Kolmogorov's Contributions to the Foundations of Probability

Andrei Nikolaevich Kolmogorov was the foremost contributor to the mathematical and philosophical foundations of probability in the twentieth century, and his thinking on the topic is still potent today. In this article we first review the three stages of Kolmogorov's work on the foundations of probability: (1) his formulation of measure-theoretic probability, 1933; (2) his frequentist theory of probability, 1963; and (3) his algorithmic theory of randomness, 1965–1987. We also discuss another approach to the foundations of probability, based on martingales, which Kolmogorov did not consider.     

The course and outcome of viral hepatitis B in drug-addicted patients

In this paper, characterization is given of clinical and biochemical features of VH B course against the background of narcomania. Recordable in such patient populations are high percentage of delta hepatitis (14.2%), unusual severity of the intoxication syndrome, protracted course with exacerbations (12.2%) and recurrences (8%), outcome being a chronic hepatitis (14.2%), slower normalization of biochemical indicators, persistently low ratio of AIAT activity in diluted and whole blood sera. The persistence of viral markers in drug addicts discharged from the hospital (68%) is fraught with danger of spreading viral hepatitis of prophylactic measures are not strictly observed.     

Low-temperature conductance measurements of surface states in HfO2–Si structures with different gate materials

Metal-oxide-semiconductor capacitors based on HfO₂ gate stack with different metal and metal compound gates (Al, TiN, NiSi and NiAlN) are compared to study the effect of the gate electrode material on the trap density at the insulator–semiconductor interface.C–V and G–ω measurements were made in the frequency range from 1 kHz to 1 MHz in the temperature range 180–300 K. From the maximum of the plot G/ω vs. ln(ω) the density of interface states was calculated, and from its position on the frequency axis the trap cross-section was found. Reducing temperature makes it possible to decrease leakage current through the dielectric and to investigate the states located closer to the band edge.The structures under study were shown to contain significant interface trap densities located near the valence band edge (around 2×10¹¹ cm⁻²eV⁻¹ for Al and up to (3.5–5.5)×10¹² cm⁻² eV⁻¹ for other gate materials). The peak in the surface state distribution is situated at 0.18 eV above the valence band edge for Al electrode. The capture cross-section is 5.8×10⁻¹⁷ cm² at 200 K for Al–HfO₂–Si structure.     

Universal probability-free prediction

We construct universal prediction systems in the spirit of Popper’s falsifiability and Kolmogorov complexity and randomness. These prediction systems do not depend on any statistical assumptions (but under the IID assumption they dominate, to within the usual accuracy, conformal prediction). Our constructions give rise to a theory of algorithmic complexity and randomness of time containing analogues of several notions and results of the classical theory of Kolmogorov complexity and randomness.     

Relative concentrations of carbon related defects in silicon

Irradiation induced defects in silicon are technologically important as they impact the electronic properties. Calculations based on density functional theory employing hybrid functionals have been previously used to investigate the structures and relative energies of defect clusters formed between vacancies, self-interstitials, carbon and oxygen atoms in silicon. In this study we employ a model to calculate the relative concentrations of carbon related defects in silicon. It is calculated that the carbon content has a significant impact upon the concentration of carbon-related defects. The C_iC_s defect is the most populous for all the conditions considered followed by the C_iO_iSi_I and the C_iO_i defects. C_iO_iSi_I and the C_iO_i become increasingly important for silicon with high carbon concentrations.     

Criterion of calibration for transductive confidence machine with limited feedback

This paper is concerned with the problem of on-line prediction in the situation where some data are unlabelled and can never be used for prediction, and even when the data are labelled, the labels may arrive with a delay. We construct a modification of randomised transductive confidence machine for this case and prove a necessary and sufficient condition for its predictions being calibrated, in the sense that in the long run they are wrong with a prespecified probability under the assumption that the data are generated independently by the same distribution. The condition for calibration turns out to be very weak: feedback should be given on more than a logarithmic fraction of steps.     

Charge trapping and interface states in hydrogen annealed HfO2–Si structures

Metal–oxide–semiconductor (MOS) capacitors based on HfO₂ gate stacks with Al and TiN gates are compared to study the effect of the gate electrode material to the properties of insulator–semiconductor interface. The structures under study were shown to contain interface trap densities of around 2 × 10¹¹ cm⁻² eV⁻¹ for Al gate and up to 5.5 × 10¹² cm⁻² eV⁻¹ for TiN gate. The peak in the surface state distribution was found at 0.19 eV above the valence band edge for Al electrode. The respective capture cross-section is 6 × 10⁻¹⁷ cm² at 200 K.The charge injection experiments have revealed the presence of hole traps inside the dielectric layer. The Al-gate structure contains traps with effective capture cross-section of 1 × 10⁻²⁰ cm², and there are two types of traps in the TiN-gate structure with cross-sections of 3.5 × 10⁻¹⁹ and 1 × 10⁻²⁰ cm². Trap concentration in the structure with Al electrode was considerably lower than in the structure with TiN electrode.