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A divisor generating q-series and cumulants arising from random graphs
No full textUchimura, in 1987, introduced a probability generating function for a random variable X and using properties of this function, he discovered an interesting q-series identity. He further showed that the m-th cumulant with respect to the random variable X is nothing but the generating function for the generalized divisor function σ m - 1 ( n ) . Simon, Crippa, and Collenberg, in 1993, explored the G n , p -model of a random acyclic digraph and defined a random variable γ n ∗ ( 1 ) . Quite interestingly, they found links between the limit of its mean and the generating function for the divisor function d(n). Later in 1997, Andrews, Crippa and Simon extended these results using q-series techniques. They calculated the limit of the mean and the variance of the random variable γ n ∗ ( 1 ) which correspond to the first and second cumulants. In this paper, we generalize the result of Andrews, Crippa and Simon by calculating the limit of the t-th cumulant in terms of the generalized divisor function. Furthermore, we also discover limit forms for identities of Uchimura and Dilcher. This provides a fourth side to the Uchimura–Ramanujan–divisor-type three-way partition identities expounded by the first four authors recently
The PLATO mission
No full textPLATO (PLAnetary Transits and Oscillations of stars) is ESA’s M3 mission designed to detect and characterise extrasolar planets and perform asteroseismic monitoring of a large number of stars. PLATO will detect small planets (down to <2R Earth ) around bright stars (<11 mag), including terrestrial planets in the habitable zone of solar-like stars. With the complement of radial velocity observations from the ground, planets will be characterised for their radius, mass, and age with high accuracy (5%, 10%, 10% for an Earth-Sun combination respectively). PLATO will provide us with a large-scale catalogue of well-characterised small planets up to intermediate orbital periods, relevant for a meaningful comparison to planet formation theories and to better understand planet evolution. It will make possible comparative exoplanetology to place our Solar System planets in a broader context. In parallel, PLATO will study (host) stars using asteroseismology, allowing us to determine the stellar properties with high accuracy, substantially enhancing our knowledge of stellar structure and evolution. The payload instrument consists of 26 cameras with 12cm aperture each. For at least four years, the mission will perform high-precision photometric measurements. Here we review the science objectives, present PLATO‘s target samples and fields, provide an overview of expected core science performance as well as a description of the instrument and the mission profile towards the end of the serial production of the flight cameras. PLATO is scheduled for a launch date end 2026. This overview therefore provides a summary of the mission to the community in preparation of the upcoming operational phases
Towards AI Safety via Interpretability and Oversight
No full textIn this thesis, we advance AI safety through mechanistic interpretability and oversight methodologies across three key areas: mathematical reasoning in large language models (LLMs), the validity of sparse autoencoders, and scalable oversight. First, we reverse-engineer addition within mid-sized LLMs and discover that LLMs represent numbers as helices. We demonstrate that LLMs perform addition via the manipulation of these helices using a "Clock" algorithm, providing the first representation-level explanation of mathematical reasoning in LLMs, verified through causal interventions on model activations. Next, we rigorously evaluate sparse autoencoders (SAEs), a popular interpretability tool, by testing their effectiveness on the downstream task of probing. We test SAEs under challenging probing conditions, including data scarcity, class imbalance, label noise, and covariate shift. While SAEs occasionally outperform baseline methods, they fail to consistently enhance task performance, underscoring a potentially critical limitation of SAEs. Lastly, we introduce a quantitative framework to evaluate scalable oversight - a promising idea where weaker AI systems supervise stronger ones - as a function of model intelligence. Applying our framework to four oversight games ("Mafia," "Debate," "Backdoor Code," and "Wargames"), we identify clear scaling patterns and extend our findings through a theoretical analysis of Nested Scalable Oversight (NSO), deriving conditions for optimal oversight structures. Together, these studies advance our understanding of AI interpretability and alignment, providing insights and frameworks to progress AI safety.M.Eng
Truth and perspective
No full textSeveral studies in experimental philosophy and semantics have shown that a substantial number of English speakers consider a statement true even if it does not align with the facts, as long as it is justified from the speaker's perspective. These findings challenge the prevailing view among philosophers that truth in the empirical domain is uniformly based on a statement's correspondence to reality. In this study, we explore how perspective-taking influences truth assessments by showing that this influence depends on how the critical question assessing the statement’s truth is phrased. Our results show that when the question targets only the proposition, e.g., “Is it true that [the uttered proposition]?”), participants typically apply a correspondence view of truth—consistent with philosophical convention. But when the question also highlights the speaker (e.g., “Is [the speaker]’s answer true?”), many participants shift toward judging the statement from the speaker’s perspective. We discuss four possible explanations for this behavior and examine the implications of the findings for other philosophical discussions concerning truth and lying, the theory of reference, and norms of assertion
RiD-kit: software package designed to do enhanced sampling using reinforced dynamics
No full textBackground Developing an efficient method to accelerate the speed of molecular dynamics is a central theme in the field of molecular simulation. One category among the methods are collective-variable-based methods, which rely on predefined collective variables. The difficulty of selecting a few important collective variables hinders the methods to be applied to large systems easily. Method Here we present RiD-kit, which can utilize a large number of collective variables for enhanced sampling. The method could be applied to various kinds of systems, including biomolecules, chemical reactions and materials. In this protocol, we guide the users through all phases of the RiD-kit workflow, from preparing the input files, setting the simulation parameters and analyzing the results. Discussion The RiD-kit workflow provides an efficient and user-friendly command line tool which could submit jobs to various kinds of platforms including the high-performance computing platform, cloud server and local machines
Census-Based Population Autonomy for Marine Robots: Theory and Experiments
No full textCollaborating groups of robots show promise due in their ability to complete missions more efficiently and with improved robustness, attributes that are particularly useful for systems operating in marine environments. A key issue is how to model, analyze, and design these multi-robot systems to realize the full benefits of collaboration even with limited communication, a challenging task since the domain of multi-robot autonomy encompasses both collective and individual behaviors. This thesis presents a layered model of multi-robot autonomy that uses the principle of census, or a weighted count of the inputs from neighbors, for collective decision-making coupled with multi-objective behavior optimization for individual decision-making. The census component is expressed as a nonlinear opinion dynamics model and the multi-objective behavior optimization is accomplished using interval programming. This model can be reduced to recover foundational algorithms in distributed optimization and control, while the full model enables new types of collective behaviors that are useful in real-world scenarios. To illustrate these points, a new method for distributed optimization of subgroup allocation is introduced where robots use a gradient descent algorithm to minimize portions of the cost functions that are locally known, while being influenced by the opinion states from neighbors to account for the unobservable costs. With this method the group can collectively use the information contained in the Hessian matrix of the total global cost. In addition, the critical issue of controlling subgroup size to minimize a collective cost signal is addressed, an initial step toward establishing a general definition of controllability of the nonlinear opinion dynamics model. The utility of this model is experimentally validated in three categorically different experiments with fleets of autonomous surface vehicles: an adaptive sampling scenario, a high value unit protection scenario, and a competitive game of capture the flag.Ph.D
High Precision Binary Trait Association on PhylogeneticTrees
No full textUnderstanding how genetic variation drives microbial phenotypes is fundamental to advancing microbiology, particularly in pathogenicity, drug resistance, and host adaptation. Traditional genome-wide association study (GWAS) methods fail to account for shared evolutionary history, confounding association analyses. Microbial GWAS approaches emerged to address this, but modern methods often lack the statistical power to detect associations while controlling false discoveries, and face computational limits at scale. Here, we present SimPhyNI (Simulation-based Phylogenetic iNteraction Inference), a computational framework for detecting binary trait-trait associations in microbial populations.
SimPhyNI uses stochastic simulations of trait evolution on phylogenetic trees to detect positive and negative associations with high precision and recall. Benchmarking on large synthetic datasets, SimPhyNI achieved a precision-recall AUC (PR AUC) of 0.987 and 0.975 for positive and negative interactions, respectively, indicating near-perfect discrimination of true from neutral associations. Competing methods showed substantially lower performance, especially for negative associations. We further applied SimPhyNI to empirical datasets, recovering known biology and generating plausible hypotheses for novel mechanisms.
Though tested here on binary traits, SimPhyNI’s design supports future extension to multi-state and continuous traits using generalized models. Its high recall also makes it well-suited for constructing gene interaction networks and identifying co-evolving trait modules. By combining evolutionary modeling with scalable statistics, SimPhyNI advances our ability to uncover the genetic interactions that drive microbial function, ecology, and disease.M.Eng
Programmable Continuous Electrowetting of Liquid Metal for Reconfigurable Electronics
No full textDynamic manipulation of the shape and position of liquid metal (LM), a conductive and deformable conductor, presents new opportunities for reconfigurable electronics, fluidic logic, and soft-actuation systems. This study combines continuous electrowetting (CEW) with electrochemical modulation of the interface of LM in electrolyte to achieve tunable and directional LM manipulation in 2D spaces. A key finding is that under a fixed external electric field, the LM moves in a direction that depends on its electrochemical potential. The LM potential is controlled using a substrate featuring patterns of laser-induced graphene (LIG) since it is non-wetting to LM and electrically conductive. This strategy enables a range of functionalities, including “valves” for on-demand LM control, LM droplet sorting, feedback sensing, and fluidic logic gates. The strategy can also control the motion of LM droplets across 2D spaces. Finally, it is utilized within a reconfigurable circuit platform where the LM functions as a dynamic interconnect for sequential activation, parallel switching, and self-healing circuits. By coupling the electrically-driven motion of LM and the versatility of LIG patterning, this work establishes a versatile framework for reconfigurable electronics, programmable fluidic systems, and adaptive systems
Report to the President for year ended June 30, 2025, History Faculty
No full textThis report contains the following sections: Highlights (Arrivals & Departures, Promotions, History and HASTS, the History Office, Teaching and Curriculum, the History of Now), Faculty and Staff Updates