Distributivity and deformation of the reals from Tsallis entropy

We propose a one-parameter family \ $\mathbb{R}_q$ \ of deformations of the reals, which is motivated by the generalized additivity of the Tsallis entropy. We introduce a generalized multiplication which is distributive with respect to the generalized addition of the Tsallis entropy. These operations establish a one-parameter family of field isomorphisms \ $\tau_q$ \ between \ $\mathbb{R}$ \ and \ $\mathbb{R}_q$ \ through which an absolute value on \ $\mathbb{R}_q$ \ is introduced. This turns out to be a quasisymmetric map, whose metric and measure-theoretical implications are pointed out.Comment: 16 pages, Standard LaTeX2e, To be published in Physica

Generalised Cantor sets and the dimension of products

In this paper we consider the relationship between the Assouad and box-counting dimension and how both behave under the operation of taking products. We introduce the notion of ‘equi-homogeneity’ of a set, which requires a uniformity in the cardinality of local covers at all length-scales and at all points, and we show that a large class of homogeneous Moran sets have this property. We prove that the Assouad and box-counting dimensions coincide for sets that have equal upper and lower box-counting dimensions provided that the set ‘attains’ these dimensions (analogous to ‘s-sets’ when considering the Hausdorff dimension), and the set is equi-homogeneous. Using this fact we show that for any α ∈ (0, 1) and any β, γ ∈ (0, 1) such that β + γ ≥ 1 we can construct two generalised Cantor sets C and D such that dimBC = αβ, dimBD = α γ, and dimAC = dimAD = dimA (C × D) = dimB (C × D) = α

The Traveling Salesman Problem: Low-Dimensionality Implies a Polynomial Time Approximation Scheme

The Traveling Salesman Problem (TSP) is among the most famous NP-hard optimization problems. We design for this problem a randomized polynomial-time algorithm that computes a (1+eps)-approximation to the optimal tour, for any fixed eps>0, in TSP instances that form an arbitrary metric space with bounded intrinsic dimension. The celebrated results of Arora (A-98) and Mitchell (M-99) prove that the above result holds in the special case of TSP in a fixed-dimensional Euclidean space. Thus, our algorithm demonstrates that the algorithmic tractability of metric TSP depends on the dimensionality of the space and not on its specific geometry. This result resolves a problem that has been open since the quasi-polynomial time algorithm of Talwar (T-04)

Anxiety, emotional processing and depression in people with multiple sclerosis.

BACKGROUND: Despite the high comorbidity of anxiety and depression in people with multiple sclerosis (MS), little is known about their inter-relationships. Both involve emotional perturbations and the way in which emotions are processed is likely central to both. The aim of the current study was to explore relationships between the domains of mood, emotional processing and coping and to analyse how anxiety affects coping, emotional processing, emotional balance and depression in people with MS. METHODS: A cross-sectional questionnaire study involving 189 people with MS with a confirmed diagnosis of MS recruited from three French hospitals. Study participants completed a battery of questionnaires encompassing the following domains: i. anxiety and depression (Hospital Anxiety and Depression Scale (HADS)); ii. emotional processing (Emotional Processing Scale (EPS-25)); iii. positive and negative emotions (Positive and Negative Emotionality Scale (EPN-31)); iv. alexithymia (Bermond-Vorst Alexithymia Questionnaire) and v. coping (Coping with Health Injuries and Problems-Neuro (CHIP-Neuro) questionnaire. Relationships between these domains were explored using path analysis. RESULTS: Anxiety was a strong predictor of depression, in both a direct and indirect way, and our model explained 48% of the variance of depression. Gender and functional status (measured by the Expanded Disability Status Scale) played a modest role. Non-depressed people with MS reported high levels of negative emotions and low levels of positive emotions. Anxiety also had an indirect impact on depression via one of the subscales of the Emotional Processing Scale ("Unregulated Emotion") and via negative emotions (EPN-31). CONCLUSIONS: This research confirms that anxiety is a vulnerability factor for depression via both direct and indirect pathways. Anxiety symptoms should therefore be assessed systematically and treated in order to lessen the likelihood of depression symptoms

Rethinking the Lebanese economic miracle: The extreme concentration of income and wealth in Lebanon

I combine household surveys, national accounts and personal income tax records for the 2005-2014 period to produce the first estimates of the national income distribution in Lebanon. I find that income is extremely concentrated, with the top 1 and 10% of the adult population receiving 25 and 55% of national income on average, placing Lebanon among the countries with the highest level of income inequality in the world. These figures, which are the first recent statistics on income inequality in an Arab country, question the view of Lebanon as a paragon of economic success in the Middle East. The dynamism of the tourism, banking and real-estate sectors has benefited only a minority of the population, while a large part still lives in extreme poverty

A Taxonomy of Emerging Markets

Focusing on emerging markets is now a significant imperative for business professionals as well as strategy, management, and international business (IB) scholars. However, there are no accepted categorizations of these countries. Furthermore, major international organizations, institutions, scholars, and multinational, all approach classifying these countries from a multitude of different perspectives. Using institutional theory as a framework and drawing on research from multiple disciplines such as IB, sociology, economics, and economic geography, this dissertation proposes a framework by which a more nuanced reclassification of emerging markets into eight subgroups is considered appropriate. The application of this multidimensional and multidisciplinary approach shows how economic, social and cultural dimensions can contribute to the emergent status of a country. Consequently, this dissertation delivers practitioners, policy makers, and academic communities with a tool to illustrate national context more effectively. In doing so, research, policy, and strategy can positively benefit from a new set of contextual and boundary conditions to frame issues of strategic importance

The Effects of Acknowledging Cultural Differences on Therapeutic Alliance in Cross-Cultural Therapy

Therapeutic alliance has been documented to have a significant impact on therapy. This study examined the impact that acknowledging visible cultural differences in the first session of treatment has on therapeutic alliance, perceived clinician cross-cultural competency, and potential attrition. A vignette study design was utilized with 26 subjects who were patients at the PCOM Center for Brief Therapy. The patients were randomly assigned one of four vignettes that consisted of a cross-cultural therapy situation, in which visible cultural differences were either addressed or not by a clinician. Following the reading of the vignette, the subjects were asked to complete the Working Alliance Inventory-Client Version, the client modified version of the Cross Cultural Counseling Inventory-Revised, and a Client Attrition Questionnaire. The results of the study indicated a significant difference in perceived clinician cultural competency in a situation where a clinician acknowledges multiple cultural differences rather than a single difference. A significant negative correlation was found between age and therapeutic alliance as a whole. Female subjects were also found to be significantly more likely than male subjects to make a higher rating of their potential to prematurely drop out of treatment. Future research should expand beyond the vignette model and utilize an intervention study to focus on the impact of broaching visible cultural differences in cross-cultural therapy during the first session of treatment

The Impact of Culture on Customer Expectations

A critical component of customer satisfaction is in the understanding of customer expectations. In this work we propose that culture plays an important role in molding those expectations. Utilizing five cultural dimensions we develop testable propositions that aims to dissect the possible impact of culture upon five sources of customer expectations: personal needs, explicit promises, implicit promises, word-of-mouth, and past experienc