MAC with Action-Dependent State Information at One Encoder

Problems dealing with the ability to take an action that affects the states of state-dependent communication channels are of timely interest and importance. Therefore, we extend the study of action-dependent channels, which until now focused on point-to-point models, to multiple-access channels (MAC). In this paper, we consider a two-user, state-dependent MAC, in which one of the encoders, called the informed encoder, is allowed to take an action that affects the formation of the channel states. Two independent messages are to be sent through the channel: a common message known to both encoders and a private message known only to the informed encoder. In addition, the informed encoder has access to the sequence of channel states in a non-causal manner. Our framework generalizes previously evaluated settings of state dependent point-to-point channels with actions and MACs with common messages. We derive a single letter characterization of the capacity region for this setting. Using this general result, we obtain and compute the capacity region for the Gaussian action-dependent MAC. The unique methods used in solving the Gaussian case are then applied to obtain the capacity of the Gaussian action-dependent point-to-point channel; a problem was left open until this work. Finally, we establish some dualities between action-dependent channel coding and source coding problems. Specifically, we obtain a duality between the considered MAC setting and the rate distortion model known as "Successive Refinement with Actions". This is done by developing a set of simple duality principles that enable us to successfully evaluate the outcome of one problem given the other.Comment: 1. Parts of this paper appeared in the IEEE International Symposium on Information Theory (ISIT 2012),Cambridge, MA, US, July 2012 and at the IEEE 27th Convention of Electrical and Electronics Engineers in Israel (IEEEI 2012), Nov. 2012. 2. This work has been supported by the CORNET Consortium Israel Ministry for Industry and Commerc

New High Dimensional Expanders from Covers

We present a new construction of high dimensional expanders based on covering spaces of simplicial complexes. High dimensional expanders (HDXs) are hypergraph analogues of expander graphs. They have many uses in theoretical computer science, but unfortunately only few constructions are known which have arbitrarily small local spectral expansion. We give a randomized algorithm that takes as input a high dimensional expander $X$ (satisfying some mild assumptions). It outputs a sub-complex $Y \subseteq X$ that is a high dimensional expander and has infinitely many simplicial covers. These covers form new families of bounded-degree high dimensional expanders. The sub-complex $Y$ inherits $X$'s underlying graph and its links are sparsifications of the links of $X$. When the size of the links of $X$ is $O(\log |X|)$, this algorithm can be made deterministic. Our algorithm is based on the groups and generating sets discovered by Lubotzky, Samuels and Vishne (2005), that were used to construct the first discovered high dimensional expanders. We show these groups give rise to many more ``randomized'' high dimensional expanders. In addition, our techniques also give a random sparsification algorithm for high dimensional expanders, that maintains its local spectral properties. This may be of independent interest

Coboundary and cosystolic expansion without dependence on dimension or degree

We give new bounds on the cosystolic expansion constants of several families of high dimensional expanders, and the known coboundary expansion constants of order complexes of homogeneous geometric lattices, including the spherical building of $SL_n(F_q)$. The improvement applies to the high dimensional expanders constructed by Lubotzky, Samuels and Vishne, and by Kaufman and Oppenheim. Our new expansion constants do not depend on the degree of the complex nor on its dimension, nor on the group of coefficients. This implies improved bounds on Gromov's topological overlap constant, and on Dinur and Meshulam's cover stability, which may have applications for agreement testing. In comparison, existing bounds decay exponentially with the ambient dimension (for spherical buildings) and in addition decay linearly with the degree (for all known bounded-degree high dimensional expanders). Our results are based on several new techniques: * We develop a new "color-restriction" technique which enables proving dimension-free expansion by restricting a multi-partite complex to small random subsets of its color classes. * We give a new "spectral" proof for Evra and Kaufman's local-to-global theorem, deriving better bounds and getting rid of the dependence on the degree. This theorem bounds the cosystolic expansion of a complex using coboundary expansion and spectral expansion of the links. * We derive absolute bounds on the coboundary expansion of the spherical building (and any order complex of a homogeneous geometric lattice) by constructing a novel family of very short cones

Boolean functions on high-dimensional expanders

We initiate the study of Boolean function analysis on high-dimensional expanders. We give a random-walk based definition of high-dimensional expansion, which coincides with the earlier definition in terms of two-sided link expanders. Using this definition, we describe an analog of the Fourier expansion and the Fourier levels of the Boolean hypercube for simplicial complexes. Our analog is a decomposition into approximate eigenspaces of random walks associated with the simplicial complexes. Our random-walk definition and the decomposition have the additional advantage that they extend to the more general setting of posets, encompassing both high-dimensional expanders and the Grassmann poset, which appears in recent work on the unique games conjecture. We then use this decomposition to extend the Friedgut-Kalai-Naor theorem to high-dimensional expanders. Our results demonstrate that a constant-degree high-dimensional expander can sometimes serve as a sparse model for the Boolean slice or hypercube, and quite possibly additional results from Boolean function analysis can be carried over to this sparse model. Therefore, this model can be viewed as a derandomization of the Boolean slice, containing only $|X(k-1)|=O(n)$ points in contrast to $\binom{n}{k}$ points in the $(k)$-slice (which consists of all $n$-bit strings with exactly $k$ ones).Comment: 48 pages, Extended version of the prior submission, with more details of expanding posets (eposets

Boolean Function Analysis on High-Dimensional Expanders

We initiate the study of Boolean function analysis on high-dimensional expanders. We describe an analog of the Fourier expansion and of the Fourier levels on simplicial complexes, and generalize the FKN theorem to high-dimensional expanders. Our results demonstrate that a high-dimensional expanding complex X can sometimes serve as a sparse model for the Boolean slice or hypercube, and quite possibly additional results from Boolean function analysis can be carried over to this sparse model. Therefore, this model can be viewed as a derandomization of the Boolean slice, containing |X(k)|=O(n) points in comparison to binom{n}{k+1} points in the (k+1)-slice (which consists of all n-bit strings with exactly k+1 ones)

The duplicube graph -- a hybrid of structure and randomness

Connect two copies of a given graph $G$ by a perfect matching. What are the properties of the graphs obtained by recursively repeating this procedure? We show that this construction shares some of the structural properties of the hypercube, such as a simple routing scheme and small edge expansion. However, when the matchings are uniformly random, the resultant graph also has similarities with a random regular graph, including: a smaller diameter and better vertex expansion than the hypercube; a semicircle law for its eigenvalues; and no non-trivial automorphisms. We propose a simple deterministic matching which we believe could provide a derandomization.Comment: 27 pages, 6 figures. Comments welcome

Links between core promoter and basic gene features influence gene expression

<p>Abstract</p> <p>Background</p> <p>Diversity in rates of gene expression is essential for basic cell functions and is controlled by a variety of intricate mechanisms. Revealing general mechanisms that control gene expression is important for understanding normal and pathological cell functions and for improving the design of expression systems. Here we analyzed the relationship between general features of genes and their contribution to expression levels.</p> <p>Results</p> <p>Genes were divided into four groups according to their core promoter type and their characteristics analyzed statistically. Surprisingly we found that small variations in the TATA box are linked to large differences in gene length. Genes containing canonical TATA are generally short whereas long genes are associated with either non-canonical TATA or TATA-less promoters. These differences in gene length are primarily determined by the size and number of introns. Generally, gene expression was found to be tightly correlated with the strength of the TATA-box. However significant reduction in gene expression levels were linked with long TATA-containing genes (canonical and non-canonical) whereas intron length hardly affected the expression of TATA-less genes. Interestingly, features associated with high translation are prevalent in TATA-containing genes suggesting that their protein production is also more efficient.</p> <p>Conclusion</p> <p>Our results suggest that interplay between core promoter type and gene size can generate significant diversity in gene expression.</p

TAFII250 Is a Bipartite Protein Kinase That Phosphorylates the Basal Transcription Factor RAP74

AbstractSome TAF subunits of transcription factor TFIID play a pivotal role in transcriptional activation by mediating protein–protein interactions, whereas other TAFs direct promoter selectivity via protein–DNA recognition. Here, we report that purified recombinant TAFII250 is a protein serine kinase that selectively phosphorylates RAP74 but not other basal transcription factors or common phosphoacceptor proteins. The phosphorylation of RAP74 also occurs in the context of the complete TFIID complex. Deletion analysis revealed that TAFII250 contains two distinct kinase domains each capable of autophosphorylation. However, both the N- and C-terminal kinase domains of TAFII250 are required for efficient transphosphorylation of RAP74 on serine residues. These findings suggest that the targeted phosphorylation of RAP74 by TAFII250 may provide a mechanism for signaling between components within the initiation complex to regulate transcription