Application of Sequential Quasi-Monte Carlo to Autonomous Positioning

Sequential Monte Carlo algorithms (also known as particle filters) are popular methods to approximate filtering (and related) distributions of state-space models. However, they converge at the slow $1/\sqrt{N}$ rate, which may be an issue in real-time data-intensive scenarios. We give a brief outline of SQMC (Sequential Quasi-Monte Carlo), a variant of SMC based on low-discrepancy point sets proposed by Gerber and Chopin (2015), which converges at a faster rate, and we illustrate the greater performance of SQMC on autonomous positioning problems.Comment: 5 pages, 4 figure

Negative association, ordering and convergence of resampling methods

We study convergence and convergence rates for resampling schemes. Our first main result is a general consistency theorem based on the notion of negative association, which is applied to establish the almost-sure weak convergence of measures output from Kitagawa's (1996) stratified resampling method. Carpenter et al's (1999) systematic resampling method is similar in structure but can fail to converge depending on the order of the input samples. We introduce a new resampling algorithm based on a stochastic rounding technique of Srinivasan (2001), which shares some attractive properties of systematic resampling, but which exhibits negative association and therefore converges irrespective of the order of the input samples. We confirm a conjecture made by Kitagawa (1996) that ordering input samples by their states in $\mathbb{R}$ yields a faster rate of convergence; we establish that when particles are ordered using the Hilbert curve in $\mathbb{R}^d$, the variance of the resampling error is ${\scriptscriptstyle\mathcal{O}}(N^{-(1+1/d)})$ under mild conditions, where $N$ is the number of particles. We use these results to establish asymptotic properties of particle algorithms based on resampling schemes that differ from multinomial resampling.Comment: 54 pages, including 30 pages of supplementary materials (a typo in Algorithm 1 has been corrected

Determinants of participation in child’s education and alternative activities in Pakistan

Using data from Pakistan, this study analyzed the effect of various individual, household, and community level characteristics on the probability that children engage in different activities. According to the existing trend of their prevalence, we considered five child’s activities, namely: secular schooling; religious education; child labor; a combination of child labor and secular schooling; and inactivity (including leisure). Data was collected through field surveys conducted in over 40 villages in four Pakistani provinces: Balochistan, Khyber Paktunkhwa, Punjab, and Sind. A total of 963 households were interviewed on the activities of 2,496 children. Multinomial Probit model was used for the analyses. Results indicated that parental perception had significant relationship to the probability of engagement in secular school attendance, religious education, and child labor. In addition, we investigated the relationships between participation in the different child activities with location (rural/urban) and children’s gender. We detected a lower probability of attending secular school and a higher probability of engaging in child labor among female children in rural areas. We also found that even parents who openly expressed appreciation of the importance of secular schooling were more likely to send male children to school than female children.Child productivity, Child’s activities, Parental perception, Gender, Community/Rural/Urban Development, Labor and Human Capital, Teaching/Communication/Extension/Profession,

Convergence of sequential quasi-Monte Carlo smoothing algorithms

International audienc

Higher-order stochastic integration through cubic stratification

We propose two novel unbiased estimators of the integral $\int_{[0,1]^{s}}f(u) du$ for a function $f$, which depend on a smoothness parameter $r\in\mathbb{N}$. The first estimator integrates exactly the polynomials of degrees $p<r$ and achieves the optimal error $n^{-1/2-r/s}$ (where $n$ is the number of evaluations of $f$) when $f$ is $r$ times continuously differentiable. The second estimator is computationally cheaper but it is restricted to functions that vanish on the boundary of $[0,1]^s$. The construction of the two estimators relies on a combination of cubic stratification and control ariates based on numerical derivatives. We provide numerical evidence that they show good performance even for moderate values of $n$

Convenient two-step synthesis of highly functionalized benzo-fused 1,4-diazepin-3-ones and 1,5-diazocin-4-ones by sequential Ugi and intramolecular SNAr reactions

Benzodiazepinones are an important family of heterocycles with very attractive pharmacological properties and peptidomimetic abilities. We report herein a rapid and efficient two-step synthesis of polysubstituted 1,4-benzodiazepin-3-ones and 1,5-benzodiazocin-4-ones using a multicomponent condensation/cyclization strategy. The approach uses an Ugi four-component reaction to condense readily available Nα -Fmoc-amino acids, amines and isocyanides with a 2- fluorobenzaldehyde derivative followed by a one-pot Fmoc-group removal, intramolecular aromatic nucleophilic substitution for ring closure and side chain deprotection. The described method gives access to benzo-fused 7- and 8-membered rings bearing a wide variety of functionalized substituents and was applied to efficiently prepare tri- and tetrasubstituted 1,4- benzodiazepin-3-ones and 1,5-benzodiazocin-4-ones in high yields in two straightforward steps

Exercise‐induced airflow changes in horses with asthma measured by electrical impedance tomography

Background: Equine asthma (EA) causes airflow impairment, which increases in severity with exercise. Electrical impedance tomography (EIT) is an imaging technique that can detect airflow changes in standing healthy horses during a histamine provocation test. Objectives: To explore EIT-calculated flow variables before and after exercise in healthy horses and horses with mild-to-moderate (MEA) and severe equine asthma (SEA). Animals: Nine healthy horses 9 horses diagnosed with MEA and 5 with SEA were prospectively included. Methods: Recordings were performed before and after 15 minutes of lunging. Absolute values from global and regional peak inspiratory (PIF, positive value) and expiratory (PEF, negative value) flows were calculated. Data were analyzed using a mixed model analysis followed by Bonferroni's multiple comparisons test to evaluate the impact of exercise and diagnosis on flow indices. Results: Control horses after exercise had significantly lower global PEF and PIF compared to horses with SEA (mean difference [95% confidence interval, CI]: 0.0859 arbitrary units [AU; 0.0339-0.1379], P < .001 and 0.0726 AU [0.0264-0.1188], P = .001, respectively) and horses with MEA (0.0561 AU [0.0129-0.0994], P = .007 and 0.0587 AU [0.0202-0.0973], P = .002, respectively). No other significant differences were detected. Conclusions and clinical importance: Electrical impedance tomography derived PIF and PEF differed significantly between healthy horses and horses with SEA or MEA after exercise, but not before exercise. Differences between MEA and SEA were not observed, but the study population was small

Surgical planning tool for robotically assisted hearing aid implantation

PURPOSE : For the facilitation of minimally invasive robotically performed direct cochlea access (DCA) procedure, a surgical planning tool which enables the surgeon to define landmarks for patient-to-image registration, identify the necessary anatomical structures and define a safe DCA trajectory using patient image data (typically computed tomography (CT) or cone beam CT) is required. To this end, a dedicated end-to-end software planning system for the planning of DCA procedures that addresses current deficiencies has been developed. METHODS :    Efficient and robust anatomical segmentation is achieved through the implementation of semiautomatic algorithms; high-accuracy patient-to-image registration is achieved via an automated model-based fiducial detection algorithm and functionality for the interactive definition of a safe drilling trajectory based on case-specific drill positioning uncertainty calculations was developed. RESULTS :    The accuracy and safety of the presented software tool were validated during the conduction of eight DCA procedures performed on cadaver heads. The plan for each ear was completed in less than 20 min, and no damage to vital structures occurred during the procedures. The integrated fiducial detection functionality enabled final positioning accuracies of [Formula: see text] mm. CONCLUSIONS :    Results of this study demonstrated that the proposed software system could aid in the safe planning of a DCA tunnel within an acceptable time