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Abstract Basic numerical skills provide an important foundation for the learning of mathematics. Thus, it is critical that researchers and educators have access to valid and reliable ways of assessing young children's numerical skills. The purpose of this study was to evaluate the concurrent, predictive, and incremental validity of a two-minute paper-and-pencil measure of children's symbolic (Arabic numerals) and non-symbolic (dot arrays) comparison skills. A sample of kindergarten children (M age = 5.86, N = 439) were assessed on the measure along with a number line estimation task, a measure of arithmetic, and several control measures. Results indicated that performance on the symbolic comparison task explained unique variance in children's arithmetic performance in kindergarten. Longitudinal analyses demonstrated that both symbolic comparison and number line estimation in kindergarten were independent predictors of 1st grade mathematics achievement. However, only symbolic comparison remained a unique predictor once language skills and processing speed were taken into account. These results suggest that a two-minute paper-and-pencil measure of children's symbolic number comparison is a reliable predictor of children's early mathematics performance. Highlights • We tested the validity and reliability of a recently developed Numeracy Screener. • Performance on the symbolic comparison task predicted kindergarten children's arithmetic performance. • Performance on the symbolic comparison task in kindergarten predicted school mathematics achievement one year later. • The Numeracy Screener may be a useful tool for early mathematics researchers and educators alike. [ABSTRACT FROM AUTHOR]

"Which graphs are determined by their spectra (DS for short)?" is an important and challenging topic in spectral graph theory. Let G be an n -vertex graph with adjacency matrix A (G) and adjacency walk matrix W A (G) = [ e , A (G) e , ... , A n − 1 (G) e ]. We call G controllable if the rank of W A (G) is n over R and noncontrollable otherwise. In Wang (2017), the author gave a simple condition for a controllable graph to be determined by their generalized adjacency spectrum (DGAS for short). However, the result fails for noncontrollable graphs. In this paper, we consider the problem in the context of the generalized distance spectrum. Let G be a connected graph with distance matrix D. A graph G is determined by its generalized distance spectrum (DG D S for short) if any graph H sharing the same generalized distance spectrum with G must be isomorphic to G. The paper aims to extend the result in Wang (2017) from generalized adjacency spectrum to generalized distance spectrum. Besides, a simple arithmetic criterion is given to determine whether a connected graph is DG D S or not, which is applicable to some kind of noncontrollable graphs, e.g., regular graphs. [ABSTRACT FROM AUTHOR]

Abstract: We recall some bibliography on fast polynomial multiplication related to the recent progress in the paper by Cenk and Ozbudak of 2011. [Copyright &y& Elsevier]

In this paper we obtain a Wiener–Hopf type factorization for a real-valued arithmetic Brownian motion with time-dependent drift and volatility. To the best of our knowledge, this paper is the very first step towards realizing the objective of deriving Wiener–Hopf type factorizations for (real-valued) time-inhomogeneous Lévy processes. In order to prove our main theorem, we derive some new results regarding time-inhomogeneous noisy Wiener–Hopf factorization. We demonstrate that in the special case of the arithmetic Brownian motion with constant drift and volatility our main result agrees with classical Wiener–Hopf factorization for this particular time-homogenous Lévy process. [ABSTRACT FROM AUTHOR]

Let G be an n -vertex graph with adjacency matrix A and let e be the all-one vector. Then the walk matrix of G is defined as W = [ e , A e , A 2 e , ... , A n − 1 e ]. We call G controllable if the rank of W is n and noncontrollable otherwise. A graph G is determined by the generalized spectrum , DGS for short, if any graph H having the same generalized spectrum as G must be isomorphic to G. In Wang [13] , the author proposed a method for a family of controllable graphs to be DGS. However, the method fails for noncontrollable graphs, and it turns out that proving a noncontrollable graph to be DGS is more difficult than proving a controllable graph to be DGS. Up to now, there are just a few attempts to investigate generalized spectral characterizations of noncontrollable graphs for which the rank of W is n − 1. In this paper, we focus on spectral characterizations of a new family of noncontrollable graphs for which the rank of W is n − 2 , denoted by G n. We present an arithmetic criterion to determine whether a given graph is DGS in G n. [ABSTRACT FROM AUTHOR]

In this paper we study admissible extensions of several theories T of reverse mathematics. The idea is that in such an extension the structure M = (N , S , ∈) of the natural numbers and collection of sets of natural numbers S has to obey the axioms of T while simultaneously one also has a set-theoretic world with transfinite levels erected on top of M governed by the axioms of Kripke-Platek set theory, KP. In some respects, the admissible extension of T can be viewed as a proof-theoretic analog of Barwise's admissible cover of an arbitrary model of set theory; see [2]. However, by contrast, the admissible extension of T is usually not a conservative extension of T. Owing to the interplay of T and KP , either theory's axioms may force new sets of naturals to exist which in turn may engender yet new sets of naturals on account of the axioms of the other. The paper discerns a general pattern though. It turns out that for many familiar theories T , the second order part of the admissible cover of T equates to T augmented by transfinite induction over all initial segments of the Bachmann-Howard ordinal. Technically, the paper uses a novel type of ordinal analysis, expanding that for KP to the higher set-theoretic universe while at the same time treating the world of subsets of N as an unanalyzed class-sized urelement structure. Among the systems of reverse mathematics, for which we determine the admissible extension, are Π 1 1 - CA 0 and ATR 0 as well as the theory of bar induction, BI. [ABSTRACT FROM AUTHOR]

The biggest challenge associated with a renewable energy source (RES) based microgrids is to maintain their frequency stability. In solving this challenge, virtual inertia control (VIC) could be viewed as an unavoidable part of alternating current (AC) microgrids. For VIC, a phase-locked loop (PLL) is essential for obtaining information regarding the changes in the frequency of the microgrid. However, implementation of PLL might cause greater oscillation in frequency because of its system dynamics. Such type of issues can be resolved by using a multistage proportional integral derivative (PID) controller which restricts the undesirable frequency measurement and thus helps in improving the stability of the microgrid. In this paper, a novel Sine augmented scaled arithmetic optimization algorithm is proposed in purpose to tune the parameters of the aforementioned controller. The effectiveness of the proposed methodology is validated through contrastive simulation results, and the impact of a few standard strategies such as a change in system boundaries and various steps of RESs penetration are also demonstrated. • The concept of virtual inertia control (VIC) is proposed for frequency control in an AC microgrid. • Impact of RESs on virtual inertia control-based AC microgrid is investigated. • By altering the original AOA algorithm, a Sine augmented scaled AOA algorithm is created. • SCA-AOA algorithm is compared with AOA and other algorithms in terms of fitness function. • A MSPID controller is designed with the SCA-AOA algorithm for the VIC-based AC microgrid. [ABSTRACT FROM AUTHOR]

In modern Digital System design, adders are widely used in many applications including Microprocessors, Digital Signal Processors, Arithmetic Logic Units and digital signal processing. Power efficiency is an important key factor for any integrated circuits. By considering the importance of Full Adder (FA) cells, their power consumption may play significant role in overall power consumption. So designing a low-power full adder is important to achieve the high-performance computing. Swing restored technique is commonly used method to reduce the signal swing at the internal nodes and it helps to reduce the power consumption and improves the circuit's speed. This paper presents a novel hybrid full adder cell design using the modified swing restored technique and complementary pass transistor logic. The Full Adder circuit was implemented using Cadence Virtuoso tool on gptk 180 nm CMOS process technology. The proposed full adder was compared with earlier reported circuits based on Delay, Power and PDP. The comparison shows that proposed circuit consumes less power with high performance. Also various process corners and noise immunity were analyzed to find the sensitivity of the circuit. Further an 8-bit Ripple Carry Adder was designed using the proposed full adder to verify the functionality in higher order bits. Simulations were performed and analyzed using the Cadence Spectre. • Designing low-power full adders is of paramount importance in modern digital system design. • The swing restored technique was employed to reduce the signal swing at the internal nodes of the full adder circuit, thereby reducing the power consumption and improving the circuit's speed. • This paper presents a novel design of a full adder circuit using the modified swing restored technique for reducing power consumption and enhancing performance. • The full adder cell introduced in this research was designed with 180 nm CMOS process technology. • A comparative study was performed between the proposed circuit and earlier reported circuits, revealing reduced power dissipation in the proposed design. [ABSTRACT FROM AUTHOR]

This paper proposes a fault-tolerant distributed Bayesian filter for multi-sensor state estimation using a peer-to-peer sensor network with incoherent local estimates problems. The proposed approach uses a Gaussian mixture rather than a single Gaussian distribution to represent the fusion result, which can effectively reduce the negative impact of corrupted local estimates on the fusion results. The resulting filter performs Bayesian recursion via Gaussian mixture. To accommodate a heterogeneous sensor network, we develop a novel arithmetic average fusion employing a set of covariance-dependent weighting coefficients, where the fusion error covariance is effectively reduced in the case of fusing information with different qualities. For intersensor communication, a partial flooding scheme is investigated, in which only valid-likely Gaussian components are disseminated and fused between neighbor sensors. Theoretically, it is shown that under reasonable assumptions, the presented fault-tolerant distributed estimator can guarantee local stability with the exponentially bounded estimation error in the mean square. The effectiveness and superiority of our approach are validated through both simulation and experiment scenarios. • The first-ever fault-tolerant distributed Bayesian filter. • Efficient fault-tolerant Bayesian filter for resolving inconsistent local estimates. • Novel arithmetic average fusion adapted to heterogeneous sensor networks. • The stability of the proposed distributed estimator can be guaranteed. • Real-world experimental validation. [ABSTRACT FROM AUTHOR]

A graph G is said to be determined by its generalized spectra (DGS for short) if for any graph H , H and G are cospectral with cospectral complements implies H is isomorphic to G. In Wang (2017) [14] , the author gave a simple condition for a graph to be DGS. More precisely, let G be a n -vertex graph with adjacency matrix A G , and let W = [ e , A G e , ... , A G n − 1 e ] be the walk-matrix of G , where e is the all-one vector. A theorem of Wang states that if 2 − ⌊ n / 2 ⌋ det ⁡ W is odd and square-free, then G is DGS. However, the above theorem fails for regular graphs. In this paper, we first generalize the notion of DGS by introducing a new matrix associated with graph G , which is essentially a rank-one perturbation of the adjacency matrix of G and is obtained by introducing a graph-vector ξ G associated with G. For a fixed graph-vector ξ G , define Φ (G) = det ⁡ (λ I − (A G + t ξ G ξ G T)). A graph G is determined by Φ (G) (Φ-DS for short) if for any graph H , Φ (G) = Φ (H) implies that H is isomorphic to G. It is not difficult to show that if ξ G is the all-one vector, then G is Φ-DS if and only if it is DGS. Thus, the notion of Φ-DS generalizes that of DGS in a natural way. Moreover, we give a simple arithmetic condition for a large family of regular graphs to be Φ-DS, which is analogous to the aforementioned theorem. Numerical experiments are also presented to illustrate the effectiveness of our results. [ABSTRACT FROM AUTHOR]

Widespread use of string solvers in the formal analysis of string-heavy programs has led to a growing demand for more efficient and reliable techniques which can be applied in this context. Designing practical algorithms for the (generally undecidable) satisfiability problem for systems of string constraints requires a deep understanding of the structure of constraints present in the targeted cases. In this paper, we first investigate relevant benchmarks containing regular expression membership predicates, extract a series of first order logic theories, and prove the decidability, respectively undecidability, of their satisfiability problem. Further, building on the theoretical results, we present a novel length-aware solving algorithm for the quantifier-free first-order theory over regular expression membership predicates and linear arithmetic over string length. We implement and evaluate this algorithm and related heuristics in the Z3 theorem prover. Besides the theoretical aspects leading to this algorithm, a crucial insight that underpins it is that real-world regex and string formulas contain a wealth of information about upper and lower bounds on lengths of strings, and such information can be used very effectively to simplify operations on automata representing regular expressions. Additionally, we present several novel general heuristics, such as the prefix/suffix method, that can be used to make a variety of regex solving algorithms more efficient in practice. We showcase the power of our algorithm and heuristics via an extensive empirical evaluation over a large and diverse benchmark of 57256 regex-heavy instances, almost 75% of which are derived from industrial applications or contributed by other solver developers. Our solver outperforms five other state-of-the-art string solvers over this benchmark. [ABSTRACT FROM AUTHOR]

Cryo-electron microscopy single particle analysis (SPA) represents a vital tool for structure determination of macromolecules. Discrete inverse problems arising in this field are extremely large and seriously contaminated by noise. The model matrix is highly structured and can not be stored explicitly. Iterative regularization methods are used here only rarely, since it is believed that they are computationally expensive and require complicated stopping criteria. In this paper, we overcome these difficulties and demonstrate that Hybrid Krylov subspace methods can be used to solve SPA inverse problems efficiently. We propose an application-driven regularization parameter selection approach and present a matrix-free implementation of the hybrid solver for GPU computations in single precision arithmetic. In comparison to Fourier-based techniques, the hybrid approach allows to compute reconstructions from full (nonreduced) SPA models even for highly noisy data sets. [ABSTRACT FROM AUTHOR]

This paper studies the complexity of constant depth propositional proofs in the cedent and sequent calculus. We discuss the relationships between the size of tree-like proofs, the size of dag-like proofs, and the heights of proofs. The main result is to correct a proof construction in an earlier paper about transformations from proofs with polylogarithmic height and constantly many formulas per cedent. [ABSTRACT FROM AUTHOR]

This paper proposes an improved variant of the arithmetic optimization algorithm (AOA), called LMRAOA, which is used to solve numerical and engineering problems. Various strategies are proposed to improve AOA. First, Multi-Leader Wandering Around Search Strategy (MLWAS) is proposed to improve the exploration ability of the algorithm on global scale. Then, Random High-Speed Jumping Strategy (RHSJ) is proposed, and the search agent performs high-speed search in the current neighborhood to improve the exploitation ability. Finally, in order to avoid local optima, adaptive lens opposition-based learning strategy is proposed, and linear changes are proposed in its parameters to further satisfy the dynamic changes. 27 classic benchmark functions, 6 engineering optimization problems, and CEC2014, CEC2019 and CEC2020 competition functions are tested by LMRAOA algorithm and comparison algorithm. The experimental results show that, in most cases, the LMRAOA outperforms other algorithms in solving engineering and numerical problems, and can provide effective solutions. [ABSTRACT FROM AUTHOR]

Aggregating data to other spatial resolutions can result in spatial aggregation errors, which can affect the data and subsequent analyses. This paper investigates the nature of spatial aggregation errors in the calculation of agglomeration benefits. The finding shows that inappropriate aggregation can result in significant errors in the monetised benefits used in transport appraisals. The error is analysed using both a stylised model and four case studies. Using arithmetic employment-weighted averages for transport costs when calculating the access to economic mass (ATEM) of the aggregated zones resulted in an error of +/-70%. An arithmetic trip-weighted average reduces errors. The error is further reduced using a harmonic employment-weighted average in the ATEM calculation, but it is not eliminated. The remaining error stems from the altered structure of the data stemming from the aggregation process, which is called the modifiable area unit problem (MAUP). Our findings, which concur with the broader MAUP literature, indicate that this error is unavoidable. Our policy recommendation is to calculate the agglomeration benefits as disaggregated as possible, but if aggregation is necessary, use the harmonic employment-weighted average for transport costs. [ABSTRACT FROM AUTHOR]

There has been continuously growing research interest in Artificial Neural Networks (ANNs) due to their vast acceptance in many real-world applications. This has led to the appearance of a variety of realization methods for multilayer perceptron (MLP) inference models. In this paper, we propose a generalized 3-stage, configurable, multiplier-less, massive parallel realization architecture for MLP inference models. We use offset binary coded distributive arithmetic (OBC-DA), which uses LUTs to reduce hardware requirements, to realize internal computing units of MLPs. The designing efforts to achieve a reduction in resource requirements are two-fold; (i) reduction in LUT size itself, which is achieved by exploiting symmetry induced by OBC-DA and thereby reducing LUT size by 50%, and (ii) reduction in total number of LUTs which is attained by sharing the LUTs. The resource efficiency of the proposed architecture is further improved by decomposing the LUTs into parallel and smaller LUTs. Moreover, the resource efficiency is also enhanced by utilizing the symmetry among the inputs in the MLP layer. The ASIC synthesis results for underlying MLPs establish that the proposed method for the realization of MLPs is much more efficient than the earlier reported methods and coincides with the findings of the generalized hardware-timing complexities. [ABSTRACT FROM AUTHOR]

During the last few years, BDD-based SMT solvers proved to be competitive in deciding satisfiability of quantified bit-vector formulas. However, these solvers usually do not perform well on input formulas with complicated arithmetic. Hitherto, this problem has been alleviated by approximations reducing effective bit-widths of bit-vector variables. In this paper, we propose an orthogonal abstraction technique that works on the level of the individual instances of bit-vector operations. In particular, we compute only several bits of the operation result, which may be sufficient to decide the satisfiability of the formula. Experimental results show that our BDD-based SMT solver Q3B extended with these abstractions can solve more quantified bit-vector formulas from the smt-lib repository than SMT solvers Boolector, CVC4, and Z3. [ABSTRACT FROM AUTHOR]

By combining tree representation of sets with the method introduced in the previous three papers I–III [39,35,37] in the series, we give a new Π 2 1 -preserving interpretation of KP ω r + (Π n + 2 - Found) + θ (Kripke–Platek set theory with the foundation schema restricted to Π n + 2 , and augmented by θ) in Σ 1 1 - AC 0 + (Π n + 2 1 - TI) + θ for any Π 2 1 sentence θ , where the language of second order arithmetic is considered as a sublanguage of that of set theory via the standard interpretation. Thus the addition of any Π 2 1 theorem of BI ≡ Σ 1 1 - AC 0 + (Π ∞ 1 - TI) does not increase the consistency strength of KP ω. Among such Π 2 1 theorems are several fixed point principles for positive arithmetical operators and ω -model reflection (the cofinal existence of coded ω -models) for theorems of BI. The reader's familiarity to the previous works I–III in the series might help, but is not necessary. [ABSTRACT FROM AUTHOR]

Quantitative Structure Activity Relation (QSAR) models are mathematical techniques used to link structural characteristics with biological activities, thus considered a useful tool in drug discovery, hazard evaluation, and identifying potentially lethal molecules. The QSAR regulations are determined by the Organization for Economic Cooperation and Development (OECD). QSAR models are helpful in discovering new drugs and chemicals to treat severe diseases. In order to improve the QSAR model's predictive power for biological activities of naturally occurring indoloquinoline derivatives against different cancer cell lines, a modified machine learning (ML) technique is presented in this paper. The Arithmetic Optimization Algorithm (AOA) operators are used in the suggested model to enhance the performance of the Sinh Cosh Optimizer (SCHO). Moreover, this improvement functions as a feature selection method that eliminates superfluous descriptors. An actual dataset gathered from previously published research is utilized to evaluate the performance of the suggested model. Moreover, a comparison is made between the outcomes of the suggested model and other established methodologies. In terms of pIC50 values for different indoloquinoline derivatives against human MV4-11 (leukemia), human HCT116 (colon cancer), and human A549 (lung cancer) cell lines, the suggested model achieves root mean square error (RMSE) of 0.6822, 0.6787, 0.4411, and 0.4477, respectively. The biological application of indoloquinoline derivatives as possible anticancer medicines is predicted with a high degree of accuracy by the suggested model, as evidenced by these findings. [Display omitted] • The primary contributions of this work can be summed up as follows: • Modified Sinh Cosh Optimizer (SCO)-QSAR model to predict pIC 50 values for various cells. • Improve the performance of SCO using Arithmetic Optimization Algorithm operators. • Assess the efficiency of the developed model using real-world QSAR datasets. [ABSTRACT FROM AUTHOR]

Résumé Dans cette revue de la littérature, nous faisons état des connaissances scientifiques concernant la relation entre l'usage des doigts dans des tâches numériques et les performances et comportements des individus dans ces mêmes tâches. Nous nous interrogeons notamment sur l'universalité de l'usage des doigts pour représenter des quantités ou pour faire des calculs arithmétiques. Dans une première partie, nous présentons les travaux sur l'adulte qui témoignent d'usages conscients et inconscients des doigts dans des tâches numériques. La seconde partie de l'article s'intéresse aux travaux menés auprès d'enfants et la question principale à laquelle nous tentons de répondre est celle du rôle des doigts dans la construction des savoirs numériques. Abstract In this literature review, we describe the state of the art of the scientific knowledge about the relationship between the use of fingers in numerical tasks and individuals' performance in those tasks. One of the questions we want to answer is related with the universality of finger use in order to represent quantities on fingers or to achieve arithmetic calculations. In a first part of the paper, we report the results of studies highlighting the conscious and unconscious use of fingers in adults when they perform simple numerical tasks. In the second part of the manuscript, we adopt a more developmental point of view and our main question is whether finger use in children shapes their mental representations of numbers. In order to answer this question, we review the literature concerning the use of fingers for counting collection of objects through pointing, for representing quantities through finger rising and for calculating through finger manipulations. One crucial issue addressed in this part of the paper is the role of finger use for a possible transition between non-symbolic and symbolic number mental representations. In the last part of the paper, we discuss whether fingers are important, necessary or useless for the construction of numerical knowledge and conclude that, despite their possible influence on adults' and children's behaviors and number understanding, they are not indispensable for developing accurate number mental representations. Finally, our review allows us to conclude that an innate view of the relationship between fingers and numbers is not fully supported in the literature and that a more functionalist view wherein fingers can support numerical acquisitions is more plausible. [ABSTRACT FROM AUTHOR]

Bateman linear chain solution is widely used for fusion activation calculations. Its first order derivatives with respect to the decay and cross section constants are implemented for the sensitivity analysis. The general formula for these derivatives is a recursive one which is lengthy and cumbersome to use. The large numbers of arithmetic operations consume considerable computational effort and grow as k 2 , where ‘k’ is the size of a linear chain. However, they provide a complete analytical treatment of the sensitivity analysis. In the present paper, the general formula for the derivatives has been reworked and further simplified without any approximations. The resulting derivatives are a set of simple yet exact recursive relations that require almost no computational labour and grow almost linearly with size ‘k’ of the chain. The derived relations can be easily used for a quicker sensitivity analysis and results are presented within the paper. Higher order derivatives can be derived using simple algebra from the first order derivatives. Further, it is shown in the paper that the first and second order derivatives of the Bateman solution can be used within a Taylor series expansion to perform multi-point analysis on fine meshes over a large geometry. Most of the current multi-point algorithms focus on the coupling or algorithmic aspects to accelerate the calculations. In the present scheme, we use taylor expansion of the Bateman solution itself to directly affect the increase in computational speed. The solution of the Bateman equations at a given reference point within the geometry can be used to estimate the results at neighbouring points through a Taylor expansion. While the method in itself is straightforward, it is made feasible with the simplified derivative relations. This methodology has been successfully implemented within the linear chain solution algorithm and a few results and inferences are provided along with the computational accuracy and efficiency. [ABSTRACT FROM AUTHOR]

• A novel VSI incorporating the phasor data available through PMU is suggested. • Objective Function consists of novel VSI, loss minimization and voltage deviation. • The optimization techniques AOA and PSO are used. • Multiple DGs supplying only active power, only reactive power is considered. With the extensive application of renewable energy operated distributed generation plants in the power system, certain issues need to be addressed. One such problem is the optimal location of these DG units, as their random placement may result in congestion in certain paths of the transmission network. This paper proposed a novel voltage stability indicator (VSI) that is incorporated in the objective function along with real power loss reduction and minimum voltage deviation. The prominent feature of this VSI is the utilization of phasor data available through Phasor Measurement Units (PMUs) in the recent power systems. This VSI performs satisfactorily for both mesh and radial networks. The developed method under the paper is tested on IEEE-30 bus network. To optimize the objective function, Arithmetic Optimization Algorithm (AOA) is used and the obtained results have been compared with Particle swarm optimization. Simulation results justified the applicability of this technique for reducing losses in the network. [Display omitted] [ABSTRACT FROM AUTHOR]

This paper presents a vector relation-centric algorithm for solving arithmetic word problems (AWPs), which uses vector relation acquisition and scene knowledge to ensure the performances of problem understanding and symbolic solver correspondingly. The vector relation acquisition procedure builds on the synergy of the vector syntax-semantics method and the deep neural miner. Compared with the syntax-semantics method, the vector syntax-semantics method decreases not only the number of models but also semantic ambiguities and computational costs. For the scene knowledge, this paper proposes a scene-aware symbolic solver which infers relations obeying scene rules to decrease the occurrences of unwanted operations. Experimental results show that the proposed algorithm is superior to the high-performance baseline algorithm in both accuracy and computational cost. In accuracy, the proposed algorithm increased the accuracy by 3.9% on the sum of the three scene subsets due to the use of the scene knowledge and vector computing; as a result, it increased the accuracy by 0.5% on the sum of six authoritative datasets. In computational cost, the proposed algorithm decreased the computing cost by more than 50%. Thus, this paper makes a significant contribution to developing instruments for solving AWPs. [ABSTRACT FROM AUTHOR]

The source code of any software is confidential and its intellectual property has to be protected from the malicious intent of the attackers. The present work offers the architecture of a cloud model for secure intellectual property protection of arithmetic expressions in a source code. The data obfuscation techniques are meant to be applied on different types of arithmetic operators in an arithmetic expression, "The required algorithms proposed in this paper are named as i) 'Adaptive Number Generation' obfuscation to be applied on all operators ii) Obfuscation by 'Carry Padding' to be applied on '+' operator iii) Three Obfuscations by 'Mixed Boolean Arithmetic' to be applied on '+', '-' and '*' operators and iv) ' A-RSA +′ obfuscation to be applied on '+' operator." Experimentations are conducted to validate their functionality and performance metrics measurements in terms of Cyclomatic complexity, Time complexity, Space complexity and Potency analysis are carried out on a set of benchmark source codes and it has been found that there is only a very slight increase of 6.57% number of lines of code in the obfuscated codes compared to the corresponding original, the average increase in the obfuscated code's execution time is 29% and the estimated average potency given by the proposed obfuscation techniques is 1.06% which is also greater than one. Also, a mathematical model is developed to estimate the Mean Obfuscated Source Code Cloud Delay (MOSCD), which is the time duration in which the obfuscated source code is available physically at the cloud server to face any possible Man-At-The-End (MATE) attacks. An attacker may build a control flow graph (CFG) out of the source code to perform attacks based on static and dynamic analysis-based reverse engineering. The time required to generate a CFG is also estimated and in comparison, with the MOSCD, it is observed that the minimum CFG build time is almost three multiples of the maximum MOSCD value we received in our experimentations it is proved that our model is strong to thwart away any possible MATE attacks. • The source code of any software is confidential and its intellectual property has to be protected from the malicious intent of the attackers. • The present work offers the architecture of a cloud model for secure intellectual property protection of arithmetic expressions in a source code. • The present work offers several data obfuscation techniques to be applied on all the arithmetic operators. • The proposed secure cloud model can able to withstand various security analysis attacks at the cloud at the expense of a slight increase in the system overheads. [ABSTRACT FROM AUTHOR]

This paper proposes new symmetric cryptography algorithms of Residue Number System and its Modified Perfect Form. According to the first method, ciphertext is regarded as a set of residues to the corresponding sets of modules (keys) and decryption or decimal number recovery from its residues takes place according to the Chinese Remainder Theorem. To simplify the calculations, it is proposed to use a Modified Perfect Form of Residue Number System, which leads to a decrease in the number of arithmetic operations (in particular, finding the inverse and multiplying by it) during the decryption process. Another method of symmetric encryption based on the Chinese Remainder Theorem can be applied when fast decryption is required. In this algorithm, the plaintext block is divided into sub-blocks that are smaller than the corresponding module and serve as remainders on dividing some number, which is a ciphertext, by these modules. Plaintext recovery is based on finding the ciphertext remainders to the corresponding modules. Examples of cryptography algorithms implementation and their encryption schemes are given. The security of the proposed methods is estimated on the basis of the Prime number theorem and the Euler function. It is investigated which bitness and a number of modules are required for the developed symmetric security systems to ensure the same security level as the largest length key of the AES algorithm does. It is found that as the number of modules increases, their bitness decreases. Graphical dependencies of cryptanalysis complexity on bitness and a number of modules are built. It is shown that with the increase of specified parameters, the security of the developed methods also increases. [ABSTRACT FROM AUTHOR]

Binary numbers converted into stochastic bitstreams enable computationally complex arithmetic to be performed using stochastic computing (SC). The fault-tolerant nature of stochastic computing has made it useful in a large number of applications. However, stochastic circuit synthesis allows for a larger solution space than classical logic synthesis. SC circuits are synthesized using heuristics in previous methods. In this paper, a novel exact synthesis method via satisfiability (SAT) is proposed to obtain an optimal SC circuit represented by majority-inverter graphs (MIGs). To accelerate the algorithm for executing the exact synthesis, we try to decompose the problem vector by using a cube assignment method for scalability. Moreover, we propose a hybrid algorithm based on both exact synthesis and heuristics. The experimental results indicate that the proposed hybrid approach can reduces the area by 14%, the delay by 9%, and the mean absolute error by 7%. • An exact synthesis method is proposed for stochastic circuit synthesis. • The proposed method can be used to reduce the solution space. • The combined exact and heuristic method is scalable. [ABSTRACT FROM AUTHOR]

A 3D mesh can be reconstructed from multiple viewpoint images or from a single structured light image. Lossy compression of such images by standard techniques such as JPEG at high compression ratios lead to 3D reconstruction being adversely affected by artifacts and missing vertices. In this paper we demonstrate an improved algorithm capable of high compression ratios without adversely affecting 3D reconstruction and with minimum data loss. The compression algorithm starts by applying block DCT over the input image, and the transformed data being quantized using an optimized quantization matrix. The quantized coefficients of each block are arranged as a 1D array and saved with other block's data in a larger matrix of coefficients. The DC coefficients are subject to a first order difference whose values are referred to as residual array. The AC coefficients are reduced by eliminating zeros and saving the non-zero values in a reduced coefficients array using a mask of 0 (for a block of zeros) and 1 (for a block of non-zeros). Finally, arithmetic coding is applied to both coefficients and residual arrays. At decompression stage, the coefficients matrix is regenerated by scanning the coefficients array and examining the headers to substitute zero and non-zero data. This matrix is then added to the residual array to obtain the original DC values. The IDCT is then applied to obtain the original image. The proposed algorithm has been tested with images of varying sizes in the context of 3D reconstruction. Results demonstrate that our proposed algorithm is superior to traditional JPEG at higher compression ratios with high perceptual quality of images and the ability to reconstruct the 3D models more effectively, both for structured light images and for sequences of multiple viewpoint images. [ABSTRACT FROM AUTHOR]

Let f r (k) be the smallest positive integer n such that every r -coloring of { 1 , 2 , ... , n } has a monochromatic solution to the nonlinear equation 1 / x 1 + ⋯ + 1 / x k = 1 / y , where x 1 , ... , x k are not necessarily distinct. Brown and Rödl [3] proved that f 2 (k) = O (k 6). In this paper, we prove that f 2 (k) = O (k 3). The main ingredient in our proof is a finite set A ⊆ N such that every 2-coloring of A has a monochromatic solution to the linear equation x 1 + ⋯ + x k = y and the least common multiple of A is sufficiently small. This approach can also be used to study f r (k) with r > 2. For example, a recent result of Boza et al. [2] implies that f 3 (k) = O (k 43). [ABSTRACT FROM AUTHOR]

This paper studies algebraic properties of fuzzy numbers under a specific arithmetic operation denoted by + 1 / 2. Specifically, this article establishes a new semigroup based on this sum and explores its algebraic properties, as well as homomorphisms between its subsemigroups. Some examples are provided in order to illustrate the results provided here. [ABSTRACT FROM AUTHOR]

Arithmetic optimization algorithm (AOA) is a meta -heuristic algorithm inspired by mathematical operations. AOA has been diffusely used for optimization issues on continuous domains, but few scholars have studied discrete optimization problems. In this paper, we proposed Binary AOA (BAOA) based on two strategies to handle the feature selection problem. The first strategy used S-shaped and V-shaped shift functions to map continuous variables to discrete variables. The second strategy was to combine four logical operations (AND, OR, XOR, XNOR) on the basis of the transfer function, and constructed a parameter model based on the sine and cosine function. An enhanced logic binary sine–cosine function arithmetic optimization algorithm (LBSCAOA) was proposed to realize the position update of variables. Its purpose was to improve the algorithm's global search capabilities and local exploitation capabilities. In the simulation experiments, 20 datasets were selected to testify the capability of the proposed algorithm. Since KNN had the advantages of easy understanding and low training time complexity, this classifier was selected for evaluation. The performance of the improved algorithm was comprehensively evaluated by comparing the average classification accuracy, the average number of selected features, the average fitness value and the average running time. Simulation results showed LBSCAOA with V-Shaped "V4" stood out among many improved algorithms. On the other hand, LBSCAOA with V-Shaped "V4" was used as a representative to compare with other typical feature selection algorithms to verify its competitivenes. [ABSTRACT FROM AUTHOR]

• Moisture affects microbial succession and volatiles generation by mediated with Lactobacillus. • The ratio of ethyl acetate to ethyl lactate and content of acid, alcohol positively relate to moisture. • Increase moisture accelerate formation of Lactobacillus -dominated fermentation microbiota. • Increase moisture enhance complexity and stability of baijiu fermentation ecological networks. Today, image segmentation methods are widely used for various applications, including object detection. Multilevel Thresholding Image Segmentation (MTIS) methods are among the efficient methods for image segmentation. In MTIS methods, it is very important to find the thresholds that gives the best performance for the MTIS and better separate and detect the objects on the image from the image background. Meta-Heuristic (MH) algorithms are among the strategies that can achieve good results in obtaining optimal thresholds to solve this problem. In this paper, we use the combination of Arithmetic Optimization Algorithm (AOA) and Harris Hawks Optimizer (HHO) to improve AOA in exploitation phase, and achieve an optimal threshold vector for MTIS. Therefore, our new hybrid AOA-HHO algorithm solves the MTIS problem with better quality than both AOA and HHO algorithms and some other MH algorithms, and can obtain better thresholds that increase the performance of the MTIS system than AOA and HHO. AOA is powerful in the exploration, and HHO in exploitation phase is powerful. Therefore, AOA-HHO uses the features of both algorithms to search the entire search space locally and globally to find the best find the solution, the high power of the AOA exploration phase, and the high power of the HHO exploitation phase. Also, we use a mathematical equation as the fitness function, that is obtained by using image features. A series of experiments were performed using seven different threshold levels on the test images. Experiments show that AOA-HHO method is better than the compared algorithms and even HHO and AOA in terms of image segmentation accuracy, fitness function value, Peak Signal-to-Noise Ratio (PSNR), Structural Similarity Index Measure (SSIM), and execution time. [ABSTRACT FROM AUTHOR]

In lattice-based cryptography, Ring Learning with Errors (RLWE) is a computationally hard cryptographic problem, comprising three basic mechanisms i.e., key generation, encryption, and decryption. Binary Ring Learning with Error (BRLWE), a new variant of RLWE has been proposed recently to reduce the key size and computational complexity compared to previous RLWE-based schemes. Based on this BRLWE scheme, efficient hardware architectures have been obtained in recent works for lightweight applications. The key operation involved in this scheme is A B + C , where A and C are integer polynomials and B is a binary polynomial. This paper proposes an efficient hardware architecture for BRLWE-based scheme targeted for lightweight applications. The architecture computes the arithmetic operation A B + C , which includes polynomial multiplication and addition over the polynomial ring Z q / (x n + 1). The proposed architecture is applied in two conditions, fixed and variable values of q. Experimental results show the architecture proposed has 50% less Area-Delay Product (ADP) and 20% less Power-Delay Product (PDP) compared to the recently reported work for n = 256. [ABSTRACT FROM AUTHOR]

Atanassov's intuitionistic fuzzy sets play a vital role in handling vagueness and uncertainty successfully as they associate an additional non-membership degree to each element of the universal set. Interval-valued intuitionistic fuzzy (IVIF) sets are more generalized quantities in this direction as they use intervals (⊂ [ 0 , 1 ]) to define the membership and non-membership grades of each element of the set. However, without defining basic arithmetic operations on the IVIF values/sets, the study is incomplete. This paper broadly examines the division and subtraction operations over any arbitrary IVIF values/sets using the concept of Hamming distance between them. A deterministic linear optimization model is proposed and solved in order to obtain the complete expressions for these operations. Next, various fundamental properties and relationships are examined and proved for the proposed arithmetic operations over IVIF values/sets. Furthermore, an example of a multi-criteria decision-making problem under uncertain conditions is studied and analyzed using the developed arithmetic operations on IVIF numbers. • Derived the generalized subtraction and division operations for IVIF values/sets. • The notion of Hamming distance and dual-simplex algorithm are used. • A deterministic LPP is proposed to obtain the expressions for the operations. • The fundamental properties and relationships for the basic operations are explored. • A case study of multi-criteria decision-making problems has been discussed. [ABSTRACT FROM AUTHOR]

• We develop a geometric counting method adaptive to the author number (N). • The credit given to the first author is N times larger than to the last author. • Among fixed-type schemes, this method fits best with existing empirical datasets. • The method balances equal scaling and equal spacing of credit among authors. With increasing research collaboration and the increasing average author number of academic papers, a reasonable counting method is needed to allocate paper credit to authors. This work analyses the features of existing counting methods, focusing on the differences between the credit assigned to each author. Considering that the ratio of credit between neighbouring authors allocated by a rational geometric counting method should change with the author number, we propose an adaptive geometric counting method in which the ratio of the credit of the first author to that of the last author equals the author number, as with fixed-type arithmetic counting and harmonic counting. The results show that the adaptive geometric counting method fits best with the existing empirical dataset among the fixed-type counting methods. In addition to keeping the same ratio of credit between neighbouring authors, the credit allocated to the authors changes with the author rank more evenly with this method than with other counting methods, except arithmetic counting, whose result is inherently linear but does not maintain the same ratio of credit between neighbouring authors. [ABSTRACT FROM AUTHOR]

• Arithmetic-geometric (AG) index was proposed in 2015 and AG matrix and its spectral radius were considered in recent several years. The AG spectral radius deserves further study. • In comparison with other spectral radii, numerical computations show that AG spectral radius studied in this paper is more stable and totipotent in predicting topological descriptors and physical properties of octane isomers. • Note that molecular graphs of octane isomers are trees. Theoretical results on the upper and lower bounds of AG spectral radii of all trees of given order are analyzed. We obtain that the path attains the lower bound and the star attains the upper bound. The chemical applications of the arithmetic-geometric spectral radius ρ a g (G) and energy E a g (G) of a graph G are explored in this paper. We firstly investigate and compare the prediction power of arithmetic-geometric spectral radius, arithmetic-geometric energy, spectral radii and energies in some other topological descriptors and some physical properties of octane isomers. It is concluded that the arithmetic-geometric spectral radius is a good indicator in forecasting Acentric Factor, Entropy and two topological descriptors SNar, HNar of octane isomers. Since molecular graphs of octane isomers are trees, we study arithmetic-geometric spectral radius of general trees. We prove that for any tree T of order n ≥ 2 , 2 cos π n + 1 < ρ a g (P n) ≤ ρ a g (T) ≤ ρ a g (S n) = n 2 , with equality holds if and only if T ≅ P n (the path of order n) for the lower bound, and if and only if T ≅ S n (the star of order n) for the upper bound. [ABSTRACT FROM AUTHOR]

Spectral characterization of graphs is a well-studied topic in spectral graph theory which has received a lot of attention from researchers. The spectral characterization of oriented graphs, however, is less studied so far. Given a simple undirected graph G with an orientation σ , the oriented graph G σ is a digraph obtained from G by assigning to every edge of G a direction according to σ. An oriented graph G σ is self-converse if it is isomorphic to its converse (G σ) T , a graph obtained from G σ by reversing each directed edge in G σ. We denote by S (G σ) the skew-adjacency matrix of G σ. For two oriented graphs G σ and H τ with skew-adjacency matrices S (G σ) and S (H τ) , respectively, we say G σ is R -cospectral to H τ , if for any t ∈ R , two matrices t J − S (G σ) and t J − S (H τ) have the same spectrum, where J is the all-one matrix. An oriented graph G σ is said to be determined by the generalized skew spectrum (DGSS for short) if, any oriented graph R -cospectral to G σ is isomorphic to G σ. Oriented graphs that are DGSS must be self-converse. In this paper, we give a simple arithmetic condition for a self-converse oriented graph being DGSS, which provides an analogue of a similar result for ordinary graphs; see [15]. More precisely, let G σ be a self-converse oriented graph with skew-adjacency matrix S (G σ) , and W (G σ) = [ e , S (G σ) e , ⋯ , S n − 1 (G σ) e ] (e is the all-one vector) be the skew-walk-matrix. We show that if 2 − ⌊ n 2 ⌋ det ⁡ W (G σ) is odd and square-free, then G σ is DGSS. Moreover, we also illustrate that our result is the best possible in certain sense. [ABSTRACT FROM AUTHOR]

The pandemic of Covid-19 has caused a shift of paradigm of education, from face-to-face to e-learning. E-learning leads to an escalation in digitalization of handwritten documents because it requires submission of homework and assignments through online. To help teachers in checking digitalized handwritten homework, this paper proposes an automatic checking system based on a convolutional neural network (CNN) for handwritten numeral recognition. The CNN is used to recognize four arithmetic operations in mathematical questions consisting of addition, deduction, multiplication and division. The performance CNN in handwritten numeral recognition have been optimized in terms of activation function and gradient descent algorithm. The proposed CNN is also trained and tested with the MNIST handwritten data set. The experimental results show that the recognition accuracy the improved CNN improves to a certain extent as compared to before optimization. [ABSTRACT FROM AUTHOR]

The paper discusses multidimensional fuzzy RDM-arithmetic and its application to solving linear fuzzy equation systems. Such arithmetic can also be used to test whether the found solution satisfies condition of nestedness and thus initially verify its correctness. The presented methods are illustrated with three examples coming from the literature. [ABSTRACT FROM AUTHOR]

The quantum-resistant attribute is a new design criterion for cryptography algorithms in the era of quantum supremacy. Lattice-based cryptography is proved to be secure against quantum computing. CRYSTALS-Kyber is a lattice-based promising candidate in the post-quantum cryptography standardization process. This paper proposes a high-performance polynomial ring processor for the CRYSTALS-Kyber algorithm. The processor executes optimized polynomial ring arithmetic, which cuts off over 20%/50% on the times of modular multiplication/addition compared with the straightforward implementations. Besides, the forward and inverse Number Theoretic Transform (NTT) reuse the control logic with the help of an efficient configurable butterfly unit to minimize the area of the finite state machine. Further, the underlying dual-column sequential storage scheme breaks the bottleneck of memory accessing. To evaluate the performance, a fully pipelined architecture is implemented on a low-cost FPGA platform. Benefiting from these optimizations, the Kyber1024processor can perform NTT operation for a 4-dimensional polynomial vector in 17.1 μ s, and it achieves speedup by a factor of 2.1 compared with the state-of-the-art implementation. • Kyber1024 processor can perform NTT operation for a 4-dimensional polynomial vector in 17.1 μ s on a low-cost FPGA. • Saving more than 20% on the times of modular multiplication operations in polynomial ring arithmetic. • Optimized NTT signal flow reuses the loop control logic to save nearly 50% of the resource. • Dual-column sequential storage improves memory bandwidth. • Configurable butterfly unit supports Cooley–Tukey butterfly-based forward NTT, Gentlemen–Sande butterfly-based inverse NTT, and other meta operations. [ABSTRACT FROM AUTHOR]

In recent days we can see that multicore computers have the ability to easily manipulate digit numbers however as numbers get bigger the computation becomes more complex, the reason is that the size of both CPU registers and buses is limited. As a result, the arithmetic operations such as addition, subtraction, multiplication, and division for CPU become more complex to perform. For solving the problem of how to do computation on big digit numbers, a number of algorithms have been developed. However, the existing algorithms are noticeably slow because they operate on bits individually and are designed to run over single-core computers only. In this paper, an AI model is presented that performs a computation on tokens of 8-digit numbers to assist boost the CPU computation performance. [ABSTRACT FROM AUTHOR]

The hardware implementation of optimization algorithms has gained significant attention due to its potential for augmenting performance and efficiency. This paper presents the hardware implementation of a Chaotic Opposition-Based Arithmetic Optimization Algorithm (COAOA). COAOA is inspired by integrating chaotic dynamics and opposition-based learning (OBL) principles in the original AOA algorithm. Inspired by chaotic maps, COAOA amplifies exploration and exploitation capabilities, while OBL enhances the search process by considering both positive and negative solution counterparts. Our proposed hardware implementation of COAOA harnesses Field-Programmable Gate Arrays (FPGAs) to accelerate optimization processes. Leveraging FPGA's parallel processing capabilities, the COAOA algorithm is efficiently parallelized and mapped onto the hardware architecture, streamlining arithmetic operations and governing algorithmic execution flow. To assess its efficacy, a comparison was made between the performance of the suggested structure and five alternative algorithms: opposition-based learning AOA (OAOA), Chaotic AOA, the original AOA, PSO and GA. Statistical analyses and tests were performed using benchmark functions like Rosenbrock, Rastrigin, Six-Hump Camel-Back, and Zirilli functions. The empirical findings indicate the substantial acceleration achieved through the hardware implementation of COAOA compared to the original AOA algorithm and its variants. This compelling outcome positions COAOA as a viable solution for real-time optimization challenges, signifying its potential to significantly expedite optimization tasks in practical applications. • An enhanced AOA variant, COAOA, is introduced with chaotic maps and OBL. • Chaotic map and OBL boost AOA's search efficiency, avoiding local minima. • COAOA's hardware design is executed on FPGA, achieving faster speed than software. • COAOA is benchmarked against AOA versions using the Xilinx Virtex-7 Pro Kit. [ABSTRACT FROM AUTHOR]

The climate change concerns, the decarbonization policies, and the technological advances allied to cost reduction form a set of favorable circumstances for large deployment of renewable-based distributed generation into the power distribution systems. However, the connection of distributed generation significantly affects the power system and its technical impacts must be evaluated. Therefore, the hosting capacity analysis has gained attention as it outputs the maximum amount of distributed generation that can be safely connected. The deterministic and stochastic methods are commonly found in the literature. However, there is a lack of hosting capacity studies based on interval analysis. Therefore, this paper proposes an interval/affine arithmetic-based hosting capacity framework, considering two performance indexes (overvoltage and ampacity), and uses a different approach for modeling generation and load curves as a finite set of correlated affine combinations. The proposed framework enables faster analysis and outputs results that are comparable to the ones from time series simulation. The proposed method also allows less conservative results, depending on the desired level of overvoltage or overload risk. • A novel interval/affine arithmetic-based method for locational HC analysis. • Load and generation modeled as affine forms by adapted discretization-aggregation. • Associating load-generation combinations to different risks. • Matching results compared to QSTS simulation approach. • Faster approach when compared to QSTS simulation. [ABSTRACT FROM AUTHOR]

• ANFIS-HA2O technique for harmonics mitigation & power quality enhancement. • Utilizing intelligent control & power converters to optimize interfacing inverters. • Achieves impressive PV module efficiency of 93 %, enhancing solar-fed DG system performance. • Comparison with other designs highlights superiority in harmonics mitigation. • Contributes to grid stability & effective integration of renewable energy sources. Recently, with a rapid progression of power generation, renewable energy sources based on distributed generation have attained a great deal of attention. Solar energy (i.e. photo voltaic) has confronted a considerable focus among all renewable energy sources since they are environmentally friendly in nature. With the innovation in intelligent control techniques as well as power converters, the distributed systems are controlled effectively thereby enhancing the usage of interfacing inverters. By employing intelligent control approaches, the interfacing inverters provide numerous ancillary functions which include mitigation of harmonics, power factor as well as voltage compensation. This paper proposes a novel Adaptive neuro fuzzy interference system based hybrid Aquila arithmetic optimization (ANFIS-HA2O) technique to enhance the power quality and to mitigate the harmonics in distributed generation (DG) system. This proposed approach extracts enhanced utilization of interfacing inverters containing solar-fed DG systems. Apart from this, the various non-linear loads are reduced by creating the harmonics, which enhance the performance of the proposed technique. Finally, the PV module efficiency and total harmonic distortion of the proposed ANFIS-HA2O design are compared with other designs and from the results; the PV module efficiency achieved is 93 %. [ABSTRACT FROM AUTHOR]

• This paper concentrates on the problem of distributed Multi-sensor Multi-target Tracking (DMMT) in the trajectory random finite set filtering framework. The trajectory probability hypothesis density (PHD) filter and the trajectory cardinality PHD are performed locally in different sensors for DMMT. • However, it is not convenient to use fusion techniques for the sets of targets directly to sets of trajectories. The reason is that optimal assignment among different trajectories in different sensors may change across time, and we should account for this in a fusion algorithm. • We pursue the trajectory association algorithm based on Clustering and Linear programming, which is one of the key ingredients of trajectories fusion. The trajectory association solves a joint optimization problem such that the cost of localization and switching over all time steps is minimized. • This paper proposes two cardinality consensus algorithms to fuse unassociated and covariance intersection (CI) fused trajectories. We also calculate the crucial parameters in CI fusion via unitary decomposition and eigenvalue decomposition. • The filters of DMMT developed by this paper can widely accommodate cardinality inconsistency between local multi-trajectory, limited computing and communication resources of nodes, various fields of view. This paper concentrates on the distributed Multi-sensor Multi-target Tracking (DMMT) in the trajectory random finite set (TRFS) filtering framework. The trajectory probability hypothesis density (TPHD) filter and the trajectory cardinality PHD (TCPHD) are performed locally in different sensors for DMMT. Our analysis shows that standard generalized covariance intersection (GCI) and weighted arithmetic average (WAA) fusion with the posterior multitrajectory densities of the TPHD and TCPHD filters rely heavily on the proper association of trajectories estimated from various sensor nodes. Then, inspired by the analysis, we develop two novel distributed fusion algorithms for the Gaussian mixture TPHD and TCPHD filters. First, we obtain the associated and unassociated trajectories at different sensors via clustering and Linear programming (LP). Second, the associated trajectories are fused via covariance intersection (CI) parallelly. Third, two principle cardinality consensus algorithms are proposed to fuse unassociated and CI fused trajectories. Moreover, two analytical expressions, which are crucial for fusion weight in CI fusion, are provided. Finally, numerical experiments demonstrate the efficacy of our proposed approaches in computational efficiency and accuracy, compared with the state-of-the-art solutions in challenging scenarios. [ABSTRACT FROM AUTHOR]