Extreme statistics of non-intersecting Brownian paths

We consider finite collections of $N$ non-intersecting Brownian paths on the line and on the half-line with both absorbing and reflecting boundary conditions (corresponding to Brownian excursions and reflected Brownian motions) and compute in each case the joint distribution of the maximal height of the top path and the location at which this maximum is attained. The resulting formulas are analogous to the ones obtained in [MFQR13] for the joint distribution of $\mathcal{M}={\rm max}_{x\in\mathbb{R}}\{\mathcal{A}_2(x)-x^2\}$ and $\mathcal{T}={\rm argmax}_{x\in\mathbb{R}}\{\mathcal{A}_2(x)-x^2\}$, where $\mathcal{A}_2$ is the Airy$_2$ process, and we use them to show that in the three cases the joint distribution converges, as $N\to\infty$, to the joint distribution of $\mathcal{M}$ and $\mathcal{T}$. In the case of non-intersecting Brownian bridges on the line, we also establish small deviation inequalities for the argmax which match the tail behavior of $\mathcal{T}$. Our proofs are based on the method introduced in [CQR13,BCR15] for obtaining formulas for the probability that the top line of these line ensembles stays below a given curve, which are given in terms of the Fredholm determinant of certain "path-integral" kernels.Comment: Minor corrections, improved exposition. To appear in Electron. J. Proba

District-level Spatial Analysis of Migration Flows in Ghana: Determinants and Implications for Policy

The present study investigates the determinants of inter-district migration flows over the 1995-2000 period in Ghana. A combination of socio-economic, natural and spatial ‘district-level’ attributes are considered as potential variables explaining the direction of migration flows. In addition to the ‘net’ migration model, ‘in’ and ‘out’ migration models are also employed within the context of the gravity model. Results in the three models consistently show that people move out of districts with less employment and choose districts with high employment rate as destinations. While shorter distance to roads encourages out-migration, districts with better water access seem to attract migrants. Generally, people move out of predominantly agrarian districts to relatively more urbanized districts.Gross migration, Net migration, Inter-district migration flows, spatial analysis, Ghana, Africa, Community/Rural/Urban Development, Labor and Human Capital,

Use of isotope dilution method to predict bioavailability of organic pollutants in historically contaminated sediments.

Many cases of severe environmental contamination arise from historical episodes, where recalcitrant contaminants have resided in the environment for a prolonged time, leading to potentially decreased bioavailability. Use of bioavailable concentrations over bulk chemical levels improves risk assessment and may play a critical role in determining the need for remediation or assessing the effectiveness of risk mitigation operations. In this study, we applied the principle of isotope dilution to quantify bioaccessibility of legacy contaminants DDT and PCBs in marine sediments from a Superfund site. After addition of 13C or deuterated analogues to a sediment sample, the isotope dilution reached a steady state within 24 h of mixing. At the steady state, the accessible fraction (E) derived by the isotope dilution method (IDM) ranged from 0.28 to 0.89 and was substantially smaller than 1 for most compounds, indicating reduced availability of the extensively aged residues. A strong linear relationship (R2=0.86) was found between E and the sum of rapid (Fr) and slow (Fs) desorption fractions determined by sequential Tenax desorption. The IDM-derived accessible concentration (Ce) was further shown to correlate closely with tissue residue in the marine benthic polychaete Neanthes arenaceodentata exposed in the same sediments. As shown in this study, the IDM approach involves only a few simple steps and may be readily adopted in laboratories equipped with mass spectrometers. This novel method is expected to be especially useful for historically contaminated sediments or soils, for which contaminant bioavailability may have changed significantly due to aging and other sequestration processes

Rigid Calabi-Yau threefolds, Picard Eisenstein series and instantons

Type IIA string theory compactified on a rigid Calabi-Yau threefold gives rise to a classical moduli space that carries an isometric action of U(2,1). Various quantum corrections break this continuous isometry to a discrete subgroup. Focussing on the case where the intermediate Jacobian of the Calabi-Yau admits complex multiplication by the ring of quadratic imaginary integers O_d, we argue that the remaining quantum duality group is an arithmetic Picard modular group PU(2,1;O_d). Based on this proposal we construct an Eisenstein series invariant under this duality group and study its non-Abelian Fourier expansion. This allows the prediction of non-perturbative effects, notably the contribution of D2- and NS5-brane instantons. The present work extends our previous analysis in 0909.4299 which was restricted to the special case of the Gaussian integers O_1=Z[i].Comment: 8 pages, for the proceedings of Quantum Theories and Symmetries V

Gating and Ionic Currents Reveal How the BKCa Channel's Ca2+ Sensitivity Is Enhanced by its β1 Subunit

Large-conductance Ca2+-activated K+ channels (BKCa channels) are regulated by the tissue-specific expression of auxiliary β subunits. β1 is predominately expressed in smooth muscle, where it greatly enhances the BKCa channel's Ca2+ sensitivity, an effect that is required for proper regulation of smooth muscle tone. Here, using gating current recordings, macroscopic ionic current recordings, and unitary ionic current recordings at very low open probabilities, we have investigated the mechanism that underlies this effect. Our results may be summarized as follows. The β1 subunit has little or no effect on the equilibrium constant of the conformational change by which the BKCa channel opens, and it does not affect the gating charge on the channel's voltage sensors, but it does stabilize voltage sensor activation, both when the channel is open and when it is closed, such that voltage sensor activation occurs at more negative voltages with β1 present. Furthermore, β1 stabilizes the active voltage sensor more when the channel is closed than when it is open, and this reduces the factor D by which voltage sensor activation promotes opening by ∼24% (16.8→12.8). The effects of β1 on voltage sensing enhance the BKCa channel's Ca2+ sensitivity by decreasing at most voltages the work that Ca2+ binding must do to open the channel. In addition, however, in order to fully account for the increase in efficacy and apparent Ca2+ affinity brought about by β1 at negative voltages, our studies suggest that β1 also decreases the true Ca2+ affinity of the closed channel, increasing its Ca2+ dissociation constant from ∼3.7 μM to between 4.7 and 7.1 μM, depending on how many binding sites are affected