4,764 research outputs found
Predicting pharmaceutical particle size distributions using kernel mean embedding
In the pharmaceutical industry, the transition to continuous manufacturing of solid dosage forms is adopted by more and more companies. For these continuous processes, high-quality process models are needed. In pharmaceutical wet granulation, a unit operation in the ConsiGmaTM-25 continuous powder-to-tablet system (GEA Pharma systems, Collette, Wommelgem, Belgium), the product under study presents itself as a collection of particles that differ in shape and size. The measurement of this collection results in a particle size distribution. However, the theoretical basis to describe the physical phenomena leading to changes in this particle size distribution is lacking. It is essential to understand how the particle size distribution changes as a function of the unit operation's process settings, as it has a profound effect on the behavior of the fluid bed dryer. Therefore, we suggest a data-driven modeling framework that links the machine settings of the wet granulation unit operation and the output distribution of granules. We do this without making any assumptions on the nature of the distributions under study. A simulation of the granule size distribution could act as a soft sensor when in-line measurements are challenging to perform. The method of this work is a two-step procedure: first, the measured distributions are transformed into a high-dimensional feature space, where the relation between the machine settings and the distributions can be learnt. Second, the inverse transformation is performed, allowing an interpretation of the results in the original measurement space. Further, a comparison is made with previous work, which employs a more mechanistic framework for describing the granules. A reliable prediction of the granule size is vital in the assurance of quality in the production line, and is needed in the assessment of upstream (feeding) and downstream (drying, milling, and tableting) issues. Now that a validated data-driven framework for predicting pharmaceutical particle size distributions is available, it can be applied in settings such as model-based experimental design and, due to its fast computation, there is potential in real-time model predictive control
Invariant subsets of scattered trees. An application to the tree alternative property of Bonato and Tardif
A tree is scattered if no subdivision of the complete binary tree is a
subtree. Building on results of Halin, Polat and Sabidussi, we identify four
types of subtrees of a scattered tree and a function of the tree into the
integers at least one of which is preserved by every embedding.
With this result and a result of Tyomkyn, we prove that the tree alternative
property conjecture of Bonato and Tardif holds for scattered trees and a
conjecture of Tyomkin holds for locally finite scattered trees
Distributional Random Forests: Heterogeneity Adjustment and Multivariate Distributional Regression
Random Forests (Breiman, 2001) is a successful and widely used regression and
classification algorithm. Part of its appeal and reason for its versatility is
its (implicit) construction of a kernel-type weighting function on training
data, which can also be used for targets other than the original mean
estimation. We propose a novel forest construction for multivariate responses
based on their joint conditional distribution, independent of the estimation
target and the data model. It uses a new splitting criterion based on the MMD
distributional metric, which is suitable for detecting heterogeneity in
multivariate distributions. The induced weights define an estimate of the full
conditional distribution, which in turn can be used for arbitrary and
potentially complicated targets of interest. The method is very versatile and
convenient to use, as we illustrate on a wide range of examples. The code is
available as Python and R packages drf
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