On the maximal number of cubic subwords in a string

We investigate the problem of the maximum number of cubic subwords (of the form $www$) in a given word. We also consider square subwords (of the form $ww$). The problem of the maximum number of squares in a word is not well understood. Several new results related to this problem are produced in the paper. We consider two simple problems related to the maximum number of subwords which are squares or which are highly repetitive; then we provide a nontrivial estimation for the number of cubes. We show that the maximum number of squares $xx$ such that $x$ is not a primitive word (nonprimitive squares) in a word of length $n$ is exactly $\lfloor \frac{n}{2}\rfloor - 1$, and the maximum number of subwords of the form $x^k$, for $k\ge 3$, is exactly $n-2$. In particular, the maximum number of cubes in a word is not greater than $n-2$ either. Using very technical properties of occurrences of cubes, we improve this bound significantly. We show that the maximum number of cubes in a word of length $n$ is between $(1/2)n$ and $(4/5)n$. (In particular, we improve the lower bound from the conference version of the paper.)Comment: 14 page

Damage detection and quantification in composite beam structure using strain energy and vibration data

10.1088/1742-6596/842/1/012027Journal of Physics: Conference Series84211202

Ischemic Preconditioning Improves Microvascular Endothelial Function in Remote Vasculature by Enhanced Prostacyclin Production.

BACKGROUND The mechanisms underlying the effect of preconditioning on remote microvasculature remains undisclosed. The primary objective was to document the remote effect of ischemic preconditioning on microvascular function in humans. The secondary objective was to test if exercise also induces remote microvascular effects. METHODS AND RESULTS A total of 12 healthy young men and women participated in 2 experimental days in a random counterbalanced order. On one day the participants underwent 4×5 minutes of forearm ischemic preconditioning, and on the other day they completed 4×5 minutes of hand-grip exercise. On both days, catheters were placed in the brachial and femoral artery and vein for infusion of acetylcholine, sodium nitroprusside, and epoprostenol. Vascular conductance was calculated from blood flow measurements with ultrasound Doppler and arterial and venous blood pressures. Ischemic preconditioning enhanced (P<0.05) the remote vasodilator response to intra-arterial acetylcholine in the leg at 5 and 90 minutes after application. The enhanced response was associated with a 6-fold increase (P<0.05) in femoral venous plasma prostacyclin levels and with a transient increase (P<0.05) in arterial plasma levels of brain-derived neurotrophic factor and vascular endothelial growth factor. In contrast, hand-grip exercise did not influence remote microvascular function. CONCLUSIONS These findings demonstrate that ischemic preconditioning of the forearm improves remote microvascular endothelial function and suggest that one of the underlying mechanisms is a humoral-mediated potentiation of prostacyclin formation

Compressed Membership for NFA (DFA) with Compressed Labels is in NP (P)

In this paper, a compressed membership problem for finite automata, both deterministic and non-deterministic, with compressed transition labels is studied. The compression is represented by straight-line programs (SLPs), i.e. context-free grammars generating exactly one string. A novel technique of dealing with SLPs is introduced: the SLPs are recompressed, so that substrings of the input text are encoded in SLPs labelling the transitions of the NFA (DFA) in the same way, as in the SLP representing the input text. To this end, the SLPs are locally decompressed and then recompressed in a uniform way. Furthermore, such recompression induces only small changes in the automaton, in particular, the size of the automaton remains polynomial. Using this technique it is shown that the compressed membership for NFA with compressed labels is in NP, thus confirming the conjecture of Plandowski and Rytter and extending the partial result of Lohrey and Mathissen; as it is already known, that this problem is NP-hard, we settle its exact computational complexity. Moreover, the same technique applied to the compressed membership for DFA with compressed labels yields that this problem is in P; for this problem, only trivial upper-bound PSPACE was known

Fingerprints in Compressed Strings

The Karp-Rabin fingerprint of a string is a type of hash value that due to its strong properties has been used in many string algorithms. In this paper we show how to construct a data structure for a string S of size N compressed by a context-free grammar of size n that answers fingerprint queries. That is, given indices i and j, the answer to a query is the fingerprint of the substring S[i,j]. We present the first O(n) space data structures that answer fingerprint queries without decompressing any characters. For Straight Line Programs (SLP) we get O(logN) query time, and for Linear SLPs (an SLP derivative that captures LZ78 compression and its variations) we get O(log log N) query time. Hence, our data structures has the same time and space complexity as for random access in SLPs. We utilize the fingerprint data structures to solve the longest common extension problem in query time O(log N log l) and O(log l log log l + log log N) for SLPs and Linear SLPs, respectively. Here, l denotes the length of the LCE