TY - CONF
AB - Many questions concerning models in quantum mechanics require a detailed analysis of the spectrum of the corresponding Hamiltonian, a linear operator on a suitable Hilbert space. Of particular relevance for an understanding of the low-temperature properties of a system is the structure of the excitation spectrum, which is the part of the spectrum close to the spectral bottom. We present recent progress on this question for bosonic many-body quantum systems with weak two-body interactions. Such system are currently of great interest, due to their experimental realization in ultra-cold atomic gases. We investigate the accuracy of the Bogoliubov approximations, which predicts that the low-energy spectrum is made up of sums of elementary excitations, with linear dispersion law at low momentum. The latter property is crucial for the superfluid behavior the system.
AU - Seiringer, Robert
ID - 8044
SN - 9788961058063
T2 - Proceeding of the International Congress of Mathematicans
TI - Structure of the excitation spectrum for many-body quantum systems
VL - 3
ER -
TY - JOUR
AB - We consider directed graphs where each edge is labeled with an integer weight and study the fundamental algorithmic question of computing the value of a cycle with minimum mean weight. Our contributions are twofold: (1) First we show that the algorithmic question is reducible to the problem of a logarithmic number of min-plus matrix multiplications of n×n-matrices, where n is the number of vertices of the graph. (2) Second, when the weights are nonnegative, we present the first (1+ε)-approximation algorithm for the problem and the running time of our algorithm is Õ(nωlog3(nW/ε)/ε),1 where O(nω) is the time required for the classic n×n-matrix multiplication and W is the maximum value of the weights. With an additional O(log(nW/ε)) factor in space a cycle with approximately optimal weight can be computed within the same time bound.
AU - Chatterjee, Krishnendu
AU - Henzinger, Monika
AU - Krinninger, Sebastian
AU - Loitzenbauer, Veronika
AU - Raskin, Michael
ID - 1375
IS - C
JF - Theoretical Computer Science
TI - Approximating the minimum cycle mean
VL - 547
ER -
TY - CONF
AB - Fault-tolerant distributed algorithms play an important role in ensuring the reliability of many software applications. In this paper we consider distributed algorithms whose computations are organized in rounds. To verify the correctness of such algorithms, we reason about (i) properties (such as invariants) of the state, (ii) the transitions controlled by the algorithm, and (iii) the communication graph. We introduce a logic that addresses these points, and contains set comprehensions with cardinality constraints, function symbols to describe the local states of each process, and a limited form of quantifier alternation to express the verification conditions. We show its use in automating the verification of consensus algorithms. In particular, we give a semi-decision procedure for the unsatisfiability problem of the logic and identify a decidable fragment. We successfully applied our framework to verify the correctness of a variety of consensus algorithms tolerant to both benign faults (message loss, process crashes) and value faults (message corruption).
AU - Dragoi, Cezara
AU - Henzinger, Thomas A
AU - Veith, Helmut
AU - Widder, Josef
AU - Zufferey, Damien
ID - 1392
TI - A logic-based framework for verifying consensus algorithms
VL - 8318
ER -
TY - CONF
AB - Probabilistic programs are usual functional or imperative programs with two added constructs: (1) the ability to draw values at random from distributions, and (2) the ability to condition values of variables in a program via observations. Models from diverse application areas such as computer vision, coding theory, cryptographic protocols, biology and reliability analysis can be written as probabilistic programs. Probabilistic inference is the problem of computing an explicit representation of the probability distribution implicitly specified by a probabilistic program. Depending on the application, the desired output from inference may vary-we may want to estimate the expected value of some function f with respect to the distribution, or the mode of the distribution, or simply a set of samples drawn from the distribution. In this paper, we describe connections this research area called \Probabilistic Programming" has with programming languages and software engineering, and this includes language design, and the static and dynamic analysis of programs. We survey current state of the art and speculate on promising directions for future research.
AU - Gordon, Andrew
AU - Henzinger, Thomas A
AU - Nori, Aditya
AU - Rajamani, Sriram
ID - 1393
T2 - Proceedings of the on Future of Software Engineering
TI - Probabilistic programming
ER -
TY - THES
AB - In this thesis I studied various individual and social immune defences employed by the invasive garden ant Lasius neglectus mostly against entomopathogenic fungi. The first two chapters of this thesis address the phenomenon of 'social immunisation'. Social immunisation, that is the immunological protection of group members due to social contact to a pathogen-exposed nestmate, has been described in various social insect species against different types of pathogens. However, in the case of entomopathogenic fungi it has, so far, only been demonstrated that social immunisation exists at all. Its underlying mechanisms r any other properties were, however, unknown. In the first chapter of this thesis I identified the mechanistic basis of social immunisation in L. neglectus against the entomopathogenous fungus Metarhizium. I could show that nestmates of a pathogen-exposed individual contract low-level infections due to social interactions. These low-level infections are, however, non-lethal and cause an active stimulation of the immune system, which protects the nestmates upon subsequent pathogen encounters. In the second chapter of this thesis I investigated the specificity and colony level effects of social immunisation. I demonstrated that the protection conferred by social immunisation is highly specific, protecting ants only against the same pathogen strain. In addition, depending on the respective context, social immunisation may even cause fitness costs. I further showed that social immunisation crucially affects sanitary behaviour and disease dynamics within ant groups. In the third chapter of this thesis I studied the effects of the ectosymbiotic fungus Laboulbenia formicarum on its host L. neglectus. Although Laboulbeniales are the largest order of insect-parasitic fungi, research concerning host fitness consequence is sparse. I showed that highly Laboulbenia-infected ants sustain fitness costs under resource limitation, however, gain fitness benefits when exposed to an entomopathogenus fungus. These effects are probably cause by a prophylactic upregulation of behavioural as well as physiological immune defences in highly infected ants.
AU - Konrad, Matthias
ID - 1395
TI - Immune defences in ants: Effects of social immunisation and a fungal ectosymbiont in the ant Lasius neglectus
ER -