Analyticity of the affinity dimension for planar iterated function systems with matrices which preserve a cone

The sub-additive pressure function $P(s)$ for an affine iterated function system (IFS) and the affinity dimension, defined as the unique solution $s_0$ to $P(s_0)=1$, were introduced by K. Falconer in his seminal 1988 paper on self-affine fractals. The affinity dimension prescribes a value for the Hausdorff dimension of a self-affine set which is known to be correct in generic cases and in an increasing range of explicit cases. It was shown by Feng and Shmerkin in 2014 that the affinity dimension depends continuously on the IFS. In this article we prove that when the linear parts of the affinities which define the IFS are $2 \times 2$ matrices which strictly preserve a common cone, the sub-additive pressure is locally real analytic as a function of the matrix coefficients of the linear parts of the affinities. In this setting we also show that the sub-additive pressure is piecewise real analytic in $s$, implying that the affinity dimension is locally analytic in the matrix coefficients. Combining this with a recent result of B\'ar\'any, Hochman and Rapaport we obtain results concerning the analyticity of the Hausdorff dimension for certain families of planar self-affine sets

Effective estimates on the top Lyapunov exponent for random matrix products

We study the top Lyapunov exponents of random products of positive $2 \times 2$ matrices and obtain an efficient algorithm for its computation. As in the earlier work of Pollicott, the algorithm is based on the Fredholm theory of determinants of trace-class linear operators. In this article we obtain a simpler expression for the approximations which only require calculation of the eigenvalues of finite matrix products and not the eigenvectors. Moreover, we obtain effective bounds on the error term in terms of two explicit constants: a constant which describes how far the set of matrices are from all being column stochastic, and a constant which measures the minimal amount of projective contraction of the positive quadrant under the action of the matrices.Comment: Updated definition of constant r, updated examples section, new section on scope for generalising results to higher dimensions, proof of lemma 2.1 correcte

Nonequilibrium transport equations and ab initio study of adsorption processes on carbon nanotubes

In a theoretical study of gas adsorption on carbon nanotubes (CNT) nonequilibrium processes of ionization, polarization, surface diffusion and desorption of atoms are considered self-consistently. The approach is based on Zubarev's method of nonequilibrium statistical operator and reaction-diffusion theory. The set of nonlinear transport equations are obtained for the chosen parameters of description: the average numbers of adsorbed atoms, ionized and polarized atoms in the electromagnetic field of CNT, and the average number of atoms desorbed from the CNT surface. Ab initio simulations are conducted for a "gas-single wall carbon nanotube" system for gases of particular practical interest: He and NO. The obtained values of adsorption energy reveal preferable localization sites of absorbed He atoms as well as their dependency on adsorption distances. A significant effect of NO adsorption on CNT electronic properties is demonstrated. The effect of presence of vacancies on adsorption nature is analyzed. It is shown that under the influence of vacancy formation the CNT structure undergoes reconstruction that enables chemisorption of NO molecules.Comment: 12 pages, 4 figure

Cross-linguistic Metaphorical Representation of the #MeToo Movement: Communicating Attitudes

The article focuses on the metaphorical conceptualisation of the #MeToo movement, which has spread virally as a hashtag used on social media in an attempt to demonstrate the widespread prevalence of sexual assault and harassment. The #MeToo movement as a social issue is looked at from the perspective of Critical Metaphor Analysis (CMA) (Charteris-Black 2005/2011, 2014, Musolff 2004, 2016, Koller 2014, De Landtsheer 2009, Hart 2010). CMA is a blend of Cognitive Metaphor Theory and Critical Discourse Analysis that aims at identifying how metaphors are used to describe socially contested issues and how they reveal speakers’ hidden intentions and attitudes (Charteris-Black, 2014, p. 174). CMA is also concerned with the different functions metaphors may perform. A predicative function, being one of many, is most likely to explain how socially sensitive issues are communicated (Charteris-Black, 2014, pp. 204-207; Musolff, 2016, p. 4). In other words, it implies positive or negative attitudes expressed towards certain issues. Thus, the paper aims to study how the predicative function of metaphor manifests in the discourse of contemporary social concerns cross-linguistically and cross-culturally. In other words, the paper looks into how different attitudes towards the #MeToo movement are communicated via metaphors in Lithuanian and English media and how they shape prevailing public attitudes

The impact of different techniques used for coronary angiography and percutaneous coronary intervention on the occurrence of procedure-related ischemic cerebral complications

Background Coronary angiography (CA) is the gold standard in diagnosing and determining the treatment of patients with coronary heart disease. Procedure-related neurological complications are rare; 0.1-0.4% for CA and percutaneous coronary intervention (PCI). In contrast, the incidence of procedure-related silent cerebral lesions, shown with diffusion-weighted magnetic resonance tomography, is considerably higher (2-35%). Cerebral microemboli have been observed during different vascular procedures and are related to new silent cerebral lesions but their clinical impact is debated. CA and PCI can be performed with different techniques, i.e. with the radial or the femoral access. As procedure-related stroke is associated with high mortality, considerable morbidity and suffering it is important to study which technique entails the lowest risk for patient injury. Methods and results Study I: Fifty-one patients with stable angina pectoris were randomised to CA with the radial or the femoral access and the number of cerebral microemboli was assessed with bilateral transcranial Doppler technique of the middle cerebral arteries (MCAs). The number of particulate cerebral microemboli was signifiantly higher with the radial compared to the femoral access. The number of cerebral microemboli was higher for both access sites during catheter exchanges compared with other specifi procedural steps during CA, with most cerebral microemboli detected in the right MCA in the radial group. This indicates a causal anatomical link, as the catheter is advanced from the right radial artery through the brachiocephalic trunk before it bends into the ascending aorta to reach the coronary ostia. Study II: Forty-one patients with stable angina pectoris or non-ST-segment-elevation myocardial infarction scheduled for CA were randomised to two different guidewire techniques with the femoral access involving catheter advancement with or without a leading guidewire over the aortic arch. After the CA was completed, including contrast injections, the opposite technique was used on the same patient without further contrast injections. At the same time, the number of cerebral microemboli was registered using bilateral transcranial Doppler technique. The number of cerebral microemboli was higher when the catheter was advanced with, rather than without a leading guidewire over the aortic arch, independent of whether a complete CA was performed or if a catheter was placed in the vicinity of the coronary ostia only. Study III: All CAs and PCIs reported between 2003 and 2011, n= 336,836, to the Swedish Coronary Angiography and Angioplasty Register with information on access site were retrospectively analysed regarding the association between access site and procedure-related stroke or transient ischemic attack (TIA). After cross-checking the reported neurological complications with the corresponding medical records the incidence of procedure-related stroke or TIA was 0.16%. After multivariable adjustment, the radial access was associated with a higher risk for procedure-related stroke or TIA (risk ratio 1.30, 95% confience interval 1.04-1.62) compared with the femoral access. Parallel to the increased use of the radial access over time, the risk for procedure-related stroke or TIA also increased, although there was no signifiant interaction between the different time intervals observed. Study IV: Ninety-three patients with suspected or stable angina pectoris scheduled for CA or PCI were tested with Montreal Cognitive Assessment (MoCA) before and twice after the coronary procedure to study postprocedural cognitive impairment. A subgroup was monitored with bilateral transcranial Doppler technique to explore the relationship between cerebral microemboli and cognitive function. The patients were also randomised to radial or femoral vascular access site to study if the access site used was related to postprocedural cognitive impairment. Cognitive function assessed with the MoCA test was not impaired after the coronary procedure. There was no signifiant correlation between the results of the MoCA test and cerebral microemboli or vascular access site. Conclusions The choice of access site and guidewire technique used for CA and PCI had an impact on the occurrence of cerebral microemboli. There may be an association between the radial access and increased risk for procedure-related stroke or TIA, which should be studied further. Earlier studies have shown that cerebral microemboli are related to new silent cerebral lesions, but we found no cognitive impairment after coronary procedures using the MoCA test. Further studies are needed to explore the clinical impact of cerebral microemboli and to minimise or prevent the occurrence of procedure-related ischemic cerebral lesions in patients undergoing CA and PCI

A new proof of the dimension gap for the Gauss map

Funding: This paper was written while the author was supported by a Leverhulme Trust Research Project Grant (RF-2016-194).In [4], Kifer, Peres and Weiss showed that the Bernoulli measures for the Gauss map T(x)=1/x mod 1 satisfy a 'dimension gap' meaning that for some c > 0, supp dim μp < 1-c, where μp denotes the (pushforward) Bernoulli measure for the countable probability vector p. In this paper we propose a new proof of the dimension gap. By using tools from thermodynamic formalism we show that the problem reduces to obtaining uniform lower bounds on the asymptotic variance of a class of potentials.Publisher PDFPeer reviewe

The FORCE Metaphor in Conceptualizing Economic Recession

Cognitive metaphor analysts comprehend metaphor as a convenient way of not only talking about real life events but also thinking about them: connecting ideas, explaining abstract ideas that are difficult to grasp, conveying messages and emotions, etc. Thus, metaphor in real-world discourse is increasingly becoming the focus of many cognitive studies. In political discourse, metaphor is seen as an ideological tool of deliberate attempts to influence, persuade and manipulate people. As Charteris-Black (2005: 16) put it, politicians try to establish themselves in a positive light or legitimize themselves, i.e., by presenting evidence that they are charismatic leaders who are capable of running their country efficiently. Legitimization goes hand in hand with delegitimization, i.e., negative other-presentation. Metaphor as a cognitive mechanism of ideology may serve both as positive self-representation and as a tool for fault-finding in others. Thus, the study focuses on how three Lithuanian socio-political groups (the leading party, the opposition, and the media) legitimize themselves and delegitimize their opponents by using force metaphors to conceptualize the worldwide economic recession. The findings indicate that although the same conceptual metaphor is used for legitimization and delegitimization, its fulfilment scenario appears to be markedly different and it carries different rhetorical implications in the three discourses.Kognityvinės metaforos tyrėjai suvokia metaforą ne tik kaip galimybę kalbėti apie gyvenimo įvykius, bet ir kaip mąstymo būdą: idėjų jungimą, abstrakčių ir sudėtingų minčių paaiškinimą, informacijos ir emocijų perteikimą, t.t. Metafora – itin populiarus kognityvinių tyrimų objektas. Politiniame diskurse metafora suvokiama kaip ideologinė priemonė, kuria siekiama paveikti, įtikinti ir manipuliuoti žmonėmis. Pasak J. Charteriso Blacko, politikai stengiasi parodyti save itin teigiamai, t. y. legitimizuotis įrodymais, atskleidžiančiais jų lyderiavimo charizmatiškumą, gebėjimus tinkamai valdyti šalį. Legitimizacija yra neatsiejama nuo delegitimizacijos, t. y. neigiamo „kito“ pristatymo. Tad pagrindinė metaforos, kognityvinio ideologijos mechanizmo, funkcija yra savęs teigiamas parodymas, o kitų – neigiamas. Straipsnyje analizuojama, kaip, konceptualizuojant pasaulinę ekonominę krizę, trys Lietuvos sociopolitinės grupės (valdančioji partija, opozicija ir žiniasklaida) legitimizuoja save ir delegitimizuoja oponentus naudodami jėgos metaforą. Tyrimas rodo, kad ta pačia konceptualiąja metafora grindžiama ir legitimizacija, ir delegitimizacija. Tačiau metaforos veikimo scenarijus skirtingas, skiriasi trijų sociopolitinių grupių diskursų retorinės implikacijos