arXiv subjects

Cristina Gava

Publications and source records attributed to Cristina Gava.

3 recordsLinked to original sources

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↗

arXiv2024

Community Consensus: Converging Locally despite Adversaries and Heterogeneous Connectivity

We introduce the concept of community consensus in the presence of malicious agents using a well-known median-based consensus algorithm. We consider networks that have multiple well-connected regions that we term communities, characterized by specific robustness and minimum degree properties. Prior work derives conditions on properties that are necessary and sufficient for achieving global consensus in a network. This, however, requires the minimum degree of the network graph to be proportional to the number of malicious agents in the network, which is not very practical in large networks. In this work, we present a natural generalization of this previous result. We characterize cases where, although global consensus is not reached, some subsets of agents $V_i$ will still converge to the same values $M_i$ among themselves. To reach this new type of consensus, we define more relaxed requirements in terms of the number of malicious agents in each community, and the number $k$ of edges connecting an agent in a community to agents external to the community.

cs.MA↗

arXiv2023

Distributed Averaging in Opinion Dynamics

We consider two simple asynchronous opinion dynamics on arbitrary graphs where every node $u$ has an initial value $ξ_u(0)$. In the first process, the NodeModel, at each time step $t\ge 0$, a random node $u$ and a random sample of $k$ of its neighbours $v_1,v_2,\cdots,v_k$ are selected. Then, $u$ updates its current value $ξ_u(t)$ to $ξ_u(t+1) = αξ_u(t) + \frac{(1-α)}{k} \sum_{i=1}^k ξ_{v_i}(t)$, where $α\in (0,1)$ and $k\ge 1$ are parameters of the process. In the second process, the EdgeModel, at each step a random pair of adjacent nodes $(u,v)$ is selected, and then node $u$ updates its value equivalently to the NodeModel with $k=1$ and $v$ as the selected neighbour. For both processes, the values of all nodes converge to $F$, a random variable depending on the random choices made in each step. For the NodeModel and regular graphs, and for the EdgeModel and arbitrary graphs, the expectation of $F$ is the average of the initial values $\frac{1}{n}\sum_{u\in V} ξ_u(0)$. For the NodeModel and non-regular graphs, the expectation of $F$ is the degree-weighted average of the initial values. Our results are two-fold. We consider the concentration of $F$ and show tight bounds on the variance of $F$ for regular graphs. We show that, when the initial values do not depend on the number of nodes, then the variance is negligible, hence the nodes are able to estimate the initial average of the node values. Interestingly, this variance does not depend on the graph structure. For the proof we introduce a duality between our processes and a process of two correlated random walks. We also analyse the convergence time for both models and for arbitrary graphs, showing bounds on the time $T_\varepsilon$ required to make all node values `$\varepsilon$-close' to each other. Our bounds are asymptotically tight under assumptions on the distribution of the initial values.

math.PR↗