Search Results (25)

In this study, a 4-D, computerized ionospheric tomography algorithm, IONOLAB-Fusion, is developed to reconstruct electron density using both actual and virtual vertical and horizontal paths for all ionospheric states. The user-friendly algorithm only requires the coordinates of the region of interest and range with the desired spatio-temporal resolutions. The model ionosphere is formed using spherical voxels in a lexicographical order so that a 4-D ionosphere can be mapped to a 2-D matrix. The model matrix is formed automatically using a background ionospheric model with an optimized retrospective or near-real time manner. The singular value decomposition is applied to extract a subset of significant singular values and corresponding signal subspace basis vectors. The measurement vector is filled automatically with the optimized number of ground-based and space-based paths. The reconstruction is obtained in closed form in the least squares sense. When the performance of IONOLAB-Fusion across Europe was compared with ionosonde profiles, a 26.51% and 32.33% improvement was observed over the background ionospheric model for quiet and disturbed days, respectively. When compared with GIM-TEC, the agreement of IONOLAB-Fusion was 37.89% and 31.58% better than those achieved with the background model for quiet and disturbed days, respectively. Full article

Chipman contended, in stark contrast to the conventional view, that, utility is not a real number but a vector, and that it is inherently lexicographic in nature. On the other hand, in recent years continuous multi-utility representations of a preorder on a topological space, which proved to be the best kind of continuous representation, have been deeply studied. In this paper, we first state a general result, which guarantees, for every preordered topological space, the existence of a lexicographic order-embedding of the Chipman type. Then, we combine the Chipman approach and the continuous multi-utility approach, by stating a theorem that guarantees, under certain general conditions, the coexistence of these two kinds of continuous representations. Full article

A symbolic analysis of Archimedes’s periodical number system is developed, from which a natural link emerges with the modern positional number systems with zero. After the publication of Fibonacci’s Liber Abaci, the decimal Indo-Arabic positional system was the basis of the algorithmic and algebraic trend of modern mathematics, but even if zero plays a crucial role in algebra and mathematical analysis, zeroless positional systems show the same capability of producing efficient arithmetical algorithms based on operation tables over digits. The crucial role of digits is assessed, by considering a representation of numbers based on strings in lexicographic order. A new algorithm for the determination of decimal periods is presented by remarking on the cruciality of this topic in number theory. Periods of ordinal numbers and enumerations of recursive enumerability are shortly recalled. Concluding remarks are formulated about the deep relationship between numbers and information, which shed new light on a red line passing through the whole history of mathematics. Full article

The clustering coefficient of a vertex v, of degree at least 2, in a graph $\Gamma$ is obtained using the formula $C\left(v\right)=\frac{2t\left(v\right)}{\mathrm{deg}\left(v\right)\left(\mathrm{deg}\right(v)-1)},$ where $t\left(v\right)$ denotes the number of triangles of the graph containing v as a vertex, and the clustering coefficient of $\Gamma$ is defined as the average of the clustering coefficient of all vertices of $\Gamma$, that is, $C(\Gamma )=\frac{1}{\left|V\right|}{\sum }_{v\in V}C\left(v\right)$, where V is the vertex set of the graph. In this paper, we give explicit expressions for the clustering coefficient of corona and lexicographic products, as well as for the Cartesian sum; such expressions are given in terms of the order and size of factors, and the degree and number of triangles of vertices in each factor. Full article

With the recent growth of the Internet, the volume of data has also increased. In particular, the increase in the amount of unstructured data makes it difficult to manage data. Classification is also needed in order to be able to use the data for various purposes. Since it is difficult to manually classify the ever-increasing volume data for the purpose of various types of analysis and evaluation, automatic classification methods are needed. In addition, the performance of imbalanced and multi-class classification is a challenging task. As the number of classes increases, so does the number of decision boundaries a learning algorithm has to solve. Therefore, in this paper, an improvement model is proposed using WordNet lexical ontology and BERT to perform deeper learning on the features of text, thereby improving the classification effect of the model. It was observed that classification success increased when using WordNet 11 general lexicographer files based on synthesis sets, syntactic categories, and logical groupings. WordNet was used for feature dimension reduction. In experimental studies, word embedding methods were used without dimension reduction. Afterwards, Random Forest (RF), Support Vector Machine (SVM) and Multi-Layer Perceptron (MLP) algorithms were employed to perform classification. These studies were then repeated with dimension reduction performed by WordNet. In addition to the machine learning model, experiments were also conducted with the pretrained BERT model with and without WordNet. The experimental results showed that, on an unstructured, seven-class, imbalanced dataset, the highest accuracy value of 93.77% was obtained when using our proposed model. Full article

Many practical decisions are more realistic concerning preventing bad decisions than seeking better ones. However, there has been no behavioral decision theory research on avoiding the worst decisions. This study is the first behavioral decision research on decision strategies from the perspective of avoiding the worst decisions. We conducted a computer simulation with the Mersenne Twister method and a psychological experiment using the monitoring information acquisition method for two-stage decision strategies of all combinations for different decision strategies: lexicographic, lexicographic semi-order, elimination by aspect, conjunctive, disjunctive, weighted additive, equally weighted additive, additive difference, and a majority of confirming dimensions. The rate of choosing the least expected utility value among the alternatives was computed as the rate of choosing the worst alternative in each condition. The results suggest that attention-based decision rules such as disjunctive strategy lead to a worse decision, and that striving to make the best choice can conversely often lead to the worst outcome. From the simulation and the experiment, we concluded that simple decision strategies such as considering what is most important can lead to avoiding the worst decisions. The findings of this study provide practical implications for decision support in emergency situations. Full article

In a trade experiment, groups of students were taught how to bargain over a pie generated in a transportation game. Data collection and detailed group reports of the bargaining process allowed us to identify the type of bargaining followed and its correspondence with cooperative game theory concepts. Explicit coalitions were rather scarce (17%), although coalition stability was implied by 47.8% of the agreements. Efficiency was achieved in the vast majority (82%) of cases, whereas in 34.8% of the agreements, students used a lexicographic ordering of multiple solutions before choosing among them. Regarding the bargaining procedure, in 40% of the agreements, quantities traded were decided before profit sharing rules were negotiated, whereas in 16% of the cases they were simultaneously agreed upon. Our findings suggest that bargaining procedures often do not imply explicit coalitions. Moreover, efficiency can be achieved even in the absence of bargaining processes. Full article

The presented research is devoted to the problem of developing new combinatorial generation algorithms for combinations. In this paper, we develop a modification of Ruskey’s algorithm for unranking m-combinations of an n-set in co-lexicographic order. The proposed modification is based on the use of approximations to make a preliminary search for the values of the internal parameter k of this algorithm. In contrast to the original algorithm, the obtained algorithm can be effectively applied when n is large and m is small because the running time of this algorithm depends only on m. Furthermore, this algorithm can be effectively used when n and m are both large but $n-m$ is small, since we can consider unranking $(n-m)$-combinations of an n-set. The conducted computational experiments confirm the effectiveness of the developed modification. Full article

We present a new space-time loop tiling approach and demonstrate its application for the generation of parallel tiled code of enhanced locality for three dynamic programming algorithms. The technique envisages that, for each loop nest statement, sub-spaces are first generated so that the intersection of them results in space tiles. Space tiles can be enumerated in lexicographical order or in parallel by using the wave-front technique. Then, within each space tile, time slices are formed, which are enumerated in lexicographical order. Target tiles are represented with multiple time slices within each space tile. We explain the basic idea of space-time loop tiling and then illustrate it by means of an example. Then, we present a formal algorithm and prove its correctness. The algorithm is implemented in the publicly available TRACO compiler. Experimental results demonstrate that parallel codes generated by means of the presented approach outperform closely related manually generated ones or those generated by using affine transformations. The main advantage of code generated by means of the presented approach is its enhanced locality due to splitting each larger space tile into multiple smaller tiles represented with time slices. Full article

In the case of the proportional allocation of goods and burdens, the shares of all agents with respect to their values are equal, i.e., they form a constant sequence. In a degressively proportional allocation this sequence is nondecreasing when agents are increasingly ordered according to their values. The division performed according to this principle is ambiguous, and its selection requires many negotiations among participants. The aim of this paper is to limit the range of such negotiations when the problem is complex, i.e., the set of feasible solutions has high cardinality. It can be done thanks to a numerical analysis of the set of all feasible solutions, and eliminating allocations favoring or disfavoring some coalitions of agents. The problem is illustrated by the case study of allocating seats in the European Parliament in its 2019–2024 term. Full article

Extensive decision-making during the vaccine preparation period is unpredictable. An account of the severity of the disease, the younger people with COVID-19 comorbidities and other chronic diseases are also at a higher risk of the COVID-19 pandemic. In this research article, the preference ranking structure for the COVID-19 vaccine is recommended for young people who have been exposed to the effects of certain chronic diseases. Multiple Criteria Decision-Making (MCDM) approach effectively handles this vague information. Furthermore, with the support of the Intuitionistic Fuzzy Soft Set (IFSS), the entries under the new extension of the Preference Ranking Organization Method for Enrichment Evaluation-II (PROMETHEE-II) is suggested for Preference Ranking Structure. The concept of intuitionistic fuzzy soft sets is parametric in nature. IFSS suggests how to exploit an intuitionistic ambiguous input from a decision-maker to make up for any shortcomings in the information provided by the decider. The weight of the inputs is calculated under the Intuitionistic Fuzzy Weighted Average (IFWA) operator, the Simply Weighted Intuitionistic Fuzzy Average (SWIFA) operator, and the Simply Intuitionistic Fuzzy Average (SIFA) operator. An Extended PROMETHEE-based ranking, outranking approach is used, and the resultant are recommended under the lexicographic order. Its sustainability and feasibility are explored for three distinct priority structures and the possibilities of the approach. To demonstrate the all-encompassing intuitionistic fuzzy PROMETHEE approach, a practical application regarding COVID-19 severity in patients is given, and then it is compared to other existing approaches to further explain its feasibility, and the sensitivity of the preference structure is examined according to the criteria. Full article

In the context of combinatorial sampling, the so-called “unranking method” can be seen as a link between a total order over the objects and an effective way to construct an object of given rank. The most classical order used in this context is the lexicographic order, which corresponds to the familiar word ordering in the dictionary. In this article, we propose a comparative study of four algorithms dedicated to the lexicographic unranking of combinations, including three algorithms that were introduced decades ago. We start the paper with the introduction of our new algorithm using a new strategy of computations based on the classical factorial numeral system (or factoradics). Then, we present, in a high level, the three other algorithms. For each case, we analyze its time complexity on average, within a uniform framework, and describe its strengths and weaknesses. For about 20 years, such algorithms have been implemented using big integer arithmetic rather than bounded integer arithmetic which makes the cost of computing some coefficients higher than previously stated. We propose improvements for all implementations, which take this fact into account, and we give a detailed complexity analysis, which is validated by an experimental analysis. Finally, we show that, even if the algorithms are based on different strategies, all are doing very similar computations. Lastly, we extend our approach to the unranking of other classical combinatorial objects such as families counted by multinomial coefficients and k-permutations. Full article

Tropical Algebra is used to model the dynamics of Timed Event Graphs (TEG), a particular class of Timed Discrete-Event System (TDES) in which we are interested only in synchronization and delay phenomena. Whenever this TEG has control inputs, we can use them to control the synchronization of the system to achieve some objective. Thus, this paper formulates a framework based on tropical algebra and lexicographic optimization to synchronize a TEG when dealing with many synchronization objectives that are ranked in previous priority order. We call this kind of problem the Tropical Lexicographic Synchronization Optimization (TLSO). This work develops a solution to this problem, based on Tropical Fractional Linear Programming (TFLP) and lexicographic optimization concepts. In this way, the basics of tropical algebra are determined, including essential terms to this paper, such as left and right residuations, and the following stages of the solution to the TLSO problem are explained. Therefore, this work presents a general framework based on structured algebraic models with application to TEG synchronization. By synchronization, we mean balancing and organizing events chronologically in order to achieve the desired goal. So, we are dealing with concepts closely related to symmetry ones. An illustrative numerical example is presented, which demonstrates the implementation of the proposed algorithms. The acquired results confirm the efficiency of the proposed methodology. Codes used for implementing the algorithms are listed in the appendix section of the article. Full article

Gutman and Trinajstić (1972) defined the connection-number based Zagreb indices, where connection number is degree of a vertex at distance two, in order to find the electron energy of alternant hydrocarbons. These indices remain symmetric for the isomorphic (molecular) networks. For the prediction of physicochemical and symmetrical properties of octane isomers, these indices are restudied in 2018. In this paper, first and second Zagreb connection coindices are defined and obtained in the form of upper bounds for the resultant networks in the terms of different indices of their factor networks, where resultant networks are obtained from two networks by the product-related operations, such as cartesian, corona, and lexicographic. For the molecular networks linear polynomial chain, carbon nanotube, alkane, cycloalkane, fence, and closed fence, first and second Zagreb connection coindices are computed in the consequence of the obtained results. An analysis of Zagreb connection indices and coindices on the aforesaid molecular networks is also included with the help of their numerical values and graphical presentations that shows the symmetric behaviour of these indices and coindices with in certain intervals of order and size of the under study (molecular) networks. Full article

One of the most important elements of a robot’s control system is its Inverse Kinematic Model (IKM), which calculates the position and velocity references required by the robot’s actuators to follow a trajectory. The methods that are commonly used to synthesize the IKM of open-chain robotic systems strongly depend on the geometry of the analyzed robot. Those methods are not systematic procedures that could be applied equally in all possible cases. This project presents the development of a systematic procedure to synthesize the IKM of non-redundant open-chain robotic systems using Groebner Basis theory, which does not depend on the geometry of the robot’s structure. The inputs to the developed procedure are the robot’s Denavit–Hartenberg parameters, while the output is the IKM, ready to be used in the robot’s control system or in a simulation of its behavior. The Groebner Basis calculation is done in a two-step process, first computing a basis with Faugère’s F4 algorithm and a grevlex monomial order, and later changing the basis with the FGLM algorithm to the desired lexicographic order. This procedure’s performance was proved calculating the IKM of a PUMA manipulator and a walking hexapod robot. The errors in the computed references of both IKMs were absolutely negligible in their corresponding workspaces, and their computation times were comparable to those required by the kinematic models calculated by traditional methods. The developed procedure can be applied to all Cartesian robotic systems, SCARA robots, all the non-redundant robotic manipulators that satisfy the in-line wrist condition, and any non-redundant open-chain robot whose IKM should only solve the positioning problem, such as multi-legged walking robots. Full article