Discrete Model of Ideological Struggle Accounting for Migration

A discrete in time model of ideological competition is formulated taking into account population migration. The model is based on interactions between global populations of non-believers and followers of different ideologies. The complex dynamics of the attracting manifolds is investigated. Conversion from one ideology to another by means of (i) mass media influence and (ii) interpersonal relations is considered. Moreover a different birth rate is assumed for different ideologies, the rate being assumed to be positive for the reference population, made of initially non-believers. Ideological competition can happen in one or several regions in space. In the latter case, migration of non-believers and adepts is allowed; this leads to an enrichment of the ideological dynamics. Finally, the current ideological situation in the Arab countries and China is commented upon from the point of view of the presently developed mathematical model. The massive forced conversion by Ottoman Turks in the Balkans is briefly discussed.Comment: 24 pages, with 5 figures and 52 refs.; prepared for a Special issue of Advances in Complex System

Incommensurate Charge Density Waves in the adiabatic Hubbard-Holstein model

The adiabatic, Holstein-Hubbard model describes electrons on a chain with step $a$ interacting with themselves (with coupling $U$) and with a classical phonon field \f_x (with coupling \l). There is Peierls instability if the electronic ground state energy F(\f) as a functional of \f_x has a minimum which corresponds to a periodic function with period ${\pi\over p_F}$, where $p_F$ is the Fermi momentum. We consider ${p_F\over\pi a}$ irrational so that the CDW is {\it incommensurate} with the chain. We prove in a rigorous way in the spinless case, when \l,U are small and {U\over\l} large, that a)when the electronic interaction is attractive $U<0$ there is no Peierls instability b)when the interaction is repulsive $U>0$ there is Peierls instability in the sense that our convergent expansion for F(\f), truncated at the second order, has a minimum which corresponds to an analytical and ${\pi\over p_F}$ periodic \f_x. Such a minimum is found solving an infinite set of coupled self-consistent equations, one for each of the infinite Fourier modes of \f_x.Comment: 16 pages, 1 picture. To appear Phys. Rev.

The U(1)-Higgs Model: Critical Behaviour in the Confinig-Higgs region

We study numerically the critical properties of the U(1)-Higgs lattice model, with fixed Higgs modulus, in the region of small gauge coupling where the Higgs and Confining phases merge. We find evidence of a first order transition line that ends in a second order point. By means of a rotation in parameter space we introduce thermodynamic magnitudes and critical exponents in close resemblance with simple models that show analogous critical behaviour. The measured data allow us to fit the critical exponents finding values in agreement with the mean field prediction. The location of the critical point and the slope of the first order line are accurately given.Comment: 21 text pages. 12 postscript figures available on reques

Antiferromagnetic 4-d O(4) Model

We study the phase diagram of the four dimensional O(4) model with first (beta1) and second (beta2) neighbor couplings, specially in the beta2 < 0 region, where we find a line of transitions which seems to be second order. We also compute the critical exponents on this line at the point beta1 =0 (F4 lattice) by Finite Size Scaling techniques up to a lattice size of 24, being these exponents different from the Mean Field ones.Comment: 26 pages LaTeX2e, 7 figures. The possibility of logarithmic corrections has been considered, new figures and tables added. Accepted for publication in Physical Review

Summing Divergent Perturbative Series in a Strong Coupling Limit. The Gell-Mann - Low Function of the \phi^4 Theory

An algorithm is proposed for determining asymptotics of the sum of a perturbative series in the strong coupling limit using given values of the expansion coefficients. Operation of the algorithm is illustrated by test examples, method for estimating errors is developed, and an optimization procedure is described. Application of the algorithm to the $\phi^4$ theory gives a behavior $\beta(g)\approx 7.4 g^{0.96}$ at large $g$ for its Gell-Mann -- Low function. The fact that the exponent is close to unity can be interpreted as a manifestation of the logarithmic branching of the type $\beta(g)\sim g (\ln g)^{-\gamma}$ (with $\gamma\approx 0.14$), which is confirmed by independent evidence. In any case, the $\phi^4$ theory is internally consistent. The procedure of summing perturbartive series with arbitrary values of expansion parameter is discussed.Comment: 23 pages, PD

Business experience and start-up size: buying more lottery tickets next time around?

This paper explores the determinants of start-up size by focusing on a cohort of 6247 businesses that started trading in 2004, using a unique dataset on customer records at Barclays Bank. Quantile regressions show that prior business experience is significantly related with start-up size, as are a number of other variables such as age, education and bank account activity. Quantile treatment effects (QTE) estimates show similar results, with the effect of business experience on (log) start-up size being roughly constant across the quantiles. Prior personal business experience leads to an increase in expected start-up size of about 50%. Instrumental variable QTE estimates are even higher, although there are concerns about the validity of the instrument

Representations of sport in the revolutionary socialist press in Britain, 1988–2012

This paper considers how sport presents a dualism to those on the far left of the political spectrum. A long-standing, passionate debate has existed on the contradictory role played by sport, polarised between those who reject it as a bourgeois capitalist plague and those who argue for its reclamation and reformation. A case study is offered of a political party that has consistently used revolutionary Marxism as the basis for its activity and how this party, the largest in Britain, addresses sport in its publications. The study draws on empirical data to illustrate this debate by reporting findings from three socialist publications. When sport did feature it was often in relation to high profile sporting events with a critical tone adopted and typically focused on issues of commodification, exploitation and alienation of athletes and supporters. However, readers’ letters, printed in the same publications, revealed how this interpretation was not universally accepted, thus illustrating the contradictory nature of sport for those on the far left

Divergent Perturbation Series

Various perturbation series are factorially divergent. The behavior of their high-order terms can be found by Lipatov's method, according to which they are determined by the saddle-point configurations (instantons) of appropriate functional integrals. When the Lipatov asymptotics is known and several lowest order terms of the perturbation series are found by direct calculation of diagrams, one can gain insight into the behavior of the remaining terms of the series. Summing it, one can solve (in a certain approximation) various strong-coupling problems. This approach is demonstrated by determining the Gell-Mann - Low functions in \phi^4 theory, QED, and QCD for arbitrary coupling constants. An overview of the mathematical theory of divergent series is presented, and interpretation of perturbation series is discussed. Explicit derivations of the Lipatov asymptotic forms are presented for some basic problems in theoretical physics. A solution is proposed to the problem of renormalon contributions, which hampered progress in this field in the late 1970s. Practical schemes for summation of perturbation series are described for a coupling constant of order unity and in the strong-coupling limit. An interpretation of the Borel integral is given for 'non-Borel-summable' series. High-order corrections to the Lipatov asymptotics are discussed.Comment: Review article, 45 pages, PD

Biomarker-based prognosis for people with mild cognitive impairment (ABIDE): a modelling study

Background Biomarker-based risk predictions of dementia in people with mild cognitive impairment are highly relevant for care planning and to select patients for treatment when disease-modifying drugs become available. We aimed to establish robust prediction models of disease progression in people at risk of dementia. Methods In this modelling study, we included people with mild cognitive impairment (MCI) from single-centre and multicentre cohorts in Europe and North America: the European Medical Information Framework for Alzheimer's Disease (EMIF-AD; n=883), Alzheimer's Disease Neuroimaging Initiative (ADNI; n=829), Amsterdam Dementia Cohort (ADC; n=666), and the Swedish BioFINDER study (n=233). Inclusion criteria were a baseline diagnosis of MCI, at least 6 months of follow-up, and availability of a baseline Mini-Mental State Examination (MMSE) and MRI or CSF biomarker assessment. The primary endpoint was clinical progression to any type of dementia. We evaluated performance of previously developed risk prediction models—a demographics model, a hippocampal volume model, and a CSF biomarkers model—by evaluating them across cohorts, incorporating different biomarker measurement methods, and determining prognostic performance with Harrell's C statistic. We then updated the models by re-estimating parameters with and without centre-specific effects and evaluated model calibration by comparing observed and expected survival. Finally, we constructed a model combining markers for amyloid deposition, tauopathy, and neurodegeneration (ATN), in accordance with the National Institute on Aging and Alzheimer's Association research framework. Findings We included all 2611 individuals with MCI in the four cohorts, 1007 (39%) of whom progressed to dementia. The validated demographics model (Harrell's C 0·62, 95% CI 0·59–0·65), validated hippocampal volume model (0·67, 0·62–0·72), and updated CSF biomarkers model (0·72, 0·68–0·74) had adequate prognostic performance across cohorts and were well calibrated. The newly constructed ATN model had the highest performance (0·74, 0·71–0·76). Interpretation We generated risk models that are robust across cohorts, which adds to their potential clinical applicability. The models could aid clinicians in the interpretation of CSF biomarker and hippocampal volume results in individuals with MCI, and help research and clinical settings to prepare for a future of precision medicine in Alzheimer's disease. Future research should focus on the clinical utility of the models, particularly if their use affects participants' understanding, emotional wellbeing, and behaviour