Model selection in multivariate adaptive regressions splines (MARS) using alternative information criteria

Multivariate Adaptive Regression Splines (MARS) is a useful non-parametric regression analysis method that can be used for model selection in high-dimensional data. Since MARS can identify and model complex, non-linear relationships between the dependent variable and independent variables without requiring any assumptions, it has advantage over simple linear regression techniques. Also, for simplifying the model building process and preventing overfitting, MARS can select automatically the variables to be included in the model, which is useful for datasets with many variables. While MARS is a flexible non-parametric regression method, generalized cross validation (GCV) technique is used within the MARS framework to avoid overfitting and to select the best model. GCV criterion is widely used and can be effective in many situations, however it has some criticism. These criticism are the arbitrary value of the smoothing parameter used in the algorithm of the GCV criterion and the models obtained using this criterion are high-dimensional. In this paper, it is aimed to obtain the barest model that best explains the relationship between the dependent variable and independent variables by using alternative information criteria (Akaike information criterion (AIC), Schwarz Bayesian criterion (SBC) and information complexity criterion (ICOMP(IFIM)PEU)) instead of the use of smoothing parameters in order to put an end to the criticism. To achieve this goal, a simulation study was first conducted with a data set composed of variables that do and do not contribute to the dependent variable to test the success of the information criteria. As a consequence of this simulation work, when variables (which do not contribute to the dependent variable) are not included in the regression model, it demonstrates the success of the criteria in model selection. As a real data set, the reasons for loan defaults were investigated between the years 2005–2019 by utilizing data from 18 banks operating in Türkiye. The results obtained reveal the success of ICOMP(IFIM)PEU criterion in model selection

A nonlocal physics-informed deep learning framework using the peridynamic differential operator

The Physics-Informed Neural Network (PINN) framework introduced recently incorporates physics into deep learning, and offers a promising avenue for the solution of partial differential equations (PDEs) as well as identification of the equation parameters. The performance of existing PINN approaches, however, may degrade in the presence of sharp gradients, as a result of the inability of the network to capture the solution behavior globally. We posit that this shortcoming may be remedied by introducing long-range (nonlocal) interactions into the network's input, in addition to the short-range (local) space and time variables. Following this ansatz, here we develop a nonlocal PINN approach using the Peridynamic Differential Operator (PDDO)---a numerical method which incorporates long-range interactions and removes spatial derivatives in the governing equations. Because the PDDO functions can be readily incorporated in the neural network architecture, the nonlocality does not degrade the performance of modern deep-learning algorithms. We apply nonlocal PDDO-PINN to the solution and identification of material parameters in solid mechanics and, specifically, to elastoplastic deformation in a domain subjected to indentation by a rigid punch, for which the mixed displacement--traction boundary condition leads to localized deformation and sharp gradients in the solution. We document the superior behavior of nonlocal PINN with respect to local PINN in both solution accuracy and parameter inference, illustrating its potential for simulation and discovery of partial differential equations whose solution develops sharp gradients

Ortodontik tedavi gören hastalarda maloklüzyon ve çapraşıklığın değerlendirilmesi

ÖZETAmaç: Bu çalışmanın amacı Atatürk Üniversitesi Diş Hekimliği Fakültesi Ortodonti Anabilim Dalında tedavi gören hastaların maloklüzyon türlerinin ve dişsel çapraşıklık miktarının incelenmesidir.Materyal ve Metot: Çalışmamızda Atatürk Üniversitesi Diş Hekimliği Fakültesi Ortodonti Anabilim Dalına ortodontik tedavi gören 639 hastaya ait başlangıç kayıtları kullanılmıştır. Hastaların alçı modelleri incelenerek Angle sınıflamasına göre hastaların maloklüzyonları tespit edilmiştir. Alt ve üst çene modelleri üzerinde ölçümler yapılarak çapraşıklık miktarları belirlenmiştir.Bulgular: Çalışmada Sınıf I maloklüzyon %38,8, Sınıf II bölüm 1 %25,6, Sınıf II bölüm 2 %16,6, Sınıf III maloklüzyon ise %19 oranında tespit edilmiştir. Üst dişlerde şiddetli çapraşıklık ( >7mm) en yüksek oranda  (%30,5) Sınıf II bölüm 2 maloklüzyon grubunda gözlenmiştir. Alt çene için şiddetli çapraşıklık tüm maloklüzyon türlerinde en az oranda tespit edilmiştir.Sonuçlar: Bu çalışmada ortodontik tedavi gören hastalarda Sınıf I en çok görülen maloklüzyonken, Sınıf II bölüm 2 en az sıklıkta görülen maloklüzyondur. Üst çenede şiddetli çapraşıklık en fazla Sınıf II bölüm 2 maloklüzyon grubunda görülmektedir. ABSTRACTObjectives: The objective of this study was to investigate the malocclusion types and the amount of crowding in patients accepted for orthodontic treatment in the Atatürk University Faculty of Dentistry Department of Orthodontics.Materials and Methods: In this study, records of 639 patients accepted for orthodontic treatment in the Department of Orthodontics, Atatürk Universty Faculty of Dentistry was used. Malocclusions were determined according to the Angle classification from examining the patients dental casts. Crowding levels were determined with measurements on maksillar and mandibular casts.Results: Class I malocclusion in % 38,8, Class II Division 1 in %25,6, Class II Division 2 in %16,6 and Class III malocclusion in %19 percentage was identified. It was observed that severe maxillar crowding ( >7mm) was the  highest percentage (%30,5) in Class II Division 2 malocclussion group. It was reported that severe mandibular crowding was the least percentage in all malocclusion groups.Conclusions: Class I malocclusion was the most frequently seen, whereas Class II Division 2 was the least common in patients accepted for orthodontic treatment. It was observed that severe maxillar crowding was the most percentage in Class II Division 2 malocclussion group

Long-term prognosis of patients with heart failure: Follow-up results of journey HF-TR study population

Background: Despite advances in therapeutic management of patients with heart failure, there is still an increasing morbidity and mortality all over the world. In this study, we aimed to present the 3-year follow-up outcomes of patients included in the Journey HF-TR study in 2016 that has evaluated the clinical characteristics and management of patients with acute heart failure admitted to the hospital and present a national registry data. Methods: The study was designed retrospectively between November 2016 and December 2019. Patient data included in the previously published Journey HF-TR study were used. Among 1606 patients, 1484 patients were included due to dropout of 122 patients due to inhospital death and due to exclusion of 173 due to incomplete data. The study included 1311 patients. Age, gender, concomitant chronic conditions, precipitating factors, New York Heart Association, and left ventricular ejection fraction factors were adjusted in the Cox regression analysis. Results: During the 3-year follow-up period, the ratio of hospitalization and mortality was 70.5% and 52.1%, respectively. Common causes of mortality were acute decompensation of heart failure and acute coronary syndrome. Angiotensin receptor blockers, beta-blockers, statin, and sacubitril/valsartan were found to reduce mortality. Hospitalization due to acute decompensated heart failure, acute coronary syndrome, lung diseases, oncological diseases, and cerebrovascular diseases was associated with the increased risk of mortality. Implantation of cardiac devices also reduced the mortality. Conclusions: Despite advances in therapeutic management of patients with heart failure, our study demonstrated that the long-term mortality still is high. Much more efforts are needed to improve the inhospital and long-term survival of patients with chronic heart failure

Nonlocal Physics Informed Machine Learning Algorithms Using Peridynamic Differential Operator

This PhD thesis focuses on the application of physics-informed machine learning (PIML) to solveforward and inverse problems in partial differential equations (PDEs). PDEs are fundamental for the mathematical description of physical systems, and obtaining forward and inverse solutions is crucial for understanding their behavior. Although conventional methods exist, they are limited by measurement noise and the difficulty of incorporating observed physics into physical models. Machine learning offers a solution to these issues, but the vanilla algorithms fail to produce physically consistent predictions. The branch of PIML combines physical laws and domain knowledge with machine learning, providing better generalization performance and understanding of physical systems. This work explores the use of nonlocal algorithms in PIML. Traditional local methods fail to capture multiscale behaviors, mathematical or domain discontinuities, and anomalous behavior. In contrast, nonlocal theories provide a bridge between classical continuum models and molecular dynamics models, and offer a solution to model these phenomena. This thesis proposes different nonlocal algorithms for each regime of PIML by employing the Peridynamic differential operator (PDDO). For the data-rich regime of PIML, a unified algorithm using sparse regression and PDDO is employed to discover PDEs from measured field data. The capability of the proposed algorithm is demonstrated using field data of challenging coupled nonlinear PDEs. To extend this work to physical phenomena with moving boundaries, a novel framework is introduced using Ensemble SINDy and PDDO. The governing equations for the divided regions is discovered using the same approach. These works correspond to the extreme edge of the data-rich regime of PIML. For the mixed regime of PIML, Physics Informed Neural Network (PINNs) are extensively used. PINN is a deep learning algorithm that can incorporate field equations in the loss function using automatic differentiation. Existing PINN approaches may degrade in the presence of sharp gradients, resulting from the inability of the network to capture the solution behavior globally. This shortcoming is remedied by developing a nonlocal PINN approach using PDDO. PDDO functions can be readily incorporated in the neural network architecture, and the nonlocality does not affect the scalability of PINNs. A new unsupervised convolutional neural network architecture with nonlocal interactions is introduced for solving partial differential equations (PDEs) in the physics-rich regime of physics- informed machine learning (PIML). The architecture utilizes the PDDO filter to evaluate derivatives of the field variable, and captures time dynamics through encoder-decoder layers with a Convolutional Long-short Term Memory (ConvLSTM) layer. The physics is incorporated through governing equations at the output of the neural network and in the reduced latent space. The performance and extrapolation capability of the architecture is tested on coupled nonlinear PDEs in 2D, and compared against PINN type solvers. The proposed nonlocal PIML algorithms are evaluated on a range of problems, including fluid dynamics, solid mechanics, and wave propagation. The results demonstrate that the nonlocal algorithms outperform existing local methods in terms of accuracy and robustness to noise. The proposed algorithms can discover governing equations from limited and noisy data, and provide accurate and physically consistent forward solutions. In conclusion, this thesis contributes to the development of nonlocal PIML algorithms, which are useful for solving complex forward and inverse problems in PDEs

Drone-borne SAR imaging and change detection

This thesis aims to carry out fundamental and systematic research on the formation of high-frequency, high-resolution drone-borne Synthetic Aperture Radar (SAR) imagery of an extended target area and the detection of both sizeable object displacements and subtle changes in it. Drone-borne systems are affordable, rapidly deployable, and capable of accessing difficult areas where human access is dangerous or unsafe. However, they are better suited to relatively short-range applications due to their limited payload capacities which restrict transmit powers and sensor sizes. At high operating frequencies, the radar form factor is reduced and the potential for obtaining very fine-resolution imagery and the sensitivity to temporal changes in the scene are improved. On the other hand, short-range operation at high frequencies leads to significant space-variant/invariant errors induced by motion errors resulting from wind turbulence and drone vibration. Further, for temporal change detection that relies on comparison of “before/after” radar imagery, motion errors are unique for each drone pass. Even if two focused images are formed, residual co-registration errors and residual spatially invariant/variant phase errors can degrade the resulting change map. The research presented in this thesis sets out to develop image formation and change detection algorithms capable of handling the mentioned difficulties above based on theoretical analyses, validate the algorithms using simulations and evaluate the experimental performance in real-world conditions using a drone-borne SAR demonstrator built within this thesis' scope. In the experiments, low-cost vehicular radars operating at 24 and 77 GHz are used, and novel short-range, fine-resolution imagery (up to 1.7 cm in cross-range) of an extended target area is formed without employing a dedicated positional system. Also, it is shown, for the first time, that a high-frequency, high-resolution drone-borne SAR system operating at short ranges is capable of discerning both sizeable object displacements such as human replacement, and subtle changes such as the human footprint or car tyre marks