Fotók a múzeumban

Interjú a Still. Fotográfia a múzeumban című kiállítás kapcsán. A kiállítás kurátora: Perenyei Monika MODEM, 2013. július 6 - október 20

Real tropicalization and negative faces of the Newton polytope

In this work, we explore the relation between the tropicalization of a real semi-algebraic set $S = \{ f_1 < 0, \dots , f_k < 0\}$ defined in the positive orthant and the combinatorial properties of the defining polynomials $f_1, \dots, f_k$. We describe a cone that depends only on the face structure of the Newton polytopes of $f_1, \dots ,f_k$ and the signs attained by these polynomials. This cone provides an inner approximation of the real tropicalization, and it coincides with the real tropicalization if $S = \{ f < 0\}$ and the polynomial $f$ has generic coefficients. Furthermore, we show that for a maximally sparse polynomial $f$ the real tropicalization of $S = \{ f < 0\}$ is determined by the outer normal cones of the Newton polytope of $f$ and the signs of its coefficients. Our arguments are valid also for signomials, that is, polynomials with real exponents defined in the positive orthant

Does a given vector-matrix pair correspond to a PH distribution?

The analysis of practical queueing problems benefits if realistic distributions can be used as parameters. Phase type (PH) distributions can approximate many distributions arising in practice, but their practical applicability has always been limited when they are described by a non-Markovian vector–matrix pair. In this case it is hard to check whether the non-Markovian vector–matrix pair defines a non-negative matrix-exponential function or not. In this paper we propose a numerical procedure for checking if the matrix-exponential function defined by a non-Markovian vector–matrix pair can be represented by a Markovian vector–matrix pair with potentially larger size. If so, then the matrix-exponential function is non-negative. The proposed procedure is based on O’Cinneide’s characterization result, which says that a non-Markovian vector–matrix pair with strictly positive density on and with a real dominant eigenvalue has a Markovian representation. Our method checks the existence of a potential Markovian representation in a computationally efficient way utilizing the structural properties of the applied representation transformation procedure

Sojourn times in fluid queues with independent and dependent input and output processes

Markov Fluid Queues (MFQs) are the continuous counterparts of quasi birth–death processes, where infinitesimally small jobs (fluid drops) are arriving and are being served according to rates modulated by a continuous time Markov chain. The fluid drops are served according to the First-Come–First-Served (FCFS) discipline. The queue length process of MFQs can be analyzed by efficient numerical methods developed for Markovian fluid models. In this paper, however, we are focusing on the sojourn time distribution of the fluid drops. In the first part of the paper we derive the phase-type representation of the sojourn time when the input and output processes of the queue are dependent. In the second part we investigate the case when the input and output processes are independent. Based on the age process analysis of the fluid drops, we provide smaller phase-type representations for the sojourn time than the one for dependent input and output processes

TRANSIENT ANALYSIS OF A PREEMPTIVE RESUME M/D/l/2/2 THROUGH PETRI NETS

Stochastic Petri Nets (SPN) are usually designed to support exponential distributions only, with the consequence that their modelling power is restricted to Markovian systems. In recent years, some attempts have appeared in the literature aimed to define SPN models with generally distributed firing times. A particular subclass, called Deterministic and Stochastic Petri Nets (DSPN), combines into a single model both exponential and deterministic transitions. The available DSPN implementations require simplifying assumptions which limit the applicability of the model to preemptive repeat different service mechanisms only. The present paper discusses a semantical generalization of the DSPNs by including preemptive mechanisms of resume type. This generalization is crucial in connection with fault tolerant systems, where the work performed before the interruption should not be lost. By means of this new approach, the transient analysis of a M/D/1/2/2 queue (with 2 customers, 1 server, exponential thinking and deterministic service time) is fully examined under different preemptive resume policies

Grundlagen des differenziellen Unterrichts und seine Organisationsformen

This paper focuses on adaptive teaching, which is characterised by the usage of differentiated instruction organised to fit individual differences among learners. Differentiation is therefore the basis of efficient learning and achieving common goals, as well as optimal development and self-realization. When using differentiated instruction a teacher needs to know student’s individual abilities and knowledge. As a result of differentiated approach, active learning in small groups occurs (individual work, pair work, group work, mosaics approach, and contradiction and discussion approach, group projects). In this kind of lesson organization, reciprocal learning quite often appears. Lately, Dalton-Plan (whose creator is Helen Parkhurst) is quite interesting, especially the way it has been used in Hungary (Hungaro-Dalton Association). There, differentiated organization of learning has a function of achieving good educational results. Dalton-Plan school - similar to Montessori, Freinet and Jena-plan schools – uses such procedures in class which lead to differentiation in teaching, individual growth of students, experience-based teaching, and active learning. Innovative teachers today use learner-centred methods in teaching, adapted to different learning styles. Learning styles can be guidelines in integration of students with difficulties – creating equal opportunities on the one hand, and foundations for the development of gifted students on the other.Preferencije učenja vrlo se razlikuju među učenicima, stoga je diferencijacija preduvjet učinkovita učenja, ali i postizanja zajedničkih zahtjeva, kao i optimalnoga razvoja i samoostvarenja. Primjena diferencijacije u jedinstvenoj zajedničkoj nastavi, organiziranoj uz uvažavanje individualnih karakteristika učenika, zajedničkom se terminologijom može nazvati adaptivnom nastavom. Upravo je to predmet istraživanja ove studije. Kod primjene diferenciranog rada nastavnik mora biti upoznat s individualnim sposobnostima učenika, razinom njihova predznanja te mora raspolagati individualnim razvojnim strategijama, kako bi za svakog učenika posebice mogao planirati sustave zadataka uz odgovarajuću motivacijsku razinu, kompleksnost nastavnih sadržaja, procesa i rezultata. Temelji su diferencijacije sljedeći: imati potrebna predznanja za obradu i primjenu novih znanja, imati određenu razinu operativnih sposobnosti, motivacije za učenje; postojanje preduvjeta za samostalni rad učenika; razvijenost u području suradnje, društvene karakteristike učenika itd. Prigodom primjene diferenciranoga rada pojavljuju se metode aktivnoga učenja u malim skupinama (individualni rad, rad u parovima, skupni rad, mozaik metoda, metoda proturječja i rasprave te skupni projekti). U navedenim oblicima rada često primjenjujemo metodu recipročnoga učenja. U posljednje vrijeme posebnu pozornost zaslužuje Dalton-plan (reformski pravac obilježen imenom Helen Parkhurst), odnosno njegova primjena u Hungaro-Daltonovoj udruzi (u Mađarskoj), u kojoj se diferencirano organiziranje učenja stavlja u funkciju postizanja dobrih rezultata obrazovnoga i odgojnog rada. Dalton-plan škola – slično Montessori, Freinet i Jena-plan školi – primjenjuje u nastavi takve postupke koji omogućuju diferencijaciju na nastavnom satu, individualni razvoj, nastavu utemeljenu na iskustvu i aktivnom učenju. Istodobno, možemo pozdraviti kao zanimljiv eksperiment novi nastavno-tehnički program, koji je izrađen pod vođenjem i koordiniranjem radne skupine „Novi laboratorij” (New Laboratory for Teaching and Learning – NLTL), a koji je nazvan „Dalton Technology Plan (DTP)”. Oba naziva upućuju na prirodnu i razvojnu vezu između škole tradicionalnoga programa i filozofije, a i nastavnoga okruženja utemeljenoga na novim tehnikama i tehnologijama. Inovativni se nastavnici danas služe metodama prilagođenima stilovima učenja učenika. Naime, stilovi učenja mogu biti niti vodilje i kod integracije učenika s poteškoćama – stvarajući time jednakost mogućnosti – ali istodobno omogućuju u velikoj mjeri i razvoj sposobnosti darovitih učenika.Die Lernpräferenz variiert stark unter den Schülern, deshalb ist die Differenzierung eine Voraussetzung für effizientes Lernen, aber auch um gemeinsame Anforderungen zu erreichen, sowie für die optimale Entwicklung und Selbstverwirklichung. Die Anwendung der Differenzierung in einem einheitlichen gemeinsamen Unterricht, der hinsichtlich der individuellen Eigenschaften der Schüler organisiert wird, kann mit Hilfe der einheitlichen Terminologie als adaptiver Unterricht bezeichnet werden. Dies ist genau der Gegenstand der vorliegenden Studie. Bei der Anwendung der differenzierten Tätigkeit muss der Lehrer mit den individuellen Fähigkeiten der Schüler und dem Niveau ihrer Vorkenntnisse vertraut sein, sowie über individuelle Entwicklungsstrategien verfügen, um für jeden einzelnen Schüler Aufgabensysteme mit entsprechenden Motivationsniveau, der Komplexität der Unterrichtsinhalte, Prozesse und Ergebnisse planen zu können. Die Grundlagen der Differenzierung sind folgende: die erforderlichen Vorkenntnisse für die Bearbeitung und Anwendung von neuem Wissen besitzen, ein gewisses Maß an operativen Fähigkeiten, Lernmotivation haben; das Vorliegen der Voraussetzungen für die selbstständige Schülerarbeit, entwickelter Bereich der Zusammenarbeit, die sozialen Merkmale der Schüler, etc. Bei der Anwendung von differenzierter Tätigkeit treten Methoden des aktiven Lernens in kleinen Gruppen auf (Einzelarbeit, Partnerarbeit, Gruppenarbeit, Mosaik-Methode, Methode der Kontroverse und Diskussion und gemeinsame Projekte). Bei diesen Arbeitsformen wird oft die Methode des reziproken Lernens angewendet. In letzter Zeit gebührt besondere Beachtung dem Daltonplan (Reformkurs, bekannt durch Helen Parkhurst), bzw. seine Anwendung im Hungaro-Dalton Verein (in Ungarn), wo die differenzierte Lernorganisation dazu dient, gute Bildungs- und Erziehungsergebnisse zu erzielen. Die Daltonplan-Schule – ähnlich wie Montessori, Freinet und Jenaplan-Schule – wendet im Unterricht solche Verfahren an, die eine Differenzierung in der Unterrichtsstunde, individuelle Entwicklung, erfahrungsorientierter Unterricht und aktives Lernen ermöglichen. Gleichzeitig können wir als ein interessantes Experiment das neue unterrichts-technische Programm begrüßen, das unter der Leitung und Koordination der Arbeitsgruppe „Neues Laboratorium“ (New Laboratory for Teaching and Learning – NLTL) ausgearbeitet wurde und „Dalton Technology Plan (DTP)” genannt wird. Die beiden Bezeichnungen weisen auf die natürliche Beziehung und Entwicklung zwischen der Schule mit traditionellem Programm und der Philosophie, sowie der Lehrumgebung, die auf neuen Techniken und Technologien basiert. Innovative Lehrer verwenden heute Methoden, die an die Lernstile der Schüler angepasst sind. Die Lernstile können nämlich auch das Leitmotiv bei der Integration von Kindern mit Schwierigkeiten sein - wodurch eine Chancengleichheit entsteht - aber sie ermöglichen gleichzeitig auch weitgehend die Entwicklungsmöglichkeiten von begabten Kindern