Estimating sample-specific regulatory networks

Biological systems are driven by intricate interactions among the complex array of molecules that comprise the cell. Many methods have been developed to reconstruct network models of those interactions. These methods often draw on large numbers of samples with measured gene expression profiles to infer connections between genes (or gene products). The result is an aggregate network model representing a single estimate for the likelihood of each interaction, or "edge," in the network. While informative, aggregate models fail to capture the heterogeneity that is represented in any population. Here we propose a method to reverse engineer sample-specific networks from aggregate network models. We demonstrate the accuracy and applicability of our approach in several data sets, including simulated data, microarray expression data from synchronized yeast cells, and RNA-seq data collected from human lymphoblastoid cell lines. We show that these sample-specific networks can be used to study changes in network topology across time and to characterize shifts in gene regulation that may not be apparent in expression data. We believe the ability to generate sample-specific networks will greatly facilitate the application of network methods to the increasingly large, complex, and heterogeneous multi-omic data sets that are currently being generated, and ultimately support the emerging field of precision network medicine

Linear And Nonlinear Arabesques: A Study Of Closed Chains Of Negative 2-Element Circuits

In this paper we consider a family of dynamical systems that we call "arabesques", defined as closed chains of 2-element negative circuits. An $n$-dimensional arabesque system has $n$ 2-element circuits, but in addition, it displays by construction, two $n$-element circuits which are both positive vs one positive and one negative, depending on the parity (even or odd) of the dimension $n$. In view of the absence of diagonal terms in their Jacobian matrices, all these dynamical systems are conservative and consequently, they can not possess any attractor. First, we analyze a linear variant of them which we call "arabesque 0" or for short "A0". For increasing dimensions, the trajectories are increasingly complex open tori. Next, we inserted a single cubic nonlinearity that does not affect the signs of its circuits (that we call "arabesque 1" or for short "A1"). These systems have three steady states, whatever the dimension is, in agreement with the order of the nonlinearity. All three are unstable, as there can not be any attractor in their state-space. The 3D variant (that we call for short "A1\_3D") has been analyzed in some detail and found to display a complex mixed set of quasi-periodic and chaotic trajectories. Inserting $n$ cubic nonlinearities (one per equation) in the same way as above, we generate systems "A2\_$n$D". A2\_3D behaves essentially as A1\_3D, in agreement with the fact that the signs of the circuits remain identical. A2\_4D, as well as other arabesque systems with even dimension, has two positive $n$-circuits and nine steady states. Finally, we investigate and compare the complex dynamics of this family of systems in terms of their symmetries.Comment: 22 pages, 12 figures, accepted for publication at Int. J. Bif. Chao

マルチパーティー計算の効率的な構成と実装

電気通信大学201

Algorithmic Bayesian Persuasion

Persuasion, defined as the act of exploiting an informational advantage in order to effect the decisions of others, is ubiquitous. Indeed, persuasive communication has been estimated to account for almost a third of all economic activity in the US. This paper examines persuasion through a computational lens, focusing on what is perhaps the most basic and fundamental model in this space: the celebrated Bayesian persuasion model of Kamenica and Gentzkow. Here there are two players, a sender and a receiver. The receiver must take one of a number of actions with a-priori unknown payoff, and the sender has access to additional information regarding the payoffs. The sender can commit to revealing a noisy signal regarding the realization of the payoffs of various actions, and would like to do so as to maximize her own payoff assuming a perfectly rational receiver. We examine the sender's optimization task in three of the most natural input models for this problem, and essentially pin down its computational complexity in each. When the payoff distributions of the different actions are i.i.d. and given explicitly, we exhibit a polynomial-time (exact) algorithm, and a "simple" $(1-1/e)$-approximation algorithm. Our optimal scheme for the i.i.d. setting involves an analogy to auction theory, and makes use of Border's characterization of the space of reduced-forms for single-item auctions. When action payoffs are independent but non-identical with marginal distributions given explicitly, we show that it is #P-hard to compute the optimal expected sender utility. Finally, we consider a general (possibly correlated) joint distribution of action payoffs presented by a black box sampling oracle, and exhibit a fully polynomial-time approximation scheme (FPTAS) with a bi-criteria guarantee. We show that this result is the best possible in the black-box model for information-theoretic reasons

Trade-offs in Private Search

Encrypted search -- performing queries on protected data -- is a well researched problem. However, existing solutions have inherent inefficiency that raises questions of practicality. Here, we step back from the goal of achieving maximal privacy guarantees in an encrypted search scenario to consider efficiency as a priority. We propose a privacy framework for search that allows tuning and optimization of the trade-offs between privacy and efficiency. As an instantiation of the privacy framework we introduce a tunable search system based on the SADS scheme and provide detailed measurements demonstrating the trade-offs of the constructed system. We also analyze other existing encrypted search schemes with respect to this framework. We further propose a protocol that addresses the challenge of document content retrieval in a search setting with relaxed privacy requirements

Modelling distributed network attacks with constraints

NeMODe is a declarative system for computer network intrusion detection, providing a declarative domain specific language for describing network intrusion signatures which can span several network packets, by stating constraints over network packets, describing relations between several packets in a declarative and expressive way. It provides several back-end detection mechanisms, all based on a constraint programming framework, to perform the detection of the desired signatures. In this work, we demonstrate how to model and perform the detection of distributed network attacks using each of the detection mechanisms provided by NeMODe, based in Gecode, adaptive search and MiniSat to perform the detection of the specific intrusions. We also use the sliding network traffic window version of the adaptive search back-end detection mechanism to simulate live network traffic and evaluate the performance of the system in conditions near to real life networks

Cambrian Hopf Algebras

Cambrian trees are oriented and labeled trees which fulfill local conditions around each node generalizing the conditions for classical binary search trees. Based on the bijective correspondence between signed permutations and leveled Cambrian trees, we define the Cambrian Hopf algebra generalizing J.-L. Loday and M. Ronco's algebra on binary trees. We describe combinatorially the products and coproducts of both the Cambrian algebra and its dual in terms of operations on Cambrian trees. We also define multiplicative bases of the Cambrian algebra and study structural and combinatorial properties of their indecomposable elements. Finally, we extend to the Cambrian setting different algebras connected to binary trees, in particular S. Law and N. Reading's Baxter Hopf algebra on quadrangulations and S. Giraudo's equivalent Hopf algebra on twin binary trees, and F. Chapoton's Hopf algebra on all faces of the associahedron.Comment: 60 pages, 43 figures. Version 2: New Part 3 on Schr\"oder Cambrian Algebra. The title change reflects this modificatio

Cryptography from tensor problems

We describe a new proposal for a trap-door one-way function. The new proposal belongs to the "multivariate quadratic" family but the trap-door is different from existing methods, and is simpler