Entropy in the category of perfect complexes with cohomology of finite length

Local and category-theoretical entropies associated with an endomorphism of finite length (i.e., with zero-dimensional closed fiber) of a commutative Noetherian local ring are compared. Local entropy is shown to be less than or equal to category-theoretical entropy. The two entropies are shown to be equal when the ring is regular, and also for the Frobenius endomorphism of a complete local ring of positive characteristic.Furthermore, given a flat morphism of Cohen–Macaulay local rings endowed with compatible endomorphisms of finite length, it is shown that local entropy is “additive”. Finally, over a ring that is a homomorphic image of a regular local ring, a formula for local entropy in terms of an asymptotic partial Euler characteristic is given.     

The Effect of Wettability on Waterflood Oil Recovery in Carbonate Rock Samples: A Systematic Multi-scale Experimental Investigation

Transport in Porous Media - On the basis of a well-based model (Model I) developed in a previous work (Liu and Valkó in SPE J 2019. https://doi.org/10.2118/197049-PA ), in which a fractional...     

Weighted coupling for geographical networks: Application to reducing consensus time in sensor networks

Although many complex real-world networks are weighted, unweighted networks are used in many applications such as sensor networks. In this Letter it is shown using properly weighted networks the performance can be greatly enhanced by reducing the time necessary for the average consensus. Random geographical models are adapted as network models and a method based on mutually coupled phase oscillators is used for providing average consensus over the network. The consensus time is calculated by numerically solving the network's differential equations and monitoring the average error. The simulation results on some sample networks show that the consensus time is dramatically reduced when the proposed weights are used for the links of the underlying network.     

Motif structure and cooperation in real-world complex networks

Networks of dynamical nodes serve as generic models for real-world systems in many branches of science ranging from mathematics to physics, technology, sociology and biology. Collective behavior of agents interacting over complex networks is important in many applications. The cooperation between selfish individuals is one of the most interesting collective phenomena. In this paper we address the interplay between the motifs’ cooperation properties and their abundance in a number of real-world networks including yeast protein-protein interaction, human brain, protein structure, email communication, dolphins’ social interaction, Zachary karate club and Net-science coauthorship networks. First, the amount of cooperativity for all possible undirected subgraphs with three to six nodes is calculated. To this end, the evolutionary dynamics of the Prisoner’s Dilemma game is considered and the cooperativity of each subgraph is calculated as the percentage of cooperating agents at the end of the simulation time. Then, the three- to six-node motifs are extracted for each network. The significance of the abundance of a motif, represented by a Z-value, is obtained by comparing them with some properly randomized versions of the original network. We found that there is always a group of motifs showing a significant inverse correlation between their cooperativity amount and Z-value, i.e. the more the Z-value the less the amount of cooperativity. This suggests that networks composed of well-structured units do not have good cooperativity properties.     

Structure and Mechanical Properties of 50/50 NR/SBR Blend/Pristine Clay Nanocomposites

A blend/clay nanocomposites of 50/50 (wt%) NR/SBR was prepared via mixing the latex of a 50/50 NR/SBR blend with an aqueous clay dispersion and co‐coagulating the mixture. The structure of the nanocomposite was characterized by transmission electron microscopy (TEM) and X-ray diffraction (XRD). Nanocomposites containing less than 10 phr clay showed a fully exfoliated structure. After increasing the clay content to 10 phr, both nonexfoliated (stacked layers) and exfoliated structures were observed in the nanocomposites. The results of mechanical tests showed that the nanocomposites presented better mechanical properties than clay‐free NR/SBR blend vulcanizate. Furthermore, tensile strength, tensile strain at break, and hardness (shore A) increased with increasing clay content, up to 6 phr, and then remained almost constant.     

Comparisons of mixed systems with decreasing failure rate component lifetimes using dispersive order

Because lifetimes of systems are not deterministic, partially, orders are used for comparison purposes which lead us to provide optimal system configurations. This paper deals with a signature‐based dispersive ordering of mixed systems. It is assumed that component lifetimes are independent and identically distributed, and the common distribution has a decreasing failure rate function. Some illustrative examples are also given.