Goce Delčev University of Štip

Uncertainty-aware decision-making increasingly relies on multimodal sensing pipelines that must fuse correlated measurements, propagate uncertainty, and trigger reliable control actions. This study develops a unified mathematical framework for multimodal data fusion and Bayesian decision-making under uncertainty. The approach integrates adaptive Covariance Intersection (aCI) for correlation-robust sensor fusion, a Gaussian state-space backbone with Kalman filtering, heteroskedastic Bayesian regression with full posterior sampling via an affine-invariant MCMC sampler, and a Bayesian likelihood-ratio test (LRT) coupled to a risk-sensitive proportional-derivative (PD) control law. Theoretical guarantees are provided by bounding the state covariance under stability conditions, establishing convexity of the aCI weight optimization on the simplex, and deriving a Bayes-risk-optimal decision threshold for the LRT under symmetric Gaussian likelihoods. A proof-of-concept agro-environmental decision-support application is considered, where heterogeneous data streams (IoT soil sensors, meteorological stations, and drone-derived vegetation indices) are fused to generate early-warning alarms for crop stress and to adapt irrigation and fertilization inputs. The proposed pipeline reduces predictive variance and sharpens posterior credible intervals (up to 34% narrower 95% intervals and 44% lower NLL/Brier score under heteroskedastic modeling), while a Bayesian uncertainty-aware controller achieves 14.2% lower water usage and 35.5% fewer false stress alarms compared to a rule-based strategy. The framework is mathematically grounded yet domain-independent, providing a probabilistic pipeline that propagates uncertainty from raw multimodal data to operational control actions, and can be transferred beyond agriculture to robotics, signal processing, and environmental monitoring applications.

We prove existence of three unique "max-exparabolas" to a triangle. Each of these parabolas is internally tangent to one edge and the two other sides. Among all like parabolas, it is characterized by having maximal parameter. We use this result to prove a more general uniqueness statement on maximal parabolas in a convex point set. In similar spirit, we demonstrate uniqueness of minimal enclosing horocycles in hyperbolic geometry, provided the enclosed set is sufficiently small.

In the seismic analysis of structures, it is common to assume that the seismic waves arrive vertically. In this paper, we consider a two-dimensional, continuum model of a building, supported by an embedded rectangular, deformable foundation and excited by a nonvertically incident P-wave pulse. The building and the foundation are assumed to be linearly elastic, while the soil can experience nonlinear deformations, such that, in compression, the soil behavior is elastoplastic, while, in tension, its resistance is limited to 10% of that for compression. Our results show that, when the stress limit in tension is exceeded at a point in the soil, redistribution of the normal stresses and strains occurs. For small nonlinearity in the soil, the system response does not differ significantly from that for linear soil, but it differs significantly for large nonlinearity. In the design of buildings, the traditional methods for computing the base shear and normal forces underestimate these quantities. We found that, for excitation by P-waves, the most significant effects are the large normal stresses occurring at the corners of the base of the building. The in-plane shear stresses at the building-foundation interface are also significant. At both locations, the stresses are caused by the foundation flexibility and nonvertical incidence of the seismic P-wave.

Male infertility contributes to nearly half of infertile couples, with asthenozoospermia and oligoasthenoteratozoospermia as predominant factors. Despite advancements in sperm processing techniques, the outcomes remain limited in severe cases, particularly concerning motility, mitochondrial function, and DNA integrity. Platelet-rich plasma (PRP), an autologous concentrate rich in platelets (>1 × 106/μL) and growth factors, has recently gained attention as an adjunctive therapy in andrology and assisted reproduction. This review systematically evaluated studies published between 2015 and 2025 investigating PRP use in sperm processing, including in vitro experiments, clinical trials, animal models, and mechanistic studies. PRP demonstrated concentration-dependent benefits, with 5% PRP yielding optimal improvements: motility increased by 15-30%, mitochondrial activity increased by up to 80% (p = 0.002), and oxidative stress was significantly reduced (p < 0.001). PRP's effects on DNA integrity differ by application method: intratesticular administration improves spermatogenesis, producing sperm with reduced DNA fragmentation (~33% relative reduction after 3 months, p < 0.001), while in vitro supplementation provides limited protection against processing-induced damage. Mechanisms involve antioxidant action, mitochondrial protection via AMP-activated protein kinaseNuclear Factor kappa-light-chain-enhancer of activated B cells (AMPK/NF-κB) modulation, membrane stabilization, and the selective preservation of higher-quality spermatozoa. PRP shows consistent biological efficacy and safety but lacks methodological standardization. Fewer than 20% of studies report platelet concentrations, limiting reproducibility. Standardized protocols distinguishing leukocyte-poor from leukocyte-rich preparations and randomized trials focusing on live birth rates are recommended. This review proposes an eight-point characterization checklist for future research.

Burdock (Arctium lappa L., Asteraceae) seeds, a rich source of dietary fibre, proteins, essential and fatty acids, also contain high levels of polyphenols and lignans, especially arctigenin and arctiin. This study investigated the incorporation of native and supercritical CO2-defatted burdock seed flour into gingerbread cookies formulated with sweetener xylitol compared to burdock seeds’ free sugar-based and xylitol-based cookies as a control. Arctiin was the dominant lignan in both native and defatted seed flours (68.30 and 75.16 mg/g, respectively), while isochlorogenic acid was the most abundant phenolic acid (7.01 and 7.86 mg/g, respectively). Among enriched formulations, xylitol cookies with defatted burdock seed flour exhibited the highest soluble dietary fibre content (0.29 g/100 g) and reduced hardness, comparable to the xylitol control. All samples achieved “good” sensory quality (18.33–19.65 points), with no significant differences among formulations (p > 0.05). Storage studies (60 days) under varying temperature and light conditions revealed a significant decline in sensory quality only for sucrose-based control cookies stored at 40 °C. The concentrations of major phenolic compounds remained stable under all storage conditions. These results demonstrate the technological and nutritional potential of defatted burdock seed flour as a functional ingredient in bakery products.