On the number of types in sparse graphs

We prove that for every class of graphs $\mathcal{C}$ which is nowhere dense, as defined by Nesetril and Ossona de Mendez, and for every first order formula $\phi(\bar x,\bar y)$, whenever one draws a graph $G\in \mathcal{C}$ and a subset of its nodes $A$, the number of subsets of $A^{|\bar y|}$ which are of the form $\{\bar v\in A^{|\bar y|}\, \colon\, G\models\phi(\bar u,\bar v)\}$ for some valuation $\bar u$ of $\bar x$ in $G$ is bounded by $\mathcal{O}(|A|^{|\bar x|+\epsilon})$, for every $\epsilon>0$. This provides optimal bounds on the VC-density of first-order definable set systems in nowhere dense graph classes. We also give two new proofs of upper bounds on quantities in nowhere dense classes which are relevant for their logical treatment. Firstly, we provide a new proof of the fact that nowhere dense classes are uniformly quasi-wide, implying explicit, polynomial upper bounds on the functions relating the two notions. Secondly, we give a new combinatorial proof of the result of Adler and Adler stating that every nowhere dense class of graphs is stable. In contrast to the previous proofs of the above results, our proofs are completely finitistic and constructive, and yield explicit and computable upper bounds on quantities related to uniform quasi-wideness (margins) and stability (ladder indices)

Conformal predictors in early diagnostics of ovarian and breast cancers

The paper describes an application of a recently developed machine learning technique called Mondrian predictors to risk assessment of ovarian and breast cancers. The analysis is based on mass spectrometry profiling of human serum samples that were collected in the United Kingdom Collaborative Trial of Ovarian Cancer Screening. The paper describes the technique and presents the results of classification (diagnosis) and the corresponding measures of confidence of the diagnostics. The main advantage of this approach is a proven validity of prediction. The paper also describes an approach to improve early diagnosis of ovarian and breast cancers since the data in the United Kingdom Collaborative Trial of Ovarian Cancer Screening were collected over a period of seven years and do allow to make observations of changes in human serum over that period of time. Significance of improvement is confirmed statistically (for up to 11 months for Ovarian Cancer and 9 months for Breast Cancer). In addition, the methodology allowed us to pinpoint the same mass spectrometry peaks as previously detected as carrying statistically significant information for discrimination between healthy and diseased patients. The results are discussed

High Speed High Sensitive Magnetooptic Materials for Promising Civilian Applications

Using new epitaxial growth technology we produced (R, Bi)3(Fe,Ga)5012 wafers possessing unique combination of static magnetic, magnetooptic (MO) and domain wall dynamic properties. New concept of numerous and promising applications of the developed materials is presented. These applications include : 1) High resolution localizator of magnetic axis for multipole magnets in nuclear accelerators with space accuracy better than 10 µm in the field gradient >0.5 T/m. 2) MO flaw detectors providing real time image of defects both in magnetic and nonmagnetic metal articles ; 3) Set of devices for latent marking of arbitrary articles : 4) Highly reliable MO bank-note tester for operative definition of bills and securities ; 5) High speed MO spatial light modulators ; 6) MO nonmechanical system for light beam scanning

MAGNETOOPTICAL PROPERTIES OF ORTHOFERRITES AND GARNETS IN INFRARED

Les propriétés magnéto-optiques de YFeO3, EuFeO3, DyFeO3 et DyIG sont étudiées dans l'infra-rouge. Le terme non diagonal |εÍ| du tenseur |ε|) et la biréfringence des orthoferrites sont assez grands. Dans la direction de l'axe optique λ la rotation Faraday de YFeO3 est estimée à partir de |εÍ|. La valeur calculée de cette rotation est 700 °/cm à λ = 1.15 µ. Le résultat expérimental est en accord avec cette estimation. La rotation Faraday du DyIG est isotrope entre 80 et 293 °K et le facteur g du Dy 3+ est égal à la valeur pour l'ion libre. On utilise l'équation du mouvement du moment magnétique avec un facteur g anisotrope pour interpréter la rotation Faraday à 25 °KMagnetooptical properties of the YFeO3, EuFeO3, DyFeO3 and DyIG were investigated in infrared. The nondiagonal components |εÍ| of tensor |ε| are large enough. Faraday Rotation (F. R.) along optical axis of YFeO3 was estimated from the value |εÍ|. The calculated value of this rotation is equal to 700 °/cm at λ = 1.15 µ. The experimental value is - 600 °/cm. The F. R. in DyIG is isotropic at 80-293 °K and g-factor Dy3+ equals its free ions value. The equation of motion of the magnetic moment with anisotropic g-factor is used for interpretation F. R. at 25 °K