Multicast Network Coding and Field Sizes

In an acyclic multicast network, it is well known that a linear network coding solution over GF($q$) exists when $q$ is sufficiently large. In particular, for each prime power $q$ no smaller than the number of receivers, a linear solution over GF($q$) can be efficiently constructed. In this work, we reveal that a linear solution over a given finite field does \emph{not} necessarily imply the existence of a linear solution over all larger finite fields. Specifically, we prove by construction that: (i) For every source dimension no smaller than 3, there is a multicast network linearly solvable over GF(7) but not over GF(8), and another multicast network linearly solvable over GF(16) but not over GF(17); (ii) There is a multicast network linearly solvable over GF(5) but not over such GF($q$) that $q > 5$ is a Mersenne prime plus 1, which can be extremely large; (iii) A multicast network linearly solvable over GF($q^{m_1}$) and over GF($q^{m_2}$) is \emph{not} necessarily linearly solvable over GF($q^{m_1+m_2}$); (iv) There exists a class of multicast networks with a set $T$ of receivers such that the minimum field size $q_{min}$ for a linear solution over GF($q_{min}$) is lower bounded by $\Theta(\sqrt{|T|})$, but not every larger field than GF($q_{min}$) suffices to yield a linear solution. The insight brought from this work is that not only the field size, but also the order of subgroups in the multiplicative group of a finite field affects the linear solvability of a multicast network

Targeted expression of truncated glued disrupts giant fiber synapse formation in Drosophila

Glued1 (Gl1) mutants produce a truncated protein that acts as a poison subunit and disables the cytoplasmic retrograde motor dynein. Heterozygous mutants have axonal defects in the adult eye and the nervous system. Here we show that selective expression of the poison subunit in neurons of the giant fiber (GF) system disrupts synaptogenesis between the GF and one of its targets, the tergotrochanteral motorneuron (TTMn). Growth and pathfinding by the GF axon and the TTMn dendrite are normal, but the terminal of the GF axon fails to develop normally and becomes swollen with large vesicles. This is a presynaptic defect because expression of truncated Glued restricted to the GF results in the same defect. When tested electrophysiologically, the flies with abnormal axons show a weakened or absent GF-TTMn connection. In Glued1 heterozygotes, GF-TTMn synapse formation appears morphologically normal, but adult flies show abnormal responses to repetitive stimuli. This physiological effect is also observed when tetanus toxin is expressed in the GFs. Because the GF-TTMn is thought to be a mixed electrochemical synapse, the results show that Glued has a role in assembling both the chemical and electrical components. We speculate that disrupting transport of a retrograde signal disrupts synapse formation and maturation

Compressive mechanical response of graphene foams and their thermal resistance with copper interfaces

We report compressive mechanical response of graphene foams (GFs) and the thermal resistance ($R_{TIM}$) between copper (Cu) and GFs, where GFs were prepared by the chemical vapor deposition (CVD) method. We observe that Young's modulus ($E_{GF}$) and compressive strength ($\sigma_{GF}$) of GFs have a power law dependence on increasing density ($\rho_{GF}$) of GFs. The maximum efficiency of absorbed energy ($\eta_{max}$) for all GFs during the compression is larger than ~0.39. We also find that a GF with a higher $\rho_{GF}$ shows a larger $\eta_{max}$. In addition, we observe that the measured $R_{TIM}$ of Cu/GFs at room temperature with a contact pressure of 0.25 MP applied increases from ~50 to ~90 $mm^2K/W$ when $\rho_{GF}$ increases from 4.7 to 31.9 $mg/cm^3$

Selective Desensitization of Growth Factor Signaling by Cell Adhesion to Fibronectin

Cell adhesion to the extracellular matrix is required to execute growth factor (GF)-mediated cell behaviors, such as proliferation. A major underlying mechanism is that cell adhesion enhances GF-mediated intracellular signals, such as extracellular signal-regulated kinase (Erk). However, because GFs use distinct mechanisms to activate Ras-Erk signaling, it is unclear whether adhesion-mediated enhancement of Erk signaling is universal to all GFs. We examined this issue by quantifying the dynamics of Erk signaling induced by epidermal growth factor, basic fibroblast growth factor (bFGF), and platelet-derived growth factor (PDGF) in NIH-3T3 fibroblasts. Adhesion to fibronectin-coated surfaces enhances Erk signaling elicited by epidermal growth factor but not by bFGF or PDGF. Unexpectedly, adhesion is not always a positive influence on GF-mediated signaling. At critical subsaturating doses of PDGF or bFGF, cell adhesion ablates Erk signaling; that is, adhesion desensitizes the cell to GF stimulation, rendering the signaling pathway unresponsive to GF. Interestingly, the timing of growth factor stimulation proved critical to the desensitization process. Erk activation significantly improved only when pre-exposure to adhesion was completely eliminated; thus, concurrent stimulation by GF and adhesion was able to partially rescue adhesion-mediated desensitization of PDGF- and bFGF-mediated Erk and Akt signaling. These findings suggest that adhesion-mediated desensitization occurs with rapid kinetics and targets a regulatory point upstream of Ras and proximal to GF receptor activation. Thus, adhesion-dependent Erk signaling is not universal to all GFs but, rather, is GF-specific with quantitative features that depend strongly on the dose and timing of GF exposure

Graph-Based Classification of Self-Dual Additive Codes over Finite Fields

Quantum stabilizer states over GF(m) can be represented as self-dual additive codes over GF(m^2). These codes can be represented as weighted graphs, and orbits of graphs under the generalized local complementation operation correspond to equivalence classes of codes. We have previously used this fact to classify self-dual additive codes over GF(4). In this paper we classify self-dual additive codes over GF(9), GF(16), and GF(25). Assuming that the classical MDS conjecture holds, we are able to classify all self-dual additive MDS codes over GF(9) by using an extension technique. We prove that the minimum distance of a self-dual additive code is related to the minimum vertex degree in the associated graph orbit. Circulant graph codes are introduced, and a computer search reveals that this set contains many strong codes. We show that some of these codes have highly regular graph representations.Comment: 20 pages, 13 figure