An O(n log n)-Time Algorithm for the k-Center Problem in Trees

We consider a classical k-center problem in trees. Let T be a tree of n vertices and every vertex has a nonnegative weight. The problem is to find k centers on the edges of T such that the maximum weighted distance from all vertices to their closest centers is minimized. Megiddo and Tamir (SIAM J. Comput., 1983) gave an algorithm that can solve the problem in O(n log^2 n) time by using Cole\u27s parametric search. Since then it has been open for over three decades whether the problem can be solved in O(n log n) time. In this paper, we present an O(n log n) time algorithm for the problem and thus settle the open problem affirmatively

Commercial Credit and Corporate Productivity

As an important form of informal finance, commercial credit is widely used among enterprises. Does commercial credit promote the total factor productivity of enterprises? According to the theoretical literature and the reality, using the large sample data of Chinese industrial enterprises, the paper empirically tests the impact of commercial credit on the productivity of enterprises from three aspects: the provision and acquisition of commercial credit and the net commercial credit. The study finds that the provision of commercial credit reduces the productivity level of enterprises; the acquisition of commercial credit fails to promote productivity; while the net commercial credit as a short-term financial buffer for enterprises can alleviate the financing constraints, faced by enterprises, especially private enterprises, which help to increase their productivity levels . In addition, the study found that the higher the marketization process in the region, the more favorable the commercial credit is to the improvement of the production efficiency of private enterprises

Differential molecular programs of cutaneous anaplastic large cell lymphoma and CD30-positive transformed mycosis fungoides

BackgroundDiscriminating between cutaneous anaplastic large cell lymphoma (cALCL) and CD30-positive transformed mycosis fungoides (CD30+ TMF) is challenging, particularly when they arise in the context of pre-existing mycosis fungoides. The development of molecular diagnostic tools was hampered by the rarity of both diseases and the limited understanding of their pathogenesis.MethodsIn this study, we established a cohort comprising 25 cALCL cases and 25 CD30+ TMF cases, with transcriptomic data obtained from 31 samples. We compared the clinicopathological information and investigated the gene expression profiling between these two entities. Furthermore, we developed an immunohistochemistry (IHC) algorithm to differentiate these two entities clinically.ResultsOur investigation revealed distinct clinicopathological features and unique gene expression programs associated with cALCL and CD30+ TMF. cALCL and CD30+ TMF displayed marked differences in gene expression patterns. Notably, CD30+ TMF demonstrated enrichment of T cell receptor signaling pathways and an exhausted T cell phenotype, accompanied by infiltration of B cells, dendritic cells, and neurons. In contrast, cALCL cells expressed high levels of HLA class II genes, polarized towards a Th17 phenotype, and exhibited neutrophil infiltration. An IHC algorithm with BATF3 and TCF7 staining emerged as potential diagnostic markers for identifying these two entities.ConclusionsOur findings provide valuable insights into the differential molecular signatures associated with cALCL and CD30+ TMF, which contribute to their distinct clinicopathological behaviors. An appropriate IHC algorithm could be used as a potential diagnostic tool

Reusability based on Life Cycle Sustainability Assessment: Case Study on WEEE

AbstractReuse is one of the key strategies of Waste Electrical and Electronic Equipment (WEEE) recycling system in China. Reuse can help realize eco-efficient and sustainable WEEE management, with environmentally friendly materials recovery. At present, reusability of products and components is determined only by the products functional situation or the economic cost benefit analysis. It does not cover all the three pillars of sustainability, including environment, economy and society. In this study, the emerging integrated method, Life Cycle Sustainability Assessment (LCSA), is employed to measure reusability of typical electrical and electronic products and components. The results of case studies show that, LCSA based reusability of typical electrical and electronic products and components will help improve WEEE management policy

Memristive Cluster Based Compact High-Density Nonvolatile Memory Design and Application for Image Storage

© 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/)As a new type of nonvolatile device, the memristor has become one of the most promising technologies for designing a new generation of high-density memory. In this paper, a 4-bit high-density nonvolatile memory based on a memristor is designed and applied to image storage. Firstly, a memristor cluster structure consisting of a transistor and four memristors is designed. Furthermore, the memristor cluster is used as a memory cell in the crossbar array structure to realize the memory design. In addition, when the designed non-volatile memory is applied to gray scale image storage, only two memory cells are needed for the storage of one pixel. Through the Pspice circuit simulation, the results show that compared with the state-of-the-art technology, the memory designed in this paper has better storage density and read–write speed. When it is applied to image storage, it achieves the effect of no distortion and fast storage.Peer reviewe