Exploiting Polyhedral Symmetries in Social Choice

A large amount of literature in social choice theory deals with quantifying the probability of certain election outcomes. One way of computing the probability of a specific voting situation under the Impartial Anonymous Culture assumption is via counting integral points in polyhedra. Here, Ehrhart theory can help, but unfortunately the dimension and complexity of the involved polyhedra grows rapidly with the number of candidates. However, if we exploit available polyhedral symmetries, some computations become possible that previously were infeasible. We show this in three well known examples: Condorcet's paradox, Condorcet efficiency of plurality voting and in Plurality voting vs Plurality Runoff.Comment: 14 pages; with minor improvements; to be published in Social Choice and Welfar

Reactor mixing angle from hybrid neutrino masses

In terms of its eigenvector decomposition, the neutrino mass matrix (in the basis where the charged lepton mass matrix is diagonal) can be understood as originating from a tribimaximal dominant structure with small deviations, as demanded by data. If neutrino masses originate from at least two different mechanisms, referred to as "hybrid neutrino masses", the experimentally observed structure naturally emerges provided one mechanism accounts for the dominant tribimaximal structure while the other is responsible for the deviations. We demonstrate the feasibility of this picture in a fairly model-independent way by using lepton-number-violating effective operators, whose structure we assume becomes dictated by an underlying $A_4$ flavor symmetry. We show that if a second mechanism is at work, the requirement of generating a reactor angle within its experimental range always fixes the solar and atmospheric angles in agreement with data, in contrast to the case where the deviations are induced by next-to-leading order effective operators. We prove this idea is viable by constructing an $A_4$-based ultraviolet completion, where the dominant tribimaximal structure arises from the type-I seesaw while the subleading contribution is determined by either type-II or type-III seesaw driven by a non-trivial $A_4$ singlet (minimal hybrid model). After finding general criteria, we identify all the $\mathbb{Z}_N$ symmetries capable of producing such $A_4$-based minimal hybrid models.Comment: 18 pages, 5 figures. v3: section including sum rules added, accepted by JHE

Diabetes mellitus and tuberculosis treatment outcomes: Interaction assessment between hyperglycemia and human immunodeficiency virus in the state of Georgia, 2015-2020

Background: Diabetes mellitus and human immunodeficiency virus (HIV) are independent risk factors for poor outcomes among people with tuberculosis (TB). To date, information on the joint impact of diabetes and HIV on TB outcomes is limited. We aimed to estimate (1) the association between hyperglycemia and mortality, and (2) the effect of joint exposure to diabetes and HIV on mortality. Methods: We conducted a retrospective cohort study among people with TB in the state of Georgia between 2015-2020. Eligible participants were 16 or older, did not have a previous TB diagnosis, and were microbiologically confirmed or clinical cases. Participants were followed during TB treatment. Robust Poisson regression was used to estimate risk ratios for all-cause mortality. Interaction between diabetes and HIV was assessed on the additive scale using the attributable proportion and on the multiplicative scale with product terms in regression models. Results: Of 1109 participants, 318 (28.7%) had diabetes, 92 (8.3%) were HIV-positive, and 15 (1.4%) had diabetes and HIV. Overall, 9.8% died during TB treatment. Diabetes was associated with an increased risk of death among people with TB (aRR = 2.59, 95% CI: 1.62, 4.13). We estimated that 26% (95% CI: -43.4%, 95.0%) of deaths among participants with DM and HIV were due to biologic interaction. Conclusions: Diabetes alone and co-occurring diabetes and HIV were associated with an increased risk of all-cause mortality during TB treatment. These data suggest a potential synergistic effect between diabetes and HIV

Phenomenological Consequences of sub-leading Terms in See-Saw Formulas

Several aspects of next-to-leading (NLO) order corrections to see-saw formulas are discussed and phenomenologically relevant situations are identified. We generalize the formalism to calculate the NLO terms developed for the type I see-saw to variants like the inverse, double or linear see-saw, i.e., to cases in which more than two mass scales are present. In the standard type I case with very heavy fermion singlets the sub-leading terms are negligible. However, effects in the percent regime are possible when sub-matrices of the complete neutral fermion mass matrix obey a moderate hierarchy, e.g. weak scale and TeV scale. Examples are cancellations of large terms leading to small neutrino masses, or inverse see-saw scenarios. We furthermore identify situations in which no NLO corrections to certain observables arise, namely for mu-tau symmetry and cases with a vanishing neutrino mass. Finally, we emphasize that the unavoidable unitarity violation in see-saw scenarios with extra fermions can be calculated with the formalism in a straightforward manner.Comment: 22 pages, matches published versio

Measuring Strategic Uncertainty in Coordination Games

Lecture on the first SFB/TR 15 meeting, Gummersbach, July, 18 - 20, 2004This paper explores predictability of behavior in coordination games with multiple equilibria. In a laboratory experiment we measure subjects' certainty equivalents for three coordination games and one lottery. Attitudes towards strategic uncertainty in coordination games are related to risk aversion, experience seeking, gender and age. From the distribution of certainty equivalents among participating students we estimate probabilities for successful coordination in a wide range of coordination games. For many games success of coordination is predictable with a reasonable error rate. The best response of a risk neutral player is close to the global-game solution. Comparing choices in coordination games with revealed risk aversion, we estimate subjective probabilities for successful coordination. In games with a low coordination requirement, most subjects underestimate the probability of success. In games with a high coordination requirement, most subjects overestimate this probability. Data indicate that subjects have probabilistic beliefs about success or failure of coordination rather than beliefs about individual behavior of other players

The Golden Ratio Prediction for the Solar Angle from a Natural Model with A5 Flavour Symmetry

We formulate a consistent model predicting, in the leading order approximation, maximal atmospheric mixing angle, vanishing reactor angle and tan {\theta}_12 = 1/{\phi} where {\phi} is the Golden Ratio. The model is based on the flavour symmetry A5 \times Z5 \times Z3, spontaneously broken by a set of flavon fields. By minimizing the scalar potential of the theory up to the next-to-leading order in the symmetry breaking parameter, we demonstrate that this mixing pattern is naturally achieved in a finite portion of the parameter space, through the vacuum alignment of the flavon fields. The leading order approximation is stable against higher-order corrections. We also compare our construction to other models based on discrete symmetry groups.Comment: 28 pages, 2 figures. Minor changes, references added. Corrected typos in Appendix A. Version appeared on JHE

Non-standard interactions versus non-unitary lepton flavor mixing at a neutrino factory

The impact of heavy mediators on neutrino oscillations is typically described by non-standard four-fermion interactions (NSIs) or non-unitarity (NU). We focus on leptonic dimension-six effective operators which do not produce charged lepton flavor violation. These operators lead to particular correlations among neutrino production, propagation, and detection non-standard effects. We point out that these NSIs and NU phenomenologically lead, in fact, to very similar effects for a neutrino factory, for completely different fundamental reasons. We discuss how the parameters and probabilities are related in this case, and compare the sensitivities. We demonstrate that the NSIs and NU can, in principle, be distinguished for large enough effects at the example of non-standard effects in the $\mu$-$\tau$-sector, which basically corresponds to differentiating between scalars and fermions as heavy mediators as leading order effect. However, we find that a near detector at superbeams could provide very synergistic information, since the correlation between source and matter NSIs is broken for hadronic neutrino production, while NU is a fundamental effect present at any experiment.Comment: 32 pages, 5 figures. Final version published in JHEP. v3: Typo in Eq. (27) correcte

Neutrinoless double beta decay in seesaw models

We study the general phenomenology of neutrinoless double beta decay in seesaw models. In particular, we focus on the dependence of the neutrinoless double beta decay rate on the mass of the extra states introduced to account for the Majorana masses of light neutrinos. For this purpose, we compute the nuclear matrix elements as functions of the mass of the mediating fermions and estimate the associated uncertainties. We then discuss what can be inferred on the seesaw model parameters in the different mass regimes and clarify how the contribution of the light neutrinos should always be taken into account when deriving bounds on the extra parameters. Conversely, the extra states can also have a significant impact, cancelling the Standard Model neutrino contribution for masses lighter than the nuclear scale and leading to vanishing neutrinoless double beta decay amplitudes even if neutrinos are Majorana particles. We also discuss how seesaw models could reconcile large rates of neutrinoless double beta decay with more stringent cosmological bounds on neutrino masses.Comment: 34 pages, 5 eps figures and 1 axodraw figure. Final version published in JHEP. NME results available in Appendi

On the importance of the 1-loop finite corrections to seesaw neutrino masses

In the standard seesaw mechanism, finite corrections to the neutrino mass matrix arise from 1-loop self-energy diagrams mediated by a heavy neutrino. We study in detail these corrections and demonstrate that they can be very significant, exceeding in several cases the tree-level result. We consider the normal and inverted hierarchy spectra for light neutrinos and compute the finite corrections to the different elements of the neutrino mass matrix. Special attention is paid to their dependence with the parameters of the seesaw model. Among the cases in which the corrections can be large, we identify the fine-tuned models considered previously in the literature, where a strong cancellation between the different parameters is required to achieve compatibility with the experimental data. As a particular example, we also analyze how these corrections modify the tribimaximal mixing pattern and find that the deviations may be sizable, in particular for $\theta_{13}$. Finally, we emphasize that due to their large size, the finite corrections to neutrino masses have to be taken into account if one wants to properly scan the parameter space of seesaw models.Comment: 24 pages, 11 figure

Neutrino Masses at LHC: Minimal Lepton Flavour Violation in Type-III See-saw

We study the signatures of minimal lepton flavour violation in a simple Type-III see - saw model in which the flavour scale is given by the new fermion triplet mass and it can be naturally light enough to be produced at the LHC. In this model the flavour structure of the lepton number conserving couplings of the triplet fermions to the Standard Model leptons can be reconstructed from the neutrino mass matrix and the smallness of the neutrino mass is associated with a tiny violation of total lepton number. Characteristic signatures of this model include suppressed lepton number violation decays of the triplet fermions, absence of displaced vertices in their decays and predictable lepton flavour composition of the states produced in their decays. We study the observability of these signals in the processes pp\rightarrow 3\ell + 2j +\Sla{E_T} and $pp\rightarrow 2\ell + 4j$ with $\ell =e$ or $\mu$ taking into account the present low energy data on neutrino physics and the corresponding Standard Model backgrounds. Our results indicate that the new fermionic states can be observed for masses up to 500 GeV depending on the CP violating Majorana phase for an integrated luminosity of 30 fb$^{-1}$. Moreover, the flavour of the final state leptons in the above processes can shed light on the neutrino mass ordering.Comment: 31 pages, 11 Figures, matches published versio