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Fish as model objects have found wide applications in biology and fundamental medicine and allow studies of behavioral and physiological responses to various environmental factors. Representatives of the genus Nothobranchius are one of the most convenient objects for such studies. Male fish belonging to the family Nothobranchiidae are characterized by extremely diverse coloration, which constantly changes, depending on the age of the fish, environmental factors, and social hierarchical status. These fish species are characterized by a short life cycle, which allows changes in coloration, an indicator of the ontogenesis stage, to be estimated. Existing methods of fish color assessments do not allow the intensity of coloration of particular body zones to be clearly differentiated. In the present study, we suggest a method of two-factor assessment of specific fish body zones using modified methods of photofixation and image processing software. We describe the protocol of the method and the results of its application to different-aged groups of male Nothobranchius guentheri. The coloration of selected areas (i.e., red spot on the gill cover (RSGC), black border on the caudal fin (BBCF), and white border on the dorsal fin (WBDF)) differed significantly according to the size and age of the fish (p < 0.05). The data obtained suggest that N. guentheri can be a model for studying aging by the intensity of body coloration in males. Full article

Nonlocal quantum theory of a one-component scalar field in D-dimensional Euclidean spacetime is studied in representations of $\mathcal{S}$ -matrix theory for both polynomial and nonpolynomial interaction Lagrangians. The theory is formulated on coupling constant g in the form of an infrared smooth function of argument x for space without boundary. Nonlocality is given by the evolution of a Gaussian propagator for the local free theory with ultraviolet form factors depending on ultraviolet length parameter l. By representation of the $\mathcal{S}$ -matrix in terms of abstract functional integral over a primary scalar field, the $\mathcal{S}$ form of a grand canonical partition function is found. By expression of $\mathcal{S}$ -matrix in terms of the partition function, representation for $\mathcal{S}$ in terms of basis functions is obtained. Derivations are given for a discrete case where basis functions are Hermite functions, and for a continuous case where basis functions are trigonometric functions. The obtained expressions for the $\mathcal{S}$ -matrix are investigated within the framework of variational principle based on Jensen inequality. Through the latter, the majorant of $\mathcal{S}$ (more precisely, of $-ln\mathcal{S}$ ) is constructed. Equations with separable kernels satisfied by variational function q are found and solved, yielding results for both polynomial theory ${\phi }^4$ (with suggestions for ${\phi }^6$ ) and nonpolynomial sine-Gordon theory. A new definition of the $\mathcal{S}$ -matrix is proposed to solve additional divergences which arise in application of Jensen inequality for the continuous case. Analytical results are obtained and numerically illustrated, with plots of variational functions q and corresponding majorants for the $\mathcal{S}$ -matrices of the theory. For simplicity of numerical calculation, the $D=1$ case is considered, and propagator for free theory G is in the form of Gaussian function typically in the Virton–Quark model, although the obtained analytical inferences are not, in principle, limited to these particular choices. Formulation for nonlocal QFT in momentum k space of extra dimensions with subsequent compactification into physical spacetime is discussed, alongside the compactification process. Full article