Philosophical Consolation

In November of 2012 my father was diagnosed with a severe form of brain cancer. In this paper, I outline how I try to use the teachings of two philosophers, Epictetus and Albert Camus, to try and find solace and consolation my father’s diagnosis and fate

Steve McCurry in India: A Balanced Approach to a Complicated Country

Steve McCurry has worked as a National Geographic photographer for over thirty years and has captured some of his most important images in India. These two photographic narratives—National Geographic, often criticized for its exotic portrayals of other countries, and India, long subject to Eurocentric perspectives and historicizing—frame McCurry’s effort to present the human condition in the far corners of the world. McCurry exploits these tensions as he seeks a more truthful, accurate, and ultimately complex representation of India and its people. This paper analyzes two of McCurry’s most well-known photographs—Dust Storm (1983) and Holi Man (1996)—arguing that his aesthetic purpose and technical skill enable him to engage Western viewers in an “empathetic probing of different lifeways, experiences and interests” that resists exploiting India as an exotic other

Metastability in Loss Networks with Dynamic Alternative Routing

Consider $N$ stations interconnected with links, each of capacity $K$, forming a complete graph. Calls arrive to each link at rate $\lambda$ and depart at rate $1$. If a call arrives to a link $x y$, connecting stations $x$ and $y$, which is at capacity, then a third station $z$ is chosen uniformly at random and the call is attempted to be routed via $z$: if both links $x z$ and $z y$ have spare capacity, then the call is held simultaneously on these two; otherwise the call is lost. We analyse an approximation of this model. We show rigorously that there are three phases according to the traffic intensity $\alpha := \lambda/K$: for $\alpha \in (0,\alpha_c) \cup (1,\infty)$, the system has mixing time logarithmic in the number of links $n := \binom N2$; for $\alpha \in (\alpha_c,1)$ the system has mixing time exponential in $n$, the number of links. Here $\alpha_c := \tfrac13 (5 \sqrt{10} - 13) \approx 0.937$ is an explicit critical threshold with a simple interpretation. We also consider allowing multiple rerouting attempts. This has little effect on the overall behaviour; it does not remove the metastability phase. Finally, we add trunk reservation: in this, some number $\sigma$ of circuits are reserved; a rerouting attempt is only accepted if at least $\sigma+1$ circuits are available. We show that if $\sigma$ is chosen sufficiently large, depending only on $\alpha$, not $K$ or $n$, then the metastability phase is removed.Comment: v2. Improved description of the path coupling. Title updated. Second author's name updated from "Thomas" to "Olesker-Taylor". To appear in AA

S21RS SGR No. 14 (Ballot, calculator renting service)

A Resolution To urge and request that funding of the expansion of the Calculator Renting Service be put on the Spring 2021 ballo

Geometric Bounds on the Fastest Mixing Markov Chain

In the Fastest Mixing Markov Chain problem, we are given a graph $G = (V, E)$ and desire the discrete-time Markov chain with smallest mixing time $\tau$ subject to having equilibrium distribution uniform on $V$ and non-zero transition probabilities only across edges of the graph. It is well-known that the mixing time $\tau_\textsf{RW}$ of the lazy random walk on $G$ is characterised by the edge conductance $\Phi$ of $G$ via Cheeger's inequality: $\Phi^{-1} \lesssim \tau_\textsf{RW} \lesssim \Phi^{-2} \log |V|$. Analogously, we characterise the fastest mixing time $\tau^\star$ via a Cheeger-type inequality but for a different geometric quantity, namely the vertex conductance $\Psi$ of $G$: $\Psi^{-1} \lesssim \tau^\star \lesssim \Psi^{-2} (\log |V|)^2$. This characterisation forbids fast mixing for graphs with small vertex conductance. To bypass this fundamental barrier, we consider Markov chains on $G$ with equilibrium distribution which need not be uniform, but rather only $\varepsilon$-close to uniform in total variation. We show that it is always possible to construct such a chain with mixing time $\tau \lesssim \varepsilon^{-1} (\operatorname{diam} G)^2 \log |V|$. Finally, we discuss analogous questions for continuous-time and time-inhomogeneous chains.Comment: 31 page

∞\infty-Diff: Infinite Resolution Diffusion with Subsampled Mollified States

We introduce $\infty$-Diff, a generative diffusion model which directly operates on infinite resolution data. By randomly sampling subsets of coordinates during training and learning to denoise the content at those coordinates, a continuous function is learned that allows sampling at arbitrary resolutions. In contrast to other recent infinite resolution generative models, our approach operates directly on the raw data, not requiring latent vector compression for context, using hypernetworks, nor relying on discrete components. As such, our approach achieves significantly higher sample quality, as evidenced by lower FID scores, as well as being able to effectively scale to higher resolutions than the training data while retaining detail