20 research outputs found
On the number of types in sparse graphs
We prove that for every class of graphs which is nowhere dense,
as defined by Nesetril and Ossona de Mendez, and for every first order formula
, whenever one draws a graph and a
subset of its nodes , the number of subsets of which are of
the form
for some valuation of in is bounded by
, for every . 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 ”m 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 propriĂ©tĂ©s magnĂ©to-optiques de YFeO3, EuFeO3, DyFeO3 et DyIG sont Ă©tudiĂ©es dans l'infra-rouge. Le terme non diagonal |ΔĂ| du tenseur |Δ|) et la birĂ©fringence des orthoferrites sont assez grands. Dans la direction de l'axe optique λ la rotation Faraday de YFeO3 est estimĂ©e Ă partir de |ΔĂ|. La valeur calculĂ©e de cette rotation est 700 °/cm à λ = 1.15 ”. Le rĂ©sultat expĂ©rimental 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 Ă©gal Ă la valeur pour l'ion libre. On utilise l'Ă©quation du mouvement du moment magnĂ©tique avec un facteur g anisotrope pour interprĂ©ter la rotation Faraday Ă 25 °KMagnetooptical properties of the YFeO3, EuFeO3, DyFeO3 and DyIG were investigated in infrared. The nondiagonal components |ΔĂ| of tensor |Δ| are large enough. Faraday Rotation (F. R.) along optical axis of YFeO3 was estimated from the value |ΔĂ|. The calculated value of this rotation is equal to 700 °/cm at λ = 1.15 ”. 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