Well-Posedness of the Cauchy Problem for Inhomogeneous Time-Fractional Pseudo-Differential Equations

Mathematics Subject Classification: 26A33, 45K05, 35A05, 35S10, 35S15, 33E12

Well-Posedness of Diffusion-Wave Problem with Arbitrary Finite Number of Time Fractional Derivatives in Sobolev Spaces H^s

Mathematics Subject Classification 2010: 26A33, 33E12, 35S10, 45K05.

Integral Transforms Method to Solve a Time-Space Fractional Diffusion Equation

Mathematical Subject Classification 2010: 35R11, 42A38, 26A33, 33E12.

N–Dimensional Orthogonal Tile Sizing Problem

AMS subject classification: 68Q22, 90C90

Regrouping metric-space search index for search engine size adaptation

This work contributes to the development of search engines that self-adapt their size in response to fluctuations in workload. Deploying a search engine in an Infrastructure as a Service (IaaS) cloud facilitates allocating or deallocating computational resources to or from the engine. In this paper, we focus on the problem of regrouping the metric-space search index when the number of virtual machines used to run the search engine is modified to reflect changes in workload. We propose an algorithm for incrementally adjusting the index to fit the varying number of virtual machines. We tested its performance using a custom-build prototype search engine deployed in the Amazon EC2 cloud, while calibrating the results to compensate for the performance fluctuations of the platform. Our experiments show that, when compared with computing the index from scratch, the incremental algorithm speeds up the index computation 2–10 times while maintaining a similar search performance.

Predegree Polynomials of Plane Configurations in Projective Space

2000 Mathematics Subject Classification: 14N10, 14C17.

Sensor Location Problem for a Multigraph

MSC 2010: 05C50, 15A03, 15A06, 65K05, 90C08, 90C35

Density of Polynomials in the L^2 Space on the Real and the Imaginary Axes and in a Sobolev Space

2000 Mathematics Subject Classification: 41A10, 30E10, 41A65.

Self-adapting parallel metric-space search engine for variable query loads

This research focuses on automatically adapting a search engine size in response to fluctuations in query workload. Deploying a search engine in an Infrastructure as a Service (IaaS) cloud facilitates allocating or deallocating computer resources to or from the engine. Our solution is to contribute an adaptive search engine that will repeatedly re-evaluate its load and, when appropriate, switch over to a dierent number of active processors. We focus on three aspects and break them out into three sub-problems as follows: Continually determining the Number of Processors (CNP), New Grouping Problem (NGP) and Regrouping Order Problem (ROP). CNP means that (in the light of the changes in the query workload in the search engine) there is a problem of determining the ideal number of processors p active at any given time to use in the search engine and we call this problem CNP. NGP happens when changes in the number of processors are determined and it must also be determined which groups of search data will be distributed across the processors. ROP is how to redistribute this data onto processors while keeping the engine responsive and while also minimising the switchover time and the incurred network load. We propose solutions for these sub-problems. For NGP we propose an algorithm for incrementally adjusting the index to t the varying number of virtual machines. For ROP we present an ecient method for redistributing data among processors while keeping the search engine responsive. Regarding the solution for CNP, we propose an algorithm determining the new size of the search engine by re-evaluating its load. We tested the solution performance using a custom-build prototype search engine deployed in the Amazon EC2 cloud. Our experiments show that when we compare our NGP solution with computing the index from scratch, the incremental algorithm speeds up the index computation 2{10 times while maintaining a similar search performance. The chosen redistribution method is 25% to 50% faster than other methods and reduces the network load around by 30%. For CNP we present a deterministic algorithm that shows a good ability to determine a new size of search engine. When combined, these algorithms give an adapting algorithm that is able to adjust the search engine size with a variable workload.

Generalized KPCA by adaptive rules in feature space

Principal component analysis (PCA) is well recognized in dimensionality reduction, and kernel PCA (KPCA) has also been proposed in statistical data analysis. However, KPCA fails to detect the nonlinear structure of data well when outliers exist. To reduce this problem, this paper presents a novel algorithm, named iterative robust KPCA (IRKPCA). IRKPCA works well in dealing with outliers, and can be carried out in an iterative manner, which makes it suitable to process incremental input data. As in the traditional robust PCA (RPCA), a binary field is employed for characterizing the outlier process, and the optimization problem is formulated as maximizing marginal distribution of a Gibbs distribution. In this paper, this optimization problem is solved by stochastic gradient descent techniques. In IRKPCA, the outlier process is in a high-dimensional feature space, and therefore kernel trick is used. IRKPCA can be regarded as a kernelized version of RPCA and a robust form of kernel Hebbian algorithm. Experimental results on synthetic data demonstrate the effectiveness of IRKPCA. © 2010 Taylor & Francis.

Type space on a purely measurable parameter space

Several game theoretical topics require the analysis of hierarchical beliefs, particularly in incomplete information situations. For the problem of incomplete information, Hars´anyi suggested the concept of the type space. Later Mertens & Zamir gave a construction of such a type space under topological assumptions imposed on the parameter space. The topological assumptions were weakened by Heifetz, and by Brandenburger & Dekel. In this paper we show that at very natural assumptions upon the structure of the beliefs, the universal type space does exist. We construct a universal type space, which employs purely a measurable parameter space structure.

Bizalom és kockázat a kapcsolatokban – egy kísérlet eredményei = Relationship between trust and risk - results of an experiment

Műhelytanulmányunkban a diadikus kapcsolatokat állítjuk az elemzés középpontjába. A Budapesti Corvinus Egyetem másodéves, gazdálkodástudományi alapszakjaira járó hallgatóiból véletlenszerűen alakított kétoldalú kapcsolatokban a felek egymás iránt érzett bizalmi szintje és különböző szintű kockázat melletti konkrét cselekvése közötti kapcsolatot vizsgáltuk. Előzetes várakozásaink szerint a felek egymás iránt érzett bizalmi szintje befolyásolja, hogy különböző kockázati szintek mellett hogyan fognak a kapcsolatban szereplő egyének viselkedni. Empirikus elemzésünk során a közgazdaságtanban is elfogadott kísérlet eszközét választottuk, s konkrét adatainkat, megfigyeléseinket e módszertannal gyűjtöttük össze. Az így kapott mintát a Magyarországon a gazdálkodás-, illetve közgazdaságtudományban tudomásunk szerint eddig még nem használt diadikus adatelemzés speciális statisztikai módszertanát alkalmazva vizsgáltuk. Műhelytanulmányunk célja volt ezért az is, hogy ennek a hálózati gazdaság építőkövének, a kapcsolatnak a vizsgálatára alkalmas elemzési módszertannak az ismertetését is megtegyük. _______ In the working paper we have focused on the analysis of trust in dyadic relationships. We have assumed that trust is a kind of coordinating mechanism in these relationships, the existence of which influences interaction between dyadic partners. We carried out an experiment with the help of bachelor students studying at the Budapest Corvinus University. Our hypothesis was that medium and high level of trust will influence the willingness to take more risky decisions. These experiments have been realized in concrete personal dyads; therefore the applied statistical analysis was the dyadic analysis that is a new analytical method developed for analyzing such dyadic problem settings.

The economic approach of advertising and the problem of allocating advertising budgets during a recession

The importance of advertising has changed in many aspects in the last decade, and mainly during the last years of the economic crisis. Economics traditionally did not find advertising a valuable factor until empirical studies demonstrated that advertisement affects consumer perception by means of indicating the quality of the underlying product. Consequently, products that are advertised more frequently, are more likely to be associated with a higher quality. Nevertheless, advertising is a strong tool in competition, which statement is confirmed by the recognition that increasing consumer knowledge contributes to the diffusion of innovation and to the reduction of research and development (R&D) costs. This contribution can be achieved nowadays by consumer interactivity, where companies deliberately rely on the involvement of their consumers. Recently, when companies were confronted to the global economic crisis, brand managers realized that allocating advertising budgets in a recession (considering the actual state of the economic conditions) is a highly important decision factor beside competition, consumer behaviour, trends or industrial conditions. Companies have to realize that their communication budgets are planned substantially in a different way in times of crisis than during an upsurge. Moreover, should a company make the best of maintaining their advertising budgets in recession times, it will indicate more trust towards their consumers and show a more favorable image towards their investors. This study assembles different approaches from the economics of advertising to draw conclusions for the subsequent analyses of advertising in times of a crisis. The main objective with the literature review is to show, that pro-cyclical actions (reducing advertising budgets in times of crisis and overspending during upsurge) of companies can lead to problems of profitability, consumer trust and competitiveness in the long run.

Bizalom az üzleti kapcsolatokban. A diadikus adatelemzés egy alkalmazása = Trust in business relations - an application of dyadic data analysis

A tanulmány arra a feltevésre épül, hogy minél erősebb a bizalomra méltóság szintje egy adott üzleti kapcsolatban, annál inkább igaz, hogy nagy kockázatú tevékenységek mennek végbe benne. Ilyen esetekben a bizalomra méltóság a kapcsolatban zajló események, cselekvések irányítási eszközévé válik, és az üzleti kapcsolatban megjelenik a cselekvési hajlandóságként értelmezett bizalom. A tanulmány felhívja a figyelmet a bizalom és a bizalomra méltóság fogalmai közötti különbségre, szisztematikus különválasztásuk fontosságára. Bemutatja az úgynevezett diadikus adatelemzés gazdálkodástudományi alkalmazását. Empirikus eredményei is igazolják, hogy ezzel a módszerrel az üzleti kapcsolatok társas jellemzőinek (köztük a bizalomnak) és a közöttük lévő kapcsolatoknak mélyebb elemzésére nyílik lehetőség. ____ The paper rests on the behavioral interpretation of trust, making a clear distinction between trustworthiness (honesty) and trust interpreted as willingness to engage in risky situations with specific partners. The hypothesis tested is that in a business relation marked by high levels of trustworthiness as perceived by the opposite parties, willingness to be involved in risky situations is higher than it is in relations where actors do not believe their partners to be highly trustworthy. Testing this hypothesis clearly calls for dyadic operationalization, measurement, and analysis. The authors present the first economic application of a newly developed statistical technique called dyadic data analysis, which has already been applied in social psychology. It clearly overcomes the problem of single-ended research in business relations analysis and allows a deeper understanding of any dyadic phenomenon, including trust/trustworthiness as a governance mechanism.

Space division multiple access for wireless sensor networks

This dissertation proposed a self-organizing medium access control protocol (MAC) for wireless sensor networks (WSNs). The proposed MAC protocol, space division multiple access (SDMA), relies on sensor node position information and provides sensor nodes access to the wireless channel based on their spatial locations. SDMA divides a geographical area into space divisions, where there is one-to-one map between the space divisions and the time slots. Therefore, the MAC protocol requirement is the sensor node information of its position and a prior knowledge of the one-to-one mapping function. The scheme is scalable, self-maintaining, and self-starting. It provides collision-free access to the wireless channel for the sensor nodes thereby, guarantees delay-bounded communication in real time for delay sensitive applications. This work was divided into two parts: the first part involved the design of the mapping function to map the space divisions to the time slots. The mapping function is based on a uniform Latin square. A Uniform Latin square of order k = m 2 is an k x k square matrix that consists of k symbols from 0 to k-1 such that no symbol appears more than once in any row, in any column, or in any m x in area of main subsquares. The uniqueness of each symbol in the main subsquares presents very attractive characteristic in applying a uniform Latin square to time slot allocation problem in WSNs. The second part of this research involved designing a GPS free positioning system for position information. The system is called time and power based localization scheme (TPLS). TPLS is based on time difference of arrival (TDoA) and received signal strength (RSS) using radio frequency and ultrasonic signals to measure and detect the range differences from a sensor node to three anchor nodes. TPLS requires low computation overhead and no time synchronization, as the location estimation algorithm involved only a simple algebraic operation.