Invariant submanifolds for affine control systems

Given an affine control system $\dot{\mathbf x} = f({\mathbf x}) + \sum_{j=1}^m g_j({\mathbf x}) u_j$ we present an algorithmic process of construction of submanifolds that are invariant under controls assuming that the linear span of $f, g_1, \ldots, g_m$ has constant rank. We use the method of reduction of Pfaffian systems to a largest integrable subsystem and finding the first integrals and the generalized first integrals for the vector fields.Comment: 11 page

Network rewiring is an important mechanism of gene essentiality change.

Gene essentiality changes are crucial for organismal evolution. However, it is unclear how essentiality of orthologs varies across species. We investigated the underlying mechanism of gene essentiality changes between yeast and mouse based on the framework of network evolution and comparative genomic analysis. We found that yeast nonessential genes become essential in mouse when their network connections rapidly increase through engagement in protein complexes. The increased interactions allowed the previously nonessential genes to become members of vital pathways. By accounting for changes in gene essentiality, we firmly reestablished the centrality-lethality rule, which proposed the relationship of essential genes and network hubs. Furthermore, we discovered that the number of connections associated with essential and non-essential genes depends on whether they were essential in ancestral species. Our study describes for the first time how network evolution occurs to change gene essentiality

Scheduling of Multicast and Unicast Services under Limited Feedback by using Rateless Codes

Many opportunistic scheduling techniques are impractical because they require accurate channel state information (CSI) at the transmitter. In this paper, we investigate the scheduling of unicast and multicast services in a downlink network with a very limited amount of feedback information. Specifically, unicast users send imperfect (or no) CSI and infrequent acknowledgements (ACKs) to a base station, and multicast users only report infrequent ACKs to avoid feedback implosion. We consider the use of physical-layer rateless codes, which not only combats channel uncertainty, but also reduces the overhead of ACK feedback. A joint scheduling and power allocation scheme is developed to realize multiuser diversity gain for unicast service and multicast gain for multicast service. We prove that our scheme achieves a near-optimal throughput region. Our simulation results show that our scheme significantly improves the network throughput over schemes employing fixed-rate codes or using only unicast communications

Rampant exchange of the structure and function of extramembrane domains between membrane and water soluble proteins.

Of the membrane proteins of known structure, we found that a remarkable 67% of the water soluble domains are structurally similar to water soluble proteins of known structure. Moreover, 41% of known water soluble protein structures share a domain with an already known membrane protein structure. We also found that functional residues are frequently conserved between extramembrane domains of membrane and soluble proteins that share structural similarity. These results suggest membrane and soluble proteins readily exchange domains and their attendant functionalities. The exchanges between membrane and soluble proteins are particularly frequent in eukaryotes, indicating that this is an important mechanism for increasing functional complexity. The high level of structural overlap between the two classes of proteins provides an opportunity to employ the extensive information on soluble proteins to illuminate membrane protein structure and function, for which much less is known. To this end, we employed structure guided sequence alignment to elucidate the functions of membrane proteins in the human genome. Our results bridge the gap of fold space between membrane and water soluble proteins and provide a resource for the prediction of membrane protein function. A database of predicted structural and functional relationships for proteins in the human genome is provided at sbi.postech.ac.kr/emdmp

Guards and Culprits in the Endoplasmic Reticulum: Glucolipotoxicity and β-Cell Failure in Type II Diabetes

The endoplasmic reticulum (ER) is a cellular organelle responsible for multiple important cellular functions including the biosynthesis and folding of newly synthesized proteins destined for secretion, such as insulin. The ER participates in all branches of metabolism, linking nutrient sensing to cellular signaling. Many pathological and physiological factors perturb ER function and induce ER stress. ER stress triggers an adaptive signaling cascade, called the unfolded protein response (UPR), to relieve the stress. The failure of the UPR to resolve ER stress leads to pathological conditions such as β-cell dysfunction and death, and type II diabetes. However, much less is known about the fine details of the control and regulation of the ER response to hyperglycemia (glucotoxicity), hyperlipidemia (lipotoxicity), and the combination of both (glucolipotoxicity). This paper considers recent insights into how the response is regulated, which may provide clues into the mechanism of ER stress-mediated β-cell dysfunction and death during the progression of glucolipotoxicity-induced type II diabetes