We give a sheaf theoretic interpretation of Potts models with external magnetic field, in terms of constructible sheaves and their Euler characteristics. We show that the polynomial countability question for the hypersurfaces defined by the vanishing of the partition function is affected by changes in the magnetic field: elementary examples suffice to see non-polynomially countable cases that become polynomially countable after a perturbation of the magnetic field. The same recursive formula for the Grothendieck classes, under edge-doubling operations, holds as in the case without magnetic field, but the closed formulae for specific examples like banana graphs differ in the presence of magnetic field. We give examples of computation of the Euler characteristic with compact support, for the set of real zeros, and find a similar exponential growth with the size of the graph. This can be viewed as a measure of topological and algorithmic complexity. We also consider the computational complexity question for evaluations of the polynomial, and show both tractable and NP-hard examples, using dynamic programming. 相似文献
The von Neumann cellular automaton appears in many different settings in Operations Research varying from applications in Formal Languages to Biology. One of the major questions related to it is to find a general condition for irreversibility of a class of two-dimensional cellular automata on square grids (σ+-automata). This question is partially answered here with the proposal of a sufficient condition for the irreversibility of σ+-automata. 相似文献
Seven transition metal molybdovanadoarsenic heteropoly compounds have been synthesized and characterized using IR, UV, TG-DTA, pH potential titration techniques. The molecular formulae of these compounds are pro-posed to be HxMyAsMO10V2O40·zH2O(x=1～3, y=1,2, M=Cr, Mn, Fe, Co, Ni, Cu, Zn).They are all keggin structure. Surface nature of these compounds have been investigated by temperature programmed desorption and temperature programmed reduction techniques. NH3-TPD results show that in TPD profiles of the compounds there are two desorption peaks corresponding to weak acid sites of desorption, respectively. Desorbing activativon energy and preexponential factor of weak acid site of desorption for compounds have been calculated. H2-TPR re-sults show that introducting transtion metal to molybdovanarsenic acid, the reduction peak temperatures of H2-TPR shift regularly with increasing d electron numbers of transition metals. In addition, Zn and Cu heteropoly com-pounds have yet apparent effect of hydrogen spill over. 相似文献
COVID-19, resulting from infection by the SARS-CoV-2 virus, caused a contagious pandemic. Even with the current vaccines, there is still an urgent need to develop effective pharmacological treatments against this deadly disease. Here, we show that the water and ethanol extracts of the root and rhizome of Polygonum cuspidatum (Polygoni Cuspidati Rhizoma et Radix), a common Chinese herbal medicine, blocked the entry of wild-type and the omicron variant of the SARS-CoV-2 pseudotyped virus into fibroblasts or zebrafish larvae, with IC50 values ranging from 0.015 to 0.04 mg/mL. The extracts were shown to inhibit various aspects of the pseudovirus entry, including the interaction between the spike protein (S-protein) and the angiotensin-converting enzyme II (ACE2) receptor, and the 3CL protease activity. Out of the chemical compounds tested in this report, gallic acid, a phytochemical in P. cuspidatum, was shown to have a significant anti-viral effect. Therefore, this might be responsible, at least in part, for the anti-viral efficacy of the herbal extract. Together, our data suggest that the extracts of P. cuspidatum inhibit the entry of wild-type and the omicron variant of SARS-CoV-2, and so they could be considered as potent treatments against COVID-19. 相似文献
African swine fever virus (ASFV) is one of the most dangerous viruses for pigs and is endemic in Africa but recently also spread into the Russian Federation and the Eastern border of the EU. So far there is no vaccine or antiviral drug available to curtail the infection. Thus, control strategies based on novel inhibitors are urgently needed. Another highly relevant virus infection in pigs is Aujeszky's disease caused by the alphaherpesvirus pseudorabies virus (PrV). This article reports the synthesis and biological evaluation of novel extracellular matrix‐inspired entry inhibitors based on polyglycerol sulfate‐functionalized graphene sheets. The developed 2D architectures bind enveloped viruses during the adhesion process and thereby exhibit strong inhibitory effects, which are equal or better than the common standards enrofloxacin and heparin as demonstrated for ASFV and PrV. Overall, the developed polyvalent 2D entry inhibitors are nontoxic and efficient nanoarchitectures, which interact with various types of enveloped viruses. Therefore they prevent viral adhesion to the host cell and especially target viruses that rely on a heparan sulfate‐dependent cell entry mechanism.
