Embodied Robot Models for Interdisciplinary Emotion Research

Due to their complex nature, emotions cannot be properly understood from the perspective of a single discipline. In this paper, I discuss how the use of robots as models is beneficial for interdisciplinary emotion research. Addressing this issue through the lens of my own research, I focus on a critical analysis of embodied robots models of different aspects of emotion, relate them to theories in psychology and neuroscience, and provide representative examples. I discuss concrete ways in which embodied robot models can be used to carry out interdisciplinary emotion research, assessing their contributions: as hypothetical models, and as operational models of specific emotional phenomena, of general emotion principles, and of specific emotion ``dimensions''. I conclude by discussing the advantages of using embodied robot models over other models.Peer reviewe

Resonant single chargino and neutralino versus fermion-antifermion production at the Linear Collider

We study single superparticle productions at the linear collider, putting particular emphasis on resonant processes. We find that there exists a wide region of model parameters where single chargino and neutralino productions dominate over R-violating fermion-antifermion final states. For certain values of mu and M_2 it is possible to produce even the heavier charginos and neutralinos at significant rates, amplifying the total cross section and obtaining interesting chains of cascade decays. Effects from initial-state radiation are also included.Comment: 7 pages, 3 figures. Presented at the 2nd ECFA/DESY study on Linear Colliders, Frascati, November 1998 (alternative theories working group). Typos correcte

Robot Models of Mental Disorders

Alongside technological tools to support wellbeing and treatment of mental disorders, models of these disorders can also be invaluable tools to understand, support and improve these conditions. Robots can provide ecologically valid models that take into account embodiment-, interaction-, and context-related elements. Focusing on Obsessive-Compulsive spectrum disorders, in this paper we discuss some of the potential contributions of robot models and relate them to other models used in psychology and psychiatry, particularly animal models. We also present some initial recommendations for their meaningful design and rigorous use.Final Accepted Versio

On the degrees of divisors of T^n-1

Fix a field $F$. In this paper, we study the sets \D_F(n) \subset [0,n] defined by [\D_F(n):= {0 \leq m \leq n: T^n-1\text{has a divisor of degree $m$ in} F[T]}.] When \D_F(n) consists of all integers $m$ with $0 \leq m \leq n$, so that $T^n-1$ has a divisor of every degree, we call $n$ an $F$-practical number. The terminology here is suggested by an analogy with the practical numbers of Srinivasan, which are numbers $n$ for which every integer $0 \leq m \leq \sigma(n)$ can be written as a sum of distinct divisors of $n$. Our first theorem states that, for any number field $F$ and any $x \geq 2$, [#{\text{$F$-practical $n\leq x$}} \asymp_{F} \frac{x}{\log{x}};] this extends work of the second author, who obtained this estimate when F=\Q. Suppose now that $x \geq 3$, and let $m$ be a natural number in $[3,x]$. We ask: For how many $n \leq x$ does $m$ belong to \D_F(n)? We prove upper bounds in this problem for both F=\Q and F=\F_p (with $p$ prime), the latter conditional on the Generalized Riemann Hypothesis. In both cases, we find that the number of such $n \leq x$ is $\ll_{F} x/(\log{m})^{2/35}$, uniformly in $m$

Can Neutrinos be Degenerate in Mass?

We reconsider the possibility that the masses of the three light neutrinos of the Standard Model might be almost degenerate and close to the present upper limits from Tritium beta decay and cosmology. In such a scenario, the cancellations required by the latest upper limit on neutrinoless double-beta decay enforce near-maximal mixing that may be compatible only with the vacuum-oscillation scenario for solar neutrinos. We argue that the mixing angles yielded by degenerate neutrino mass-matrix textures are not in general stable under small perturbations. We evaluate within the MSSM the generation-dependent one-loop renormalization of neutrino mass-matrix textures that yielded degenerate masses and large mixing at the tree level. We find that m_{nu_e} > m_{nu_mu} > m_{nu_tau} after renormalization, excluding MSW effects on solar neutrinos. We verify that bimaximal mixing is not stable, and show that the renormalized masses and mixing angles are not compatible with all the experimental constraints, even for tanbeta as low as unity. These results hold whether the neutrino masses are generated by a see-saw mechanism with heavy neutrinos weighing approx. 10^{13} GeV or by non-renormalizable interactions at a scale approx. 10^5 GeV. We also comment on the corresponding renormalization effects in the minimal Standard Model, in which m_{nu_e} < m_{nu_mu} < m_{nu_tau}. Although a solar MSW effect is now possible, the perturbed neutrino masses and mixings are still not compatible with atmospheric- and solar-neutrino data.Comment: 17 pages, 4 figures. Corrections to typos and notation: rephrased and clarified statements on impact of induced deviations from bimaximal mixin

Arithmetic functions at consecutive shifted primes

For each of the functions $f \in \{\phi, \sigma, \omega, \tau\}$ and every natural number $k$, we show that there are infinitely many solutions to the inequalities $f(p_n-1) < f(p_{n+1}-1) < \dots < f(p_{n+k}-1)$, and similarly for $f(p_n-1) > f(p_{n+1}-1) > \dots > f(p_{n+k}-1)$. We also answer some questions of Sierpi\'nski on the digit sums of consecutive primes. The arguments make essential use of Maynard and Tao's method for producing many primes in intervals of bounded length.Comment: Made some improvements in the organization and expositio