Стохастичні моделі в задачах штучного інтелекту

In this paper, we consider some properties of stochastic random matrices of large dimensions under conditions of independence of matrix elements or under conditions of independence of rows (columns). The main properties of stochastic random matrices spectrum are analyzed and the result of convergence to 0 is proved of almost all eigenvalues. Also, the application of these results to clustering problems and selection of the optimal number of clusters is considered. Note that the results obtained in this work are consistent with the Marchenko - Pastur theorem on the asymptotic distribution of eigenvalues of random matrices with independent elements. The results proved in this paper can be interpreted as a law of large numbers and will be used in the study of the asymptotic behavior of the maximum. Pages of the article in the issue: 53 - 57 Language of the article: UkrainianУ роботі розглянуто деякі властивості стохастичних матриць великих розмірностей за умов незалежності елементів матриці або за умов незалежності рядків (стовпців). Проаналізовано основні властивості спектру стохастичної матриці. Також розглянуто застосування даних результатів до задач кластеризації та вибору оптимального числа кластерів

Vibrational Sum-Frequency Spectroscopic Investigation of the Structure and Azimuthal Anisotropy of Propynyl-Terminated Si(111) Surfaces

Vibrational sum-frequency generation (VSFG) spectroscopy was used to investigate the orientation and azimuthal anisotropy of the C–H stretching modes for propynyl-terminated Si(111) surfaces, Si—C≡C—CH_3. VSFG spectra revealed symmetric and asymmetric C–H stretching modes in addition to a Fermi resonance mode resulting from the interaction of the asymmetric C–H bending overtone with the symmetric C–H stretching vibration. The polarization dependence of the C–H stretching modes was consistent with the propynyl groups oriented such that the Si—C≡C– bond is normal to the Si(111) surface. The azimuthal angle dependence of the resonant C–H stretching amplitude revealed no rotational anisotropy for the symmetric C–H stretching mode and a 3-fold rotational anisotropy for the asymmetric C–H stretching mode in registry with the 3-fold symmetric Si(111) substrate. The results are consistent with the expectation that the C–H stretching modes of a –CH_3 group are decoupled from the Si substrate due to a −C≡C– spacer. In contrast, the methyl-terminated Si(111) surface, Si–CH_3, was previously reported to have pronounced vibronic coupling of the methyl stretch modes to the electronic bath of bulk Si. Vacuum-annealing of propynyl-terminated Si(111) resulted in increased 3-fold azimuthal anisotropy for the symmetric stretch, suggesting that removal of propynyl groups from the surface upon annealing allowed the remaining propynyl groups to tilt away from the surface normal into one of three preferred directions toward the vacated neighbor sites

Vibrational Sum Frequency Spectroscopic Investigation of the Azimuthal Anisotropy and Rotational Dynamics of Methyl-Terminated Silicon(111) Surfaces

Polarization-selected vibrational sum frequency generation spectroscopy (SFG) has been used to investigate the molecular orientation of methyl groups on CH_(3)-terminated Si(111) surfaces. The symmetric and asymmetric C–H stretch modes of the surface-bound methyl group were observed by SFG. Both methyl stretches showed a pronounced azimuthal anisotropy of the 3-fold symmetry in registry with the signal from the Si(111) substrate, indicating that the propeller-like rotation of the methyl groups was hindered at room temperature. The difference in the SFG line widths for the CH_3 asymmetric stretch that was observed for different polarization combinations (SPS and PPP for SFG, visible, and IR) indicated that the rotation proceeded on a 1–2 ps time scale, as compared to the 100 fs rotational dephasing of a free methyl rotor at room temperature

Studying rare genetic syndromes as a method of investigating aetiology of normal variation in educationally relevant traits

No description supplie

Steric Hindrance of Photoswitching in Self-Assembled Monolayers of Azobenzene and Alkane Thiols

Surface-bound azobenzenes exhibit reversible photoswitching via trans–cis photoisomerization and have been proposed for a variety of applications such as photowritable optical media, liquid crystal displays, molecular electronics, and smart wetting surfaces. We report a novel synthetic route using simple protection chemistry to form azobenzene-functionalized SAMs on gold and present a mechanistic study of the molecular order, orientation, and conformation in these self-assembled monolayers (SAMs). We use vibrational sum-frequency generation (VSFG) to characterize their vibrational modes, molecular orientation, and photoisomerization kinetics. Trans–cis conformational change of azobenzene leads to the change in the orientation of the nitrile marker group detected by VSFG. Mixed SAMs of azobenzene and alkane thiols are used to investigate the steric hindrance effects. While 100% azobenzene SAMs do not exhibit photoisomerization due to tight packing, we observe reversible switching (>10 cycles) in mixed SAMs with only 34% and 50% of alkane thiol spacers

Annealing-Induced Changes in the Molecular Orientation of Poly-3-hexylthiophene at Buried Interfaces

The molecular organization at interfaces of organic semiconducting materials plays a crucial role in the performance of organic photovoltaics and field effect transistors. Vibrational sum-frequency generation (VSFG) was used to characterize the molecular orientation at interfaces of regioregular poly-3-hexylthiophene (rrP3HT). Polarization-selected VSFG spectra of the CC stretch of the thiophene ring yield the orientation of the conjugated backbone of P3HT, which is directly relevant to the electronic properties at the interface. The molecular orientation at buried polymer–substrate interfaces was compared for films spin-cast on SiO₂ and AlO_X substrates, before and after thermal annealing at 145 °C. On SiO₂, annealing results in the thiophene rings adopting a more edge-on orientation, tilting away from the surface plane by Δθ = +(3–10)°. In contrast, an opposite change is observed for films deposited on AlO_<i>x</i>, Δθ = −(3–26)°, where annealing leads to a more face-on orientation of the thiophene rings of the polymer. Although subtle, such orientational changes may significantly affect the electron transfer rates across interfaces and hence the overall photovoltaic efficiency