Vol. 12, No. 01 [January 2026]

Transformer models have significantly advanced Natural Language Processing (NLP) by replacing recurrence with self-attention mechanisms [1]. While standard Transformers compute attention uniformly across heads and tokens, this may dilute task-specific importance in classification problems [2,8]. This paper proposes a Weighted Self-Attention Optimization (WSAO) framework that introduces adaptive token-level weighting into the Transformer encoder to enhance discriminative feature learning. Using a public benchmark dataset, we demonstrate that the proposed formulation improves classification performance compared to baseline Transformer [1] and LSTM models [3]. Mathematical formulation, experimental evaluation, and comparative analysis are presented to highlight the effectiveness of the approach.
Keywords: Transformer Models, Self-Attention Optimization, Text Classification, Cross-Entropy Loss, NLP

The increasing emphasis on sustainability and climate change mitigation has driven the construction industry to seek environmentally responsible alternatives to conventional reinforced concrete. Steel-reinforced concrete, although widely used and structurally efficient, is associated with high embodied energy and significant carbon dioxide emissions, primarily due to cement production and steel manufacturing. In this context, bamboo-reinforced concrete (BRC) has gained attention as a potential sustainable alternative, owing to bamboo’s rapid renewability, carbon sequestration capacity, low density, and high tensile strength.
This study presents a comparative evaluation of bamboo-reinforced concrete, conventional steel-reinforced concrete (SRC), and hybrid bamboo–steel reinforced (HYB) systems, with particular focus on the flexural behavior of reinforced concrete beams. The research synthesizes results from peer-reviewed experimental and analytical studies to assess mechanical performance, including tensile capacity, load–deflection response and flexural strength. Emphasis is placed on bamboo selection, treatment, and preparation techniques aimed at improving mechanical efficiency and compatibility with concrete while mitigating moisture sensitivity and bond degradation.
A qualitative meta-analysis methodology is employed to normalize data from different studies, enabling meaningful comparison across reinforcement systems. Numerical results extracted from the literature are used to identify performance trends and evaluate structural efficiency. Findings indicate that while bamboo reinforcement cannot replace steel in high-load or aggressive environmental conditions, it demonstrates adequate performance for low-rise and low-to-moderate load applications when appropriate design modifications and treatment measures are applied. Hybrid reinforcement systems further enhance stiffness, ductility, and overall structural reliability.
An economic assessment suggests that bamboo-based and hybrid reinforcement systems can be cost-effective, particularly in regions where bamboo is locally available. The study concludes that bamboo, alone or in combination with steel, represents a viable and environmentally sustainable reinforcement solution for selected structural applications. Practical design considerations are highlighted, with relevance to the Albanian construction context, while identifying key research gaps for future development.
Keywords: Bamboo-reinforced concrete, Bond behavior, Compressive strength, Eco-friendly material, Flexural strength, Hybrid reinforcement, Low-cost construction, Sustainable construction, Tensile strength

The rapid pace of urban expansion and population growth has led to an increased demand for concrete, resulting in the extensive depletion of natural aggregates such as sand. Simultaneously, the accumulation of electronic plastic waste (EPW) has become a critical environmental concern due to improper disposal practices and its non-biodegradable nature. This study investigates the feasibility of using EPW as a partial replacement for fine aggregates in concrete to address both resource depletion and waste management challenges. Five concrete mixes were prepared with EPW replacing sand at 0%, 5%, 10%, 15%, and 20% by weight. Mechanical properties—including compressive strength, splitting tensile strength, and flexural strength—were evaluated at 7 and 28 days of curing, along with durability characteristics such as water permeability and electrical resistivity. The results demonstrated a decline in mechanical properties with increasing EPW content, with the highest reductions recorded at the 20% replacement level. In contrast, durability improved with higher EPW percentages. The mix with 15% EPW showed the best improvement in water permeability (28.81%), while the 20% EPW mix achieved the highest increase in electrical resistance (250.76%) compared to the control mix. Additionally, machine learning models were used to predict mechanical performance, with Linear Regression (LR) outperforming Random Forest (RF) in terms of predictive accuracy. These findings suggest that incorporating up to 15% EPW as a sand replacement in concrete is a promising, sustainable approach that enhances durability while contributing to plastic waste reduction.
Keywords: Mechanical Properties, Electronic Plastic Waste, Machine Learning, Electrical Resistance.

Classical spectral graph theory and graph signal processing rely on a symmetry principle: undirected graphs induce symmetric (self-adjoint) adjacency/Laplacian operators, yielding orthogonal eigenbases and energy-preserving Fourier expansions. Real-world networks are typically directed and hence asymmetric, producing non-self-adjoint and frequently non-normal operators for which orthogonality fails and spectral coordinates can be ill-conditioned. In this paper we develop an original harmonic-analysis framework for directed networks centered on the adjacency operator. We propose a Biorthogonal Graph Fourier Transform (BGFT) built from left/right eigenvectors, formulate directed "frequency" and filtering in the non-Hermitian setting, and quantify how asymmetry and non-normality affect stability via condition numbers and a departure-from-normality functional. We prove exact synthesis/analysis identities under diagonalizability, establish sampling-and-reconstruction guarantees for BGFT-bandlimited signals, and derive perturbation/stability bounds that explain why naive orthogonal-GFT assumptions break down on non-normal directed graphs. We provide a reproducible protocol to compare undirected versus directed cycles and a perturbed directed cycle, illustrating when orthogonal-GFT assumptions fail and how BGFT behaves across asymmetric regimes.
Keywords:directed graphs; adjacency operator; non-normal matrices; biorthogonal bases; graph Fourier transform; sampling on graphs; symmetry/asymmetry.

We present a binary-power decomposition for every integer; express an integer 𝑎 as the sum of successive powers of 2 and identify any missing terms (called defectors). This yields a unique partition of 𝑎 into a complete part (a full geometric sequence of 2-powers) minus a defector sum. We introduce the notion of an integer’s rank (the highest exponent in its decomposition) and develop an algebra governing parity and exponentiation directly from these binary-power sums. As a principal application, we revisit the Diophantine equation (Xⁿ + Yⁿ = Zⁿ for n≥3). By analyzing parity patterns and exploiting uniqueness of the binary-power decomposition, we show that no nontrivial solutions exist in N³ when n≥3, recovering Fermat’s Last Theorem through an elementary combinatorial-parity argument.
Keywords:binary-power decomposition, complete integer, incomplete integer, defector, Fermat’s Last Theorem, Diophantine equations.