Abelian repetitions in partial words

AbstractWe study abelian repetitions in partial words, or sequences that may contain some unknown positions or holes. First, we look at the avoidance of abelian pth powers in infinite partial words, where p>2, extending recent results regarding the case where p=2. We investigate, for a given p, the smallest alphabet size needed to construct an infinite partial word with finitely or infinitely many holes that avoids abelian pth powers. We construct in particular an infinite binary partial word with infinitely many holes that avoids 6th powers. Then we show, in a number of cases, that the number of abelian p-free partial words of length n with h holes over a given alphabet grows exponentially as n increases. Finally, we prove that we cannot avoid abelian pth powers under arbitrary insertion of holes in an infinite word

Avoiding abelian squares in partial words

AbstractErdős raised the question whether there exist infinite abelian square-free words over a given alphabet, that is, words in which no two adjacent subwords are permutations of each other. It can easily be checked that no such word exists over a three-letter alphabet. However, infinite abelian square-free words have been constructed over alphabets of sizes as small as four. In this paper, we investigate the problem of avoiding abelian squares in partial words, or sequences that may contain some holes. In particular, we give lower and upper bounds for the number of letters needed to construct infinite abelian square-free partial words with finitely or infinitely many holes. Several of our constructions are based on iterating morphisms. In the case of one hole, we prove that the minimal alphabet size is four, while in the case of more than one hole, we prove that it is five. We also investigate the number of partial words of length n with a fixed number of holes over a five-letter alphabet that avoid abelian squares and show that this number grows exponentially with n

Extrapolation and Correlation Using the Empirical Mode Decomposition: An Application to Economic Time Series

Senior Project submitted to The Division of Mathematics of Bard College

Effect of miR-21 on Apoptosis in Lung Cancer Cell Through Inhibiting the PI3K/ Akt/NF-κB Signaling Pathway in Vitro and in Vivo

Background/Aims: Lung cancer is one of the most common malignancies in the world. Apoptosis-stimulating protein of p53 (ASPP2), a tumorigenesis related protein, plays a critical role in the initiation and development of various types of cancers. However, the effect of ASPP2 on lung cancer remains unknown. The purpose of this study aims to investigate the mechanism of ASPP2 regulated by miR-21 in lung cancer in vitro and in vivo. Methods: In the study, migration and invasion assays, apoptosis assay, caspase activity assay, TUNEL staining, real time PCR and western blot were used to investigate the mechanism of ASPP2 regulated by miR-21 in lung cancer in vitro and in vivo. Results: We demonstrated that the miR-21 inhibitor induced apoptosis through inhibiting the PI3K/Akt/NF-κB signaling pathway in non-small cell lung carcinoma (NSCLC). Moreover, ASPP2 was directly targeted by miR-21 in NSCLC cells. Down-regulation of miR-21 suppressed cell migration and invasion, as well as the EMT signaling pathway in NSCLC cells. Furthermore, the miR-21 inhibitor induced cell apoptosis via the caspase dependent pathway in NSCLC cells. The miR-21 inhibitor enhanced caspase-3, 8, 9 activity in NSCLC cells. In addition, the caspase inhibitor significantly reduced the apoptosis induced by the miR-21 inhibitor in NSCLC cells. Conclusions: Our results revealed that the miR-21 inhibitor could induce apoptosis through inhibiting the PI3K/Akt/NF-κB signaling pathway in human NSCLC cells, and might serve as a therapeutic strategy to treat NSCLC

Signal Activity Detection for Fiber Optic Distributed Acoustic Sensing with Adaptive-Calculated Threshold

The key point on analyzing the data stream measured by fiber optic distributed acoustic sensing (DAS) is signal activity detection separating measured signals from environmental noise. The inability to calculate the threshold for signal activity detection accurately and efficiently without affecting the measured signals is a bottleneck problem for current methods. In this article, a novel signal activity detection method with the adaptive-calculated threshold is proposed to solve the problem. With the analysis of the time-varying random noise’s statistical commonality and the short-term energy (STE) of real-time data stream, the top range of the total STE distribution of the noise is found accurately for real-time data stream’s ascending STE, thus the adaptive dividing level of signals and noise is obtained as the threshold. Experiments are implemented with simulated database and urban field database with complex noise. The average detection accuracies of the two databases are 97.34% and 90.94% only consuming 0.0057 s for a data stream of 10 s, which demonstrates the proposed method is accurate and high efficiency for signal activity detection

Comparison of properties of traditional and accelerated carbonated solidified/stabilized contaminated soils

The investigation of the long-term performance of solidified/stabilized (S/S) contaminated soils was carried out in a trial site in southeast UK. The soils were exposed to the maximum natural weathering for four years and sampled at various depths in a controlled manner. The chemical properties (e.g., degree of carbonation (DOC), pH, electrical conductivity (EC)) and physical properties (e.g., moisture content (MC), liquid limit (LL), plastic limit (PL), plasticity index (PI)) of the samples untreated and treated with the traditional and accelerated carbonated S/S processes were analyzed. Their variations on the depths of the soils were also studied. The result showed that the broad geotechnical properties of the soils, manifested in their PIs, were related to the concentration of the water soluble ions and in particular the free calcium ions. The samples treated with the accelerated carbonation technology (ACT), and the untreated samples contained limited number of free calcium ions in solutions and consequently interacted with waters in a similar way. Compared with the traditional cement-based S/S technology, e.g., treatment with ordinary portland cement (OPC) or EnvirOceM, ACT caused the increase of the PI of the treated soil and made it more stable during long-term weathering. The PI values for the four soils ascended according to the order: the EnvirOceM soil, the OPC soil, the ACT soil, and the untreated soil while their pH and EC values descended according to the same order

Effects of Sulfidation, Magnetization, and Oxygenation on Azo Dye Reduction by Zerovalent Iron

Applications of zerovalent iron (ZVI) for water treatment under aerobic conditions include sequestration of metals (e.g., in acid mine drainage) and decolorization of dyes (in wastewaters from textile manufacturing). The processes responsible for contaminant removal can be a complex mixture of reduction, oxidation, sorption, and coprecipitation processes, which are further complicated by the dynamics of oxygen intrusion, mixing, and oxide precipitation. To better understand such systems, the removal of an azo dye (Orange I) by micron-sized granular ZVI at neutral pH was studied in open (aerobic) stirred batch reactors, by measuring the kinetics of Orange I decolorization and changes in “geochemical” properties (DO, Fe­(II), and Eh), with and without two treatments that might improve the long-term performance of this system: sulfidation by pretreatment with sulfide and magnetization by application of a weak magnetic field (WMF). The results show that the changes in solution chemistry are coupled to the dynamics of oxygen intrusion, which was modeled as analogous to dissolved oxygen sag curves. Both sulfidation and magnetization increased Orange I removal rates 2.4–71.8-fold, but there was little synergistic benefit to applying both enhancements together. Respike experiments showed that the enhancement from magnetization carries over from magnetization to sulfidation, but not the reverse

Discovery of ERD-3111 as a Potent and Orally Efficacious Estrogen Receptor PROTAC Degrader with Strong Antitumor Activity.

Estrogen receptor α (ERα) is a prime target for the treatment of ER-positive (ER+) breast cancer. Despite the development of several effective therapies targeting ERα signaling, clinical resistance remains a major challenge. In this study, we report the discovery of a new class of potent and orally bioavailable ERα degraders using the PROTAC technology, with ERD-3111 being the most promising compound. ERD-3111 exhibits potent in vitro degradation activity against ERα and demonstrates high oral bioavailability in mice, rats, and dogs. Oral administration of ERD-3111 effectively reduces the levels of wild-type and mutated ERα proteins in tumor tissues. ERD-3111 achieves tumor regression or complete tumor growth inhibition in the parental MCF-7 xenograft model with wild-type ER and two clinically relevant ESR1 mutated models in mice. ERD-3111 is a promising ERα degrader for further extensive evaluations for the treatment of ER+ breast cancer.http://deepblue.lib.umich.edu/bitstream/2027.42/177662/2/Discovery of ERD-3111.pdfPublished onlin