Composition law of κ-entropy for statistically independent systems.

The intriguing and still open question concerning the composition law of κ-entropy S_{κ}(f)=1/2κ∑_{i}(f_{i}^{1-κ}-f_{i}^{1+κ}) with 0<κ<1 and ∑_{i}f_{i}=1 is here reconsidered and solved. It is shown that, for a statistical system described by the probability distribution f={f_{ij}}, made up of two statistically independent subsystems, described through the probability distributions p={p_{i}} and q={q_{j}}, respectively, with f_{ij}=p_{i}q_{j}, the joint entropy S_{κ}(pq) can be obtained starting from the S_{κ}(p) and S_{κ}(q) entropies, and additionally from the entropic functionals S_{κ}(p/e_{κ}) and S_{κ}(q/e_{κ}),e_{κ} being the κ-Napier number. The composition law of the κ-entropy is given in closed form and emerges as a one-parameter generalization of the ordinary additivity law of Boltzmann-Shannon entropy recovered in the κ→0 limit.

Methods for the assessment of the efficacy of products and slimming treatments for cellulite according to the Italian Interdisciplinary Group for the standardization of efficacy tests on cosmetic products.

Cellulite is a very common skin alteration with a complex pathogenesis; different degrees of severity of cellulite can be observed in most part of people after puberty, and numerous cosmetic or more invasive treatments have been proposed, with variable efficacy. Since reproducible methods of evaluation of the effectiveness of cellulite treatments are lacking, the purpose of our group was to define and set general testing principles for evaluating the efficacy of slimming products and treatments/remodeling methods for cellulite, to achieve a delineation of reliable and reproducible research steps following a well-designed and scientifically valid methodology. After a careful review of literature and textbooks and according to personal experience, we defined assessment protocols based on clinical and instrumental tools. In order to make studies reliable, reproducible and safe, a protocol standardization is needed. The sponsor is responsible for assuring quality and information concerning the product under investigation; moreover, investigators should be experienced on cellulite evaluation and treatment, and, finally, the duration and modalities of application of the product should be specified. A treated VS non treated area comparison can be performed, to evaluate the severity of cellulite and the clinical outcomes of the treatment. Besides clinical evaluation, instrumental methods should always be implemented to provide objective data for treatment outcome.

Efficacy of a topical cosmetic slimming treatment for postmenopausal women: a randomized, double-blind, placebo controlled trial.

AIM: The aim of this paper was to evaluate by clinical and non-invasive instrumental evaluations, the efficacy and the tolerance of a cosmetic slimming treatment for menopausal women used topically (for at least 3 years) under dermatological control. METHODS: A controlled double blind, randomised study was performed to compare the slimming efficacy of the cosmetic slimming treatment versus placebo after 4 weeks of treatment. RESULTS: Cosmetic slimming treatment twice a day for 4 weeks reduced abdomen and hips fat, with no significant variation in body weight in comparison with the placebo. CONCLUSION: The present study evidenced the clinical effectiveness and women satisfaction of a slimming treatment specifically studies for postmenopausal adipose tissue with potential interesting consequences on measures of quality of life and on health-care programs.

An image-processing analysis of skin textures.

BACKGROUND: This paper discusses an image-processing method applied to skin texture analysis. Considering that the characterisation of human skin texture is a task approached only recently by image processing, our goal is to lay out the benefits of this technique for quantitative evaluations of skin features and localisation of defects. METHODS: We propose a method based on a statistical approach to image pattern recognition. The results of our statistical calculations on the grey-tone distributions of the images are proposed in specific diagrams, the coherence length diagrams. RESULTS: Using the coherence length diagrams, we were able to determine grain size and anisotropy of skin textures. Maps showing the localisation of defects are also proposed. CONCLUSION: According to the chosen statistical parameters of grey-tone distribution, several procedures to defect detection can be proposed. Here, we follow a comparison of the local coherence lengths with their average values. More sophisticated procedures, suggested by clinical experience, can be used to improve the image processing.

'Healthy skin': significance and results of an Italian study on healthy population with particular regard to 'sensitive' skin.

There is an increasing demand in general population regarding skin healthiness and improvement of aesthetical appearance, indicating that people require more information about how to treat healthy skin and to prevent skin disease. This study is the result of a campaign on healthy skin organized by the International Society of Plastic Dermatology. This campaign was at the same time an occasion to perform an epidemiological study on Italian population and was conducted during only one month (March 2004) throughout Italy. In total, 462 dermatologists all over Italy joined the project. Study protocol and diagnostic kits were provided to all adhering dermatologists. After signing an informed consent, subjects were assigned to undergo anamnesis, medical examination and stinging test with 10% lactic acid at the level of nasolabial fold. A total of 2101 duly compiled case record forms were sent back by the dermatologists. The analysis of the demographic features and lifestyle of the subjects who were attracted by the campaign allows us to draw the identikit of people interested in the maintenance of a healthy skin, i.e. mainly young women, who already lead a healthy life and took care of their skin. Sensitive skin was common in this healthy population.

Ptosis of submental skin: objective measurements and effect of age.

BACKGROUND/PURPOSE: Sagging of the face skin is a visible and unattractive characteristic of skin ageing. This phenomenon, due to both gravitational force and age-related alterations in the mechanical properties of skin, has never been quantitatively studied. The aim of this paper was, first, to define a method and a precise procedure allowing the objective measurement of this phenomenon and, second,to study how it is related to age. METHODS: We used an electronically controlled bed that allows the comparison of submental skin profiles in both the reclined and the upright positions. A parameter that characterises the sagging amplitude for an individual was defined and the reproducibility of measurement of this parameter was verified. RESULTS: Results, obtained from 66 female volunteers, demonstrated a statistically significant positive correlation between this new parameter and age, and also between this new parameter and the elastic recovery parameter of skin, as measured by torquemeter. CONCLUSION: Age-related changes of the skin's mechanical properties and of the various underlying skin tissues would explain this phenomenon. This new method and procedure should allow objective evaluation of the efficacy of any treatments (cosmetic, medical or surgical) proposed for rendering the appearance of people younger.

Irregularity skin index (ISI): a tool to evaluate skin surface texture.

BACKGROUND/AIMS: Irregularity of skin surface microtopography is difficult to evaluate in Euclidean geometry. Using a fast Fourier transform (FFT), it is possible to convert a space field into a frequency field and to obtain quantitative evaluation of this important feature of the skin. The aim of the present study was to test the applicability of a new parameter, derived from computer assisted FFT, to skin texture, in order to quantify its irregularity. This parameter has the additional advantage of being anisotropic. METHOD: The study was conducted on 50 female volunteers. Skin replicas were performed on a healthy area that was not chronically photo-exposed. A new parameter, called "irregularity skin index" (ISI), was identified from FFT. The correlation with volunteers' age was calculated. RESULTS: ISI was calculated by FFT in two different directions (referred to the x and y axis of the diagram of the FFT and named, respectively, ISIomegax and ISIomegay). The irregularity skin indexes increased with age of the subjects, showing a correlation with age of r=0.47 (ISIomegax) and r=0.51 (ISIomegay). CONCLUSION: By showing a relatively good correlation with age, ISI seems to be a promising parameter for the study of ageing skin.