst). The decolourisation rate of the dye was not statistically significant between the two approaches with ca. 75% decolourisation achieved in 24 h. The anodic dye degradation products were unstable when exposed to air resulting in what seems to be induced diazotization and regaining of colour. In case of degradation by laccase in the cathode chamber, the decolourisation products were stable and simpler in chemical structure (e.g. presence of aliphatic compounds) as determined by GC-MS. This work suggests that feeding azo dyes in cathode chambers of MFCs containing laccase is a better way of treating the dyes than the commonly used approach of feeding the dye in the anode chamber

Hybrid mutation particle swarm optimisation method for available transfer capability enhancement

A Hybrid Mutation Particle Swarm Optimisation (HMPSO) technique for improved estimation of Available Transfer Capacity (ATC) is proposed in this paper. This is achieved by firstly comparing a typical application of the Particle Swarm Optimisation (PSO) technique with conventional Genetic Algorithm (GA) methods. Secondly, a multi-objective optimisation problem concerning optimal installation and capacity allocation of Flexible AC Transmission Systems (FACTS) devices is presented and demonstrated. Modern heuristic techniques such as PSO have been demonstrated to be suitable in solving non-linear power systems problems. The outcome of this research further demonstrates that with better utilisation of FACTS devices it is possible to improve transmission capabilities. The motivation of this research is a direct consequence of the deregulation of electricity industries and markets worldwide. The current deregulated environment provides transmission systems operators (TSO) with more options when procuring transmission services. The effectiveness of the proposed algorithm is demonstrated across a range of case studies and the results are validated through analyses conducted on IEEE 30-bus and 57-bus test systems

Real roots of Random Polynomials: Universality close to accumulation points

We identify the scaling region of a width O(n^{-1}) in the vicinity of the accumulation points $t=\pm 1$ of the real roots of a random Kac-like polynomial of large degree n. We argue that the density of the real roots in this region tends to a universal form shared by all polynomials with independent, identically distributed coefficients c_i, as long as the second moment \sigma=E(c_i^2) is finite. In particular, we reveal a gradual (in contrast to the previously reported abrupt) and quite nontrivial suppression of the number of real roots for coefficients with a nonzero mean value \mu_n = E(c_i) scaled as \mu_n\sim n^{-1/2}.Comment: Some minor mistakes that crept through into publication have been removed. 10 pages, 12 eps figures. This version contains all updates, clearer pictures and some more thorough explanation

Circulating brain injury biomarkers increase after endoscopic surgery for pituitary tumors

Pituitary tumors and subsequent treatment with endoscopic transsphenoidal surgery (ETSS) may cause injury to suprasellar structures, causing long-term fatigue and neurocognitive impairment. A method to quantify brain injury after ETSS is not available. In this prospective, exploratory study of patients undergoing ETSS for pituitary tumors, a novel approach to detect possible neuronal damage is presented. Plasma concentrations of brain injury biomarkers (glial fibrillary acidic protein [GFAP], tau, and neurofilament light [NFL]) were measured the day before surgery, immediately after surgery, at day 1 and 5, and at 6 and 12 months after surgery, using enzyme-linked immunosorbent assays. The association between the increase of biomarkers with preoperative tumor extension and postoperative patient-perceived fatigue was evaluated. Suprasellar tumor extension was assessed from MRI scans, and self-perceived fatigue was assessed using the Multidimensional Fatigue Inventory before and 6 months after surgery. Thirty-five patients were included in the analysis. Compared to baseline, GFAP showed a maximal increase at day 1 after surgery (p = 0.0005), tau peaked postoperatively on the day of surgery (p = 0.019), and NFL reached its maximum at day 5 after surgery (p < 0.0001). The increase in GFAP correlated with preoperative chiasmal compression (p = 0.020). The increase in tau was correlated with preoperative chiasmal (p = 0.011) and hypothalamus compression (p = 0.016), and fatigue score 6 months after surgery (p = 0.016). In conclusion, the concentrations of brain injury biomarkers in blood increased after ETSS for pituitary tumors. The results indicate that postoperative plasma GFAP and tau might reflect astroglial and neuronal damage after ETSS

Designing an information system for updating land records in Bangladesh: action design ethnographic research (ADER)

Open Access. This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution, and reproduction in any medium, provided the original author(s) and the source are credited.This article has been made available through the Brunel Open Access Publishing Fund.Information Systems (IS) has developed through adapting, generating and applying diverse methodologies, methods, and techniques from reference disciplines. Further, Action Design Research (ADR) has recently developed as a broad research method that focuses on designing and redesigning IT and IS in organizational contexts. This paper reflects on applying ADR in a complex organizational context in a developing country. It shows that ADR requires additional lens for designing IS in such a complex organizational context. Through conducting ADR, it is seen that an ethnographic framework has potential complementarities for understanding complex contexts thereby enhancing the ADR processes. This paper argues that conducting ADR with an ethnographic approach enhances design of IS and organizational contexts. Finally, this paper aims presents a broader methodological framework, Action Design Ethnographic Research (ADER), for designing artefacts as well as IS. This is illustrated through the case of a land records updating service in Bangladesh

Early changes in biochemical markers of bone formation during teriparatide therapy correlate with improvements in vertebral strength in men with glucocorticoid-induced osteoporosis

Summary: Changes of the bone formation marker PINP correlated positively with improvements in vertebral strength in men with glucocorticoid-induced osteoporosis (GIO) who received 18-month treatment with teriparatide, but not with risedronate. These results support the use of PINP as a surrogate marker of bone strength in GIO patients treated with teriparatide. Introduction: To investigate the correlations between biochemical markers of bone turnover and vertebral strength estimated by finite element analysis (FEA) in men with GIO. Methods: A total of 92 men with GIO were included in an 18-month, randomized, open-label trial of teriparatide (20 μg/day, n = 45) and risedronate (35 mg/week, n = 47). High-resolution quantitative computed tomography images of the 12th thoracic vertebra obtained at baseline, 6 and 18 months were converted into digital nonlinear FE models and subjected to anterior bending, axial compression and torsion. Stiffness and strength were computed for each model and loading mode. Serum biochemical markers of bone formation (amino-terminal-propeptide of type I collagen [PINP]) and bone resorption (type I collagen cross-linked C-telopeptide degradation fragments [CTx]) were measured at baseline, 3 months, 6 months and 18 months. A mixed-model of repeated measures analysed changes from baseline and between-group differences. Spearman correlations assessed the relationship between changes from baseline of bone markers with FEA variables. Results: PINP and CTx levels increased in the teriparatide group and decreased in the risedronate group. FEA-derived parameters increased in both groups, but were significantly higher at 18 months in the teriparatide group. Significant positive correlations were found between changes from baseline of PINP at 3, 6 and 18 months with changes in FE strength in the teriparatide-treated group, but not in the risedronate group. Conclusions: Positive correlations between changes in a biochemical marker of bone formation and improvement of biomechanical properties support the use of PINP as a surrogate marker of bone strength in teriparatide-treated GIO patients