Quasi Exactly Solvable 2×\times2 Matrix Equations

We investigate the conditions under which systems of two differential eigenvalue equations are quasi exactly solvable. These systems reveal a rich set of algebraic structures. Some of them are explicitely described. An exemple of quasi exactly system is studied which provides a direct counterpart of the Lam\'e equation.Comment: 14 pages, Plain Te

Canonical and Lie-algebraic twist deformations of κ\kappa-Poincare and contractions to κ\kappa-Galilei algebras

We propose canonical and Lie-algebraic twist deformations of $\kappa$-deformed Poincare Hopf algebra which leads to the generalized $\kappa$-Minkowski space-time relations. The corresponding deformed $\kappa$-Poincare quantum groups are also calculated. Finally, we perform the nonrelativistic contraction limit to the corresponding twisted Galilean algebras and dual Galilean quantum groups.Comment: 16 pages, no figures, v3: few changes provided - version for journal, v2: submitted incidentally, v4: the page numbers for all references in preprint version are provide

Field theory on κ\kappa--Minkowski space revisited: Noether charges and breaking of Lorentz symmetry

This paper is devoted to detailed investigations of free scalar field theory on $\kappa$-Minkowski space. After reviewing necessary mathematical tools we discuss in depth the Lagrangian and solutions of field equations. We analyze the spacetime symmetries of the model and construct the conserved charges associated with translational and Lorentz symmetry. We show that the version of the theory usually studied breaks Lorentz invariance in a subtle way: There is an additional trans-Planckian mode present, and an associated conserved charge (the number of such modes) is not a Lorentz scalar.Comment: 22 pages, 1 figure, formulas in sect. III correcte

Psychological targeting as an effective approach to digital mass persuasion

People are exposed to persuasive communication across many different contexts: governments, companies, and political parties use persuasive appeals to encourage people to eat healthier, purchase a particular product, or vote for a specific candidate. Laboratory studies show that such persuasive appeals are more effective in influencing behavior when they are tailored to individuals’ unique psychological characteristics. Yet, the investigation of large-scale psychological persuasion in the real world has been hindered by the questionnaire-based nature of psychological assessment. Recent research, however, shows that people’s psychological characteristics can be accurately predicted from their digital footprints, such as their Facebook Likes or Tweets. Capitalizing on this new form of psychological assessment from digital footprints, we test the effects of psychological persuasion on people’s actual behavior in an ecologically valid setting. In three field experiments that reached over 3.5 million individuals with psychologically-tailored advertising, we find that matching the content of persuasive appeals to individuals’ psychological characteristics significantly altered their behavior as measured by clicks and purchases. Persuasive appeals that were matched to people’s extraversion or openness-to-experience level resulted in up to 40% more clicks and up to 50% more purchases than their mismatching or un-personalized counterparts. Our findings suggest that the application of psychological targeting makes it possible to influence the behavior of large groups of people by tailoring persuasive appeals to the psychological needs of the target audiences. We discuss both the potential benefits of this method for helping individuals make better decisions and the potential pitfalls related to manipulation and privacy

Scalar field theory on κ\kappa-Minkowski space-time and Doubly Special Relativity

In this paper we recall the construction of scalar field action on $\kappa$-Minkowski space-time and investigate its properties. In particular we show how the co-product of $\kappa$-Poincar\'e algebra of symmetries arises from the analysis of the symmetries of the action, expressed in terms of Fourier transformed fields. We also derive the action on commuting space-time, equivalent to the original one. Adding the self-interaction $\Phi^4$ term we investigate the modified conservation laws. We show that the local interactions on $\kappa$-Minkowski space-time give rise to 6 inequivalent ways in which energy and momentum can be conserved at four-point vertex. We discuss the relevance of these results for Doubly Special Relativity.Comment: 17 pages; some editing done, final version to be published in Int. J. Mod. Phys.

Scalar field propagation in the phi^4 kappa-Minkowski model

In this article we use the noncommutative (NC) kappa-Minkowski phi^4 model based on the kappa-deformed star product, ({*}_h). The action is modified by expanding up to linear order in the kappa-deformation parameter a, producing an effective model on commutative spacetime. For the computation of the tadpole diagram contributions to the scalar field propagation/self-energy, we anticipate that statistics on the kappa-Minkowski is specifically kappa-deformed. Thus our prescription in fact represents hybrid approach between standard quantum field theory (QFT) and NCQFT on the kappa-deformed Minkowski spacetime, resulting in a kappa-effective model. The propagation is analyzed in the framework of the two-point Green's function for low, intermediate, and for the Planckian propagation energies, respectively. Semiclassical/hybrid behavior of the first order quantum correction do show up due to the kappa-deformed momentum conservation law. For low energies, the dependence of the tadpole contribution on the deformation parameter a drops out completely, while for Planckian energies, it tends to a fixed finite value. The mass term of the scalar field is shifted and these shifts are very different at different propagation energies. At the Planckian energies we obtain the direction dependent kappa-modified dispersion relations. Thus our kappa-effective model for the massive scalar field shows a birefringence effect.Comment: 23 pages, 2 figures; To be published in JHEP. Minor typos corrected. Shorter version of the paper arXiv:1107.236

κ\kappa-Deformation of Poincar\'e Superalgebra with Classical Lorentz Subalgebra and its Graded Bicrossproduct Structure

The $\kappa$-deformed $D=4$ Poincar{\'e} superalgebra written in Hopf superalgebra form is transformed to the basis with classical Lorentz subalgebra generators. We show that in such a basis the $\kappa$-deformed $D=4$ Poincare superalgebra can be written as graded bicrossproduct. We show that the $\kappa$-deformed $D=4$ superalgebra acts covariantly on $\kappa$-deformed chiral superspace.Comment: 13 pages, late

Poincare covariant mechanics on noncommutative space

The Dirac approach to constrained systems can be adapted to construct relativistic invariant theories on a noncommutative (NC) space. As an example, we propose and discuss relativistic invariant NC particle coupled to electromagnetic field by means of the standard term $A^\mu\dot x_\mu$. Poincare invariance implies deformation of the free particle NC algebra in the interaction theory. The corresponding corrections survive in the nonrelativistic limit.Comment: 7 pages, JHEP style, final versio

Women are warmer but no less assertive than men: gender and language on Facebook

Using a large social media dataset and open-vocabulary methods from computational linguistics, we explored differences in language use across gender, affiliation, and assertiveness. In Study 1, we analyzed topics (groups of semantically similar words) across 10 million messages from over 52,000 Facebook users. Most language differed little across gender. However, topics most associated with self-identified female participants included friends, family, and social life, whereas topics most associated with self-identified male participants included swearing, anger, discussion of objects instead of people, and the use of argumentative language. In Study 2, we plotted male- and female-linked language topics along two interpersonal dimensions prevalent in gender research: affiliation and assertiveness. In a sample of over 15,000 Facebook users, we found substantial gender differences in the use of affiliative language and slight differences in assertive language. Language used more by self-identified females was interpersonally warmer, more compassionate, polite, and—contrary to previous findings—slightly more assertive in their language use, whereas language used more by self-identified males was colder, more hostile, and impersonal. Computational linguistic analysis combined with methods to automatically label topics offer means for testing psychological theories unobtrusively at large scale.This work was supported by the Templeton Religion Trust