Variations on language modeling for information retrieval

Search engine technology builds on theoretical and empirical research results in the area of information retrieval (IR). This dissertation makes a contribution to the field of language modeling (LM) for IR, which views both queries and documents as instances of a unigram language model and defines the matching function between a query and\ud each document as the probability that the query terms are generated by the document language model

How much of the inflaton potential do we see?

We discuss the latest constraints on a Taylor-expanded scalar inflaton potential, obtained focusing on its observable part only. This is in contrast with other works in which an extrapolation of the potential is applied using the slow-roll hierarchy. We find significant differences. The results discussed here apply to a broader range of models, since no assumption about the invisible e-folds of inflation has to be made, thereby remaining conservative.Comment: 5 pages, 2 figures. Talk given at Cargese Summer School: Cosmology and Particle Physics Beyond the Standard Models. To appear in Po

Fragmentation in the Governance of EU External Relations: Legal Institutional Dilemmas and the New Constitution for Europe

The European Union, an Ongoing Process of Integration contains 27 original contributions authored by prominent EU lawyers from academia and practice and concentrates on the three main areas of European integration that mark the career path of Alfred E. Kellermann: institutional and constitutional aspects (part I), general principles and substantive aspects (part II), and new Member States and Eastern Europe (part III). The contributions included in this Liber Amicorum vary from thematic in-depth studies to studies of a comparative nature. Their themes cover, inter alia, the structure of the Union according to the Constitution for Europe, the changes and challenges with which the Union¿s institutions are faced, including the creation of the positions of the President of the European Council and the Union Minister for Foreign Affairs, the future paths of flexibility (enhanced cooperation, partial agreements and pioneer groups), the role of national competition authorities and national courts under Regulation 1/2003, the constitutional preparation for EU accession in the new Member States, and the influence of European integration on the development of law in Russia. All contributions have been written in honour of Alfred E. Kellermann. Born in The Hague, raised in Switzerland during the Second World War and having studied and trained at Leiden University and at the European Commission¿s Legal Service in Brussels in the founding years of the European integration process, Doctor Honoris Causa Alfred E. Kellermann is a European by nature and vocation. For almost forty years, Alfred E. Kellermann has worked for the T.M.C. Asser Institute in The Hague. For many, he has become the face of the Institute in the Netherlands and abroad. This is the result of his work as a lecturer and consultant in EU law in countless short and long-term projects all over Europe, including Russia. Perhaps his finest accomplishment in raising awareness and expertise in the law of the European Union concerns the organisation of the famous `Asser Colloquia¿ on EU law and the publication of their proceedings

Spin dynamics of the bilinear-biquadratic S=1S=1 Heisenberg model on the triangular lattice: a quantum Monte Carlo study

We study thermodynamic properties as well as the dynamical spin and quadrupolar structure factors of the O(3)-symmetric spin-1 Heisenberg model with bilinear-biquadratic exchange interactions on the triangular lattice. Based on a sign-problem-free quantum Monte Carlo approach, we access both the ferromagnetic and the ferroquadrupolar ordered, spin nematic phase as well as the SU(3)-symmetric point which separates these phases. Signatures of Goldstone soft-modes in the dynamical spin and the quadrupolar structure factors are identified, and the properties of the low-energy excitations are compared to the thermodynamic behavior observed at finite temperatures as well as to Schwinger-boson flavor-wave theory.Comment: 7 pages, 8 figure

On the accuracy of N-body simulations at very large scales

We examine the deviation of Cold Dark Matter particle trajectories from the Newtonian result as the size of the region under study becomes comparable to or exceeds the particle horizon. To first order in the gravitational potential, the general relativistic result coincides with the Zel'dovich approximation and hence the Newtonian prediction on all scales. At second order, General Relativity predicts corrections which overtake the corresponding second order Newtonian terms above a certain scale of the order of the Hubble radius. However, since second order corrections are very much suppressed on such scales, we conclude that simulations which exceed the particle horizon but use Newtonian equations to evolve the particles, reproduce the correct trajectories very well. The dominant relativistic corrections to the power spectrum on scales close to the horizon are at most of the order of $\sim 10^{-5}$ at $z=49$ and $\sim 10^{-3}$ at $z=0$. The differences in the positions of real space features are affected at a level below $10^{-6}$ at both redshifts. Our analysis also clarifies the relation of N-body results to relativistic considerations.Comment: 7 pages, 2 figures; v2: 7 pages, 3 figures, matches version published in MNRA

Excitation Gap Scaling near Quantum Critical Three-Dimensional Antiferromagnets

By means of large-scale quantum Monte Carlo simulations, we examine the quantum critical scaling of the magnetic excitation gap (the triplon gap) in a three-dimensional dimerized quantum antiferromagnet, the bicubic lattice, and identify characteristic multiplicative logarithmic scaling corrections atop the leading mean-field behavior. These findings are in accord with field-theoretical predictions that are based on an effective description of the quantum critical system in terms of an asymptotically-free field theory, which exhibits a logarithmic decay of the renormalized interaction strength upon approaching the quantum critical point. Furthermore, using bond-based singlet spectroscopy, we identify the amplitude (Higgs) mode resonance within the antiferromagnetic region. We find a Higgs mass scaling in accord with field-theoretical predictions that relate it by a factor of $\sqrt{2}$ to the corresponding triplon gap in the quantum disordered regime. In contrast to the situation in lower-dimensional systems, we observe in this three-dimensional coupled-dimer system a distinct signal from the amplitude mode also in the dynamical spin structure factor. The width of the Higgs mode resonance is observed to scale linearly with the Higgs mass near criticality, indicative of this critically well-defined excitation mode of the symmetry broken phase.Comment: 4 pages, 4 figures 2 pages, 2 figures supplemental materia

Quantum phase transitions in effective spin-ladder models for graphene zigzag nanoribbons

We examine the magnetic correlations in quantum spin models that were derived recently as effective low-energy theories for electronic correlation effects on the edge states of graphene nanoribbons. For this purpose, we employ quantum Monte Carlo simulations to access the large-distance properties, accounting for quantum fluctuations beyond mean-field-theory approaches to edge magnetism. For certain chiral nanoribbons, antiferromagnetic inter-edge couplings were previously found to induce a gapped quantum disordered ground state of the effective spin model. We find that the extended nature of the intra-edge couplings in the effective spin model for zigzag nanoribbons leads to a quantum phase transition at a large, finite value of the inter-edge coupling. This quantum critical point separates the quantum disordered region from a gapless phase of stable edge magnetism at weak intra-edge coupling, which includes the ground states of spin-ladder models for wide zigzag nanoribbons. To study the quantum critical behavior, the effective spin model can be related to a model of two antiferromagnetically coupled Haldane-Shastry spin-half chains with long-ranged ferromagnetic intra-chain couplings. The results for the critical exponents are compared also to several recent renormalization group calculations for related long-ranged interacting quantum systems.Comment: 12 pages, 15 figure

Critical Entropy of Quantum Heisenberg Magnets on Simple-Cubic Lattices

We analyze the temperature dependence of the entropy of the spin-1/2 Heisenberg model on the three-dimensional simple-cubic lattice, for both the case of antiferromagnetic and ferromagnetic nearest neighbor exchange interactions. Using optimized extended ensemble quantum Monte Carlo simulations, we extract the entropy at the critical temperature for magnetic order from a finite-size scaling analysis. For the antiferromagnetic case, the critical entropy density equals 0.341(5)$k_B$, whereas for the ferromagnet, a larger value of 0.401(5) $k_B$ is obtained. We compare our simulation results to estimates put forward recently in studies assessing means of realizing the antiferromagnetic N\'eel state in ultra-cold fermion gases in optical lattices.Comment: 3 pages, 2 figures; published versio

Lecture notes on ridge regression

The linear regression model cannot be fitted to high-dimensional data, as the high-dimensionality brings about empirical non-identifiability. Penalized regression overcomes this non-identifiability by augmentation of the loss function by a penalty (i.e. a function of regression coefficients). The ridge penalty is the sum of squared regression coefficients, giving rise to ridge regression. Here many aspect of ridge regression are reviewed e.g. moments, mean squared error, its equivalence to constrained estimation, and its relation to Bayesian regression. Finally, its behaviour and use are illustrated in simulation and on omics data. Subsequently, ridge regression is generalized to allow for a more general penalty. The ridge penalization framework is then translated to logistic regression and its properties are shown to carry over. To contrast ridge penalized estimation, the final chapter introduces its lasso counterpart