On Gödel’s Incompleteness Theorem

Godel's Incompleteness Theorem is about the logic of mathematics. It is that a certain mathematical structure is so rich that its theory cannot be completely axiomatized. This means there will always be true statements about the structure that cannot be proved as theorems from previously given axioms. To give meaning to this conclusion, we review some examples of mathematical theorems, and their proofs, in geometry, algebra, and logic; we also give an example of a structure that is so simple (while still being interesting) that its theory can be completely axiomatized. First we look at a couple of popular descriptions of Godel's Theorem; these can be misleading. We pass to Raymond Smullyan's interpretation of Godel's Theorem as a puzzle; then to an analogy with the incompleteness of an English guide to English style. Godel's argument relies on converting statements about numbers into numbers themselves; we note how to argue similarly by understanding geometrical statements as geometrical diagrams. Geometry is thus somehow incomplete; likewise, physics

Crisis, Conflict and Celebration: Ethnographic Studies of European Cities

The 2000s will be remembered with the neoliberal urbanism that has rapidly transformed the metropolises throughout the world. Large-scale urban regeneration and renewal activities together with mega projects transformed cities not only spatially but also economically and socially. New accommodation, work, and entertainment spaces and forms were introduced (Todd, 1995). The consequences of this transformation include but are not limited to undermining spatial justice, increasing social inequalities, causing ecological destruction, and displacing many people. These deep wounds inflicted by neoliberal urbanism through dispossession and enclosure are becoming increasingly ordinary in metropolitan areas (Harvey, 2012; Merrifield, 2013). © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2024

THE LIGHT AND DARK EFFECT OF GIORGIO MORANDI'S ENGRAVINGS ON THE AXIS OF ART PRACTICE

Öz: Bu çalışmanın amacı İtalyan ressam Giorgio Morandi’nin sanat hayatının bir döneminde önemli yer teşkil eden gravür çalışmalarını incelemektir. Sanatçı üretim pratiğinde bakış açısını sabit kurallar temeline oturtup sınırlı sayıda nesne ile yetinme noktasında ısrarcı olmuştur. Gravür baskı çalışmalarının temel problematiği haline getirdiği açık koyu sorununa yaklaşımını, hangi plastik sorunları irdelediğini ortaya koymak çalışmanın ana hatlarını oluşturmaktadır. Seçilen örneklerin benzer ve farklılıkları plastik açıdan açık koyu bağlamında değerlendirilmiştir. Sanat anlayışı ekseninde gravür tekniğinin sunduğu olanaklar dâhilinde sıradan bir natürmort ressamı olmanın ötesine taşıdığı baskılarındaki nesne yorumu, nesneyi ele alışı, kompozisyon kaygıları araştırmanın kapsamı dâhilindedir. Çalışmada nitel araştırma yöntem olarak kullanılmıştır. Çalışmanın içeriğine dair basılı kitaplar, makaleler, müze verileri, dijital kaynaklar referans alınarak literatür taraması yapıl-mıştır. Gravür baskı üzerine yazılı kaynaklarla karşılaşılmış olmasına rağmen Morandi’nin sanat pratiği ekseninde gravürleri-nin analiz edilmemiş olması, çalışmanın alana sağlayacağı katkıyı ortaya koymaktadır

Reformulation of the urban narrative of the public domain of Al Quds Jerusalem as a city of conflict

This chapter explores how Jerusalem’s urban narrative reflects political and sociocultural shifts over time, shaped by changes in authority, regime, and historical context. Focusing on the transformation of public spaces like Damascus Gate (Bab Al-Amud), it highlights the tension between local and imposed narratives. Jerusalem, a city with deep religious and political significance, has experienced ongoing transitions from Christian to Islamic dominance and now Israeli control, with each era reshaping the city’s identity. The chapter explores how contemporary governance mechanisms exert control through rituals and legislation, shaping public spaces to reflect authority and order. At the same time, local inhabitants reclaim these spaces as platforms for self-expression and cultural preservation, asserting their identity and resisting external influence. This dynamic underscores the inherent tension between centralized, top-down governance and the empowering agency of grassroots movements within contested urban landscapes. Damascus Gate stands as a central point in the ongoing narrative conflict, where governing authorities assert sovereignty, while local communities utilize the space to express belonging and solidarity. This study examines this urban contest through an analysis of documents, legal frameworks, and spatial mappings, shedding light on how public spaces in Jerusalem transform into arenas for competing narratives of identity, authority, and ownership. These dynamics highlight the complex interplay between spatial governance and community agency in contested urban environments

A Systematic Literature Review of Disability and Earthquake Studies: Understanding the Potential Contributions of Inclusive Design

Disasters are situations that can drastically change our lives and daily routines on a temporary or permanent basis and can create new challenges in the short, medium or long term, depending on the scale of the disaster. Individuals’ psychological, sociological and physiological conditions are directly impacted when living spaces are affected by disasters. Research, which shows that persons with disability or special needs, children, elderly people, and so forth are more vulnerable to disasters, underlines the high importance of developing inclusive approaches and tools for the pre/during/post-disaster processes. This study examines the issue in the context of earthquakes—which are among the most damaging natural hazards—and disability, and explores the context and gaps of the topic and the issues that can be explored by the design/architecture disciplines, through conducting a systematic literature review study. © 2025 The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG

Revisiting mortality in acromegaly using machine learning

Objective To evaluate predictors of mortality in acromegaly using machine learning (ML) models. Methods We analyzed 607 patients with acromegaly. A grid search was applied to compare five types of prediction models in 1,200 configurations. Each model predicted mortality based on 40 disease characteristics, assessed using the Matthews’ correlation coefficient (MCC) and the area under the curve (AUC) metrics. To ensure robust and reliable predictions, we constructed a virtual ensemble model by generating 100 Explainable Boosting Machine (EBM) variants and evaluating their performance across 50 random train–test splits. Results The single EBM model fitted to all data achieved an MCC of 0.88 and an AUC of 0.99. Feature importance analysis identified hypertension, first-line transsphenoidal surgery (TSS), disease duration, baseline insulin-like growth factor 1 levels, hypopituitarism, and repeat TSS as key predictors of mortality. A virtual ensemble prediction model showed good generalization performance, with an MCC of 0.64 ± 0.08 and an AUC of 0.96 ± 0.015 across 50 random data splits. 58% of the cohort were female, and 66.9% had macroadenomas. The first-line treatment was TSS in 83.2% of cases. Additional treatments were repeat TSS (16.6%), somatostatin analogs (57%), cabergoline (35.6%), pegvisomant (10.9%), and radiotherapy (16.6%), achieving a 77.8% overall success rate. Hypertension (37.2%) and diabetes (36.4%) were the most common comorbidities. The mortality rate was 8.4%, mainly from cardiovascular disease (41.2%) and cancer (21.6%). Conclusion ML demonstrated strong performance in classifying survival status and identifying mortality predictors in acromegaly. The ensemble model provides a reliable and interpretable tool, balancing accuracy with the robustness required for clinical decision-making. Explore related subject

Enhancing AI-based decision support system with automatic brain tumor segmentation for EGFR mutation classification

Glioblastoma (GBM) carries poor prognosis; epidermal-growth-factor-receptor (EGFR) mutations further shorten survival. We propose a fully automated MRI-based decision-support system (DSS) that segments GBM and classifies EGFR status, reducing reliance on invasive biopsy. The segmentation module (UNet SI) fuses multiresolution, entropy-ranked shearlet features with CNN features, preserving fine detail through identity long-skip connections, to yield a Lightweight 1.9 M-parameter network. Tumour masks are fed to an Inception ResNet-v2 classifier via a 512-D bottleneck. The pipeline was five-fold cross-validated on 98 contrast-enhanced T1-weighted scans (Memorial Hospital; Ethics 24.12.2021/008) and externally validated on BraTS 2019. On the Memorial cohort UNet SI achieved Dice 0.873, Jaccard 0.853, SSIM 0.992, HD95 24.19 mm. EGFR classification reached Accuracy 0.960, Precision 1.000, Recall 0.871, AUC 0.94, surpassing published state-of-the-art results. Inference time is ≤ 0.18 s per slice on a 4 GB GPU. By combining shearlet-enhanced segmentation with streamlined classification, the DSS delivers superior EGFR prediction and is suitable for integration into routine clinical workflows. © International Federation for Medical and Biological Engineering 2025

Planning social housing in 1960s Türkiye: policies, institutions, and projects

This article focuses on Türkiye in the 1960s because the process that beganwith the new constitution following the 1960 military coup constituted aturning point in Türkiye history, economic, political, social, and cultural. Theconcept of social housing also came to the fore for the first time duringthese years. This article examines the emergence and conceptualization ofsocial housing in 1960s Türkiye from a planning perspective. It situates thedevelopment of social housing within the broader framework of welfarestate policies and state-led planning practices shaped by the 1961Constitution and the Five-Year Development Plans. Particular attention isgiven to the role of the Real Estate Credit Bank as a key state institution infinancing and implementing housing schemes. Through an analysis ofselected housing projects, the article demonstrates how social housingpolicies were translated into architectural and spatial practices, and howthese projects reflected ownership-based models distinct from the rental-oriented systems common in Western Europe. By connecting policies,institutions, and projects, the study highlights the significance of the 1960sas a formative period in Türkiye’s housing history, when the planning ofsocial housing became closely intertwined with the construction of thewelfare state

Seramik Sanatında “Belirsizlik” Kavramına İlişkin Bir İnceleme

Uncertainty is a concept at the intersection of various disciplines, such as art, philosophy, and science. Although it often has a negative connotation, it is a force that stimulates creativity. It is an essential element that encourages creative thinking in human discovery and invention processes. The human mind has endeavored to make sense ofthe world with quantities and numerical expressions by seeking certainty instead of abstract and uncertain relationships. This tendency can be traced back to the origins of mathematics and geometry. Ancient Greece was central to the Presocratic thinkers' efforts to explain the basic components ofthe universe and events. In the 20th century, with the emergence of the philosophy of indeterminism, the concept of uncertainty brought up other concepts, such as chance, coincidence, and unpredictability in art. It paved the way for artists to address these concepts. In ceramic art, the production process inevitably involves uncertainties, which allows artists to integrate unpredictable elements and unexpected outcomes, particularly during the firing stage. In addition, it has been observed thatthe uncertainties created bythe imitation skills ofthe ceramic material and the various decor methods that artists can apply to its surface and the uncertainties created by perception are frequently addressed. In this context, the concept of uncertainty is investigated in the triangle of science-philosophy-art, how it takes place in art is explained, and its role in both the production process and perception in ceramic art is analyzed.Belirsizlik; sanat, felsefe ve bilim gibi çeşitli disiplinlerin kesişim noktasında bulunan bir kavramdır. Çoğunlukla olumsuz bir çağrışım yapsa da yaratıcılığı harekete geçiren bir güç niteliğindedir. İnsanın keşif ve icat süreçlerinde yaratıcı düşünceyi teşvik eden temel unsurlardan biridir. İnsanın zihni, soyut ve belirsiz ilişkiler yerine kesinlik arayışına yönelerek, dünyayı nicelikler ve sayısal ifadelerle anlamlandırma gayreti göstermiştir. Bu yönelimin matematik ve geometrinin kökenlerine dek uzandığı, Antik Yunan’da ise, Presokratik düşünürlerin evrenin temel bileşenleri ve olayları açıklama çabalarının merkezinde yer aldığı görülmektedir. 20. yüzyıla gelindiğinde, indeterminizm felsefesinin ortaya çıkışıyla birlikte belirsizlik kavramı sanatta; şans, rastlantı ve öngörülemezlik gibi diğer kavramları gündeme getirmiş ve bu kavramların sanatçılar tarafından ele alınmasının önünü açmıştır. Seramik malzeme özelinde bakıldığında, üretim sürecindeki kaçınılmaz belirsizlikler, seramik sanatçıları için öngörülemeyen unsurları ve pişirme sürecinde ortaya çıkabilecek beklenmedik sonuçları sanat pratiklerine dahil edebildikleri bir ortamı yaratmış olur. Bunun yanı sıra, seramik malzemenin taklit becerisi ve yüzeyine uygulanabilen çeşitli dekor yöntemleri ile algılamanın yarattığı belirsizliklerin de sıklıkla ele alındığı gözlemlenmiştir. Bu bağlamda, belirsizlik kavramı bilim-felsefe-sanat üçgeninde araştırılarak, sanatta nasıl yer edindiği açıklanmış ve seramik sanatı özelinde hem üretim sürecindeki hem de algılamadaki rolü üzerinde incelemeler yapılmıştır

Application of adaptive harmony search and machine learning on optimization problems about strength of materials

In structural design, the strength of materials is the key factor in design and applications including optimization covers the strength of material theory in design. The constraints are generally related to the strength of the material for different types of stress that occur under various external loading. The number of design problems using metaheuristics in the subject is high and these problems are generally used as benchmark examples in structural optimization. In this chapter, adaptive harmony search is presented for these problems and multiple cases of these problems are solved to obtain machine learning data. Then, artificial intelligence models that predict optimum results without a rerun of the iterative optimization process are generated. The models used are compared with performance metrics. These performance metrics are Coefficient of determination (R2), Root Mean Square Error (RMSE), Mean Absolute Error (MAE) and Mean Square Error (MSE). When the success of all regression models was analysed, it was seen that the model with the highest R2 (0.9994) and the low error values was Random Forest. © 2025 Elsevier Ltd. All rights reserved