Scientia Iranica
Volume:28 Issue: 3, May-Jun 2021

The capacitated minimum spanning tree problem (CMSTP), a well-known combinatorial optimiza- tion problem, holds a central place in telecommunication network design. This problem is to find a minimum cost spanning tree with an extra cardinality limitation on the orders of the subtrees incident to a certain root node. The balanced capacitated minimum spanning tree problem (BCMSTP) is a special case that aims to balance the orders of the subtrees. We show this problem is NP-hard and present two approximation algorithms, in this paper. Considering the maximum order of the subtrees Q, we provide a (3 - 1 /Q)-approximation algorithm to find a balanced solution. We improve this result to a (2:5 + epsilon)-approximation algorithm (for every given epsilon > 0), in the 2d-Euclidean spaces. Also, we present a polynomial time approximation scheme (PTAS) for CMSTP.

‎We ‎revisit the problem of online conflict-free coloring of intervals on a line‎, ‎where each newly inserted interval must be assigned a color upon insertion such that the coloring remains conflict-free‎, ‎i.e‎. ‎for each point $p$ in the union of the current intervals‎, ‎there must be an interval $I$ with a unique color among all intervals covering $p$‎. ‎To best of our knowledge, the ‎best-‎known ‎algorithm ‎uses‎ $O(log^3 n )$ ‎colors, where $n$ is the number of current intervals‎. ‎We‎ present a simple greedy algorithm that uses only $O(log n)$ colors. Therefore, we settle down the open problem raised in cite{ars1‎4‎}.

In the gaming industry, creating well-balanced games is one of the major challenges developers are currently facing. Balance in games has different meanings depending on the game type. But, most of the existing definitions are esteemed from the flow theory. Flow theory in video games is stating that the level of challenge existing in the game must be neither too easy nor too difficult for the player. Games that are not balanced will have a high churn rate and will suffer in terms of monetization. Hence, nowadays a trending research area is focused on establishing mechanisms to create automatic balance in an algorithmic way. In this research, we have used generative adversarial networks (GANs) to automatically create balanced levels. In the proposed work, a level of a 2D platformer game is fed to the network. Finally, the network automatically generates new balanced levels and the levels are checked to see if they have the game’s minimum necessary requirements and also to check if they can be solved by the reinforcement learning agent. In the series of performed evaluations, it is shown that after the training process, the proposed approach is capable of generating levels that are well-balanced with considerable accuracy.

In this paper, the problem of exploring a grid environment in the offline setting has been studied. The goal is to propose an algorithm to find the minimum number of robots for exploring a rectangular grid environment with $n$ rows and $m$ columns, denoted by $R(n,m)$, in a predefined time $T$. In the case that there are no obstacles in the environment, an optimal solution has been proposed for the problem. In the other case when the environment may contain some obstacles, it has been pointed out that the problem is NP-complete and cannot be approximated within better than a factor 2. Finally, a $4$-approximation algorithm has been presented in order to explore $R(n,m)$ in the presence of obstacles.

The concept of Homunculus from human neurophysiology is extended to artificially intelligent systems. It is assumed that an artificially intelligent processing system behaves similar to a minicolumn or ganglion in the natural animal brain, where in general there is a layer of afferent (input) neurons, a number of interconnecting processing cells, and a layer of efferent (output) neurons or organs. The objective is to identify the correlation between the stimulus to each afferent neuron and the corresponding response from each efferent organ when the intelligent system is subjected to its expected stimuli. To illustrate the general concept a small 3-layered feedforward neural network is used as a simple example and a NNculus is built. Building NN and AI culi for autonomous robots can be used in their design and for performance quality control. Another useful application is in studying the topographic organization in internal layers of the minicolumns of human brain through hardware or numerical simulations.

Weapon-Target Assignment (WTA) as an important part of aerial defense cycle has long been ‎studied. Challenges are usually finding fast-computing methods to search optimal or near-‎optimal solution in cases of a large number of weapons and targets. This viewpoint is more ‎mathematically considerable but practically has limited usage in the mentioned context. A ‎real-time search algorithm is proposed which decomposes the WTA problem and by ‎decreasing the size of solution space and deleting impossible solutions, enables real-time ‎exhaustive search algorithm. Implementation of the algorithm for three typical scenarios shows ‎excellent real-time performance and the possibility of finding exact solutions for large-scale ‎problems.‎

In this paper, we propose a new model to describe variations in interpretation and perception of a simple sentence by different people. To show the understandability of a simple sentence in the prediction of future situations, the meaning of a sentence is modeled as a fuzzy if-then rule, and the fuzzy model is investigated in an iterative process. The main goal of the paper is modeling a linguistic rule. This is done using an if-then rule and its variation through one person to another. The model predicts that the interpretation reaching the final person in the following years can be chaotic and thus unpredictable.

A key parameter for analyzing the human balance dynamics during standing is the center of pressure (CoP). But, so far no conclusive idea has been posed with respect to elicited dynamics of the CoP signal during quiet standing. In this paper, a heuristic algorithm has been proposed to prove the chaotic behavior of the CoP signal with high confidence. In the proposed algorithm, at first the deterministic and non-deterministic (may be stochastic or may be chaotic) components of CoP signal are extracted using the empirical mode decomposition (EMD) method. Then the nonlinear features of the extracted components such as fractal dimension, Lyapunov exponent, correlation dimension, and alpha parameter are computed. Then according to the quantitative value of the computed features, the chaotic component is selected among the extracted components. Finally, using the recurrence quantitative analysis (RQA), the selected chaotic component is reanalyzed to give assurance of correct selecting the chaotic component. In this manner, the kind of CoP dynamics can be determined with high confidence. The analyzed CoP signals were recorded through some experiments on 12 healthy subjects being between 20 to 70 years old. The results of this study show that CoP is a chaotic signal whit high confidence.

Short-term memory discrete-time finite impulse response (FIR) controller design along with an optimized tuning method is presented in this paper. For this purpose, the loop shaping scheme is employed in the linear matrix inequalities (LMIs) framework for adjusting some characteristics of the open-loop frequency response such as phase margin and bandwidth to the desired values at appropriate frequencies. Unlike the conventional methods which work based on state-space models, the proposed procedure generates LMIs directly in the frequency domain. The proposed controller design procedure was applied to several integrating time-delay systems to illustrate its performance and the results were compared with some other competing methods

This paper presents a response-based generating rejection scheme (GRS) based on an angular stability prediction logic to initiate the outage of accelerated generating units while saving the rest of generating units from the loss of synchronism. First trigonometric, polynomial, and hybrid models of rotor angle trajectory based on the reasonable assumptions are proofed. Then, by taking these models in the prediction step, through the maximum use of measured data based on defining the forecast horizon (FH) and data window with incremental length, the stability/instability of generating units is separately predicted. Next, the status of tripping signal based on a combinational logic of the output results of the angular stability prediction method is specified. In the developed logic, if at least two models of the three designated models yield the same response about the unit stability status, the trip signal is accordingly fired or blocked. The proposed method is examined on the one machine infinite bus and the WSCC standard test bed under different operation and fault scenarios. The obtained results demonstrate that beside simplicity, low computational burden, and very short processing time, the proposed combinatorial method outperforms the existing ones working with individual prediction models.

This paper is concerned with the tele-operation of autonomous vehicles over analog Additive White Gaussian Noise (AWGN) channel, which is subject to transmission noise and power constraint. The nonlinear dynamic of autonomous vehicle is described by the unicycle model and is cascaded with a bandpass filter acting as encoder. Using the describing function method, the nonlinear dynamic of autonomous vehicle is represented by an approximate linear system. Then, the available results for linear control over analog AWGN channel are extended to account for linear continuous time systems with non - real valued and multiple real valued eigenvalues and for tracking a non-zero reference signal. Subsequently, by applying the extended results on the describing function of autonomous vehicles, a mean square control technique including an encoder, decoder and a controller is presented for reference tracking of the tele-operation of autonomous vehicles over AWGN channel. The satisfactory performance of the proposed control technique is illustrated by computer simulations.

This paper addresses the problem of global practical stabilization of discrete-time switched affine systems via switched Lyapunov functions with the objectives of achieving less conservative stability conditions and less conservative size of the ultimate invariant set of attraction. The main contribution is to propose a state-dependent switching controller synthesis that guarantees simultaneously the invariance and global attractive properties of a convergence set around a desired equilibrium point. This set is constructed by the intersection of a family of ellipsoids associated with each of switched quadratic Lyapunov functions. The global practical stability conditions are proposed as a set of Bilinear Matrix Inequalities (BMIs) for which an optimization problem is established to minimize the size of the ultimate invariant set of attraction. A DC-DC buck converter is considered to illustrate the effectiveness of the proposed stabilization and controller synthesis method.

This paper presents new sufficient conditions as a set of Bilinear Matrix Inequalities (BMIs) for the global practical stabilization of discrete-time switched affine systems. The main contribution is on proposing the stability conditions based on a common quadratic Lyapunov function that can be used to stabilize the discrete-time switched affine systems around a desired equilibrium point for which it is not required to find any Schur stable convex combination of operating modes as a pre-processing stage, that needs special algorithms and is an NP-hard problem. The result is that the existing two-stage stabilization methods based on a pre-calculation of a Schur stable convex combination of operating modes are simplified to a single-stage method by which a high degree of applicability is obtained. The proposed stability conditions are developed in a way the size of the convergence ellipsoid is minimized. Moreover, it is not required the equilibrium point, around which the invariant set of attraction is constructed, be inside a predetermined set of attainable equilibrium points. The satisfactory operation of the proposed stability conditions is illustrated by an academic example and application on various DC-DC converters.

Studying the growth of HIV virus in the human body as one of the fastest infectious viruses is very important. Using mathematical modeling can make experimental tests easier to process and evaluate. It can also help to predict the disease progress and provide a better insight into the virus development. In this study, a new nonlinear differential equation model is introduced to investigate the interaction of the HIV virus with the body immune system. This is a physiological-based model capable of representing complex behaviors. The bifurcation analysis with a variation of activated healthy T cells is carried out. It is shown that the chaotic development of the virus is available for some ranges of activated healthy T cells. This may explain why the virus develops differently in different individuals or under different circumstances. The chaotic region contains some narrow periodic windows, in which the chaotic mode suddenly ends at some critical points, and the system starts a periodic behavior for a tiny range of active healthy T cells. This may indicate the possibility of controllable development of the HIV virus even when it is in the random-like phase of the disease. For more illustration, the system's state space is represented.

Recently, resilience has attracted lots of attention in the study of biological systems. The goal of this paper is investigating the slowness in ischemic stroke patients. A Trier Social Stress Test (TSST) is used to reveal the slowness of the biological system. The slowness of dynamics is calculated for the ECG of healthy individuals and patients with ischemic stroke. The ECG is investigated in four stages: before stress, right after stress, 20 minutes after stress, and 40 minutes after stress. Ten healthy individuals and nine ischemic stroke patients are studied. Six early warning indicators based on slowness and variability are used in this study. The indicators are applied to the RR interval of individuals in four stages. Also, the results were normalized with the rest state of each individual. Heart rate variations were studied as another measure of the slowness of the dynamics. The results reveal that there is no significant difference in the slowness of healthy and patient cases. So, in this case, resilience cannot be used in predicting health problems.

The coexistence of coherent and incoherent clusters, which is named chimera state, has been observed in various coupling configurations. The majority of the studies have considered a static scheme for the network. In this paper, the synchronization patterns of a time-varying network with discontinuous coupling (on/off links) are studied. At first, the prerequisites for the synchronization of continuous and discontinuous coupling are found by the master stability function method. It is observed that when the network with continuous coupling is set in the synchronous region, changing the coupling to a discontinuous one leads to the emergence of a pattern consisting of alternating synchronization, asynchronization, and chimera state. We call this pattern intermittent transient chimera. The study is completed by investigating the effect of the rate of discontinuity on the network behavior.

Synchronization in networks of oscillatory units is an emergent phenomenon that has been observed in various systems, from power grids to ensembles of nerve cells. Many real-world networks have adaptive properties, meaning that their connectivities change with time, depending on the dynamical state of the system. Networks of adaptively coupled oscillators show various synchronization phenomena, such as hierarchical multifrequency clusters, traveling waves, or chimera states. While these self-organized patterns have been previously studied on all-to-all coupled networks, this work extends the investigations towards more complex networks, analyzing the influence of random network topologies for various degrees of dilution of the connectivities. Using numerical and analytical approaches, we investigate the robustness of multicluster states on networks of adaptively coupled Kuramoto-Sakaguchi oscillators against the random dilution of the underlying network topology. We utilize the master stability approach for adaptive networks in order to highlight the interplay between adaptivity and topology. With this, we show the robustness of multifrequency cluster states to diluted connectivities.

Different single computational neuron models have been proposed in the literature. Most of them belong to the Hodgkin–Huxley (H-H) type, in which they can produce complex behavior of the neuron and have efficient computational cost. In this paper, a modified FitzHugh-Rinzel (FH-R) model considering the effect of magnetic induction is proposed. Different features of the model are explored from a complex and nonlinear perspective. For instance, the impact of the magnetic field on the stability of the equilibrium points is studied by stability analysis. Bifurcation analysis reveals that the proposed neuron model has multi-stability. Furthermore, the spatiotemporal behavior of the proposed model is investigated in the complex network consisting of FH-R oscillators, and the effect of external stimuli is explored on wave propagation of the network.