Adaptive algorithm adjusts the system coefficients based on the measured data. This paper presents a dichotomous coordinate descent method to reduce the computational complexity and to improve the tracking ability based on the variable forgetting factor. Vedic mathematics is used to implement the multiplier and the divider operations in the VFF equations. The proposed method decreases the area and increases the computation speed. The linear exponentially weighted recursive least squares as the main algorithm is implemented in many applications such as the adaptive controller, the system identification, active noise cancellation techniques, and etc. The DCD method calculates the inverse matrix in the ERLS algorithm and decreases the resources used in the field-programmable gate array, also the designer can use the cheaper FPGA board to implement the adaptive algorithm because the method doesn't need lots of resources. The proposed method leads to implementing complex algorithms with simple structures and high technology. The proposed method is implemented with ISE software on the Spartan 6 Xilinx board. The proposed algorithm calculates the multiplication result with less than 15ns time and reduces the used FPGA resources to lower than 20% as compared with the classic RLS.

The domination game is played on an arbitrary graph G by two players, Dominator and Staller. It is known that verifying whether the game domination number of a graph is bounded by a given integer k is PSPACE-complete. On the other hand, it is showed in this paper that the problem can be solved for a graph G in O(D(G).|V (G)|k) time. In the special case when k=3 and the graph G considered has maximum diameter, the complexity is improved to O(|V (G)|.|E(G)|+D(G)3).

A perfect Roman dominating function (PRDF) on a graph $G$ is a function $ f:V(G)\to \{0,1,2\}$ satisfying the condition that every vertex $u$ with $f(u) = 0$ is adjacent to exactly one vertex $v$ for which $f(v) = 2$ . The weight of a PRDF $f$ is the sum of the weights of the vertices under $f$ . The perfect Roman domination number of $G$ is the minimum weight of a PRDF in $G$ . In this paper we study algorithmic and computational complexity aspects of the minimum perfect Roman domination problem (MPRDP) . We first correct the proof of a result published in [Bulletin Iran . Math . Soc . 14(2020) , 342--351] , and using a similar argument , show that MPRDP is APX-hard for graphs with bounded degree 4 . We prove that the decision problem associated to MPRDP is NP-complete even when restricted to star convex bipartite graphs . Moreover , we show that MPRDP is solvable in linear time for bounded tree-width graphs . We also show that the perfect domination problem and perfect Roman domination problem are not equivalent in computational complexity aspects . Finally we propose an integer linear programming formulation for MPRDP .

—In order to provide access control on encrypted data, Attribute-based encryption (ABE) defines each user using a set of attributes. Fuzzy identity-based encryption (FIBE) is a variant of ABE that allows for a threshold access structure for users. To address the potential threat posed by future quantum computers, this paper presents a postquantum fuzzy IBE scheme based on lattices. However, current lattice-based ABE schemes face challenges related to computational complexity and the length of ciphertext and keys. This paper aims to improve the performance of an existing fuzzy IBE scheme by reducing key length and computational complexity during the encryption phase. While negative attributes are not utilized in our scheme, we prove its security under the learning with error (LWE) hard problem assumption in the selective security model. These improvements have significant implications for the field of ABE.

A new implementation of a synthetic aperture focusing technique is presented in the paper. Standard medical ultrasound imaging is done using line-by-line transmission with classical Delay-and-Sum (DAS) image reconstruction. Synthetic aperture imaging, however, has a better resolution and frame rate in cost of more computational load. To overcome this problem, block processing algorithms are used in radar and sonar which are relatively unknown in medical. To extend the methods to medical field, one should concern the parameters difference such as carrier frequency, signal band width, beam width and depth of imaging. In this paper, we extended one of these methods called wavenumber to medical ultrasound imaging with a simple model of synthetic aperture focus. We have also used chirp pulse excitation followed by matched filtering, windowing and spotlighting algorithm to compensate the effect of differences in parameters between radar and medical imaging. computational complexity of the two reconstruction methods, wavenumber and DAS, have been calculated. Field II simulated point data has been used to evaluate the results in terms of resolution and contrast. Evaluations with simulated data show that for typical phantoms, reconstruction by wavenumber algorithm is almost 20 times faster than classical DAS while retaining the resolution.

Cooperative positioning utilizes information received from all the nodes in a network to estimate the position of a target node. This requires high amount of data exchange and data processing in high density networks. This paper proposes a low computational complexity algorithm to select a number of nodes among all possible nodes to cooperate in position finding. Position of nodes are estimated using both the distances between the target node and its cooperated nodes and also the information shared by these nodes. The nodes selection algorithm is proposed according to the Cramer-Rao Lower Bound, which considers the precision of distance measurements, the geometry of nodes and the uncertainty in the information shared by nodes. This fast computing algorithm reduces required computations without significantly decreasing the position estimation performance.

Guess-and-determine attack is one of the general attacks on stream ciphers.It is a common cryptanalysis tool for evaluating security of stream ciphers.The effdeectiveness of this attack is based on the number of unknown bits which will be guessed by the attacker to break the cryptosystem. In this work, we present a relation between the minimum number of the guessed bits and uniquely restricted matching of a graph. This leads us to see that finding the minimum number of the guessed bits is NP-complete. Although fixed parameter tractability of the problem in term of minimum number of the guessed bits remains an open question, we provide some related results.Moreover, we introduce some closely related graph concepts and problems including alternating cycle free matching, jump number and forcing number of a perfect matching.

Objective: Schizophrenia is a complex neurodevelopmental illness that is associated with different deficits in the cerebral cortex and neural networks, resulting in irregularity of brain waves. Various neuropathological hypotheses have been proposed for this irregularity that we intend to examine in this computational study. Method: We used a mathematical model of a neuronal population based on cellular automata to examine two hypotheses about the neuropathology of schizophrenia: first, reducing neuronal stimulation thresholds to increase neuronal excitability,and second, increasing the percentage of excitatory neurons and decreasing the percentage of inhibitory neurons to increase the excitation to inhibition ratio in the neuronal population. Then, we compare the complexity of the output signals produced by the model in both cases with real healthy resting-state electroencephalogram (EEG) signals using the Lempel-Ziv complexity measure and see if these changes alter (increase or decrease) the complexity of the neuronal population dynamics. Results: By lowering the neuronal stimulation threshold (i. e., the first hypothesis), no significant change in the pattern and amplitude of the network complexity was observed, and the model complexity was very similar to the complexity of real EEG signals (P > 0. 05). However, increasing the excitation to inhibition ratio (i. e., the second hypothesis) led to significant changes in the complexity pattern of the designed network (P < 0. 05). More interestingly, in this case, the complexity of the output signals of the model increased significantly compared to real healthy EEGs (P = 0. 002) and the model output of the unchanged condition (P = 0. 028) and the first hypothesis (P = 0. 001). Conclusion: Our computational model suggests that imbalances in the excitation to inhibition ratio in the neural network are probably the source of abnormal neuronal firing patterns and thus the cause of increased complexity of brain electrical activity in schizophrenia.

Purpose: The artificial aperture imaging method owns a good contrast in the data recording and imaging process. However, this method is very time consuming that prevents its practical implementation. Materials and Methods: In this paper, the separated waveforms are sent by two elements together, instead of a single element, and the combination of the methods of independent component analysis and adaptive filtering both are used to extract different components in the received echoes. The obtained result illustrates that the imaging is performed in less time, and the computational complexity of this method is declined. Results: The proposed algorithm has been evaluated on two sets of simulated data and experimental data. The results indicate that the proposed method in the point phantom mode is only 1. 5% worse in the resolution than the conventional artificial aperture method. Also, from the contrasting viewpoint, the proposed method has made the CR parameter worse by about 1. 34dB than the conventional artificial aperture method. These adverse points of resolution and contrast in the proposed method are neglected than the conventional artificial aperture method because of a slight decrease in image quality than the artificial aperture method. Conclusion: However, the proposed method improves the computational complexity by 45% than the conventional artificial aperture method. As a result, it has brought the researchers closer to the practical implementation of artificial aperture imaging.