Discrete Models of Time-Fractional Diffusion in a Potential Well

Mathematics Subject Classification: 26A33, 45K05, 60J60, 60G50, 65N06, 80-99.

Dietary patterns are associated with general and central obesity in elderly living in a Brazilian city

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Characterization of unitary processes with independent and stationary increments

This is a continuation of the earlier work (Publ. Res. Inst. Math. Sci. 45 (2009) 745-785) to characterize unitary stationary independent increment Gaussian processes. The earlier assumption of uniform continuity is replaced by weak continuity and with technical assumptions on the domain of the generator, unitary equivalence of the process to the solution of an appropriate Hudson-Parthasarathy equation is proved.

Technological aids for the rehabilitation of memory and executive functioning in children and adolescents with acquired brain injury (Review).

Background The use of technology in healthcare settings is on the increase and may represent a cost-effective means of delivering rehabilitation. Reductions in treatment time, and delivery in the home, are also thought to be benefits of this approach. Children and adolescents with brain injury often experience deficits in memory and executive functioning that can negatively affect their school work, social lives, and future occupations. Effective interventions that can be delivered at home, without the need for high-cost clinical involvement, could provide a means to address a current lack of provision. We have systematically reviewed studies examining the effects of technology-based interventions for the rehabilitation of deficits in memory and executive functioning in children and adolescents with acquired brain injury. Objectives To assess the effects of technology-based interventions compared to placebo intervention, no treatment, or other types of intervention, on the executive functioning and memory of children and adolescents with acquired brain injury. Search methods We ran the search on the 30 September 2015. We searched the Cochrane Injuries Group Specialised Register, the Cochrane Central Register of Controlled Trials (CENTRAL), Ovid MEDLINE(R), Ovid MEDLINE(R) In-Process & Other Non-Indexed Citations, Ovid MEDLINE(R) Daily and Ovid OLDMEDLINE(R), EMBASE Classic + EMBASE (OvidSP), ISI Web of Science (SCI-EXPANDED, SSCI, CPCI-S, and CPSI-SSH), CINAHL Plus (EBSCO), two other databases, and clinical trials registers. We also searched the internet, screened reference lists, and contacted authors of included studies. Selection criteria Randomised controlled trials comparing the use of a technological aid for the rehabilitation of children and adolescents with memory or executive-functioning deficits with placebo, no treatment, or another intervention. Data collection and analysis Two review authors independently reviewed titles and abstracts identified by the search strategy. Following retrieval of full-text manuscripts, two review authors independently performed data extraction and assessed the risk of bias. Main results Four studies (involving 206 participants) met the inclusion criteria for this review. Three studies, involving 194 participants, assessed the effects of online interventions to target executive functioning (that is monitoring and changing behaviour, problem solving, planning, etc.). These studies, which were all conducted by the same research team, compared online interventions against a 'placebo' (participants were given internet resources on brain injury). The interventions were delivered in the family home with additional support or training, or both, from a psychologist or doctoral student. The fourth study investigated the use of a computer program to target memory in addition to components of executive functioning (that is attention, organisation, and problem solving). No information on the study setting was provided, however a speech-language pathologist, teacher, or occupational therapist accompanied participants. Two studies assessed adolescents and young adults with mild to severe traumatic brain injury (TBI), while the remaining two studies assessed children and adolescents with moderate to severe TBI. Risk of bias We assessed the risk of selection bias as low for three studies and unclear for one study. Allocation bias was high in two studies, unclear in one study, and low in one study. Only one study (n = 120) was able to conceal allocation from participants, therefore overall selection bias was assessed as high. One study took steps to conceal assessors from allocation (low risk of detection bias), while the other three did not do so (high risk of detection bias). Primary outcome 1: Executive functioning: Technology-based intervention versus placebo Results from meta-analysis of three studies (n = 194) comparing online interventions with a placebo for children and adolescents with TBI, favoured the intervention immediately post-treatment (standardised mean difference (SMD) -0.37, 95% confidence interval (CI) -0.66 to -0.09; P = 0.62; I2 = 0%). (As there is no 'gold standard' measure in the field, we have not translated the SMD back to any particular scale.) This result is thought to represent only a small to medium effect size (using Cohen’s rule of thumb, where 0.2 is a small effect, 0.5 a medium one, and 0.8 or above is a large effect); this is unlikely to have a clinically important effect on the participant. The fourth study (n = 12) reported differences between the intervention and control groups on problem solving (an important component of executive functioning). No means or standard deviations were presented for this outcome, therefore an effect size could not be calculated. The quality of evidence for this outcome according to GRADE was very low. This means future research is highly likely to change the estimate of effect. Primary outcome 2: Memory One small study (n = 12) reported a statistically significant difference in improvement in sentence recall between the intervention and control group following an eight-week remediation programme. No means or standard deviations were presented for this outcome, therefore an effect size could not be calculated. Secondary outcomes Two studies (n = 158) reported on anxiety/depression as measured by the Child Behavior Checklist (CBCL) and were included in a meta-analysis. We found no evidence of an effect with the intervention (mean difference -5.59, 95% CI -11.46 to 0.28; I2 = 53%). The GRADE quality of evidence for this outcome was very low, meaning future research is likely to change the estimate of effect. A single study sought to record adverse events and reported none. Two studies reported on use of the intervention (range 0 to 13 and 1 to 24 sessions). One study reported on social functioning/social competence and found no effect. The included studies reported no data for other secondary outcomes (that is quality of life and academic achievement). Authors' conclusions This review provides low-quality evidence for the use of technology-based interventions in the rehabilitation of executive functions and memory for children and adolescents with TBI. As all of the included studies contained relatively small numbers of participants (12 to 120), our findings should be interpreted with caution. The involvement of a clinician or therapist, rather than use of the technology, may have led to the success of these interventions. Future research should seek to replicate these findings with larger samples, in other regions, using ecologically valid outcome measures, and reduced clinician involvement.

Memory and attention problems in children with brain tumors at diagnosis

Purpose: Results from previous studies indicate that children with brain tumors (BT) might present with cognitive problems at diagnosis and thus before the start of any medical treatment. The question remains whether these problems are due to the underlying tumor itself or due to the high level of emotional and physical stress which is involved at diagnosis of a malignant disorder. All children with a de novo oncological diagnosis not involving the central nervous systems (CNS) are usually exposed to a comparable level of distress. However, patients with cancer not involving the CNS are not expected to show disease-related cognitive problems. Thus they serve as a well-balanced control group (CG) to help distinguish between the probable causes of the effect. Method: In a pilot study we analyzed an array of cognitive functions in 16 children with BT and 17 control patients. In both groups, tests were administered in-patient at diagnosis before any therapeutic intervention such as surgery, chemotherapy od irradiation. Results: Performance of children with BT was comparable to that of CG patients in the areas of intelligence, perceptual reasoning, verbal comprehension, working memory, and processing speed. In contrast, however, BT patients performded significantly worse in verbal memory and attention. Conclusion: Memory and attention seem to be the most vulnerable funstions affected by BT, with other functions being preserved at the time of diagnosis. It ist to be expected that this vulnerability might exacerbate the cognitive decline after chemotherapy and radiation treatment - known to impair intellectual performance. The findings highlight the need of early cognitive assessments in children with BT in order to introduce cognitive training as early as possible to minimize or even prevent cognitive long-term sequelae. This might improve long-term academic and professional outcome of these children, but especially helps their return to school after hospitalization.

Asymptotic theory of time varying networks with memory and heterogeneous activation pattern

In this thesis work we develop a new generative model of social networks belonging to the family of Time Varying Networks. The importance of correctly modelling the mechanisms shaping the growth of a network and the dynamics of the edges activation and inactivation are of central importance in network science. Indeed, by means of generative models that mimic the real-world dynamics of contacts in social networks it is possible to forecast the outcome of an epidemic process, optimize the immunization campaign or optimally spread an information among individuals. This task can now be tackled taking advantage of the recent availability of large-scale, high-quality and time-resolved datasets. This wealth of digital data has allowed to deepen our understanding of the structure and properties of many real-world networks. Moreover, the empirical evidence of a temporal dimension in networks prompted the switch of paradigm from a static representation of graphs to a time varying one. In this work we exploit the Activity-Driven paradigm (a modeling tool belonging to the family of Time-Varying-Networks) to develop a general dynamical model that encodes fundamental mechanism shaping the social networks' topology and its temporal structure: social capital allocation and burstiness. The former accounts for the fact that individuals does not randomly invest their time and social interactions but they rather allocate it toward already known nodes of the network. The latter accounts for the heavy-tailed distributions of the inter-event time in social networks. We then empirically measure the properties of these two mechanisms from seven real-world datasets and develop a data-driven model, analytically solving it. We then check the results against numerical simulations and test our predictions with real-world datasets, finding a good agreement between the two. Moreover, we find and characterize a non-trivial interplay between burstiness and social capital allocation in the parameters phase space. Finally, we present a novel approach to the development of a complete generative model of Time-Varying-Networks. This model is inspired by the Kaufman's adjacent possible theory and is based on a generalized version of the Polya's urn. Remarkably, most of the complex and heterogeneous feature of real-world social networks are naturally reproduced by this dynamical model, together with many high-order topological properties (clustering coefficient, community structure etc.).

Stochastic modelling of financial time series with memory and multifractal scaling

Financial processes may possess long memory and their probability densities may display heavy tails. Many models have been developed to deal with this tail behaviour, which reflects the jumps in the sample paths. On the other hand, the presence of long memory, which contradicts the efficient market hypothesis, is still an issue for further debates. These difficulties present challenges with the problems of memory detection and modelling the co-presence of long memory and heavy tails. This PhD project aims to respond to these challenges. The first part aims to detect memory in a large number of financial time series on stock prices and exchange rates using their scaling properties. Since financial time series often exhibit stochastic trends, a common form of nonstationarity, strong trends in the data can lead to false detection of memory. We will take advantage of a technique known as multifractal detrended fluctuation analysis (MF-DFA) that can systematically eliminate trends of different orders. This method is based on the identification of scaling of the q-th-order moments and is a generalisation of the standard detrended fluctuation analysis (DFA) which uses only the second moment; that is, q = 2. We also consider the rescaled range R/S analysis and the periodogram method to detect memory in financial time series and compare their results with the MF-DFA. An interesting finding is that short memory is detected for stock prices of the American Stock Exchange (AMEX) and long memory is found present in the time series of two exchange rates, namely the French franc and the Deutsche mark. Electricity price series of the five states of Australia are also found to possess long memory. For these electricity price series, heavy tails are also pronounced in their probability densities. The second part of the thesis develops models to represent short-memory and longmemory financial processes as detected in Part I. These models take the form of continuous-time AR(∞) -type equations whose kernel is the Laplace transform of a finite Borel measure. By imposing appropriate conditions on this measure, short memory or long memory in the dynamics of the solution will result. A specific form of the models, which has a good MA(∞) -type representation, is presented for the short memory case. Parameter estimation of this type of models is performed via least squares, and the models are applied to the stock prices in the AMEX, which have been established in Part I to possess short memory. By selecting the kernel in the continuous-time AR(∞) -type equations to have the form of Riemann-Liouville fractional derivative, we obtain a fractional stochastic differential equation driven by Brownian motion. This type of equations is used to represent financial processes with long memory, whose dynamics is described by the fractional derivative in the equation. These models are estimated via quasi-likelihood, namely via a continuoustime version of the Gauss-Whittle method. The models are applied to the exchange rates and the electricity prices of Part I with the aim of confirming their possible long-range dependence established by MF-DFA. The third part of the thesis provides an application of the results established in Parts I and II to characterise and classify financial markets. We will pay attention to the New York Stock Exchange (NYSE), the American Stock Exchange (AMEX), the NASDAQ Stock Exchange (NASDAQ) and the Toronto Stock Exchange (TSX). The parameters from MF-DFA and those of the short-memory AR(∞) -type models will be employed in this classification. We propose the Fisher discriminant algorithm to find a classifier in the two and three-dimensional spaces of data sets and then provide cross-validation to verify discriminant accuracies. This classification is useful for understanding and predicting the behaviour of different processes within the same market. The fourth part of the thesis investigates the heavy-tailed behaviour of financial processes which may also possess long memory. We consider fractional stochastic differential equations driven by stable noise to model financial processes such as electricity prices. The long memory of electricity prices is represented by a fractional derivative, while the stable noise input models their non-Gaussianity via the tails of their probability density. A method using the empirical densities and MF-DFA will be provided to estimate all the parameters of the model and simulate sample paths of the equation. The method is then applied to analyse daily spot prices for five states of Australia. Comparison with the results obtained from the R/S analysis, periodogram method and MF-DFA are provided. The results from fractional SDEs agree with those from MF-DFA, which are based on multifractal scaling, while those from the periodograms, which are based on the second order, seem to underestimate the long memory dynamics of the process. This highlights the need and usefulness of fractal methods in modelling non-Gaussian financial processes with long memory.

Birth Weight, Working Memory and Epigenetic Signatures in IGF2 and Related Genes: A MZ Twin Study

Neurodevelopmental disruptions caused by obstetric complications play a role in the etiology of several phenotypes associated with neuropsychiatric diseases and cognitive dysfunctions. Importantly, it has been noticed that epigenetic processes occurring early in life may mediate these associations. Here, DNA methylation signatures at IGF2 (insulin-like growth factor 2) and IGF2BP1-3 (IGF2-binding proteins 1-3) were examined in a sample consisting of 34 adult monozygotic (MZ) twins informative for obstetric complications and cognitive performance. Multivariate linear regression analysis of twin data was implemented to test for associations between methylation levels and both birth weight (BW) and adult working memory (WM) performance. Familial and unique environmental factors underlying these potential relationships were evaluated. A link was detected between DNA methylation levels of two CpG sites in the IGF2BP1 gene and both BW and adult WM performance. The BW-IGF2BP1 methylation association seemed due to non-shared environmental factors influencing BW, whereas the WM-IGF2BP1 methylation relationship seemed mediated by both genes and environment. Our data is in agreement with previous evidence indicating that DNA methylation status may be related to prenatal stress and later neurocognitive phenotypes. While former reports independently detected associations between DNA methylation and either BW or WM, current results suggest that these relationships are not confounded by each other.

Alcohol gel ingestion amongst homeless Eastern and Central Europeans in London: assessing the effects on cognitive functioning and psychological health

Background: Intentional consumption of alcohol based hand gels has been reported especially amongst non-UK national, alcohol dependent, homeless individuals in London. Whilst alcohol misuse is known to be associated with impaired cognitive functioning and mental health problems, the effects of additional ingestion of alcohol gel are unknown. Objectives: To explore cognitive and psychological functioning in users who intentionally ingest alcohol gel compared with ethyl-alcohol only misusers and controls. Methods: Male, Central and Eastern European alcohol only misusers, (n=14; mean age 39 years), alcohol gel users (n=14; mean age 43 years) and controls (n=12; mean age 31 years) were recruited from a London Homeless Service during 2013/14. Alcohol misusers, alcohol gel users and controls were compared on the Forwards and Backwards Digit Span Test; Block Design test; Retrospective and Prospective Memory Questionnaire (PRMQ) and the Hospital and Anxiety Depression Scale (HADS). Results: Alcohol gel users performed significantly worse on the Block Design task (p<0.01) and PRMQ (p<0.01) relative to both alcohol only and control groups, and significantly worse on the digit span relative to controls (p=0.01). Both alcohol misusing groups scored comparatively on digit span backwards (p<0.01), with both groups performing significantly worse than controls. The alcohol gel group reported significantly higher levels of anxiety relative to controls (p=0.02). Conclusions: Whilst there could be constitutional differences between alcohol misusers who additionally abuse alcohol gel, the findings suggest that alcohol gel ingestion may have a greater impact on psychological functioning than traditional alcohol misuse.

Lack of association between lipaemia and central adiposity in subjects with an atherogenic lipoprotein phenotype (ALP)

OBJECTIVE: To investigate the associations between indices of adiposity and cardiovascular risk factors in individuals with an atherogenic lipoprotein phenotype (ALP). SUBJECTS: Fifty-five men, aged 34-69 y, body mass index (BMI) 22-35 kg/m2, with an ALP lipid profile (triglycerides (TG) 1.5-4.0 mmol/l, HDL<1.1 mmol/l; %LDL-3>40% total LDL). DESIGN: Each participant provided a fasting blood sample and underwent an 8 h postprandial assessment and had anthropometric measurements taken. OUTCOME MEASURES: BMI, waist circumference (W), waist-to-hip ratio (W/H), sum of skinfolds (SSK), fasting and postprandial concentrations of glucose, insulin and plasma lipids, post-heparin lipase activity, and apoE genotype. RESULTS: The expected positive associations between BMI, W and SSK and fasting and postprandial insulin were observed (r=0.42-0.65). Little association between glucose responses and any measures of adiposity was evident. Unexpectedly, there were no positive associations between measures of central adiposity (W and W/H) and fasting and postprandial TG responses, with a trend towards negative associations in this study group (TG AUC vs W, r=-0.23, P=0.097; TG IAUC vs W/H, r=-0.26, P=0.068). Subgroup analysis indicated that lack of a positive association between central adiposity and postprandial TG values was more evident in those with one E4 allele (r=-0.42, P=0.077) relative to non-E4 carriers (r=-0.16, P=0.430). The expected positive associations between insulin and TG responses were not observed (r=-0.03 to -0.36). CONCLUSION: In this ALP group the expected positive association between TG responses and a centralized distribution of body fat was not observed, particularly in individuals with an apoE4 genotype. Our findings are not in line with the view that there is a clear causal relationship between insulin resistance and the lipid abnormalities associated with ALP.

Vitamin D and central hypersensitivity in patients with chronic pain.

BACKGROUND Low vitamin D is implicated in various chronic pain conditions with, however, inconclusive findings. Vitamin D might play an important role in mechanisms being involved in central processing of evoked pain stimuli but less so for spontaneous clinical pain. OBJECTIVE This study aims to examine the relation between low serum levels of 25-hydroxyvitamin D3 (25-OH D) and mechanical pain sensitivity. DESIGN We studied 174 patients (mean age 48 years, 53% women) with chronic pain. A standardized pain provocation test was applied, and pain intensity was rated on a numerical analogue scale (0-10). The widespread pain index and symptom severity score (including fatigue, waking unrefreshed, and cognitive symptoms) following the 2010 American College of Rheumatology preliminary diagnostic criteria for fibromyalgia were also assessed. Serum 25-OH D levels were measured with a chemiluminescent immunoassay. RESULTS Vitamin deficiency (25-OH D < 50 nmol/L) was present in 71% of chronic pain patients; another 21% had insufficient vitamin D (25-OH D < 75 nmol/L). After adjustment for demographic and clinical variables, there was a mean ± standard error of the mean increase in pain intensity of 0.61 ± 0.25 for each 25 nmol/L decrease in 25-OH D (P = 0.011). Lower 25-OH D levels were also related to greater symptom severity (r = -0.21, P = 0.008) but not to the widespread pain index (P = 0.83) and fibromyalgia (P = 0.51). CONCLUSIONS The findings suggest a role of low vitamin D levels for heightened central sensitivity, particularly augmented pain processing upon mechanical stimulation in chronic pain patients. Vitamin D seems comparably less important for self-reports of spontaneous chronic pain.

Theory of mind and central coherence in adults with high-functioning autism or Asperger syndrome

The study investigated theory of mind and central coherence abilities in adults with high-functioning autism (HFA) or Asperger syndrome (AS) using naturalistic tasks. Twenty adults with HTA/AS correctly answered significantly fewer theory of mind questions than 20 controls on a forced-choice response task. On a narrative task, there were no differences in the proportion of mental state words between the two groups, although the participants with HFA/AS were less inclined to provide explanations for characters' mental states. No between-group differences existed on the central coherence questions of the forced-choice response task, and the participants with HTA/AS included an equivalent proportion of explanations for non-mental state phenomena in their narratives as did controls. These results support the theory of mind deficit account of autism spectrum disorders, and suggest that difficulties in mental state attribution cannot be exclusively attributed to weak central coherence.

Negative mood, implicit alcohol-related memory, and alcohol use in young adults: The moderating effect of alcohol expectancy

Objective Alcohol-related implicit (preconscious) cognitive processes are established and unique predictors of alcohol use, but most research in this area has focused on alcohol-related implicit cognition and anxiety. This study extends this work into the area of depressed mood by testing a cognitive model that combines traditional explicit (conscious and considered) beliefs, implicit alcohol-related memory associations (AMAs), and self-reported drinking behavior. Method Using a sample of 106 university students, depressed mood was manipulated using a musical mood induction procedure immediately prior to completion of implicit then explicit alcohol-related cognition measures. A bootstrapped two-group (weak/strong expectancies of negative affect and tension reduction) structural equation model was used to examine how mood changes and alcohol-related memory associations varied across groups. Results Expectancies of negative affect moderated the association of depressed mood and AMAs, but there was no such association for tension reduction expectancy. Conclusion Subtle mood changes may unconsciously trigger alcohol-related memories in vulnerable individuals. Results have implications for addressing subtle fluctuations in depressed mood among young adults at risk of alcohol problems.