An upper bound on the Bayesian error bars for generalized linear regression

In the Bayesian framework, predictions for a regression problem are expressed in terms of a distribution of output values. The mode of this distribution corresponds to the most probable output, while the uncertainty associated with the predictions can conveniently be expressed in terms of error bars. In this paper we consider the evaluation of error bars in the context of the class of generalized linear regression models. We provide insights into the dependence of the error bars on the location of the data points and we derive an upper bound on the true error bars in terms of the contributions from individual data points which are themselves easily evaluated.

Regression with Gaussian processes

The Bayesian analysis of neural networks is difficult because the prior over functions has a complex form, leading to implementations that either make approximations or use Monte Carlo integration techniques. In this paper I investigate the use of Gaussian process priors over functions, which permit the predictive Bayesian analysis to be carried out exactly using matrix operations. The method has been tested on two challenging problems and has produced excellent results.

Capacity of the upstart algorithm

The storage capacity of multilayer networks with overlapping receptive fields is investigated for a constructive algorithm within a one-step replica symmetry breaking (RSB) treatment. We find that the storage capacity increases logarithmically with the number of hidden units K without saturating the Mitchison-Durbin bound. The slope of the logarithmic increase decays exponentionally with the stability with which the patterns have been stored.

Organisational learning - a critical systems thinking discipline

Original Paper European Journal of Information Systems (2001) 10, 135–146; doi:10.1057/palgrave.ejis.3000394 Organisational learning—a critical systems thinking discipline P Panagiotidis1,3 and J S Edwards2,4 1Deloitte and Touche, Athens, Greece 2Aston Business School, Aston University, Aston Triangle, Birmingham, B4 7ET, UK Correspondence: Dr J S Edwards, Aston Business School, Aston University, Aston Triangle, Birmingham, B4 7ET, UK. E-mail: j.s.edwards@aston.ac.uk 3Petros Panagiotidis is Manager responsible for the Process and Systems Integrity Services of Deloitte and Touche in Athens, Greece. He has a BSc in Business Administration and an MSc in Management Information Systems from Western International University, Phoenix, Arizona, USA; an MSc in Business Systems Analysis and Design from City University, London, UK; and a PhD degree from Aston University, Birmingham, UK. His doctorate was in Business Systems Analysis and Design. His principal interests now are in the ERP/DSS field, where he serves as project leader and project risk managment leader in the implementation of SAP and JD Edwards/Cognos in various major clients in the telecommunications and manufacturing sectors. In addition, he is responsible for the development and application of knowledge management systems and activity-based costing systems. 4John S Edwards is Senior Lecturer in Operational Research and Systems at Aston Business School, Birmingham, UK. He holds MA and PhD degrees (in mathematics and operational research respectively) from Cambridge University. His principal research interests are in knowledge management and decision support, especially methods and processes for system development. He has written more than 30 research papers on these topics, and two books, Building Knowledge-based Systems and Decision Making with Computers, both published by Pitman. Current research work includes the effect of scale of operations on knowledge management, interfacing expert systems with simulation models, process modelling in law and legal services, and a study of the use of artifical intelligence techniques in management accounting. Top of pageAbstract This paper deals with the application of critical systems thinking in the domain of organisational learning and knowledge management. Its viewpoint is that deep organisational learning only takes place when the business systems' stakeholders reflect on their actions and thus inquire about their purpose(s) in relation to the business system and the other stakeholders they perceive to exist. This is done by reflecting both on the sources of motivation and/or deception that are contained in their purpose, and also on the sources of collective motivation and/or deception that are contained in the business system's purpose. The development of an organisational information system that captures, manages and institutionalises meaningful information—a knowledge management system—cannot be separated from organisational learning practices, since it should be the result of these very practices. Although Senge's five disciplines provide a useful starting-point in looking at organisational learning, we argue for a critical systems approach, instead of an uncritical Systems Dynamics one that concentrates only on the organisational learning practices. We proceed to outline a methodology called Business Systems Purpose Analysis (BSPA) that offers a participatory structure for team and organisational learning, upon which the stakeholders can take legitimate action that is based on the force of the better argument. In addition, the organisational learning process in BSPA leads to the development of an intrinsically motivated information organisational system that allows for the institutionalisation of the learning process itself in the form of an organisational knowledge management system. This could be a specific application, or something as wide-ranging as an Enterprise Resource Planning (ERP) implementation. Examples of the use of BSPA in two ERP implementations are presented.

Mathematica Balkanica New Series Book Volume 24 2010

Muharem Avdispahic 1 Coordinator of the TEMPUS Project SEE Doctoral Studies in Mathematical Sciences (144703-TEMPUS-2008-BA-TEMPUS-JPCR) The main goals of the TEMPUS Project ”SEE Doctoral Studies in Math- ematical Sciences”, funded by European Commission under the TEMPUS IV first call, consist of the development of a model of structured doctoral studies in Mathematical Sciences involving the network of Western Balkans universi- ties, the curricula design based on the existing strenghts and tendencies in the areas of Pure Mathematics, Applied Mathematics and Theoretical Computer Science and the first phase of implementation of the agreed model during the SEE Doctoral Year in Mathematical Sciences 2011. A decisive step in this direction was ”SEE Young Researchers Workshop” held in Ohrid, FYR Macedonia, September 16-20, 2009, as a part of the Math- ematical Society of South-Eastern Europe (MASSEE) International Congress on Mathematics - MICOM 2009. MICOM 2009 continued the tradition of two previous highly successful MASSEE congresses that took place in Bulgaria in 2003 and in Cyprus in 2006. This volume of the journal Mathematika Balkanica contains the talks de- livered at Ohrid Workshop by South-Eastern European PhD students in various stage of their research towards a doctoral degree in mathematics or informat- ics. Facilitating publication efforts of young researchers from the universities of Sarajevo, Tuzla, Belgrade, Skopje, Stip, Graz, and Sofia fully coincides with MASSEE goals to promote, organize and support scientific, research and edu- cational activities in South-Eastern Europe. The consent of the Editorial Board of Mathematica Balkanica to publish ”SEE Young Researchers Workshop” contributions aptly meets intentions of European reform processes aimed at creating the European Higher Education Area and European Research Area. It is an encouragement to these young researchers in the first place and at the same time an encouragement to their institutions in overcoming fragmentation and enhancing their capacities through fostering reciprocal development of human resources.

On the Factorization of the Poincaré Polynomial: A Survey

2000 Mathematics Subject Classification: 13P05, 14M15, 14M17, 14L30.

Иновации в математическото образование: европейските проекти InnoMathEd и Fibonacci

Petar Kenderov The paper considers the participation of the Institute of Mathematics and Informatics at the Bulgarian Academy of Sciences, into two European projects, InnoMathEd and Fibonacci. Both projects address substantial innovations in mathematics education and their dissemination on European level. Inquiry based learning is the central focus of the two projects. A special emphasis is paid on the outcomes of the projects in terms of didactic concepts, pedagogical methodologies and innovative learning environments aimed at pupils’ active, self-responsible and exploratory learning.

Проблеми в обучението на учителите по математика

Kiril Bankov What mathematics do teachers need to know to teach effectively? This question has been of great importance in the studies of mathematics teacher preparation for the last decade. Many theoretical papers have been published but there is not a common understanding yet. Large scale studies have also contributed to the issue. This paper presents some results of an international study in this area and discusses problems in preparation of mathematics teachers in Bulgaria.

How to Select a Topic for a Project

Иванка Марашева-Делинова - В настоящата работа се разглежда избора на тема при разработване на проекти в непрофилирани по математика класове. Посочват се критерии за подбор на тема. Предлагат се примерни теми и източници за разработка, съобразени с възрастовите и индивидуални особености на учениците, както и техните общи и индивидуални интереси.

Evaluating the Quality of Student Web Design Projects

Иван Шотлеков, Асен Рахнев - В настоящата работа се представя набор от критерии за оценяване на качеството на студентски проекти за уеб дизайн. Критериите са подходящи за разработване, самооценяване, колегиално оценяване и оценка на уеб сайтове, проектирани от студенти. Тази оценъчна скала е апробирана по време на курс “Английски език в информационните технологии”, проведен със студенти от първи курс по информатика във Факултета по математика и информатика на Пловдивски университет “Паисий Хилендарски”. Тя помага на студентите при разработването на мултидисциплинарен проект за уеб дизайн да придобият не само технически умения, свързани с проектирането на качествени уеб сайтове, но и някои процесуални умения, които ще им бъдат необходими в реалната практика.

A Problem on Infinite Series: Difficult or Easy?

Петра Стайнова - Разглежда се един стандартен въпрос за намиране на сумата на реда на Лайбниц. Дават се две различни решения, използващи знания от различен материал. След преформулиране на проблема се оказва, че решението му е възможно с директно използване само на основни понятия. По този начин е показано, че въз основа на една и съща базисна математическа идея могат да бъдат формулирани задачи, допускащи както стандартни, така и нестандартни решения.

Въвеждане на рекурсията чрез абстракция и редици от задачи

Pavel Azalov - Recursion is a powerful technique for producing simple algorithms. It is a main topics in almost every introductory programming course. However, educators often refer to difficulties in learning recursion, and suggest methods for teaching recursion. This paper offers a possible solutions to the problem by (1) expressing the recursive definitions through base operations, which have been predefined as a set of base functions and (2) practising recursion by solving sequences of problems. The base operations are specific for each sequence of problems, resulting in a smooth transitions from recursive definitions to recursive functions. Base functions hide the particularities of the concrete programming language and allows the students to focus solely on the formulation of recursive definitions.

Оптимизация на учителския състав в училище

Silvia Baeva - In the Ministry of Education and Science’s system it has been talked about optimization of the school network; this optimization can be carried out in different directions and be supported by laws. An important aspect in the optimization of the school network is to reduce costs and increase overall efficiency in each school. We will formulate this aspect as a problem of the multicriteria decisions making and by appropriate numbers of methods and criteria it can be transformed to the problem of unicriterion optimization. This problem is separated into two stages: 1-th stage – determining the minimum number of classes in a school under certain statutory provisions for the size of each of them; 2-th stage – the appointment of a minimum number of teachers and achievement of maximal effectiveness of teaching and acquiring of knowledge and skills by students according to certain statutory provisions for teachers’ annual norms of subjects and number of hours in a particular subject area and the salaries of teachers. The achievement of maximum overall efficiency is a priority in all schools.

Едно обобщение на Наполеоновите триъгълници

Dimitar Belev, Vasilka Ignatova-Beleva - We present a generalization of the Napoleon triangles and investigate some of their properties.

Един начин за преговор на формулите по тригонометрия в средното училище

Kliment Vasilev - The trigonometry formulas are given in the form of mathematical problems. Some of these problems are solved, and it is shown how the others can be solved with the help of adequate guidance that includes the previous problems. This method is suitable for revision in the secondary school, as well as for preparation for school-leaving exams and matriculation.