Grouping Based Blind Interference Alignment for KK-user MISO Interference Channels

We propose a blind interference alignment (BIA) through staggered antenna switching scheme with no ideal channel assumption. Contrary to the ideal assumption that channels remain constant during BIA symbol extension period, when the coherence time of the channel is relatively short, channel coefficients may change during a given symbol extension period. To perform BIA perfectly with realistic channel assumption, we propose a grouping based supersymbol structure for $K$-user interference channels which can adjust a supersymbol length to given coherence time. It is proved that the supersymbol length could be reduced significantly by an appropriate grouping. Furthermore, it is also shown that the grouping based supersymbol achieves higher degrees of freedom than the conventional method with given coherence time.Comment: 5 pages, 3 figures, to appear in IEEE ISIT 201

Geometric Permutations of Non-Overlapping Unit Balls Revisited

Given four congruent balls $A, B, C, D$ in $R^{d}$ that have disjoint interior and admit a line that intersects them in the order $ABCD$, we show that the distance between the centers of consecutive balls is smaller than the distance between the centers of $A$ and $D$. This allows us to give a new short proof that $n$ interior-disjoint congruent balls admit at most three geometric permutations, two if $n\ge 7$. We also make a conjecture that would imply that $n\geq 4$ such balls admit at most two geometric permutations, and show that if the conjecture is false, then there is a counter-example of a highly degenerate nature

Maintaining Contour Trees of Dynamic Terrains

We consider maintaining the contour tree $\mathbb{T}$ of a piecewise-linear triangulation $\mathbb{M}$ that is the graph of a time varying height function $h: \mathbb{R}^2 \rightarrow \mathbb{R}$. We carefully describe the combinatorial change in $\mathbb{T}$ that happen as $h$ varies over time and how these changes relate to topological changes in $\mathbb{M}$. We present a kinetic data structure that maintains the contour tree of $h$ over time. Our data structure maintains certificates that fail only when $h(v)=h(u)$ for two adjacent vertices $v$ and $u$ in $\mathbb{M}$, or when two saddle vertices lie on the same contour of $\mathbb{M}$. A certificate failure is handled in $O(\log(n))$ time. We also show how our data structure can be extended to handle a set of general update operations on $\mathbb{M}$ and how it can be applied to maintain topological persistence pairs of time varying functions

Maintaining Contour Trees of Dynamic Terrains

We study the problem of maintaining the contour tree T of a terrain Sigma, represented as a triangulated xy-monotone surface, as the heights of its vertices vary continuously with time. We characterize the combinatorial changes in T and how they relate to topological changes in Sigma. We present a kinetic data structure (KDS) for maintaining T efficiently. It maintains certificates that fail, i.e., an event occurs, only when the heights of two adjacent vertices become equal or two saddle vertices appear on the same contour. Assuming that the heights of two vertices of Sigma become equal only O(1) times and these instances can be computed in O(1) time, the KDS processes O(kappa + n) events, where n is the number of vertices in Sigma and kappa is the number of events at which the combinatorial structure of T changes, and processes each event in O(log n) time. The KDS can be extended to maintain an augmented contour tree and a join/split tree

Polycystin-1 inhibits eIF2α phosphorylation and cell apoptosis through a PKR-eIF2α pathway.

Autosomal dominant polycystic kidney disease (ADPKD) is caused by mutations in PKD1 or PKD2 which encodes polycystin-1 (PC1) and polycystin-2, respectively. PC1 was previously shown to slow cell proliferation and inhibit apoptosis but the underlying mechanisms remain elusive or controversial. Here we showed in cultured mammalian cells and Pkd1 knockout mouse kidney epithelial cells that PC1 and its truncation mutant comprising the last five transmembrane segments and the intracellular C-terminus (PC1-5TMC) down-regulate the phosphorylation of protein kinase R (PKR) and its substrate eukaryotic translation initiation factor 2 alpha (eIF2α). PKR is known to be activated by interferons and dsRNAs, inhibits protein synthesis and induces apoptosis. By co-immunoprecipitation experiments we found that PC1 truncation mutants associate with PKR, or with PKR and its activator PACT. Further experiments showed that PC1 and PC1-5TMC reduce phosphorylation of eIF2α through inhibiting PKR phosphorylation. Our TUNEL experiments using tunicamycin, an apoptosis inducer, and GADD34, an inhibitor of eIF2α phosphorylation, demonstrated that PC1-5TMC inhibits apoptosis of HEK293T cells in a PKR-eIF2α-dependent manner, with concurrent up- and down-regulation of Bcl-2 and Bax, respectively, revealed by Western blotting. Involvement of PC1-regulated eIF2α phosphorylation and a PKR-eIF2α pathway in cell apoptosis may be an important part of the mechanism underlying ADPKD pathogenesis