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A set D of vertices in a graph G is a dominating set of G if every vertex outside D is adjacent in G to some vertex in D. A set D of vertices in G is a semitotal dominating set of G if D is a dominating set of G and every vertex in D is within distance 2 from another vertex of D. Given a graph G and a positive integer k, the semitotal domination problem is to decide whether G has a semitotal dominating set of cardinality at most k. The semitotal domination problem is known to be NP-complete for chordal graphs and bipartite graphs as shown in [M.A. Henning and A. Pandey, Algorithmic aspects of semitotal domination in graphs, Theoret. Comput. Sci. 766 (2019) 46–57]. In this paper, we present a linear time algorithm to compute a minimum semitotal dominating set in block graphs. On the other hand, we show that the semitotal domination problem remains NP-complete for undirected path graphs.

The catalytic activity of a Ru complex 1, bearing a fused π‐conjugated imidazo[1,2–a][1,8]naphthyridine‐based mesoionic carbene (MIC) ligand, is examined for the oxidation of primary amines. Complex 1 affords nitrile or imine depending on the nature of the terminal oxidants and solvents used in the reactions. Primary amines are converted to nitriles using NaIO4 in EtOAc/H2O mixture, whereas imines are obtained under O2 balloon pressure in toluene. A variety of nitriles and imines are accessed with high yields and selectivity. A set of control experiments, reaction profiles, and kinetic studies are undertaken to disclose the mechanistic details for nitrile and imine formation. The catalytic reactions illustrate a subtle dependency on the choice of oxidants and solvents in the oxidation of primary amines. [ABSTRACT FROM AUTHOR]

In a graph G, a vertex is said to 2-step dominate itself and all the vertices which are at distance 2 from it in G. A set D of vertices in G is called a hop dominating set of G if every vertex outside D is 2-step dominated by some vertex of D. Given a graph G and a positive integer k, the hop domination problem is to decide whether G has a hop dominating set of cardinality at most k. The hop domination problem is known to be NP-complete for bipartite graphs. In this paper, we design a linear time algorithm for computing a minimum hop dominating set in chordal bipartite graphs. [ABSTRACT FROM AUTHOR]

The purpose of this study was to determine the effects of botulinum neurotoxin type A (BoNT‐A) on vastus lateralis:vastus medialis (VL:VM) muscle balance, patellar tracking, and pain in patients with chronic patellofemoral (PF) pain. We recruited 13 participants (9 females, 4 males) with recalcitrant PF pain who underwent ultrasound‐guided BoNT‐A injections into the distal third of the VL muscle, followed by a 6‐week home exercise program to strengthen their VM muscle. We imaged the participants in a C‐arm computed tomography (CT) scanner before and after the intervention. We calculated VL:VM ratios from CT images from a supine, nonweight‐bearing condition. We obtained patellar tilt and bisect offset values from CT images from an upright, weight‐bearing condition. We recorded functional pain scores before, immediately after, and 2–4 years after the intervention. We classified the participants into normal tracking and maltracking groups based on their patellar tilt and bisect offset values. BoNT‐A with home exercise reduced VL:VM ratio (18%; p < 0.001), patellar tilt (19%; p = 0.020), and bisect offset (5%; p = 0.025). Four participants classified as maltrackers before the intervention transitioned to normal tracking after the intervention. Functional pain scores improved immediately after the intervention (13%, p < 0.001) and remained improved at 2‐year follow‐up (12%, p = 0.011). Statement of Clinical Significance: This study provides new evidence in support of BoNT‐A for treatment of PF pain. Classification of patients under weight‐bearing conditions may identify individuals who will most benefit from a BoNT‐A treatment. [ABSTRACT FROM AUTHOR]

Background: To evaluate the treatment cost and cost effectiveness of a risk‐stratified therapy to treat pediatric acute lymphoblastic leukemia (ALL) in India. Methods: The cost of total treatment duration was calculated for a retrospective cohort of ALL children treated at a tertiary care facility. Children were risk stratified into standard (SR), intermediate (IR) and high (HR) for B‐cell precursor ALL, and T‐ALL. Cost of therapy was obtained from the hospital electronic billing systems and details of outpatient (OP) and inpatient (IP) from electronic medical records. Cost effectiveness was calculated in disability‐adjusted life years. Results: One hundred and forty five patients, SR (50), IR (36), HR (39), and T‐ALL (20) were analyzed. Median cost of the entire treatment for SR, IR, HR, and T‐ALL was found to be $3900, $5500, $7400, and $8700, respectively, with chemotherapy contributing to 25%–35% of total cost. Out‐patient costs were significantly lower for SR (p < 0.0001). OP costs were higher than in‐patient costs for SR and IR, while in‐patient costs were higher in T‐ALL. Costs for non‐therapy admissions were significantly higher in HR and T‐ALL (p < 0.0001), representing over 50% of costs of in‐patient therapy. HR and T‐ALL also had longer durations of non‐therapy admissions. Based on WHO‐CHOICE guidelines, the risk‐stratified approach was very cost effective for all categories of patients. Conclusions: Risk‐stratified approach to treat childhood ALL is very cost‐effective for all categories in our setting. The cost for SR and IR patients is significantly reduced through decreased IP admissions for both, chemotherapy and non‐chemotherapy reasons. [ABSTRACT FROM AUTHOR]