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The most significant tool of mathematical chemistry is the numerical descriptor called topological index. Topological indices are extensively used in modelling of chemical compounds to analyse the studies on quantitative structure activity/property/toxicity relationships and combinatorial library virtual screening. In this work, an attempt is made in defining three novel descriptors, namely, neighborhood geometric-harmonic, harmonic-geometric, and neighborhood harmonic-geometric indices. Also, the aforementioned three indices along with the geometric-harmonic index are tested for physicochemical properties of octane isomers using linear regression models and computed for some carbon nanotubes.

In chemistry, graphs are commonly used to show the structure of chemical compounds, with nodes and edges representing the atom and bond types, respectively. Edge resolving set λe is an ordered subset of nodes of a graph C, in which each edge of C is distinctively determined by its distance vector to the nodes in λ. The cardinality of a minimum edge resolving set is called the edge metric dimension of C. An edge resolving set Le,f of C is fault-tolerant if λe,f∖b is also an edge resolving set, for every b in λe,f. Resolving set allows obtaining a unique representation for chemical structures. In particular, they were used in pharmaceutical research for discovering patterns common to a variety of drugs. In this paper, we determine the exact edge metric and fault-tolerant edge metric dimension of benzenoid tripod structure and proved that both parameters are constant.

The most abundant polycarbonates that are found in food are polysaccharides. A long chain of monosaccharide with glycosidic linkages forms polymeric carbohydrates. These carbohydrates with water in the process of hydrolysis produces sugar monosaccharides or oligosaccharides. The examples of polysaccharides include starch, galactogen, and glycogen. They contribute various applications mainly in food storage, pharmaceutical industry, and petroleum extraction. In this work, a polysaccharide known as guar gum is studied and also ten degree-based topological indices, namely, Zagreb indices, Randic index, general Randic index, forgotten index, ABC index, GA index, GH index, Sombor index, and SS index are computed. The chemical derivatives of guar gum such as HPG, CMG, and CMHPG are studied, and topological indices are determined. Finally, numerical and graphical comparison of all the above said ten indices are made for guar gum and its chemical derivatives.

Porous material such as metal-natural constructions and their particular partner metal-natural poly-hydra are made up of inorganic clusters with no saturation and exhibit great capability for utilization in the absorption of gas and ascending opening in optics and detecting biotechnology and hardware. Cuboctahedral bi-metallic structure is an often-quoted example of metal-natural polyhedra class. In this study, we have calculated the first and second Zagreb index, the augmented Zagreb index, and the inverse Randic, as well as general Randic index, the symmetric division, and harmonic index. We have also discussed these topological indices graphically and have found that the value of almost all indices goes higher and higher as the value of n goes higher.

In a molecular network, molecules are correlated with numerical values, which are referred to as topological indices. The chemical and physical properties of chemical substances can be determined using topological indices. Mathematicians frequently use topological indices to calculate the strain energy, melting point, boiling temperature, distortion, and stability of chemical compounds. Topological indices also serve as a connection between a compound’s biological activity and its physical properties. In this research paper, we have computed degree-based topological descriptors and polynomials to analyze the structure of antimony telluride.

Background Psychosis treatment guidelines recommend cognitive behaviour therapy (CBT) and family intervention (FI), for all patients with first episode psychosis (FEP), though guidance borrows heavily from literature in adults from high income countries. To our knowledge, there are few randomized controlled trials (RCTs) examining the comparative effect of these commonly endorsed psychosocial interventions in individuals with early psychosis from high-income countries and no such trials from low and middle-income countries (LMICs). The present study aims to confirm the clinical-efficacy and cost-effectiveness of delivering culturally adapted CBT (CaCBT) and culturally adapted FI (CulFI) to individuals with FEP in Pakistan. Method A multi-centre, three-arm RCT of CaCBT, CulFI, and treatment as usual (TAU) for individuals with FEP ( n  = 390), recruited from major centres across Pakistan. Reducing overall symptoms of FEP will be the primary outcome. Additional aims will include improving patient and carer outcomes and estimating the economic impact of delivering culturally appropriate psychosocial interventions in low-resource settings. This trial will assess the clinical-efficacy and cost-effectiveness of CaCBT and CulFI compared with TAU in improving patient (positive and negative symptoms of psychosis, general psychopathology, depressive symptoms, quality of life, cognition, general functioning, and insight) and carer related outcomes (carer experience, wellbeing, illness attitudes and symptoms of depression and anxiety). Conclusions A successful trial may inform the rapid scale up of these interventions not only in Pakistan but other low-resource settings, to improve clinical outcomes, social and occupational functioning, and quality of life in South Asian and other minority groups with FEP. Trial registration NCT05814913.

The ability to resolve the dynamics of matter on its native temporal and spatial scales constitutes a key challenge and convergent theme across chemistry, biology, and materials science. The last couple of decades have witnessed ultrafast electron diffraction (UED) emerge as one of the forefront techniques with the sensitivity to resolve atomic motions. Increasingly sophisticated UED instruments are being developed that are aimed at increasing the beam brightness in order to observe structural signatures, but so far they have been limited to low average current beams. Here, we present the technical design and capabilities of the HiRES (High Repetition-rate Electron Scattering) instrument, which blends relativistic electrons and high repetition rates to achieve orders of magnitude improvement in average beam current compared to the existing state-of-the-art instruments. The setup utilizes a novel electron source to deliver femtosecond duration electron pulses at up to MHz repetition rates for UED experiments. Instrument response function of sub-500 fs is demonstrated with < 100 fs time resolution targeted in future. We provide example cases of diffraction measurements on solid-state and gas-phase samples, including both micro- and nanodiffraction (featuring 100 nm beam size) modes, which showcase the potential of the instrument for novel UED experiments.

IntroductionLow and middle-income countries (LMICs) hold the majority of disease burden attributed to major depressive disorder (MDD). Despite this, there remains a substantial gap for access to evidence-based treatments for MDD in LMICs like Pakistan. Measurement-based care (MBC) incorporates systematic administration of validated outcome measures to guide treatment decision making and is considered a low-cost approach to optimise better clinical outcomes for individuals with MDD but there is a paucity of evidence on the efficacy of MBC in LMICs.ObjectivesThis protocol highlights a randomized trial which will include Pakistani outpatients with moderate to severe major depression.MethodsParticipants will be randomised to either MBC (guided by schedule), or standard treatment (guided by clinicians’ judgement), and will be prescribed with paroxetine (10–60mg/day) or mirtazapine (7.5–45mg/day) for 24 weeks. Outcomes will be evaluated by raters blind to study protocol and treatment.ResultsNational Bioethics Committee (NBC) of Pakistan has given full ethics approval. The trial is being conducted and reported as per recommendation of the CONSORT statement for RCTs.ConclusionsWith increasing evidence from high-income settings supporting the effectiveness of MBC for MDD, it is now necessary to explore its feasibility, utility. and efficacy in low-resource settings. The results of the proposed trial could inform the development of a low-cost and scalable approach to efficiently optimise outcomes for individuals with MDD in Pakistan.Disclosure of InterestNone Declared

Among the various ideas that appear while studying graph theory, which has gained much attraction especially in graph labeling, labeling of graphs gives mathematical models which value for a vast range of applications in high technology (data security, cryptography, various problems of coding theory, astronomy, data security, telecommunication networks, etc.). A graph label is a designation of graph elements, i.e., the edges and/or vertex of a group of numbers (natural numbers), and is called assignment or labeling. The vertex or edge labeling is related to their domain asset of vertices or edges. Likewise, for total labeling, we take the domain as vertices and edges both at the same time. The reflexive edge irregularity strength (res) is total labeling in which weights of edges are not the same for all edges and the weight of an edge is taken as the sum of the edge labels and the vertices associated with that edge. In the res, the vertices are labeled with nonnegative even integers while the edges are labeled with positive integers. We have to make the labels minimum, whether they are associated with vertices or edges. If such labeling exists, then it is called the res of H and is represented as sresH. In this paper, we have computed the res for the Cartesian product of path and cycle graph which is also known as generalizing prism.

Polycyclic aromatic hydrocarbons (PAHs) are compounds with two or more fused benzene rings produced by incomplete combustion of organic substances involved in natural and anthropogenic processes. Children are exposed to these compounds through inhalation, dietary ingestion, and, also, soil at the playground. It has been well established that PAHs have carcinogenic, mutagenic, and teratogenic effects. Considering possible health risks due to PAHs exposure among children, the present study was carried out in collaboration with the Pediatrics Department, King George's Medical University (KGMU), Lucknow, to determine its exposure in children by estimating blood PAHs levels. Due to the variable composition of PAHs mixtures emitted from different environmental sources, any single compound or metabolite may not be representative of all exposure conditions. For these reasons, the measurement of blood PAHs levels as a possible biomarker, especially of the EPA (Environmental Protection Agency, USA) priority list, has been proposed. Acenaphthylene, anthracene, phenanthrene, fluoranthene, naphthalene, pyrene, benzo(b)fluoranthene, benzo(k)fluoranthene, and benzo(a)pyrene were determined by HPLC-FD/UV. On the basis of the individual compound, the median (50th percentile) of naphthalene (19 ppb) was highest, however, benzo(a)pyrene (4.0 ppb) level was found to be lowest among all detected PAHs. The median level of total noncarcinogenic PAHs (113.55 ppb) was higher than the total carcinogenic PAHs (32.35 ppb) in blood samples of children. A significant correlation was found between period of time spent in the surrounding breathing zone of the cooking place and total noncarcinogenic PAHs (p < 0.05), while the blood carcinogenic PAHs level in children was found to be associated with lower status of their families (p < 0.05). It is speculated that there may be chances of health hazards through exposure to PAHs, those not yet declared hazardous and present at higher concentrations in the Indian environment. Further study with a larger sample size and accompanying environmental data is desired to validate the findings of this pilot study and strengthen the database of PAHs exposure in India.