Development and external validation of a machine learning model for the prediction of persistent acute kidney injury stage 3 in multi-centric, multi-national intensive care cohorts.

BACKGROUND: The aim of this retrospective cohort study was to develop and validate on multiple international datasets a real-time machine learning model able to accurately predict persistent acute kidney injury (AKI) in the intensive care unit (ICU). METHODS: We selected adult patients admitted to ICU classified as AKI stage 2 or 3 as defined by the "Kidney Disease: Improving Global Outcomes" criteria. The primary endpoint was the ability to predict AKI stage 3 lasting for at least 72 h while in the ICU. An explainable tree regressor was trained and calibrated on two tertiary, urban, academic, single-center databases and externally validated on two multi-centers databases. RESULTS: A total of 7759 ICU patients were enrolled for analysis. The incidence of persistent stage 3 AKI varied from 11 to 6% in the development and internal validation cohorts, respectively and 19% in external validation cohorts. The model achieved area under the receiver operating characteristic curve of 0.94 (95% CI 0.92-0.95) in the US external validation cohort and 0.85 (95% CI 0.83-0.88) in the Italian external validation cohort. CONCLUSIONS: A machine learning approach fed with the proper data pipeline can accurately predict onset of Persistent AKI Stage 3 during ICU patient stay in retrospective, multi-centric and international datasets. This model has the potential to improve management of AKI episodes in ICU if implemented in clinical practice.

Realizable algorithm for approximating Hilbert-Schmidt operators via Gabor Multipliers.

In this work, we consider new computational aspects to improve the approximation of Hilbert-Schmidt operators via generalized Gabor multipliers. One aspect is to consider the approximation of the symbol of an Hilbert-Schmidt operator as L2 projection in the spline-type space associated to a Gabor multiplier. This gives the possibility to employ a selection procedure of the analysis and synthesis function, interpreted as time-frequency lag; hence, with the related algorithm it is possible to handle both underspread and overspread operators. In the numerical section, we exploit the case of approximating overspread operators having compact and smooth spreading function and discontinuous time-varying systems. For the latter, the approximation of discontinuities in the symbol is not straightforward achievable in the generalized Gabor multipliers setting. For this reason, another aspect is to further process the symbol through a Hough transform, to detect discontinuities and to smooth them using a new class of approximants. This procedure creates a bridge between features detections techniques and harmonic analysis methods and in specific cases it almost doubles the accuracy of approximation.

Detection of the mandibular canal in orthopantomography using a Gabor-filtered anisotropic generalized Hough transform.

In this paper, we explore the possibility of applying the anisotropic generalized Hough transform (AGHT) enhanced with a Gabor based time-frequency filtering (GTF) for the determination of the mandibular canal in digital dental panoramic radiographs. The proposed method is based on template matching using the fact that the shape of the mandibular canal is usually the same, followed by a filtering of the accumulator space in the Gabor domain for a precise detection of the position. The proposed procedure consists of a detailed description of the shape of the canal in its canonical form and on preserving Gabor filtering information for sorting the hierarchy of location candidates after applying anisotropically the extraction algorithm. The experimental results show that the proposed procedure is robust to recognition under occlusion and under the presence of additional structures e.g. teeth, projection errors.

Numerical stability of spline-based Gabor-like systems.

The paper provides a theorem for the characterization of numerical stability of spline-type systems. These systems are generated through shifted copies of a given atom over a time lattice. Also, we reformulate the well known Gabor systems via modulated spline-type systems and we apply the corresponding numerical stability to these systems. The numerical stability is tested for consistency against deformations.

Stability of Spline-Type Systems in the Abelian Case.

In this paper, the stability of translation-invariant spaces of distributions over locally compact groups is stated as boundedness of synthesis and projection operators. At first, a characterization of the stability of spline-type spaces is given, in the standard sense of the stability for shift-invariant spaces, that is, linear independence characterizes lower boundedness of the synthesis operator in Banach spaces of distributions. The constructive nature of the proof for Theorem 2 enabled us to constructively realize the biorthogonal system of a given one. Then, inspired by the multiresolution analysis and the Lax equivalence for general discretization schemes, we approached the stability of a sequence of spline-type spaces as uniform boundedness of projection operators. Through Theorem 3, we characterize stable sequences of stable spline-type spaces.

Constructive realizable multiresolution wavelet-like systems based on multi-windows spline-type spaces.

In this paper, we present a constructive realizable procedure for obtaining a multiresolution wavelet-like system in the framework of stability for spline-type spaces, considering only the generators that prominently intersect the spectrum of the signal to be approximated and stable under deformations through frequency shifts. The realizable system constructed in this way, can analyse jointly three different features of a signal namely time, scale and frequency. We present numerical tests and a detailed complexity analysis to compare the performances of our method against standard constructions.

Approximate Duals of Gabor-like Frames Based on Realizable Multi-Window Spline-Type Constructions.

In the multi-window spline-type spaces, the fast computation of the realizable dual frame could be achieved through a constructive reformulation of the biorthogonal relations. In this paper, we extend the results obtained in spline-type spaces, for the constructive realization of an approximate dual Gabor-like frame. We demonstrate the advantages of this approach in both flexibility and speed. The method allows in a natural way to handle non standard Gabor constructions like non-uniformity in frequency and the reductions of the number of used modulations. Experimental tests are presented in support of the algorithm.