Inversible Max-Plus Algebras and Integrable systems

We present an extended version of max-plus algebra which includes the inverse operator of "max". This algebra enables us to ultra-discretize the system including subtractions and obtain new ultra-discrete equations. The known ultra-discrete equations can also be recovered by this construction.Comment: 21 page

Unveiling the directional network behind the financial statements data using volatility constraint correlation

Financial data, such as financial statements, stores valuable and critical information to potentially assist stakeholders and investors optimize their capital so that it maximizes overall economic growth. Since there are many variables in financial statements, it is important to determine the causal relationships, that is, the directional influence between them in a structural way, as well as to understand the related accounting mechanisms. However, the analysis of variable-to-variable relationships in financial information by using the standard correlation functions is not sufficient to unveil directionality. Here, we use the volatility constrained correlation (VC correlation) method that enables us to predict the directional relationship between the two variables. To be precise, we apply the VC correlation method to five major financial information variables (revenue, net income, operating income, own capital and market capitalization) of 2321 firms in 28 years from 1990 to 2018 listed on Tokyo Stock Exchange in order to identify which variables are influential and which are susceptible variables. Our findings show that operating income is the most influential variable and market capital and revenue are the most susceptible variables among the five major accounting variables. Surprisingly, the results are different from the existing intuitive understanding suggested by widely used investment strategy indicators known as PER and PBR, which report that net income and own capital are the most influential variable on market capital. Taken together, the presented analysis may assist managers, stakeholders and investors to improve performance of financial management as well as optimize financial strategies for firms in future operations.Comment: 14 pages, 4 figure

Structurally Robust Control of Complex Networks

Robust control theory has been successfully applied to numerous real-world problems using a small set of devices called {\it controllers}. However, the real systems represented by networks contain unreliable components and modern robust control engineering has not addressed the problem of structural changes on a large network. Here, we introduce the concept of structurally robust control of complex networks and provide a concrete example using an algorithmic framework that is widely applied in engineering. The developed analytical tools, computer simulations and real network analyses lead herein to the discovery that robust control can be achieved in scale-free networks with exactly the same order of controllers required in a standard non-robust configuration by adjusting only the minimum degree. The presented methodology also addresses the probabilistic failure of links in real systems, such as neural synaptic unreliability in {\it C. elegans}, and suggests a new direction to pursue in studies of complex networks in which control theory has a role.Comment: 36 pages, 22 figures. This paper was submitted to a journal in May 2014 and still under review. Please cite the arxiv version if your work is related to our researc

Clustering under the line graph transformation: application to reaction network

BACKGROUND: Many real networks can be understood as two complementary networks with two kind of nodes. This is the case of metabolic networks where the first network has chemical compounds as nodes and the second one has nodes as reactions. In general, the second network may be related to the first one by a technique called line graph transformation (i.e., edges in an initial network are transformed into nodes). Recently, the main topological properties of the metabolic networks have been properly described by means of a hierarchical model. While the chemical compound network has been classified as hierarchical network, a detailed study of the chemical reaction network had not been carried out. RESULTS: We have applied the line graph transformation to a hierarchical network and the degree-dependent clustering coefficient C(k) is calculated for the transformed network. C(k) indicates the probability that two nearest neighbours of a vertex of degree k are connected to each other. While C(k) follows the scaling law C(k) ~ k(-1.1 )for the initial hierarchical network, C(k) scales weakly as k(0.08 )for the transformed network. This theoretical prediction was compared with the experimental data of chemical reactions from the KEGG database finding a good agreement. CONCLUSIONS: The weak scaling found for the transformed network indicates that the reaction network can be identified as a degree-independent clustering network. By using this result, the hierarchical classification of the reaction network is discussed

Prospect Theory for Online Financial Trading

Prospect theory is widely viewed as the best available descriptive model of how people evaluate risk in experimental settings. According to prospect theory, people are typically risk-averse with respect to gains and risk-seeking with respect to losses, known as the “reflection effect”. People are much more sensitive to losses than to gains of the same magnitude, a phenomenon called “loss aversion”. Despite of the fact that prospect theory has been well developed in behavioral economics at the theoretical level, there exist very few large-scale empirical studies and most of the previous studies have been undertaken with micro-panel data. Here we analyze over 28.5 million trades made by 81.3 thousand traders of an online financial trading community over 28 months, aiming to explore the large-scale empirical aspect of prospect theory. By analyzing and comparing the behavior of winning and losing trades and traders, we find clear evidence of the reflection effect and the loss aversion phenomenon, which are essential in prospect theory. This work hence demonstrates an unprecedented large-scale empirical evidence of prospect theory, which has immediate implication in financial trading, e.g., developing new trading strategies by minimizing the impact of the reflection effect and the loss aversion phenomenon. Moreover, we introduce three novel behavioral metrics to differentiate winning and losing traders based on their historical trading behavior. This offers us potential opportunities to augment online social trading where traders are allowed to watch and follow the trading activities of others, by predicting potential winners based on their historical trading behavior

Evolutionary history and functional implications of protein domains and their combinations in eukaryotes

A rapid emergence of animal-specific domains was observed in animals, contributing to specific domain combinations and functional diversification, but no similar trends were observed in other clades of eukaryotes

Local and global modes of drug action in biochemical networks

It becomes increasingly accepted that a shift is needed from the traditional target-based approach of drug development to an integrated perspective of drug action in biochemical systems. We here present an integrative analysis of the interactions between drugs and metabolism based on the concept of drug scope. The drug scope represents the set of metabolic compounds and reactions that are potentially affected by a drug. We constructed and analyzed the scopes of all US approved drugs having metabolic targets. Our analysis shows that the distribution of drug scopes is highly uneven, and that drugs can be classified into several categories based on their scopes. Some of them have small scopes corresponding to localized action, while others have large scopes corresponding to potential large-scale systemic action. These groups are well conserved throughout different topologies of the underlying metabolic network. They can furthermore be associated to specific drug therapeutic properties

A global view of drug-therapy interactions

Network science is already making an impact on the study of complex systems and offers a promising variety of tools to understand their formation and evolution (1-4) in many disparate fields from large communication networks (5,6), transportation infrastructures (7) and social communities (8,9) to biological systems (1,10,11). Even though new highthroughput technologies have rapidly been generating large amounts of genomic data, drug design has not followed the same development, and it is still complicated and expensive to develop new single-target drugs. Nevertheless, recent approaches suggest that multi-target drug design combined with a network-dependent approach and large-scale systems-oriented strategies (12-14) create a promising framework to combat complex multigenetic disorders like cancer or diabetes. Here, we investigate the human network corresponding to the interactions between all US approved drugs and human therapies, defined by known drug-therapy relationships. Our results show that the key paths in this network are shorter than three steps, indicating that distant therapies are separated by a surprisingly low number of chemical compounds. We also identify a sub-network composed by drugs with high centrality measures (15), which represent the structural back-bone of the drug-therapy system and act as hubs routing information between distant parts of the network. These findings provide for the first time a global map of the largescale organization of all known drugs and associated therapies, bringing new insights on possible strategies for future drug development. Special attention should be given to drugs which combine the two properties of (a) having a high centrality value and (b) acting on multiple targets.Comment: 16 pages, 4 figures. It was submitted to peer review on August 15, 200

Modularity in Protein Complex and Drug Interactions Reveals New Polypharmacological Properties

Recent studies have highlighted the importance of interconnectivity in a large range of molecular and human disease-related systems. Network medicine has emerged as a new paradigm to deal with complex diseases. Connections between protein complexes and key diseases have been suggested for decades. However, it was not until recently that protein complexes were identified and classified in sufficient amounts to carry out a large-scale analysis of the human protein complex system. We here present the first systematic and comprehensive set of relationships between protein complexes and associated drugs and analyzed their topological features. The network structure is characterized by a high modularity, both in the bipartite graph and in its projections, indicating that its topology is highly distinct from a random network and that it contains a rich and heterogeneous internal modular structure. To unravel the relationships between modules of protein complexes, drugs and diseases, we investigated in depth the origins of this modular structure in examples of particular diseases. This analysis unveils new associations between diseases and protein complexes and highlights the potential role of polypharmacological drugs, which target multiple cellular functions to combat complex diseases driven by gain-of-function mutations