Materials genetics regards the deformation law as a manifestation of the internal structure of a material encoded in a nonintegrable variational 1-form. Its stationarity condition generates a differential operator that factorizes into allele operators and then into gene operators; the fundamental solutions of the latter form the material genes, while their expansion coefficients determine the gene phenotype of the realized deformation response. This representation makes it possible to separate structural and physical identification of an experimental curve. At the first, geometric stage, the final morphology of the curve is determined: the number of segments, the coordinates of internal boundaries, and the local classes C⁰, C¹, and C². In the present work this morphology is regarded as fixed, and only the first inverse physical problem is solved: construction of an approximation spline and identification of the physical characteristics of the material without changing the architecture. For this purpose, the Reinsch smoothing principle is generalized by replacing the external scalar regularization parameter with a tensor structure of physical properties. The complete tensor is represented as C = A + B, where the symmetric positive-definite tensor A describes reversible properties and the antisymmetric tensor B describes oriented dissipative channels of the nonintegrable variational 1-form. For the maximum local class C², this structure contains nine independent characteristics—six components of A and three components of B; classes C⁰ and C¹ are nested projections of the same physical structure. Stationarity at fixed material properties leads to a linear differential equation whose solution is represented by an expansion in genes; the characteristic roots and natural boundary conditions serve as observable physical features of the first inverse problem. Thus, the novelty of the work consists in constructing the physical approximation level of materials genetics for a prescribed morphology and in formulating a tensor physical passport as a basis for subsequent machine recognition. Numerical verification on four benchmark datasets shows that, at fixed architecture, physical closure replaces the purely geometric representation by a physically identified realization; the geometric residual may either decrease or increase because minimum geometric error is not the objective of the physical stage. Variation of the architecture itself, the system of isoperimetric conditions arising from variation of material properties, and the associated second inverse problem are not considered here and are assigned to subsequent studies of material mutations.
A hierarchical variational generalization of the Reinsch principle is proposed for constructing an adaptive interpolationspline architecture from a finite experimental sample of the deformation curve of an elastoplastic material. The approach separates three interrelated levels. At the first level, stationarity of the integral part of the variational functional determines the admissible structure of local solutions, including their fundamental functions and variationally consistent boundary and contact conditions. The C² class is adopted as the preferred maximum local smoothness class, while information-insufficient segments are represented by the highest admissible lower class according to the hierarchy C²→C¹→C⁰. At the second level, for each fixed architecture, minimization of the discrete part determines the phenotypic coefficients of the local fundamental solutions from the experimental sample. At the third level, DOE (Design of Experiments) is used to organize and compare the successive architectural states of the deterministic genealogy generated by Geometry Builder; no global search over all admissible spline architectures is performed. The genealogical construction starts from a full-range C² model and develops through greedy multiplication. At each iteration, the segment containing the experimental point of the global maximum Euclidean point-to-curve defect is selected as the parent segment. This point becomes the mandatory new internal boundary and the common experimental point of the two child segments. Their highest admissible local classes are determined by information capacity, whereas insufficient approximation accuracy leads to subsequent multiplication rather than artificial reduction of the local class. Previously accepted boundaries are neither relocated nor removed, so the architecture evolves monotonically. Construction terminates either when both the distributed root-mean-square tolerance and the geometric point-to-curve tolerance are satisfied or when no further information-supported multiplication is possible and the information limit is reached. The terminal morphology is defined exclusively by the number of spline segments and the coordinates of their internal boundaries and is therefore distinguished from the complete computational architecture, which additionally contains local smoothness classes, fundamental solutions, phenotypic coefficients, and boundary and contact conditions. A theorem onmorphological stability is formulated, and numerical examples demonstrate automatic construction of different deformation-curve morphologies without prescribing the number of segments in advance. The resulting morphology constitutes an independent geometric result and a fixed basis for the subsequent construction of an approximation template and identification of physical material parameters by the Material Builder module within the Computational Platform for Machine Recognition of Elastoplastic Materials.
Heritage masonry buildings in Kathmandu Valley are highly vulnerable to earthquake damage because of their age, unreinforced masonry construction, weak mortar, irregular geometry, and limited seismic detailing. This study evaluates the seismic vulnerability of Bal Mandir, a historic Rana-era masonry building in Kathmandu, Nepal, using a 3 Dimensional macro finite element model (FEM) developed in ETABS v20. Material properties were obtained from relevant literature, and seismic loading was defined in accordance with NBC 105:2020. The building was analyzed using response spectrum analysis and linear time-history analysis with seven earthquake ground-motion records matched to the target response spectrum. The first-mode period obtained from the numerical model was 0.348 s, which was close to the empirical value recommended by NBC 105:2020. Fragility curves were developed using roof-displacement demand obtained from the time-history analyses and damage-state thresholds adopted from the FEMA HAZUS-MH methodology for the URMM (Unreinforced Masonry, Mid-Rise) building class. At the Kathmandu design PGA of 0.35 g, corresponding to a 475-year return period, the probabilities of exceedance for Slight, Moderate, Extensive, and Complete damage were estimated as 100%, 99.32%, 84.03%, and 55.17%, respectively. The results indicate a high likelihood of severe damage under the design-level earthquake and highlight the need for appropriate seismic strengthening and conservation measures for Bal Mandir. The assessment is based on linear structural analysis and generalized HAZUS damage thresholds and should therefore be interpreted as a global vulnerability estimate rather than a detailed prediction of local nonlinear damage mechanisms.
The conformation of cities is not isolated events, neither in space nor in time; one of the paths that enable their understanding is the study of their geometric patterns and archetypes behind which we can interpret the underlying social and cultural implications of ideologies and ways of life; each stroke refers to a conception of the world in time. The Andean cities of Peru owe much of their genesis and consolidation to European thought of the sixteenth century characterized by its pendular trajectory between the statements of Christianity and Renaissance ideals confronted and carried to the stroke by means of string and rule in territories that by their characteristics demanded a memory of their complex settlements; in spite of this, contained in their configuration, visible elements of cohesion and socio-cultural syncretism of rooting and influence for the others that later settled. The research is carried out in three main cities (Cajamarca, Jauja and Cusco), through an analytical historical methodology that analyzes traces of multiple scriptures, legible in their urban architectural warp amalgamated for centuries and that have been conforming various palimpsests. These urban hypertexts have been undermined by incessant anthropic erosion and banalization of their spaces; however, they show unique characteristics that turned into strengths can mitigate tendencies towards urban aporías due to the inertia in front of the desire to follow the questionable way of the big cities.
Rapid urbanization and the continuous growth of migrant populations in Ho Chi Minh City have created significant pressure on the urban housing system, particularly in the affordable housing sector. However, the development of low-cost housing for migrants still faces many challenges related to construction costs, land availability, construction duration, and environmental sustainability. This study focuses on exploring sustainable, affordable housing models for migrants through the application of prefabricated construction technology in Ho Chi Minh City. The research employs methods of literature review, comparative analysis, and evaluation of domestic and international prefabricated housing practices to identify the advantages and feasibi lity of this construction approach. The findings indicate that prefabricated construction technology offers numerous benefits, including reduced construction time, lower labor costs, improved quality control, minimized material waste, and enhanced environmental performance. Based on these advantages, the paper proposes a sustainable multi-storey affordable housing model suitable for the socio-economic and urban conditions of Ho Chi Minh City, emphasizing flexibility, adaptability, cost efficiency, and improved living quality for low-income migrants. The study concludes that prefabricated construction technology can become an effective solution for promoting sustainable, affordable housing development while contributing to the industrialization and modernization of Vietnam’s construction sector.
