The Minimum Wiener Connector

The Wiener index of a graph is the sum of all pairwise shortest-path distances between its vertices. In this paper we study the novel problem of finding a minimum Wiener connector: given a connected graph $G=(V,E)$ and a set $Q\subseteq V$ of query vertices, find a subgraph of $G$ that connects all query vertices and has minimum Wiener index. We show that The Minimum Wiener Connector admits a polynomial-time (albeit impractical) exact algorithm for the special case where the number of query vertices is bounded. We show that in general the problem is NP-hard, and has no PTAS unless $\mathbf{P} = \mathbf{NP}$. Our main contribution is a constant-factor approximation algorithm running in time $\widetilde{O}(|Q||E|)$. A thorough experimentation on a large variety of real-world graphs confirms that our method returns smaller and denser solutions than other methods, and does so by adding to the query set $Q$ a small number of important vertices (i.e., vertices with high centrality).Comment: Published in Proceedings of the 2015 ACM SIGMOD International Conference on Management of Dat

On the Impact of the Global Financial Crisis on the Euro Area

This paper analyses the impact of the Global Financial Crisis on the Euro area utilizing a simple dynamic macroeconomic model with interaction between monetary policy and �fiscal policy. The model consists of an IS curve, a Phillips curve, a term structure relation, a debt accumulation equation and a Taylor monetary policy rule supplemented with a Zero Lower Bound, and a fi�scal policy rule. The model is calibrated/estimated for EU-16 countries for the period 1980Q1{2009Q4. The impact of the Global Financial Crisis is studied by means of impulse responses following a combined, prolonged aggregate demand and public debt shock. The simulation mimicking the GFC turns out to work fairly well. However, the required size of the shock is quite large

Isostaticity, auxetic response, surface modes, and conformal invariance in twisted kagome lattices

Model lattices consisting of balls connected by central-force springs provide much of our understanding of mechanical response and phonon structure of real materials. Their stability depends critically on their coordination number $z$. $d$-dimensional lattices with $z=2d$ are at the threshold of mechanical stability and are isostatic. Lattices with $z<2d$ exhibit zero-frequency "floppy" modes that provide avenues for lattice collapse. The physics of systems as diverse as architectural structures, network glasses, randomly packed spheres, and biopolymer networks is strongly influenced by a nearby isostatic lattice. We explore elasticity and phonons of a special class of two-dimensional isostatic lattices constructed by distorting the kagome lattice. We show that the phonon structure of these lattices, characterized by vanishing bulk moduli and thus negative Poisson ratios and auxetic elasticity, depends sensitively on boundary conditions and on the nature of the kagome distortions. We construct lattices that under free boundary conditions exhibit surface floppy modes only or a combination of both surface and bulk floppy modes; and we show that bulk floppy modes present under free boundary conditions are also present under periodic boundary conditions but that surface modes are not. In the the long-wavelength limit, the elastic theory of all these lattices is a conformally invariant field theory with holographic properties, and the surface waves are Rayleigh waves. We discuss our results in relation to recent work on jammed systems. Our results highlight the importance of network architecture in determining floppy-mode structure.Comment: 12 pages, 7 figure

The Expectation Monad in Quantum Foundations

The expectation monad is introduced abstractly via two composable adjunctions, but concretely captures measures. It turns out to sit in between known monads: on the one hand the distribution and ultrafilter monad, and on the other hand the continuation monad. This expectation monad is used in two probabilistic analogues of fundamental results of Manes and Gelfand for the ultrafilter monad: algebras of the expectation monad are convex compact Hausdorff spaces, and are dually equivalent to so-called Banach effect algebras. These structures capture states and effects in quantum foundations, and also the duality between them. Moreover, the approach leads to a new re-formulation of Gleason's theorem, expressing that effects on a Hilbert space are free effect modules on projections, obtained via tensoring with the unit interval.Comment: In Proceedings QPL 2011, arXiv:1210.029

Floppy modes and the free energy: Rigidity and connectivity percolation on Bethe Lattices

We show that negative of the number of floppy modes behaves as a free energy for both connectivity and rigidity percolation, and we illustrate this result using Bethe lattices. The rigidity transition on Bethe lattices is found to be first order at a bond concentration close to that predicted by Maxwell constraint counting. We calculate the probability of a bond being on the infinite cluster and also on the overconstrained part of the infinite cluster, and show how a specific heat can be defined as the second derivative of the free energy. We demonstrate that the Bethe lattice solution is equivalent to that of the random bond model, where points are joined randomly (with equal probability at all length scales) to have a given coordination, and then subsequently bonds are randomly removed.Comment: RevTeX 11 pages + epsfig embedded figures. Submitted to Phys. Rev.

Public Deliberations, Discursive Participation and Citizen Engagement: A Review of the Empirical Literature

Many theorists have long extolled the virtues of public deliberation as a crucial component of a responsive and responsible democracy. Building on these theories, in recent years practitioners - from government officials to citizen groups, nonprofits, and foundations - have increasingly devoted time and resources to strengthening citizen engagement through deliberative forums. Although empirical research has lagged behind theory and practice, a body of literature has emerged that tests the presumed individual and collective benefits of public discourse on citizen engagement. We begin our review of this research by defining public deliberation ; we place it in the context of other forms of what we call discursive participation while distinguishing it from other ways in which citizens can voice their individual and collective views on public issues.We then discuss the expectations, drawn from deliberative democratic theory, regarding the benefits (and, for some, pitfalls) assumed to derive from public deliberation. The next section reviews empirical research as it relates to these theoretical expectations.We conclude with recommendations on future directions for research in this area

Two classes of nonlocal Evolution Equations related by a shared Traveling Wave Problem

We consider reaction-diffusion equations and Korteweg-de Vries-Burgers (KdVB) equations, i.e. scalar conservation laws with diffusive-dispersive regularization. We review the existence of traveling wave solutions for these two classes of evolution equations. For classical equations the traveling wave problem (TWP) for a local KdVB equation can be identified with the TWP for a reaction-diffusion equation. In this article we study this relationship for these two classes of evolution equations with nonlocal diffusion/dispersion. This connection is especially useful, if the TW equation is not studied directly, but the existence of a TWS is proven using one of the evolution equations instead. Finally, we present three models from fluid dynamics and discuss the TWP via its link to associated reaction-diffusion equations

Witnessing microtubule-based transport in the living brain: Impact of the cargomotor receptor, amyloid precursor protein, and Alzheimer’s plaques

Most amyloid precursor protein (APP)-based Alzheimer’s models overexpress mutant human APP resulting in Abeta plaques. Yet the relative contribution of this elevated APP and the presence of plaques to neurodegeneration remains a big question. APP’s role as a cargo-motor receptor for axonal transport suggests that overexpression might lead to increased transport. Indeed we showed that transport is increased in Down’s syndrome and decreased in APP knockout mice. Hence transport may be elevated in APP overexpressors and lead to either beneficial or deleterious consequences. Here we use high field microMRI with Mn2+, an MR contrast agent useful as a track-tracer, to pose this cell biological quest ion within the whole living brains of wildtype and Alzheimer’s model mice. Injection of Mn2+ into the CA3 region of the hippocampus results in measurable transport over time. Application of 3D unbiased whole brain image analysis detects all circuitry emanating from the hippocampus. By driving APP Swe/Ind transgene expression with a tetracycline-sensitive promoter, APPSwe/Ind expression can be decoupled from the presence of plaques with doxycycline (doxy). Three groups of mice were studied: group ‘A’ (no doxy, +plaques, +APP); group ‘B’ (doxy at 8 days before sacrifice, +plaques, no APP), and group ‘C’ (doxy prior to conception, and stopped 8 days before sacrifice, no plaques, +APP). Images were captured before and sequentionally after Mn2+ injection into CA 3 (1, 7, 25 hr). Images were aligned and analyzed by statistical parametric mapping to identify differential accumulation within the hippocampal projections. Histopathology revealed well-developed plaques in A and B, and Western blots showed human APP expressed five-fold over WT in in A and C. Our preliminary results show increased transport in A and C, with APP Swe/Ind expression when compared with B, where expression is suppressed. Cholinergic neurons in the medial septal nucleus were decreased as determined by anti-ChAT staining in Group C (p=0.0006 by one-way ANOVA, n=15). In conclusion, the effects of elevated APP expression are separable from consequences of plaque, and each may