Z^\widehat{Z} at large NN: from curve counts to quantum modularity

Reducing a 6d fivebrane theory on a 3-manifold $Y$ gives a $q$-series 3-manifold invariant $\widehat{Z}(Y)$. We analyse the large-$N$ behaviour of $F_K=\widehat{Z}(M_K)$, where $M_K$ is the complement of a knot $K$ in the 3-sphere, and explore the relationship between an $a$-deformed ($a=q^N$) version of $F_{K}$ and HOMFLY-PT polynomials. On the one hand, in combination with counts of holomorphic annuli on knot complements, this gives an enumerative interpretation of $F_K$ in terms of counts of open holomorphic curves. On the other, it leads to closed form expressions for $a$-deformed $F_K$ for $(2,2p+1)$-torus knots. They suggest a further $t$-deformation based on superpolynomials, which can be used to obtain a $t$-deformation of ADO polynomials, expected to be related to categorification. Moreover, studying how $F_K$ transforms under natural geometric operations on $K$ indicates relations to quantum modularity in a new setting.Comment: 42 pages, 4 figure

Sectoral Productivity and Real Exchange Rate Appreciation: Much Ado about Nothing?

Using panel data for selected national economies, we estimate relative price changes stemming from fluctuations in sectoral productivity. Subsequently, we calculate the cross-country CPIinflation differentials implied by sectorally unbalanced productivity growth, taking into account country-specific weights of non-tradables in consumption (value added) and assuming there are no adjustments in nominal exchange rates. We find that sectoral productivity developments have a statistically significant impact on relative prices in the EU countries and also in the Czech Republic, but the magnitude of the impact is not as strong as the Balassa-Samuelson Effect (BSEF) would predict. The final impact of relative productivity on inflation (on the real exchange rate) is even weaker, and moreover, in the case of the Czech Republic the impact is negligible. Thus, contrary to the prevailing view, we question the meaning of the BSEF as a plausible explanatory variable of (equilibrium) real exchange rate determination in the Czech Republic. The same situation we simulate for the future, should productivity growth in the traded sector not accelerate dramatically.Balassa-Samuelson Effect, cross-country inflation differentials, nominal and real convergence, real exchange rates.

Testing excitation models of rapidly oscillating Ap stars with interferometry

Rapidly oscillating Ap stars are unique objects in the potential they offer to study the interplay between a number of important physical phenomena, in particular, pulsations, magnetic fields, diffusion, and convection. Nevertheless, the simple understanding of how the observed pulsations are excited in these stars is still in progress. In this work we perform a test to what is possibly the most widely accepted excitation theory for this class of stellar pulsators. The test is based on the study of a subset of members of this class for which stringent data on the fundamental parameters are available thanks to interferometry. For three out of the four stars considered in this study, we find that linear, non-adiabatic models with envelope convection suppressed around the magnetic poles can reproduce well the frequency region where oscillations are observed. For the fourth star in our sample no agreement is found, indicating that a new excitation mechanism must be considered. For the three stars whose observed frequencies can be explained by the excitation models under discussion, we derive the minimum angular extent of the region where convection must be suppressed. Finally, we find that the frequency regions where modes are expected to be excited in these models is very sensitive to the stellar radius. This opens the interesting possibility of determining this quantity and related ones, such as the effective temperature or luminosity, from comparison between model predictions and observations, in other targets for which these parameters are not well determined.Comment: Accepted for publication in the MNRA

Modeling ϵ\epsilon Eridani and asteroseismic tests of element diffusion

Taking into account the helium and metal diffusion, we explore the possible evolutionary status and perform seismic analysis of MOST target: the star $\epsilon$ Eridani. We adopt the different input parameters to construct the models by fitting the available observational constraints: e.g., $T_{eff}$, $L$, $R$, $[Fe/H]$. From computation, we obtain the average large spacings of $\epsilon$ Eridani about $194\pm 1 \mu$Hz. The age of the diffused models has been found to be about 1 Gyr, which is younger than one determined previously by models without diffusion. We found that the effect of pure helium diffusion on the internal structure of the young low-mass star is slight, but the metal diffusion influence is obvious. The metal diffusion leads the models to have much higher temperature in the radiation interior, correspondingly the higher sound speed in the interior of the model, thereby the larger frequency and spacings.Comment: 16 pages, 4 figures, accepted for publication in ChjA

The dynamics of single spike-evoked adenosine release in the cerebellum

The purine adenosine is a potent neuromodulator in the brain, with roles in a number of diverse physiological and pathological processes. Modulators such as adenosine are difficult to study as once released they have a diffuse action (which can affect many neurones) and, unlike classical neurotransmitters, have no inotropic receptors. Thus rapid postsynaptic currents (PSCs) mediated by adenosine (equivalent to mPSCs) are not available for study. As a result the mechanisms and properties of adenosine release still remain relatively unclear. We have studied adenosine release evoked by stimulating the parallel fibres in the cerebellum. Using adenosine biosensors combined with deconvolution analysis and mathematical modelling, we have characterised the release dynamics and diffusion of adenosine in unprecedented detail. By partially blocking K+ channels, we were able to release adenosine in response to a single stimulus rather than a train of stimuli. This allowed reliable sub-second release of reproducible quantities of adenosine with stereotypic concentration waveforms that agreed well with predictions of a mathematical model of purine diffusion. We found no evidence for ATP release and thus suggest that adenosine is directly released in response to parallel fibre firing and does not arise from extracellular ATP metabolism. Adenosine release events showed novel short-term dynamics, including facilitated release with paired stimuli at millisecond stimulation intervals but depletion-recovery dynamics with paired stimuli delivered over minute time scales. These results demonstrate rich dynamics for adenosine release that are placed, for the first time, on a quantitative footing and show strong similarity with vesicular exocytosis

Fingering convection induced by atomic diffusion in stars: 3D numerical computations and applications to stellar models

Iron-rich layers are known to form in the stellar subsurface through a combination of gravitational settling and radiative levitation. Their presence, nature and detailed structure can affect the excitation process of various stellar pulsation modes, and must therefore be modeled carefully in order to better interpret Kepler asteroseismic data. In this paper, we study the interplay between atomic diffusion and fingering convection in A-type stars, and its role in the establishment and evolution of iron accumulation layers. To do so, we use a combination of three-dimensional idealized numerical simulations of fingering convection, and one-dimensional realistic stellar models. Using the three-dimensional simulations, we first validate the mixing prescription for fingering convection recently proposed by Brown et al. (2013), and identify what system parameters (total mass of iron, iron diffusivity, thermal diffusivity, etc.) play a role in the overall evolution of the layer. We then implement the Brown et al. (2013) prescription in the Toulouse-Geneva Evolution code to study the evolution of the iron abundance profile beneath the stellar surface. We find, as first discussed by Th\'eado et al. (2009), that when the concurrent settling of helium is ignored, this accumulation rapidly causes an inversion in the mean molecular weight profile, which then drives fingering convection. The latter mixes iron with the surrounding material very efficiently, and the resulting iron layer is very weak. However, taking helium settling into account partially stabilizes the iron profile against fingering convection, and a large iron overabundance can accumulate. The opacity also increases significantly as a result, and in some cases ultimately triggers dynamical convection.Comment: 38 pages, 16 figures, submitted to Ap

Beyond Structural Causal Models: Causal Constraints Models

Structural Causal Models (SCMs) provide a popular causal modeling framework. In this work, we show that SCMs are not flexible enough to give a complete causal representation of dynamical systems at equilibrium. Instead, we propose a generalization of the notion of an SCM, that we call Causal Constraints Model (CCM), and prove that CCMs do capture the causal semantics of such systems. We show how CCMs can be constructed from differential equations and initial conditions and we illustrate our ideas further on a simple but ubiquitous (bio)chemical reaction. Our framework also allows to model functional laws, such as the ideal gas law, in a sensible and intuitive way.Comment: Published in Proceedings of the 35th Annual Conference on Uncertainty in Artificial Intelligence (UAI-19

Gender equality and investments in adolescents in the rural Philippines:

"...Many studies have looked at the way resources are distributed to men, women, and especially to small children, but one age group within the family has been largely ignored: the adolescents. Adolescence is a crucial period in that teenagers can make major contributions to their families' welfare through their labor and earnings, in and outside the household, but may sacrifice their own wishes and future well-being in the process if such contributions come at the expense of investments in their education. The research methodology in this report, combining regression analysis with ethnography, provides a lesson in how complementarities between methodological approaches can be exploited...The research finds that parents are not unduly influenced by short-term needs and are ready to make substantial sacrifices in terms of current consumption in order to invest in their children's future. The research also concludes that boys and girls in this rural area of the Philippines are generally treated equally, provid ing a contrast with other Asian settings where discrimination by gender is common." (Forward by Per Pinstrup- Andersen)Teenagers Philippines Social conditions., Rural families Philippines., Gender, Health and nutrition, Education Economic aspects Philippines., Household resource allocation, Health.,