Mean field games with common noise

A theory of existence and uniqueness is developed for general stochastic differential mean field games with common noise. The concepts of strong and weak solutions are introduced in analogy with the theory of stochastic differential equations, and existence of weak solutions for mean field games is shown to hold under very general assumptions. Examples and counter-examples are provided to enlighten the underpinnings of the existence theory. Finally, an analog of the famous result of Yamada and Watanabe is derived, and it is used to prove existence and uniqueness of a strong solution under additional assumptions

Determining The Value-at-risk In The Shadow Of The Power Law: The Case Of The SP-500 Index

In extant financial market models, including the Black-Scholes’ contruct, the dramatic events of October 1987 and August 2007 are totally unexpected, because these models are based on the assumptions of ‘independent price fluctuations’ and the existence of some ‘fixed-point equilibrium’. This paper argues that the convolution of a generalized fractional Brownian motion (into an array in frequency or time domain) and their corresponding amplitude spectra describes the surface of the attractor driving the evolution of prices. This more realistic approach shows that the SP-500 Index is characterized by a high long term Hurst exponent and hence by a ‘black noise’ with a power spectrum proportional to f-b (b > 2). In that set up, the above dramatic events are expected and their frequencies are determined. The paper also constructs an exhaustive frequency-variation relationship which can be used as practical guide to assess the ‘value at risk’.Market Collapse; Fractional Brownian Motion; Fractal Attractors; Maximum Hausdorff Dimension of Markets and Affine Profiles; Hurst Exponent; Power Spectrum Exponent; Value at Risk

Investigating differences in vigilance tactic use within and between the sexes in eastern grey kangaroos

Peer reviewedPostprin

BIOMECHANICAL OPTIMIZATION OF SURGICAL SKILLS: INFLUENCE OF HEIGHT ADJUSTMENT OF SURGICAL TABLE ON MOVEMENTS ACCURACY AND MUSCULAR FATIGUE

The purpose of this study was to investigate the influence of the height of the surgical table on movements accuracy and muscular fatigue, as well as on alignment of mechanical axes at the wrist and at the shoulder level. A "standard" table height was compared with an "ergonomic" height which was set 10% lower. Nine (9) first year residents in surgery performed a surgical procedure and were evaluated on movements accuracy and shoulder muscular fatigue. Results obtained with the table set at "ergonomic" height demonstrated higher accuracy (p < 0.01) and less shoulder fatigue (p < 0.01), as well as smaller deviations from neutral position both at the shoulder level (p < 0.01) and at the wrist level (

Nonlinear optical crystals designed with 4-nitrophenolate chromophores: an engineering route using a multidipolar chromophore, 3-hydroxy-2,4,6-trinitrophenolate

4-Nitrophenol derivatives are interesting chromophores for nonlinear optics (NLO), being typical donor-acceptor system connected by p conjugation. Due to the presence of the acidic phenolic proton, they also readily form salts with suitably selected organic and metallic bases. The so-formed 4-nitrophenolates have increased molecular hyperpolarizabilities (&#946; ). The phenolate and nitro oxygens are strong hydrogen bond acceptors and the nitro group has a tendency to coordinate with metal centers. This opens up two different engineering routes to build NLO materials from these chromophores: (a) organic-organic and (b) metal-organic salts. This paper reviews the crystal packing and nonlinear optical (NLO) efficiency in nitrophenolate crystals engineered through these routes and presents the crystal structure of a new NLO efficient organic-organic salt, 1-hydroxy-4-methylpyridinium 3-hydroxy-2,4,6-trinitrophenolate (P21). In this crystal both the multidipolar anion and dipolar cation are NLO chromophores. The anions form herringbone mediated chain with intra and intermolecular O-H&#8230;O hydrogen bonds and the cations are attached to them through strong O-H&#8230;O- hydrogen bonds

Sodium 4-nitrophenolate 4-nitrophenol dihydrate crystal: a new herringbone structure for quadratic nonlinear optics

Sodium 4-nitrophenolate 4-nitrophenol dihydrate is a new nonlinear optical crystal of C2 monoclinic symmetry composed of two distinct organic chromophores of respective calculated molecular hyperpolarisabilities &#946; xxx =18.2&#215;10-30 and 5.2&#215;10-30 esu. The chromophores are organised in herringbone motifs along inorganic chains of NaO6 edge shared octahedra. A short H-bond network assembles the herringbone motifs. A remarkable feature is the unique proton shared between the two chromophores respecting the twofold symmetry. The structure is isotypic with that of the magnesium bis(4-nitrophenolate) dihydrate. Structural analogies with other known metal nitrophenolates are pointed out and the nonlinear optical efficiency is discussed

Quantum Corrections for Translation-Invariant Renormalizable Non-Commutative Phi^4 Theory

In this paper we elaborate on the translation-invariant renormalizable Phi^4 theory in 4-dimensional non-commutative space which was recently introduced by the Orsay group. By explicitly performing Feynman graph calculations at one loop and higher orders we illustrate the mechanism which overcomes the UV/IR mixing problem and ultimately leads to a renormalizable model. The obtained results show that the IR divergences are also suppressed in the massless case, which is of importance for the gauge field theoretic generalization of the scalar field model.Comment: 18 pages, v2: slightly extended version including a new section on one-loop renormalization, v3: minor revisio

The crime-related views of first-year criminology students attending two parallel-medium South African universities

In addition to the provision of tertiary education, Institutions of Higher Education are expected to instil critical and independent thinking skills in students. Students often bring into the learning environment their own subjective views about the world they live in. We conducted a self-administered survey among 867 first-year students registered for Criminology at two parallel-medium universities (University of the Freestate and the University of Pretoria). The aim of the study was to determine their views and perceptions about the crime phenomenon in South Africa. The survey was undertaken at the beginning of the academic year in order to minimise the possible influence of academic modules on their views and perceptions. Tests of significance (chi-square and effect size) revealed some differences in respect of the gender of students. However, significant differences mostly featured across population groups, in particular between African and White students’ views about personal safety and vulnerability to crime, the causes of crime, sentencing, law enforcement and imprisonment. In terms of the careers that students wish to pursue, differences in views appear to be influenced by their backgrounds instead of the professions they aim to fill. The findings call on Criminology lecturers to incorporate materials in their curricula that will challenge the misconceptions students may hold about crime in South Africa. In addition, platforms are needed where students can confront their own assumptions and existing beliefs about crime, ultimately to strengthen social cognition in this domain. Such activities could prove difficult in parallel-medium institutions where the languages of tuition create two discernible student profiles. Follow-up research is needed to gauge the impact of tertiary education on the crime-related views and perceptions of students.http://www.crimsa.ac.za/am2013gv201

Engineering of non-linear optical crystals displaying a quasi perfect polar alignment of chromophores

Four non-linear optically active crystals based on organic salts obtained by bis-protonation of four diamines (trans-(&#177; )-1,2-, trans-(1R,2R)-(-)-, cis-1,2-diaminocyclohexane or R-(-)-2-methylpiperazine) by 2-methoxy-4-nitrophenol have been prepared. Their crystal structures and non-linear optical efficiencies have been studied. The two adjacent proton acceptor sites in 1,2-diaminocyclohexanes play an important role in aligning the 2-methoxy-4-nitrophenolate chromophores in a quasi-perfect polar arrangement by anchoring through short hydrogen bonds. In the case of the methylpiperazinium derivative the symmetrical 1,4 location of proton acceptor sites directs the chromophores to near antiparallel alignment by forming short hydrogen bonds. The second harmonic generation efficiencies at 1.064 &#956; m of Nd3+:YAG laser light are equivalent to that of POM (3-methyl-4-nitropyridine-1-oxide) for the three diammoniocyclohexane derivatives and equivalent to twice that of urea for the methylpiperazinium derivative