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The recently observed honey bee colony losses have already raised concerns about the future of the managed honey bees and the bees in general. One of the most powerful approach to simulate and predict the dynamics of a complex system, which a honey bee colony undoubtedly is, is the mathematical modelling. We have adopted a compartment model to study the behaviour in a honey bee colony. A system of three ordinary differential equations with a control on the mites was introduced to model the populations of the hive bees, forager bees and mites. We solve a parameter identification inverse problem to reconstruct the values, which are directly unobservable but vital in honeybee management. We apply an adjoint equation optimization approach to solve the inverse problem. Numerical test examples are discussed and the paper is concluded with important implications about the honey bee management. [ABSTRACT FROM AUTHOR]

It was shown that the radioresistance and Acute Lethal Ooses (ALO) of gamma-radiation during evolution from Viruses and Bacteria to Mammals and Birds decreases from about 15000-30 000 Gy in Viruses and Bacteria to 4-12 Gy in Mammals and Birds. It is established a correlation between ALO (in Gy) of organisms and time of appearance of ones in evolution T (in MYr): ALD = 6.223×10−5 T2.5183 with R2=0.84. It has been suggested that the therapeutic and radioprotective effects of radioresistant organisms on higher mammals are due to the high content of gene regulators in their cells. When they enter the human body, they exert a regulatory influence on the biochemical processes at the genetic level. [ABSTRACT FROM AUTHOR]

A negative correlation between the mammalian erythrocyte lifespan (Tls, days) with increasing lifespan (mouse, guinea pig, rabbit, cat, horse, dog, human, goat, cow, sheep), and sodium, and potassium ion membrane permeability coefficients (PNa+, K+, m/s) of erythrocytes exists: Tls = 2.2×10-3 /PNa+, K+0.39 with corresponding coefficient R2=0.858. In different pathological conditions of red blood cells (hemolytic anemia, hereditary stomatocytosis, hereditary spherocytosis, hereditary elliptocytosis and thalasemias) the erythrocytes change the permeability coefficient as well as the lifespan, according to the same alometric relationship. [ABSTRACT FROM AUTHOR]

The model is a system of two nonlinear ordinary differential equations (ODEs) with dependent variables: the number of bees working in the hive and the number of bees that work outside the hive referred here as foragers. The population dynamics is studied. In this small study we present an effective simple algorithm to solve the parameter identification problem of the model in [10]. The parameters are identified using a least square method combined with backward Euler approximation of the ODE system and a Newton method technique for optimization of the cost functional. Numerical results of the parameters, representing the solution to the inverse problem are provided. [ABSTRACT FROM AUTHOR]

The study aims to apply multicriteria mathematical model to determine the optimal honeybee colony's location in regions without overpopulation. The approach including two optimization criteria: 1) One criterion maximizes the beekeeper's desire to distribute bee colonies in certain places. 2) The other criterion minimizes the possibility some bee colonies not be able to be fully nourished. The optimal Pareto solutions have been found in the proposed multicriteria model. In the first decision, a higher value of the first criterion is observed, ie the beekeeper's wishes regarding the location of the hives are given priority over the non-fed hives. In the second solution, greater priority is given to the feeding of bee colonies, as a result of which the number of non-fed bee colonies has decreased. The model is also applied on a real apiculture example of experimental apiaries in Batishnica region (50 km far from Ruse) without overpopulation of the studied area. The optimal distribution of the hives in places has been found. From the fact that the area is without overpopulation, it follows that all beehives will be fed and practically the task is one-criteria, with priority given to the potential location of the hives. [ABSTRACT FROM AUTHOR]

Inverse, or coefficient identification problem for honey bee colony population model is considered. On the base of the numerical solution to a weakly coupled system of ordinary differential equations (ODEs) with initial conditions, specific constant parameters are found by minimization of a quadratic discrete functional, which expresses the difference between the computed and measured numbers of bees working in and outside the hive. The optimization procedure uses quasilinearization which assures second order of convergence. Numerical simulations with synthetic and real data are discussed. [ABSTRACT FROM AUTHOR]

The correlation coefficient between bird eggs volume to surface ratio and incubation time in 28 eggs (from Struthio camelus to Calypte anna) is R =0.561. The eggs volume (Vegg, m³), eggs surface (Segg, m²), incubation times (Tinc, s) and oxygen permeability coefficient (KO2, m/s) trough inner egg membrane are connected by allometric relationship: Vegg /(Segg·Tinc)=KO2 (for 1 Torr oxygen pressure trough egg shell membranes). This relationship allows calculate dynamics of oxygen permeability coefficient trough inner egg shell membrane during bird embryonal development. [ABSTRACT FROM AUTHOR]

COPD is a chronic inflammatory lung disease which is associated with variety of co-morbidities, as the obesity and cardiovascular diseases (CVDs) are the most frequent. The aim of the current study was to explore the correlations of the age and BMI with the anthropometric indices associated with abdominal obesity in individuals with COPD and to explore the possible difference between the genders. Material and methods: This cross-sectional analysis included 851 citizens from the region of Yambol, Bulgaria. They were interviewed and blood pressure was measured during events organized at the World Diabetes Day, November 14, 2016-2018. One hundred and three of the individuals reported previous diagnosis of COPD. The further statistical analyses were performed only in this group of individuals applying SPSS 16.0 for Windows (SPSS Inc.). Results: Thirty three (32%) of the individuals with COPD were men with a mean age of 58.12 ±13.76 years, while the rest of 70 (68%) persons were women with a mean age of 66.70±10.73 years (p=0.001). The body mass index (BMI) correlated positively with the anthropometric indices associated with central obesity: the waist circumferences (WC, r=0.601, p<0.0001), the hip circumferences (HC, r=0.619, p<0.0001) and waist-to-hip ratio (WHR, r=0.214, p=0.033). The age correlated positively only with the WHR ratio in men (r=0.390, p=0.025), but not in women. When comparing the BMI between genders we did not observed difference (p=0.802). However when classified into groups according to the BMI, women were more frequently with normal weight (30.4%) and obese (33.3%) compared to men (25.8% and 16.1%, respectively), while men were more often with overweight than women (58.1% vs. 36.2%, p=0.091). Men had higher WC (99.23±11.40 cm, p=0.080) and especially WHR (0.922±0.067, p<0.0001) than women (94.17±14.50 cm and 0.855±0.084, respectively). According to the WHR the abdominal obesity was more frequently observed in men with COPD (78.8%) than in COPD women (58.6%. p=0.045). The measured high blood pressure was significantly associated with central obesity both in women (p=0.038) and in men (p=0.035). Conclusions: The results of our study confirm the positive correlation of the BMI with other anthropometric indices associated with abdominal obesity. Based on the results we could conclude that central obesity is more common in men than in women and determines a risk for higher blood pressure in patients with COPD. [ABSTRACT FROM AUTHOR]

A new method for calculating vibrational modes in the infrared region of the spectrum is proposed. The method is based on the thermodynamic parameters of the molecules: standard molar Gibbs free energy change of the molecular formation ΔG0f, standard molar enthalpy change of molecular formation ΔH0f and standard molar entropy of molecule S0. From these thermodynamics parameters the vibrational modes can be calculated using TG=ΔG0f/S0 and TH=ΔH0f/S0 as apparent temperatures. After conversion of the thermal energy kTG and kTH (where k is Boltzmann constant) to energy of electromagnetic quanta hfG and hfH (where f is the frequency), one can calculate the wavenumbers of vibrational modes as: kTG/(ch) and kTH/(ch) (where c is the speed of light and h is the Planck constant). [ABSTRACT FROM AUTHOR]

The study present relationship between the total metabolic energy (ETME(c), J) derived as a function of body chemical energy (Gchem, J) and absolute temperature (Tb, K) in mammals: ETME(c) =Gchem (Tb/Tn). In formula the temperature Tn =2.73K appears normalization temperature. The calculated total metabolic energy ETME(c) differs negligible from the total metabolic energy ETME(J), received as a product between the basal metabolic rate (Pm, J/s) and the lifespan (Tls, s) of mammals: ETME = Pm×Tls. The physical nature and biological mean of the normalization temperature (Tn, K) is unclear. It is made the hypothesis that the kTn energy (where k= 1.3806×10-23 J/K -Boltzmann constant) presents energy of excitation states (modes) in biomolecules and body structures that could be in equilibrium with chemical energy accumulated in body. This means that the accumulated chemical energy allows trough all body molecules and structures to propagate excitations states with kTn energy with wavelength in the rage of width of biological membranes. The accumulated in biomolecules chemical energy maintains spread of the excited states through biomolecules without loss of energy. [ABSTRACT FROM AUTHOR]

During organismal development the moment of sexual maturity can be characterizes by nearly maximum basal metabolic rate and body mass. Once the living organism reaches extreme values of the mass and the basal metabolic rate, it reaches near equilibrium thermodynamic steady state physiological level with maximum organismal complexity. Such thermodynamic systems that reach equilibrium steady state level at maximum mass-energy characteristics can be regarded from the prospective of thermodynamics of negative temperature. In these systems the increase of the internal and free energy is accompanied with decrease of the entropy. In our study we show the possibility the living organisms to regard as thermodynamic system with negative temperature. [ABSTRACT FROM AUTHOR]

The unicellular organisms and phages are the first appeared fundamental living organisms on the Earth. The total metabolic energy (Els, J) of these organisms can be expressed by their lifespan metabolic potential (Als, J/kg) and body mass (M, kg): Els =Als M. In this study we found a different expression - by Boltzmann's constant (k, J/K), nucleon mass (mp+, kg) of protons (and neutrons), body mass (M, kg) of organism or mass (Ms) of biomolecules (proteins, nucleotides, polysaccharides and lipids) building organism, and the absolute temperature (T, K). The found equations are: Els= (M/mp+)kT for phages and Els=(Ms/mp+)kT for the unicellular organisms. From these equations the lifespan metabolic potential can be expressed as: Als=Els/M= (k/mp+)T for phages and Als=Els/M= (k/3.3mp+)T for unicellular organisms. The temperature-normated lifespan metabolic potential (Als/T, J/K·kg) is equals to the ratio between Boltzmann's constant and nucleon mass: Als/T=k/mp+ for phages and Als/T=k/3.3mp+ for unicellular organisms. The numerical value of the k/mp+ ratio is equals to 8.254×10³ J/K·kg, and the numerical value of k/3.3mp+ ratio is equal to 2.497×10³ J/K·kg. These values of temperature-normated lifespan metabolic potential could be considered fundamental for the unicellular organisms. [ABSTRACT FROM AUTHOR]

Here is developed the hypothesis that the cell parameters of unicellular organisms (Prokaryotes and Eukaryotes) are determined by the gravitational constant (G, N·m²/kg²), Planck constant (h, J·s) and growth rate of cells. By scaling analyses it was shown that the growth rate vgr(m/s) of unicellular bacteria and protozoa is relatively constant parameter, ranging in a narrow window of 10-12 - 10-10 m/s, in comparison to the diapason of cell mass, ranging 10 orders of magnitudes from 10-17 kg in bacteria to 10-7 kg in amoebas. By dimensional analyses it was shown that the combination between the growth rate of cells, gravitational constant and Planck constant gives equations with dimension of mass M(vgr)=(h·vgr/G) ½ in kg, length L(vgr)= (h·G/vgr 3) ½ in meter, time T(vgr) =(h·G/vgr5) ½ in seconds, and density ρ((vgr)= vgr .3.5/hG2 in kg/m³. For growth rate vgr in diapason of 1×10-11 m/s - 1×10-9.5 m/s the calculated numerical values for mass (3×10-18 -1×10-16 kg), length (5×10-8 -1×10-5 m), time (1×10² -1×106 s) and density (1×10-1 - 1×104 kg/m³) overlaps with diapason of experimentally measured values for cell mass (3×10-18 -1×10-15 kg), volume to surface ratio (1×10-7 -1×10-4 m), doubling time (1×10³ -1×107 s), and density (1050 - 1300 kg/m³) in bacteria and protozoa. These equations show that appearance of the first living cells could be mutually connected to the physical constants. [ABSTRACT FROM AUTHOR]

The scaling of physical and biological characteristics of the living organisms is a basic method for searching of new biophysical laws. In series of previous studies the author showed that in Poikilotherms, Mammals and Aves, the volume to surface ratio V×S-1 (m) of organisms is proportional to their generation time Tgt(s) via growth rate v (m s-1 ): V×S-1 = vgr ×T¹ . The power and the correlation coefficients are near to 1.0. Aim of this study is: i) to prove with experimental data the validity of the above equation for Unicellular organisms and ii) to show that perhaps, the cells are quantum-mechanical systems. The data for body mass M (kg), density p (kg/m³), minimum and maximum doubling time Tdt (s) for 50 unicellular organisms are assembled from scientific sources, and the computer program 'Statistics' is used for calculations. In result i) the analytical relationship from type: V×S-1 = 4.46-10-11×Tdt was found, where vgr = 4.46×10-11 m/s and ii) it is shown that the products between cell mass M, cell length expressed by V/S ratio and growth rate vgr satisfied the Heisenberg uncertainty principle i.e. the inequalities V/S×M#215;vgr > h/2π and Tdt ×M×vgr² > h/2π are valid, where h= 6.626×10-34 J-s is the Planck constant. This rise the question: do cells appear quantum-mechanical systems? [ABSTRACT FROM AUTHOR]

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Small description of the symposium. The early 21st century is characterized by the rapid development of biophysical and biomedicine sciences. In biology and medicine continuously are found application new physical theories, methods, technics and other scientific approaches. As new physical theories we can regard these theories explaining new empiric relationships and laws between others biological and medical characteristics of human and living organisms. In this scientific area fall application of quantum mechanics and thermodynamics in life processes, metabolic theories, cancer theories, empiric and statistical relationships between cellular and organismal characteristics. As new scientific methods and technics we can take these ones, which have not been used so far, but are recently developed by various researches. As example, we can take some computerized methods and technics in physics, electronics, radiology and X-ray technics developed for medical purpose. As a new mathematical method in biology and medicine we can take predominantly method of scaling and empiric (alometric) relationships between other biological and biomedical characteristics of human and living organisms. [ABSTRACT FROM AUTHOR]