Stability of a Stochastic Model of an SIR Epidemic with Vaccination

We prove almost sure exponential stability for the disease-free equilibrium of a stochastic differential equations model of an SIR epidemic with vaccination. The model allows for vertical transmission. The stochastic perturbation is associated with the force of infection and is such that the total population size remains constant in time. We prove almost sure positivity of solutions. The main result concerns especially the smaller values of the diffusion parameter, and describes the stability in terms of an analogue \(\mathcal{R}_\sigma\) of the basic reproduction number \(\mathcal{R}_0\) of the underlying deterministic model, with \(\mathcal{R}_\sigma \le \mathcal{R}_0\). We prove that the disease-free equilibrium is almost sure exponentially stable if \(\mathcal{R}_\sigma <1\).     

Optimal foraging behavior with an explicit consideration of within-individual behavioral variation: an example of predation

Animal behavior is flexible, and the same individual can exhibit variable expressions under the equivalent ecological situations (i.e., within-individual behavioral variation). This study examines the evolution of within-individual behavioral variation using an individual-based model. A common predation scenario is considered where a predator spends a period h to handle and consume a captured prey. The model assumes the handling time of the predator to be a random variable. The average and within-individual variance of handling time are described by \(\mu _h\) and \(\sigma _h^2\), respectively, where each individual has its own unique \(\mu _h\) and \(\sigma _h^2\). Using a genetic algorithm, the evolution of \(\sigma _h^2\) is traced. The results show that natural selection acts on both \(\mu _h\) and \(\sigma _h^2\), and the optimal behavioral variation depends on the density of prey. In particular, individuals with high behavioral variance \(\sigma _h^2\) are more likely selected when prey density is low. Individual based modeling can be a useful tool for studying the ultimate significance of within-individual behavioral variation and generating empirically testable predictions. The mechanisms of the evolution of within-individual behavioral variation and their ecological implications are discussed.     

A finite-element model of mechanosensation by a Pacinian corpuscle cluster in human skin

The Pacinian corpuscle (PC) is the cutaneous mechanoreceptor responsible for sensation of high-frequency (20–1000 Hz) vibrations. PCs lie deep within the skin, often in multicorpuscle clusters with overlapping receptive fields. We developed a finite-element mechanical model of one or two PCs embedded within human skin, coupled to a multiphysics PC model to simulate action potentials elicited by each PC. A vibration was applied to the skin surface, and the resulting mechanical signal was analyzed using two metrics: the deformation amplitude ratio (\({\rho }_{\mathrm{1S}} \), \({\rho }_{\mathrm{2S}} )\) and the phase shift of the vibration (\({\delta }_{\mathrm{S}1}^{\mathrm{mech}} \), \({\delta }_{\mathrm{S}2}^{\mathrm{mech}} )\) between the stimulus and the PC. Our results showed that the amplitude attenuation and phase shift at a PC increased with distance from the stimulus to the PC. Differences in amplitude (\(\rho _{12} )\) and phase shift (\({\delta }_{12}^{\mathrm{mech}} )\) between the two PCs in simulated clusters directly affected the interspike interval between the action potentials elicited by each PC (\({\delta }_{12}^{\mathrm{spike}} )\). While \({\delta }_{12}^{\mathrm{mech}} \) had a linear relationship with \({\delta }_{12}^{\mathrm{spike}} \), \(\rho _{12} \)’s effect on \({\delta }_{12}^{\mathrm{spike}} \) was greater for lower values of \(\rho _{12} \). In our simulations, the separation between PCs and the distance of each PC from the stimulus location resulted in differences in amplitude and phase shift at each PC that caused \({\delta }_{12}^{\mathrm{spike}} \) to vary with PC location. Our results suggest that PCs within a cluster receive different mechanical stimuli which may enhance source localization of vibrotactile stimuli, drawing parallels to sound localization in binaural hearing.     

Association of <Emphasis Type="BoldItalic">lactase</Emphasis> 13910 C/T polymorphism with bone mineral density and fracture risk: a meta-analysis

A number of studies have investigated the association of lactase (LCT, C/T-13910) gene polymorphism with bone mineral density (BMD) and fracture risk, but previous results were inconclusive. In this study, a meta-analysis was performed to quantify the association of LCT (C/T-13910) polymorphism with BMD and fracture risk. Eligible publications were searched in the PubMed, Web of Science, Embase databases, Google Scholar, Yahoo and Baidu. Pooled weighed mean difference (WMD) or odds ratio (OR) with their 95% confidence interval (CI) were calculated using a fixed-effects or random-effects model. A total of nine articles with 8871 subjects were investigated in the present meta-analysis. Overall, the TT/TC genotypes of LCT 13910 C/T polymorphism showed significantly higher BMD than those with the CC genotype at femur neck (FN) (\(\hbox {WMD} = 0.011\,\hbox {g/cm}^{2}\), 95% CI \(=\) 0.004–0.018, \(P = 0.003\)). Besides, LCT 13910 C/T polymorphism may decrease the risk of any site fractures (for TT versus TC \(+\) CC, OR \(=\) 0.813, 95% CI \(=\) 0.704–0.938, \(P = 0.005\); for T allele versus C allele, OR \(=\) 0.885, 95% CI \(=\) 0.792–0.989, \(P = 0.032\)). However, there was no significant association of LCT 13910 C/T polymorphism with BMD at lumbar spine and risk of vertebral fractures under all genetic contrast models (all P values were \({>}0.05\)). The meta-analysis suggests that there are significant effects of LCT 13910 C/T polymorphism on BMD and fracture risk. Large-scale studies with different ethnic populations will be needed to further investigate the possible race-specific effect of LCT 13910 C/T polymorphism on BMD and fracture risk.     

A genetic variant in COL11A1 is functionally associated with lumbar disc herniation in Chinese population

This study aimed to explore whether the genetic variant of COL11A1 is functionally associated with the development of lumbar disc herniation (LDH) in Chinese population. SNP rs1676486 of COL11A1 was genotyped in 647 patients and 532 healthy controls. The differences of genotype and allele distributions between LDH patients and healthy controls were evaluated using the \(\upchi ^{2}\) test. One-way ANOVA test was used to compare the relationship between genotypes and clinical features including tissue expression of COL11A1 and the degree of disc degeneration. Patients were found to have a significantly higher frequency of TT than the controls (10.2% versus 7.3%, \(P=0.004\)). Besides, the frequency of allele T was found to be remarkably higher in the patients than the controls (34.8% versus 28.1%, \(P < 0.001\)) with an odds ratio of 1.36 (95% confidential interval \(=\) 1.14–1.63). Patients with genotype TT were found to have remarkably more severe disc degeneration (\(P=0.02\)). Besides, the expression of COL11A1 in the lumbar disc was significantly lower in the patients with genotype TT than in those with genotype CT or CC (\(P < 0.001\)). Moreover, the expression level was inversely correlated with the severity of disc degeneration (\(P < 0.001\)). We confirmed that the rs1676486 of COL11A may be functionally associated with LDH in the Chinese population. Extracellular matrix related proteins may play an important role in the pathogenesis of LDH. Our findings shed light on a better understanding of the pathogenesis of LDH, which could be a promising target for a novel treatment modality of LDH.     

Analysis of two susceptibility SNPs in HLA region and evidence of interaction between rs6457617 in <Emphasis Type="BoldItalic">HLA-DQB1</Emphasis> and <Emphasis Type="BoldItalic">HLA-DRB1</Emphasis>*04 locus on Tunisian rheumatoid arthritis

Previous genomewide association studies (GWAS) and meta-analyses have enumerated several genes/loci in major histocompatibility complex region, which are consistently associated with rheumatoid arthritis (RA) in different ethnic populations. Given the genetic heterogeneity of the disease, it is necessary to replicate these susceptibility loci in other populations. In this case, we investigate the analysis of two SNPs, rs13192471 and rs6457617, from the human leukocyte antigen (HLA) region with the risk of RA in Tunisian population. These SNPs were previously identified to have a strong RA association signal in several GWAS studies. A case–control sample composed of 142 RA patients and 123 healthy controls was analysed. Genotyping of rs13192471 and rs6457617 was carried out using real-time PCR methods by TaqMan allelic discrimination assay. A trend of significant association was found in rs6457617 TT genotype with susceptibility to RA (\(P = 0.04\), \(p_{c} = 0.08\), \(\hbox {OR} = 1.73\)). Moreover, using multivariable analysis, the combination of rs6457617*TT–HLA-DRB1*\(04^{+}\) increased risk of RA (\(\hbox {OR} = 2.38\)), which suggest a gene–gene interaction event between rs6457617 located within the HLA-DQB1 and HLA-DRB1. Additionally, haplotypic analysis highlighted a significant association of rs6457617*T–HLA-DRB1*\(04^{+}\) haplotype with susceptibility to RA (\(P = 0.018\), \(p_{c} = 0.036\), \(\hbox {OR} = 1.72\)). An evidence of association was shown subsequently in \(\hbox {antiCCP}^{+}\) subgroup with rs6457617 both in T allele and TT genotype (\(P = 0.01\), \(p_{c} = 0.03\), \(\hbox {OR} = 1.66\) and \(P = 0.008\), \(p_{c} = 0.024\), \(\hbox {OR} = 1.28\), respectively). However, no association was shown for rs13192471 polymorphism with susceptibility and severity to RA. This study suggests the involvement of rs6457617 locus as risk variant for susceptibility/severity to RA in Tunisian population. Secondly, it highlights the gene–gene interaction between HLA-DQB1 and HLA-DRB1.     

Contribution of left ventricular residual stress by myocytes and collagen: existence of inter-constituent mechanical interaction

We quantify the contribution of myocytes, collagen fibers and their interactions to the residual stress field found in the left ventricle (LV) using both experimental and theoretical methods. Ring tissue samples extracted from normal rat, male and female, LV were treated with collagenase and decellularization to isolate myocytes and collagen fibers, respectively. Opening angle tests were then performed on these samples as well as intact tissue samples containing both constituents that served as control. Our results show that the collagen fibers are the main contributor to the residual stress fields found in the LV. Specifically, opening angle measured in collagen-only samples (106.45\(^\circ \) ± 23.02\(^\circ \)) and myocytes-only samples (21.00\(^\circ \) ± 4.37\(^\circ \)) was significantly higher and lower than that of the control (57.88\(^\circ \) ± 12.29\(^\circ \)), respectively. A constrained mixture (CM) modeling framework was then used to infer these experimental results. We show that the framework cannot reproduce the opening angle found in the intact tissue with measurements made on the collagen-only and myocytes-only samples. Given that the CM framework assumes that each constituent contributes to the overall mechanics simply by their mere presence, this result suggests the existence of some myocyte–collagen mechanical interaction that cannot be ignored in the LV. We then propose an extended CM formulation that takes into account of the inter-constituent mechanical interaction in which constituents are deformed additionally when they are physically combined into a mixture. We show that the intact tissue opening angle can be recovered in this framework.     

Invasions Slow Down or Collapse in the Presence of Reactive Boundaries

Motivated by the propagation of thin bacterial films around planar obstacles, this paper considers the dynamics of travelling wave solutions to the Fisher–KPP equation \(u_t = u(1-u) + u_{xx} + u_{yy}\) in a planar strip \(-\infty< x < \infty \), \(0 \le y \le L\). We examine the propagation of fronts in the presence of a mixed boundary condition (also referred to as a ‘partially absorbing’ or ‘reactive’ boundary) \(u_y = \alpha u\), with \(\alpha >0\), at \(y=0\). The presence of boundary conditions of this kind leads to the development of front solutions that propagate in x but contain transverse structure in y. Motivated by the observation that the speed of propagation in the Fisher–KPP equation is determined (for exponentially decaying initial conditions) by the behaviour at the leading edge, we analyse the linearised Fisher–KPP equation in order to estimate the speed of the stable travelling front, a function of the width L and the imposed boundary conditions. For wide strips the speed estimate based on the linearised equation agrees well with the results of numerical simulations. For narrow channels numerical simulations indicate that the stable front propagates more slowly, and for sufficiently small L or sufficiently large \(\alpha \) the front speed falls to zero and the front collapses. The reason for the collapse is the non-existence, far behind the front, of a stable positive equilibrium solution u(x, y). While existence of these equilibrium states can be demonstrated via phase plane arguments, the investigation of stability is similar to calculations of critical patch sizes carried out in similar ecological models.     

Simulation of extracellular matrix remodeling by fibroblast cells in soft three-dimensional bioresorbable scaffolds

To culture functional soft tissues and organs in three-dimensional scaffolds, it is essential to elucidate the optimal scaffold mechanical properties. However, mechanoregulated soft tissue remodeling is not well understood. In this study, we hypothesized that individual cells are capable of remodeling extracellular matrix within a short proximity of themselves in order to match the stiffness of the broader surrounding matrix. This theory was implemented in a three-dimensional finite element model to simulate soft tissue remodeling of human fibroblast cells in two collagen–chitosan scaffolds with different mechanical properties. Simulation results closely matched with previously reported experimental data, showing that soft tissue growth in compliant (Scaf-A, 4.30 kPa) and stiff (Scaf-B, 17.03 kPa) scaffolds led to an almost eightfold difference in the resulting stiffnesses after 10 days (8.40 kPa for Scaf-A, 59.25 kPa for Scaf-B). Furthermore, varying the simulated rate for tissue remodeling by \(\pm \)50 % caused unequal changes in the resulting stiffness (+3.6 and \(-\)23 % for Scaf-A, +5 and \(-\)17 % for Scaf-B), and \(\pm \)50 % changes in the assumed upper limit on tissue stiffness only had larger effects on the stiff scaffold (+42 and \(-\)44 % for Scaf-B). These results reinforce the notion that soft tissue remodeling is governed by the stiffness of the surrounding matrix, until meeting an upper limit on tissue stiffness.     

Mitochondrial dysfunction in protein conformational disorders

Protein aggregation is a hallmark of many neurodegenerative diseases. In Parkinson’s disease protein misfolding of \(\upalpha \)-synuclein involves conformational changes in the protein structure that often results in self-association and aggregation leading to accumulation of \(\upalpha \)-synuclein in neuronal cells. The underlying mechanisms by which aggregations can lead to impaired cellular functions are often not understood. Meanwhile, there is growing evidence that links mitochondrial dysfunction to Parkinson’s disease. As both mitochondria and protein aggregation of \(\upalpha \)-synuclein have been shown to play a major role in Parkinson’s disease, it seems likely that a converging mechanism exists that links the two pathways.     

Cell Volume Regulation in the Proximal Tubule of Rat Kidney

We developed a dynamic model of a rat proximal convoluted tubule cell in order to investigate cell volume regulation mechanisms in this nephron segment. We examined whether regulatory volume decrease (RVD), which follows exposure to a hyposmotic peritubular solution, can be achieved solely via stimulation of basolateral K\(^+\) and \(\hbox {Cl}^-\) channels and \(\hbox {Na}^+\)–\(\hbox {HCO}_3^-\) cotransporters. We also determined whether regulatory volume increase (RVI), which follows exposure to a hyperosmotic peritubular solution under certain conditions, may be accomplished by activating basolateral \(\hbox {Na}^+\)/H\(^+\) exchangers. Model predictions were in good agreement with experimental observations in mouse proximal tubule cells assuming that a 10% increase in cell volume induces a fourfold increase in the expression of basolateral K\(^+\) and \(\hbox {Cl}^-\) channels and \(\hbox {Na}^+\)–\(\hbox {HCO}_3^-\) cotransporters. Our results also suggest that in response to a hyposmotic challenge and subsequent cell swelling, \(\hbox {Na}^+\)–\(\hbox {HCO}^-_3\) cotransporters are more efficient than basolateral K\(^+\) and \(\hbox {Cl}^-\) channels at lowering intracellular osmolality and reducing cell volume. Moreover, both RVD and RVI are predicted to stabilize net transcellular \(\hbox {Na}^+\) reabsorption, that is, to limit the net \(\hbox {Na}^+\) flux decrease during a hyposmotic challenge or the net \(\hbox {Na}^+\) flux increase during a hyperosmotic challenge.     

Morphology and the gradient of a symmetric potential predict gait transitions of dogs

Gaits and gait transitions play a central role in the movement of animals. Symmetry is thought to govern the structure of the nervous system, and constrain the limb motions of quadrupeds. We quantify the symmetry of dog gaits with respect to combinations of bilateral, fore–aft, and spatio-temporal symmetry groups. We tested the ability of symmetries to model motion capture data of dogs walking, trotting and transitioning between those gaits. Fully symmetric models performed comparably to asymmetric with only a \(22\%\) increase in the residual sum of squares and only one-quarter of the parameters. This required adding a spatio-temporal shift representing a lag between fore and hind limbs. Without this shift, the symmetric model residual sum of squares was \(1700\%\) larger. This shift is related to (linear regression, \(n=5\), \(p=0.0328\)) dog morphology. That this symmetry is respected throughout the gaits and transitions indicates that it generalizes outside a single gait. We propose that relative phasing of limb motions can be described by an interaction potential with a symmetric structure. This approach can be extended to the study of interaction of neurodynamic and kinematic variables, providing a system-level model that couples neuronal central pattern generator networks and mechanical models.     

An improved Four-Russians method and sparsified Four-Russians algorithm for RNA folding

Background

The basic RNA secondary structure prediction problem or single sequence folding problem (SSF) was solved 35 years ago by a now well-known \(O(n^3)\)-time dynamic programming method. Recently three methodologies—Valiant, Four-Russians, and Sparsification—have been applied to speedup RNA secondary structure prediction. The sparsification method exploits two properties of the input: the number of subsequence Z with the endpoints belonging to the optimal folding set and the maximum number base-pairs L. These sparsity properties satisfy \(0 \le L \le n / 2\) and \(n \le Z \le n^2 / 2\), and the method reduces the algorithmic running time to O(LZ). While the Four-Russians method utilizes tabling partial results.

Results

In this paper, we explore three different algorithmic speedups. We first expand the reformulate the single sequence folding Four-Russians \(\Theta \left(\frac{n^3}{\log ^2 n}\right)\)-time algorithm, to utilize an on-demand lookup table. Second, we create a framework that combines the fastest Sparsification and new fastest on-demand Four-Russians methods. This combined method has worst-case running time of \(O(\tilde{L}\tilde{Z})\), where \(\frac{{L}}{\log n} \le \tilde{L}\le min\left({L},\frac{n}{\log n}\right)\) and \(\frac{{Z}}{\log n}\le \tilde{Z} \le min\left({Z},\frac{n^2}{\log n}\right)\). Third we update the Four-Russians formulation to achieve an on-demand \(O( n^2/ \log ^2n )\)-time parallel algorithm. This then leads to an asymptotic speedup of \(O(\tilde{L}\tilde{Z_j})\) where \(\frac{{Z_j}}{\log n}\le \tilde{Z_j} \le min\left({Z_j},\frac{n}{\log n}\right)\) and \(Z_j\) the number of subsequence with the endpoint j belonging to the optimal folding set.

Conclusions

The on-demand formulation not only removes all extraneous computation and allows us to incorporate more realistic scoring schemes, but leads us to take advantage of the sparsity properties. Through asymptotic analysis and empirical testing on the base-pair maximization variant and a more biologically informative scoring scheme, we show that this Sparse Four-Russians framework is able to achieve a speedup on every problem instance, that is asymptotically never worse, and empirically better than achieved by the minimum of the two methods alone.

     

A novel real-time driving fatigue detection system based on wireless dry EEG

Development of techniques for detection of mental fatigue has varied applications in areas where sustaining attention is of critical importance like security and transportation. The objective of this study is to develop a novel real-time driving fatigue detection methodology based on dry Electroencephalographic (EEG) signals. The study has employed two methods in the online detection of mental fatigue: power spectrum density (PSD) and sample entropy (SE). The wavelet packets transform (WPT) method was utilized to obtain the \(\theta \) (4–7 Hz), \(\alpha \) (8–12 Hz) and \(\beta \) (13–30 Hz) bands frequency components for calculating corresponding PSD of the selected channels. In order to improve the fatigue detection performance, the system was individually calibrated for each subject in terms of fatigue-sensitive channels selection. Two fatigue-related indexes: (\(\theta +\alpha \))/\(\beta \) and \(\theta \)/\(\beta \) were computed and then fused into an integrated metric to predict the degree of driving fatigue. In the case of SE extraction, the mean of SE averaged across two EEG channels (‘O1h’ and ‘O2h’) was used for fatigue detection. Ten healthy subjects participated in our study and each of them performed two sessions of simulated driving. In each session, subjects were required to drive simulated car for 90 min without any break. The results demonstrate that our proposed methods are effective for fatigue detection. The prediction of fatigue is consistent with the observation of reaction time that was recorded during simulated driving, which is considered as an objective behavioral measure.     

Towards the prediction of flow-induced shear stress distributions experienced by breast cancer cells in the lymphatics

Tumour metastasis in the lymphatics is a crucial step in the progression of breast cancer. The dynamics by which breast cancer cells (BCCs) travel in the lymphatics remains poorly understood. The goal of this work is to develop a model capable of predicting the shear stresses metastasising BCCs experience using numerical and experimental techniques. This paper models the fluidic transport of large particles (\(\eta =d_{\mathrm{p}}/W=0.1-0.4\) where \(d_{\mathrm{p}}\) is the particle diameter and W is the channel width) subjected to lymphatic flow conditions (\({ Re}=0.04\)), in a \(100\times 100\,\upmu \hbox {m}\) microchannel. The feasibility of using the dynamic fluid body interaction (DFBI) method to predict particle motion was assessed, and particle tracking experiments were performed. The experiments found that particle translational velocity decreased from the undisturbed fluid velocity with increasing particle size (5–14% velocity lag for \(\eta =0.1-0.3\)). DFBI simulations were found to better predict particle behaviour than theoretical predictions; however, mesh restrictions in the near-wall region (\(0.2\,\mathrm{W}>y>0.8\,\mathrm{W}\)) result in computationally expensive models. The simulations were in good agreement with the experiments (\(<12\%\) difference) across the channel (\(0.2\,\mathrm{W}\le y\le 0.8\,\mathrm{W}\)), with differences up to 25% in the near-wall region. Particles experience a range of shear stresses (0.002–0.12 Pa) and spatial shear gradients (\(0.004-0.137\,\hbox {Pa}/\upmu \hbox {m}\)) depending on their size and radial position. The predicted shear gradients are far in excess of values associated with BCC apoptosis (\(0.004-0.023\,\hbox {Pa}/\upmu \hbox {m}\)). Increasing our understanding of the shear stress magnitudes and gradients experienced by BCCs could be leveraged to elucidate whether a particular BCC size or location exists that encourages metastasis within the lymphatics.     

Genetic variability and structure of an isolated population of <Emphasis Type="Italic">Ambystoma altamirani</Emphasis>, a mole salamander that lives in the mountains of one of the largest urban areas in the world

Amphibians are globally threatened by habitat loss and fragmentation; species within the order Ambystoma are not the exception, as there are 18 species of mole salamanders in México, of which 16 are endemic and all species are under some national or international status of protection. The mole salamander, Ambystoma altamirani is a microendemic species, which is distributed in central México, within the trans-Mexican volcanic belt, and is one of the most threatened species due to habitat destruction and the introduction of exotic species. Nine microsatellite markers were used to determine the genetic structure, genetic variability, effective population size, presence of bottlenecks and inbreeding coefficient of one population of A. altamirani to generate information which might help to protect and conserve this threatened species. We found two genetic subpopulations with significant level of genetic structure (\(F_{\mathrm{ST}}= 0.005\)) and high levels of genetic variability (\(H_{\mathrm{o}}= 0.883\); \(H_{\mathrm{e}}= 0.621\)); we also found a small population size (\(N_{\mathrm{e}} = 8.8\)), the presence of historical (\(M =\) 0.486) and recent bottlenecks under IAM and TPM models, with a low, but significant coefficient of inbreeding (\(F_{\mathrm{IS}} = -\)0.451). This information will help us to raise conservation strategies of this microendemic mole salamander species.