arXiv subjects

Nancy Lynch

Publications and source records attributed to Nancy Lynch.

At least 19 recordsLinked to original sources

arXiv2025

Nanobot Algorithms for Treatment of Diffuse Cancer

Motile nanosized particles, or "nanobots", promise more effective and less toxic targeted drug delivery because of their unique scale and precision. We consider the case in which the cancer is "diffuse", dispersed such that there are multiple distinct cancer sites. We investigate the problem of a swarm of nanobots locating these sites and treating them by dropping drug payloads at the sites. To improve the success of the treatment, the drug payloads must be allocated between sites according to their "demands"; this requires extra nanobot coordination. We present a mathematical model of the behavior of the nanobot agents and of their colloidal environment. This includes a movement model for agents based upon experimental findings from actual nanoparticles in which bots noisily ascend and descend chemical gradients. We present three algorithms: The first algorithm, called KM, is the most representative of reality, with agents simply following naturally existing chemical signals that surround each cancer site. The second algorithm, KMA, includes an additional chemical payload which amplifies the existing natural signals. The third algorithm, KMAR, includes another additional chemical payload which counteracts the other signals, instead inducing negative chemotaxis in agents such that they are repelled from sites that are already sufficiently treated. We present simulation results for all algorithms across different types of cancer arrangements. For KM, we show that the treatment is generally successful unless the natural chemical signals are weak, in which case the treatment progresses too slowly. For KMA, we demonstrate a significant improvement in treatment speed but a drop in eventual success, except for concentrated cancer patterns. For KMAR, our results show great performance across all types of cancer patterns, demonstrating robustness and adaptability.

cs.MA↗

arXiv2025

Modeling Feasible Locomotion of Nanobots for Cancer Detection and Treatment

Deploying motile nanosized particles, also known as ``nanobots'', in the human body promises to improve selectivity in drug delivery and reduce side effects. We consider a swarm of nanobots locating a single cancerous region and treating it by releasing an onboard payload of drugs at the site. At nanoscale, the computation, communication, sensing, and locomotion capabilities of individual agents are extremely limited, noisy, and/or nonexistent. We present a general model to formally describe the individual and collective behavior of agents in a colloidal environment, such as the bloodstream, for cancer detection and treatment by nanobots. This includes a feasible and precise model of agent locomotion, inspired by actual nanoparticles that, in the presence of an external chemical gradient, move towards areas of higher concentration by means of self-propulsion. We present two variants of our general model: The first assumes an endogenous chemical gradient that is fixed over time and centered at the targeted cancer site; the second is a more speculative and dynamic variant in which agents themselves create and amplify a chemical gradient centered at the cancer site. In both settings, agents can sense the gradient and ascend it noisily, locating the cancer site more quickly than via simple Brownian motion. For the first variant of the model, we present simulation results to show the behavior of agents under our locomotion model, as well as {analytical results} to bound the time it takes for the agents to reach the cancer site. For the second variant, simulation results highlight the collective benefit in having agents issue their own chemical signal. While arguably more speculative in its agent capability assumptions, this variant shows a significant improvement in runtime performance over the first variant, resulting from its chemical signal amplification mechanism.

cs.MA↗

arXiv2025

Building a Theory of Distributed Systems: Work by Nancy Lynch and Collaborators

In this manuscript I overview my work on developing a Theory for Distributed Systems -- work that has involved many students and other collaborators. This effort started at Georgia Tech in the late 1970s, and has continued at MIT since 1981. This manuscript emphasizes the earlier contributions, and their impact on the directions of the field. These contributions include new distributed algorithms; rigorous proofs and analysis; discovery of errors in previous algorithms; lower bounds and other impossibility results expressing inherent limitations on the power of distributed systems; general mathematical foundations for modeling and analyzing distributed systems; and applications of these methods to understanding a variety of practical distributed systems, including distributed data-management systems, wired and wireless communication systems, and biological systems.

cs.DC↗

arXiv2024

Swarm Algorithms for Dynamic Task Allocation in Unknown Environments

Robot swarms, systems of many robots that operate in a distributed fashion, have many applications in areas such as search-and-rescue, natural disaster response, and self-assembly. Several of these applications can be abstracted to the general problem of task allocation in an environment, in which robots must assign themselves to and complete tasks. While several algorithms for task allocation have been proposed, most of them assume either prior knowledge of task locations or a static set of tasks. Operating under a discrete general model where tasks dynamically appear in unknown locations, we present three new swarm algorithms for task allocation. We demonstrate that when tasks appear slowly, our variant of a distributed algorithm based on propagating task information completes tasks more efficiently than a Levy random walk algorithm, which is a strategy used by many organisms in nature to efficiently search an environment. We also propose a division of labor algorithm where some agents are using our algorithm based on propagating task information while the remaining agents are using the Levy random walk algorithm. Finally, we introduce a hybrid algorithm where each agent dynamically switches between using propagated task information and following a Levy random walk. We show that our division of labor and hybrid algorithms can perform better than both our algorithm based on propagated task information and the Levy walk algorithm, especially at low and medium task rates. When tasks appear fast, we observe the Levy random walk strategy performs as well or better when compared to these novel approaches. Our work demonstrates the relative performance of these algorithms on a variety of task rates and also provide insight into optimizing our algorithms based on environment parameters.

cs.MA↗

arXiv2024

Abstraction in Neural Networks

We show how brain networks, modeled as Spiking Neural Networks, can be viewed at different levels of abstraction. Lower levels include complications such as failures of neurons and edges. Higher levels are more abstract, making simplifying assumptions to avoid these complications. We show precise relationships between executions of networks at different levels, which enables us to understand the behavior of lower-level networks in terms of the behavior of higher-level networks. We express our results using two abstract networks, A1 and A2, one to express firing guarantees and the other to express non-firing guarantees, and one detailed network D. The abstract networks contain reliable neurons and edges, whereas the detailed network has neurons and edges that may fail, subject to some constraints. Here we consider just initial stopping failures. To define these networks, we begin with abstract network A1 and modify it systematically to obtain the other two networks. To obtain A2, we simply lower the firing thresholds of the neurons. To obtain D, we introduce failures of neurons and edges, and incorporate redundancy in the neurons and edges in order to compensate for the failures. We also define corresponding inputs for the networks, and corresponding executions of the networks. We prove two main theorems, one relating corresponding executions of A1 and D and the other relating corresponding executions of A2 and D. Together, these give both firing and non-firing guarantees for the detailed network D. We also give a third theorem, relating the effects of D on an external reliable actuator neuron to the effects of the abstract networks on the same actuator neuron.

cs.NE↗

arXiv2024

Using Single-Neuron Representations for Hierarchical Concepts as Abstractions of Multi-Neuron Representations

Brain networks exhibit complications such as noise, neuron failures, and partial synaptic connectivity. These can make it difficult to model and analyze their behavior. This paper describes a way to address this difficulty, namely, breaking down the models and analysis using levels of abstraction. We describe the approach for the problem of recognizing hierarchically-structured concepts. Realistic models for representing hierarchical concepts use multiple neurons to represent each concept [10,1,7,3]. These models are intended to capture some behaviors of actual brains; however, their analysis can be complicated. Mechanisms based on single-neuron representations can be easier to understand and analyze [2,4], but are less realistic. Here we show that these two types of models are compatible, and in fact, networks with single-neuron representations can be regarded as formal abstractions of networks with multi-neuron representations. We do this by relating networks with multi-neuron representations like those in [3] to networks with single-neuron representations like those in [2]. Specifically, we consider two networks, H and L, with multi-neuron representations, one with high connectivity and one with low connectivity. We define two abstract networks, A1 and A2, with single-neuron representations, and prove that they recognize concepts correctly. Then we prove correctness of H and L by relating them to A1 and A2. In this way, we decompose the analysis of each multi-neuron network into two parts: analysis of abstract, single-neuron networks, and proofs of formal relationships between the multi-neuron network and single-neuron networks. These examples illustrate what we consider to be a promising, tractable approach to analyzing other complex brain mechanisms.

cs.DS↗

arXiv2024

Learning Hierarchically Structured Concepts

We study the question of how concepts that have structure get represented in the brain. Specifically, we introduce a model for hierarchically structured concepts and we show how a biologically plausible neural network can recognize these concepts, and how it can learn them in the first place. Our main goal is to introduce a general framework for these tasks and prove formally how both (recognition and learning) can be achieved. We show that both tasks can be accomplished even in presence of noise. For learning, we analyze Oja's rule formally, a well-known biologically-plausible rule for adjusting the weights of synapses. We complement the learning results with lower bounds asserting that, in order to recognize concepts of a certain hierarchical depth, neural networks must have a corresponding number of layers.

cs.AI↗

arXiv2023

Learning Hierarchically-Structured Concepts II: Overlapping Concepts, and Networks With Feedback

We continue our study from Lynch and Mallmann-Trenn (Neural Networks, 2021), of how concepts that have hierarchical structure might be represented in brain-like neural networks, how these representations might be used to recognize the concepts, and how these representations might be learned. In Lynch and Mallmann-Trenn (Neural Networks, 2021), we considered simple tree-structured concepts and feed-forward layered networks. Here we extend the model in two ways: we allow limited overlap between children of different concepts, and we allow networks to include feedback edges. For these more general cases, we describe and analyze algorithms for recognition and algorithms for learning.

cs.NE↗

arXiv2023

A Comparison of New Swarm Task Allocation Algorithms in Unknown Environments with Varying Task Density

Task allocation is an important problem for robot swarms to solve, allowing agents to reduce task completion time by performing tasks in a distributed fashion. Existing task allocation algorithms often assume prior knowledge of task location and demand or fail to consider the effects of the geometric distribution of tasks on the completion time and communication cost of the algorithms. In this paper, we examine an environment where agents must explore and discover tasks with positive demand and successfully assign themselves to complete all such tasks. We first provide a new discrete general model for modeling swarms. Operating within this theoretical framework, we propose two new task allocation algorithms for initially unknown environments -- one based on N-site selection and the other on virtual pheromones. We analyze each algorithm separately and also evaluate the effectiveness of the two algorithms in dense vs. sparse task distributions. Compared to the Levy walk, which has been theorized to be optimal for foraging, our virtual pheromone inspired algorithm is much faster in sparse to medium task densities but is communication and agent intensive. Our site selection inspired algorithm also outperforms Levy walk in sparse task densities and is a less resource-intensive option than our virtual pheromone algorithm for this case. Because the performance of both algorithms relative to random walk is dependent on task density, our results shed light on how task density is important in choosing a task allocation algorithm in initially unknown environments.

cs.MA↗

arXiv2022

A Basic Compositional Model for Spiking Neural Networks

We present a formal, mathematical foundation for modeling and reasoning about the behavior of $synchronous$, $stochastic$ $Spiking$ $Neural$ $Networks$ $(SNNs)$, which have been widely used in studies of neural computation. Our approach follows paradigms established in the field of concurrency theory. Our SNN model is based on directed graphs of neurons, classified as input, output, and internal neurons. We focus here on basic SNNs, in which a neuron's only state is a Boolean value indicating whether or not the neuron is currently firing. We also define the $external$ $behavior$ of an SNN, in terms of probability distributions on its external firing patterns. We define two operators on SNNs: a $composition$ $operator$, which supports modeling of SNNs as combinations of smaller SNNs, and a $hiding$ $operator$, which reclassifies some output behavior of an SNN as internal. We prove results showing how the external behavior of a network built using these operators is related to the external behavior of its component networks. Finally, we define the notion of a $problem$ to be solved by an SNN, and show how the composition and hiding operators affect the problems that are solved by the networks. We illustrate our definitions with three examples: a Boolean circuit constructed from gates, an $Attention$ network constructed from a $Winner$-$Take$-$All$ network and a $Filter$ network, and a toy example involving combining two networks in a cyclic fashion.

cs.DC↗

arXiv2022

A Superconducting Nanowire-based Architecture for Neuromorphic Computing

Neuromorphic computing is poised to further the success of software-based neural networks by utilizing improved customized hardware. However, the translation of neuromorphic algorithms to hardware specifications is a problem that has been seldom explored. Building superconducting neuromorphic systems requires extensive expertise in both superconducting physics and theoretical neuroscience. In this work, we aim to bridge this gap by presenting a tool and methodology to translate algorithmic parameters into circuit specifications. We first show the correspondence between theoretical neuroscience models and the dynamics of our circuit topologies. We then apply this tool to solve linear systems by implementing a spiking neural network with our superconducting nanowire-based hardware.

cs.ET↗

arXiv2022

Symbolic Knowledge Structures and Intuitive Knowledge Structures

This paper proposes that two distinct types of structures are present in the brain: Symbolic Knowledge Structures (SKSs), used for formal symbolic reasoning, and Intuitive Knowledge Structures (IKSs), used for drawing informal associations. The paper contains ideas for modeling and analyzing these structures in an algorithmic style based on Spiking Neural Networks, following the paradigm used in earlier work by Lynch, Musco, Parter, and co-workers. The paper also contains two examples of use of these structures, involving counting through a memorized sequence, and understanding simple stylized sentences. The ideas presented here are preliminary and speculative, and do not (yet) comprise a complete, coherent, algorithmic theory. I hope that posting this preliminary version will help the ideas to evolve into such a theory.

cs.DC↗

arXiv2022

A Geometry-Sensitive Quorum Sensing Algorithm for the Best-of-N Site Selection Problem

The house hunting behavior of the Temnothorax albipennis ant allows the colony to explore several nest choices and agree on the best one. Their behavior serves as the basis for many bio-inspired swarm models to solve the same problem. However, many of the existing site selection models in both insect colony and swarm literature test the model's accuracy and decision time only on setups where all potential site choices are equidistant from the swarm's starting location. These models do not account for the geographic challenges that result from site choices with different geometry. For example, although actual ant colonies are capable of consistently choosing a higher quality, further site instead of a lower quality, closer site, existing models are much less accurate in this scenario. Existing models are also more prone to committing to a low quality site if it is on the path between the agents' starting site and a higher quality site. We present a new model for the site selection problem and verify via simulation that is able to better handle these geographic challenges. Our results provide insight into the types of challenges site selection models face when distance is taken into account. Our work will allow swarms to be robust to more realistic situations where sites could be distributed in the environment in many different ways.

cs.MA↗

arXiv2021

A Spatially Dependent Probabilistic Model for House Hunting in Ant Colonies

Ant species such as Temnothorax albipennis select a new nest site in a distributed fashion that, if modeled correctly, can serve as useful information for site selection algorithms for robotic swarms and other applications. Studying and replicating the ants' house hunting behavior will also illuminate useful distributed strategies that have evolved in nature. Many of the existing models of househunting behaviour for T. albipennis make the assumption that all candidate nest sites are equally distant from the ants' home nest, or that an ant has an equal probability of finding each candidate nest site. However, realistically this is not the case, as nests that are further away from the home nest and nests that are difficult to access are less likely to be found, even if they are of higher quality. We extend previous house-hunting models to account for a pairwise distance metric between nests, compare our results to those of real colonies, and use our results to examine the effects of house hunting in nests of different spatial orientations. Our incorporation of distances in the ant model appear to match empirical data in situations where a distance-quality tradeoff between nests is relevant. Furthermore, the model continues to be on par with previous house-hunting models in experiments where all candidate nests are equidistant from the home nest, as is typically assumed.

cs.MA↗

arXiv2021

ARES: Adaptive, Reconfigurable, Erasure coded, atomic Storage

Atomicity or strong consistency is one of the fundamental, most intuitive, and hardest to provide primitives in distributed shared memory emulations. To ensure survivability, scalability, and availability of a storage service in the presence of failures, traditional approaches for atomic memory emulation, in message passing environments, replicate the objects across multiple servers. Compared to replication based algorithms, erasure code-based atomic memory algorithms has much lower storage and communication costs, but usually, they are harder to design. The difficulty of designing atomic memory algorithms further grows, when the set of servers may be changed to ensure survivability of the service over software and hardware upgrades, while avoiding service interruptions. Atomic memory algorithms for performing server reconfiguration, in the replicated systems, are very few, complex, and are still part of an active area of research; reconfigurations of erasure-code based algorithms are non-existent. In this work, we present ARES, an algorithmic framework that allows reconfiguration of the underlying servers, and is particularly suitable for erasure-code based algorithms emulating atomic objects. ARES introduces new configurations while keeping the service available. To use with ARES we also propose a new, and to our knowledge, the first two-round erasure code based algorithm TREAS, for emulating multi-writer, multi-reader (MWMR) atomic objects in asynchronous, message-passing environments, with near-optimal communication and storage costs. Our algorithms can tolerate crash failures of any client and some fraction of servers, and yet, guarantee safety and liveness property. Moreover, by bringing together the advantages of ARES and TREAS, we propose an optimized algorithm where new configurations can be installed without the objects values passing through the reconfiguration clients.

cs.DC↗

arXiv2021

SNOW Revisited: Understanding When Ideal READ Transactions Are Possible

READ transactions that read data distributed across servers dominate the workloads of real-world distributed storage systems. The SNOW Theorem stated that ideal READ transactions that have optimal latency and the strongest guarantees, i.e. "SNOW" READ transactions, are impossible in one specific setting that requires three or more clients: at least two readers and one writer. However, it left many open questions. We close all of these open questions with new impossibility results and new algorithms. First, we prove rigorously the result from the The SNOW Theorem paper saying that it is impossible to have a READ transactions system that satisfies SNOW properties with three or more clients. The insight we gained from this proof led to teasing out the implicit assumptions that are required to state the results and also, resolving the open question regarding the possibility of SNOW with two clients. We show that it is possible to design an algorithm, where SNOW is possible in a multi-writer, single-reader (MWSR) setting when a client can send messages to other clients; on the other hand, we prove it is impossible to implement SNOW in a multi-writer, single-reader (MWSR) setting, which is more general than the two-client setting, when client-to-client communication is disallowed. We also correct the previous claim in The SNOW Theorem paper that incorrectly identified one existing system, Eiger, as supporting the strongest guarantees (SW) and whose read-only transactions had bounded latency. Thus, there were no previous algorithms that provided the strongest guarantees and had bounded latency. Finally, we introduce the first two algorithms to provide the strongest guarantees with bounded latency.

cs.DC↗

arXiv2020

A superconducting nanowire spiking element for neural networks

As the limits of traditional von Neumann computing come into view, the brain's ability to communicate vast quantities of information using low-power spikes has become an increasing source of inspiration for alternative architectures. Key to the success of these largescale neural networks is a power-efficient spiking element that is scalable and easily interfaced with traditional control electronics. In this work, we present a spiking element fabricated from superconducting nanowires that has pulse energies on the order of ~10 aJ. We demonstrate that the device reproduces essential characteristics of biological neurons, such as a refractory period and a firing threshold. Through simulations using experimentally measured device parameters, we show how nanowire-based networks may be used for inference in image recognition, and that the probabilistic nature of nanowire switching may be exploited for modeling biological processes and for applications that rely on stochasticity.

q-bio.NC↗

arXiv2020

Integrating Temporal Information to Spatial Information in a Neural Circuit

In this paper, we consider networks of deterministic spiking neurons, firing synchronously at discrete times; such spiking neural networks are inspired by networks of neurons and synapses that occur in brains. We consider the problem of translating temporal information into spatial information in such networks, an important task that is carried out by actual brains. Specifically, we define two problems: "First Consecutive Spikes Counting (FCSC)" and "Total Spikes Counting (TSC)", which model spike and rate coding aspects of translating temporal information into spatial information respectively. Assuming an upper bound of $T$ on the length of the temporal input signal, we design two networks that solve these two problems, each using $O(\log T)$ neurons and terminating in time $1$. We also prove that there is no network with less than $T$ neurons that solves either question in time $0$.

cs.DC↗