Regular Form Research Articles

Nonlinear Static Analysis of RC Buildings: Effects of Soil Type and Seismic Code Differences on Structural Performance

Reinforced concrete (RC) building construction remains predominant in Northern Cyprus, offering resilience against natural disasters when appropriately designed and implemented. The study presents a seismic analysis of RC building models across different soil classes, stories, and configurations, according to multiple seismic design codes: Eurocode 8 (EC8), Northern Cyprus Seismic Code 2015 (NCSC-2015), and Turkish Buildings Earthquake Code 2018 (TBEC-2018). This paper compares regular and irregular forms of Moment Resisting Frame (MRF) and MRF combined with Shear Walls (MRF+SW) systems in various configurations. These configurations include G+3, G+7, and G+11 for regular buildings, and only G+11 for irregular buildings. Pushover analysis using ETABSv18 was employed to assess the base shear, plastic hinge behavior, and displacement. The results indicate that the regularity of the structures enhances resistance and longevity compared to irregular configurations, with shear walls augmenting resistance against earthquake loads in both regular and irregular buildings. Furthermore, soil class emerges as a significant factor influencing results across the codes. While variations among the codes were not consistently observed, EC 8 and TBEC-2018 often appeared more conservative, with TBEC-2018 demonstrating greater adaptability to advanced technologies and a more detailed parameter consideration.

Nonlinear Static Analysis of RC Buildings: Effects of Soil Type and Seismic Code Differences on Structural Performance

Reinforced concrete (RC) building construction remains predominant in Northern Cyprus, offering resilience against natural disasters when appropriately designed and implemented. The study presents a seismic analysis of RC building models across different soil classes, stories, and configurations, according to multiple seismic design codes: Eurocode 8 (EC8), Northern Cyprus Seismic Code 2015 (NCSC-2015), and Turkish Buildings Earthquake Code 2018 (TBEC-2018). This paper compares regular and irregular forms of Moment Resisting Frame (MRF) and MRF combined with Shear Walls (MRF+SW) systems in various configurations. These configurations include G+3, G+7, and G+11 for regular buildings, and only G+11 for irregular buildings. Pushover analysis using ETABSv18 was employed to assess the base shear, plastic hinge behavior, and displacement. The results indicate that the regularity of the structures enhances resistance and longevity compared to irregular configurations, with shear walls augmenting resistance against earthquake loads in both regular and irregular buildings. Furthermore, soil class emerges as a significant factor influencing results across the codes. While variations among the codes were not consistently observed, EC 8 and TBEC-2018 often appeared more conservative, with TBEC-2018 demonstrating greater adaptability to advanced technologies and a more detailed parameter consideration.

Enhancing Learning to Solve Multicomponent Fractional Viscoelastic Equations with U-net Fourier Neural Operators

Abstract The research of viscoelastic media is currently a hot topic in the interpretation and processing of seismic data. To accurately simulate the propagation of seismic waves in viscoelastic media, the fractional viscoelastic equation has emerged as an indispensable method. However, solving this equation numerically has proven to be challenging due to the complexity introduced by its fractional Laplacian operators. Recently, deep learning, especially Fourier neural operators (FNO), has shown excellent performance in learning to fast solve partial differential equations. Traditional FNO methods may face crosstalk problem and make it difficult to achieve satisfactory accuracy, when solving the multi-component fractional order viscoelastic equation. To solve this problem, we introduce a novel approach based on U-net Fourier neural operator (U-FNO). As an enhanced learning method to the traditional FNO-based method, the U-FNO-based method integrates a U-Fourier layer following the standard Fourier layer as a form of regularization, thereby achieving superior prediction accuracy for multi-component equations. Specifically, both the Fourier layers and U-Fourier layers in U-FNO are trained with the solutions of the equation from previous time steps as inputs. This training process enables the U-FNO to efficiently produce more accurate solutions for subsequent wavefield. Numerical simulations reveal that the U-FNO-based method efficiently learns to solve the fractional viscoelastic wave equation independent of fractional Laplacian operators. Additionally, U-FNO-based method offers superior prediction accuracy in comparison with the traditional FNO-based method.

Regularized dynamic mode decomposition algorithm for time sequence predictions

Dynamic Mode Decomposition (DMD) aims at extracting intrinsic mechanisms in a time sequence via linear recurrence relation of its observables, thereby predicting later terms in the sequence. Stability is a major concern in DMD predictions. We adopt a regularized form and propose a Regularized DMD (ReDMD) algorithm to determine the regularization parameter. This leverages stability and accuracy. Numerical tests for Burgers’ equation demonstrate that ReDMD effectively stabilizes the DMD prediction while maintaining accuracy. Comparisons are made with the truncated DMD algorithm.

Specific clinical and radiological characteristics of anti-NMDA receptor autoimmune encephalitis following herpes encephalitis.

Herpes simplex virus encephalitis (HSE) frequently triggers secondary anti-N-methyl-D-aspartate receptor encephalitis (NMDARE), but markers predicting the occurrence of this entity (HSE-NMDARE) are lacking. We conducted a retrospective description of patients with HSE-NMDARE diagnosed between July 2014 and August 2022 and compared them to both patients with regular forms of HSE and NMDARE. Among the 375 patients with NMDARE, 13 HSE-NMDARE were included. The median age was 19years (0.5-73), 4/13 (31%) were children < 4years old, and 7/13 (54%) were male. The median time between HSE and NMDARE onset was 30days (21-46). During NMDARE, symptoms differed from HSE, including increased behavioral changes (92% vs 23%, p = 0.008), movements disorders (62% vs 0%, p = 0.013), and dysautonomia (54% vs 0%, p = 0.041). Compared to 21 patients with regular HSE, patients with HSE-NMDARE more often achieved severity-associated criteria on initial MRIs, with extensive lesions (11/11, 100% vs 10/21, 48%, p = 0.005) and bilateral diffusion-weighted imaging sequence abnormalities (9/10, 90% vs 6/21, 29%, p = 0.002). Compared to 198 patients with regular NMDARE, patients with HSE-NMDARE were more frequently males (7/13, 54% vs 43/198, 22%; p = 0.015) and children < 4 (4/13, 31% vs 14/198, 7%; p = 0.016), with a worse 12-month mRS (2[1-6] vs 1[0-6], p = 0.023). Herein, patients with HSE-NMDARE have a poorer long-term prognosis than patients with regular NMDARE. We report a greater rate of severity-associated criteria on initial MRIs for HSE-NMDARE compared to regular HSE, which may help identify patients with higher risk of HSE-NMDARE.

Phyto-Active Components Delivered through Lipid Nanodrug Carriers as a Promising Avenue for the Treatment of Alzheimer’s Disease: Their Present Status and Industrial Viability

Introduction: Present years have witnessed an unprecedented growth of Alzheimer’s disease (AD) with limited scope for conventional therapeutics. Plant-derived active components (PACs) are being widely utilized as alternate, compatible, efficacious, eco-friendly strategies to ameliorate therapeutic benefits in AD while minimizing toxic effects. However, delivery of PACs in the regular dosage form often faces challenges due to low stability and bioavailability, brainspecific delivery, dose-related toxic effects, etc., which can be subsided by experimentally fabricated Lipid Nano Drug Carriers (LNCs). The objective of this study is to provide a comprehensive, evidence-based review on recent progress in the PACs-loaded lipid nanocarriers (PLNs)-based therapeutic strategies for AD. Methods: For the study implementation, a systematic literature review was carried out from various scientific potential databases like Scopus, Pubmed, Web of Science, etc., and relevant evidence- based pre-clinical research data was pooled to draw conclusive outcomes. Results: LNCs are treated as promising avenues to effectively deliver various PACs into the brain due to their high lipophilicity with ultra-micron size and tunable surface features, which make them eligible to pass through the blood-brain barrier. Both passive and active targeting of PLNs has been explored to target AD by overcoming the off-target bio delivery problems. Conclusion: The review provided updated preclinical study-based data on the potentialities of PLNs in overcoming AD. Simultaneously, equal weightage was devoted to the issues faced beyond the laboratory in their successful technology transfer. The study would be beneficial in unveiling important insights into the implications of PLNs for their futuristic clinical applicability.

Developing equity-aware safety performance functions for identifying hotspots of pedestrian-involved crashes

Crashes are frequently disproportionally observed in disadvantaged areas. Despite the evident disparities in transportation safety, there has been limited exploration of quantitative approaches to incorporating equity considerations into road safety management. This study proposes a novel concept of equity-aware safety performance functions (SPFs), enabling a distinct treatment of equity-related variables such as race and income. Equity-aware SPFs introduce a fairness distance and integrate it into the log-likelihood function of the negative binomial regression as a form of partial lasso regularization. A parameter λ is used to control the importance of the regularization term. Equity-aware SPFs are developed for pedestrian-involved crashes at the census tract level in Virginia, USA, and then employed to compute the potential for safety improvement (PSI), a prevalent metric used in hotspot identification. Results show that equity-aware SPFs can diminish the effects of equity-related variables, including poverty ratio, black ratio, Asian ratio, and the ratio of households without vehicles, on the expected crash frequencies, generating higher PSIs for disadvantaged areas. Based on the results of Wilcoxon signed-rank tests, it is evident that there are significant differences in the rankings of PSIs when equity awareness is considered, especially for disadvantaged areas. This study adds to the literature a new quantitative approach to harmonize equity and effectiveness considerations, empowering more equitable decision-making in safety management, such as allocating resources for safety enhancement.

Equilibrium Solution of Two – Dimensional Non-Homogeneous Equations in the Theory of Elastic Mixtures

Abstract: The problem of plane elasticity for a doubly connected body with inner and outer boundaries in a regular polygonal form with common centre and parallel sides has been studied. The sides of the polygon were exposed to external forces. The nature of the force term was determined by application of complex variable theory. Kolosov’s method of solution was applied to obtain the biharmonic equation of the forcing term. The forces on the particle were studied under 2-dimensions from which the compatibility and equilibrium equations were derived. The compatibility and equilibrium equations were used to derive the force – stress relations. The results shows that there is a significant relationship between the angle of the force term on the plane of the particle and the stress state of the particle, which is in conformity with existing experimental results.

FedCCL: Federated dual-clustered feature contrast under domain heterogeneity

Federated learning (FL) facilitates a privacy-preserving neural network training paradigm through collaboration between edge clients and a central server. One significant challenge is that the distributed data is not independently and identically distributed (non-IID), typically including both intra-domain and inter-domain heterogeneity. However, recent research is limited to simply using averaged signals as a form of regularization and only focusing on one aspect of these non-IID challenges. Given these limitations, this paper clarifies these two non-IID challenges and attempts to introduce cluster representation to address them from both local and global perspectives. Specifically, we propose a dual-clustered feature contrast-based FL framework with dual focuses. First, we employ clustering on the local representations of each client, aiming to capture intra-class information based on these local clusters at a high level of granularity. Then, we facilitate cross-client knowledge sharing by pulling the local representation closer to clusters shared by clients with similar semantics while pushing them away from clusters with dissimilar semantics. Second, since the sizes of local clusters belonging to the same class may differ for each client, we further utilize clustering on the global side and conduct averaging to create a consistent global signal for guiding each local training in a contrastive manner. Experimental results on multiple datasets demonstrate that our proposal achieves comparable or superior performance gain under intra-domain and inter-domain heterogeneity.

A novel pharmacological strategy using nanoparticles with glutathione and virgin coconut oil to treat gentamicin-induced acute renal failure in rats.

In acute renal failure (ARF), the glomerular filtration rate is reduced, and nitrogenous waste products accumulate persistently, which can last anywhere from a few hours to several days. There is hope for a reversal of the rapid loss of renal function caused by this condition. This study, with gentamicin-induced acute ARF as a prospective setting, sets out to examine the reno-protective benefits of virgin coconut oil (VCO) and GSH. Furthermore, the study evaluated the effect of medication nanoparticle compositions on several kidney function markers. The induction of ARF is achieved with the intraperitoneal injection of gentamicin. To assess renal function, rats underwent 24h of dehydration and hunger before their deaths. The study examined various aspects, including kidney function tests, markers of oxidative stress, histology of kidney tissue, inflammatory cytokines, immunohistochemistry expression of nuclear factor-kappa B (NF-κB), and specific biomarkers for kidney tissue damage, such as kidney injury molecule-1 (KIM-1) and neutrophil gelatinase-associated lipocalin (NGAL). The results of our study indicated that the combination of VCO and GSH, using both regular and nanoparticle formulations, had a better protective impact on the kidneys compared to using either drug alone. The recovery of renal tissue and serum markers, which are symptomatic of organ damage, indicates improvement. This was also demonstrated by the reduction in tubular expression of TNF-α, IL-1β, KIM-1, and NGAL. The immunohistochemical studies showed that the combination therapy, especially with the nanoforms, greatly improved the damaged cellular changes in the kidneys, as shown by higher levels of NF-κB. The study shows that VCO and GSH, when administered individually or combined, significantly improve ARF in a gentamicin-induced rat model, highlighting potential therapeutic implications. Notably, the combined nanoparticulate formulations exhibit substantial effectiveness.

Formulating facial mesh tracking as a differentiable optimization problem: a backpropagation-based solution

Facial mesh tracking enables the production of topologically consistent 3D facial meshes from stereo video input captured by calibrated cameras. This technology is an integral part of many digital human applications, such as personalized avatar creation, audio-driven 3D facial animation, and talking face video generation. Currently, most facial mesh tracking methods are built on computer graphics techniques, which involve complex procedures and often necessitate human annotation within pipelines. As a result, these approaches are difficult to implement and hard to generalize across various scenarios. We propose a backpropagation-based solution that formulates facial mesh tracking as a differentiable optimization problem called the BPMT. Our solution leverages visual clues extracted from the stereo input to estimate vertex-wise geometry and texture information. The BPMT is composed of two steps: automatic face analysis and mesh tracking. In the first step, a range of visual clues are automatically extracted from the input, including facial point clouds, multi-view 2D landmarks, 3D landmarks in the world coordinate system, motion fields, and image masks. The second step can be viewed as a differentiable optimization problem, with constraints comprising stereo video input and facial clues. The primary objective is to achieve topologically consistent 3D facial meshes across frames. Additionally, the parameters to be optimized encompass the positions of free-form deformed vertices and a shared texture UV map. Furthermore, the 3D morphable model (3DMM) is introduced as a form of regularization to enhance the convergence of the optimization process. Leveraging the fully developed backpropagation software, we progressively register the facial meshes to the recorded object, generating high-quality 3D faces with consistent topologies. The BPMT requires no manual labeling within the pipeline, making it suitable for producing large-scale stereo facial data. Moreover, our method exhibits a high degree of flexibility and extensibility, positioning it as a promising platform for future research in the community.

Spatial entropy as an inductive bias for vision transformers

Recent work on Vision Transformers (VTs) showed that introducing a local inductive bias in the VT architecture helps reducing the number of samples necessary for training. However, the architecture modifications lead to a loss of generality of the Transformer backbone, partially contradicting the push towards the development of uniform architectures, shared, e.g., by both the Computer Vision and the Natural Language Processing areas. In this work, we propose a different and complementary direction, in which a local bias is introduced using an auxiliary self-supervised task, performed jointly with standard supervised training. Specifically, we exploit the observation that the attention maps of VTs, when trained with self-supervision, can contain a semantic segmentation structure which does not spontaneously emerge when training is supervised. Thus, we explicitly encourage the emergence of this spatial clustering as a form of training regularization. In more detail, we exploit the assumption that, in a given image, objects usually correspond to few connected regions, and we propose a spatial formulation of the information entropy to quantify this object-based inductive bias. By minimizing the proposed spatial entropy, we include an additional self-supervised signal during training. Using extensive experiments, we show that the proposed regularization leads to equivalent or better results than other VT proposals which include a local bias by changing the basic Transformer architecture, and it can drastically boost the VT final accuracy when using small-medium training sets. The code is available at https://github.com/helia95/SAR.

Study Protocol: Pegasus: psychotherapy incorporating horses for ‘therapy-resistant’ adolescents with autism spectrum disorders, a study with series of randomised, baseline controlled n-of-1 trials

BackgroundFor people with autism spectrum disorder (ASD), daily life can be highly stressful with many unpredictable events that can evoke emotion dysregulation (ED): a strong difficulty with appropriately negative affect regulation. For some of the patients with ASD, treatment as usual does not prove to be effective for ED. They may be at risk of life-long impairment, development of other disorders and loss of motivation for most regular forms of therapy. A highly promising method that may prove effective for therapy-resistant individuals with ASD is Psychotherapy incorporating horses (PIH). PIH uses the interactions of the horse and the patients on the ground and does not include horseriding. While often met with prejudgment and scepticism, reports from parents and therapists as well as a recent systematic review suggest that PIH may have beneficial effects on youths with ASD. Therefore, we examine clinical outcomes both in the short and in the long terms of PIH offered to adolescents with ASD and severe ED despite regular therapy.MethodsA total of 35 adolescents aged 11–18 years with ASD will receive PIH during 15 sessions once a week with randomization to five different groups differentiating in baseline phase from 2 to 6 weeks. PIH uses horses to promote social awareness and self-awareness as well as relationship management and self-management. The primary outcome is the response to treatment on the Emotion Dysregulation Index (EDI). The secondary outcome measures include ASD symptom severity, quality of life, self-esteem, global and family functioning, and goal attainment. Assessments take place at the baseline (T0), at the end of baseline phase A (T1), after completion of intervention phase B (T2), after the end of post-measurement phase C (T3) and after one year (T4). Qualitative interviews of participants, parents and therapists will be held to reveal facilitators and barriers of PIH and a cost-effectiveness study will be performed.DiscussionThis study aims at contributing to clinical practice for adolescents with ASD and persistent emotion regulation problems despite 1.5 year of treatment by offering Psychotherapy incorporating horses in a study with series of randomised, baseline controlled n-of-1 trials.Trial registrationwww.ClinicalTrials.gov NCT05200351, December 10th 2021.

Analysis of Prescription Pattern of Anti-diabetic Medications in a Teaching Hospital in North India.

This retrospective observational study aimedto comprehensively analyse the clinical profile and treatment modalities of patients diagnosed with type 2 diabetes mellitus (T2DM) who were treatedat a tertiary care centre. The study included a cohort of 300 individuals who sought medical care at the hospital from January 2023 to January 2024. The analysis primarily examined parameters such as the mean number of anti-diabetic medications per prescription, the proportion of various categories of anti-diabetic medications prescribed, the predominant class and type of anti-diabetic medications prescribed, and the proportion of anti-diabetic medications prescribed from the essential drug lists. The age distribution demonstrated that 52.0% of participants were above 60 years old, showcasing a substantial elderly representation. Gender distribution emphasized a male predominance at 65.0%, highlighting potential gender-specific implications in type II diabetes. The blood profile analysis of patients with T2DM revealed a range of values for key parameters. Fasting blood glucose levels ranged from a minimum of 101 mg/dL to a maximum of 359 mg/dL, with a mean of 180.01 mg/dl. The comprehensive analysis of anti-diabetic drug utilization, based on the total number of units prescribed, sheds light on the diverse treatment approaches employed for managing diabetes mellitus (DM). Insulin, comprising 31.3% of the total units, plays a pivotal role in glycemic control, with both regular and biphasic formulations contributing significantly at 26.3% and 9.3%, respectively. Among the 300 patients, the overall utilization of anti-diabetic drugs reveals that 38.7% of individuals are using a combination of insulin with oral anti-diabetic drugs, while 61.3% are relying on oral anti-diabetic drugs alone. The most frequently prescribed drug combinations for diabetes management include sulphonylurea with biguanides, emerging as the most prevalent combination with 22 occurrences. The study's findings contribute valuable insights into the socio-demographic profiles and anti-diabetic drug utilization patterns among diabetes patients.

Rational cross‐sections, bounded generation, and orders on groups

AbstractWe provide new examples of groups without rational cross‐sections (also called regular normal forms), using connections with bounded generation and rational orders on groups. Our examples contain a finitely presented HNN‐extension of the first Grigorchuk group. This last group is the first example of finitely presented group with solvable word problem and without rational cross‐sections. It is also not autostackable, and has no left‐regular complete rewriting system.

Generalized Loewy length of Cohen-Macaulay local and graded rings

We generalize a theorem of Ding relating the generalized Loewy length gℓℓ(R) and index of a one-dimensional Cohen-Macaulay local ring (R,m,k). Ding proved that if R is Gorenstein, the associated graded ring is Cohen-Macaulay, and k is infinite, then the generalized Loewy length and index of R are equal. However, if k is finite, equality may not hold. We prove that if the index of a one-dimensional Cohen-Macaulay local ring is finite and the associated graded ring has a homogeneous nonzerodivisor of degree t, then gℓℓ(R)≤index(R)+t−1. Next we prove that if R is a one-dimensional hypersurface ring with a witness to the generalized Loewy length that induces a regular initial form on the associated graded ring, then the generalized Loewy length achieves this upper bound. We then compute the generalized Loewy lengths of several families of examples of one-dimensional hypersurface rings over finite fields. Finally, we study a graded version of the generalized Loewy length and determine its value for numerical semigroup rings.

Composite convolution: A flexible operator for deep learning on 3D point clouds

Deep neural networks require specific layers to process point clouds, as the scattered and irregular location of 3D points prevents the use of conventional convolutional filters. We introduce the composite layer, a flexible and general alternative to the existing convolutional operators that process 3D point clouds. We design our composite layer to extract and compress the spatial information from the 3D coordinates of points and then combine this with the feature vectors. Compared to mainstream point-convolutional layers such as ConvPoint and KPConv, our composite layer guarantees greater flexibility in network design and provides an additional form of regularization. To demonstrate the generality of our composite layers, we define both a convolutional composite layer and an aggregate version that combines spatial information and features in a nonlinear manner, and we use these layers to implement CompositeNets. Our experiments on synthetic and real-world datasets show that, in both classification, segmentation, and anomaly detection, our CompositeNets outperform ConvPoint, which uses the same sequential architecture, and achieve similar results as KPConv, which has a deeper, residual architecture. Moreover, our CompositeNets achieve state-of-the-art performance in anomaly detection on point clouds. Our code is publicly available at https://github.com/sirolf-otrebla/CompositeNet.

Additions to Crepidotus species (Basidiomycota): Six new species and two new records from Thailand

Six new species and two new records of Crepidotus are described from Thailand. Macroscopic and microscopic descriptions with photoplates, as well as a multigene phylogeny, are provided. Crepidotus chiangraiensis sp. nov. is recognized as densely velutinous with white hairs longer near the point of attachment, not striate margin, and not hygrophanous. Crepidotus- flavocarpus sp. nov. is recognized by yellow to yellowish pileus basidiomata, margin discolorous paler yellow, densely velutinous with white hairs near the point of attachment, smooth globose basidiospores, and inverse hymenophoral trama. Crepidotus thailandicus sp. nov. is recognized by a tomentose surface with white hair when primordial to early stages and then disappearing with age when mature present long translucent-striate reward to the point of attachment becoming fade away at central. Crepidotus roseocarpus sp. nov. is recognized by large basidiomata, pileus, lamellae, and context are pastel pink, concolorous darker pink at the margin, hymenophoral trama convergent, with cylindrical terminal elements. Crepidotus-ungulatus sp. nov. is recognized by ungulate basidiomata, brownish orange near the point of attachment, the basidiomata color changed to light brown in three hours, and the margin is concolorous to the surface of the pileus. Crepidotus viscidus sp. nov. is recognized by white semicircular pileus, translucent-striate with gray to dark grey margin, lamellae pale orange to orange-white, glutinous context, smooth basidiospore and hymenophoral trama present regular form. Crepidotus lateralipes and C. striatus are reported as new records to Thailand.

The preterite of Spanish andar: An “unbiased” history of non-standard vs. standard forms

Abstract Alongside the standard irregular preterite of Sp. andar (anduve ‘I walked’) there exist non-standard regular forms (andé ‘I walked’). Scholars have assumed that the non-standard regular forms have resulted from analogy with the preterite of regular -ar verbs, agree that the irregular preterite of andar was formed by analogy with the etymological irregular preterite of estar, and have assumed that the earliest forms were the irregular ones. But if the preterite of andar was formed by analogy with that of estar, what were the etymological forms of the preterite of andar inherited from Latin? This question has not been raised hitherto because of “standard language bias”, a phenomenon recently introduced by Maiden (2022). It will be revealed here that non-standard forms in and- appear by the early thirteenth century. Their early appearance, together with comparative Romance evidence, points to the likelihood that they were not formed by later processes of analogy and regularization, but that they were, and are, direct descendants of one of a number of possible Latin etyma. Finally, it will be explained why forms in anduv- eclipsed the original forms in and-, eventually becoming the standard, as well as why they have persisted as such to date.

Syntactic variation in Hong Kong English

Kirkpatrick and Lixun (2021) maintain that two significant morphosyntactic processes have been at play in early Englishes. These are simplification and regularization. Simplification refers to the relatively simplified inflectional morphology in English today. Kirkpatrick and Lixun (2021) provide an example for the word stan (i.e., stone in Old English) that showed great differences in the singular and plural form in nominative, accusative, genitive and dative case in Old English. Another process is regularization, through which some of the strong verb forms for past tense in English have changed to take the weak or the regular form. To illustrate, the past tense of work was wrought but over time, it has changed to worked.