Formal proofs of operator identities by a single formal computation

A formal computation proving a new operator identity from known ones is, in principle, restricted by domains and codomains of linear operators involved, since not any two operators can be added or composed. Algebraically, identities can be modelled by noncommutative polynomials and such a formal computation proves that the polynomial corresponding to the new identity lies in the ideal generated by the polynomials corresponding to the known identities. In order to prove an operator identity, however, just proving membership of the polynomial in the ideal is not enough, since the ring of noncommutative polynomials ignores domains and codomains. We show that it suffices to additionally verify compatibility of this polynomial and of the generators of the ideal with the labelled quiver that encodes which polynomials can be realized as linear operators. Then, for every consistent representation of such a quiver in a linear category, there exists a computation in the category that proves the corresponding instance of the identity. Moreover, by assigning the same label to several edges of the quiver, the algebraic framework developed allows to model different versions of an operator by the same indeterminate in the noncommutative polynomials.     

Perturbative manifolds and the Noether generators of nth-order Poisson equations

A manifold that contains small perturbations will induce a perturbed partial differential equation. The partial differential equation that we select is the Poisson equation – in order to explore the interplay between the geometry of the manifold and the perturbations. Specifically, we show how the problem of symmetry determination, for higher-order perturbations, can be elegantly expressed via geometric conditions.     

Chemical characterisation of bioactive compounds in Medicago sativa growing in the desert of Oman

Medicago sativa Linn growing in Omani desert were chemically characterised using flame photometry, inductively coupled plasma, gas chromatography–mass spectrometry and high performance liquid chromatographic (HPLC) analysis. HPLC analyses were performed to determine the phenolics and flavonoids present in M. sativa. The major compounds detected in M. sativa leaves were protchaechenic acid (3.22%), hydroxyl benzoic acid (1.05%), β-Phenyl caffate (0.97%) and kaempherol (0.89%). Pterostilbene, a cholesterol-lowering compound, was detected in M. sativa.     

Chemical Validation of Mycobacterium tuberculosis Phosphopantetheine Adenylyltransferase Using Fragment Linking and CRISPR Interference**

The coenzyme A (CoA) biosynthesis pathway has attracted attention as a potential target for much-needed novel antimicrobial drugs, including for the treatment of tuberculosis (TB), the lethal disease caused by Mycobacterium tuberculosis (Mtb). Seeking to identify inhibitors of Mtb phosphopantetheine adenylyltransferase (MtbPPAT), the enzyme that catalyses the penultimate step in CoA biosynthesis, we performed a fragment screen. In doing so, we discovered three series of fragments that occupy distinct regions of the MtbPPAT active site, presenting a unique opportunity for fragment linking. Here we show how, guided by X-ray crystal structures, we could link weakly-binding fragments to produce an active site binder with a K_D <20 μM and on-target anti-Mtb activity, as demonstrated using CRISPR interference. This study represents a big step toward validating MtbPPAT as a potential drug target and designing a MtbPPAT-targeting anti-TB drug.     

Kinetic,isotherm, and mechanism investigations of the removal of nitrate and nitrite from water by the synthesized hydrotalcite Mg–Al

Research on Chemical Intermediates - The objective of this work is to test the effectiveness of hydrotalcite as an adsorbent for the retention of nitrate and nitrite ions and to study the influence...     

Survey of Phenolic Acids,Flavonoids and In Vitro Antioxidant Potency Between Fig Peels and Pulps: Chemical and Chemometric Approach

In the present study, chromatic coordinates, phenolic acids, flavonoids and antioxidant capacity assessed by 1,1-diphenyl-2-picrylhydrazyl (DPPH), 2,2′-azino-bis (3-ethylbenzothiazoline-6-sulfonate (ABTS) and lipid peroxidation inhibition capacity (LPIC) essays and their relative IC50 were investigated in 25 fig cultivars growing in Morocco. The aims of this study were to determine (i) the variation in these compounds among light and dark-colored cultivars, (ii) their partitioning between fruit peel and pulp and (iii) to display network connections among these variables. Twelve phenolic compounds (PCs) were isolated in peel extract versus eight in pulp samples. Anthocyanins, mainly cyanidin-3,5-diglucoside and cyanidin-3-O-rutinoside, were the predominant compounds in peels, where the mean concentrations were 75.90 ± 18.76 and 77.97 ± 18.95 µg/g dw, respectively. On the other hand, (−)-epicatechin and cyanidin-3-O-rutinoside were the major compounds in the pulp extracts, where the mean values were 5.23 ± 4.03 and 9.01 ± 5.67 µg/g dw, respectively. A two-dimensional hierarchically clustered heatmap was applied to the dataset to explore correlations in the dataset and similarities between cultivars, without dimensionality reduction. Results showed that anthocyanins, particularly pelargonidin-3-O-rutinoside, cyanidin-3,5-diglucoside and cyanidin-3-O-rutinoside, were the main contributors to the peels’ free radical scavenging capacity. This capacity was particularly higher in the peel of dark-colored figs compared to the fruit pulp. The local cultivar “INRA 1301” showed the most promising phenolic profile due to its very high levels of almost all detected PCs, especially (−)-epicatechin, quercetin-3-O-rutinoside, quercetin-3-O-glucoside, cyanidine-3,5-diglucoside, cyanidine-3-O-rutinoside and pelargonidin-3-O-rutinoside (54.66, 141.08, 35.48, 494.08, 478.66, 12.56 µg/g dw, respectively). Having the darkest figs in the collection (L* = 25.72, c* = 22.09 and h° = 20.99), this cultivar has also combined promising IC50 values, which were of 19.85, 40.58 and 124.78 µg/mL for DPPH, ABTS and LPIC essays, respectively.     

Formulation of Piperine–Chitosan-Coated Liposomes: Characterization and In Vitro Cytotoxic Evaluation

The present research work is designed to prepare and evaluate piperine liposomes and piperine–chitosan-coated liposomes for oral delivery. Piperine (PPN) is a water-insoluble bioactive compound used for different diseases. The prepared formulations were evaluated for physicochemical study, mucoadhesive study, permeation study and in vitro cytotoxic study using the MCF7 breast cancer cell line. Piperine-loaded liposomes (PLF) were prepared by the thin-film evaporation method. The selected liposomes were coated with chitosan (PLFC) by electrostatic deposition to enhance the mucoadhesive property and in vitro therapeutic efficacy. Based on the findings of the study, the prepared PPN liposomes (PLF3) and chitosan coated PPN liposomes (PLF3C1) showed a nanometric size range of 165.7 ± 7.4 to 243.4 ± 7.5, a narrow polydispersity index (>0.3) and zeta potential (−7.1 to 29.8 mV). The average encapsulation efficiency was found to be between 60 and 80% for all prepared formulations. The drug release and permeation study profile showed biphasic release behavior and enhanced PPN permeation. The in vitro antioxidant study results showed a comparable antioxidant activity with pure PPN. The anticancer study depicted that the cell viability assay of tested PLF3C2 has significantly (p < 0.001)) reduced the IC₅₀ when compared with pure PPN. The study revealed that oral chitosan-coated liposomes are a promising delivery system for the PPN and can increase the therapeutic efficacy against the breast cancer cell line.     

An exact algorithm for the sequential ordering problem and its application to switching energy minimization in compilers

This article presents an exact algorithm for the precedence-constrained traveling salesman problem, which is also known as the sequential ordering problem. This NP-hard problem has applications in various domains, including operational research and compilers. In this article, the problem is presented and solved in the context of minimizing switching energy in compilers. Most previous work on minimizing switching energy in the compiler domain has been limited to simple heuristics that are not guaranteed to give an optimal solution. In this work, we present an exact algorithm for solving the switching energy minimization problem using a branch-and-bound approach. The proposed algorithm is simple and intuitive, yet powerful. It is the first exact algorithm for the switching energy problem that is shown to solve real instances of the problem within a few seconds per instance. Compared to previous work in the operational research domain, the proposed algorithm is believed to be the most powerful exact algorithm that does not require a linear programming formulation. The proposed algorithm is experimentally evaluated using instances taken from a production compiler. The results show that with a time limit of 10 ms per node, the proposed algorithm optimally solves 99.8 % of the instances. It optimally solves instances with up to 598 nodes within a few seconds. The resulting switching cost is 16 % less than that produced without energy awareness and 5 % less than that produced by a commonly used heuristic.