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It is not simple to consider the world from only one side, but analyzing all sides can cloud comprehension without reaching deep insight found at the core. In a word as a whole, there is potential for telling the whole world in one word, i.e., data, leading to interpretations as phenomena and paradigms at the core of this review. The tug of war between the two sides explains that data represent the world, or vice versa, and present a fundamental view that systems or subsystems frame the world, even though they are encoded and composed of culture, rules, or approaches such as the threshold of democracy. When the COVID-19 pandemic posed a threat, human efforts contributed to finding potentially answers to questions presented by the world: what, who, where, when, why, and how (5 wh); a calling in the form of a challenge, where facts show something. All these questions resulted in research, education, and service activities, with their respective data frameworks producing results. This paper aims to reveal the meaning of the outcomes through an observation from an outside perspective. Therefore, like COVID-19 and its vaccines, the assertion of convexity and concave contradictions in the treatment of data leads to a mutually conjugate treatment of data. In this regard, statistics and artificial intelligence play separate and complementary roles. [ABSTRACT FROM AUTHOR]

An important goal in researching the biology of olfaction is to link the perception of smells to the chemistry of odorants. In other words, why do some odorants smell like fruits and others like flowers? While the so-called stimulus-percept issue was resolved in the field of color vision some time ago, the relationship between the chemistry and psycho-biology of odors remains unclear up to the present day. Although a series of investigations have demonstrated that this relationship exists, the descriptive and explicative aspects of the proposed models that are currently in use require greater sophistication. One reason for this is that the algorithms of current models do not consistently consider the possibility that multiple chemical rules can describe a single quality despite the fact that this is the case in reality, whereby two very different molecules can evoke a similar odor. Moreover, the available datasets are often large and heterogeneous, thus rendering the generation of multiple rules without any use of a computational approach overly complex. We considered these two issues in the present paper. First, we built a new database containing 1689 odorants characterized by physicochemical properties and olfactory qualities. Second, we developed a computational method based on a subgroup discovery algorithm that discriminated perceptual qualities of smells on the basis of physicochemical properties. Third, we ran a series of experiments on 74 distinct olfactory qualities and showed that the generation and validation of rules linking chemistry to odor perception was possible. Taken together, our findings provide significant new insights into the relationship between stimulus and percept in olfaction. In addition, by automatically extracting new knowledge linking chemistry of odorants and psychology of smells, our results provide a new computational framework of analysis enabling scientists in the field to test original hypotheses using descriptive or predictive modeling. [ABSTRACT FROM AUTHOR]

Networks have been a general tool for representing, analyzing, and modeling relational data arising in several domains. One of the most important aspect of network analysis is community detection or network clustering. Until recently, the major focus have been on discovering community structure in single (i.e., monoplex) networks. However, with the advent of relational data with multiple modalities, multiplex networks, i.e., networks composed of multiple layers representing different aspects of relations, have emerged. Consequently, community detection in multiplex network, i.e., detecting clusters of nodes shared by all layers, has become a new challenge. In this paper, we propose Network Fusion for Composite Community Extraction (NF-CCE), a new class of algorithms, based on four different non-negative matrix factorization models, capable of extracting composite communities in multiplex networks. Each algorithm works in two steps: first, it finds a non-negative, low-dimensional feature representation of each network layer; then, it fuses the feature representation of layers into a common non-negative, low-dimensional feature representation via collective factorization. The composite clusters are extracted from the common feature representation. We demonstrate the superior performance of our algorithms over the state-of-the-art methods on various types of multiplex networks, including biological, social, economic, citation, phone communication, and brain multiplex networks. [ABSTRACT FROM AUTHOR]

Abstract Throughout the last decade, we have seen much progress towards characterising and computing the minimum hybridisation number for a set P of rooted phylogenetic trees. Roughly speaking, this minimum quantifies the number of hybridisation events needed to explain a set of phylogenetic trees by simultaneously embedding them into a phylogenetic network. From a mathematical viewpoint, the notion of agreement forests is the underpinning concept for almost all results that are related to calculating the minimum hybridisation number for when | P | = 2. However, despite various attempts, characterising this number in terms of agreement forests for | P | > 2 remains elusive. In this paper, we characterise the minimum hybridisation number for when P is of arbitrary size and consists of not necessarily binary trees. Building on our previous work on cherry-picking sequences, we first establish a new characterisation to compute the minimum hybridisation number in the space of tree-child networks. Subsequently, we show how this characterisation extends to the space of all rooted phylogenetic networks. Moreover, we establish a particular hardness result that gives new insight into some of the limitations of agreement forests. [ABSTRACT FROM AUTHOR]

Although the deterministic equation of life predicted and recognized by Albert Einstein is not yet defined, there are clear marks and signs of mathematical regularity which appear in nature showing fascinating accuracy. One of those "God's imprints" in the world that surrounds us is the Fibonacci Sequence, which represents more likely a starting point in revealing certain universal formula of life. The main idea of this paper is to enlighten two points: the Fibonacci sequence and the Golden Ratio, as well as to stress out the importance of reveling the perfect mathematical patterns that exist both in the organic as well as in the inorganic world. Thus, we might be able to understand the physical, spiritual and mental aspect of a human nature more clearly and completely. [ABSTRACT FROM AUTHOR]

Although the deterministic equation of life predicted and recognized by Albert Einstein is not yet defined, there are clear marks and signs of mathematical regularity which appear in nature showing fascinating accuracy. One of those "God's imprints" in the world that surrounds us is the Fibonacci Sequence, which represents more likely a starting point in revealing certain universal formula of life. The main idea of this paper is to enlighten two points: the Fibonacci sequence and the Golden Ratio, as well as to stress out the importance of reveling the perfect mathematical patterns that exist both in the organic as well as in the inorganic world. Thus, we might be able to understand the physical, spiritual and mental aspect of a human nature more clearly and completely. [ABSTRACT FROM AUTHOR]

In the animal world, various kinds of collective motions have been found and proven to be efficient ways of carrying out some activities such as searching for food and avoiding predators. Many scholars research the interactions of collective behaviors of human beings according to the rules of collective behaviors of animals. Based on the Lennard-Jones potential function and a self-organization process, our paper proposes a topological communication model to simulate the collective behaviors of human beings. In the results of simulations, we find various types of collective behavior and fission behavior and discover the threshold for the emergence of collective behavior, which is the range five to seven for the number of topology K. According to the analysis of network properties of the model, the in-degree of individuals is always equal to the number of topology. In the stable state, the out-degrees of individuals distribute around the value of the number of topology K, except that the out-degree of a single individual is approximately double the out-degrees of the other individuals. In addition, under different initial conditions, some features of different kinds of networks emerge from the model. We also find the leader and herd mentality effects in the characteristics of the behaviors of human beings in our model. Thus, this work could be used to discover how to promote the emergence of beneficial group behaviors and prevent the emergence of harmful behaviors. [ABSTRACT FROM AUTHOR]

The Human Genome Project introduced large-scale collaborations involving dozens to hundreds of scientists into biology. It also created a pressing need to solve discrete mathematics problems involving tens of thousands of elements. In this paper, we use minimal path lengths in the Erdős Collaboration Graph between prominent individual researchers as a measure of the distance between disciplines, and we show that the Human Genome Project brought laboratory biology as a whole closer to mathematics. We also define a novel graph reduction method and a metric that emphasizes the robustness of collaborative connections between researchers; these can facilitate the analysis of both within- and between- community connectivity in collaboration graphs. [ABSTRACT FROM AUTHOR]