Improved Approximation Algorithm for Graph Burning on Trees

Given a graph $G=(V,E)$, the problem of \gb{} is to find a sequence of nodes from $V$, called burning sequence, in order to burn the whole graph. This is a discrete-step process, in each step an unburned vertex is selected as an agent to spread fire to its neighbors by marking it as a burnt node. A node that is burnt spreads the fire to its neighbors at the next consecutive step. The goal is to find the burning sequence of minimum length. The \gb{} problem is NP-Hard for general graphs and even for binary trees. A few approximation results are known, including a $3$-approximation algorithm for general graphs and a $2$- approximation algorithm for trees. In this paper, we propose an approximation algorithm for trees that produces a burning sequence of length at most $\lfloor 1.75b(T) \rfloor + 1$, where $b(T)$ is length of the optimal burning sequence, also called the burning number of the tree $T$. In other words, we achieve an approximation factor of $(\lfloor 1.75b(T) \rfloor + 1)/b(T)$

Programmed death ligand-1 expression on donor T cells drives graft-versus-host disease lethality

Programmed death ligand-1 (PD-L1) interaction with PD-1 induces T cell exhaustion and is a therapeutic target to enhance immune responses against cancer and chronic infections. In murine bone marrow transplant models, PD-L1 expression on host target tissues reduces the incidence of graft-versus-host disease (GVHD). PD-L1 is also expressed on T cells; however, it is unclear whether PD-L1 on this population influences immune function. Here, we examined the effects of PD-L1 modulation of T cell function in GVHD. In patients with severe GVHD, PD-L1 expression was increased on donor T cells. Compared with mice that received WT T cells, GVHD was reduced in animals that received T cells from Pdl1–/– donors. PD-L1–deficient T cells had reduced expression of gut homing receptors, diminished production of inflammatory cytokines, and enhanced rates of apoptosis. Moreover, multiple bioenergetic pathways, including aerobic glycolysis, oxidative phosphorylation, and fatty acid metabolism, were also reduced in T cells lacking PD-L1. Finally, the reduction of acute GVHD lethality in mice that received Pdl1–/– donor cells did not affect graft-versus-leukemia responses. These data demonstrate that PD-L1 selectively enhances T cell–mediated immune responses, suggesting a context-dependent function of the PD-1/PD-L1 axis, and suggest selective inhibition of PD-L1 on donor T cells as a potential strategy to prevent or ameliorate GVHD

Mining of protein contact maps for protein fold prediction

The three-dimensional structure of proteins is useful to carry out the biophysical and biochemical functions in a cell. Approaches to protein structure/fold prediction typically extract amino acid sequence features, and machine learning approaches are then applied to classification problem. Protein contact maps are two-dimensional representations of the contacts among the amino acid residues in the folded protein structure. This paper highlights the need for a systematic study of these contact networks. Mining of contact maps to derive features pertaining to fold information offers a new mechanism for fold discovery from the protein sequence via the contact maps. These ideas are explored in the structural class of all-alpha proteins to identify structural elements. A simple and computationally inexpensive algorithm based on triangle subdivision method is proposed to extract additional features from the contact map. The method successfully characterizes the off-diagonal interactions in the contact map for predicting specific 'folds'. The decision tree classification results show great promise in developing a new and simple tool for the challenging problem of fold prediction

A Sustainable Green Inventory System with Novel Eco-Friendly Demand Incorporating Partial Backlogging under Fuzziness

Environmentally friendly goods are market-oriented goods that create less environmental damage. Their manufacture is related to a product development process designed to consider the environmental consequences that might develop throughout their life cycle. In reality, the global demand for herbal goods is expanding since herbal products are manufactured from plant extracts such as leaves, roots, flowers, and seeds, among others, and cause less environmental destruction. This study introduces a novel, eco-friendly demand determined by the usage of herbal and chemical substances in products. In this context, companies producing these products are encouraged. Firms are interested in producing eco-friendly products while keeping an eye on carbon emissions. This paper presents a sustainable inventory model of non-instantaneous decaying items that follow this eco-friendly demand under partially backlogged shortages. In this study, emission releases due to inventory setup, degradation, and holding were estimated, as were carbon emissions under cap and tax policies. This approach invests in green and preservation technologies to reduce carbon emissions and deterioration. To address the imprecision of the model’s cost parameters, we converted them to Pythagorean fuzzy numbers. The optimum profit of the inventory model with carbon emissions is estimated by considering the time that the inventory level takes to reach zero and the replenishment time as decision variables. Numerical examples and a sensitivity analysis of significant parameters have been conducted to examine the effect of variation in the optimal inventory policy