Fundamental Structure of General Stochastic Dynamical Systems: High-Dimension Case

No one has proved that mathematically general stochastic dynamical systems have a special structure. Thus, we introduce a structure of a general stochastic dynamical system. According to scientific understanding, we assert that its deterministic part can be decomposed into three significant parts: the gradient of the potential function, friction matrix and Lorenz matrix. Our previous work proved this structure for the low-dimension case. In this paper, we prove this structure for the high-dimension case. Hence, this structure of general stochastic dynamical systems is fundamental

THE GENERALIZED LYAPUNOV FUNCTION as AO’S POTENTIAL FUNCTION: EXISTENCE in DIMENSIONS 1 and 2

By using Ao\u27s decomposition for stochastic dynamical systems, a new notion of potential function has been introduced by Ao and his collabora-tors recently. We show that this potential function agrees with the generalized Lyapunov function of the deterministic part of the stochastic dynamical sys-tem. We further prove the existence of Ao\u27s potential function in dimensions 1 and 2 via the solution theory of first-order partial differential equations. Our framework reveals the equivalence between Ao\u27s potential function and Lyapunov function, the latter being one of the most significant central notions in dynamical systems. Using this equivalence, our existence proof can also be interpreted as the proof of existence of Lyapunov function for a general dynamical system

Bhlhb5 Regulates the Postmitotic Acquisition of Area Identities in Layers II-V of the Developing Neocortex

While progenitor-restricted factors broadly specify area identities in developing neocortex, the downstream regulatory elements involved in acquisition of those identities in post-mitotic neurons are largely unknown. Here, we identify Bhlhb5, a transcription factor expressed in layers II–V, as a post-mitotic regulator of area identity. Bhlhb5 is initially expressed in a high caudomedial to low rostrolateral gradient that transforms into a sharp border between sensory and rostral motor cortices. Bhlhb5-null mice exhibit aberrant expression of area-specific genes and structural organization in the somatosensory and caudal motor cortices. In somatosensory cortex, Bhlhb5-null mice display post-synaptic disorganization of vibrissal barrels. In caudal motor cortex, Bhlhb5-null mice exhibit anomalous differentiation of corticospinal motor neurons, accompanied by failure of corticospinal tract formation. Together, these results demonstrate Bhlhb5’s function as an area-specific transcription factor that regulates the post-mitotic acquisition of area identities and elucidate the genetic hierarchy between progenitors and post-mitotic neurons driving neocortical arealization.Stem Cell and Regenerative Biolog

Potential applications of wastes from energy generation particularly biochar in Malaysia.

In Malaysia, abundant agricultural wastes are generated yearly. Therefore it is beneficial to discover new ways to utilize the wastes and employ the carbon source in different industries. Biochar are produced through many heat treatments such as combustion, gasification and pyrolysis for energy generation. The characteristics of these stable carbons such as the physical properties, chemical composition, surface area and surface chemistry determine the effectiveness of the cabon in different applications. Biochar has the ability to retain carbon and this condition is advantageous to prevent the release of carbon back to the atmosphere in the form of carbon dioxide. Application of biochar to soil helps to improve soil fertility and raise agricultural productivity. Biochar also has the ability to reduce carbon dioxide in the flue gas system. There have only been a few studies that discuss on the potential applications of this agriculture waste. The biochar's potential application as carbon sequester for soil application, energy production and dye sorption is being explored in this paper

Fundamental Structure of General Stochastic Dynamical Systems: High-Dimension Case

No one has proved that mathematically general stochastic dynamical systems have a special structure. Thus, we introduce a structure of a general stochastic dynamical system. According to scientific understanding, we assert that its deterministic part can be decomposed into three significant parts: the gradient of the potential function, friction matrix and Lorenz matrix. Our previous work proved this structure for the low-dimension case. In this paper, we prove this structure for the high-dimension case. Hence, this structure of general stochastic dynamical systems is fundamental

A new modified CKD-EPI equation for Chinese patients with type 2 diabetes.

OBJECTIVE: To improve the performance of glomerular filtration rate (GFR) estimating equation in Chinese type 2 diabetic patients by modification of the CKD-EPI equation. DESIGN AND PATIENTS: A total of 1196 subjects were enrolled. Measured GFR was calibrated to the dual plasma sample 99mTc-DTPA-GFR. GFRs estimated by the re-expressed 4-variable MDRD equation, the CKD-EPI equation and the Asian modified CKD-EPI equation were compared in 351 diabetic/non-diabetic pairs. And a new modified CKD-EPI equation was reconstructed in a total of 589 type 2 diabetic patients. RESULTS: In terms of both precision and accuracy, GFR estimating equations all achieved better results in the non-diabetic cohort comparing with those in the type 2 diabetic cohort (30% accuracy, P≤0.01 for all comparisons). In the validation data set, the new modified equation showed less bias (median difference, 2.3 ml/min/1.73 m2 for the new modified equation vs. ranged from -3.8 to -7.9 ml/min/1.73 m2 for the other 3 equations [P<0.001 for all comparisons]), as was precision (IQR of the difference, 24.5 ml/min/1.73 m2 vs. ranged from 27.3 to 30.7 ml/min/1.73 m2), leading to a greater accuracy (30% accuracy, 71.4% vs. 55.2% for the re-expressed 4 variable MDRD equation and 61.0% for the Asian modified CKD-EPI equation [P = 0.001 and P = 0.02]). CONCLUSION: A new modified CKD-EPI equation for type 2 diabetic patients was developed and validated. The new modified equation improves the performance of GFR estimation

Contrasting nutrients input along with groundwater discharge to east Dongting Lake, central China: A geological perspective

The spatial patterns of lacustrine groundwater discharge (LGD) and associated nutrient inputs are crucial for effective management and protection of lakes. Multiple factors have been found to influence the spatial differences in LGD rates and associated nutrients loads, but the influence of geological conditions on the differences have not been well understood. In this study, we quantified LGD rates and associated nutrients loads on the west and east of the lake with contrasting geological conditions of East Dongting Lake (EDL) within central Yangtze catchment and discuss the influence of geology on the spatial differences, through 222Rn mass-balance model, water chemistry coupled with existing geological data. The results showed that LGD rates were 34.76 ± 23.36 mm/d in the east EDL which is characterized by hilly geomorphy, deep/fast/narrow flowing, coarse-grained lakebed and large hydraulic gradients (0.004–0.006). Surprisingly, LGD rates were higher (71.47 ± 52.16 mm/d) in the west EDL which is characterized by alluvial-lacustrine plain geomorphology, shallow/sluggish flowing, clayey or silty lakebed and low hydraulic gradients (0.0002–0.0015). The remaining factor determining the higher LGD rates in the west EDL is the permeability of the porous aquifer connected with the lake. The groundwater around the east EDL existed in a less confined environment, and frequent flushing led to low concentrations of nutrients. By contrast, rapid burial of sediments and deposition of paleo-lake sediments since Last Deglaciation formed an organic-rich and reducing environment, which facilitated the enrichment of geogenic nutrients. As a result, the loads of LGD-derived nutrients in the west generally exceeded that in the east by one order of magnitude. The study provides new understanding of the spatial differences in LGD and associated nutrients input to the large lakes resulting from variations in geological conditions, thus serving as a reference for ecological protection of lakes