Minimax Structured Normal Means Inference

We provide a unified treatment of a broad class of noisy structure recovery problems, known as structured normal means problems. In this setting, the goal is to identify, from a finite collection of Gaussian distributions with different means, the distribution that produced some observed data. Recent work has studied several special cases including sparse vectors, biclusters, and graph-based structures. We establish nearly matching upper and lower bounds on the minimax probability of error for any structured normal means problem, and we derive an optimality certificate for the maximum likelihood estimator, which can be applied to many instantiations. We also consider an experimental design setting, where we generalize our minimax bounds and derive an algorithm for computing a design strategy with a certain optimality property. We show that our results give tight minimax bounds for many structure recovery problems and consider some consequences for interactive sampling

Binary GH Sequences for Multiparty Communication

This paper investigates cross correlation properties of sequences derived from GH sequences modulo p, where p is a prime number and presents comparison with cross correlation properties of pseudo noise sequences. For GH sequences modulo prime, a binary random sequence B(n) is constructed, based on whether the period is p-1 (or a divisor) or 2p+2 (or a divisor). We show that B(n) sequences have much less peak cross correlation compared to PN sequence fragments obtained from the same generator. Potential applications of these sequences to cryptography are sketched.Comment: 7 pages, 6 figure

(White) Tyranny and the Democratic Value of Distrust

This paper makes an argument for the democratic value of distrust. It begins by analyzing distrust, since distrust is not merely the negation of trust. The account that it develops is based primarily on Martin Luther King Jr.’s work in Why We Can’t Wait. On this view, distrust is the confident belief that another individual or group of individuals or an institution will not act justly or as justice requires. It is a narrow normative account of distrust, since it concerns a specific normative task. Distinctions between vertical and horizontal distrust, as well as trust and agnostic trust are also discussed. This paper argues that distrust’s democratic value lies in its ability to secure democracy by protecting political minorities from having their voices ignored. As such, distrust can be viewed as a kind of Madisonian “check and balance” that works to prevent tyranny. Distrust also works to secure democracy by forging new or alternative forms of democratic participation. The main example discussed in this paper is King’s involvement in the Birmingham Campaign during the Black Civil Rights movement in America. In this case, King and his supporters’ distrust of fellow White citizens and political institutions led to alternative forms of political expression such as non-violent protests, boycotts, and other forms of civil disobedience, all of which led to greater racial justice by working to alleviate White tyranny

The stochastic behavior of a molecular switching circuit with feedback

Background: Using a statistical physics approach, we study the stochastic switching behavior of a model circuit of multisite phosphorylation and dephosphorylation with feedback. The circuit consists of a kinase and phosphatase acting on multiple sites of a substrate that, contingent on its modification state, catalyzes its own phosphorylation and, in a symmetric scenario, dephosphorylation. The symmetric case is viewed as a cartoon of conflicting feedback that could result from antagonistic pathways impinging on the state of a shared component. Results: Multisite phosphorylation is sufficient for bistable behavior under feedback even when catalysis is linear in substrate concentration, which is the case we consider. We compute the phase diagram, fluctuation spectrum and large-deviation properties related to switch memory within a statistical mechanics framework. Bistability occurs as either a first-order or second-order non-equilibrium phase transition, depending on the network symmetries and the ratio of phosphatase to kinase numbers. In the second-order case, the circuit never leaves the bistable regime upon increasing the number of substrate molecules at constant kinase to phosphatase ratio. Conclusions: The number of substrate molecules is a key parameter controlling both the onset of the bistable regime, fluctuation intensity, and the residence time in a switched state. The relevance of the concept of memory depends on the degree of switch symmetry, as memory presupposes information to be remembered, which is highest for equal residence times in the switched states. Reviewers: This article was reviewed by Artem Novozhilov (nominated by Eugene Koonin), Sergei Maslov, and Ned Wingreen.Comment: Version published in Biology Direct including reviewer comments and author responses, 28 pages, 7 figure