Lemaître's law and the spatial distributions of the cone photoreceptors in the retinas of vertebrates

By applying the principle of maximum entropy, we demonstrate the universality of the spatial distributions of the cone photoreceptors in the retinas of vertebrates. We obtain Lemaître's law as a special case of our formalism.

On the Inverse Fourier Transform of the Planck-Einstein law

After proposing a natural metric for the space in which particles spin which implements the principle of maximum frequency, E=hf is generalised and its inverse Fourier transform is calculated. As a necessary result, a metric is found for the space in which quantum particles spin, hence the possibility of explanation of correlation of spacelike-separated particles is opened up.

Entropy-Based Temporal Downscaling of Precipitation as Tool for Sediment Delivery Ratio Assessment

Many regions around the globe are subjected to precipitation-data scarcity that often hinders the capacity of hydrological modeling. The entropy theory and the principle of maximum entropy can help hydrologists to extract useful information from the scarce data available. In this work, we propose a new method to assess sub-daily precipitation features such as duration and intensity based on daily precipitation using the principle of maximum entropy. Particularly in arid and semiarid regions, such sub-daily features are of central importance for modeling sediment transport and deposition. The obtained features were used as input to the SYPoME model (sediment yield using the principle of maximum entropy). The combined method was implemented in seven catchments in Northeast Brazil with drainage areas ranging from 10−3 to 10+2 km2 in assessing sediment yield and delivery ratio. The results show significant improvement when compared with conventional deterministic modeling, with Nash–Sutcliffe efficiency (NSE) of 0.96 and absolute error of 21% for our method against NSE of −4.49 and absolute error of 105% for the deterministic approach.

A Weakly Informative Prior for Resonance Frequencies

We derive a weakly informative prior for a set of ordered resonance frequencies from Jaynes’ principle of maximum entropy. The prior facilitates model selection problems in which both the number and the values of the resonance frequencies are unknown. It encodes a weakly inductive bias, provides a reasonable density everywhere, is easily parametrizable, and is easy to sample. We hope that this prior can enable the use of robust evidence-based methods for a new class of problems, even in the presence of multiplets of arbitrary order.

Application of biomimetic design in concept of small terrain electric vehicle, MODULO

Biomimetic Design is based on basic natural principles. One of the basic natural principle is principle of maximum and minimum. Biological structures or systems can achieve maximum performance and durability with minimal material and energy consumption. More developed system in nature, means the more favorable ratio of this principle. Therefore, this natural principle of maximum and minimum is the basis for trends in biomimetic design. Trends of biomimetic design (functional morphology, optimal arrangement, determination of functionality, multi-functionality, energy use, and so on) are presented for concept of small terrain electric vehicle in this paper. The electric vehicle model has 2 parts: front and rear module with a choice of accumulator size, and with a choice of 4x2 or 4x4 drives. The transport of people (including injured people) or transport of cargo to hard-to-reach places is main concept idea of terrain electric vehicle. This work is supported by the Slovak Research and Development Agency under the contract no. APVV-18-0457, Special Light Electric Vehicle from Unconventional Materials to Heavy Conditions and Terrain – LEV.

Application of biomimetic design in concept of small terrain electric vehicle, MODULO

Biomimetic Design is based on basic natural principles. One of the basic natural principle is principle of maximum and minimum. Biological structures or systems can achieve maximum performance and durability with minimal material and energy consumption. More developed system in nature, means the more favorable ratio of this principle. Therefore, this natural principle of maximum and minimum is the basis for trends in biomimetic design. Trends of biomimetic design (functional morphology, optimal arrangement, determination of functionality, multi-functionality, energy use, and so on) are presented for concept of small terrain electric vehicle in this paper. The electric vehicle model has 2 parts: front and rear module with a choice of accumulator size, and with a choice of 4x2 or 4x4 drives. The transport of people (including injured people) or transport of cargo to hard-to-reach places is main concept idea of terrain electric vehicle. This work is supported by the Slovak Research and Development Agency under the contract no. APVV-18-0457, Special Light Electric Vehicle from Unconventional Materials to Heavy Conditions and Terrain – LEV.

Entropy and Wealth

While entropy was introduced in the second half of the 19th century in the international vocabulary as a scientific term, in the 20th century it became common in colloquial use. Popular imagination has loaded “entropy” with almost every negative quality in the universe, in life and in society, with a dominant meaning of disorder and disorganization. Exploring the history of the term and many different approaches to it, we show that entropy has a universal stochastic definition, which is not disorder. Hence, we contend that entropy should be used as a mathematical (stochastic) concept as rigorously as possible, free of metaphoric meanings. The accompanying principle of maximum entropy, which lies behind the Second Law, gives explanatory and inferential power to the concept, and promotes entropy as the mother of creativity and evolution. As the social sciences are often contaminated by subjectivity and ideological influences, we try to explore whether maximum entropy, applied to the distribution of a wealth-related variable, namely annual income, can give an objective description. Using publicly available income data, we show that income distribution is consistent with the principle of maximum entropy. The increase in entropy is associated to increases in society’s wealth, yet a standardized form of entropy can be used to quantify inequality. Historically, technology has played a major role in the development of and increase in the entropy of income. Such findings are contrary to the theory of ecological economics and other theories that use the term entropy in a Malthusian perspective.

Organization of suburban communication in the conditions of repair work on the railway section

The organization of transport services for suburban routes during the periods of providing "windows" should be based on logistics approaches and the principle of maximum use of the possibilities of railway transport for the development of a given and predicted passenger traffic. Intermodal transport is the most progressive and efficient method of passenger transportation, which is most convenient and more understandable to a person from the point of view of the organization-the responsibility of one carrier for the entire transport process on the route.

On the Inverse Fourier Transform of the Planck-Einstein law

After proposing a natural metric for the space in which particles spin which implements the principle of maximum frequency, E=hf is generalised and its inverse Fourier transform is calculated.