A digital interface for Gaussian relay networks: lifting codes from the discrete superposition model to Gaussian relay networks

For every Gaussian relay network with a single source-destination pair, it is known that there exists a corresponding deterministic network called the discrete superposition network that approximates its capacity uniformly over all SNR's to within a bounded number of bits. The next step in this program of rigorous approximation is to determine whether coding schemes for discrete superposition models can be lifted to Gaussian relay networks with a bounded rate loss independent of SNR. We establish precisely this property and show that the superposition model can thus serve as a strong surrogate for designing codes for Gaussian relay networks. We show that a code for a Gaussian relay network, with a single source-destination pair and multiple relay nodes, can be designed from any code for the corresponding discrete superposition network simply by pruning it. In comparison to the rate of the discrete superposition network's code, the rate of the Gaussian network's code only reduces at most by a constant that is a function only of the number of nodes in the network and independent of channel gains. This result is also applicable for coding schemes for MIMO Gaussian relay networks, with the reduction depending additionally on the number of antennas. Hence, the discrete superposition model can serve as a digital interface for operating Gaussian relay networks.Comment: 5 pages, 2010 IEEE Information Theory Workshop, Cair

A digital interface for Gaussian relay and interference networks: Lifting codes from the discrete superposition model

For every Gaussian network, there exists a corresponding deterministic network called the discrete superposition network. We show that this discrete superposition network provides a near-optimal digital interface for operating a class consisting of many Gaussian networks in the sense that any code for the discrete superposition network can be naturally lifted to a corresponding code for the Gaussian network, while achieving a rate that is no more than a constant number of bits lesser than the rate it achieves for the discrete superposition network. This constant depends only on the number of nodes in the network and not on the channel gains or SNR. Moreover the capacities of the two networks are within a constant of each other, again independent of channel gains and SNR. We show that the class of Gaussian networks for which this interface property holds includes relay networks with a single source-destination pair, interference networks, multicast networks, and the counterparts of these networks with multiple transmit and receive antennas. The code for the Gaussian relay network can be obtained from any code for the discrete superposition network simply by pruning it. This lifting scheme establishes that the superposition model can indeed potentially serve as a strong surrogate for designing codes for Gaussian relay networks. We present similar results for the K x K Gaussian interference network, MIMO Gaussian interference networks, MIMO Gaussian relay networks, and multicast networks, with the constant gap depending additionally on the number of antennas in case of MIMO networks.Comment: Final versio

Epidermal growth factor-mediated T-cell factor/lymphoid enhancer factor transcriptional activity is essential but not sufficient for cell cycle progression in nontransformed mammary epithelial cells

Because beta-catenin target genes such as cyclin D1 are involved in cell cycle progression, we examined whether beta-catenin has a more pervasive role in normal cell proliferation, even upon stimulation by non-Wnt ligands. Here, we demonstrate that epidermal growth factor (EGF) stimulates T-cell factor/lymphoid enhancer factor (Tcf/Lef) transcriptional activity in nontransformed mammary epithelial cells (MCF-10A) and that its transcriptional activity is essential for EGF-mediated progression through G(1)/S phase. Thus, expression of dominant-negative Tcf4 blocks EGF-mediated Tcf/Lef transcriptional activity and bromodeoxyuridine uptake. In fact, the importance of EGF-mediated Tcf/Lef transcriptional activity for cell cycle progression may lie further upstream at the G(1)/S phase transition. We demonstrate that dominant-negative Tcf4 inhibits a reporter of cyclin D1 promoter activity in a dose-dependent manner. Importantly, dominant-negative Tcf4 suppresses EGF- mediated cell cycle activity specifically by thwarting EGF- mediated Tcf/Lef transcriptional activity, not by broader effects on EGF signaling. Thus, although expression of dominant-negative Tcf4 blocks EGF- mediated TOPFLASH activation, it has no effect on either EGF receptor or ERK phosphorylation, further underscoring the fact that Tcf/ Lef-mediated transcription is essential for cell cycle progression, even when other pro-mitogenic signals are at normal levels. Yet, despite its essential role, Tcf/Lef transcriptional activity alone is not sufficient for cell cycle progression. Serum also stimulates Tcf/ Lef transcriptional activation in MCF-10A cells but is unable to promote DNA synthesis. Taken together, our data support a model wherein EGF promotes Tcf/ Lef transcriptional activity, and this signal is essential but not sufficient for cell cycle activity

Bioengineering models of cell signaling

Strategies for rationally manipulating cell behavior in cell-based technologies and molecular therapeutics and understanding effects of environmental agents on physiological systems may be derived from a mechanistic understanding of underlying signaling mechanisms that regulate cell functions. Three crucial attributes of signal transduction necessitate modeling approaches for analyzing these systems: an ever-expanding plethora of signaling molecules and interactions, a highly interconnected biochemical scheme, and concurrent biophysical regulation. Because signal flow is tightly regulated with positive and negative feedbacks and is bidirectional with commands traveling both from outside-in and inside-out, dynamic models that couple biophysical and biochemical elements are required to consider information processing both during transient and steady-state conditions. Unique mathematical frameworks will be needed to obtain an integrated perspective on these complex systems, which operate over wide length and time scales. These may involve a two-level hierarchical approach wherein the overall signaling network is modeled in terms of effective "circuit" or "algorithm" modules, and then each module is correspondingly modeled with more detailed incorporation of its actual underlying biochemical/biophysical molecular interactions