A distributed procedure for computing stochastic expansions with Mathematica

The solution of a (stochastic) differential equation can be locally approximated by a (stochastic) expansion. If the vector field of the differential equation is a polynomial, the corresponding expansion is a linear combination of iterated integrals of the drivers and can be calculated using Picard Iterations. However, such expansions grow exponentially fast in their number of terms, due to their specific algebra, rendering their practical use limited. We present a Mathematica procedure that addresses this issue by reparametrizing the polynomials and distributing the load in as small as possible parts that can be processed and manipulated independently, thus alleviating large memory requirements and being perfectly suited for parallelized computation. We also present an iterative implementation of the shuffle product (as opposed to a recursive one, more usually implemented) as well as a fast way for calculating the expectation of iterated Stratonovich integrals for Brownian motion

Entropy based adaptive particle filter

We propose a particle filter for the estimation of a partially observed Markov chain that has a non dynamic component. Such systems arise when we include unknown parameters or when we decompose non ergodic systems to their ergodic classes. Our main assumption is that the value of the non dynamic component determines the limiting distribution of the observation process. In such cases, we do not want to resample the particles that correspond to the non dynamic component of the Markov chain. Instead, we take a weighted average of particle filters corresponding to different values of the non dynamic component. The computation of the weights is based on entropy and the number of particles corresponding to each particle filter is proportional to the weights

A Distributed Procedure for Computing Stochastic Expansions with Mathematica

The solution of a (stochastic) differential equation can be locally approximated by a (stochastic) expansion. If the vector field of the differential equation is a polynomial, the corresponding expansion is a linear combination of iterated integrals of the drivers and can be calculated using Picard Iterations. However, such expansions grow exponentially fast in their number of terms, due to their specific algebra, rendering their practical use limited. We present a Mathematica procedure that addresses this issue by re-parametrising the polynomials and distributing the load in as small as possible parts that can be processed and manipulated independently, thus alleviating large memory requirements and being perfectly suited for parallelized computation. We also present an iterative implementation of the shuffle product (as opposed to a recursive one, more usually implemented) as well as a fast way for calculating the expectation of iterated Stratonovich integrals for Brownian Motion.Comment: 15 pages, 2 figures. Submitte

PolliRS: A 3D Printed Pollicization Retractor System that improves access and autonomy during the surgical procedure.

We demonstrate the design, manufacture, and deployment of the first custom-made 3-dimensional (3D)-printed hand retractor for the pollicization procedure. Radiological images of the patient’s hand were taken preoperatively to measure anatomical dimensions and guide the design of the device in a patient-precise manner. The 3D-printed, sterilizable, device was autoclaved and successfully used on a patient that underwent a pollicization procedure in our unit. The radiolucency of the device and the fluency enabled by the ability to exchange between different positions demonstrated the potential of this device in increasing the overall autonomy afforded to the lead-surgeon during the operation and demonstrated the potential of rapid-prototyping techniques such as 3D printing for producing patient-precise tools on-the-fly that taken account the specific needs of the patient

Parameter estimation and asymptotic stability in stochastic filtering

In this paper, we study the problem of estimating a Markov chain X(signal) from its noisy partial information Y, when the transition probability kernel depends on some unknown parameters. Our goal is to compute the conditional distribution process P{Xn|Yn,..., Y1}, referred to hereafter as the optimal filter. Following a standard Bayesian technique, we treat the parameters as a nondynamic component of the Markov chain. As a result, the new Markov chain is not going to be mixing, even if the original one is. We show that, under certain conditions, the optimal filters are still going to be asymptotically stable with respect to the initial conditions. Thus, by computing the optimal filter of the new system, we can estimate the signal adaptively. Key words: nonlinear filtering, asymptotic stability, ergodic decomposition, Bayesian estimators

Maximum likelihood estimation for multiscale Ornstein-Uhlenbeck processes

We study the problem of estimating the parameters of an Ornstein-Uhlenbeck (OU) process that is the coarse-grained limit of a multiscale system of OU processes, given data from the multiscale system. We consider both the averaging and homogenization cases and both drift and diffusion coefficients. By restricting ourselves to the OU system, we are able to substantiall y improve the results in [23, 21] and provide some intuition of what to expect in the general case. In particular, in the homogenisation case we derive optimal rates of sub-sampling, proving the conjecture in [23]

A Manual for Project Governance and Asset Management

Students, practitioners, and businesses will all benefit from this free eBook, which focuses on project governance and asset management. Documenting best practices from design to implementation, including a review of existing frameworks, this eBook provides direction in the field of governance and asset management. Here, the ideas of assets and governance are brought together, and an agile governance framework is introduced. We hope to examine how these ideas may be used in project management in order to discover beneficial methodologies and approaches. If you’re looking to build trust and transparency in decision-making processes, this eBook is a must-read. It is intended for individuals who wish to create an atmosphere that accelerates strategy execution and the attainment of organisational objectives while offering good advice. Everyone in the organisation, including project managers and stakeholders from outside the company, can have an influence on the governance framework of projects and the management of the business’s assets to capture value and strengthen the strategic direction. By providing the necessary leadership, direction, and protocols, an organisation’s asset management and project governance frameworks may assist to guarantee that its strategy and execution are in sync

Local Food to Early Care Solutions Initiative: Farm to ECE Supply Chains Report

The current food supply chains traditionally accessed by Early Care and Education Providers (ECEs) in Georgia,US are lacking in their ability to easily and affordably provide fresh, local foods. This greatly impacts the young children who attend ECEs, as nutritiously dense food has shown to increase a child's readiness to learn. Exploring a variety of fresh produce and associated activities, such as hands-on food preparation and gardening, seamlessly integrate with the learning style of young children, meet educational standards, improve the learning environment, and promote health. Identifying and increasing opportunities for ECEs to source healthy, local foods can expand food access for our most vulnerable children, encourage family engagement, and provide market opportunities for local farmers. Currently, opportunities exist to put local, healthy food into the little hands of the children filling the rooms of metro Atlanta's ECEs, but barriers for centers to source healthy food from local, organic farmers are prevalent