Strong inapproximability of the shortest reset word

The \v{C}ern\'y conjecture states that every $n$-state synchronizing automaton has a reset word of length at most $(n-1)^2$. We study the hardness of finding short reset words. It is known that the exact version of the problem, i.e., finding the shortest reset word, is NP-hard and coNP-hard, and complete for the DP class, and that approximating the length of the shortest reset word within a factor of $O(\log n)$ is NP-hard [Gerbush and Heeringa, CIAA'10], even for the binary alphabet [Berlinkov, DLT'13]. We significantly improve on these results by showing that, for every $\epsilon>0$, it is NP-hard to approximate the length of the shortest reset word within a factor of $n^{1-\epsilon}$. This is essentially tight since a simple $O(n)$-approximation algorithm exists.Comment: extended abstract to appear in MFCS 201

A Fast Algorithm Finding the Shortest Reset Words

In this paper we present a new fast algorithm finding minimal reset words for finite synchronizing automata. The problem is know to be computationally hard, and our algorithm is exponential. Yet, it is faster than the algorithms used so far and it works well in practice. The main idea is to use a bidirectional BFS and radix (Patricia) tries to store and compare resulted subsets. We give both theoretical and practical arguments showing that the branching factor is reduced efficiently. As a practical test we perform an experimental study of the length of the shortest reset word for random automata with $n$ states and 2 input letters. We follow Skvorsov and Tipikin, who have performed such a study using a SAT solver and considering automata up to $n=100$ states. With our algorithm we are able to consider much larger sample of automata with up to $n=300$ states. In particular, we obtain a new more precise estimation of the expected length of the shortest reset word $\approx 2.5\sqrt{n-5}$.Comment: COCOON 2013. The final publication is available at http://link.springer.com/chapter/10.1007%2F978-3-642-38768-5_1

Improvement in coronary endothelial function is independently associated with a slowed progression of coronary artery calcification in type 2 diabetes mellitus

Aims To examine a relationship between alterations of structure and function of the arterial wall in response to glucose-lowering therapy in type 2 diabetes mellitus (DM) after a 1-year follow-up (FU). Methods and results In DM (n = 22) and in healthy controls (n = 17), coronary artery calcification (CAC) was assessed with electron beam tomography and carotid intima-media thickness (IMT) with ultrasound, whereas coronary function was determined with positron emission tomography-measured myocardial blood flow (MBF) at rest, during cold pressor testing (CPT), and during adenosine stimulation at baseline and after FU. The decrease in plasma glucose in DM after a mean FU of 14 ± 1.9 months correlated with a lower progression of CAC and carotid IMT (r = 0.48, P ≤ 0.036 and r = 0.46, P ≤ 0.055) and with an improvement in endothelium-related ΔMBF to CPT and to adenosine (r = 0.46, P ≤ 0.038 and r = 0.36, P ≤ 0.056). After adjusting for metabolic parameters by multivariate analysis, the increases in ΔMBF to CPT after glucose-lowering treatment remained a statistically significant independent predictor of the progression of CAC (P ≤ 0.001 by one-way analysis of variance). Conclusion In DM, glucose-lowering treatment may beneficially affect structure and function of the vascular wall, whereas the observed improvement in endothelium-related coronary artery function may also mediate direct preventive effects on the progression of CA

Checking Whether an Automaton Is Monotonic Is NP-complete

An automaton is monotonic if its states can be arranged in a linear order that is preserved by the action of every letter. We prove that the problem of deciding whether a given automaton is monotonic is NP-complete. The same result is obtained for oriented automata, whose states can be arranged in a cyclic order. Moreover, both problems remain hard under the restriction to binary input alphabets.Comment: 13 pages, 4 figures. CIAA 2015. The final publication is available at http://link.springer.com/chapter/10.1007/978-3-319-22360-5_2

Double-Stranded RNA Attenuates the Barrier Function of Human Pulmonary Artery Endothelial Cells

Circulating RNA may result from excessive cell damage or acute viral infection and can interact with vascular endothelial cells. Despite the obvious clinical implications associated with the presence of circulating RNA, its pathological effects on endothelial cells and the governing molecular mechanisms are still not fully elucidated. We analyzed the effects of double stranded RNA on primary human pulmonary artery endothelial cells (hPAECs). The effect of natural and synthetic double-stranded RNA (dsRNA) on hPAECs was investigated using trans-endothelial electric resistance, molecule trafficking, calcium (Ca2+) homeostasis, gene expression and proliferation studies. Furthermore, the morphology and mechanical changes of the cells caused by synthetic dsRNA was followed by in-situ atomic force microscopy, by vascular-endothelial cadherin and F-actin staining. Our results indicated that exposure of hPAECs to synthetic dsRNA led to functional deficits. This was reflected by morphological and mechanical changes and an increase in the permeability of the endothelial monolayer. hPAECs treated with synthetic dsRNA accumulated in the G1 phase of the cell cycle. Additionally, the proliferation rate of the cells in the presence of synthetic dsRNA was significantly decreased. Furthermore, we found that natural and synthetic dsRNA modulated Ca2+ signaling in hPAECs by inhibiting the sarco-endoplasmic Ca2+-ATPase (SERCA) which is involved in the regulation of the intracellular Ca2+ homeostasis and thus cell growth. Even upon synthetic dsRNA stimulation silencing of SERCA3 preserved the endothelial monolayer integrity. Our data identify novel mechanisms by which dsRNA can disrupt endothelial barrier function and these may be relevant in inflammatory processes

Lung vasodilatory response to inhaled iloprost in experimental pulmonary hypertension: amplification by different type phosphodiesterase inhibitors

Inhaled prostanoids and phosphodiesterase (PDE) inhibitors have been suggested for treatment of severe pulmonary hypertension. In catheterized rabbits with acute pulmonary hypertension induced by continuous infusion of the stable thromboxane analogue U46619, we asked whether sildenafil (PDE1/5/6 inhibitor), motapizone (PDE3 inhibitor) or 8-Methoxymethyl-IBMX (PDE1 inhibitor) synergize with inhaled iloprost. Inhalation of iloprost caused a transient pulmonary artery pressure decline, levelling off within <20 min, without significant changes in blood gases or systemic hemodynamics. Infusion of 8-Methoxymethyl-IBMX, motapizone and sildenafil caused each a dose-dependent decrease in pulmonary artery pressure, with sildenafil possessing the highest efficacy and at the same time selectivity for the pulmonary circulation. When combining a per se ineffective dose of each PDE inhibitor (200 μg/kg × min 8-Methoxymethyl-IBMX, 1 μg/kg × min sildenafil, 5 μg/kg × min motapizone) with subsequent iloprost nebulization, marked amplification of the prostanoid induced pulmonary vasodilatory response was noted and the area under the curve of P(PA )reduction was nearly threefold increased with all approaches, as compared to sole iloprost administration. Further amplification was achieved with the combination of inhaled iloprost with sildenafil plus motapizone, but not with sildenafil plus 8MM-IBMX. Systemic hemodynamics and gas exchange were not altered for all combinations. We conclude that co-administration of minute systemic doses of selective PDE inhibitors with inhaled iloprost markedly enhances and prolongs the pulmonary vasodilatory response to inhaled iloprost, with maintenance of pulmonary selectivity and ventilation perfusion matching. The prominent effect of sildenafil may be operative via both PDE1 and PDE5, and is further enhanced by co-application of a PDE3 inhibitor

Algebraic synchronization criterion and computing reset words

We refine a uniform algebraic approach for deriving upper bounds on reset thresholds of synchronizing automata. We express the condition that an automaton is synchronizing in terms of linear algebra, and obtain upper bounds for the reset thresholds of automata with a short word of a small rank. The results are applied to make several improvements in the area. We improve the best general upper bound for reset thresholds of finite prefix codes (Huffman codes): we show that an $n$-state synchronizing decoder has a reset word of length at most $O(n \log^3 n)$. In addition to that, we prove that the expected reset threshold of a uniformly random synchronizing binary $n$-state decoder is at most $O(n \log n)$. We also show that for any non-unary alphabet there exist decoders whose reset threshold is in $\varTheta(n)$. We prove the \v{C}ern\'{y} conjecture for $n$-state automata with a letter of rank at most $\sqrt[3]{6n-6}$. In another corollary, based on the recent results of Nicaud, we show that the probability that the \v{C}ern\'y conjecture does not hold for a random synchronizing binary automaton is exponentially small in terms of the number of states, and also that the expected value of the reset threshold of an $n$-state random synchronizing binary automaton is at most $n^{3/2+o(1)}$. Moreover, reset words of lengths within all of our bounds are computable in polynomial time. We present suitable algorithms for this task for various classes of automata, such as (quasi-)one-cluster and (quasi-)Eulerian automata, for which our results can be applied.Comment: 18 pages, 2 figure