Properties and Computational Algorithm for Fastest Quaternary Linearly Independent Transforms

An algorithm that generates fixed-polarity Reed-Muller (FPRM) spectral coefficients for five-valued functions is presented in this paper. The presented algorithm takes the disjoint cubes reduced representation of the input function and directly operates on it to obtain its FPRM spectral coefficients. It is simple and can be implemented with small amount of storage space. At the end of the paper, experimental results of the algorithm for several five-valued test files are shown. Generation of the used test files from MCNC binary benchmarks is also described.

xvi 5.17 Number of non-zero spectral coefficients for FQLI 5.18 Calculation times for FQLI 5.19 Forward and inverse QLI transforms in Class 1 5.20 Forward butterfly diagrams for QLI transforms Lb -4.b 5.21 Number of non-zero spectral coefficients for QLI transforms in Class 1 6.1 Four types of QLIA transforms 6.2 QLIA transforms in Class A 6.3 QAH transforms and their corresponding butterfly diagrams when n = 2 298 6.4 Computational costs for QAH transforms 298 6.5 Number of non-zero spectral coefficients for RPH and RNH transforms 299 6.6 Calculation times for RPH and RNH transforms 300 6.7 Number of non-zero spectral coefficients for a M _1 and b M~1. . .

We consider a production system consisting of >N processing stages. The actual leadtimes at the stages are stochastic. The objective is to determine the planned leadtimes at each stage so as to minimize the expected total inventory costs, tardiness penalties, and a backlog penalty for not meeting demand due date at the last stage. Recursive relationships are used for automatic generation and efficient computation of the objective function. The efficiency of the proposed algorithms allows us to obtain new insights regarding operating policies, leadtime delivery reliability, and production line design. The problem is formulated as a convex non-linear programming problem. The latter is then solved using classical convex optimization algorithms. For the special case of exponentially distributed leadtimes, the objective function is derived in a closed form.

Efficient computation of the P.M.F. and the C.D.F. of the generalized binomial distribution

This chapter introduces inductively defined sets and simple inductive data types such as natural numbers, words, lists and trees with emphasis on definition patterns. For these sets and data types, recursive equations in Backus-Naur form are introduced and it is shown how, e.g., propositional formulae and simple while programs can be specified in this format. Next it is explained how functions can be defined inductively on such sets and data types. Examples include the factorial function, Harmonic numbers, Fibonacci numbers, addition and multiplication on natural numbers and functions that compute the length of a word or list and the height of a tree. In contrast, recursive functions are defined in a way that does not necessarily lead to terminating evaluations. Recursive procedures are also described, with examples presented of various sorting algorithms and the Towers of Hanoi puzzle.

Incompletely specified logic functions are often met in computer science and engineering and their compact representations are a subject of a wide research interest. In this paper, we present a method for determining an assignment of unspecified function values that will produce compact decision diagrams. The method is based on the analysis of Walsh and Vilenkin-Chrestenson spectral coefficients for binary and multiple-valued functions, respectively, and the operation of spectral translation of logic functions. Spectral transforms are used to identify the linear function with strongest correlation with the initial function and assign the unspecified values as well as to specify the spectral translation that will result in a compact decision diagram.

A weighted, oriented topological structure, denoted by <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">G</tex> and called a flow graph, is associated with a set of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</tex> equations in <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</tex> variables, denoted by <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">KX = 0</tex> , such that <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</tex> is a connection matrix and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">X</tex> a vertex weight matrix of the associated graph. This same set of equations can be written as <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">A_{-v:}^{-} C(A+)'X = 0</tex> where <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">A_{-}^{-v:}</tex> and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">A^{+}</tex> are negative and positive incidence matrices and where <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">C</tex> and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">X</tex> are respectively branch and vertex weight matrices of the graph. By familiar algebraic procedures, an expression for the weight <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x_p</tex> , of a nonreference vertex of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">G</tex> is obtained as a linear combination of the weights of the reference vertices (vertices with zero negative order) and can be written as <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x_p = \Sigma_{j=1}^{s} \zeta p{\dot}r_{j}x_{r_j}</tex> . To these algebraic results there correspond topological expressions in terms of subgraphs of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">G</tex> for the coefficients, <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\zeta P{\dot}r_j</tex> . A similar correspondence is obtained between the topological operation of deleting a vertex from the flow graph and the algebraic operation of eliminating a variable from the set of equations. These results are derived from the algebraic equations written in terms of the incidence and weight matrices of the graph. They are similar to those given for the familiar Signal-Flow-Graph, although they are more convient to use, since the topological properties of the flow graph depend only upon the algebraic properties of the set of equations. A flow graph can be drawn directly from an electric network diagram, and the flow-graph properties, used to obtain a solution of the network equations. Examples of this for two types of feedback networks are shown.

As the computing capacity of existing mobile devices cannot fully meet the needs of users for communication quality, a computing resource allocation strategy for 5G communication in the Internet of Things (IoT) environment is proposed by applying UAV-assisted edge computing. First, a system model is constructed with the UAV deployed with mobile edge computing (MEC) servers to provide assisted computing services for multiple users on the ground. Based on the optimization of the UAV trajectory, communication scheduling, and the energy consumption model of the UAV, the problem of the total computational cost minimization is formulated. Then, the genetic algorithm is improved by introducing a penalty function to solve this problem, in which selection, crossover, and mutation operations are iterated to obtain the optimal allocation strategy for computational resources. Finally, a simulation platform is constructed to analyze the proposed method. The results show that the total cost and total time of the proposed strategy are better than other comparison strategies.

This research aims to determine the financial feasibility on the farming business of breeding balinese cattle who uses KUPS Credit Scheme. Data was collected through observation and interview. Respondents were all members of the “Satwa Winangun” farmers in Tangkas village, Klungkung Regency. Financial feasibility is determined by evaluating the eligibility criteria such: NPV, Net B/C, IRR, and payback period. The assessment was based on 2 calculation systems, (1) calculation of cash costs in which forage and labor are not calculated as the cost (existing condition), and (2) total cost calculation, in which two components are calculated as cost. Based on the calculation of cash costs, cultivation of Bali cattle by utilizing KUPS credit in this village is financially feasible to be implemented. This was indicated by the NPV value of Rp. 274.103.000, IRR 20.16%, Net B/C 1.55, and investments has been able to return within 3.52 years. The result of sensitivity analysis shows that as far as KUPS interest rate is lower than 18.37% per year, this farming is still financially feasible. Breakeven point can be achieved when the number of cattle parents maintained is 37, or when the price of calves at the age of 6 months is an average of Rp. 1.764.022 per cattle. However, based on the calculation of total cost, this farming system is not financially feasible. This is shown by the negative NPV of Rp. -285.721.000, IRR 2.87%, and Net B/C 0,54. This farming system is not financially feasible despite the 0% / year KUPS rate. The break-even point can be reached when the price of calves at the age of 6 months averages Rp. 4.288.367 per cattle.

The non-zero component graph of a vector space with finite dimension over a finite field F is the graph \(G~ = ~\left( {V,E} \right)\), where vertices of G are the non-zero vectors in V, two of which are adjacent if they have at least one basis vector with non-zero coefficient common in their basic representation. In this paper, we discuss certain properties of the non-zero component graphs of vector spaces with finite dimension over finite fields and their graph invariants.

Social Internet of Things (SIoT) has become an emerging network paradigm, where IoT devices with Artificial Intelligence (AI) and social relations can automatically establish a collaborative group to identify events locally. On the other hand, mobile users can act as ubiquitous and versatile sensors to improve the accuracy of SIoT event detection. In this paper, we explore the SIoT Collaboration with Crowdsourcing (SCC) problem to jointly select SIoT devices and hire users to monitor events and locations with accuracy requirements, while minimizing the total SIoT communication and computation costs and the user hiring cost. We prove that SCC is NP-hard and cannot be approximated by any factor unless P = NP. Then, we propose a new algorithm, Accuracy- and Social-aware SIoT and User Selection (ASSUS), with the idea of Collaborative Tree (CT) and Accuracy Profit (AP), where CT exploits users' social relations to properly choose intermediate SIoTs. Simulation results manifest that ASSUS can effectively reduce more than 50% of the total cost compared with state-of-the-art algorithms.

AIM: To demonstrate based on a schizophrenia case study model that System Dynamics Modelling (SDM), a set of conceptual tools that help understanding the structure and dynamics of complex systems, can be a useful method in the field of health care evaluation, specifically to assess cost of illness and budget impact of complex diseases. METHODS: Using the specific Vensim DSS and Venapp software tools, a case study model was programmed, simulating schizophrenia costs in Germany up to the year 2050. Fixed model input was the age structure of the German population, the suicidal rate for the general population and for people diagnosed with schizophrenia, the general death rate and the proportion of suicides and schizophrenia prevalence and incidence. Subsystems of the model were: patient stocks and flows, medication cost, treatment cost, other relevant cost, occupational disability cost, early retirement cost, total schizophrenia cost, age distribution and auxiliary calculations. RESULTS: The case study schizophrenia SDM model allows analyzing the distribution of schizophrenia costs in the German health systems and demonstrates how the cost distribution changes with changing conditions (e. g. reduced relapse rate with the spread of more efficient medication). For the base case scenario - at the beginning of the model in the year 2000 - early retirement cost accounted for almost 50 % of the monthly total costs of schizophrenia of 474 180 000 €, followed by hospital costs, costs of occupational disability, and costs of non-medical complementary offerings. Indirect costs were much more important than direct costs. Costs of schizophrenia reached a peak around the year 2010 and decreased thereafter. With an increasing percentage of patients taking atypicals overall costs were decreasing. CONCLUSIONS: This paper supports system dynamics modelling as an alternative, flexible and user friendly modelling technique for application in health care evaluation.

Current and future economic performance of first and second generation biofuels in developing countries

In this paper, we propose a new PAPR reduction by using a partial transmit sequences (PTS) method with coded side information (SI) technique. These methods are used in an orthogonal frequency division multiplexing (OFDM) system. The OFDM employs orthogonal sub-carriers for data modulation. These sub-carriers unexpectedly present a large peak to average power ratio (PAPR) in some cases. In order to reduce PAPR, the sequence of input data is partitioned into disjoint sub-block of PTS. If number of sub-block increases, high efficiency of PAPR reduction can be obtained. However, a quite large calculation cost must be demanded and thus it is impossible to obtain the optimum PTS. In the proposed method, we introduce a coded side information technique assuming the pseudo-optimum condition into the PTS. The total calculation cost becomes drastically reduced and side information bits for recovering original data in demodulation. In simulation results, the proposed method demonstrated the improvement of PAPR and bit error rate (BER) performance.

This paper proposes a method to distinguish handwritten character regions from machine-printed ones using Hough transform (HT). The Gabor filtering in the human early vision realizes a type of Fourier transform (FT). Previously we proposed a FT-based distinction method successfully. However, we noticed simultaneously that the HT, instead of FT, may extract more features when we deal with characters which are regarded as piles of line segments. Experiments show that HT-based method, in combination with real-space features, achieves higher accuracy than the FT-based method. At the same time, the total calculation cost is found lower.