Time Tau Research Articles

Comparison of topological charge definitions in Lattice QCD

In this paper, we show a comparison of different definitions of the topological charge on the lattice. We concentrate on one small-volume ensemble with 2 flavours of dynamical, maximally twisted mass fermions and use three more ensembles to analyze the approach to the continuum limit. We investigate several fermionic and gluonic definitions. The former include the index of the overlap Dirac operator, the spectral flow of the Wilson–Dirac operator and the spectral projectors. For the latter, we take into account different discretizations of the topological charge operator and various smoothing schemes to filter out ultraviolet fluctuations: the gradient flow, stout smearing, APE smearing, HYP smearing and cooling. We show that it is possible to perturbatively match different smoothing schemes and provide a well-defined smoothing scale. We relate the smoothing parameters for cooling, stout and APE smearing to the gradient flow time tau . In the case of hypercubic smearing the matching is performed numerically. We investigate which conditions have to be met to obtain a valid definition of the topological charge and susceptibility and we argue that all valid definitions are highly correlated and allow good control over topology on the lattice.

Relaxation dynamics and crystallization study of glass-forming chiral-nematic liquid crystal S,S-2,7-bis(4-pentylphenyl)-9,9-dimethylbutyl 9H-fluorene (5P-Am*FLAm*-P5)

.The chiral nematic S,S-2,7-bis(4-pentylphenyl)-9,9-dimethylbutyl9H-fluorene (5P-Am*FLAm*-P5) liquid crystal shows a complex phase diagram strongly dependent on thermal treatment as identified by Polarizing Optical Microscopy (POM) and differential scanning calorimeter (DSC). The molecular dynamics in various thermodynamics states was studied by means of broadband dielectric spectroscopy (BDS). The vitrification of a chiral nematic phase (N*) is manifested by a Vogel-Fulcher-Tammann (VFT)-type temperature dependence of structural relaxation time (tau_{alpha}). Three dielectric relaxation processes exhibiting Arrhenius-like thermal activation were found in conformationally disordered (condis) Cr1 and Cr2 structures. The isothermal cold crystallization process of Cr2 occurs in the metastable N* phase; however, in the non-isothermal experiments, the Cr2 phase is formed in the isotropic phase obtained on heating the metastable N* phase. The findings for the isothermal process were compared with those regarding non-isothermal crystallization.Graphical abstract

Поляризованная флуоресценция молекул NADH при двухфотонном возбуждении фемтосекундными лазерными импульсами с длиной волны 720-780 nm

The decay of polarized fluorescence in coenzyme NADH upon two-photon excitation by femtosecond laser pulses at the wavelength range of 720- 780 nm in water/methanol solution has been investigated. Decay fluorescence times tau_1 and tau_2, rotation diffusion time tau_rot, and preexponential factors a_1/a_2 ratio have been determined from experiment. The results obtained have been compared with previous results in NADH in aqueous solution. polarized fluorescence, NADH, adenine, nicotinamide, spectroscopy, time correlation single photon spectroscopy

102. Address the dosimetry in radiometabolic therapy; relationship between dosimetric value and clinical parameters in differentiated thyroid cancer

Purpose Use rationally the Red Marrow (RM) and Whole Body (WB) dosimetry pre and during therapy in Differentiated Thyroid Cancer (DTC) focalinzing the relationship between clinical parameters. Methods We enrolled 120 patients (278 dosimetries-196 with complete clinical data) with DTC (March 2012–December 2017). We made double dosimetric study the week before the therapy (19 MBq 131I) and during therapy (range 1019–9342 MBq, mean 6253 MBq, median 6208 MBq), collecting serial blood samples and WB counts according to the AIFM Italian dosimetric protocol and EANM SOP. With a simple regression analysis, we studied the capability of residence times (tau) and mGy/MBq (RM and WB) to predict the respective post therapy values (Fig. 1). We moreover considered a multivariate multiple regression model to control for clinical values (sex, age, histology, variant, multifocality, bilaterality, Tsh Ipo, Tg Ipo, FT4, staging and another tumour). Results All the variables pre-treatment have a significant role in explaining the levels of the corresponding variables post-treatment (Fig. 1). For all the variables, a PRE unitary increase determines a much smaller increase in post values (from 0.3 to 0.5). When considering all the variables as possible predictors (Table 1), none of them seems to have an effect on WBposttau, apart from WBpretau. For RMposttau, instead, we found correlation with RMpretau, WBpretau, age and the presence of another tumour. Concerning WBpostmGyMBq and RMpostmGyMBq, both appear to be reduced for N1b staging; WBpostmGyMBq reduced for advanced tumours and increased for large values of WBpretau. RMpostmGyMBq increases with age and RMpretau. A large parte of the total variability of WBpostmGyMBq and RMpostmGyMBq remains unexplained. Conclusions Dosimetry connected with clinical values could be a useful tool to help in patient management to predict behaviour and efficacy. Mandatory next step is to study follow up. Download : Download high-res image (220KB) Download : Download full-size image

The Reissner\u2013Nordstr\xf6m black hole with the fastest relaxation rate

Numerous numerical investigations of the quasinormal resonant spectra of Kerr-Newman black holes have revealed the interesting fact that the characteristic relaxation times tau ({bar{a}},{bar{Q}}) of these canonical black-hole spacetimes can be described by a two-dimensional function {{bar{tau }}}equiv tau /M which increases monotonically with increasing values of the dimensionless angular-momentum parameter {bar{a}}equiv J/M^2 and, in addition, is characterized by a non-trivial (non-monotonic) functional dependence on the dimensionless charge parameter {bar{Q}}equiv Q/M. In particular, previous numerical investigations have indicated that, within the family of spherically symmetric charged Reissner–Nordström spacetimes, the black hole with {bar{Q}}simeq 0.7 has the fastest relaxation rate. In the present paper we use analytical techniques in order to investigate this intriguing non-monotonic functional dependence of the Reissner–Nordström black-hole relaxation rates on the dimensionless physical parameter {bar{Q}}. In particular, it is proved that, in the eikonal (geometric-optics) regime, the black hole with {bar{Q}}={{sqrt{51-3sqrt{33}}}over {8}}simeq 0.73 is characterized by the fastest relaxation rate (the smallest dimensionless relaxation time {{bar{tau }}}) within the family of charged Reissner–Nordström black-hole spacetimes.

Chronic Sleep Disruption Advances the Temporal Progression of Tauopathy in P301S Mutant Mice.

Brainstem locus ceruleus neurons (LCn) are among the first neurons across the lifespan to evidence tau pathology, and LCn are implicated in tau propagation throughout the cortices. Yet, events influencing LCn tau are poorly understood. Activated persistently across wakefulness, LCn experience significant metabolic stress in response to chronic short sleep (CSS). Here we explored whether CSS influences LCn tau and the biochemical, neuroanatomical, and/or behavioral progression of tauopathy in male and female P301S mice. CSS in early adult life advanced the temporal progression of neurobehavioral impairments and resulted in a lasting increase in soluble tau oligomers. Intriguingly, CSS resulted in an early increase in AT8 and MC1 tau pathology in the LC. Over time tau pathology, including tangles, was evident in forebrain tau-vulnerable regions. Sustained microglial and astrocytic activation was observed as well. Remarkably, CSS resulted in significant loss of neurons in the two regions examined: the basolateral amygdala and LC. A second, distinct form of chronic sleep disruption, fragmentation of sleep, during early adult life also increased tau deposition and imparted early neurobehavioral impairment. Collectively, the findings demonstrate that early life sleep disruption has important lasting effects on the temporal progression in P301S mice, influencing tau pathology and hastening neurodegeneration, neuroinflammation, and neurobehavioral impairments.SIGNIFICANCE STATEMENT Chronic short sleep (CSS) is pervasive in modern society. Here, we found that early life CSS influences behavioral, biochemical, and neuroanatomic aspects of the temporal progression of tauopathy in a mouse model of the P301S tau mutation. Specifically, CSS hastened the onset of motor impairment and resulted in a greater loss of neurons in both the locus ceruleus and basolateral/lateral amygdala. Importantly, despite a protracted recovery opportunity after CSS, mice evidenced a sustained increase in pathogenic tau oligomers, and increased pathogenic tau in the locus ceruleus and limbic system nuclei. These findings unveil early life sleep habits as an important determinant in the progression of tauopathy.

Geometry of distribution-constrained optimal stopping problems

We adapt ideas and concepts developed in optimal transport (and its martingale variant) to give a geometric description of optimal stopping times tau of Brownian motion subject to the constraint that the distribution of tau is a given probability mu . The methods work for a large class of cost processes. (At a minimum we need the cost process to be measurable and (mathcal {F}^0_{t})_{t ge 0}-adapted. Continuity assumptions can be used to guarantee existence of solutions.) We find that for many of the cost processes one can come up with, the solution is given by the first hitting time of a barrier in a suitable phase space. As a by-product we recover classical solutions of the inverse first passage time problem/Shiryaev’s problem.

The Distance between N and C Termini of Tau and of FTDP-17 Mutants Is Modulated by Microtubule Interactions in Living Cells.

The microtubule (MT)-associated protein Tau is a natively unfolded protein, involved in a number of neurodegenerative disorders, collectively called tauopathies, aggregating in neurofibrillary tangles (NFT). It is an open question how the conversion from a MT bound molecule to an aggregation-prone Tau species occurs and, also, if and how tauopathy-related mutations affect its behavior in the cell. To address these points, we exploited a genetically encoded FRET sensor based on the full length Tau protein, to monitor in real time Tau conformational changes in different conditions in live cells. By studying the FRET signal we found that soluble Tau molecules, detached from MTs, display an unfolded structure. On the contrary, we observed an increased FRET signal generated by Tau monomers bound to MT, indicating that the association with MTs induced a folding of Tau protein, decreasing the distance between its N and C termini. We exploited the FRET sensor to investigate the impact of FTDP-17 mutations and of phosphorylation-site mutations on Tau folding and mobility in live cells. We demonstrated that the FTDP-17 Tau mutations weaken the interaction of Tau with cellular MTs, shifting the equilibrium towards the soluble pool while, conversely, phosphorylation site mutations shift the equilibrium of Tau towards the MT-bound state and a more closed conformation.

Optical turbulence forecast: ready for an operational application

One of the main goals of the feasibility study MOSE (MOdellig ESO Sites) is to evaluate the performances of a method conceived to forecast the optical turbulence above the ESO sites of the Very Large Telescope and the European-Extremely Large Telescope in Chile. The method implied the use of a dedicated code conceived for the optical turbulence (OT) called Astro-Meso-Nh. In this paper we present results we obtained at conclusion of this project concerning the performances of this method in forecasting the most relevant parameters related to the optical turbulence (CN2, seeing , isoplanatic angle theta_0 and wavefront coherence time tau_0). Numerical predictions related to a very rich statistical sample of nights uniformly distributed along a solar year and belonging to different years have been compared to observations and different statistical operators have been analyzed such as classical bias, RMSE and and more sophisticated statistical operators derived by the contingency tables that are able to quantify the score of success of a predictive method such as the percentage of correct detection (PC) and the probability to detect a parameter within a specific range of values (POD). The main conclusions of the study tell us that the Astro-Meso-Nh model provides performances that are already very good to definitely guarantee a not negligible positive impact on the Service Mode of top-class telescopes and ELTs. A demonstrator for an automatic and operational version of the Astro-Meso-Nh model will be soon implemented on the sites of VLT and E-ELT.

Decaying dark matter: the case for a deep X-ray observation of Draco

Recent studies of M31, the Galactic Centre (GC), and galaxy clusters have made tentative detections of an X-ray line at similar to 3.5 keV that could be produced by decaying dark matter. We use high-resolution simulations of the Aquarius project to predict the likely amplitude of the X-ray decay flux observed in the GC relative to that observed in M31, and also of the GC relative to other parts of the Milky Way halo and to dwarf spheroidal galaxies. We show that the reported detections from M31 and the GC are compatible with each other, and with upper limits arising from high galactic latitude observations, and imply a decay time tau similar to 10(28) s. We argue that this interpretation can be tested with deep observations of dwarf spheroidal galaxies: in 95 per cent of our mock observations, a 1.3 Ms pointed observation of Draco with XMM-Newton will enable us to discover or rule out at the 3 sigma level an X-ray feature from dark matter decay at 3.5 keV, for decay times tau < 0.8 x 10(28) s.

Ageing single file motion

The mean squared displacement of a tracer particle in a single file of identical particles with excluded volume interactions shows the famed Harris scaling aEurox (2)(t)aEuro parts per thousand a parts per thousand integral K (1/2) t (1/2) as function of time. Here we study what happens to this law when each particle of the single file interacts with the environment such that it is transiently immobilised for times tau with a power-law distribution psi(tau) a parts per thousand integral (tau(a similar to...))(alpha), and different ranges of the exponent alpha are considered. We find a dramatic slow-down of the motion of a tracer particle from Harris' law to an ultraslow, logarithmic time evolution aEurox (2)(t)aEuro parts per thousand a parts per thousand integral K (0) log (1/2)(t) when 0 < alpha < 1. In the intermediate case 1 < alpha < 2, we observe a power-law form for the mean squared displacement, with a modified scaling exponent as compared to Harris' law. Once alpha is larger than two, the Brownian single file behaviour and thus Harris' law are restored. We also point out that this process is weakly non-ergodic in the sense that the time and ensemble averaged mean squared displacements are disparate.

Abstract 20209: Spontaneous Post Myocardial Infarction Arrhythmia is Potentiated by Calcium Alternans in Type I Diabetic Akita Mice

Introduction: Myocardial infarction (MI) is the most common cause of mortality in diabetes. Diabetics have been shown to be twice as likely to die suddenly from MI out of hospital compared to non diabetic patients. The mechanism of sudden death in the diabetic population is unclear. Here we use the Akita Type I diabetic mouse as an animal model for the study of post MI ventricular tachycardia arrhythmias (VT) and the role of abnormalities of Ca2+ homeostasis in the pathogenesis of post MI VT. Methods: To determine the effect of MI on the incidence of VT, EKG transmitters were implanted into WT and Akita mice. MIs were generated by permanent ligation of the left coronary artery resulting in infarctions affecting more than 30% of the LV as demonstrated by echocardiographic analysis and TTC staining. Dual calcium-voltage optical mapping was performed on the isolated Langendorf heart after MI. Left ventricular myocytes were isolated for calcium imaging studies. Sarcomere shortening and Ca2+transients were measured by Ionoptix system and Ca2+ sparks by confocal microscopy. Results: Compared to WT, Akita diabetic mice developed a high incidence of non sustained and sustained VT in the first 30h post MI peaking at 18 h. Epicardial optical mapping demonstrated pacing induced: Ca2+ alternans which was most marked in the peri-infarction zone of Akitas and VT also originating in the peri-infarction zone in the Akita mice, but not in WT. Single cardiomyocytes from Akita displayed both contractile and Ca2+ alternans when pacing rate was increased above 3Hz, but none in cells from WT mice. Ca2+ imaging studies were performed to determine whether alterations in Sacroplasmic reticulum(SR) Ca2+ function contributes to Ca2+ alternans. In Akita myocytes, Ca2+ transient decay time( Tau) was significantly increased ( 0.171±0.01s, N=23 ) compared to WT(0.139±0.007s, N=20, P&lt;0.05), The frequency of spontaneous Ca2+ sparks in Akita mocytes increased from 0.043 ± 0.003 sparks/100μm/s (N=23) in the WT to 0.266 ± 0.023 sparks/100μm/s ( P&lt;0.05, N=36). Conclusions: The type 1 diabetic Akita mice demonstrate a high incidence of spontaneous post MI VT associated with pronounced Ca2+ alternans in the peri-infarction zone and abnormalities of Ca2+ homeostasis.

Characterization of tau oligomeric seeds in progressive supranuclear palsy.

BackgroundProgressive supranuclear palsy (PSP) is a neurodegenerative tauopathy which is primarily defined by the deposition of tau into globose-type neurofibrillary tangles (NFT). Tau in its native form has important functions for microtubule dynamics. Tau undergoes alternative splicing in exons 2, 3, and 10 which results in six different isoforms. Products of splicing on exon 10 are the most prone to mutations. Three repeat (3R) and four repeat (4R) tau, like other disease-associated amyloids, can form oligomers which may then go on to further aggregate and form fibrils. Recent studies from our laboratory and others have provided evidence that tau oligomers, not NFTs, are the most toxic species in neurodegenerative tauopathies and seed the pathological spread of tau.ResultsAnalysis of PSP brain sections revealed globose-type NFTs, as well as both phosphorylated and unphosphorylated tau oligomers. Analysis of PSP brains via Western blot and ELISA revealed the presence of increased levels of tau oligomers compared to age-matched control brains. Oligomers were immunoprecipitated from PSP brain and were capable of seeding the oligomerization of both 3R and 4R tau isoforms.ConclusionsThis is the first time tau oligomers have been characterized in PSP. These results indicate that tau oligomers are an important component of PSP pathology, along with NFTs. The ability of PSP brain-derived tau oligomers to seed 3R and 4R tau suggests that these oligomers represent the pathological species responsible for disease propagation and the presence of oligomers in a pure neurodegenerative tauopathy implies a common neuropathological process for tau seen in diseases with other amyloid proteins.

Analysis on RF Parameters of Nanoscale Tunneling Field-Effect Transistor Based on InAs/InGaAs/InP Heterojunctions

Tunneling field-effect transistors (TFETs) based on the quantum mechanical band-to-band tunneling (BTBT) have advantages such as low off-current and subthreshold swing (S) below 60 mV/dec at room temperature. For these reasons, TFETs are considered as promising devices for low standby power (LSTP) applications. On the other hand, silicon (Si)-based TFETs have a drawback in low on-state current (lon) drivability. In this work, we suggest a gate-all-around (GAA) TFET based on compound semiconductors to improve device performances. The proposed device materials consist of InAs (source), InGaAs (channel), and InP (drain). According to the composition (x) of Ga in In1-xGa(x)As layer of the channel region, simulated devices have been investigated in terms of both direct-current (DC) and RF parameters including tunneling rate, transconductance (g(m)), gate capacitance (Cg), intrinsic delay time (tau), cut-off frequency (fT) and maximum oscillation frequency (f(max)). In this study, the obtained maximum values of tau, fT, and f(max) for GAA InAs/In0.9Ga0.1As/InP heterojunction TFET were 21.2 fs, 7 THz, and 18 THz, respectively.

Effect of Adjacent Bit-Line Cell Interference on Low Frequency Noise in NAND Flash Memory Cell Strings

The effect of adjacent bit-line (BL) interference on low frequency in 26 nm NAND flash memory was characterized. With the program (P) and erase (E) states of adjacent cells, current fluctuation (deltaI(BL)) and corner frequency (f(c)) of Lorentzian spectrum were changed. DeltaI(BL) due to RTN ranges from approximately 67.3 nA to approximately 45.9 nA with 4 different modes (P/P, P/E, E/P, E/E) of the state of adjacent cells and f(c) ranges from 48 Hz to 89 Hz. Using measured deltaI(BL) and extracted capture (tau(c)) and emission times (tau(e)) with 4 different modes, we calculated tau and f(c), and extracted the position of a trap in the channel width direction with deltaI(BL) and simulated data. The calculated data showed excellent agreement with measured spectra. Finally, we prepared energy band diagrams in P/P and P/E modes using 3-D device simulation and clarified the effect of adjacent bit-line cell interference. The control gate bias is slightly higher in P/P mode than P/E mode, and then trap energy in P/P mode is relatively lower than that in P/E mode, resulting in shorter capture time in P/P mode.

Annealing-induced magnetic moments detected by spin precession measurements in epitaxial graphene on SiC

We present results of non-local and three terminal (3T) spin precession measurements on spin injection devices fabricated on epitaxial graphene on SiC. The measurements were performed before and after an annealing step at 150 degrees Celsius for 15 minutes in vacuum. The values of spin relaxation length L_s and spin relaxation time tau_s obtained after annealing are reduced by a factor 2 and 4, respectively, compared to those before annealing. An apparent discrepancy between spin diffusion constant D_s and charge diffusion constant D_c can be resolved by investigating the temperature dependence of the g-factor, which is consistent with a model for paramagnetic magnetic moments.

Dynamic heterogeneities above and below the mode-coupling temperature: Evidence of a dynamic crossover

We examine dynamic heterogeneities in a model glass-forming fluid, a binary harmonic sphere mixture, above and below the mode-coupling temperature T(c). We calculate the ensemble independent susceptibility χ4(τ(α)) and the dynamic correlation length ξ4(τ(α)) at the α-relaxation time τ(α). We also examine in detail the temperature dependence of τ(α) and the diffusion coefficient D. For higher temperatures, we find that the standard Stokes-Einstein relationship, D∼τ(α)(-1), holds, but at lower temperatures a fractional Stokes-Einstein relationship, D∼τ(α)(-σ) with σ = 0.65, emerges. By examining the relationships between τ(α), D, χ4(τ(α)), and ξ4(τ(α)) we determine that the emergence of the fractional Stokes-Einstein relationship is accompanied by a dynamic crossover from τ(α)∼e(k2ξ4) at higher temperatures to τ(α)∼e(k1ξ4(3/2)) at lower temperatures.

On the Robust Optimal Stopping Problem

We study a robust optimal stopping problem with respect to a set P of mutually singular probabilities. This can be interpreted as a zero-sum controller-stopper game in which the stopper is trying to maximize its pay-off while an adverse player wants to minimize this payoff by choosing an evaluation criteria from P. We show that the upper Snell envelope Z of the reward process Y is a supermartingale with respect to an appropriately defined nonlinear expectation E, and Z is further an E-martingale up to the first time tau when Z meets Y . Consequently, tau is the optimal stopping time for the robust optimal stopping problem and the corresponding zero-sum game has a value. Although the result seems similar to the one obtained in the classical optimal stopping theory, the mutual singularity of probabilities and the game aspect of the problem give rise to major technical hurdles, which we circumvent using some new methods.

Superparamagnetic State by Linear and Non-Linear AC Magnetic Susceptibility in Mn&lt;SUB&gt;0.5&lt;/SUB&gt;Zn&lt;SUB&gt;0.5&lt;/SUB&gt;Fe&lt;SUB&gt;2&lt;/SUB&gt;O&lt;SUB&gt;4&lt;/SUB&gt; Ferrites Nanoparticles

The Mn0.5Zn0.5Fe2O4 nanoparticles has been synthesized using citrate-gel-precursor method. The direct mixing of nitrates and acetates yields homogeneous nanoparticles. Phase formation and crystal structure of the synthesized powder were examined through the X-ray diffraction (XRD). Fourier transform infrared (FTIR) spectra of the sample confirm the spinel structure. The average particle size was determined by transmission electron microscopy (TEM) and field emission scanning electron microscopy (FESEM). The average particle size is found to be about 13 nm. Superparamagnetic-like nature of the nanoparticles of Mn0.5Zn0.5Fe2O4 has been revealed through various dc and linear and non-linear ac magnetization measurements. However, the nanoparticles do not behave like ideal non-interacting superparamagnets. The magnetic particle size is found to be about 8 nm with saturation magnetization about 18.1 emu/g. The blocking temperature (T(B)) of the nanoparticle assembly is found to be about 150 K as observed from dc and ac magnetization measurements. The frequency dependence of the blocking temperature (T(B)) is found to follow Vogel-Fulcher law. The associated characteristic time tau0 is found to be 10(-5) s. This value is different from that generally found for non-interacting superparamagnetic (SPM) systems (tau0 = 10(-9)-10(-10) s).

Commitment Versus Persuasion in the Three-Party Constrained Voter Model

In the framework of the three-party constrained voter model, where voters of two radical parties (A and B) interact with "centrists" (C and Cz), we study the competition between a persuasive majority and a committed minority. In this model, A's and B's are incompatible voters that can convince centrists or be swayed by them. Here, radical voters are more persuasive than centrists, whose sub-population consists of susceptible agents C and a fraction zeta of centrist zealots Cz. Whereas C's may adopt the opinions A and B with respective rates 1+delta_A and 1+delta_B (with delta_A>=delta_B>0), Cz's are committed individuals that always remain centrists. Furthermore, A and B voters can become (susceptible) centrists C with a rate 1. The resulting competition between commitment and persuasion is studied in the mean field limit and for a finite population on a complete graph. At mean field level, there is a continuous transition from a coexistence phase when zeta<Delta_c=delta_A/(1+delta_A) to a phase where centrism prevails when zeta>= Delta_c. In a finite population of size N, demographic fluctuations lead to centrism consensus and the dynamics is characterized by the mean consensus time tau. Because of the competition between commitment and persuasion, here consensus is reached much slower (zeta<Delta_c) or faster (zeta>=Delta_c) than in the absence of zealots (when tau\simN). In fact, when zeta<Delta_c and there is an initial minority of centrists, the mean consensus time asymptotically grows as tau\simN^{-1/2} e^{N gamma}, where gamma is determined. The dynamics is thus characterized by a metastable state where the most persuasive voters and centrists coexist when delta_A>delta_B, whereas all species coexist when delta_A=delta_B. When zeta>=Delta_c and the initial density of centrists is low, one finds tau\simln N (when N>>1). Our analytical findings are corroborated by stochastic simulations.