Nudging the particle filter

We investigate a new sampling scheme aimed at improving the performance of particle filters whenever (a) there is a significant mismatch between the assumed model dynamics and the actual system, or (b) the posterior probability tends to concentrate in relatively small regions of the state space. The proposed scheme pushes some particles towards specific regions where the likelihood is expected to be high, an operation known as nudging in the geophysics literature. We re-interpret nudging in a form applicable to any particle filtering scheme, as it does not involve any changes in the rest of the algorithm. Since the particles are modified, but the importance weights do not account for this modification, the use of nudging leads to additional bias in the resulting estimators. However, we prove analytically that nudged particle filters can still attain asymptotic convergence with the same error rates as conventional particle methods. Simple analysis also yields an alternative interpretation of the nudging operation that explains its robustness to model errors. Finally, we show numerical results that illustrate the improvements that can be attained using the proposed scheme. In particular, we present nonlinear tracking examples with synthetic data and a model inference example using real-world financial data

Bir Adalet Pee vardı

Taha Toros Arşivi, Dosya No: 199-Varyete ve Raksİstanbul Kalkınma Ajansı (TR10/14/YEN/0033) İstanbul Development Agency (TR10/14/YEN/0033

A geometric model for Hochschild homology of Soergel bimodules

An important step in the calculation of the triply graded link homology theory of Khovanov and Rozansky is the determination of the Hochschild homology of Soergel bimodules for SL(n). We present a geometric model for this Hochschild homology for any simple group G, as equivariant intersection homology of B x B-orbit closures in G. We show that, in type A these orbit closures are equivariantly formal for the conjugation T-action. We use this fact to show that in the case where the corresponding orbit closure is smooth, this Hochschild homology is an exterior algebra over a polynomial ring on generators whose degree is explicitly determined by the geometry of the orbit closure, and describe its Hilbert series, proving a conjecture of Jacob Rasmussen.Comment: 19 pages, no figure

Openness and Accountability in Turkey in the Context of Accession to the European Union

There are many indicators showing the need for restructuring of the Turkish public administration. The basic nature and problems of the administrative functioning are mostly related to the bureaucratic culture from the past. Turkey has made important public administration reforms in recent years in order to change this bureaucratic culture, which is based on centralization and secrecy. The European Union (EU) is the most important external dynamic of these reforms aiming at openness, transparency, accountability, participation and ethical structuring in public administration. These principles are also an element of the European Administrative Space (EAS), EU governance and the subject of Europeanization in public administration. Among these principles, openness and accountability constitute the subject of this paper. Openness, transparency and accountability of government bear critical importance for the proper functioning of accession process. Within this period, a number of regulations have been passed to ensure institutionalization of an open and accountable administration, resulting in the establishment of new agencies in Turkey. However, although essential steps were taken in terms of openness and accountability before the accession negotiations began on October 3, 2005, the reforms entered into a phase of deceleration thereafter. Therefore, the reforms appear to have been affected by the development course of Turkey-EU relations and slowed down as the relations deteriorated. In this context, these reforms are examined under the following dimensions based on EU progress reports and relevant legal regulations: (i) openness and right to information, (ii) financial transparency and accountability, (iii) ethical principles for public officials

On the Factorization of the Poincaré Polynomial: A Survey

2000 Mathematics Subject Classification: 13P05, 14M15, 14M17, 14L30.Factorization is an important and very difficult problem in mathematics. Finding prime factors of a given positive integer n, or finding the roots of the polynomials in the complex plane are some of the important problems not only in algorithmic mathematics but also in cryptography

Yabancı Uyruklu Öğrencilerin Devam Ettiği Okullardaki Sınıf Öğretmenlerinin Çokkültürlü Yeterlik Algıları ile Demokratik Değerleri Arasındaki İlişki

The aim of this study is investigating the relatioship between multicultural competency perceptions and democratic values of the primary teachers at schools foreigner students attend. In the research, 499 primary teachers among 1980 teachers working at primary schools that foreigner students attend in Trabzon, Rize, Giresun, Ordu, Samsun provincial centers in 2015-2016 school year are included according to the volunteering and impartiality rules. The data is collected by using "Multicultural Competency Perceptions Scale" and “Democratic Values Scale". As a result of the study, it is found that the primary teachers at schools foreigner students attend perceive their multicultural competencies in awareness, knowledge and skills dimensions as "sufficient". Teachers opinions in seeking fairness dimension of democratic values is at the level of "I agree"; in justice, respect to the differences and equity dimensions are at the level of "completely agree". It is seen that, the participant teachers internalized the justice, respect to differences and equity dimensions of democratic values higher than the seeking fairness dimension. It is determined that there is a medium level relation, positively, between the multicultural competency perceptions and democratic values. It is observed that as the democratic values of teachers increase, their multicultural competencies perceptions increase; as democratic values decrease, multicultural competency perceptions decrease either. It is concluded that the reason of having higher multicultural competency perception is related to the internalizing the democratic values for teachers.Bu araştırmanın amacı, yabancı uyruklu öğrencilerin devam ettiği okullarda görev yapan sınıf öğretmenlerinin çokkültürlü yeterlik algıları ile demokratik değerlerinin belirlenmesi ve aralarında bir ilişkinin olup olmadığının incelenmesidir. Çalışmaya, 2015-2016 öğretim yılında, Trabzon, Rize, Giresun, Ordu ve Samsun il merkezlerinde yabancı uyruklu öğrencilerin devam ettiği ilkokullarda görev yapan 1980 sınıf öğretmeninden, gönüllülük ve yansızlık kuralına göre ölçeği doldurmayı kabul eden 499 sınıf öğretmeni katılmıştır. Veriler, “Çok Kültürlü Yeterlik Algıları Ölçeği” ve “Demokratik Değerler Ölçeği” kullanılarak toplanmıştır. Araştırma sonucunda, yabancı uyruklu öğrencilerin devam ettiği okullarda görev yapan öğretmenlerin çokkültürlü yeterliklerinin farkındalık, bilgi ve beceri boyutlarında kendilerini “yeterli” algıladıkları tespit edilmiştir. Öğretmenlerin demokratik değerlerin hak arama boyutu ile ilgili görüşleri “katılıyorum” düzeyinde; adalet, farklılıklara saygı ve eşitlik boyutlarıyla ilgili görüşleri ise “tamamen katılıyorum” düzeyinde benimsedikleri bulgusuna ulaşılmıştır. Katılımcı öğretmenlerin demokratik değerlerin adalet, farklılıklara saygı ve eşitlik boyutu ile ilgili görüşleri daha yüksek düzeyde benimsedikleri, hak arama boyutu ile ilgili görüşleri ise daha düşük düzeyde benimsedikleri anlaşılmıştır. Öğretmenlerin çokkültürlü yeterlik algıları ile demokratik değerleri arasında pozitif yönde, orta düzeyde bir ilişki saptanmıştır. Öğretmenlerin demokratik değerleri yükseldikçe çokkültürlü yeterlik algılarının da yükseldiği, demokratik değerleri düştükçe çokkültürlü yeterlik algılarının da düştüğü gözlenmiştir. Öğretmenlerin çokkültürlü yeterlik algılarının yüksek düzeyde olmasının öğretmenlerin demokratik değerleri benimsemesi ile ilişkili olduğu sonucuna varılmıştır