Problems in number theory and hyperbolic geometry

In the first part of this thesis we generalize a theorem of Kiming and Olsson concerning the existence of Ramanujan-type congruences for a class of eta quotients. Specifically, we consider a class of generating functions analogous to the generating function of the partition function and establish a bound on the primes ℓ for which their coefficients c(n) obey congruences of the form c(ℓn + a) ≡ 0 (mod ℓ). We use this last result to answer a question of H.C. Chan. In the second part of this thesis [S2] we explore a natural analog of D. Calegari’s result that there are no hyperbolic once-punctured torus bundles over S^1 with trace field having a real place. We prove a contrasting theorem showing the existence of several infinite families of pairs (−χ, p) such that there exist hyperbolic surface bundles over S^1 with trace field of having a real place and with fiber having p punctures and Euler characteristic χ. This supports our conjecture that with finitely many known exceptions there exist such examples for each pair ( −χ, p).

Local Field Potentials in the Gustatory Cortex Carry Taste Information

It has been recently shownthat localfield potentials (LFPs)fromthe auditory and visual cortices carry information about sensory stimuli, but whether this is a universal property of sensory cortices remains to be determined. Moreover, little is known about the temporal dynamics of sensory information contained in LFPs following stimulus onset. Here we investigated the time course of the amount of stimulus information in LFPs and spikes from the gustatory cortex of awake rats subjected to tastants and water delivery on the tongue. We found that the phase and amplitude of multiple LFP frequencies carry information about stimuli, which have specific time courses after stimulus delivery. The information carried by LFP phase and amplitude was independent within frequency bands, since the joint information exhibited neither synergy nor redundancy. Tastant information in LFPs was also independent and had a different time course from the information carried by spikes. These findings support the hypothesis that the brain uses different frequency channels to dynamically code for multiple features of a stimulus.

The use of animal models in multiple myeloma

International audience

A new method for conditioning stochastic groundwater flow models in fractured media

Many geological formations consist of crystalline rocks that have very low matrix permeability but allow flow through an interconnected network of fractures. Understanding the flow of groundwater through such rocks is important in considering disposal of radioactive waste in underground repositories. A specific area of interest is the conditioning of fracture transmissivities on measured values of pressure in these formations. This is the process where the values of fracture transmissivities in a model are adjusted to obtain a good fit of the calculated pressures to measured pressure values. While there are existing methods to condition transmissivity fields on transmissivity, pressure and flow measurements for a continuous porous medium there is little literature on conditioning fracture networks. Conditioning fracture transmissivities on pressure or flow values is a complex problem because the measurements are not linearly related to the fracture transmissivities and they are also dependent on all the fracture transmissivities in the network. We present a new method for conditioning fracture transmissivities on measured pressure values based on the calculation of certain basis vectors; each basis vector represents the change to the log transmissivity of the fractures in the network that results in a unit increase in the pressure at one measurement point whilst keeping the pressure at the remaining measurement points constant. The fracture transmissivities are updated by adding a linear combination of basis vectors and coefficients, where the coefficients are obtained by minimizing an error function. A mathematical summary of the method is given. This algorithm is implemented in the existing finite element code ConnectFlow developed and marketed by Serco Technical Services, which models groundwater flow in a fracture network. Results of the conditioning are shown for a number of simple test problems as well as for a realistic large scale test case.

Changing family models in Spain: the impact of the sociodemographic factors

Abstract During the last few decades, there has been an increasing international recognition of the studies related to the analysis of the family models change, the focus being the determinants of the female employment and the problems related to the work family balance (Lewis, 2001; Petit & Hook, 2005Saraceno, Crompton & Lyonette, 20062008; Pfau-Effinger, 2012). The majority of these studies have been focused on the analysis of the work-family balance problems as well as the effectiveness of the family and gender policies in order to encourage female employment (Korpi et al., 2013). In Spain, special attention has been given to the family policies implemented, the employability of women and on the role of the father in the family (Flaquer et al., 2015; Meil, 2015); however, there has been far less emphasis on the analysis of the family cultural models (González and Jurado, 2012; Crespi and Moreno, 2016). The purpose of this paper is to present some of the first results on the influence of the socio-demographic factors on the expectations and attitudes about the family models. This study offers an analytical reflection upon the foundation of the determinants of the family ambivalence in Spain from the cultural and the institutional dimension. This study shows the Spanish family models of preferences following the Pfau-Effinger (2004) classification of the famiy living arrangements. The reason for this study is twofold; on the one hand, there is confirmed the scarcity of studies that have focused their attention on this objective in Spain; on the other hand, the studies carried out in the international context have confirmed the analytical effectiveness of researching on the attitude and value changes to explain the meaning and trends of the family changes. There is also presented some preliminary results that have been obtained from the multinomial analysis related to the influence of the socio-demographic factors on the family model chosen by the individuals in Spain (father and mother working full time; mother part-time father full-time; mother not at work father full-time; mother and father part-time). 3 The database used has been the International Social Survey Programme: Family and Changing Gender Roles IV- ISSP 2012-. Spain is the only country of South Europe that has participated in the survey. For this reason it has been considered as a representative case study.

Deformation field variations in equal channel angular extrusion due to back pressure

Flow lines were analysed in aluminium alloy 6061 during equal channel angular extrusion (ECAE) in a 90° die with and without the application of back pressure during pressing. The lines appeared much more rounded when a back pressure was applied compared to the case of conventional ECAE testing. With the help of an analytic flow function, the deformation field was obtained. It is shown that back pressure slightly lowers the total strain, strongly increases the size of the plastic zone and significantly reduces the plastic strain rate.

Correlation of throwing velocity to the results of lower-body field tests in male college baseball players

Baseball-specific athleticism, potential, and performance have been difficult to predict. Increased muscle strength and power can increase throwing velocity but the majority of research has focused on the upper body. The present study sought to determine if bilateral or unilateral lower-body field testing correlates with throwing velocity. Baseball throwing velocity scores were correlated to the following tests: medicine ball (MB) scoop toss and squat throw, bilateral and unilateral vertical jumps, single and triple broad jumps, hop and stop in both directions, lateral to medial jumps, 10- and 60-yd sprints, and both left and right single-leg 10-yd hop for speed in 42 college baseball players. A multiple regression analysis (forward method), assessing the relationship between shuffle and stretch throwing velocities and lower-body field test results determined that right-handed throwing velocity from the stretch position was most strongly predicted by lateral to medial jump right (LMJR) and body weight (BW; R = 0.322), whereas lateral to medial jump left (LMJL; R = 0.688) predicted left stretch throw. Right-handed shuffle throw was most strongly predicted by LMJR and MB scoop (R = 0.338), whereas LMJL, BW, and LMJR all contributed to left-handed shuffle throw (R = 0.982). Overall, this study found that lateral to medial jumps were consistently correlated with high throwing velocity in each of the throwing techniques, in both left-handed and right-handed throwers. This is the first study to correlate throwing velocity with a unilateral jump in the frontal plane, mimicking the action of the throwing stride.

Conceptualization of the sexual response models in men: are there differences between sexually functional and dysfunctional men?

Introduction: Research to validate models of sexual response empirically in men with and without sexual dysfunction (MSD), as currently defined, is limited.Aim: To explore the extent to which the traditional linear or the Basson circular model best represents male sexual response for men with MSD and sexually functional men.Methods: In total, 573 men completed an online questionnaire to assess sexual function and aspects of the models of sexual response. In total, 42.2% of men (242) were sexually functional, and 57.8% (331) had at least one MSD. Models were built and tested using bootstrapping and structural equation modeling.Main Outcome Measures: Fit of models for men with and without MSD.Results: The linear model and the initial circular model were a poor fit for men with and without MSD. A modified version of the circular model demonstrated adequate fit for the two groups and showed important interactions between psychological factors and sexual response for men with and without MSD.Conclusion: Male sexual response was not represented by the linear model for men with or without MSD, excluding possible healthy responsive desire. The circular model provided a better fit for the two groups of men but demonstrated that the relations between psychological factors and phases of sexual response were different for men with and without MSD as currently defined.

'Are you sure you're going to have another one of those?': a qualitative analysis of the social control and social support models in type 2 diabetes

While there is evidence that spouses can impact the self-management of adults with type 2 diabetes mellitus, less is known about the influence of the wider social network. This qualitative study explored the perceived impact of the family as well as friends and work colleagues on type 2 diabetes mellitus self-management. A total of 25 adults with type 2 diabetes mellitus participated in semi-structured interviews regarding their social experiences of living with diabetes. Deductive thematic analysis was applied to the data. Pre-existing themes of health-related social control and social support were identified in the wider social network, with additional themes of non-involvement and unintentional undermining also emerging.

Guidelines for developing and reporting machine learning predictive models in biomedical research : a multidisciplinary view

BACKGROUND: As more and more researchers are turning to big data for new opportunities of biomedical discoveries, machine learning models, as the backbone of big data analysis, are mentioned more often in biomedical journals. However, owing to the inherent complexity of machine learning methods, they are prone to misuse. Because of the flexibility in specifying machine learning models, the results are often insufficiently reported in research articles, hindering reliable assessment of model validity and consistent interpretation of model outputs.

OBJECTIVE: To attain a set of guidelines on the use of machine learning predictive models within clinical settings to make sure the models are correctly applied and sufficiently reported so that true discoveries can be distinguished from random coincidence.

METHODS: A multidisciplinary panel of machine learning experts, clinicians, and traditional statisticians were interviewed, using an iterative process in accordance with the Delphi method.

RESULTS: The process produced a set of guidelines that consists of (1) a list of reporting items to be included in a research article and (2) a set of practical sequential steps for developing predictive models.

CONCLUSIONS: A set of guidelines was generated to enable correct application of machine learning models and consistent reporting of model specifications and results in biomedical research. We believe that such guidelines will accelerate the adoption of big data analysis, particularly with machine learning methods, in the biomedical research community.

Transferability of environmental favourability models in geographic space: The case of the Iberian desman (Galemys pyrenaicus) in Portugal and Spain

Transferring distribution models between different geographical areas may be problematic, as the performance of models outside their original scope is hard to predict. A modelling procedure is needed that gets the gist of the environmental descriptors of a distribution area, without either overfitting to the training data or overestimating the species’ distribution potential.We tested the transferability power of the favourability function, a generalized linear model, on the distribution of the Iberian desman (Galemys pyrenaicus) in the Iberian territories of Portugal and Spain.We also tested the effects of two of the main potential constraints on model transferability: the analysed ranges of the predictor variables, and the completeness of the species distribution data. We modelled 10 km×10km presence/absence data from Portugal and Spain separately, extrapolated each model to the other country, and compared predictions with observations. The Spanish model, despite arguably containing more false absences, showed good predictive ability in Portugal. The Portuguese model, whose predictors ranged between only a subset of the values observed in Spain, overestimated desman distribution when transferred.We discuss possible reasons for this differential model behaviour, and highlight the importance of this kind of models for prediction and conservation applications

Spatial scale effects of sampling on the interpolation of species distribution models in the southwestern Amazon.

Knowledge of the geographical distribution of timber tree species in the Amazon is still scarce. This is especially true at the local level, thereby limiting natural resource management actions. Forest inventories are key sources of information on the occurrence of such species. However, areas with approved forest management plans are mostly located near access roads and the main industrial centers. The present study aimed to assess the spatial scale effects of forest inventories used as sources of occurrence data in the interpolation of potential species distribution models. The occurrence data of a group of six forest tree species were divided into four geographical areas during the modeling process. Several sampling schemes were then tested applying the maximum entropy algorithm, using the following predictor variables: elevation, slope, exposure, normalized difference vegetation index (NDVI) and height above the nearest drainage (HAND). The results revealed that using occurrence data from only one geographical area with unique environmental characteristics increased both model overfitting to input data and omission error rates. The use of a diagonal systematic sampling scheme and lower threshold values led to improved model performance. Forest inventories may be used to predict areas with a high probability of species occurrence, provided they are located in forest management plan regions representative of the environmental range of the model projection area.

Entanglement entropy from the holographic stress tensor

We consider entanglement entropy in the context of gauge/gravity duality for conformal field theories in even dimensions. The holographic prescription due to Ryu and Takayanagi (RT) leads to an equation describing how the entangling surface extends into the bulk geometry. We show that setting to zero, the timetime component of the Brown-York stress tensor evaluated on the co-dimension 1 entangling surface, leads to the same equation. By considering a spherical entangling surface as an example, we observe that the Euclidean actionmethods in AdS/CFT will lead to the RT area functional arising as a counterterm needed to regularize the stress tensor. We present arguments leading to a justification for the minimal area prescription.

Desingularization of the Milne Universe

Resolution of cosmological singularities is an important problem in any full theory of quantum gravity. The Milne orbifold is a cosmology with a big-bang/big-crunch singularity, but being a quotient of flat space it holds potential for resolution in string theory. It is known, however, that some perturbative string amplitudes diverge in the Milne geometry. Here we show that flat space higher spin theories can effect a simple resolution of the Milne singularity when one embeds the latter in 2 + 1 dimensions. We explain how to reconcile this with the expectation that non-perturbative string effects are required for resolving Milne. Along the way, we introduce a Grassmann realization of the inonfi-Wigner contraction to export much of the AdS technology to -our flat space computation. (C) 2014 The Authors. Published by Elsevier BAT.