A mathematical framework for critical transitions: normal forms, variance and applications

Critical transitions occur in a wide variety of applications including mathematical biology, climate change, human physiology and economics. Therefore it is highly desirable to find early-warning signs. We show that it is possible to classify critical transitions by using bifurcation theory and normal forms in the singular limit. Based on this elementary classification, we analyze stochastic fluctuations and calculate scaling laws of the variance of stochastic sample paths near critical transitions for fast subsystem bifurcations up to codimension two. The theory is applied to several models: the Stommel-Cessi box model for the thermohaline circulation from geoscience, an epidemic-spreading model on an adaptive network, an activator-inhibitor switch from systems biology, a predator-prey system from ecology and to the Euler buckling problem from classical mechanics. For the Stommel-Cessi model we compare different detrending techniques to calculate early-warning signs. In the epidemics model we show that link densities could be better variables for prediction than population densities. The activator-inhibitor switch demonstrates effects in three time-scale systems and points out that excitable cells and molecular units have information for subthreshold prediction. In the predator-prey model explosive population growth near a codimension two bifurcation is investigated and we show that early-warnings from normal forms can be misleading in this context. In the biomechanical model we demonstrate that early-warning signs for buckling depend crucially on the control strategy near the instability which illustrates the effect of multiplicative noise.Comment: minor corrections to previous versio

supplementing zn mn and cu from amino acid complexes and co from cobalt glucoheptonate during the peripartal period benefits postpartal cow performance and blood neutrophil function

Abstract The physiologic and metabolic stresses that dairy cows experience during the transition into early lactation can promote oxidative stress, inflammation, and immune dysfunction. Optimal supply of micronutrients such as trace minerals (e.g., Zn, Mn, Cu, and Co) via more bioavailable forms (e.g., AA complexes) might minimize these negative effects. Multiparous Holstein cows were enrolled at 60 d before dry-off (~110 d before calving) and remained on experiment until 30 d in milk (DIM). Cows were offered a common diet supplemented entirely with inorganic trace minerals (INO) from −110 to −30 d before calving. From −30 to calving cows received a common prepartal [1.5Mcal/kg of dry matter (DM), 15% crude protein] diet, and from calving to 30 DIM a common postpartal (1.76Mcal/kg of DM, 18% crude protein) diet. Both diets were partially supplemented with an INO mix of Zn, Mn, and Cu to supply 35, 45, and 6mg/kg, respectively, of the total diet DM. Cows were assigned to treatments in a randomized complete block design to receive an oral bolus with a mix of INO (n=21) or organic AA complexes (AAC; n=16) of Zn, Mn, Cu, and Co to achieve supplemental levels of 75, 65, 11, and 1mg/kg, respectively, in the total diet DM. Inorganic trace minerals were provided in sulfate form and AAC were supplied via Availa Zn, Availa Mn, Availa Cu, and COPRO (Zinpro Corp., Eden Prairie, MN). Liver tissue was harvested on −30, −15, 10, and 30 d, and blood samples for biomarker analyses were obtained more frequently from −30 to 30 DIM. Short-term changes in blood ketones were measured via Precision Xtra (Abbott Diabetes Care, Alameda, CA) every other day from 1 to 15 d postpartum. Prepartal DM intake was lower in AAC cows. In contrast, a tendency for a diet by time (D × T) interaction resulted in greater postpartal DM intake of approximately 2kg/d in cows fed AAC. Milk and milk protein yield had a D × T interaction because AAC cows produced approximately 3.3kg/d more milk and 0.14kg/d more protein during the first 30 DIM. Although blood glucose, fatty acids, and liver triacylglycerol were not affected by diet, the Precision Xtra ketones (1.44 vs. 2.18mmol/L) and γ-glutamyltransferase (liver function biomarker) were lower in AAC than INO. Furthermore, feeding AAC increased (D × T) polymorphonuclear neutrophilic lymphocyte phagocytosis, antioxidant capacity postpartum, and overall concentration of liver tissue Co and Cu. Overall, the positive response in milk yield and milk protein in AAC cows might be partly explained by the beneficial effects of AAC on postpartal DM intake driven at least in part by better liver and immune function as a result of improved antioxidant status

Better postpartal performance in dairy cows supplemented with rumen-protected methionine compared with choline during the peripartal period

The onset of lactation in dairy cows is characterized by high output of methylated compounds in milk when sources of methyl group are in short supply. Methionine and choline (CHOL) are key methyl donors and their availability during this time may be limiting for milk production, hepatic lipid metabolism, and immune function. Supplementing rumen-protected Met and CHOL may improve overall performance and health of transition cows. The objective of this study was to evaluate the effect of supplemental rumen-protected Met and CHOL on performance and health of transition cows. Eighty-one multiparous Holstein cows were used in a randomized, complete, unbalanced block design with 2×2 factorial arrangement of Met (Smartamine M, Adisseo NA, Alpharetta, GA) and CHOL (ReaShure, Balchem Inc., New Hampton, NY) inclusion (with or without). Treatments (20 to 21 cows each) were control (CON), CON+Met (SMA), CON+CHOL (REA), and CON+Met+CHOL (MIX). From -50 to -21d before expected calving, all cows received the same diet (1.40Mcal of NEL/kg of DM) with no Met or CHOL. From -21d to calving, cows received the same close-up diet (1.52Mcal of NEL/kg of DM) and were assigned randomly to treatments (CON, SMA, REA, or MIX) supplied as top dresses. From calving to 30 DIM, cows were fed the same postpartal diet (1.71Mcal of NEL/kg of DM) and continued to receive the same treatments through 30 DIM. The Met supplementation was adjusted daily at 0.08% DM of diet and REA was supplemented at 60g/d. Incidence of clinical ketosis and retained placenta tended to be lower in Met-supplemented cows. Supplementation of Met (SMA, MIX) led to greater DMI compared with other treatments (CON, REA) in both close-up (14.3 vs. 13.2kg/d, SEM 0.3) and first 30d postpartum (19.2 vs. 17.2kg/d, SEM 0.6). Cows supplemented with Met (SMA, MIX) had greater yields of milk (44.2 vs. 40.4kg/d, SEM 1.2), ECM (44.6 vs. 40.5kg/d, SEM 1.0), and FCM (44.6 vs. 40.8kg/d, SEM 1.0) compared with other (CON, REA) treatments. Milk fat content did not differ in response to Met or CHOL. However, milk protein content was greater in Met-supplemented (3.32% vs. 3.14%, SEM 0.04%) but not CHOL-supplemented (3.27 vs. 3.19%, SEM 0.04%) cows. Supplemental CHOL led to greater blood glucose and insulin concentrations with lower glucose:insulin ratio. No Met or CHOL effects were detected for blood fatty acids or BHB, but a Met × time effect was observed for fatty acids due to higher concentrations on d 20. Results from the present study indicate that peripartal supplementation of rumen-protected Met but not CHOL has positive effects on cow performance

Gold electrodeposition for microelectronic, optoelectronic and microsystem applications

The electrodeposition of gold is a key technology in the fabrication of many microelectronic, optoelectronic and microsystem devices. In this review, we examine some recent applications, and consider the suitability of various gold plating systems for device fabrication. The properties of gold cyanide and sulfite baths and their limitations are considered first. This is followed by an analysis of the latest generation of non-cyanide baths, including the thiosulfate, sulfite-thiosulfate and ammonium gold systems. Plating baths containing mercapto-alkylsulfonic acid and hydantoin ligands are also briefly discussed. Finally an analysis of the stability of gold plating baths is presented