ARTICLE | doi:10.20944/preprints202301.0290.v1
Subject: Computer Science And Mathematics, Analysis Keywords: generalized Sonin condition; general fractional integral; general fractional derivative of arbitrary order; regularized general fractional derivative of arbitrary order; 1st level general fractional derivative; 1st fundamental theorem of fractional calculus; 2nd fundamental theorem of fractional calculus
Online: 17 January 2023 (01:34:12 CET)
In this paper, the 1st level general fractional derivatives of arbitrary order are defined and investigated for the first time. We start with a generalization of the Sonin condition for the kernels of the general fractional integrals and derivatives and then specify a set of the kernels that satisfy this condition and posses an integrable singularity of power law type at the origin. The 1st level general fractional derivatives of arbitrary order are integro-differential operators of convolution type with the kernels from this set. They contain both the general fractional derivatives of arbitrary order of the Riemann-Liouville type and the regularized general fractional derivatives of arbitrary order considered in the literature so far. For the 1st level general fractional derivatives of arbitrary order, some important properties including the 1st and the 2nd fundamental theorems of Fractional Calculus are formulated and proved.
ARTICLE | doi:10.20944/preprints202209.0435.v1
Subject: Engineering, Electrical And Electronic Engineering Keywords: Federated Learning Strategies; Relational-Regularized Autoencoder; Time-Series Classification
Online: 28 September 2022 (09:06:58 CEST)
Increasingly measured data in the context of smart cities can be used to develop new and innovative business models to increase efficiency and the value of life. A time-series classification algorithm can support to automatize many different processes such as forecasting services. In order to ensure data security and privacy, Federated Learning trains a global model collaboratively on multiple clients. Having different data-distributions and data-quantities across participating clients, neural networks suffer from slow convergence and overfitting. Based on different data-distributions, data-quantities and number of clients, we develop and evaluate different data-clustering strategies to update global model weights in comparison to the state of the art. We use public time-series data, generate various synthetic datasets and train a Relational-Regularized Autoencoder for classification purposes. Our results show an improvement of model performance concerning generalization.
ARTICLE | doi:10.20944/preprints202109.0400.v1
Subject: Computer Science And Mathematics, Computational Mathematics Keywords: Stokes flow; propulsion; swimming; regularized stokeslets; double-layer; squirmer; undulating swimmer
Online: 23 September 2021 (11:02:27 CEST)
The method of regularized stokeslets is widely-used to model microscale biological propulsion. The method is usually implemented with only the single layer potential, with the double layer potential being neglected, despite this formulation often not being justified a priori due to non-rigid surface deformation. We describe a meshless approach enabling inclusion of the double layer which is applied to several Stokes flow problems in which neglect of the double layer is not strictly valid: the drag on a spherical droplet with partial slip boundary condition, swimming velocity and rate of working of a force-free spherical squirmer, and trajectory, swimmer-generated flow and rate of working of undulatory swimmers of varying slenderness. The resistance problem is solved accurately with modest discretization on a notebook computer with the inclusion of the double layer ranging from no-slip to free slip limits; neglect of the double layer potential results in up to 24% error, confirming the importance of the double layer in applications such as nanofluidics, in which partial slip may occur. The squirming swimmer problem is also solved for both velocity and rate of working to within a few percent error when the double layer potential is included, but the error in the rate of working is above 250% when the double layer is neglected. The undulating swimmer problem by contrast produces a very similar value of the velocity and rate of working for both slender and non-slender swimmers, whether or not the double layer is included, which may be due to the deformation’s `locally rigid body’ nature, providing empirical evidence that its neglect may be reasonable in many problems of interest. Inclusion of the double layer enables us to confirm robustly that slenderness provides major advantages in efficient motility despite minimal qualitative changes to the flow field and force distribution.
ARTICLE | doi:10.20944/preprints202202.0035.v1
Subject: Biology And Life Sciences, Insect Science Keywords: Aedes albopictus; ovitrap; regularized logistic regression; ecological niche model; environmental factors; surveillance
Online: 2 February 2022 (13:18:11 CET)
Background: In Switzerland, Aedes albopictus is well established in Ticino, south of the Alps, where surveillance and control are implemented. The mosquito has also been observed in Swiss cities north of the Alps. Decision-making tools are urgently needed by the local authorities in order to optimize surveillance and control. Methods: A regularized logistic regression was used to link the long-term dataset of Ae. albopictus occurrence in Ticino with socio-environmental predictors. The probability of establishment of Ae. albopictus was extrapolated to Switzerland and more finely to the cities of Basel and Zurich. Results: The model performed well, with an AUC of 0.86. Ten so-cio-environmental predictors were selected as informative, including the road-based distance in minutes of travel by car from the nearest cell established in the previous year. The risk maps showed high suitability for Ae. albopictus establishment in the Central Plateau, the area of Basel and the lower Rhone Valley in the Canton of Valais. Conclusions: The areas identified as suitable for Ae. albopictus establishment are consistent with the actual current findings of tiger mosquito. Our approach provides a useful tool to prompt authorities’ intervention in the areas where there is higher risk of introduction and establishment of Ae. albopictus.
ARTICLE | doi:10.20944/preprints202007.0269.v1
Subject: Computer Science And Mathematics, Mathematics Keywords: regularized latent class analysis; regularization; fused regularization; fused grouped regularization; distractor analysis
Online: 12 July 2020 (16:59:18 CEST)
The last series of Raven's standard progressive matrices (SPM-LS) test were studied with respect to its psychometric properties in a series of recent papers. In this paper, the SPM-LS dataset is analyzed with regularized latent class models (RLCM). For dichotomous item response data, an alternative estimation approach for RLCMs is proposed. For polytomous item responses, different alternatives for performing regularized latent class analysis are proposed. The usefulness of the proposed methods is demonstrated in a simulated data illustration and for the SPM-LS dataset. For the SPM-LS dataset, it turned out the regularized latent class model resulted in five partially ordered latent classes.
ARTICLE | doi:10.20944/preprints202001.0083.v1
Subject: Arts And Humanities, Architecture Keywords: Chinese ancient architecture; bracket set; tile work; regularized reconstruction; parametric; algorithm modeling; Grasshopper; HBIM; built heritage
Online: 9 January 2020 (11:57:24 CET)
By the study of the pattern book Ying Zao Fa Shi (building regulations of Song Dynasty, 1103 AD), while analyzing the combining and dimensioning rule of timber framework and tile work, a model self-generating program has been compiled for the first time. The operating framework has been firstly defined, while solving the issues of clustering principle, connecting method, output classification, etc. with the detailed description of algorithm theory. Taking the corner bracket set and nine-ridge roof for example, after the compilation and debug by Grasshopper, according to various input parameters, various models have been generated automatically by the plugin, proving the velocity and the veracity of the algorithm.
ARTICLE | doi:10.20944/preprints202007.0715.v1
Subject: Engineering, Civil Engineering Keywords: 3D-concrete-printing; additive manufacturing; extrusion processes simulation; regularized Bingham model; fresh concrete; particle finite element method
Online: 30 July 2020 (10:46:53 CEST)
To enable purposeful design and implementation of automated concrete technologies, precise assessment and prediction of the complex material flow at various stages of the process chain are necessary. This paper investigates the intermediate stage of the extrusion and deposition processes in extrusion-based 3D-concrete-printing, using a numerical model based on the Particle Finite Element Method (PFEM). In PFEM, due to the Lagrangian description of motion, remeshing algorithms and the alpha shape method are used to track the free surface during large deformation scenarios. The Bingham constitutive model was used for describing the rheological behaviour of fresh concrete. This model is validated by comparing the numerically predicted layer geometries with those obtained from laboratory 3D printing experiments. Extensive parametric studies were then conducted using the numerical simulation, delineating the influence of process and material parameters on the layer geometries, the dynamic surface forces generated under the extrusion nozzle and the inter-layer interactions.