We present a new approach for the approximate K-nearest neighbor search based on navigable small world graphs with controllable hierarchy (Hierarchical NSW, HNSW). The proposed solution is fully graph-based, without any need for additional search structures, which are typically used at the coarse search stage of the most proximity graph techniques. Hierarchical NSW incrementally builds a multi-layer structure consisting from hierarchical set of proximity graphs (layers) for nested subsets of the stored elements. The maximum layer in which an element is present is selected randomly with an exponentially decaying probability distribution. This allows producing graphs similar to the previously studied Navigable Small World (NSW) structures while additionally having the links separated by their characteristic distance scales. Starting search from the upper layer together with utilizing the scale separation boosts the performance compared to NSW and allows a logarithmic complexity scaling. Additional employment of a heuristic for selecting proximity graph neighbors significantly increases performance at high recall and in case of highly clustered data. Performance evaluation has demonstrated that the proposed general metric space search index is able to strongly outperform previous opensource state-of-the-art vector-only approaches. Similarity of the algorithm to the skip list structure allows straightforward balanced distributed implementation.

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Second harmonic generation and two-photon luminescence from colloidal gold nanoparticles in the 980–1300 nm wavelength range of exciting femtosecond radiation were investigated experimentally. The measured polarization and spectral characteristics of the second harmonic and two-photon luminescence demonstrate that the observed nonlinear optical signal is determined by the dimers constituting several percent of the total nanoparticle number.

We demonstrated experimentally the formation of monoenergetic beams of accelerated electrons by focusing femtosecond laser radiation with an intensity of 2 × 10 17 W/cm 2 onto the edge of an aluminum foil. The electrons had energy distributions peaking in the 0.2-0.8 MeV range with energy spread less than 20%. The acceleration mechanism related to the generation of a plasma wave as a result of self-modulation instability of a laser pulse in a dense plasma formed by a prepulse (arriving 12 ns before the main pulse) is considered. One-dimensional and two-dimensional Particle in Cell (PIC) simulations of the laser-plasma interaction showed that effective excitation of a plasma wave as well as trapping and acceleration of an electron beam with an energy on the order of 1 MeV may occur in the presence of sharp gradients in plasma density and in the temporal shape of the pulse.