Stability and Invariant Random Subgroups

Consider $\operatorname{Sym}(n)$, endowed with the normalized Hamming metric $d_n$. A finitely-generated group $\Gamma$ is \emph{P-stable} if every almost homomorphism $\rho_{n_k}\colon \Gamma\rightarrow\operatorname{Sym}(n_k)$ (i.e., for every $g,h\in\Gamma$, $\lim_{k\rightarrow\infty}d_{n_k}( \rho_{n_k}(gh),\rho_{n_k}(g)\rho_{n_k}(h))=0$) is close to an actual homomorphism $\varphi_{n_k} \colon\Gamma\rightarrow\operatorname{Sym}(n_k)$. Glebsky and Rivera observed that finite groups are P-stable, while Arzhantseva and P\u{a}unescu showed the same for abelian groups and raised many questions, especially about P-stability of amenable groups. We develop P-stability in general, and in particular for amenable groups. Our main tool is the theory of invariant random subgroups (IRS), which enables us to give a characterization of P-stability among amenable groups, and to deduce stability and instability of various families of amenable groups.Comment: 24 pages; v2 includes minor updates and new reference

Politicians' Outside Earnings and Electoral Competition

This paper deals with the impact of electoral competition on politicians' outside earnings. We propose a simple theoretical model with politicians facing a tradeoff between allocating their time to political effort or to an alternative use generating outside earnings. The model has a testable implication stating that the amount of time spent on outside work is negatively related to the degree of electoral competition. We test this implication using a new dataset on outside earnings of members of the German federal assembly. Taking into account the potential endogeneity of measures of political competition that depend on past election outcomes, we find that politicians facing low competition have substantially higher outside earnings

Politicians' outside earnings and electoral competition

This paper deals with the impact of electoral competition on politicians´ outside earnings. We propose a simple theoretical model with politicians facing a tradeoff between allocating their time to political effort or to an alternative use generating outside earnings. The model has a testable implication stating that the amount of time spent on outside work is negatively related to the degree of electoral competition. We test this implication using a new dataset on outside earnings of members of the German federal assembly. Taking into account the potential endogeneity of measures of political competition that depend on past election outcomes, we find that politicians facing low competition have substantially higher outside earnings. --Political competition,outside earnings,political rents

Near-Optimal Approximate Shortest Paths and Transshipment in Distributed and Streaming Models

We present a method for solving the transshipment problem - also known as uncapacitated minimum cost flow - up to a multiplicative error of $1 + \varepsilon$ in undirected graphs with non-negative edge weights using a tailored gradient descent algorithm. Using $\tilde{O}(\cdot)$ to hide polylogarithmic factors in $n$ (the number of nodes in the graph), our gradient descent algorithm takes $\tilde O(\varepsilon^{-2})$ iterations, and in each iteration it solves an instance of the transshipment problem up to a multiplicative error of $\operatorname{polylog} n$. In particular, this allows us to perform a single iteration by computing a solution on a sparse spanner of logarithmic stretch. Using a randomized rounding scheme, we can further extend the method to finding approximate solutions for the single-source shortest paths (SSSP) problem. As a consequence, we improve upon prior work by obtaining the following results: (1) Broadcast CONGEST model: $(1 + \varepsilon)$-approximate SSSP using $\tilde{O}((\sqrt{n} + D)\varepsilon^{-3})$ rounds, where $D$ is the (hop) diameter of the network. (2) Broadcast congested clique model: $(1 + \varepsilon)$-approximate transshipment and SSSP using $\tilde{O}(\varepsilon^{-2})$ rounds. (3) Multipass streaming model: $(1 + \varepsilon)$-approximate transshipment and SSSP using $\tilde{O}(n)$ space and $\tilde{O}(\varepsilon^{-2})$ passes. The previously fastest SSSP algorithms for these models leverage sparse hop sets. We bypass the hop set construction; computing a spanner is sufficient with our method. The above bounds assume non-negative edge weights that are polynomially bounded in $n$; for general non-negative weights, running times scale with the logarithm of the maximum ratio between non-zero weights.Comment: Accepted to SIAM Journal on Computing. Preliminary version in DISC 2017. Abstract shortened to fit arXiv's limitation to 1920 character

Which One is Me?: Identifying Oneself on Public Displays

While user representations are extensively used on public displays, it remains unclear how well users can recognize their own representation among those of surrounding users. We study the most widely used representations: abstract objects, skeletons, silhouettes and mirrors. In a prestudy (N=12), we identify five strategies that users follow to recognize themselves on public displays. In a second study (N=19), we quantify the users' recognition time and accuracy with respect to each representation type. Our findings suggest that there is a significant effect of (1) the representation type, (2) the strategies performed by users, and (3) the combination of both on recognition time and accuracy. We discuss the suitability of each representation for different settings and provide specific recommendations as to how user representations should be applied in multi-user scenarios. These recommendations guide practitioners and researchers in selecting the representation that optimizes the most for the deployment's requirements, and for the user strategies that are feasible in that environment