Vladimir Ejov

Spring constant calibration techniques for next-generation fast-scanning atomic force microscope cantilevers.

As a recent technological development, high-speed atomic force microscopy (AFM) has provided unprecedented insights into dynamic processes on the nanoscale, and is capable of measuring material property variation over short timescales. Miniaturized cantilevers developed specifically for high-speed AFM differ greatly from standard cantilevers both in size and dynamic properties, and calibration of the cantilever spring constant is critical for accurate, quantitative measurement. This work investigates specifically, the calibration of these new-generation cantilevers for the first time. Existing techniques are tested and the challenges encountered are reported and the most effective approaches for calibrating fast-scanning cantilevers with high accuracy are identified, providing a resource for microscopists in this rapidly developing field. Not only do these cantilevers offer faster acquisition of images and force data but due to their high resonant frequencies (up to 2 MHz) they are also excellent mass sensors. Accurate measurement of deposited mass requires accurate calibration of the cantilever spring constant, therefore the results of this work will also be useful for mass-sensing applications.

Hamiltonian Cycles and Singularly Perturbed Markov Chains

We consider the Hamiltonian cycle problem embedded in a singularly perturbed Markov decision process. We also consider a functional on the space of deterministic policies of the process that consists of the (1,1)-entry of the fundamental matrices of the Markov chains induced by the same policies. We show that when the perturbation parameter, e, is less than or equal to 1/ N2, the Hamiltonian cycles of the directed graph are precisely the minimizers of our functional over the space of deterministic policies. In the process, we derive analytical expressions for the possibleN distinct values of the functional over the, typically, much larger space of deterministic policies.

Deterministic “Snakes and Ladders” Heuristic for the Hamiltonian cycle problem

We present a polynomial complexity, deterministic, heuristic for solving the Hamiltonian cycle problem (HCP) in an undirected graph of order

Markov Chains and Optimality of the Hamiltonian Cycle

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Refined MDP-Based Branch-and-Fix Algorithm for the Hamiltonian Cycle Problem

n. Although finding a Hamiltonian cycle is not theoretically guaranteed, we have observed that the heuristic is successful even in cases where such cycles are extremely rare, and it also performs very well on all HCP instances of large graphs listed on the TSPLIB web page. The heuristic owes its name to a visualisation of its iterations. All vertices of the graph are placed on a given circle in some order. The graph’s edges are classified as either snakes or ladders, with snakes forming arcs of the circle and ladders forming its chords. The heuristic strives to place exactly

Genetic theory for cubic graphs

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