The Rhetorical Algorithm: WikiLeaks and the Elliptical Secrets of Donald J. Trump

Algorithms were a generative force behind many of the leaks and secrets that dominated the 2016 election season. Taking the form of the identity-anonymizing Tor software that protected the identity of leakers, mathematical protocols occupied a prominent place in the secrets generated during the presidential campaign. This essay suggests that the rhetorical trope of ellipsis offers an equally crucial, algorithmic formula for explaining the public production of these secrets and leaks. It then describes the 2016 DNC leak and Donald Trump’s “I love Wikileaks” moment using the trope of ellipsis, which marks a discursive omission or gap in official executive discourse

Averaged large deviations for random walk in a random environment

In his 2003 paper, Varadhan proves the averaged large deviation principle for the mean velocity of a particle taking a nearest-neighbor random walk in a uniformly elliptic i.i.d. environment on $\mathbb{Z}^d$ with $d\geq1$, and gives a variational formula for the corresponding rate function $I_a$. Under Sznitman's transience condition (T), we show that $I_a$ is strictly convex and analytic on a non-empty open set $\mathcal{A}$, and that the true velocity of the particle is an element (resp. in the boundary) of $\mathcal{A}$ when the walk is non-nestling (resp. nestling). We then identify the unique minimizer of Varadhan's variational formula at any velocity in $\mathcal{A}$.Comment: 14 pages. In this revised version, I state and prove all of the results under Sznitman's (T) condition instead of Kalikow's condition. Also, I rewrote many parts of Section 1, streamlined some of the proofs in Section 2, fixed some typos, and improved the wording here and there. Accepted for publication in Annales de l'Institut Henri Poincar

The stochastic encounter-mating model

We propose a new model of permanent monogamous pair formation in zoological populations with multiple types of females and males. According to this model, animals randomly encounter members of the opposite sex at their so-called firing times to form temporary pairs which then become permanent if mating happens. Given the distributions of the firing times and the mating preferences upon encounter, we analyze the contingency table of permanent pair types in three cases: (i) definite mating upon encounter; (ii) Poisson firing times; and (iii) Bernoulli firing times. In the first case, the contingency table has a multiple hypergeometric distribution which implies panmixia. The other two cases generalize the encounter-mating models of Gimelfarb (1988) who gives conditions that he conjectures to be sufficient for panmixia. We formulate adaptations of his conditions and prove that they not only characterize panmixia but also allow us to reduce the model to the first case by changing its underlying parameters. Finally, when there are only two types of females and males, we provide a full characterization of panmixia, homogamy and heterogamy.Comment: 27 pages. We shortened the abstract, added Section 1.1 (Overview), and updated reference

A Fast-CSMA Algorithm for Deadline-Constrained Scheduling over Wireless Fading Channels

Recently, low-complexity and distributed Carrier Sense Multiple Access (CSMA)-based scheduling algorithms have attracted extensive interest due to their throughput-optimal characteristics in general network topologies. However, these algorithms are not well-suited for serving real-time traffic under time-varying channel conditions for two reasons: (1) the mixing time of the underlying CSMA Markov Chain grows with the size of the network, which, for large networks, generates unacceptable delay for deadline-constrained traffic; (2) since the dynamic CSMA parameters are influenced by the arrival and channel state processes, the underlying CSMA Markov Chain may not converge to a steady-state under strict deadline constraints and fading channel conditions. In this paper, we attack the problem of distributed scheduling for serving real-time traffic over time-varying channels. Specifically, we consider fully-connected topologies with independently fading channels (which can model cellular networks) in which flows with short-term deadline constraints and long-term drop rate requirements are served. To that end, we first characterize the maximal set of satisfiable arrival processes for this system and, then, propose a Fast-CSMA (FCSMA) policy that is shown to be optimal in supporting any real-time traffic that is within the maximal satisfiable set. These theoretical results are further validated through simulations to demonstrate the relative efficiency of the FCSMA policy compared to some of the existing CSMA-based algorithms.Comment: This work appears in workshop on Resource Allocation and Cooperation in Wireless Networks (RAWNET), Princeton, NJ, May, 201

Differing averaged and quenched large deviations for random walks in random environments in dimensions two and three

We consider the quenched and the averaged (or annealed) large deviation rate functions $I_q$ and $I_a$ for space-time and (the usual) space-only RWRE on $\mathbb{Z}^d$. By Jensen's inequality, $I_a\leq I_q$. In the space-time case, when $d\geq3+1$, $I_q$ and $I_a$ are known to be equal on an open set containing the typical velocity $\xi_o$. When $d=1+1$, we prove that $I_q$ and $I_a$ are equal only at $\xi_o$. Similarly, when d=2+1, we show that $I_a<I_q$ on a punctured neighborhood of $\xi_o$. In the space-only case, we provide a class of non-nestling walks on $\mathbb{Z}^d$ with d=2 or 3, and prove that $I_q$ and $I_a$ are not identically equal on any open set containing $\xi_o$ whenever the walk is in that class. This is very different from the known results for non-nestling walks on $\mathbb{Z}^d$ with $d\geq4$.Comment: 21 pages. In this revised version, we corrected our computation of the variance of $D(B_1)$ for $d=2+1$ (page 11 of the old version, after (2.31)). We also added details explaining precisely how the space-only case is handled, by mapping the appropriate objects to the space-time setup (see pages 14--17 in the new version). Accepted for publication in Communications in Mathematical Physics