DIPKIP: A Connectionist Knowledge Management System to Identify Knowledge Deficits in Practical Cases This study presents a novel, multidisciplinary research project entitled DIPKIP (data acquisition, intelligent processing, knowledge identification and proposal), which is a Knowledge Management (KM) system that profiles the KM status of a company. Qualitative data is fed into the system that allows it not only to assess the KM situation in the company in a straightforward and intuitive manner, but also to propose corrective actions to improve that situation. DIPKIP is based on four separate steps. An initial "Data Acquisition" step, in which key data is captured, is followed by an "Intelligent Processing" step, using neural projection architectures. Subsequently, the "Knowledge Identification" step catalogues the company into three categories, which define a set of possible theoretical strategic knowledge situations: knowledge deficit, partial knowledge deficit, and no knowledge deficit. Finally, a "Proposal" step is performed, in which the "knowledge processes"-creation/acquisition, transference/distribution, and putting into practice/updating-are appraised to arrive at a coherent recommendation. The knowledge updating process (increasing the knowledge held and removing obsolete knowledge) is in itself a novel contribution. DIPKIP may be applied as a decision support system, which, under the supervision of a KM expert, can provide useful and practical proposals to senior management for the improvement of KM, leading to flexibility, cost savings, and greater competitiveness. The research also analyses the future for powerful neural projection models in the emerging field of KM by reviewing a variety of robust unsupervised projection architectures, all of which are used to visualize the intrinsic structure of high-dimensional data sets. The main projection architecture in this research, known as Cooperative Maximum-Likelihood Hebbian Learning (CMLHL), manages to capture a degree of KM topological ordering based on the application of cooperative lateral connections. The results of two real-life case studies in very different industrial sectors corroborated the relevance and viability of the DIPKIP system and the concepts upon which it is founded.Key words: data and knowledge visualization, connectionism and neural nets, knowledge-based systems, knowledge management applications, discovery-based science. Knowledge Management (KM), a relatively new and fast-growing discipline, enables organizations to capture, share, and apply the collective experience and know-how (knowledge) of their staff, which is fundamental to competing in the knowledge economy. Exponential increases in data volumes are increasingly viewed as important and essential sources of information that may eventually be turned into knowledge.. KM can be successfully applied in organizations by developing and implementing knowledge infrastructures (Sivan 2000) . These knowledge infrastructures consist of three main dimensions: people, organizational, and technological systems. However, from a KM point of view, knowledge is defined as information that is relevant for business activities (Strohmaier 2003) . This research is mainly based on an understanding of the distinctions between transformations in states of data and knowledge: from the lowest level (raw data and information) up to higher levels, such as knowledge itself and its management, and individual or organizational responsibilities.. Nowadays, a heterogeneous set of KM technologies (Maier and Remus 2002; Maurer and Tochtermann 2002; Rollett 2003; Nielsen and Michailova 2007) is available from industrial vendors (Hyperwave; OPENTEXT; IBM) as well as from academia (Dustdar 2002; Woitsch and Karagiannis 2002; Wang 2004; Chen et al. 2005) .. In recent years, the deployment of information technology has become a crucial tool for enterprises to achieve a competitive advantage and organizational innovation (Shu-MeiThe paper is structured in the following way. Section 2 introduces some unsupervised neural projection methods. Section 3 describes DIPKIP, the proposed KM system, whereas Section 4 presents the main connectionist model applied in this research along with earlier ones that have supported its development. Section 5 describes the empirical validation of this research, starting with the description of the two real-life case studies and the highdimensional data sets they generated. This section also presents results, discussions, and a comparative study (several neural models are applied to the same case studies to compare their projection performance). Finally, Section 6 presents the conclusions and a number of proposals for future work in the same field. In this study, KM is understood as a system that integrates its specific functions and processes to create/acquire, transfer/distribute, and put into practice/update the ideas and knowledge held by a company and its personnel. By doing so, KM, in its various forms, allows people to achieve greater levels of creativity, ensures permanent training and recycling in their specialist areas, and helps them to share and pass on the benefits of their knowledge to other workers, who are also willing to integrate the knowledge held by their colleagues into their own work. Thus, DIPKIP, a novel, neural KM system, has been applied in two different real-life case studies. This model has demonstrated its ability to analyze knowledge situations and to propose improvements from the standpoint of KM. The research has also analyzed the impact of the proposals, which were applied in the case studies to demonstrate the way in which DIPKIP improved the KM level.. In both cases, DIPKIP proved itself to be a robust tool for the analysis and identification of critical situations that enable companies to take decisions in the field of KM, concerning the acquisition, transfer, and updating of the knowledge. The updating of knowledge processes enables a company to make use of the latest knowledge, to access the most recent innovations, and to keep the KM system updated with all of its attendant benefits.. One of the main objectives propelling this study was the desire to introduce greater rigor and robustness into the field of KM research, thereby bridging the gap between theoretical formulations and satisfactory practical applications. The model ensures a complete diagnosis of the current situation, and subsequently an appropriate decision-making process for the effective application of the actions that it proposes in response to such situations.. The application of the neural projection architecture to the new KM system presented in this study not only enabled data to be grouped together and ordered, but it also produced results of great interest that may be used in decision making. Among these results, the following may be highlighted.. The location of the knowledge is clearly identified according to the particular parameters used in the study, such as importance, level of urgency, or diffusion of knowledge. This technique enables the KM situation in any company to be mapped out in a very short space of time and it is consequently of use in the related decision-making process. More specifically, the results verify:. • whether the knowledge or knowledge deficit of the company is critical to the implementation of its strategy; • the level at which the knowledge is held or should be held; • whether its acquisition or updating is urgent; and • whether such knowledge is shared between the people in the company who require it.. The data sets provide information on the type of knowledge held by a company or companies. In addition, they can also justify a variety of actions, on a case by case basis, to situate knowledge in the best possible spaces, to move it between areas, and to abandon knowledge that is no longer advisable or is ineffective.. In short, the KM system described in this research may be used to identify the knowledge held by a company in an easy and accurate manner and to map out actions for progress in the future.. Alternative methods such as PCA, MLHL, SOM, or CCA were evaluated when performing the second step of DIPKIP (intelligent processing). CMLHL was shown to provide sparser projections and to capture some type of global ordering in the data sets.. In conclusion, we may say that a novel system for KM is proposed in this research, which responds to the need for information management and knowledge flows within a KM organization, through the incorporation in the KM system of knowledge updating processes.. Future work will be based on the study of different distributions and learning rules to improve the architecture as a whole, and it is anticipated that this neural architecture will eventually be embedded inside a more complex hybrid KM system.. An upgraded version of DIPKIP is also envisaged in the future. The model will be extended to improve its outcomes by cataloguing various classes of knowledge in a map of knowledge lines. Once the strategic lines of knowledge are identified, DIPKIP could then propose corrective actions concerning different classes of knowledge and different departments.

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I I B I I I B I B I I B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


Brachiaria species identification using imaging techniques based on fractal descriptors The use of a rapid and accurate method in diagnosis and classification of species and/or cultivars of forage has practical relevance, scientific and trade in various areas of study. Thus, leaf samples of fodder plant species Brachiaria were previously identified, collected and scanned to be treated by means of artificial vision to make the database and be used in subsequent classifications. Forage crops used were: Brachiaria decumbens cv. IPEAN; Brachiaria ruziziensis Germain & Evrard; Brachiaria Brizantha (Hochst. ex. A. Rich.) Stapf; Brachiaria arrecta (Hack.) Stent. and Brachiaria spp. The images were analyzed by the fractal descriptors method, where a set of measures are obtained from the values of the fractal dimension at different scales. Therefore such values are used as inputs for a state-of-the-art classifier, the Support Vector Machine, which finally discriminates the images according to the respective species. The knowledge and understanding of functional properties of plants make possible to develop advances in several areas like medicine to cure diseases, produce and improve species to feed people and animals [1] . Involving this last topic, the analysis of consumption by animals is very important because the animal production can be improved from grazed pastures. Specifically, ruminants have their amount of feeding directly linked with the processes of particle-size reduction during the feeding. Due to the physical strength of grasses, ruminant animals consume larger quantities of forages with lower resistance to breakdown [2] . Since the grass is extremely important for animal food, it becomes the object of study here being one of the main forms of ruminant feeding is through grazing Brachiaria.. The genus Brachiaria consists of herbaceous, perennial or annual, erect or decumbent. Belonging to the grass family, it presents approximately one hundred species, and therefore their correct classification is of great importance for the genetic improvement of forage species and purity of the species in the field of seed production [3] [4] [5] . Grouping plants into genus is a way of facilitating the understanding of the diversity of the grasses, according to the particularities of each species [3] .. The classification of grasses is mainly based on the characters of the spikelet structure and its arrangement. The main taxonomic feature of the genus Brachiaria, despite not being present in many species, is the reversed or adaxial position of the spikelet and of ligule. This spikelet is relatively large, oval or oblong and it is arranged regularly in a row along one side of the rachis. However, the taxonomy of this genus is not satisfactory, both in terms of species composition and in their interrelationship with other genus. Problems related to incorrect classifications often occur among Brachiaria species commonly used in pastures, as well as among accessions of germplasm collections.. Since there is a great variability among natural species of Brachiaria, to identify really discriminant characters becomes a difficult task so that seeking for techniques that improve the identification will contribute to studies within this theme, as well as provide a reasonable system of classification, since there is no such system for the genus Brachiaria. Thus, the objective of this study was arXiv:1412.7849v1 [cs.CV] 25 Dec 2014 to take the volumetric Bouligand-Minkowski and Probability fractal descriptors associated with the Principal Component Analysis transform to classify samples from five species of Brachiaria cultivars. This methodology provides a set of coefficients for each image that will characterize it. The tests were performed in a large database with almost ten thousand of samples including the superior and inferior face of leaves obtaining 92.84% of correctness rate in the classification (of all leaves).. The text in this paper is organized as follows. In Sections II, III and IV the theory of the methods is explained. In Section V the description of the method Bouligand-Minkowski with probability dimension applyed to texture characterization. Section VI shows the experiments in a database of Brachiaria leaves and in Section VII the results are analysed. The paper is concluded in Section VIII. The graph in the Figure 5 shows the success rate of each compared texture descriptors when the number of descriptors is varied. We notice that even with only 4 elements, the proposed method achieves a correctness rate close to 90%. Gabor and Fourier have a close behavior, while the fractal descriptors presents an outstanding performance for any number of elements greater than 3.. The Table I shows the best success rate achieved by each method by using an optimal number of descriptors. The success rate is accompanied by other important measures related to the performance of each approach applied to discriminate the grass species. In this table, N D is the number of descriptors, CR is the correctness rate, κ is the κ index and AE1 and AE2 are the type 1 and 2 errors. The number of descriptors ranges from 1 to 30, as after this point the performance tends to stabilise. The greatest success rate and smallest errors were obtained by the combined fractal descriptors. Such outcome confirms the effectiveness of the proposed methodology in this classification task, providing an excellent categorization of the plant species. Table I . Success rate for different approaches.. The tables II, III and IV exhibit the confusion matrices for each compared descriptor. These tables are helpful to describe either the correctly classified samples as well as the false negatives and false positives, outside the main diagonal. We observe that, despite some minor differences among the methods, the methodology developed in the present study demonstrated to be the most reliable solution to identify the grass samples. Reinforcing the values on the The great performance achieved by the proposed fractal descriptors is due to the nature of the fractal modeling, as mathematical fractals and natural objects have a great deal in common. The similarities are related to the high complexity usually found in the nature as well as the self-similarity property, which also appears often in parts of plants, like leaves, flowers, etc. Actually, the fractal descriptors are tightly related to important physical attributes of the leaf, such as roughness, reflectance and distribution of colors and brightness levels. In turn, this set of properties is capable of identify plant species faithfully, using their digital image representation, as demonstrated in [11] . The present study confirms such reliability and robustness of fractal descriptors and shows that this is a powerful tool for the species categorization of the grasses analyzed here.

B I I O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O


A genetic algorithm for the routing and carrier selection problem Abstract. In this paper we present new evolutionary approach for solving the Routing and Carrier Selection Problem (RCSP). New encoding scheme is implemented with appropriate objective function. This approach in most cases keeps the feasibility of individuals by using specific representation and modified genetic operators. The numerical experiments were carried out on the standard data sets known from the literature and results were successful comparing to two other recent heuristic for solving RCSP. The delivery of goods from a warehouse to local customers is an important and practical problem of the logistics management. It has to decide which customers are to be served by the heterogeneous internal fleet and to route the vehicles of the internal fleet. A internal vehicle allows a company to consolidate several shipments, going to different destinations, in a single route. This problem with internal fleet and external carriers has also known as VRPPC (vehicle routing problem with private fleet and common carriers) in the literature ( [4] ). Demand of remaining customers must be served by external carriers. An external carrier usually assumes the responsibility for routing each shipment from origin to destination. The freight charged by a external carrier is usually much higher than the cost of a vehicle in internal fleet. Therefore, in some cases, it may be more economical to use external carriers instead of using an internal This research was partially supported by Serbian Ministry of Education and Science under the grant no. 174010. vehicle to serve one or very few customers. Also, if total demand is greater than whole capacity of the heterogeneous internal fleet, logistics managers have to consider using an external carrier. Selecting the right mode to transport a shipment may yield significant cost savings to the company.. Routing and Carrier Selection Problem (RCSP) consists of the routing fixed number of vehicles with the limited capacity from the central warehouse to the customers with known demand. The objective is to minimize overall cost, which consists of the three parts: fixed cost of the using necessary vehicles in the internal fleet, variable transportation cost of routing every vehicle and a cost of freight for remaining customers (not served by internal fleet) charged by external carriers. RCSP is a NP-hard problem, as an generalization of the well known vehicle routing problem. We present new heuristic, based on a genetic search framework, for solving the Routing and Carrier Selection Problem. Arranging unserved customers in non-decreasing order by their distances from current customer directs GA to promising search regions. Computational experiments on existing RCSP instances demonstrate the robustness of the proposed algorithms with the respect to the solution quality and running times. Comparisons with results from the literature show the appropriateness of proposed algorithm. Our future research will be directed to parallelization of the presented GA, incorporation it in exact methods and its applying in solving similar routing problems. The routing problems are well-known combinatorial optimization problems and many approaches for solving these have been proposed. Good survey of new contributions can be found in [10] and for multi-objective case in [11] .. However, only in several papers the problem with the vehicle routing when external carrier services are available, was considered. In [2] a fleet planning problem for long-haul deliveries with fixed delivery locations and an option to use an external carrier is considered. Static problem with a fixed fleet size and optional use of a outside carrier is considered in [1] . In [12] is described a methodology to address the fleet size planning and to route limited vehicles from a central warehouse to customers with random daily demands is developed. Paper [7] considered the problem where the company has only one vehicle.. In [5] selected customers were served by the external carriers, then used the modified version of heuristic proposed by [6] to construct the routes to serve the remaining customers and finally uses the local search (steepest descent heuristics) to improve the obtained solution.. The method proposed in [3] , is named SRI (Selection, Routing and Improvement) heuristic, and it is composed of the following steps: (a) select customers to be served by the external carrier, (b) construct a first initial solution, (c) improve the obtained solution, (d) construct another initial solution, and (e) improve the second solution. Then, the best obtained solution is retained as a final solution. Use of two initial solutions increases chance to get good solutions within a very reasonable computation time.. Paper [4] describes metaheuirstic that uses perturbation procedure in the construction and improvement phases. It also performs exchanges between the sets of customers served by the private fleet and the common carrier. The obtained results clearly indicate that perturbation metaheuirstic is useful tool for solving RCSP.. A tabu search heuristic with a neighborhood structure based on ejection chains is described in [20] . In is empirically demonstrated that proposed algorithm slightly outperforms previous approaches reported in the literature.

O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


DVB-T2 technology improvements challenge current strategic planning of ubiquitous media networks This article presents an analysis of the key technology improvements of the second generation of Digital Video Broadcasting -Terrestrial (DVB-T2) over its first generation (DVB-T) and an estimation method of the new technology influence on the broadcasting business case used in digital terrestrial networks. This article addresses the current challenges in broadcasting wireless network design and strategic planning of ubiquitous media by taking the multidisciplinary approach. The model presented supports decision-making process driven by an optimal investment cost and the techno-economic analysis of digital terrestrial wireless technologies using innovation service diffusion Bass model. The method of estimating the benefits of advanced digital dividend exploits the capacity gained due to DVB-T2 technology novelties. The simulation results for Serbia show that the profitability of broadcast network is achieved in some cases already after 2 years if DVB-T2 standard is used. There are several standards currently used worldwide for digital terrestrial broadcasting [1] . The first introduced was the Advanced Television Systems Committee (ATSC), now used in North America and South Korea. Digital Video Broadcasting -Terrestrial (DVB-T) is the European-based consortium standard, used apart from Europe in Australia, India, and some other Asian and African countries. The Japanese standard for digital terrestrial television is called Integrated Services Digital Broadcasting -Terrestrial (ISDB-T), adopted after ATSC and DVB-T taking into account the experience gained with the older standards and it is widely used in South America. Besides those three international standards for digital terrestrial broadcasting, there is also Chinese Digital Terrestrial Multimedia Broadcast standard for fixed and mobile users. Two significant standards for terrestrial mobile TV reception are Terrestrial -Digital Multimedia Broadcasting (T-DMB) and Digital Video Broadcasting -Handheld (DVB-H). The first one was developed in South Korea and its physical parameters are identical to the European Digital Audio Broadcasting (DAB) standard. T-DMB is being put into use in many countries around the world. On the other side, DVB-H is the preferred technology for terrestrial mobile broadcasting services in Europe.. The focus of this article is the performance analysis and efficiency estimation method applied to the technologies for fixed reception used in our region -Europe. The new technologies, like compression standard Moving Picture Experts Group 4 (MPEG-4) part 10, or H.264/AVC (hereinafter called MPEG-4) and the second generation of digital terrestrial broadcasting standard (DVB-T2), provide increased capacity and ruggedness in the terrestrial transmission environment. As we indicated in our previous research [2] , when considering the whole picture, it is evident that the latest technologies besides technical benefits, increased capacity for new services and higher quality of service, bring also a higher system cost. The viability of digital broadcasting business case is directly influenced by this issue and could make or break the project. We conducted a research with the similar idea as in [3] , where broadband wireless access efficiency and economic analysis for licensed TV bands were developed, and as in [4] , where the profitability evaluation of high-altitude platforms was performed for broadband multimedia services in Korea.. Prior efforts to determine the relationship between technical and economical performance of digital broadcasting technologies, to the best of authors' knowledge, have been rare and different in scope. We believe that is especially the case with DVB-T2.. Since the early days of digital terrestrial broadcasting there were researches [5] toward techno-economic analysis which models market prospects, convergence (Telco, IT, broadcasting), and its regulatory implications. The analysis [5] explores technological issues and drivers in the development of digital terrestrial TV in Denmark. On the other hand, the analysis [6] of the economics of IP datacast service to mobile users over terrestrial DVB system offers techno-economic simulation model which builds business case for a greenfield operator. This model calculates the cost of building and operating IP datacast DVB-H network. The article [7] focuses on DVB-H and DAB standards comparison by analyzing radio and mobile TV services in Sweden in terms of capacity demand and network cost. For that scenario, profit/loss simulation model was not developed. In the analysis [8] , we can find techno-economic planning considerations for digital TV systems. The saidarticle proposes generic growth equation for HDTV, IPTV, and mobile TV services. The equation defines driving force (propelling factor) in terms of market penetration growth in % per annum giving Scurve for growth. It is related with S-curve of technological diffusion that we use in this article as one part of our simulation model;however, we use Bass Diffusion Model which will be explained later. The comprehensive study [9] , compiled by Analysys Mason, DotEcon and Hogan&Hartson for the European Commission regarding exploiting the digital dividend, touches apparently very similar topics as we do in this article and our previous research [2] , still this is true only at first sight. Even though there are similarities, such as that the study generally estimates economic benefits for different technology profiles (MPEG-2/ DVB-T, MPEG-4/DVB-T, MPEG-4/DVBT2), there are a lot of differences, for instance the estimated economic benefit is taken as the value that potential uses of the digital dividend could generate as the sum of consumer and producer surplus -not as profit/loss break-even analysis, which makes study [9] and our research not directly comparable. First, the approach taken in [9] estimates general welfare of the good to the society instead of estimating the return on investment (ROI) to the investor. Second, we can find in the report [9] that the estimation is based on incremental value generated by digital dividend (value generated by service in 470-862 MHz band above the value that would be realized if the service were only provided by alternate means -different frequency band or telecom network), we calculate incremental benefit (profit) only within the same band. Besides that, one major difference is that in our study we directly compare technical and economical performance of different technology profiles ("head-to-head") for one or multiple multiplexes gained by efficiency difference of different profiles, while the analysis [9] calculates economic value for different technical and demand scenarios for digital dividend gained by switchover from analog-to-digital TV without comparing directly the efficiency of digital technology profiles. Furthermore, the study [9] fills the digital dividend band with a mixture of services and analyzes the value for the whole EU, while we take one service at a time to fill the digital dividend (data or PayTV) for one particular country. On the whole, there is a different purpose of the study [9] than our approach; they analyzed the issues for the purpose of running EU policy against digital dividend 470-862 MHz, while we conducted technical and ROI analysis for the investor. Because of this and other mentioned scope differences with [9] , our research could not be directly compared with it.. Generally, there are four stages in techno-economic studies for network deployment planning: scope, model, evaluate, and refine. This approach is known as the Shewhart cycle and it is extended by Deming [10] . In modern literature, we can learn that the cyclic nature is important as it suggests a gradual refinement of the researched business case [11] . We have taken that approach and this article refines the digital broadcasting techno-economic efficiency simulation model presented in [2] .. In this article, we improve our previously developed method [2] of estimating the benefits of digital dividend. After a short analysis of DVB-T2 technology improvements over DVB-T, the article presentsthe model which estimates the break-even point where in time the revenue from the new service brought by MPEG-4/DVB-T2 meets the system investment level. We proposed a PayTV service to be used within the gained capacity and to generate revenue. For the purpose of estimating the service acceptance rate, we applied Bass Diffusion Model to PayTV service within DVB-T/T2. Alternatively, the simulation model could combine two revenue components: PayTV service and spectrum auction. The break-even analysis takes into account multiple multiplex scenarios. In this way, the techno-economic analysis of multimedia networks strategic planning is expressed through the model which is applied to the Serbian broadcast market. After the presentation of simulation results, the analysis discussion is performed, followed by appropriate conclusions. This article analyses the technical parameters for deploying the latest broadcast technologies and proposes a model that evaluates the economic efficiency of DVB-T against DVB-T2. Our previous research caused a method of estimating the benefits of digital dividend which is in this article refined by comparing directly DVB-T2 and DVB-T, applying the model to multiple multiplex scenario, estimating PayTV service acceptance rate by Bass Diffusion Model and evaluating the breakeven point for the overall investment in DVB-T2 broadcasting infrastructure, based on the revenue from capacity gain (advanced digital dividend) due to DVB-T2 technology improvements. The proposed model is simple and flexible, but it is also very useful for estimating the efficiency of technology and for strategic decision making in the field of ubiquitous media enabled by digital broadcasting wireless network.. The model was applied to the Serbian broadcast market. The results from simulation show that if for the revenue we use only PayTV service, the DVB-T2 broadcast network profitability could be achieved in approximately 3 years if four multiplexes/RF channels are used, or even faster (2 years) -depending on the market situation. If for the revenue we use PayTV service and the spectrum auction at the same time, for more than four multiplexes the profitability is achieved immediately.

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O B I I O B O O B O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O


Fast Isogeometric Boundary Element Method based on Independent Field Approximation An isogeometric boundary element method for problems in elasticity is presented, which is based on an independent approximation for the geometry, traction and displacement field. This enables a flexible choice of refinement strategies, permits an efficient evaluation of geometry related information, a mixed collocation scheme which deals with discontinuous tractions along non-smooth boundaries and a significant reduction of the right hand side of the system of equations for common boundary conditions. All these benefits are achieved without any loss of accuracy compared to conventional isogeometric formulations. A tailored integration procedure maintains the precision for the computation of the coefficients of the system matrices. These matrices are approximated by means of hierarchical matrices to reduce the computational complexity for large scale analysis. For the required geometrical bisection of the domain, a strategy for the evaluation of bounding boxes containing the supports of NURBS basis functions is presented. The versatility and accuracy of the proposed methodology is demonstrated by convergence studies showing optimal rates and real world examples in two and three dimensions. Isogeometric analysis (IGA) [1] has received much attention in recent years and it has been successfully applied to a variety of applications. It offers precise and efficient geometric modeling, refinement without the need for communication with the design model and control over the smoothness of the basis functions. The most important feature of IGA is that the discretisation is based on the computer aided design (CAD) representation and therefore it is geometrically exact regardless of the fineness of the underlying basis. This unified representation facilitates the integration of design and analysis model. Hence the overall analysis time, including the creation and improvement of the analysis model, can be reduced significantly [2] .. However, the main challenge in the context of an isogeometric finite element analysis (FEA) is the generation of a volume discretisation from CAD models which are usually based on a boundary representation (B-Rep). This task is far from trivial and is still an open research topic [3, 4] . For linear problems, a volume discretisation can be completely avoided by using an analysis which is based on boundary integral equations, such as the boundary element method (BEM). The distinguishing feature of BEM is that it is based on a B-Rep as well. Hence the CAD model can be used for the simulation without the need for a volume discretisation.. This natural connection is possibly the reason for some early attempts to include CAD representations in a BEM framework. A BEM formulation based on cubic splines was, for example, proposed by [5] and [6] to solve groundwater problems and the Laplace's equation, respectively. Cubic B-splines were applied to potential problems [7, 8] and for coplanar waveguides [9] . The analysis of electromagnetic problems with three dimensional Bézier patches has been demonstrated in [10, 11] . Turco and Aristodemo [12] suggested to use three dimensional B-spline elements to solve elasticity problems. In [13] B-spline surfaces are used by means of the panel method which is a variation of the BEM for solving the potential flow around aerodynamic bodies. To the best of the authors' knowledge, the integration of rational non-uniform B-splines (NURBS) surfaces into a BEM analysis has been first investigated by [14, 15] in the context of the method of moments, a Galerkin approach to solve Maxwell's equations.. The introduction of IGA for FEA [1, 2] has reignited the usage of CAD representation in the BEM community. The isogeometric BEM has been applied to the Laplace's equation [16, 17] , linear elasticity [18, 19, 20, 21, 22] , Stokes flow [23] , low-frequency acoustic problems [24] , electro-magnetic problems [25] and an extended formulation for the Helmholtz equation in two dimensions [26] .. Despite the fact that IGA and BEM complement each other extremely well, the BEM naturally comes with a high degree of complexity: the system matrix is fully populated and the solution of the linear system requires a significant numerical effort. For the past three decades, much research has been dedicated to the reduction of the algorithmic complexity. The most important approaches are the fast multipole method (FMM) [27] , hierarchical matrices (H-matrices) [28] , the wavelet method [29] and fast Fourier transformation based methods [30] .. Only a few publications deal with the application of fast BEM formulations to analysis involving Bézier, B-splines or NURBS functions. González et al. [31] presented the combination of a multilevel FMM and Bézier patches. This is the first application of a fast solution method in that context. Harbrecht and Randrianarivony [32] applied the wavelet method to trimmed NURBS patches by means of a decomposition into four-sided patches. In [33] the authors compared different customised fast solution techniques on NURBS patches solving Laplace's problem. The same problem applied to the FMM in two dimensions has been studied in [34] .. In this paper the first application of a fast solution technique to isogeometric BEM in elasticity is presented. The H-matrices approach is employed with a scheme for the geometric bisection which is tailored towards NURBS patches. An efficient formulation is introduced which is based on an independent discretisation for geometry, displacement field and traction field. Due to this flexibility, the refinement can be specifically performed for fields where a finer resolution is necessary, while for others a coarse representation is maintained. This results in an efficient evaluation of geometry related information and a minimisation of the right hand side of the system of equations and its storage requirements. In addition, this formulation allows discontinuous tractions along non-smooth boundaries while maintaining the physical constraint of continuous displacements. The proposed approach violates the isoparametric concept. However, it is still isogeometric since the same functions as in the CAD model are used and, hence the geometry representation is still exact.. The paper is organised in the following sections. First a brief overview on the boundary value problem and its corresponding boundary integral equation is given. The main part is found in section 3. Here the customised and individual discretisation with NURBS basis functions is described as well as the collocation scheme and the blocksystem of equations. Section 4 is devoted to the numerical integration of the resulting boundary integrals with an adaptive scheme, customised for NURBS patches. This is a crucial point to preserve accuracy. In section 5 the concept of H-matrices and their application to the formulation is described, focusing on the geometric bisection of NURBS patches. Finally, numerical results demonstrate convergence and efficiency of the method presented. A novel isogeometric boundary element method (BEM) based on collocation with NURBS basis functions has been introduced in this paper. The formulation uses an independent description of geometry and Cauchy data and applies the concept of hierarchical matrices (H-matrices). Since the resulting NURBS patches do not strictly follow the isoparametric idea, they are denoted as subparametric patches.. The efficiency of the method presented stems from the fact that the conventional isoparametric concept in isogeometric analysis can be viewed as a process which introduces redundancy: geometry and the Cauchy data are described by more control parameters than actually necessary. This superfluous information is solely introduced because refinement is mandatory for a sufficient accurate approximation of the solution. Refinement is performed independently for each field with subparametric patches and redundant information is thus avoided. The separation of the field discretisations is beneficial, especially in the context of isogeometric analysis, since known boundary data are defined over a whole patch rather than as an element in standard BEM formulations. This results in a significant reduction of computational effort for the evaluation of the right hand side of the system of equations. Additionally, the quadratic computational complexity of the left hand side is reduced to almost linear by means of H-matrices. This is achieved by a block-wise setting of integral equations which leads to strictly separated discrete integral operators. The system matrices are approximated by means of adaptive cross approximation. The necessary geometrical bisection uses the convex hull property of NURBS patches with respect to their control points. Several numerical tests in two and three dimensions confirm the optimal convergence and accuracy of the presented method, as well as the potential reduction of storage requirements and computational effort compared to conventional isogeometric BEM formulations. The approximation of the Cauchy data with B-splines or NURBS leads to almost identical results. Using non-smooth Bézier segments reduces the accuracy with respect to the number of degrees of freedom. This approximation is not to be mistaken with Bézier extraction procedure.. An adaptive integration scheme has been developed to ensure the accuracy of the integration. In order to improve the efficiency of the numerical integration more sophisticated strategies should be developed. The choice of discontinuous collocation points presented here is suitable for the examples shown. However, the issue of their optimal position needs to be investigated in further detail.

O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O B O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O B O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


Counting occurrences of some subword patterns We find generating functions for the number of strings (words) containing a specified number of occurrences of certain types of order-isomorphic classes of substrings called subword patterns. In particular, we find generating functions for the number of strings containing a specified number of occurrences of a given 3-letter subword pattern.We say that the patterns β and γ are strongly Wilf-equivalent, or are in the same strong Wilf class, if the number of words in [k] n containing β exactly r times is the same as the number of words in [k] n containing γ exactly r times, for any r ≥ 0.By Theorem 2.7 and the symmetry operations "reversal" and "complement," we immediately get the following corollary. Corollary 2.10 The subword patterns 1121 and 1221 are in the same strong Wilf class. Counting the number of words which contain a set of given strings as substrings a certain number of times is a classical problem in combinatorics. This problem can, for example, be attacked using the transfer matrix method (see [20, Section 4.7] ). In particular, it is a well-known fact that the generating function of such words is always rational. For example, in [20, Example 4.7.5] it is shown that the generating function for the number of words in [3] n where neither 11 nor 23 appear as two consecutive digits is given by. In this paper, we present, in several cases, a complete solution for the problem of the enumeration of words containing a subword pattern (see below for the precise definition) of length l exactly r times. For example, we find the number of words in [3] n containing the subword pattern 111 exactly r times, that is, the number of words which contain 111, 222, and 333 as substrings a total of r times.. Régnier and Szpankowski [18] used a combinatorial approach to study the frequency of occurrences of strings (which they also called a "pattern") from a given set in a random word, when overlapping copies of the "patterns" are counted separately (see [18, Theorem 2.1] ). We note that the term "pattern" in [18] is used to denote an exact string rather than its type with respect to order isomorphism. For example, the "pattern" 112 in [18] is the actual string 112, whereas in our setting an occurrence of the subword pattern 112 is any substring aab of the ambient string with a < b. Although, in principle, it is possible to deduce our results from the result by Régnier and Szpankowski, our direct derivations are much simpler. Goulden and Jackson [12] also consider sequences with distinguished substrings and use the term "pattern of a sequence". However, their "pattern" is more locally defined than in this paper in that only order relations between adjacent elements of a string are considered, rather than order relations between any pair of elements of a string, as is done in this paper. For example, the pattern "rise, non-rise" (or (<, ≥), or π 1 π 2 ) as defined in [12] includes the subword patterns 121, 122, 132, 231 as defined in this paper. However, we show that each of the subword patterns 121, 122, 132 is avoided by a different number of words (of a given length on a given alphabet) than the other two patterns.. In what follows, we use analytical and combinatorial means to find a complete answer for several cases of counting strings with a specified number of occurrences of certain patterns.

O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


Content-based retrieval of historical Ottoman documents stored as textual images There is an accelerating demand to access the visual content of documents stored in historical and cultural archives. Availability of electronic imaging tools and effective image processing techniques makes it feasible to process the multimedia data in large databases. In this paper, a framework for content-based retrieval of historical documents in the Ottoman Empire archives is presented. The documents are stored as textual images, which are compressed by constructing a library of symbols occurring in a document, and the symbols in the original image are then replaced with pointers into the codebook to obtain a compressed representation of the image. The features in wavelet and spatial domain based on angular and distance span of shapes are used to extract the symbols. In order to make content-based retrieval in historical archives, a query is specified as a rectangular region in an input image and the same symbol-extraction process is applied to the query region. The queries are processed on the codebook of documents and the query images are identified in the resulting documents using the pointers in textual images. The querying process does not require decompression of images. The new content-based retrieval framework is also applicable to many other document archives using different scripts.Index Terms-Angular and distance span, binary wavelet decomposition, content-based retrieval, historical document compression, partial symbol-wise matching. In this paper, a content-based retrieval system for the Ottoman documents is presented. Documents in the database are compressed using an improved version of the textual image coding scheme developed in [2] . An important characteristic of the symbol extraction process used in data compression is its scale invariance, which enables to query any type of textual image region successfully.. The Ottoman documents compressed in this special textual form are effectively queried by specifying rectangular regions in document images without any limitation on the size of the query region. The querying takes place using only the compressed data. Our symbol matching scheme ranks the resulting document images in the decreasing order of similarities with respect to the number of symbols matched. The total similarity is computed by comparing the symbols in the query region with the pointers to the codebook. The resulting documents are presented by identifying the matched region of each document in a rectangle.. The symbol extraction and correlation process is scale-invariant and three features from spatial and wavelet domain are extracted. Angular span is a vector whose entries are the number of black pixels in -degree slices centered at the center of mass of a symbol with respect to the horizontal axis. Distance span is also a vector whose entries are the number of black pixels in concentric circles centered at the center of mass and separated by equal distances. These span vectors are normalized to provide scale invariance. Scale-invariant features are also extracted from the extrema of the wavelet transform computed by the Adaptive Subband Decomposition (ASD).. Our framework ensures the storage and content-based retrieval of documents written in ordinary and connected scripts, or even documents containing text mixed with pictures, figures, signs, etc. Our symbol-extraction scheme allows us to process gray level textual images without a binarization process for symbol-extraction which may disturb the originality of the historical documents. The proposed framework for content-based retrieval is also applicable to other historical and cultural archives using different scripts.. Effectiveness of the retrieval process was evaluated using interpolated precision-recall graphs for each of the features separately, and better results are obtained by linearly combining the three features. Experimental studies show that the system successfully retrieve documents containing the keyword image.

B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I I O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O B I I B I B I I B I I O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


Adaptable Multi-Agent Systems: The Case of the Gaia Methodology Changes and adaptations are always necessary after the deployment of a multi-agent system (MAS), as well as of any other type of software systems. Some of these changes may be simply perfective and have local impact only. However, adaptive changes to meet new situations in the operational environment of the MAS may impact globally on the overall design. More specifically, those changes usually affect the organizational structure of the MAS. In this paper we analyze the issue of design change/adaptation in a MAS organization, and the specific problem of how to properly model/design a MAS so as to make it ready to adaptation. Special attention is paid to the Gaia methodology, whose suitability in dealing with adaptable MAS organizations is discussed also with the help of an illustrative application example. In this paper, we have discussed the issue of design change/adaptation that may affect a MAS during its lifetime, by focussing on the organizational aspects. We used the Conference Management System as a representative example of adaptive MAS, to show how changes may require re-structuring the global organization of a MAS. Then, also with the help of the case study, we have discusses how the Gaia methodology -or, more precisely, the way in which Gaia models and organizes the identification of the organizational structure and of the rules governing the general behavior of the MAS -can to some extent facilitate engineers in tackling the likely changes that will appear in a MAS organization after its deployment. Furthermore, we infer some of the main characteristics that agent-based methodologies should feature in order to deal with such kind of adaptation, that is, to explicitly model the organizational structure and organizational rule of the MAS-to-be, as well as the adoption of relevant software engineering principles such as modularity and separation of concerns. Also, we discussed other related contributions from the traditional software engineering, from methods or frameworks for specific domains other than agents, and also from other AOSE methodologies which devote special interest to the organizational perspective.. Our current research work is focused on proposing more specific guidelines and conceptual tools to support engineers in the adaptive maintenance of a MAS system, as well as, for the same purposes, in integrating in Gaia a more iterative and agile software process [5] . Another very important issue concerns adaptation at the implementation level, i.e., how does changes in the design reflect in the implementation, and what different problems may arise at this level that we have still not identified? The final long-term goal of our research is to eventually reach a point in which we will be able to develop and deploy MAS that autonomously self-adapt their behavior and re-structure their internal organization in response to contingencies. Table 1 caption: The Size of the ISAS/SCI Conference. Table 2 caption: The Environment Model for the Review Sub-organization. Table 3 caption: The ReviewCatcher functional role schema. Table 4 caption: The ReviewPartitioner organizational role schema. Table 5 Table 5 . The ReceivePaperAssignement interaction protocol.. Protocol Name: ReceivePaperAssignement Initiator: ReviewCatcher Partner: ReviewPartitioner Input: paper submitted Description: The ReviewPartitioner, having checked the area Output: The paper is of the paper, assigns the paper to the corresponding ReviewCatcher assigned to a specific area (the Vice-Chair in charge of that area).. and the DB Submission is updated Figure 5 caption: The paper review organization structure for a simple hierarchy Figure 6 caption: The paper review organization structure for a hybrid structure Figure 7 caption: The paper review organization structure for a multilevel hierarchy As discussed in the Conference Management System example, Gaia prescribes the clear separation between the analysis phase -where the basic features of the systemto-be are captured and organized -and the architectural design phase-where all the results of the analysis are put at work in order to identify the most suitable organizational structure. Along with the specific structuring of the analysis phase and of its models, such a clear separation is an essential factor in order to facilitate adaptive changes. The result of the analysis phase in Gaia is quite a modular one, keeping distinct the basic characteristics/functionalities of the systems, -i.e., the preliminary roles and interactions models -from the characteristics of the operational environment -i.e., the environmental model -and from any additional constraints that the MAS will have to respect-i.e., the organizational rules. This implies that whenever contingencies call for a re-thinking of some of the MAS specifications, the clear separation of concerns of the Gaia analysis models is likely to avoid global re-thinking of the whole analysis and, depending on the types of contingencies, to promote a local tuning of a limited set of models. For instance, some functional changes to how a sub-task is expected to be achieved would impact on the preliminary role model only; on the other hand, changes to the global constraints the MAS has to respect would imply changes in the organizational rules only.. The prescriptions to explicitly model the organizational structure and delay its identification to the architectural design phase are also of paramount importance. In fact, more than the outcome of the analysis, it is the choice of a specific organizational structure that is more likely to be affected by contingencies. Besides properly structuring the functional requirements of the analysis phase, the choice of a specific organizational structure has to take into account and is affected by a number of non-functional requirements and by various characteristics of the operational environment. Thus, whenever contingencies call for adaptive changes in the MAS, it is very likely that a new organizational structure will be required, which can be selected in Gaia without affecting the global design. Actually, as discussed in the Conference Management System example, modifications are mainly concerned with the architectural design phase, and do not affect in practice the analysis effort.

O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


Flooding Management using Hybrid Model Predictive Control: Application to the Spanish Ebro River In this paper, the problem of flooding management using hybrid model predictive control is presented and applied to the Ebro River in Spain. The Ebro river presents flooding episodes in the city of Zaragoza during spring when snow melts in the Pyrenees. To avoid flooding in living areas, some lands outside the city are prepared to be flooded. This paper presents a control approach to determine and fix the level of flooding in pre-established zones by controlling side gates that determine the water input to the land to be flooded. Finally, several scenarios are used to validate the performance of the proposed approach. River flooding are extreme episodes necessary for the adequate functioning of rivers and their associated ecosystems. In order to coexist in harmony with flooding, their prevention and control is an important topic in the management of those systems. The reason is due to the fact that river flooding may cause large economic losses when they are not appropriately managed.. The most common and utilised technique for flooding management is based on operating rules, which merge heuristic approaches, operator judgement and experience. While these approaches may be adequate in most of the cases, the best operational policies may be quite complex for large-scale interconnected systems. On the other hand, decision support systems (DSS), which are based on mathematical models of the system operation and optimal control techniques, provide useful guidance for efficient management of flooding in rivers [5] .. Model Predictive Control (MPC) is a technique that allows to take into account physical and operational constraints, multivariable and large-scale features, transport delays, disturbance forecasting and multi-objective operational goals [14] . The optimal strategies are computed by optimising a mathematical function describing the operational goals in a given time horizon and using a representative model of the system dynamics, as well as disturbance forecasts, if available. Thus, MPC is a suitable technique to deal with the flooding management in rivers because of the multivariate and complex dynamics of those systems, which make the control 1 INTRODUCTION problem challenging. Moreover, since rivers present important transport delays, MPC allows to compute optimal control strategies ahead in time for all the control elements of the river system.. In most water systems, the regulated elements, namely pumps, gates and retention devices, are typically controlled locally, i.e., they are controlled by a remote station according to the measurements of sensors connected only to that station. However, a global real-time control (RTC) system requires the use of an operational model of the system dynamics in order to compute, ahead of time, optimal control strategies for the actuators based on the current state of the system provided by supervisory control and data acquisition (SCADA) sensors, the current disturbance measurements and appropriate disturbance predictions. The computation procedure of an optimal global control law should take into account all the physical and operational constraints of the dynamical system to produce set-points that allows to achieve the given control objectives. Within this global control framework, MPC has shown to be a suitable strategy to implement global RTC of water systems since it has important features to deal with complex behaviours and features such as big delays compensation, the use of physical constraints, relatively simple for people without deep knowledge of control, multi-variable systems handling, among others. MPC, as global control law, determines the optimal set-points for local controllers already existing in the field.. Reviewing the literature, MPC has already been proposed for flooding management by several authors. In [24] , a multiple-model MPC scheme for a large drainage canal system in the Netherlands is proposed. This control approach allows to deal with uncertainty in the expected inflow by minimizing an objective function in which the risk of damage is used by applying different scenarios to multiple identical models. On the other hand, in [3] a non-linear MPC scheme to address the flooding problem of the Demer river in Belgium is presented. The proposed MPC approach is based on a new semi-condensed optimization procedure combined with a line search approach.. The use of optimal/predictive control techniques for flooding management requires the development of control-oriented dynamic models to represent open-channel systems and associated hydraulic structures (e.g., gates, weirs, dams), which might have non-linear responses to control actions. On the other hand, the storage (tanks and dams) and control elements (gates, valves and pumps), with a pre-determined operational range, lead to the inclusion of constraints besides the model formulation. Moreover, there exist several inherent phenomena and/or elements in the system that result in distinct behaviour depending on its state. These discontinuous behaviours can not be neglected nor can be modelled by a pure linear model. To take into account these behaviours, a control-oriented model methodology that allows considering and incorporating flooding and other logical dynamics in some of the system elements is needed. In previous works reported by the authors, a hybrid modelling approach based on the Mixed Logical Dynamical (MLD) form, introduced in [2] , was used to model hybrid elements in sewer networks (see [19] for further details).. However, the inclusion of those discontinuous behaviours in the MPC problem increases the computation time of the control law [18] . Therefore, some relaxation should be thought in the modelling approach such that it can be considered within the RTC of river systems. Thus, one of the contributions of this paper is to propose a control-oriented modelling approach that takes into account the continuous/discrete dynamic behaviours that can be used when performing an MPC-based RTC scheme for river systems. The proposed approach models the hybrid behaviours by using piece-wise linear (PWL) functions, following the ideas proposed in [22] . The aim of this modelling approach, namely in the sequel PWLF model, is to reduce the complexity of the MPC problem by avoiding the logical variables introduced by a mathematical system representation such as MLD form. The idea behind the PWLF modelling approach consists in having a description of the network using functions that, despite their discontinuous nature, are considered as quasi-convex [4] and hence the optimization problems associated to the non-linear MPC strategy used for RTC of the river system. In this way, the resulting optimization problems do not include integer variables, which allows saving computation time.. As the case study, this paper presents the flooding management problem in the basin of the Ebro river in Spain. In the past, the Ebro basin experienced several flooding. In order to reduce the associated hazard in a given area, the local water administration usually set up several flooding-controlled areas for being able to store the excessive water volume during periods of extreme rainfall. To control the flows from/to the flooding zones, hydraulic control structures have been put in place. Through these actions, it is planned to have a significant reduction of the flooding risk in the basin. Simulations of these past events in a hydrodynamic river model will show that flooding can be further reduced if the hydraulic structures are controlled using MPC to decide the optimal time to open/close the gates. Notice that the formulation of both the system model and the associated MPC strategy are deeply related to the placement of the gates, here called side gates. This feature makes the problem more challenging due to its special structure.. The paper is organised as follows. In Section 2 the Ebro river case study is introduced. Section 3 describes the control-oriented modelling principles used as well as their application to the case study. Section 4 presents the Hybrid MPC (HMPC) strategy used in this paper to manage flooding in the Ebro river case study. The main simulation results of the closedloop scheme proposed here are collected and discussed in Section 5, while in Section 6 the most relevant conclusions are drawn. In this paper, the problem of flooding control at the Ebro River in Spain is presented. The Ebro River presents flooding episodes in the city of Zaragoza in spring when snow melts in the Pyrenees. To avoid flooding in living areas, some lands outside the city are prepared to be flooded. This paper has presented a predictive control approach to manage induced flooding in pre-established areas by manipulating the side gates that regulate the water inflow to the land to be flooded. Several scenarios have been used to validate the performance of the proposed approach. Obtained results are promising to validate that flows at control points can be reduced. However, these results can be further improved by replacing the considered side gates by active

O O O O O B I O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


Minimizing Dispersive Errors in Smoothed Particle Magnetohydrodynamics for Strongly Magnetized Medium In this study, we investigate the dispersive properties of smoothed particle magnetohydrodynamics (SPM) in a strongly magnetized medium by using linear analysis. In modern SPM, a correction term proportional to the divergence of the magnetic fields is subtracted from the equation of motion to avoid a numerical instability arising in a strongly magnetized medium. From the linear analysis, it is found that SPM with the correction term suffer from significant dispersive errors, especially for slow waves propagating along magnetic fields. The phase velocity for all wave numbers is significantly larger than the exact solution and has a peak at a finite wavenumber. These excessively large dispersive errors occur because magnetic fields contribute an unphysical repulsive force along magnetic fields. The dispersive errors cannot be reduced, even with a larger smoothing length and smoother kernel functions such as the Gaussian or quintic spline kernels. We perform the linear analysis for this problem and find that the dispersive errors can be removed completely while keeping SPM stable if the correction term is reduced by half. These findings are confirmed by several simple numerical experiments. Smoothed particle hydrodynamics (SPH) is an entirely Lagrangian particle method for simulating fluid flows [1, 2] . This Lagrangian nature offers major advantages when SPH is applied to problems with a large, dynamic range of spatial scales. Furthermore, SPH can easily incorporate other physics such as self-gravity, radiative transfer, or chemistry. Thus, SPH is widely used in a variety of astrophysical problems such as formation of large-scale structures, galaxies, stars, and planets.. Recently, several authors have tried to extend SPH to magnetohydrodynamics (MHD) because magnetic fields play an important role in a variety of astrophysical environments. In this study, we call SPH for MHD "smoothed particle magnetohydrodynamics" (SPM). Price and Monaghan [3] has developed an SPM method with artificial viscosity and resistivity [also see 4] . Iwasaki and Inutsuka [5] have applied Godunov's method to SPM. We call it "GSPM". Recently, Iwasaki and Inutsuka [6] have modified their original GSPM formulation, based on their derivation of the equation of motion in GSPM from an action principle.. Unfortunately, conservative formulations of SPM are known to inevitably suffer from numerical instability for low β plasma because of negative stress, where β is the ratio of the gas pressure to the magnetic pressure. This instability has already been pointed out by Phillips and Monaghan [7] [also see 8] . Among several methods proposed for removing the numerical instability [7, 8, 3] , an approach by Børve, Omang, and Trulsen [9] is widely used in modern SPM methods [e.g., 4, 5, 6, 10] . A broad discussion of stable SPM schemes is found in a review by Price [11] . In the approach of Børve, Omang, and Trulsen [9] , a correction term, B(∇ · B)/4π, is subtracted from the righthand side of the equation of motion. The correction term is essentially zero if ∇ · B = 0 is satisfied. By a linear analysis of SPM, Børve, Omang, and Trulsen [12] (hereafter BOT04) found that half of the correction term, or B(∇ · B)/8π, is large enough to remove the numerical instability. This was confirmed by Barnes, Kawata, and Wu [13] , who found that half the correction term provided the least error and minimized the violation of energy and momentum conservation in a variety of test calculations. Børve, Omang, and Trulsen [14] have proposed a sophisticated method, wherein the size of the correction term varies among the SPH particles.. However, it is still unclear how the correction term affects the capability of SPM to accurately model fluid flows. Guiding the optimal selection of the amount of correction in a rigorous manner is important. Balsara [15] have investigated the linear stability of various SPH formulations, kernel functions, and ratios of smoothing length to interparticle distance [also see 8, 16] . They have suggested an optimal range of parameters from obtained dispersion relations. Although these analyses are valid only for the linear regime and a regular particle configuration, they provide us with a lot of knowledge for achieving further improvements to SPM schemes. Pioneering work for SPM has been done by BOT04, who investigate the dispersive properties of SPM. They parameterize the size of the correction term with a free parameter ξ (0 ≤ ξ ≤ 1), and use ξ × B∇ · B/4π as the correction term. They found that as mentioned above, ξ = 1/2 is large enough to stabilize SPM for low β plasma, and also suggested that smoother kernels, such as Gaussian or the quintic spline kernels, reproduce correct phase velocities, while the cubic spline causes large dispersion errors. However, their study is restricted to several linear waves in the long-wavelength limit and to the case with ξ = 1/2 although many authors still adopt ξ = 1.. In this study, we investigate detailed dispersive properties of SPM for low β plasma by changing ξ, the kernel functions, and the ratio of smoothing length to interparticle distance. From the results, a suggestion of an optimal choice of the size of the correction term is provided.. The paper is organized as follows: in Section 2, the basic equations of SPM are reviewed. In Section 3, a dispersion relation is derived from the basic equations of SPM and its asymptotic behavior in the long-and shortwavelength limits is discussed. The results of the linear analysis are presented in Section 4. To confirm the results of the linear analysis, several numerical experiments are demonstrated in Section 5. Our results are discussed in Section 6. Section 7 offers a summary. In this study, we have investigated the dispersive properties of SPM with a correction term introduced to remove numerical instability in a strongly magnetized medium [9] . The size of the correction term is parametrized by ξ (see equation (2)). The findings in this study are summarized as follows:. • As numerically found by Børve, Omang, and Trulsen [12] , the minimum value of ξ for removing the numerical instability is analytically derived as a function of the plasma β value in Section 3.1.1.. • For the fast modes, it is found that SPM can reproduce correct phase velocities regardless of ξ. The dispersion properties are similar to those without magnetic fields.. • The phase velocities of the slow modes is shown to significantly depend on ξ. For ξ = 1, which is used in most schemes, it is found that SPM suffers from significant dispersion errors with all kernel functions. The dispersion errors become worse for a lower value of β. In the long-wavelength limit (λ/2π = 10 3 ∆x/π), the numerical phase velocities are largely different from the exact values especially for the cubic spline kernel. A larger smoothing length and a smoother kernel functions are not ultimate solution if β is sufficiently small (see Fig. 2 ). The dispersion relations have an off-center peak of the phase velocities around |k|∆x/π ∼ 0.4 and θ ∼ 0, where θ is the angle between k and B 0 . Furthermore, the phase velocities are supersonic for all wavenumbers above the Nyquist wavenumber π/∆x (see Fig. 5 ). The reason for this anomalous behavior is that a parallel magnetic field numerically works as an additional repulsive force and the phase velocities of the slow wave become supersonic. This fact can be understood by examining the dispersion relation with respect to the slow wave propagating along a magnetic field.. On the other hand, for ξ = 1/2, the dispersion errors found for ξ = 1 completely disappear. This can be understood analytically from the dispersion relation.. • To confirm the findings of the linear analysis, several simple numerical experiments are demonstrated. For the tests of linear isolated waves and hydrostatic equilibrium, SPM with ξ = 1 leads to unphysical results while the exact solutions can be reproduced for ξ = 1/2. On the other hand, SPM with ξ = 1 can treat the parallel shock waves if Alfvén Mach number is larger than 0.5. This is because the shock condition is determined only by the conservation properties and slow waves cannot propagate toward upstream. If the shock speeds are smaller, waves propagate upstream against the flow and cause disturbances. These results are consistent with the linear analysis.. This study clearly shows that corrected SPM with ξ = 1 over-stabilizes the numerical instability and significantly modifies the dispersion properties of the slow modes. To eliminate such dispersion errors, we suggests that ξ = 1/2 is the best choice. These abnormal dispersion properties have not been found in the previous works, (e.g., the blast wave tests used to test the capability of schemes for low β) because, as shown in Section 5.2, SPM can treat shock waves even for ξ = 1 as long as the shock speed is large. Thus, it is difficult to identify the dispersion errors found in this study from the blast wave test. The errors can be serious; for instance, in sub-Alfvénic turbulence for low β plasma, the phase velocity of the waves propagating along magnetic fields may be significantly overestimated.. The linear analysis and the numerical experiments suggest that the best choice of ξ is 1/2 from the point of view of accuracy. However, as discussed in Section 6.1, SPM with ξ = 1/2 tends to less stable against particle disorder because of the small repulsive force. In dynamical environments where strong shock waves are important, a value of ξ = 1 is acceptable if the Alfvén Mach number is larger than 0.5.

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