Bounded Representations of Interval and Proper Interval Graphs

Klavik et al. [arXiv:1207.6960] recently introduced a generalization of recognition called the bounded representation problem which we study for the classes of interval and proper interval graphs. The input gives a graph G and in addition for each vertex v two intervals L_v and R_v called bounds. We ask whether there exists a bounded representation in which each interval I_v has its left endpoint in L_v and its right endpoint in R_v. We show that the problem can be solved in linear time for interval graphs and in quadratic time for proper interval graphs. Robert's Theorem states that the classes of proper interval graphs and unit interval graphs are equal. Surprisingly the bounded representation problem is polynomially solvable for proper interval graphs and NP-complete for unit interval graphs [Klav\'{\i}k et al., arxiv:1207.6960]. So unless P = NP, the proper and unit interval representations behave very differently. The bounded representation problem belongs to a wider class of restricted representation problems. These problems are generalizations of the well-understood recognition problem, and they ask whether there exists a representation of G satisfying some additional constraints. The bounded representation problems generalize many of these problems

Evaluation of concentrated growth factor as an adjuvant on crestal bone levels around dental implants

Background: Dental implants have a long-term success rate when the osteointegration is maintained with minimal crestal bone loss yearly. The present study evaluates the crestal bone loss around Osseointegrated implants using a concentrated growth factor as an added factor to preserve the crestal bone levels.Methods: Total of 20 patients with a single edentulous site were included in the study and divided into test and control groups. Test group concentrated growth factor is placed along with implant, and the control group implant placed without concentrated growth factor. Soft tissue parameters like modified sulcus bleeding index (mSBI) and modified plaque index (mPI) were done three and nine-month after implant placement. Hard tissue parameters like crestal bone levels (CBL), bone density, and volume were done immediately after implant placement and nine-month of implant placement using cone-beam computed tomography (CBCT).Results: Intragroup comparison from baseline to nine-month in the test group showed a significant difference at nine months at different points compared to the control group in hard and soft tissue parameters. On intergroup comparison was statically insignificant.Conclusions: Concentrated growth factor aids in enhancing bone density and faster healing around dental implants, so it can be used as an advancement in personalized medicine and promoting osseous regeneration by increasing the density and volume of bone around the dental implants.

Selectivity estimation on set containment search

© Springer Nature Switzerland AG 2019. In this paper, we study the problem of selectivity estimation on set containment search. Given a query record Q and a record dataset S, we aim to accurately and efficiently estimate the selectivity of set containment search of query Q over S. The problem has many important applications in commercial fields and scientific studies. To the best of our knowledge, this is the first work to study this important problem. We first extend existing distinct value estimating techniques to solve this problem and develop an inverted list and G-KMV sketch based approach IL-GKMV. We analyse that the performance of IL-GKMV degrades with the increase of vocabulary size. Motivated by limitations of existing techniques and the inherent challenges of the problem, we resort to developing effective and efficient sampling approaches and propose an ordered trie structure based sampling approach named OT-Sampling. OT-Sampling partitions records based on element frequency and occurrence patterns and is significantly more accurate compared with simple random sampling method and IL-GKMV. To further enhance performance, a divide-and-conquer based sampling approach, DC-Sampling, is presented with an inclusion/exclusion prefix to explore the pruning opportunities. We theoretically analyse the proposed techniques regarding various accuracy estimators. Our comprehensive experiments on 6 real datasets verify the effectiveness and efficiency of our proposed techniques

Large Colloids in Cholesteric Liquid Crystals

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Process integration for purification and concentration of red cabbage (Brassica oleracea L.) anthocyanins

Multistage aqueous two phase extraction was carried out using polyethylene glycol (PEG) 4000/magnesium sulfate (14.8/10.3%, w/w) system. The phase forming polymer (PEG 4000) was successfully separated from anthocyanins employing organic–aqueous extraction. Different processes employed for the purification and concentration of anthocyanins were compared with one another. The highest concentration of anthocyanins (3123.45 mg/L and 43 °Brix) was obtained in case of integration of aqueous two phase extraction with forward osmosis. Non-enzymatic browning index (0.11) and degradation constant (0.21) were found to be lowest in case of the integrated process involving aqueous two phase extraction followed by forward osmosis when compared to other processes. Color density was found to increase from 0.6 to 14.56 and stability of anthocyanins (with respect to pH and temperature) was found to be more in case of integrated process (aqueous two phase extraction followed by forward osmosis)

Differential partitioning for purification of anthocyanins from Brassica oleracea L.

Aqueous two phase extraction was employed as an alternate method for the downstream processing of anthocyanins. Polyethylene glycol (PEG) 4000/magnesium sulphate (14.8%/10.3% w/w) was found to be the most suitable system. Tie line length of 32.61% and volume ratio of 0.73 have resulted in maximum partitioning of anthocyanins to the PEG-rich phase (yield – 98.19%) and sugars to the salt-rich phase (yield – 73.16%). Multistage aqueous two phase extraction resulted in an increase in removal of sugars (to about 96.5%) with 91.9% yield of anthocyanins. The phase forming polymer (PEG 4000) was successfully separated from anthocyanins employing organic–aqueous extraction resulting in 2.3 fold increase in the concentration of anthocyanins. High performance liquid chromatography (HPLC)–Mass spectroscopy (MS)/MS was carried out to confirm the structural stability of anthocyanins

Purification of anthocyanins from jamun (Syzygium cumini L.) employing adsorption

The present study deals with the downstream processing of anthocyanins from jamun (Syzygium cumini L.) in order to obtain anthocyanins in a purified form. Adsorption was carried out employing six different adsorbents and among these, Amberlite XAD7HP showed the highest adsorption capacity (1.07 mg/mL of adsorbent) and desorption ratio (87.62%). Aqueous acidified ethanol (above 40%, v/v) could effectively elute the anthocyanins. Adsorption results were found to correlate best using the Langmuir equation at all the temperatures studied. Second order kinetics model was found to be more appropriate to describe the adsorption of anthocyanins. The dynamic adsorption process parameters for the purification of anthocyanins using Amberlite XAD7HP arrived at were as follows; for adsorption: processing volume, flow rate and temperature were 6.5 BV, 1 mL/min and 25 ± 1 °C, respectively and for desorption: eluent volume and flow rate were 4 BV of acidified aqueous ethanol (40%, v/v) and 1 mL/min, respectively. Anthocyanins extract after purification was found to be free of sugars, which are the major cause for degradation of anthocyanins. After the purification by adsorption, the degradation constant and non-enzymatic browning index of anthocyanins were found to decrease from 0.93 to 0.19 and 0.45 to 0.29, respectively. The qualitative determination of anthocyanins after adsorption was evaluated by the physio-chemical characteristics and the structural stability was confirmed by HPLC–MS/MS