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The fields of succinct data structures and compressed text indexing have seen quite a bit of progress over the last 15 years. An important achievement, primarily using techniques based on the Burrows-Wheeler Transform (BWT), was obtaining the full functionality of suffix tree in the optimal number of bits. A crucial property that allows the use of BWT for(More)
Given a string X[1, n] and a position k ∈ [1, n], the Shortest Unique Substring of X covering k, denoted by S k , is a substring X[i, j] of X which satisfies the following conditions: (i) i ≤ k ≤ j, (ii) i is the only position where there is an occurrence of X[i, j], and (iii) j − i is minimized. The best-known algorithm [Hon et al., ISAAC 2015] can find S(More)
J o u r n a l o f P r o b a b i l i t y Electron. Abstract The paper deals with convergence of solutions of a class of stochastic differential equations driven by infinite-dimensional semimartingales. The infinite-dimensional semimartingales considered in the paper are Hilbert-space valued. The theorems presented generalize the convergence result obtained(More)
Let H be a separable Banach space. We considered the sequence of stochastic integrals {X n− · Y n } where {Y n } is a sequence of infinite dimesnional H # semimartingales and X n are H valued cadlag processes. Assuming that {(X n , Y n)} satisfies large deviation principle, a uniform exponential tightness condition is described under which large deviation(More)
Two equal-length strings S and S are a parameterized-match (p-match) iff there exists a one-to-one function that renames the characters in S to those in S. Let P be a collection of d patterns of total length n characters that are chosen from an alphabet Σ of cardinality σ. The task is to index P such that we can support the following operations: search(T):(More)
Interface modification for control of ultrafast magnetic properties using low-dose focused ion beam irradiation is demonstrated for bilayers of two technologically important materials: Ni81Fe19 and Pt. Magnetization dynamics were studied using an all-optical time-resolved magneto-optical Kerr microscopy method. Magnetization relaxation, precession, damping(More)