Introduction/Purpose: High-dimensional datasets often lie on nonlinear manifolds, where standard techniques like t-SNE, is unable to recover the basic geometric structure. We propose a geodesic-based extension of the t-SNE algorithm, which replaces Euclidean distances with pairwise geodesic distances computed via shortest paths on a k-nearest neighbor graph. Using random initialization and precomputed geodesic metrics, the method keeps up relationships in the embedding. Experiments with manifold-structured datasets show that the quality of the visualizations is better because they show structures that regular t-SNE distorts. Method: A modification to the t-distributed Stochastic Neighbor Embedding (t-SNE) algorithm wherein the standard use of pairwise Euclidean distances is replaced by approximate geodesic distances computed over a k-nearest neighbor graph. Result: The result shows better performance of kNN-based t-SNE, compared to standard t-SNE. Conclusion: A Riemannian variant of t-SNE that leverages localized neighborhood structures via k-nearest neighbors and adapts gradient updates to respect the geometry of underlying manifolds. By relying on sparse affinity computation and geodesic-aware optimization, the method retains both fine-grained local relationships and larger-scale cluster separation, while significantly reducing memory and computational overhead compared to classical t-SNE. The algorithm is especially suited to high-dimensional, non-Euclidean data and demonstrates consistent performance across a range of geometrically structured datasets. Empirical results validate that our approach produces more stable and interpretable visualizations while preserving the manifold-aware relational topology.
Introduction/purpose: Physical terrain models play an important role in military training, operational planning, and education, as they enable an intuitive and tactile understanding of complex spatial relationships. Although modern digital tools allow advanced three-dimensional visualization, physical models remain a valuable complementary instrument for terrain analysis and decision-making. The aim of this paper is to develop and test a methodology for transforming digital elevation models (DEMs) into accurate physical three-dimensional models using CNC technology. Particular emphasis is placed on integrating geospatial analysis, cartographic techniques, and digital fabrication in order to produce a functional terrain model applicable to military training and planning. Methods: The research was conducted on the example of the "Pasuljanske livade" military training ground in central Serbia. A digital terrain model obtained from the Shuttle Radar Topography Mission (SRTM) database was used as the primary data source. Contour lines with a 20 m interval were extracted from these data and then cartographically processed using line simplification and smoothing tools in ArcGIS Pro. A stepped raster elevation model was subsequently created and converted to STL format using the DEMto3D plugin in QGIS. The three-dimensional model was then scaled in Blender and prepared for CNC machining in Aspire. The physical model was fabricated from walnut wood by subtractive manufacturing on a CNC machine, followed by finishing through sanding and varnishing. Results: The proposed methodology resulted in the successful fabrication of a physical stepped terrain model that faithfully represents the morphological characteristics of the study area. A test sample measuring 159 × 175 mm, representing approximately one-seventh of the complete model, was produced. The model provides a clear visualization of elevation differences and the positions of valleys, ridges, and slopes, while the stepped contour structure facilitates relief interpretation. Tactile interaction with the model significantly improves spatial perception and the understanding of topographic relationships compared to conventional two-dimensional representations. Conclusion: The proposed methodology demonstrates that digital geospatial data and CNC technology can be effectively combined to produce accurate physical terrain models. Such models are a useful tool for military training, planning, and education, as well as for applications in other fields such as risk management, urban planning, and geoscience teaching. Future research may focus on integrating physical models with augmented reality technologies to dynamically display additional geospatial information.
Introduction/purpose: It is obvious that the use of traditional petroleum road bitumen (residual or semi-blown) is unable to provide the required interval between repairs of road surfaces. Therefore, the use of modified bitumen, called polymer bitumen binders (PmB), is increasingly being envisaged in design solutions. The fundamental difference between ordinary bitumen and PmB is that the latter contains polymers of a specific nature, styrene-butadiene thermoelastoplasts (SBS polymers), which create an elastic spatial mesh inside the binder, providing the binders with low-temperature crack resistance and increased elastic recovery. At the same time, the process of using such binders and polymer asphalt concrete mixtures based on them does not undergo fundamental technological changes. Methods: Two types of bitumen were used as binders: semi-blown petroleum road bitumen BND 50/70 and polymer-modified binder PmB 60. Various polymer modifiers were introduced into their composition: thermoelastoplast class polymers consisting of styrene and butadiene monomers. A feature of these polymers is their different spatial structure, and topology, while maintaining the styrene butadiene 30/70 ratio. The studies were carried out under standard modes and temperatures, specified by the requirements of the national standard GOST R 52056-2003 "Polymer-bitumen road binders based on styrene-butadiene-styrene block copolymers. Technical specifications". Results: The replacement of the type of road binder used from viscous bitumen (BND) to viscoelastic binder (PmB) is a factor that undoubtedly improves the operational parameters of the pavement, including, in particular, resistance to permanent viscoplastic deformation (rutting) and critical low-temperature stresses (formation of temperature cracks). Conclusion: The use of linear grades of SBS polymers, including grades produced in Russia (primarily with 1.2-addition in the side polymer chain), is advisable when correcting the properties of viscous petroleum road bitumen. For bitumen-polymer compositions based on other bitumen and bitumen-containing petroleum products, when the required polymer content which exceeds the standards for road binders, radial grades with a branched structure of the main polymer chain are more effective.
Introduction/purpose: This paper investigates a novel class of symmetric maximum-type matrices, characterized by entries formulated through generalized third-order linear recurrence relations. The study responds to the need for structured matrices with explicit analytical properties, which are particularly pertinent in computational applications, especially within the field of digital security. Methods: An n× n symmetric matrix of the form T = [Tk]n×n, where k = max(i,j)+1 and Tk is a positive integer generated by a third-order recurrence relation. Results: The determinant, inverse, and various matrix norms of the proposed symmetric matrix are derived. The matrix is further applied to a watermarking framework, which demonstrates its effectiveness in strengthening data security and authenticity in digital media. Conclusion: A symmetric matrix defined by a third-order recurrence relation was analyzed with respect to its determinant, inverse, and norms. The application of this structured matrix to a frequency-domain watermarking scheme showed strong imperceptibility and robustness.
Introduction: Self compacting mortar is known as a highly fluid mortar that can flow and fill all spaces under its own weight without vibration or compaction. This experimental work aims to produce a self-compacting mortar (SCM) that can be used to repair damaged structural concrete by replacing a proportion of ordinary Portland cement with metakaolin (MK) and adding glass fibers (GF). Methods: Mixtures including various percentages of MK and GF were prepared and tested. All mixtures were tested in the fresh state to assess fluidity and viscosity through mini-slump flow and mini V-funnel flow time tests, respectively. Physical and mechanical properties of all mixtures were measured, such as compressive strength, flexural strength and water absorption. In order to check the performance of prepared SCM in structural repair two experiments were conducted on damaged reinforced concrete beam and cylindrical specimens. Results: The results showed that the addition of GF and MK needs an increase in SP dosage to reduce their negative effect on the fluidity and the viscosity of SCM mixtures. The use of MK up to 10% of cement as replacement resulted in a compressive strength gain of 11 MPa at 28 days and 13 MPa at 56 days. Similar behavior was observed in the mixture containing 0.4% of GF and 10% of MK. Adding GF with 0.2, 0.4, and 0.6% led to flexural strength gains of 4, 6, and 15%, respectively. Water absorption was reduced by 29% when 15% of MK was incorporated. Using MK improves the bond between the repair mortar and the concrete substrate. Conclusion: Following a rigorous analysis of the obtained results, it can be concluded that MK and GF can be used to improve mechanical properties and reduce water absorption of SCM mixtures. The mixture including 0.4% of GF and 10% of MK exhibited the best performance and was considered more suitable for repairing damaged SCC beams.
