The generalized Lichnerowicz formula and analysis of Dirac operators

We study Dirac operators acting on sections of a Clifford module ${\cal E}$\ over a Riemannian manifold $M$. We prove the intrinsic decomposition formula for their square, which is the generalisation of the well-known formula due to Lichnerowicz [L]. This formula enables us to distinguish Dirac operators of simple type. For each Dirac operator of this natural class the local Atiyah-Singer index theorem holds. Furthermore, if $M$\ is compact and {{\petit \rm dim}\;M=2n\ge 4}, we derive an expression for the Wodzicki function $W_{\cal E}$, which is defined via the non-commutative residue on the space of all Dirac operators ${\cal D}({\cal E})$. We calculate this function for certain Dirac operators explicitly. From a physical point of view this provides a method to derive gravity, resp. combined gravity/Yang-Mills actions from the Dirac operators in question.Comment: 25 pages, plain te

Unification of Gravity and Yang-Mills-Higgs Gauge Theories

In this letter we show how the action functional of the standard model and of gravity can be derived from a specific Dirac operator. Far from being exotic this particular Dirac operator turns out to be structurally determined by the Yukawa coupling term. The main feature of our approach is that it naturally unifies the action of the standard model with gravity.Comment: 8 pages, late

Magnetoelectric properties of A2A_2[FeCl5_5(H2_2O)] with A=A = K, Rb, Cs

The compounds $A_2$[FeCl$_5$(H$_2$O)] with $A=$ K, Rb, Cs are identified as new linear magnetoelectric materials. We present a detailed investigation of their linear magnetoelectric properties by measurements of pyroelectric currents, dielectric constants and magnetization. The anisotropy of the linear magnetoelectric effect of the K-based and Rb-based compound is consistent with the magnetic point group $m'm'm'$, already reported in literature. A symmetry analysis of the magnetoelectric effect of the Cs-based compound allows to determine the magnetic point group $mmm'$ and to develop a model for its magnetic structure. In addition, magnetic-field versus temperature phase diagrams are derived and compared to the closely related multiferroic (NH$_4$)$_2$[FeCl$_5$(H$_2$O)].Comment: 17 pages, 10 figures (updated to the weakly revised version that has been accepted for publication

Anisotropy study of multiferroicity in the pyroxene NaFeGe2_2O6_6

We present a study of the anisotropy of the dielectric, magnetic and magnetoelastic properties of the multiferroic clinopyroxene NaFeGe$_2$O$_6$. Pyroelectric currents, dielectric constants and magnetic susceptibilities as well as the thermal expansion and the magnetostriction were examined on large synthetic single crystals of NaFeGe$_2$O$_6$. The spontaneous electric polarization detected below $T_{\rm C}\simeq 11.6$ K in an antiferromagnetically ordered state ($T_{\rm N}\simeq 13$ K) is mainly lying within the $ac$ plane with a small component along $b$, indicating a triclinic symmetry of the multiferroic phase of NaFeGe$_2$O$_6$. The electric polarization can be strongly modified by applying magnetic fields along different directions. We derive detailed magnetic-field versus temperature phase diagrams and identify three multiferroic low-temperature phases, which are separated by a non-ferroelectric, antiferromagnetically ordered state from the paramagnetic high-temperature phase.Comment: 14 pages, 8 figures. (minor modifications and corrections of the text

Rationales and functions of disliked music: An in-depth interview study

BACKGROUND AND OBJECTIVES: With a few exceptions, musical taste has been researched via likes or preferences of certain types of music. The present study focuses on disliked music and takes a broad approach to cover explanatory strategies related to personal dislikes. METHODS: In-depth interviews were conducted with 21 participants in five age groups. Interviewees were asked to prepare a list of their disliked music, and for each item they were asked about the reasons for the dislike. To ensure that the complexity and range of the participants’ dislikes and rationales were captured in the analysis, a structuring content analysis as a mostly theory-driven approach was combined with inductive category creation out of the interview data. RESULTS: The most often mentioned type of dislike was musical style, followed by artist and genre. Five main reference points were identified for describing musical dislikes: the music itself, lyrics, performance, artist, and the people who listen to it. The identified rationales for disliked music were assigned to three larger categories: object-related reasons, such as music-compositional aspects, aesthetic dichotomies or lyrics; subject-related reasons, such as emotional or bodily effects, or discrepancies with the self-image; social reasons, which refer to one’s social environment and the taste judgments common to it (in-group) or to other groups of which the participants do not feel part of (out-group). Apart from the rationales for disliked music, the participants described specific reactions when they are confronted with their disliked music, such as emotional, physical, and social reactions. CONCLUSIONS: While musical dislikes have already been shown to fulfill important social functions, the current study extends the rationales to music-related and self-related reasons. Musical dislikes fulfill similar functions to liked music, such as preservation of a good mood, identity expression and construction, strengthening of group cohesion as well as social distinction

Review on Neutrino Telescopes

I will discuss the motivations for Neutrino Astronomy and its prospects given the current experimental scenario, which is the main focus of this paper. I will also go through the first results of the IceCube detector deep in the ice and of the ANTARES undersea telescope underlying complementary aspects, common and different challenges. It is an exciting time for this science since the first completed undersea detector is successfully taking data and the first cubic kilometer detector is going to be shortly more than half-way from its completion in Antarctica.Comment: Proceeding of CRIS2008 Conference, Salina, Sept. 2008, 9 pages, 8 figure

On Existence and Properties of Approximate Pure Nash Equilibria in Bandwidth Allocation Games

In \emph{bandwidth allocation games} (BAGs), the strategy of a player consists of various demands on different resources. The player's utility is at most the sum of these demands, provided they are fully satisfied. Every resource has a limited capacity and if it is exceeded by the total demand, it has to be split between the players. Since these games generally do not have pure Nash equilibria, we consider approximate pure Nash equilibria, in which no player can improve her utility by more than some fixed factor $\alpha$ through unilateral strategy changes. There is a threshold $\alpha_\delta$ (where $\delta$ is a parameter that limits the demand of each player on a specific resource) such that $\alpha$-approximate pure Nash equilibria always exist for $\alpha \geq \alpha_\delta$, but not for $\alpha < \alpha_\delta$. We give both upper and lower bounds on this threshold $\alpha_\delta$ and show that the corresponding decision problem is ${\sf NP}$-hard. We also show that the $\alpha$-approximate price of anarchy for BAGs is $\alpha+1$. For a restricted version of the game, where demands of players only differ slightly from each other (e.g. symmetric games), we show that approximate Nash equilibria can be reached (and thus also be computed) in polynomial time using the best-response dynamic. Finally, we show that a broader class of utility-maximization games (which includes BAGs) converges quickly towards states whose social welfare is close to the optimum

Solving kk-means on High-dimensional Big Data

In recent years, there have been major efforts to develop data stream algorithms that process inputs in one pass over the data with little memory requirement. For the $k$-means problem, this has led to the development of several $(1+\varepsilon)$-approximations (under the assumption that $k$ is a constant), but also to the design of algorithms that are extremely fast in practice and compute solutions of high accuracy. However, when not only the length of the stream is high but also the dimensionality of the input points, then current methods reach their limits. We propose two algorithms, piecy and piecy-mr that are based on the recently developed data stream algorithm BICO that can process high dimensional data in one pass and output a solution of high quality. While piecy is suited for high dimensional data with a medium number of points, piecy-mr is meant for high dimensional data that comes in a very long stream. We provide an extensive experimental study to evaluate piecy and piecy-mr that shows the strength of the new algorithms.Comment: 23 pages, 9 figures, published at the 14th International Symposium on Experimental Algorithms - SEA 201