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The phenomenon of Heider (structural) balance is known for a long time (P. Bonacich and P. Lu, Introduction to Mathematical Sociology, Princeton UP, 2012). Yet it attracts attention of numerous computational scholars, as it is an example of a macroscopic ordering which emerges as a consequence of local interactions. In this paper, we investigate the thermal evolution (driven by thermal noise level $T$) of the work function $U(T)$ for Heider balance on several Archimedean lattices that contain separated triangles, pairs of triangles, chains of triangles and complex structures of triangles. To that end, the heat-bath algorithm is applied. Two schemes of link values updating are considered: synchronous and asynchronous. In the latter case, the analytical formula $U(T)=-\tanh(1/T)$ based on the partition function is provided. The Archimedean lattices are encoded with adjacency matrices, and Fortran procedures for their construction are provided. Finally, we present the mathematical proof that for any two-dimensional lattice, perfect structural (Heider) balance is unreachable at $T>0$., Comment: 12 pages, 13 figures, 5 procedures

A project (e.g., writing a collaborative research paper) is often a group effort. At the end, each contributor identifies their contribution, often verbally. The reward, however, is very frequently financial. It leads to the question of what (percentage) share in the creation of the paper is due to individual authors. Different authors may have various opinions on the matter; even worse, their opinions may have different relevance. In this paper, we present simple models that allow aggregation of experts' views, linking the priority of his preference directly to the assessment made by other experts. In this approach, the more significant the contribution of a given expert, the greater the importance of his opinion. The presented method can be considered an attempt to find consensus among peers involved in the same project. Hence, its applications may go beyond the proposed study example of writing a scientific paper., Comment: 25 pages, 3 figures

Most decision-making models, including the pairwise comparison method, assume the decision-makers honesty. However, it is easy to imagine a situation where a decision-maker tries to manipulate the ranking results. This paper presents three simple manipulation methods in the pairwise comparison method. We then try to detect these methods using appropriately constructed neural networks. Experimental results accompany the proposed solutions on the generated data, showing a considerable manipulation detection level., Comment: 19 pages, 5 figures, 2 tables

Abstract Like electoral systems, decision-making methods are also vulnerable to manipulation by decision-makers. The ability to effectively defend against such threats can only come from thoroughly understanding the manipulation mechanisms. In the presented article, we show two algorithms that can be used to launch a manipulation attack. They allow for equating the weights of two selected alternatives in the pairwise comparison method and, consequently, choosing a leader. The theoretical considerations are accompanied by a Monte Carlo simulation showing the relationship between the size of the PC matrix, the degree of inconsistency, and the ease of manipulation. This work is a continuation of our previous research published in the paper (Szybowski et al., 2023), Comment: 9 figures, 19 pages

Nano-machines circulating inside the human body, collecting data on tissue conditions, represent a vital part of next-generation medical diagnostic systems. However, for these devices to operate effectively, they need to relay not only their medical measurements but also their positions. This paper introduces a novel localization method for in-body nano-machines based on the magnetic field, leveraging the advantageous magnetic permeability of all human tissues. The entire proposed localization system is described, starting from 10x10 ${\mu}m^2$ magnetometers to be integrated into the nano-machines, to a set of external wires generating the magnetic field. Mathematical equations for the localization algorithm are also provided, assuming the nano-machines do not execute the computations themselves, but transmit their magnetic field measurements together with medical data outside of the body. The whole system is validated with computer simulations that capture the measurement error of the magnetometers, the error induced by the Earth magnetic field, and a human body model assuming different possible positions of nano-machines. The results show a very high system accuracy with localization errors even below 1 cm.

The role of an expert in the decision-making process is crucial, as the final recommendation depends on his disposition, clarity of mind, experience, and knowledge of the problem. However, the recommendation also depends on their honesty. But what if the expert is dishonest? Then, the answer on how difficult it is to manipulate in a given case becomes essential. In the presented work, we consider manipulation of a ranking obtained by comparing alternatives in pairs. More specifically, we propose an algorithm for finding an almost optimal way to swap the positions of two selected alternatives. Thanks to this, it is possible to determine how difficult such manipulation is in a given case. Theoretical considerations are illustrated by a practical example., Comment: 18 pages

In decision-making methods, it is common to assume that the experts are honest and professional. However, this is not the case when one or more experts in the group decision making framework, such as the group analytic hierarchy process (GAHP), try to manipulate results in their favor. The aim of this paper is to introduce two heuristics in the GAHP, setting allowing to detect the manipulators and minimize their effect on the group consensus by diminishing their weights. The first heuristic is based on the assumption that manipulators will provide judgments which can be considered outliers with respect to those of the rest of the experts in the group. The second heuristic assumes that dishonest judgments are less consistent than the average consistency of the group. Both approaches are illustrated with numerical examples and simulations., Comment: 32 pages

Decision-making methods very often use the technique of comparing alternatives in pairs. In this approach, experts are asked to compare different options, and then a quantitative ranking is created from the results obtained. It is commonly believed that experts (decision-makers) are honest in their judgments. In our work, we consider a scenario in which experts are vulnerable to bribery. For this purpose, we define a framework that allows us to determine the intended manipulation and present three algorithms for achieving the intended goal. Analyzing these algorithms may provide clues to help defend against such attacks., Comment: 23 pages, 6 compound figures

A new model of an evolution of ranks of employees due to staff turnover in an organization is designed. If the rank is determined only by the performance, the rank shift of incumbents due to the turnover is proportional to the initial rank: the status of high staff is reduced only slightly. This effect that has been observed in the literature. However, if the status also depends on some other variable, the positions of high staff may be greatly deteriorated. In that case, the effect depends nonlinearly on the time $\tau$ between subsequent replacements of staff., Comment: 10 pages, 6 figures

The Heuristic Rating Estimation Method enables decision-makers to decide based on existing ranking data and expert comparisons. In this approach, the ranking values of selected alternatives are known in advance, while these values have to be calculated for the remaining ones. Their calculation can be performed using either an additive or a multiplicative method. Both methods assumed that the pairwise comparison sets involved in the computation were complete. In this paper, we show how these algorithms can be extended so that the experts do not need to compare all alternatives pairwise. Thanks to the shortening of the work of experts, the presented, improved methods will reduce the costs of the decision-making procedure and facilitate and shorten the stage of collecting decision-making data., Comment: 13 pages

The system of two resources $R_1$, $R_2$ and one consumer $C$ is investigated within the Rosenzweig-MacArthur model with Holling type II functional response. The rates $\beta_i$ of consumption of resources $i=1,2$ are coupled by the condition $\beta_1+\beta_2=1$. The dynamic switching is introduced by a maximization of $C$: $d\beta_1/dt=(1/\tau) dC/d\beta_1$, where the characteristic time $\tau$ is large but finite. The space of parameters where both resources coexist is explored numerically. The results indicate that oscillations of $C$ and mutually synchronized $R_i$ which appear at $\beta_i=0.5$ are destabilized for $\beta_i$ larger or smaller. Then, the system is driven to one of fixed points where either $\beta_1>0.5$ and $R_1

One of the most widespread multi-criteria decision-making methods is the Analytic Hierarchy Process (AHP). AHP successfully combines the pairwise comparisons method and the hierarchical approach. It allows the decision-maker to set priorities for all ranked alternatives. But what if, for some of them, their ranking value is known (e.g., it can be determined differently)? The Heuristic Rating Estimation (HRE) method proposed in 2014 tried to bring the answer to this question. However, the considerations were limited to a model that did not consider many criteria. In this work, we go a step further and analyze how HRE can be used as part of the AHP hierarchical framework. The theoretical considerations are accompanied by illustrative examples showing HRE as a multiple-criteria decision-making method., Comment: 24 pages, 2 figures

This paper examines the differences in ordinal rankings obtained from a pairwise comparison matrix using the eigenvalue method and the geometric mean method. First, we introduce several propositions on the (dis)similarity of both rankings concerning the matrix size and its inconsistency expressed by the Koczkodaj's inconsistency index. Further on, we examine the relationship between differences in both rankings and Kendall's rank correlation coefficient $\tau$ and Spearman's rank coefficient $\rho$. Apart from theoretical results, intuitive numerical examples and Monte Carlo simulations are also provided., Comment: 13 pages, 4 figures

We discuss a cellular automaton simulating the process of reaching Heider balance in a fully connected network. The dynamics of the automaton is defined by a deterministic, synchronous and global update rule. The dynamics has a very rich spectrum of attractors including fixed points and limit cycles, the length and number of which change with the size of the system. In this paper we concentrate on a class of limit cycles that preserve energy spectrum of the consecutive states. We call such limit cycles perfect. Consecutive states in a perfect cycle are separated from each other by the same Hamming distance. Also the Hamming distance between any two states separated by $k$ steps in a perfect cycle is the same for all such pairs of states. The states of a perfect cycle form a very symmetric trajectory in the configuration space. We argue that the symmetry of the trajectories is rooted in the permutation symmetry of vertices of the network and a local symmetry of a certain energy function measuring the level of balance/frustration of triads., Comment: 6 pages, 1 figure

In this paper, we propose a new method for the derivation of a priority vector from an incomplete pairwise comparisons (PC) matrix. We assume that each entry of a PC matrix provided by an expert is also evaluated in terms of the expert's confidence in a particular judgment. Then, from corresponding graph representations of a given PC matrix, all spanning trees are found. For each spanning tree, a unique priority vector is obtained with the weight corresponding to the confidence levels of entries that constitute this tree. At the end, the final priority vector is obtained through an aggregation of priority vectors achieved from all spanning trees. Confidence levels are modeled by real (crisp) numbers and triangular fuzzy numbers. Numerical examples and comparisons with other methods are also provided. Last, but not least, we introduce a new formula for an upper bound of the number of spanning trees, so that a decision maker gains knowledge (in advance) on how computationally demanding the proposed method is for a given PC matrix., Comment: 25 pages, 7 figures

We study a simple deterministic map that leads a fully connected network to Heider balance. The map is realized by an algorithm that updates all links synchronously in a way depending on the state of the entire network. We observe that the probability of reaching a balanced state increases with the system size N. Jammed states become less frequent for larger N. The algorithm generates also limit cycles, mostly of length $2$, but also of length 3, 4, 6, 12 or 14. We give a simple argument to estimate the mean size of basins of attraction of balanced states and discuss symmetries of the system including the automorphism group as well as gauge invariance of triad configurations. We argue that both the symmetries play an essential role in the occurrence of cycles observed in the synchronous dynamics realized by the algorithm.

Terahertz-based nano-networks are emerging as a groundbreaking technology able to play a decisive role in future medical applications owing to their ability to precisely quantify figures, such as the viral load in a patient or to predict sepsis shock or heart attacks before they occur. Due to the extremely limited size of the devices composing these nano-networks, the use of the Terahertz (THz) band has emerged as the enabling technology for their communication. However, the characteristics of the THz band, which strictly reduce the communication range inside the human body, together with the energy limitations of nano-nodes make the in-body deployment of nano-nodes a challenging task. To overcome these problems, we propose a novel in-body flow-guided nano-network architecture consisting of three different devices: i) nano-node, ii) nano-router, and iii) bio-sensor. As the performance of this type of nano-network has not been previously explored, a theoretical framework capturing all its particularities is derived to properly model its behavior and evaluate its feasibility in real medical applications. Employing this analytical model, a thorough sensitivity study of its key parameters is accomplished. Finally, we analyze the terahertz flow-guided nano-network design to satisfy the requirements of several medical applications of interest.

This paper is concerned with a novel method allowing communication between FRET nanonetworks and nerve cells. It is focused on two system components: fluorophores and channelrhodopsins which serve as transmitters and receivers, respectively. Channelrhodopsins are used here also as a FRET signal-to-voltage converter. The trade-off between throughput and bit error rate is also investigated.

This article presents an overview of future truly personal communications, ranging from networking inside the human body to the exchange of data with external wireless devices in the surrounding environment. At the nano- and micro-scales, communications can be realized with the aid of molecular mechanisms, Forster resonance energy transfer phenomenon, electromagnetic or ultrasound waves. At a larger scale, in the domain of Body Area Networks, a wide range of communication mechanisms is available, including smart-textiles, inductive- and body-couplings, ultrasounds, optical and wireless radio transmissions, a number of mature technologies existing already. The main goal of this article is to identify the potential mechanisms that can be exploited to provide interfaces in between nano- and micro-scale systems and Body Area Networks. These interfaces have to bridge the existing gap between the two worlds, in order to allow for truly personal communication systems to become a reality. The extraordinary applications of such systems are also discussed, as they are strong drivers of the research in this area.

There are many priority deriving methods for pairwise comparison matrices. It is known that when these matrices are consistent all these methods result in the same priority vector. However, when they are inconsistent, the results may vary. The presented work formulates an estimation of the difference between priority vectors in the two most popular ranking methods: the eigenvalue method and the geometric mean method. The estimation provided refers to the inconsistency of the pairwise comparison matrix. Theoretical considerations are accompanied by Montecarlo experiments showing the discrepancy between the values of both methods., Comment: 18 pages, 4 figures

In a recent work [R. Shojaei et al, Physical Review E 100, 022303 (2019)] the Authors calculate numerically the critical temperature $T_c$ of the balanced-imbalanced phase transition in a fully connected graph. According to their findings, $T_c$ decreases with the number of nodes $N$. Here we calculate the same critical temperature using the heat-bath algorithm. We show that $T_c$ increases with $N$ as $N^{\gamma}$, with $\gamma$ close to 0.5 or 1.0. This value depends on the initial fraction of positive bonds., Comment: 4 pages, 3 figures

The Heider balance is investigated in a chain of actors, with periodic boundary conditions and the neighborhood of range $r$, with $r$ as a parameter. Two model dynamics are applied: a deterministic cellular automaton (Malarz et al, Physica D 411 (2020) 132556) and the heat-bath algorithm, with the density of unbalanced-balanced triads in the role of energy. The outcome is a spectrum of energy in stationary and blinking states and a balanced-unbalanced network transition driven by thermal noise. The critical point $T_c$ increases with the range $r$ and it does not depend on the system size., Comment: Contribution to the special issue of Physica A in memory of Dietrich Stauffer

The state of structural balance (termed also `Heider balance') of a social network is often discussed in social psychology and sociophysics. In this state, actors at network nodes classify other individuals as enemies or friends. Hence, the network contains two kinds of links: positive and negative. Here a new cellular automaton is designed and investigated, which mimics the time evolution towards the structural balance. The automaton is deterministic and synchronous. The medium is the triangular lattice with some fraction $f$ of links removed. We analyse the number of unbalanced triads (parameterized as `energy'), the frequencies of balanced triads and correlations between them. The time evolution enhances the local correlations of balanced triads. Local configurations of unbalanced triads are found which are blinking with period of two time steps., Comment: For Physica D; Special Issue on Discrete Models of Complex Systems: recent trends and analytical challenges

Recent studies have adopted an approach of selecting accurate and diverse trees based on individual or collective performance within an ensemble for classification and regression problems. This work follows in the wake of these investigations and considers the possibility of growing a forest of optimal survival trees. Initially, a large set of survival trees are grown using the method of random survival forest. The grown trees are then ranked from smallest to highest value of their prediction error using out-of-bag observations for each respective survival tree. The top ranked survival trees are then assessed for their collective performance as an ensemble. This ensemble is initiated with the survival tree which stands first in rank, then further trees are tested one by one by adding them to the ensemble in order of rank. A survival tree is selected for the resultant ensemble if the performance improves after an assessment using independent training data. This ensemble is called an optimal trees ensemble (OSTE). The proposed method is assessed using 17 benchmark datasets and the results are compared with those of random survival forest, conditional inference forest, bagging and a non tree based method, the Cox proportional hazard model. In addition to improve predictive performance, the proposed method reduces the number of survival trees in the ensemble as compared to the other tree based methods. The method is implemented in an R package called "OSTE"., Comment: The paper is 24 pages long with 27 figures and 3 tables

Chlorophylls and carotenoids, key components of photosynthetic systems, are proposed for molecular communications at the nanoscale with the mechanism of resonance energy transfer. Both types of pigments are introduced focusing on their exceptional properties like energy harvesting, ultra-low energy consumption during transmissions, picoseconds delays, an ability for signal conversions, and bio-compatibility. The theoretical considerations are supported by two spectroscopic experiments on the photosystem II complex. The first experiment aims at the description of the photosystem II including calculation of the energy transfer efficiency between carotenoids and chlorophylls. In the second one, the photochemical efficiency is estimated, showing how effective the chlorophylls are in further energy processing. With the experimentally determined values, communication and energetic performance are analyzed, the probability of channel blockage is calculated and the energy consumption per bit is estimated. Treating carotenoid molecules as transmitters, chlorophylls as receivers, and the energy transfer between them as a way to encode information, a throughput up to 1 Gbit/s is achievable with a bit error rate below 10^-3, average transmission delays about 20 ps, and energy consumption c.a. 2.0x10^-18 J/bit. These results indicate a high potential of photosynthetic systems for nanocommunications and other related applications, due to suitable energetic characteristics in terms of energy harvesting abilities and low consumption for data transmissions.

We introduce two new inconsistency measures for the incomplete pairwise comparisons matrices and show several examples of their calculation. We also carry out a comparative analysis of the new inconsistency indices with the existing ones based on the Monte Carlo simulation., Comment: 20 pages, 10 figures

We examine satisfaction of the condition of order preservation (COP) with respect to different levels of inconsistency for randomly generated multiplicative pairwise comparison matrices (MPCMs) of the order n = {3,4,...,9}, where a priority vector is derived both by the eigenvalue method (EV) and the geometric mean (GM) method. Our results suggest the GM method and the EV method preserve the COP condition almost identically, both for the less inconsistent matrices (with Saaty's consistency index CI <0.10), and the more inconsistent matrices (with CI >= 0.10). Further, we find that the frequency of the COP violations grows (almost linearly) with increasing inconsistency of MPCMs measured by Koczkodaj's inconsistency index and Saaty's consistency index respectively, and we provide graphs to illustrate these relationships for MPCMs of the order n ={4, 7, 9}., Comment: 15 pages, 14 figures

We discuss the self-deprecating strategy introduced by Peter Blau as one of stages of the process of social integration. Recently we have introduced a two-dimensional space of status, real and surface one ($A$ and $B$), and we have demonstrated that with this setup, the self-deprecating strategy efficiently prevents the rejection [K. Malarz and K. Kulakowski, International Journal of Modern Physics C 30, 1950040 (2019)]. There, the process of reducing the conflict was described by master equations, i.e. a set of differential equations describing evolution of density $v(A,B)$ of actors of status $(A,B)$. Here we reformulate the problem in terms of probabilistic cellular automata. The obtained results for number $n(A,B)$ of actors of status $(A,B)$ are qualitatively the same as in the previous approach, both for synchronous and asynchronous version of the automaton. Namely, an enhancement of the surface status compensates a deficiency of the real one., Comment: 5 pages, 2 figures, 10 movies available online; for FENS10 conference

When creating the ranking based on the pairwise comparisons very often, we face difficulties in completing all the results of direct comparisons. In this case, the solution is to use the ranking method based on the incomplete PC matrix. The article presents the extension of the well known geometric mean method for incomplete PC matrices. The description of the methods is accompanied by theoretical considerations showing the existence of the solution and the optimality of the proposed approach., Comment: 15 pages

We consider the dynamics of interpersonal relations which leads to balanced states in a fully connected network. Here this approach is applied to directed networks with asymmetric relations, and it is generalized to include self-evaluation of actors, according to the 'looking-glass self' theory. A new index of self-acceptance is proposed: the relation of an actor to him/herself is positive, if the majority of his/her positive relations to others are reciprocated. Sets of stable configurations of relations are obtained under the dynamics, where the self-evaluation of some actors is negative. Within each set all configurations have the same structure., Comment: 11 pages, 5 figures

Comparing alternatives in pairs is a very well known technique of ranking creation. The answer to how reliable and trustworthy ranking is depends on the inconsistency of the data from which it was created. There are many indices used for determining the level of inconsistency among compared alternatives. Unfortunately, most of them assume that the set of comparisons is complete, i.e. every single alternative is compared to each other. This is not true and the ranking must sometimes be made based on incomplete data. In order to fill this gap, this work aims to adapt the selected twelve existing inconsistency indices for the purpose of analyzing incomplete data sets. The modified indices are subjected to Monte Carlo experiments. Those of them that achieved the best results in the experiments carried out are recommended for use in practice., Comment: 30 pages, 5 figures

According to Peter M. Blau [Exchange and Power in Social Life, Wiley and Sons, p. 43], the process of integration of a newly formed group has a paradoxical aspect: most attractive individuals are rejected because they raise fear of rejection. Often, their solution is to apply a self-deprecating strategy, which artificially raises the social statuses of their opponents. Here we introduce a two-dimensional space of status, and we demonstrate that with this setup, the self-deprecating strategy efficiently can prevent the rejection. Examples of application of this strategy in the scale of a society are provided., Comment: 10 pages, 11 videos, 1 source code

Alongside consistency, completeness of information is one of the key factors influencing data quality. The objective of this paper is to define ways of treating missing entries in pairwise comparisons (PC) method with respect to inconsistency and sensitivity. Two important factors related to the incompleteness of PC matrices have been identified, namely the number of missing pairwise comparisons and their arrangements. Accordingly, four incompleteness indices have been developed, simple to calculate, each of them take into account both: the total number of missing data and their distribution in the PC matrix. A numerical study of the properties of these indices has been also conducted using a series of Montecarlo experiments. It demonstrated that both incompleteness and inconsistency of data equally contribute to the sensitivity of the PC matrix. Although incompleteness is only just one of the factors influencing sensitivity, a relative simplicity of the proposed indices may help decision makers to quickly estimate the impact of missing comparisons on the quality of final result., Comment: 12 pages, 7 figures

Recent generalization of the coevolving voter model (J. Toruniewska et al, PRE 96 (2017) 042306) is further generalized here, including spin-dependent probability of rewiring. Mean field results indicate that either the system splits into two separate networks with different spins, or one of spin orientation goes extinct. In both cases, the density of active links is equal to zero. The results are discussed in terms of homophily in social contacts., Comment: 7 pages, 6 figures

A practical, biologically motivated case of protein complexes (immunoglobulin G and FcRII receptors) moving on the surface of mastcells, that are common parts of an immunological system, is investigated. Proteins are considered as nanomachines creating a nanonetwork. Accurate molecular models of the proteins and the fluorophores which act as their nanoantennas are used to simulate the communication between the nanomachines when they are close to each other. The theory of diffusion-based Brownian motion is applied to model movements of the proteins. It is assumed that fluorophore molecules send and receive signals using the Forster Resonance Energy Transfer. The probability of the efficient signal transfer and the respective bit error rate are calculated and discussed., Comment: It is the extended version of the paper, presented later (in shorter version) on the NanoCom 2016

Nanocommunications, understood as communications between nanoscale devices, is commonly regarded as a technology essential for cooperation of large groups of nanomachines and thus crucial for development of the whole area of nanotechnology. While solutions for point-to-point nanocommunications have been already proposed, larger networks cannot function properly without routing. In this article we focus on the nanocommunications via Forster Resonance Energy Transfer (FRET), which was found to be a technique with a very high signal propagation speed, and discuss how to route signals through nanonetworks. We introduce five new routing mechanisms, based on biological properties of specific molecules. We experimentally validate one of these mechanisms. Finally, we analyze open issues showing the technical challenges for signal transmission and routing in FRET-based nanocommunications.

The phenomenon of Forster Resonance Energy Transfer, commonly used to measure the distances between fluorophore molecules and to study interactions between fluorescent-tagged proteins in life sciences, can also be applied in nanocommunication networks to transfer information bits. The mechanism offers a relatively large throughput and very small delays, but at the same time the channel bit error rate is too high and the transmission ranges are too limited for communication purposes. In this paper, multiple donors at the transmitter side and multiple acceptors at the receiver side are considered to decrease the bit error rate. As nanoantennas, the DyLight fluorescent dyes, which are very well suited to long range nanocommunication due to their large Forster distances and high degrees of labeling, are proposed. The reported results of the recent laboratory experiments confirm efficient communication on distances over 10 nm.

Nano-communication has gained significant attention in the last few years, as a means to establish information transfer between future nano-machines. Comparing with other communication techniques for nano-scale (calcium ions signaling, molecular or catalytic nanomotors, pheromones propagation, bacteria-based communication), the phenomenon called Forster Resonance Energy Transfer (FRET) offers significantly smaller propagation delays and high channel throughput. In this paper, we report our recent experiments on FRET-based nano-networks performed in the Laboratory of Cell Biophysics of the Jagiellonian University, Krakow. We propose to use Alexa Fluor dyes as nano transmitters and receivers, as they enable to create multiple-input multi-output (MIMO) FRET communication channels and thus enhance FRET efficiency. We measure FRET efficiency values, calculate bit error rates for the measured scenarios and extend the calculations to consider a general case of MIMO (n,m) FRET channels.