arXiv subjects

Giovanni Resta

Publications and source records attributed to Giovanni Resta.

6 recordsLinked to original sources

arXiv2026

Soohak: A Mathematician-Curated Benchmark for Evaluating Research-level Math Capabilities of LLMs

Following the recent achievement of gold-medal performance on the IMO by frontier LLMs, the community is searching for the next meaningful and challenging target for measuring LLM reasoning. Whereas olympiad-style problems measure step-by-step reasoning alone, research-level problems use such reasoning to advance the frontier of mathematical knowledge itself, emerging as a compelling alternative. Yet research-level math benchmarks remain scarce because such problems are difficult to source (e.g., Riemann Bench and FrontierMath-Tier 4 contain 25 and 50 problems, respectively). To support reliable evaluation of next-generation frontier models, we introduce Soohak, a 439-problem benchmark newly authored from scratch by 64 mathematicians. Soohak comprises two subsets. On the Challenge subset, frontier models including Gemini-3-Pro, GPT-5, and Claude-Opus-4.5 reach 30.4%, 26.4%, and 10.4% respectively, leaving substantial headroom, while leading open-weight models such as Qwen3-235B, GPT-OSS-120B, and Kimi-2.5 remain below 15%. Notably, beyond standard problem solving, Soohak introduces a refusal subset that probes a capability intrinsic to research mathematics: recognizing ill-posed problems and pausing rather than producing confident but unjustified answers. On this subset, no model exceeds 50%, identifying refusal as a new optimization target that current models do not directly address. To prevent contamination, the dataset will be publicly released in late 2026, with model evaluations available upon request in the interim.

cs.CL↗

arXiv2025

The Value of Patience in Online Grocery Shopping

Since the COVID-19 pandemic, online grocery shopping has rapidly reshaped consumer behavior worldwide, fueled by ever-faster delivery promises aimed at maximizing convenience. Yet, this growth has also substantially increased urban traffic congestion, emissions, and pollution. Despite extensive research on urban delivery optimization, little is known about the trade-off between individual convenience and these societal costs. In this study, we investigate the value of marginal extensions in delivery times, termed customer patience, in mitigating the traffic burden caused by grocery deliveries. We first conceptualize the problem and present a mathematical model that highlights a convex relationship between patience and traffic congestion. The theoretical predictions are confirmed by an extensive, network-science based analysis leveraging two large-scale datasets encompassing over 8 million grocery orders in Dubai. Our findings reveal that allowing just five additional minutes in delivery time reduces daily delivery mileage by approximately 30 percent and life-cycle CO2 emissions by 20 percent. Beyond ten minutes of added patience, however, marginal benefits diminish significantly. These results highlight that modest increases in consumer patience can deliver substantial gains in traffic reduction and sustainability, offering a scalable strategy to balance individual convenience with societal welfare in urban delivery systems.

cs.SI↗

arXiv2024

The Comma Sequence: A Simple Sequence With Bizarre Properties

The ``comma sequence'' starts with 1 and is defined by the property that if k and k' are consecutive terms, the two-digit number formed from the last digit of k and the first digit of k' is equal to the difference k'-k. If there is more than one such k', choose the smallest, but if there is no such k' the sequence terminates. The sequence begins 1, 12, 35, 94, 135, ... and, surprisingly, ends at term 2137453, which is 99999945. The paper analyzes the sequence and its generalizations to other starting values and other bases. A slight change in the rules allows infinitely long comma sequences to exist.

math.NT↗

arXiv2016

Scaling Law of Urban Ride Sharing

Sharing rides could drastically improve the efficiency of car and taxi transportation. Unleashing such potential, however, requires understanding how urban parameters affect the fraction of individual trips that can be shared, a quantity that we call shareability. Using data on millions of taxi trips in New York City, San Francisco, Singapore, and Vienna, we compute the shareability curves for each city, and find that a natural rescaling collapses them onto a single, universal curve. We explain this scaling law theoretically with a simple model that predicts the potential for ride sharing in any city, using a few basic urban quantities and no adjustable parameters. Accurate extrapolations of this type will help planners, transportation companies, and society at large to shape a sustainable path for urban growth.

physics.soc-ph↗

arXiv2014

Quantifying the benefits of vehicle pooling with shareability networks

Taxi services are a vital part of urban transportation, and a considerable contributor to traffic congestion and air pollution causing substantial adverse effects on human health. Sharing taxi trips is a possible way of reducing the negative impact of taxi services on cities, but this comes at the expense of passenger discomfort quantifiable in terms of a longer travel time. Due to computational challenges, taxi sharing has traditionally been approached on small scales, such as within airport perimeters, or with dynamical ad-hoc heuristics. However, a mathematical framework for the systematic understanding of the tradeoff between collective benefits of sharing and individual passenger discomfort is lacking. Here we introduce the notion of shareability network which allows us to model the collective benefits of sharing as a function of passenger inconvenience, and to efficiently compute optimal sharing strategies on massive datasets. We apply this framework to a dataset of millions of taxi trips taken in New York City, showing that with increasing but still relatively low passenger discomfort, cumulative trip length can be cut by 40% or more. This benefit comes with reductions in service cost, emissions, and with split fares, hinting towards a wide passenger acceptance of such a shared service. Simulation of a realistic online system demonstrates the feasibility of a shareable taxi service in New York City. Shareability as a function of trip density saturates fast, suggesting effectiveness of the taxi sharing system also in cities with much sparser taxi fleets or when willingness to share is low.

physics.soc-ph↗

arXiv2012

Flooding Time in Opportunistic Networks under Power Law and Exponential Inter-Contact Times

Performance bounds for opportunistic networks have been derived in a number of recent papers for several key quantities, such as the expected delivery time of a unicast message, or the flooding time (a measure of how fast information spreads). However, to the best of our knowledge, none of the existing results is derived under a mobility model which is able to reproduce the power law+exponential tail dichotomy of the pairwise node inter-contact time distribution which has been observed in traces of several real opportunistic networks. The contributions of this paper are two-fold: first, we present a simple pairwise contact model -- called the Home-MEG model -- for opportunistic networks based on the observation made in previous work that pairs of nodes in the network tend to meet in very few, selected locations (home locations); this contact model is shown to be able to faithfully reproduce the power law+exponential tail dichotomy of inter-contact time. Second, we use the Home-MEG model to analyze flooding time in opportunistic networks, presenting asymptotic bounds on flooding time that assume different initial conditions for the existence of opportunistic links. Finally, our bounds provide some analytical evidences that the speed of information spreading in opportunistic networks can be much faster than that predicted by simple geometric mobility models.

cs.SI↗