The decision problem of modal product logics with a diagonal, and faulty counter machines

In the propositional modal (and algebraic) treatment of two-variable first-order logic equality is modelled by a `diagonal' constant, interpreted in square products of universal frames as the identity (also known as the `diagonal') relation. Here we study the decision problem of products of two arbitrary modal logics equipped with such a diagonal. As the presence or absence of equality in two-variable first-order logic does not influence the complexity of its satisfiability problem, one might expect that adding a diagonal to product logics in general is similarly harmless. We show that this is far from being the case, and there can be quite a big jump in complexity, even from decidable to the highly undecidable. Our undecidable logics can also be viewed as new fragments of first- order logic where adding equality changes a decidable fragment to undecidable. We prove our results by a novel application of counter machine problems. While our formalism apparently cannot force reliable counter machine computations directly, the presence of a unique diagonal in the models makes it possible to encode both lossy and insertion-error computations, for the same sequence of instructions. We show that, given such a pair of faulty computations, it is then possible to reconstruct a reliable run from them

Importance sampling methods for Bayesian discrimination between embedded models

This paper surveys some well-established approaches on the approximation of Bayes factors used in Bayesian model choice, mostly as covered in Chen et al. (2000). Our focus here is on methods that are based on importance sampling strategies rather than variable dimension techniques like reversible jump MCMC, including: crude Monte Carlo, maximum likelihood based importance sampling, bridge and harmonic mean sampling, as well as Chib's method based on the exploitation of a functional equality. We demonstrate in this survey how these different methods can be efficiently implemented for testing the significance of a predictive variable in a probit model. Finally, we compare their performances on a real dataset

Equality of P-partition Generating Functions

To every partially ordered set (poset), one can associate a generating function, known as the P-partition generating function. We find necessary conditions and sufficient conditions for two posets to have the same P-partition generating function. We define the notion of a jump sequence for a labeled poset and show that having equal jumpsequences is a necessary condition for generating function equality. We also develop multiple ways of modifying posets that preserve generating function equality. Finally, we are able to give a complete classification of equalities among partially ordered setswith exactly two linear extensions

Stabilization of markovian systems via probability rate synthesis and output feedback

This technical note is concerned with the stabilization problem of Markovian jump linear systems via designing switching probability rate matrices and static output-feedback gains. A novel necessary and sufficient condition is established to characterize the switching probability rate matrices that guarantee the mean square stability of Markovian jump linear systems. Based on this, a necessary and sufficient condition is provided for the existence of desired controller gains and probability rate matrices. Extensions to the polytopic uncertain case are also provided. All the conditions are formulated in terms of linear matrix inequalities with some equality constraints, which can be solved by two modified cone complementarity linearization algorithms. Examples are given to show the effectiveness of the proposed method. © 2010 IEEE.published_or_final_versio

The polynomial-time hierarchy

AbstractThe polynomial-time hierarchy is that subrecursive analog of the Kleene arithmetical hierarchy in which deterministic (nondeterministic) polynomial time plays the role of recursive (recursively enumerable) time. Known properties of the polynomial-time hierarchy are summarized. A word problem which is complete in the second stage of the hierarchy is exhibited. In the analogy between the polynomial-time hierarchy and the arithmetical hierarchy, the first order theory of equality plays the role of elementary arithmetic (as the ω-jump of the hierarchy). The problem of deciding validity in the theory of equality is shown to be complete in polynomial-space, and close upper and lower bounds on the space complexity of this problem are established

Leadership in Africa: A hermeneutic dialogue with Kwame Nkrumah and Julius Nyerere on equality and human development

This study deals with leadership and 'humanness' and compares the perceptions of human equality of two outstanding African leaders, 'fathers of their nations', Kwame Nkrumah, first president of Ghana, and Julius Nyerere, first president of Tanganyika, later Tanzania. Leadership is a key issue for political, economic and social development in Africa and worldwide. This is especially true in times of financial and economic globalisation that affects people in poor African countries significantly. Half a century after the independence of most countries on the continent, poverty is the daily experience of the majority of Africa's people. Public criticism about the present political leadership and their 'delivery' of goods and services to the people is widespread and profound. This problem prompted me to study the leadership experiences of Nkrumah and Nyerere. The overall goal of this research is to better understand Nkrumah and Nyerere as leaders in Africa. Therefore, my study has two research questions: what are their perceptions on equality and human development - and what is their historical and contemporary relevance, in times of human rights violations and increasing inequalities. The methodological choice is critical hermeneutics (Gadamer 1990, 2013; Ricoeur 1991b; Habermas 1992b, 1996), which allows a multi-cultural historical and contemporary dialogue with Nkrumah and Nyerere through their text. Hermeneutics also has relevance in Africa (Oruka 1990; Serequeberhan 1994; Mbembe 2001). I name my method the "triple jump" (Häussler 2009a). The study is a combination of a quantitative and a qualitative method with a hermeneutic conversation. The core-keywords of the dialogues are colonialism, unity, socialism, equality, freedom and development. There are three significant findings that contribute new knowledge to our understanding of Nkrumah and Nyerere as leaders. First, that using the hermeneutic dialogue (my "triple jump") as a holistic and practical model enables a 'better' understanding of Nkrumah and Nyerere. Second, interpreting their perceptions on human equality reveals that both leaders prioritise education as a critical part of human development and achieving equality in society. It also unveils differences in their focus: Nkrumah on de-colonisation and African unity; Nyerere on social and economic self-reliance, and equal rights. Thirdly, the study reveals tensions between their discourses on equality and freedom and their personal capacity to deal with power, opposition, human rights and idealism. My study concludes with recommendations for the development of ethical leadership and for personal support for leaders in office

Anomaly and quantum corrections to solitons in two-dimensional theories with minimal supersymmetry

We reexamine the issue of the soliton mass in two-dimensional models with N =1 supersymmetry. The superalgebra has a central extension, and at the classical level the soliton solution preserves 1/2 of supersymmetry which is equivalent to BPS saturation. We prove that the property of BPS saturation, i.e. the equality of the soliton mass to the central charge, remains intact at the quantum level in all orders of the weak coupling expansion. Our key finding is an anomaly in the expression for the central charge. The classical central charge, equal to the jump of the superpotential, is amended by an anomalous term proportional to the second derivative of the superpotential. The anomaly is established by various methods in explicit one-loop calculations. We argue that this one-loop result is not affected by higher orders. We discuss in detail how the impact of the boundary conditions can be untangled from the soliton mass calculation. In particular, the soliton profile and the energy distribution are found at one loop. A "supersymmetry" in the soliton mass calculations in the non-supersymmetric models is observed.Comment: 50 pages, LaTex, 2 figures. The version exactly matching that published in Phys.Rev. D. The most essential addition is a footnote, clarifying multiplet shortenin