Simple and Nearly Optimal Polynomial Root-finding by Means of Root Radii Approximation

We propose a new simple but nearly optimal algorithm for the approximation of all sufficiently well isolated complex roots and root clusters of a univariate polynomial. Quite typically the known root-finders at first compute some crude but reasonably good approximations to well-conditioned roots (that is, those isolated from the other roots) and then refine the approximations very fast, by using Boolean time which is nearly optimal, up to a polylogarithmic factor. By combining and extending some old root-finding techniques, the geometry of the complex plane, and randomized parametrization, we accelerate the initial stage of obtaining crude to all well-conditioned simple and multiple roots as well as isolated root clusters. Our algorithm performs this stage at a Boolean cost dominated by the nearly optimal cost of subsequent refinement of these approximations, which we can perform concurrently, with minimum processor communication and synchronization. Our techniques are quite simple and elementary; their power and application range may increase in their combination with the known efficient root-finding methods.Comment: 12 pages, 1 figur

Terrestrial water load and groundwater fluctuation in the Bengal Basin

Groundwater-level fluctuations represent hydraulic responses to changes in groundwater storage due to aquifer recharge and drainage as well as to changes in stress that include water mass loading and unloading above the aquifer surface. The latter ‘poroelastic’ response of confined aquifers is a well-established phenomenon which has been demonstrated in diverse hydrogeological environments but is frequently ignored in assessments of groundwater resources. Here we present high-frequency groundwater measurements over a twelve-month period from the tropical, fluvio-deltaic Bengal Aquifer System (BAS), the largest aquifer in south Asia. The groundwater level fluctuations are dominated by the aquifer poroelastic response to changes in terrestrial water loading by processes acting over periods ranging from hours to months; the effects of groundwater flow are subordinate. Our measurements represent the first direct, quantitative identification of loading effects on groundwater levels in the BAS. Our analysis highlights the potential limitations of hydrogeological analyses which ignore loading effects in this environment. We also demonstrate the potential for employing poroelastic responses in the BAS and across other tropical fluvio-deltaic regions as a direct, in-situ measure of changes in terrestrial water storage to complement analyses from the Gravity and Climate Experiment (GRACE) mission but at much higher resolution

Testing the cognitive-behavioural maintenance models across DSM-5 bulimic-type eating disorder diagnostic groups: A multi-centre study

The original cognitive-behavioural (CB) model of bulimia nervosa, which provided the basis for the widely used CB therapy, proposed that specific dysfunctional cognitions and behaviours maintain the disorder. However, amongst treatment completers, only 40–50 % have a full and lasting response. The enhanced CB model (CB-E), upon which the enhanced version of the CB treatment was based, extended the original approach by including four additional maintenance factors. This study evaluated and compared both CB models in a large clinical treatment seeking sample (N = 679), applying both DSM-IV and DSM-5 criteria for bulimic-type eating disorders. Application of the DSM-5 criteria reduced the number of cases of DSM-IV bulimic-type eating disorders not otherwise specified to 29.6 %. Structural equation modelling analysis indicated that (a) although both models provided a good fit to the data, the CB-E model accounted for a greater proportion of variance in eating-disordered behaviours than the original one, (b) interpersonal problems, clinical perfectionism and low self-esteem were indirectly associated with dietary restraint through over-evaluation of shape and weight, (c) interpersonal problems and mood intolerance were directly linked to binge eating, whereas restraint only indirectly affected binge eating through mood intolerance, suggesting that factors other than restraint may play a more critical role in the maintenance of binge eating. In terms of strength of the associations, differences across DSM-5 bulimic-type eating disorder diagnostic groups were not observed. The results are discussed with reference to theory and research, including neurobiological findings and recent hypotheses

Impairment of Auditory-Motor Timing and Compensatory Reorganization after Ventral Premotor Cortex Stimulation

Integrating auditory and motor information often requires precise timing as in speech and music. In humans, the position of the ventral premotor cortex (PMv) in the dorsal auditory stream renders this area a node for auditory-motor integration. Yet, it remains unknown whether the PMv is critical for auditory-motor timing and which activity increases help to preserve task performance following its disruption. 16 healthy volunteers participated in two sessions with fMRI measured at baseline and following rTMS (rTMS) of either the left PMv or a control region. Subjects synchronized left or right finger tapping to sub-second beat rates of auditory rhythms in the experimental task, and produced self-paced tapping during spectrally matched auditory stimuli in the control task. Left PMv rTMS impaired auditory-motor synchronization accuracy in the first sub-block following stimulation (p<0.01, Bonferroni corrected), but spared motor timing and attention to task. Task-related activity increased in the homologue right PMv, but did not predict the behavioral effect of rTMS. In contrast, anterior midline cerebellum revealed most pronounced activity increase in less impaired subjects. The present findings suggest a critical role of the left PMv in feed-forward computations enabling accurate auditory-motor timing, which can be compensated by activity modulations in the cerebellum, but not in the homologue region contralateral to stimulation

Kinetic modelling of competition and depletion of shared miRNAs by competing endogenous RNAs

Non-conding RNAs play a key role in the post-transcriptional regulation of mRNA translation and turnover in eukaryotes. miRNAs, in particular, interact with their target RNAs through protein-mediated, sequence-specific binding, giving rise to extended and highly heterogeneous miRNA-RNA interaction networks. Within such networks, competition to bind miRNAs can generate an effective positive coupling between their targets. Competing endogenous RNAs (ceRNAs) can in turn regulate each other through miRNA-mediated crosstalk. Albeit potentially weak, ceRNA interactions can occur both dynamically, affecting e.g. the regulatory clock, and at stationarity, in which case ceRNA networks as a whole can be implicated in the composition of the cell's proteome. Many features of ceRNA interactions, including the conditions under which they become significant, can be unraveled by mathematical and in silico models. We review the understanding of the ceRNA effect obtained within such frameworks, focusing on the methods employed to quantify it, its role in the processing of gene expression noise, and how network topology can determine its reach.Comment: review article, 29 pages, 7 figure

Mapping interactions with the chaperone network reveals factors that protect against tau aggregation.

A network of molecular chaperones is known to bind proteins ('clients') and balance their folding, function and turnover. However, it is often unclear which chaperones are critical for selective recognition of individual clients. It is also not clear why these key chaperones might fail in protein-aggregation diseases. Here, we utilized human microtubule-associated protein tau (MAPT or tau) as a model client to survey interactions between ~30 purified chaperones and ~20 disease-associated tau variants (~600 combinations). From this large-scale analysis, we identified human DnaJA2 as an unexpected, but potent, inhibitor of tau aggregation. DnaJA2 levels were correlated with tau pathology in human brains, supporting the idea that it is an important regulator of tau homeostasis. Of note, we found that some disease-associated tau variants were relatively immune to interactions with chaperones, suggesting a model in which avoiding physical recognition by chaperone networks may contribute to disease

Relevance of BCAR4 in tamoxifen resistance and tumour aggressiveness of human breast cancer

Background:Breast cancer anti-oestrogen resistance 4 (BCAR4) was identified in a search for genes involved in anti-oestrogen resistance in breast cancer. We explored whether BCAR4 is predictive for tamoxifen resistance and prognostic for tumour aggressiveness, and studied its function.Methods:BCAR4 mRNA levels were measured in primary breast tumours, and evaluated for association with progression-free survival (PFS) and clinical benefit in patients with oestrogen receptor (ERα)-positive tumours receiving tamoxifen as first-line monotherapy for advanced disease. In a separate cohort of patients with lymph node-negative, ERα-positive cancer, and not receiving systemic adjuvant therapy, BCAR4 levels were evaluated for association with distant metastasis-free survival (MFS). The function of BCAR4 was studied with immunoblotting and RNA interference in a cell model.Results:Multivariate analyses established high BCAR4 mRNA levels as an independent predictive factor for poor PFS after start of tamoxifen therapy for recurrent disease. High BCAR4 mRNA levels were associated with poor MFS and overall survival, reflecting tumour aggressiveness. In BCAR4-expressing cells, phosphorylation of v-erb-b2 erythroblastic leukaemia viral oncogene homolog (ERBB)2, ERBB3, and their downstream mediators extracellular signal-regulated kinase 1/2 and v-akt murine thymoma viral oncogene homolog (AKT) 1/2, was increased. Selective knockdown of ERBB2 or ERBB3 inhibited proliferation, confirming their role in BCAR4-induced tamoxifen resistance.Conclusion:BCAR4 may have clinical relevance for tumour aggressiveness and tamoxifen resistance. Our cell model suggests that BCAR4-positive breast tumours are driven by ERBB2/ERBB3 signalling. Patients with such tumours may benefit from ERBB-targeted therapy

Effect of Cry1Ab Protein on Rhizobacterial Communities of Bt-Maize over a Four-Year Cultivation Period

Background: Bt-maize is a transgenic variety of maize expressing the Cry toxin from Bacillus turingiensis. The potential accumulation of the relative effect of the transgenic modification and the cry toxin on the rhizobacterial communities of Btmaize has been monitored over a period of four years. Methodology/Principal Findings: The accumulative effects of the cultivation of this transgenic plant have been monitored by means of high throughput DNA pyrosequencing of the bacterial DNA coding for the 16S rRNA hypervariable V6 region from rhizobacterial communities. The obtained sequences were subjected to taxonomic, phylogenetic and taxonomicindependent diversity studies. The results obtained were consistent, indicating that variations detected in the rhizobacterial community structure were possibly due to climatic factors rather than to the presence of the Bt-gene. No variations were observed in the diversity estimates between non-Bt and Bt-maize. Conclusions/Significance: The cultivation of Bt-maize during the four-year period did not change the maize rhizobacterial communities when compared to those of the non-Bt maize. This is the first study to be conducted with Bt-maize during such a long cultivation period and the first evaluation of rhizobacterial communities to be performed in this transgenic plant using Next Generation Sequencing

Mathematical model describing erythrocyte sedimentation rate. Implications for blood viscosity changes in traumatic shock and crush syndrome

BACKGROUND: The erythrocyte sedimentation rate (ESR) is a simple and inexpensive laboratory test, which is widespread in clinical practice, for assessing the inflammatory or acute response. This work addresses the theoretical and experimental investigation of sedimentation a single and multiple particles in homogeneous and heterogeneous (multiphase) medium, as it relates to their internal structure (aggregation of solid or deformed particles). METHODS: The equation system has been solved numerically. To choose finite analogs of derivatives we used the schemes of directional differences. RESULTS: (1) Our model takes into account the influence of the vessel wall on group aggregation of particles in tubes as well as the effects of rotation of particles, the constraint coefficient, and viscosity of a mixture as a function of the volume fraction. (2) This model can describe ESR as a function of the velocity of adhesion of erythrocytes; (3) Determination of the ESR is best conducted at certain time intervals, i.e. in a series of periods not exceeding 5 minutes each; (4) Differential diagnosis of various diseases by means of ESR should be performed using the aforementioned timed measurement of ESR; (5) An increase in blood viscosity during trauma results from an increase in rouleaux formation and the time-course method of ESR will be useful in patients with trauma, in particular, with traumatic shock and crush syndrome. CONCLUSION: The mathematical model created in this study used the most fundamental differential equations that have ever been derived to estimate ESR. It may further our understanding of its complex mechanism