Optimal control of predictive mean-field equations and applications to finance

We study a coupled system of controlled stochastic differential equations (SDEs) driven by a Brownian motion and a compensated Poisson random measure, consisting of a forward SDE in the unknown process $X(t)$ and a \emph{predictive mean-field} backward SDE (BSDE) in the unknowns $Y(t), Z(t), K(t,\cdot)$. The driver of the BSDE at time $t$ may depend not just upon the unknown processes $Y(t), Z(t), K(t,\cdot)$, but also on the predicted future value $Y(t+\delta)$, defined by the conditional expectation $A(t):= E[Y(t+\delta) | \mathcal{F}_t]$. \\ We give a sufficient and a necessary maximum principle for the optimal control of such systems, and then we apply these results to the following two problems:\\ (i) Optimal portfolio in a financial market with an \emph{insider influenced asset price process.} \\ (ii) Optimal consumption rate from a cash flow modeled as a geometric It\^ o-L\' evy SDE, with respect to \emph{predictive recursive utility}

Nonassociative differential extensions of characteristic p

Let F be a field of characteristic p. We define and investigate nonassociative differential extensions of F and of a finite-dimensional central division algebra over F and give a criterium for these algebras to be division. As special cases, we obtain classical results for associative algebras by Amitsur and Jacobson. We construct families of nonassociative division algebras which can be viewed as generalizations of associative cyclic extensions of a purely inseparable field extension of exponent one or a central division algebra. Division algebras which are nonassociative cyclic extensions of a purely inseparable field extension of exponent one are particularly easy to obtain

Computing in Additive Networks with Bounded-Information Codes

This paper studies the theory of the additive wireless network model, in which the received signal is abstracted as an addition of the transmitted signals. Our central observation is that the crucial challenge for computing in this model is not high contention, as assumed previously, but rather guaranteeing a bounded amount of \emph{information} in each neighborhood per round, a property that we show is achievable using a new random coding technique. Technically, we provide efficient algorithms for fundamental distributed tasks in additive networks, such as solving various symmetry breaking problems, approximating network parameters, and solving an \emph{asymmetry revealing} problem such as computing a maximal input. The key method used is a novel random coding technique that allows a node to successfully decode the received information, as long as it does not contain too many distinct values. We then design our algorithms to produce a limited amount of information in each neighborhood in order to leverage our enriched toolbox for computing in additive networks

Outpatient CBT for Motor Functional Neurological Disorder and Other Neuropsychiatric Conditions: A Retrospective Case Comparison

OBJECTIVE: No gold-standard treatment exists for motor functional neurological disorder (mFND), and limited evidence has been found for the effectiveness of cognitive-behavioral therapy (CBT) in treating the disorder. This study examined sociodemographic and clinical characteristics, treatment outcomes, and treatment dropout among patients with and without mFND who received CBT in a neuropsychiatric outpatient clinic in the United Kingdom. METHODS: Data from a large anonymized psychiatric register were used to identify patients who received outpatient CBT in a neuropsychiatry clinic between 2006 and 2016 and who had either mFND (N=98) or other neuropsychiatric conditions (ONP) (N=76, control group). The study examined sociodemographic characteristics, physical symptom improvement, and changes in clinical outcome and scores on three instruments measuring psychological distress, psychiatric sequelae of brain injury, and depression. RESULTS: The most common mFND symptoms were weakness, pain, and tremors. A logistic regression analysis found no sociodemographic differences between patients with mFND who dropped out early and those who completed CBT. Pre- and post-CBT scores on the three instruments were available for only a small subset of patients; both mFND and ONP patients showed significant improvements in overall scores. A logistic regression analysis found only a single predictor of symptom improvement in the mFND group: acceptance of a psychological explanation of symptoms prior to treatment. CONCLUSIONS: Improvements in physical and psychological functioning were similar for patients with mFND and patients with ONP who were treated in a specialist CBT clinic. This study provides evidence that CBT is feasible and effective for some patients with mFND

From Matrices to Strings and Back

We discuss an explicit construction of a string dual for the Gaussian matrix model. Starting from the matrix model and employing Strebel differential techniques we deduce hints about the structure of the dual string. Next, following these hints a worldheet theory is constructed. The correlators in this string theory are assumed to localize on a finite set of points in the moduli space of Riemann surfaces. To each such point one associates a Feynman diagram contributing to the correlator in the dual matrix model, and thus recasts the worldsheet expression as a sum over Feynman diagrams.Comment: 27 pages, 3 figure

A Neuroanatomical Signature for Schizophrenia Across Different Ethnic Groups

Schizophrenia is a disabling clinical syndrome found across the world. While the incidence and clinical expression of this illness are strongly influenced by ethnic factors, it is unclear whether patients from different ethnicities show distinct brain deficits. In this multicentre study, we used structural Magnetic Resonance Imaging to investigate neuroanatomy in 126 patients with first episode schizophrenia who came from 4 ethnically distinct cohorts (White Caucasians, African-Caribbeans, Japanese, and Chinese). Each patient was individually matched with a healthy control of the same ethnicity, gender, and age (±1 year). We report a reduction in the gray matter volume of the right anterior insula in patients relative to controls (P < .05 corrected); this reduction was detected in all 4 ethnic groups despite differences in psychopathology, exposure to antipsychotic medication and image acquisition sequence. This finding provides evidence for a neuroanatomical signature of schizophrenia expressed above and beyond ethnic variations in incidence and clinical expression. In light of the existing literature, implicating the right anterior insula in bipolar disorder, depression, addiction, obsessive-compulsive disorder, and anxiety, we speculate that the neuroanatomical deficit reported here may represent a transdiagnostic feature of Axis I disorders

A gender-sensitised weight loss and healthy living programme for overweight and obese men delivered by Scottish Premier League football clubs (FFIT): a pragmatic randomised controlled trial.

BACKGROUND: The prevalence of male obesity is increasing but few men take part in weight loss programmes. We assessed the effect of a weight loss and healthy living programme on weight loss in football (soccer) fans. METHODS: We did a two-group, pragmatic, randomised controlled trial of 747 male football fans aged 35-65 years with a body-mass index (BMI) of 28 kg/m(2) or higher from 13 Scottish professional football clubs. Participants were randomly assigned with SAS (version 9·2, block size 2-9) in a 1:1 ratio, stratified by club, to a weight loss programme delivered by community coaching staff in 12 sessions held every week. The intervention group started a weight loss programme within 3 weeks, and the comparison group were put on a 12 month waiting list. All participants received a weight management booklet. Primary outcome was mean difference in weight loss between groups at 12 months, expressed as absolute weight and a percentage of their baseline weight. Primary outcome assessment was masked. Analyses were based on intention to treat. The trial is registered with Current Controlled Trials, number ISRCTN32677491. FINDINGS: 374 men were allocated to the intervention group and 374 to the comparison group. 333 (89%) of the intervention group and 355 (95%) of the comparison group completed 12 month assessments. At 12 months the mean difference in weight loss between groups, adjusted for baseline weight and club, was 4·94 kg (95% CI 3·95-5·94) and percentage weight loss, similarly adjusted, was 4·36% (3·64-5·08), both in favour of the intervention (p<0·0001). Eight serious adverse events were reported, five in the intervention group (lost consciousness due to drugs for pre-existing angina, gallbladder removal, hospital admission with suspected heart attack, ruptured gut, and ruptured Achilles tendon) and three in the comparison group (transient ischaemic attack, and two deaths). Of these, two adverse events were reported as related to participation in the programme (gallbladder removal and ruptured Achilles tendon). INTERPRETATION: The FFIT programme can help a large proportion of men to lose a clinically important amount of weight; it offers one effective strategy to challenge male obesity. FUNDING: Scottish Government and The UK Football Pools funded delivery of the programme through a grant to the Scottish Premier League Trust. The National Institute for Health Research Public Health Research Programme funded the assessment (09/3010/06)