arXiv subjects

Robert Morris

Publications and source records attributed to Robert Morris.

At least 19 recordsLinked to original sources

arXiv2026

Fast end-to-end cloud application cold-start with initscripts

Serverless functions are a popular way of deploying cloud applications. Because many of these functions are short- running and experience frequent cold-starts, start latencies often dominate their execution latency. Start latency can be broken down into two components: setup and initialization. Setup involves steps the cloud platform takes when starting an application, such as downloading its binary and creating an isolated execution environment. Initialization involves steps the application takes after it has started running but before it can do useful work, such as connecting to other services, coordinating to claim work, and downloading inputs. This paper contributes initscripts, which provide a script- able interface for developers to specify their application's initialization routine to the cloud platform. The platform can then run an application's initscript and reduce application start latency by overlapping setup and initialization steps. Once the application is up and running, the initscript bootstraps the application by transferring initialization results to it. Using initscripts, we were able to speed up cold-starts of several of the ServerlessBench Python applications by an average 1.67X with no modifications to the application. Initscripts also speed up start times for a serverless image recognition workload by 1.81X, and off-the-shelf microservices like etcd and memcached.

cs.DC↗

arXiv2026

On the Erd\H{o}s-Rogers function

We show that the Erd\H{o}s-Rogers function $f_{s,s+1}(n)$ satisfies $$f_{s,s+1}(n) = \Theta( \sqrt{n \log n} )$$ for every $s \ge 2$. More precisely, we construct a $K_{s+1}$-free graph on $n$ vertices in which every set of at least $C(s)\sqrt{n \log n}$ vertices contains a copy of $K_s$ for some constant $C(s)$, which implies the upper bound. The matching lower bound follows from a theorem of Joret, Micek, Reed and Smid on the clique chromatic number of a graph.

math.CO↗

arXiv2026

Some recent results in Ramsey theory

The purpose of this survey is to provide a gentle introduction to several recent breakthroughs in graph Ramsey theory. In particular, we will outline the proofs (due to various groups of authors) of exponential improvements to the diagonal, near-diagonal, and multicolour Ramsey numbers, improved lower bounds on $R(3,k)$ and $R(4,k)$, and an exponential upper bound on the induced Ramsey numbers.

math.CO↗

arXiv2025

Evaluation of A National Digitally-Enabled Health Promotion Campaign for Mental Health Awareness using Social Media Platforms Tik Tok, Facebook, Instagram, and YouTube

Mental health disorders rank among the 10 leading contributors to the global burden of diseases, yet persistent stigma and care barriers delay early intervention. This has inspired efforts to leverage digital platforms for scalable health promotion to engage at-risk populations. To evaluate the effectiveness of a digitally-enabled mental health promotion (DEHP) campaign, we conducted an observational cross-sectional study of a 3-month (February-April 2025) nation-wide campaign in Singapore. Campaign materials were developed using a marketing funnel framework and disseminated across YouTube, Facebook, Instagram, and TikTok. This included narrative videos and infographics to promote symptom awareness, coping strategies, and/or patient navigation to Singapore's Mindline website, as the intended endpoint for user engagement and support. Primary outcomes include anonymised performance analytics (impressions, unique reach, video content view, engagements) stratified by demographics, device types, and sector. Secondary outcomes measured cost-efficiency metrics and traffic to the Mindline website respectively. This campaign generated 3.49 million total impressions and reached 1.39 million unique residents, with a Cost Per Click at 29.33 SGD, Cost Per Mille at 26.90 SGD and Cost Per Action at 6.06 SGD. Narrative videos accumulated over 630,000 views and 18,768 engagements. Overall, we demonstrate that DEHP campaigns can achieve national engagement for mental health awareness through multi-channel distribution and creative, narrative-driven designs.

cs.SI↗

arXiv2025

Probabilistic modelling and safety assurance of an agriculture robot providing light-treatment

Continued adoption of agricultural robots postulates the farmer's trust in the reliability, robustness and safety of the new technology. This motivates our work on safety assurance of agricultural robots, particularly their ability to detect, track and avoid obstacles and humans. This paper considers a probabilistic modelling and risk analysis framework for use in the early development phases. Starting off with hazard identification and a risk assessment matrix, the behaviour of the mobile robot platform, sensor and perception system, and any humans present are captured using three state machines. An auto-generated probabilistic model is then solved and analysed using the probabilistic model checker PRISM. The result provides unique insight into fundamental development and engineering aspects by quantifying the effect of the risk mitigation actions and risk reduction associated with distinct design concepts. These include implications of adopting a higher performance and more expensive Object Detection System or opting for a more elaborate warning system to increase human awareness. Although this paper mainly focuses on the initial concept-development phase, the proposed safety assurance framework can also be used during implementation, and subsequent deployment and operation phases.

cs.RO↗

arXiv2025

Random cliques in random graphs revisited

We study the distribution of the set of copies of some given graph $H$ in the random graph $G(n,p)$, focusing on the case when $H = K_r$. Our main results capture the 'leading term' in the difference between this distribution and the 'independent hypergraph model', where (in the case $H = K_r$) each copy is present independently with probability $\pi = p^{\binom{r}{2}}$. As a concrete application, we derive a new upper bound on the number of $K_r$-factors in $G(n,p)$ above the threshold for such factors to appear. We will prove our main results in a much more general setting, so that they also apply to random hypergraphs, and also (for example) to the case when $p$ is constant and $r = r(n) \sim 2\log_{1/p}(n)$.

math.CO↗

arXiv2024

Upper bounds for multicolour Ramsey numbers

The $r$-colour Ramsey number $R_r(k)$ is the minimum $n \in \mathbb{N}$ such that every $r$-colouring of the edges of the complete graph $K_n$ on $n$ vertices contains a monochromatic copy of $K_k$. We prove, for each fixed $r \geqslant 2$, that $$R_r(k) \leqslant e^{-\delta k} r^{rk}$$ for some constant $\delta = \delta(r) > 0$ and all sufficiently large $k \in \mathbb{N}$. For each $r \geqslant 3$, this is the first exponential improvement over the upper bound of Erd\H{o}s and Szekeres from 1935. In the case $r = 2$, it gives a different (and significantly shorter) proof of a recent result of Campos, Griffiths, Morris and Sahasrabudhe.

math.CO↗

arXiv2023

An exponential improvement for diagonal Ramsey

The Ramsey number $R(k)$ is the minimum $n \in \mathbb{N}$ such that every red-blue colouring of the edges of the complete graph $K_n$ on $n$ vertices contains a monochromatic copy of $K_k$. We prove that \[ R(k) \leqslant (4 - \varepsilon)^k \] for some constant $\varepsilon > 0$. This is the first exponential improvement over the upper bound of Erd\H{o}s and Szekeres, proved in 1935.

math.CO↗

arXiv2022

A lower bound for set-colouring Ramsey numbers

The set-colouring Ramsey number $R_{r,s}(k)$ is defined to be the minimum $n$ such that if each edge of the complete graph $K_n$ is assigned a set of $s$ colours from $\{1,\ldots,r\}$, then one of the colours contains a monochromatic clique of size $k$. The case $s = 1$ is the usual $r$-colour Ramsey number, and the case $s = r - 1$ was studied by Erd\H{o}s, Hajnal and Rado in 1965, and by Erd\H{o}s and Szemer\'edi in 1972. The first significant results for general $s$ were obtained only recently, by Conlon, Fox, He, Mubayi, Suk and Verstra\"ete, who showed that $R_{r,s}(k) = 2^{\Theta(kr)}$ if $s/r$ is bounded away from $0$ and $1$. In the range $s = r - o(r)$, however, their upper and lower bounds diverge significantly. In this note we introduce a new (random) colouring, and use it to determine $R_{r,s}(k)$ up to polylogarithmic factors in the exponent for essentially all $r$, $s$ and $k$.

math.CO↗

arXiv2022

Erd\H{o}s covering systems

A covering system is a finite collection of arithmetic progressions whose union is the set of integers. The study of these objects was initiated by Erd\H{o}s in 1950, and over the following decades he asked many questions about them. Most famously, he asked whether there exist covering systems with distinct moduli whose minimum modulus is arbitrarily large. This problem was resolved in 2015 by Hough, who showed that in any such system the minimum modulus is at most $10^{16}$. The purpose of this note is to give a gentle exposition of a simpler and stronger variant of Hough's method, which was recently used to answer several other questions about covering systems. We hope that this technique, which we call the distortion method, will have many further applications in other combinatorial settings.

math.CO↗

arXiv2022

CheckSync: Using Runtime-Integrated Checkpoints to Achieve High Availability}

CheckSync provides applications with high availability via runtime-integrated checkpointing. This allows CheckSync to take checkpoints of a process running in a memory-managed language (Go, for now), which can be resumed on another machine after a failure. CheckSync uses the runtime to checkpoint only the process' live memory, doing without requiring significant changes to applications. CheckSync maintains the ease of use provided by virtual machines for the applications it supports without requiring that an entire virtual machine image be snapshotted. Because CheckSync captures only the memory used by an application, it produces checkpoints that are smaller (by an order of magnitude) than virtual machine snapshots if the memory footprint of the application is relatively small compared to the state of the rest of the operating system. Additionally, when running go-cache, a popular in-memory key/value store, CheckSync reduces throughput by only 12% compared to the 78% throughput loss when using go-cache's snapshot functionality, the 45% loss when using CRIU, and the 68% loss when using virtual machine live migration.

cs.DC↗

arXiv2022

Towards Hadwiger's conjecture via Bourgain Slicing

In 1957, Hadwiger conjectured that every convex body in $\mathbb{R}^d$ can be covered by $2^d$ translates of its interior. For over 60 years, the best known bound was of the form $O(4^d \sqrt{d} \log d)$, but this was recently improved by a factor of $e^{\Omega(\sqrt{d})}$ by Huang, Slomka, Tkocz and Vritsiou. In this note we take another step towards Hadwiger's conjecture by deducing an almost-exponential improvement from the recent breakthrough work of Chen, Klartag and Lehec on Bourgain's slicing problem. More precisely, we prove that, for any convex body $K \subset \mathbb{R}^d$, $$\exp\bigg( - \Omega\bigg( \frac{d}{(\log d)^8} \bigg) \bigg) \cdot 4^d$$ translates of $\text{int}(K)$ suffice to cover $K$. We also show that a positive answer to Bourgain's slicing problem would imply an exponential improvement for Hadwiger's conjecture.

math.MG↗

arXiv2022

Universality for monotone cellular automata

In this paper we study monotone cellular automata in $d$ dimensions. We develop a general method for bounding the growth of the infected set when the initial configuration is chosen randomly, and then use this method to prove a lower bound on the critical probability for percolation that is sharp up to a constant factor in the exponent for every 'critical' model. This is one of three papers that together confirm the Universality Conjecture of Bollob\'as, Duminil-Copin, Morris and Smith.

math.PR↗

arXiv2022

The critical length for growing a droplet

In many interacting particle systems, relaxation to equilibrium is thought to occur via the growth of 'droplets', and it is a question of fundamental importance to determine the critical length at which such droplets appear. In this paper we construct a mechanism for the growth of droplets in an arbitrary finite-range monotone cellular automaton on a $d$-dimensional lattice. Our main application is an upper bound on the critical probability for percolation that is sharp up to a constant factor in the exponent. Our method also provides several crucial tools that we expect to have applications to other interacting particle systems, such as kinetically constrained spin models on $\mathbb{Z}^d$. This is one of three papers that together confirm the Universality Conjecture of Bollob\'as, Duminil-Copin, Morris and Smith.

math.PR↗

arXiv2022

Subcritical monotone cellular automata

We study monotone cellular automata (also known as $\mathcal{U}$-bootstrap percolation) in $\mathbb{Z}^d$ with random initial configurations. Confirming a conjecture of Balister, Bollob\'as, Przykucki and Smith, who proved the corresponding result in two dimensions, we show that the critical probability is non-zero for all subcritical models.

math.PR↗

arXiv2021

GJ 367b: A dense ultra-short period sub-Earth planet transiting a nearby red dwarf star

Ultra-short-period (USP) exoplanets have orbital periods shorter than one day. Precise masses and radii of USPs could provide constraints on their unknown formation and evolution processes. We report the detection and characterization of the USP planet GJ 367b using high precision photometry and radial velocity observations. GJ 367b orbits a bright (V-band magnitude = 10.2), nearby, red (M-type) dwarf star every 7.7 hours. GJ 367b has a radius of $0.718 \pm 0.054$ Earth-radii, a mass of $0.546 \pm 0.078$ Earth-masses, making it a sub-Earth. The corresponding bulk density is $8.106 \pm 2.165$ g cm$^-3$, close to that of iron. An interior structure model predicts the planet has an iron core radius fraction of $86 \pm 5\%$, similar to Mercury's interior.

astro-ph.EP↗

arXiv2020

Early Time Light Curves of Type Ia Supernovae Observed with TESS

We present early time light curves of Type Ia supernovae observed in the first six sectors of TESS data. Ten of these supernovae were discovered by ASAS-SN, seven by ATLAS, six by ZTF, and one by \textit{Gaia}. For nine SNe with sufficient dynamic range ($>$3.0 mag from detection to peak), we fit power law models and search for signatures of companion stars. We find a diversity of early time light curve shapes, although most of our sources are consistent with fireball models where the flux increases $\propto t^2$. Three SN display a flatter rise with flux $\propto t$. We do not find any evidence for additional structure such as multiple power law components in the early rising light curves. For assumptions about the SN properties and the observer viewing angle, and further assuming that companion stars would be in Roche-lobe overflow, we place limits on the radii of companions for six SNe with complete coverage of the early time light curves. The upper limits are $\lesssim$\,32 R$_\odot$ for these six supernovae, $\lesssim$\,20 R$_\odot$ for five of these six, and $\lesssim$\,4 R$_\odot$ for two of these six. The small sample size does not constrain occurrence rates of single degenerate Type Ia SN progenitors, but we expect that TESS observed enough SNe in its primary mission (26 sectors) to inform this measurement. We also show that TESS is capable of detecting emission from a 1 \rsun\ companion for a Type Ia SN within 50 Mpc, and may do so after about six years.

astro-ph.SR↗

arXiv2020

On the singularity of random symmetric matrices

A well-known conjecture states that a random symmetric $n \times n$ matrix with entries in $\{-1,1\}$ is singular with probability $Θ\big( n^2 2^{-n} \big)$. In this paper we prove that the probability of this event is at most $\exp\big( - Ω( \sqrt{n} ) \big)$, improving the best known bound of $\exp\big( - Ω( n^{1/4} \sqrt{\log n} ) \big)$, which was obtained recently by Ferber and Jain. The main new ingredient is an inverse Littlewood-Offord theorem in $\mathbb{Z}_p^n$ that applies under very mild conditions, whose statement is inspired by the method of hypergraph containers.

math.CO↗