Facticity as the amount of self-descriptive information in a data set

Using the theory of Kolmogorov complexity the notion of facticity {\phi}(x) of a string is defined as the amount of self-descriptive information it contains. It is proved that (under reasonable assumptions: the existence of an empty machine and the availability of a faithful index) facticity is definite, i.e. random strings have facticity 0 and for compressible strings 0 < {\phi}(x) < 1/2 |x| + O(1). Consequently facticity measures the tension in a data set between structural and ad-hoc information objectively. For binary strings there is a so-called facticity threshold that is dependent on their entropy. Strings with facticty above this threshold have no optimal stochastic model and are essentially computational. The shape of the facticty versus entropy plot coincides with the well-known sawtooth curves observed in complex systems. The notion of factic processes is discussed. This approach overcomes problems with earlier proposals to use two-part code to define the meaningfulness or usefulness of a data set.Comment: 10 pages, 2 figure

Weighted distances in scale-free configuration models

In this paper we study first-passage percolation in the configuration model with empirical degree distribution that follows a power-law with exponent $\tau \in (2,3)$. We assign independent and identically distributed (i.i.d.)\ weights to the edges of the graph. We investigate the weighted distance (the length of the shortest weighted path) between two uniformly chosen vertices, called typical distances. When the underlying age-dependent branching process approximating the local neighborhoods of vertices is found to produce infinitely many individuals in finite time -- called explosive branching process -- Baroni, Hofstad and the second author showed that typical distances converge in distribution to a bounded random variable. The order of magnitude of typical distances remained open for the $\tau\in (2,3)$ case when the underlying branching process is not explosive. We close this gap by determining the first order of magnitude of typical distances in this regime for arbitrary, not necessary continuous edge-weight distributions that produce a non-explosive age-dependent branching process with infinite mean power-law offspring distributions. This sequence tends to infinity with the amount of vertices, and, by choosing an appropriate weight distribution, can be tuned to be any growing function that is $O(\log\log n)$, where $n$ is the number of vertices in the graph. We show that the result remains valid for the the erased configuration model as well, where we delete loops and any second and further edges between two vertices.Comment: 24 page

The aetiology and pathogenesis of tropical ulcer

Tropical ulcer is a very specific form of cutaneous ulceration. It occurs worldwide in most tropical and a number of subtropical areas. The disease occurs mainly in older children and young adults with children under the age of 5 and adults over 45 years rarely being affected. Ulcers occur most commonly on the lower leg but may occur on the upper limb. Although most ulcers normally heal slowly over many weeks or months, some ulcers may recur. Recognised complications include squamous cell carcinoma, gangrene and osteitis, although these are rare. A number of authors have reported on the disease and suggested diet, trauma and infection as aetiological factors for this condition. This survey was thus conducted to assess as many of these factors as possible. The study took place in 5 tropical areas, namely Zambia, Gambia, southern India, Fiji and Papua New Guinea. Consultations took place at hospitals, rural clinics, health centres and villages. Although many authors have suggested that the disease is related to malnutrition, few have objectively assessed the nutritional status of the patients and compared it with controls. Those studies which included objective assessments were limited to small areas and only investigated specific parameters. In order to investigate the immune response of the host to an anaerobic infection, the antibody levels to the organisms isolated from the ulcers were measured by an ELISA test. The local host response to an infection with a Fusobacterium species was assessed by the number of antibody secreting B-lymphocytes at the site of the ulcers. These parameters may play a role in the localisation of the ulcers and account for recurrent infections

To aggravate, simulate and malinger in personality assessment

Psychodiagnostici die gebruik maken van de Minnesota Multiphasic Personality 2 (MMPI-2) bij personen die ernstige psychopathologie ervaren, worden vaak geconfronteerd met de prevalentie van sterk verhoogde F- en Fb-scores in deze populatie. Dit heeft tot gevolg dat het gebruik van de oorspronkelijke afbreekscores voor deze schalen om niet valide testprotocollen te identificeren ernstig tekort schiet. Deze studie onderzocht de mogelijkheden van de MMPI-2 validiteitsschalen en een Nederlandse variant van de Fp-schaal om overdrijven en nabootsen van ernstige psychopathologie bij poli(klinische) psychiatrische op te sporen