On Stability Estimate of Optimal Transport Maps Using m-th Polynomial Convexity

2024-05-28T10:22:55+08:00

In 1781, Gaspard Monge first proposed the practical problem of relocating building materials while minimizing workers’ effort. Mathematically, the problem can be reiterated as finding a mapping T0 that transforms a random variable (X) following probability measure (μ) into a random variable (Y) following probability measure (ν), with minimal cost. Afterward, it has been widely studied and applied in statistics, machine learning, and economics, which concern the study of “distance” between usually a pair of probability distributions. The focus of this paper is centered on investigating and generalizing stability estimates for optimal transport plans, particularly through the lens of strong polynomial convexity. Building on previous research using plug-in estimators to strengthen the convergence rate of discrete or semi-discrete estimators for optimal transport plans, this paper introduces a novel stability estimate leveraging L-Lipschitz continuity and a paradigmatic methodology based on polynomial convexity, the understanding of which remains limited.

An Experience of the Conservation of Historic Buildings’ Facades in Old Saida City

2024-07-05T20:54:08+08:00

This article delves into the nuanced experience and challenges involved in conserving historic building facades within an old Saida city neighborhood marked by neglect and limited restoration efforts due to class dynamics and discrimination by heritage curators. Nevertheless, its buildings have been subjected to lack of maintenance and repair which led to processes of degradation with time and loss of some cultural heritage [6]. Focusing on a deprived area, the paper examines the challenges and opportunities encountered in conserving architectural heritage amidst socioeconomic constraints. Damage related to the collapse of building elements necessitates an investigation into the underlying causes to prevent such occurrences. This involves identifying a set of parameters to assess the hazards of façades and public exposure. Through a blend of community involvement in close coordination between the author who drives innovative conservation techniques, UNDP and the Municipality of Saida, the project sheds light on the potential for safeguarding the historical character to the damaged historic Musalkhiyyeh street arcades and façades, Kaniset el-amercani, Musallabiyyeh old market streets amongst with a specific square called “Furn el Saha” in old Saida historic city. The project falls under the UNDP project “Improving Living Conditions in Gatherings Host Communities”. The conservation project aimed to conserve those buildings, and promoted histories of places and people’s memories connected to the selected heritage sites. The project rehabilitated internally and externally for the three selected areas. It addressed both the physical deterioration and build the knowledge about the importance of the sites. By documenting this journey, valuable lessons emerge for policymakers, urban planners, and conservationists seeking to address heritage preservation in marginalized communities. Historic structures design and construction tell us much about the cultures and the history of a community that created them and about the traditions and events from which our society grew.

International Journal of Applied Science

On Stability Estimate of Optimal Transport Maps Using m-th Polynomial Convexity

An Experience of the Conservation of Historic Buildings’ Facades in Old Saida City