arXiv subjects

Laura Florescu

Publications and source records attributed to Laura Florescu.

8 recordsLinked to original sources

arXiv2025

GOD model: Privacy Preserved AI School for Personal Assistant

Personal AI assistants (e.g., Apple Intelligence, Meta AI) offer proactive recommendations that simplify everyday tasks, but their reliance on sensitive user data raises concerns about privacy and trust. To address these challenges, we introduce the Guardian of Data (GOD), a secure, privacy-preserving framework for training and evaluating AI assistants directly on-device. Unlike traditional benchmarks, the GOD model measures how well assistants can anticipate user needs-such as suggesting gifts-while protecting user data and autonomy. Functioning like an AI school, it addresses the cold start problem by simulating user queries and employing a curriculum-based approach to refine the performance of each assistant. Running within a Trusted Execution Environment (TEE), it safeguards user data while applying reinforcement and imitation learning to refine AI recommendations. A token-based incentive system encourages users to share data securely, creating a data flywheel that drives continuous improvement. Specifically, users mine with their data, and the mining rate is determined by GOD's evaluation of how well their AI assistant understands them across categories such as shopping, social interactions, productivity, trading, and Web3. By integrating privacy, personalization, and trust, the GOD model provides a scalable, responsible path for advancing personal AI assistants. For community collaboration, part of the framework is open-sourced at https://github.com/PIN-AI/God-Model.

cs.CR↗

arXiv2017

Optimal control for diffusions on graphs

Starting from a unit mass on a vertex of a graph, we investigate the minimum number of "\emph{controlled diffusion}" steps needed to transport a constant mass $p$ outside of the ball of radius $n$. In a step of a controlled diffusion process we may select any vertex with positive mass and topple its mass equally to its neighbors. Our initial motivation comes from the maximum overhang question in one dimension, but the more general case arises from optimal mass transport problems. On $\mathbb{Z}^{d}$ we show that $Θ( n^{d+2} )$ steps are necessary and sufficient to transport the mass. We also give sharp bounds on the comb graph and $d$-ary trees. Furthermore, we consider graphs where simple random walk has positive speed and entropy and which satisfy Shannon's theorem, and show that the minimum number of controlled diffusion steps is $\exp{( n \cdot h / \ell ( 1 + o(1) ))}$, where $h$ is the Avez asymptotic entropy and $\ell$ is the speed of random walk. As examples, we give precise results on Galton-Watson trees and the product of trees $\mathbb{T}_d \times \mathbb{T}_k$.

math.CO↗

arXiv2016

Spectral Thresholds in the Bipartite Stochastic Block Model

We consider a bipartite stochastic block model on vertex sets $V_1$ and $V_2$, with planted partitions in each, and ask at what densities efficient algorithms can recover the partition of the smaller vertex set. When $|V_2| \gg |V_1|$, multiple thresholds emerge. We first locate a sharp threshold for detection of the partition, in the sense of the results of \cite{mossel2012stochastic,mossel2013proof} and \cite{massoulie2014community} for the stochastic block model. We then show that at a higher edge density, the singular vectors of the rectangular biadjacency matrix exhibit a localization / delocalization phase transition, giving recovery above the threshold and no recovery below. Nevertheless, we propose a simple spectral algorithm, Diagonal Deletion SVD, which recovers the partition at a nearly optimal edge density. The bipartite stochastic block model studied here was used by \cite{feldman2014algorithm} to give a unified algorithm for recovering planted partitions and assignments in random hypergraphs and random $k$-SAT formulae respectively. Our results give the best known bounds for the clause density at which solutions can be found efficiently in these models as well as showing a barrier to further improvement via this reduction to the bipartite block model.

math.PR↗

arXiv2015

Heat diffusion with frozen boundary

Consider "Frozen Random Walk" on $\mathbb{Z}$: $n$ particles start at the origin. At any discrete time, the leftmost and rightmost $\lfloor{\frac{n}{4}}\rfloor$ particles are "frozen" and do not move. The rest of the particles in the "bulk" independently jump to the left and right uniformly. The goal of this note is to understand the limit of this process under scaling of mass and time. To this end we study the following deterministic mass splitting process: start with mass $1$ at the origin. At each step the extreme quarter mass on each side is "frozen". The remaining "free" mass in the center evolves according to the discrete heat equation. We establish diffusive behavior of this mass evolution and identify the scaling limit under the assumption of its existence. It is natural to expect the limit to be a truncated Gaussian. A naive guess for the truncation point might be the $1/4$ quantile points on either side of the origin. We show that this is not the case and it is in fact determined by the evolution of the second moment of the mass distribution.

math.PR↗

arXiv2014

The range of a rotor walk

In a \emph{rotor walk} the exits from each vertex follow a prescribed periodic sequence. On an infinite Eulerian graph embedded periodically in $\R^d$, we show that any simple rotor walk, regardless of rotor mechanism or initial rotor configuration, visits at least on the order of $t^{d/(d+1)}$ distinct sites in $t$ steps. We prove a shape theorem for the rotor walk on the comb graph with i.i.d.\ uniform initial rotors, showing that the range is of order $t^{2/3}$ and the asymptotic shape of the range is a diamond. Using a connection to the mirror model and critical percolation, we show that rotor walk with i.i.d.\ uniform initial rotors is recurrent on two different directed graphs obtained by orienting the edges of the square grid, the Manhattan lattice and the $F$-lattice. We end with a short discussion of the time it takes for rotor walk to cover a finite Eulerian graph.

math.PR↗

arXiv2014

Sandpiles and Dominos

We consider the subgroup of the abelian sandpile group of the grid graph consisting of configurations of sand that are symmetric with respect to central vertical and horizontal axes. We show that the size of this group is (i) the number of domino tilings of a corresponding weighted rectangular checkerboard; (ii) a product of special values of Chebyshev polynomials; and (iii) a double-product whose factors are sums of squares of values of trigonometric functions. We provide a new derivation of the formula due to Kasteleyn and to Temperley and Fisher for counting the number of domino tilings of a 2m x 2n rectangular checkerboard and a new way of counting the number of domino tilings of a 2m x 2n checkerboard on a Möbius strip.

math.CO↗

arXiv2013

Escape rates for rotor walk in Z^d

Rotor walk is a deterministic analogue of random walk. We study its recurrence and transience properties on Z^d for the initial configuration of all rotors aligned. If n particles in turn perform rotor walks starting from the origin, we show that the number that escape (i.e., never return to the origin) is of order n in dimensions d>=3, and of order n/log(n) in dimension 2.

math.PR↗

arXiv2013

Derivation of Radiation from a Dipole immersed in a Homogenous Magnetized Plasma

We are considering a dipole antenna immersed in cold plasma and investigate its radiation patterns. We are solving Maxwell's equations using (1) analytic solutions for the case when the antenna is parallel to the magnetic field $B_0$ and (2) numerical solutions for any orientation and angle $θ$ of the antenna. We investigate various phase velocities regimes as well as the effect of varying the frequency and the plasma parameters on the electromagnetic waves are presented and discussed.

physics.plasm-ph↗