Abstract
There is a clear gap in the literature on comparing entrepreneurship in urban and rural areas and analysing distinct differences between them, impacting their survival and growth. This study aims to find the motivations and classifications of success for urban and rural entrepreneurs. A case study approach was adopted, with six cases on urban and rural Scottish enterprises. These contrasting motivations and conceptions of success have been linked to the way companies strategise. Our findings contribute to the literature by adding an understanding of the motivations of entrepreneurs in rural and urban businesses, respectively. Further, the study was conducted in Scotland, which adds a subsequent understanding of the motivations of entrepreneurs within the country specifically, which can be used in future research within the country.

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Programs with a continuous state space or that interact with physical processes often require notions of equivalence going beyond the standard binary setting in which equivalence either holds or does not hold. In this paper we explore the idea of equivalence taking values in a quantale V, which covers the cases of (in)equations and (ultra)metric equations among others.Our main result is the introduction of a V-equational deductive system for linear lambda-calculus together with a proof that it is sound and complete. In fact we go further than this, by showing that linear lambda-theories based on this V-equational system form a category equivalent to a category of autonomous categories enriched over 'generalised metric spaces'. If we instantiate this result to inequations, we get an equivalence with autonomous categories enriched over partial orders. In the case of (ultra)metric equations, we get an equivalence with autonomous categories enriched over (ultra)metric spaces. Additionally, we show that this syntax-semantics correspondence extends to the affine setting.We use our results to develop examples of inequational and metric equational systems for higher-order programming in the setting of real-time, probabilistic, and quantum computing.

Abstract
The gastrointestinal tract is responsible for the entire digestive process. Several diseases, including colorectal cancer, can affect this pathway. Among the deadliest cancers, colorectal cancer is the second most common. It arises from benign tumors in the colon, rectum, and anus. These benign tumors, known as colorectal polyps, can be diagnosed and removed during colonoscopy. Early detection is essential to reduce the risk of cancer. However, approximately 28% of polyps are lost during this examination, mainly because of limitations in diagnostic techniques and image analysis methods. In recent years, computer-aided detection techniques for these lesions have been developed to improve detection quality during periodic examinations. We proposed an automatic method for polyp detection using colonoscopy images. This study presents a two-stage polyp detection method for colonoscopy images using transformers. In the first stage, a saliency map extraction model is supported by the extracted depth maps to identify possible polyp areas. The second stage of the method consists of detecting polyps in the extracted images resulting from the first stage, combined with the green and blue channels. Several experiments were performed using four public colonoscopy datasets. The best results obtained for the polyp detection task were satisfactory, reaching 91% Average Precision in the CVC-ClinicDB dataset, 92% Average Precision in the Kvasir-SEG dataset, and 84% Average Precision in the CVC-ColonDB dataset. This study demonstrates that polyp detection in colonoscopy images can be efficiently performed using a combination of depth maps, salient object-extracted maps, and transformers.