arXiv subjects

Efe Onaran

Publications and source records attributed to Efe Onaran.

7 recordsLinked to original sources

arXiv2024

Ising Disks: Topology Preserving Glauber Dynamics

We introduce a dynamic model where the state space is the set of contractible cubical sets in the Euclidian space. The permissible state transitions, that is addition and removal of a cube to/from the set, are closest to Eden model with topological constraints, and, we show, are locally decidable. We prove that in the planar special case the state space is connected. We then define a continuous time Markov chain with a fugacity (tendency to grow) parameter. Using the correspondence between our model on the plane and the self-avoiding polygons, we prove that the Markov chain is irreducible (due to state connectivity), and is also ergodic if the fugacity is smaller than a threshold.

math.PR↗

arXiv2023

Central Limit Theorems for Local Functionals of Dynamic Point Processes

We establish finite-dimensional central limit theorems for local, additive, interaction functions of temporally evolving point processes. The dynamics are those of a spatial Poisson process on the flat torus with points subject to a birth-death mechanism, and which move according to Brownian motion while alive. The results reveal the existence of a phase diagram describing at least three distinct structures for the limiting processes, depending on the extent of the local interactions and the speed of the Brownian motions. The proofs, which identify three different limits, rely heavily on Malliavin-Stein type CLTs for $U$-statistics on a representation of the dynamic point process via a distributionally equivalent marked point process.

math.PR↗

arXiv2022

Shuffled linear regression through graduated convex relaxation

The shuffled linear regression problem aims to recover linear relationships in datasets where the correspondence between input and output is unknown. This problem arises in a wide range of applications including survey data, in which one needs to decide whether the anonymity of the responses can be preserved while uncovering significant statistical connections. In this work, we propose a novel optimization algorithm for shuffled linear regression based on a posterior-maximizing objective function assuming Gaussian noise prior. We compare and contrast our approach with existing methods on synthetic and real data. We show that our approach performs competitively while achieving empirical running-time improvements. Furthermore, we demonstrate that our algorithm is able to utilize the side information in the form of seeds, which recently came to prominence in related problems.

stat.CO↗

arXiv2022

Functional Central Limit Theorems for Local Statistics of Spatial Birth-Death Processes in the Thermodynamic Regime

We present normal approximation results at the process level for local functionals defined on dynamic Poisson processes in $\mathbb{R}^d$. The dynamics we study here are those of a Markov birth-death process. We prove functional limit theorems in the so-called thermodynamic regime. Our results are applicable to several functionals of interest in the stochastic geometry literature, including subgraph and component counts in the random geometric graphs.

math.PR↗

arXiv2018

Gbps User Rates Using mmWave Relayed Backhaul with High Gain Antennas

Delivering Gbps high user rate over long distances (around 1 km) is challenging, and the abundant spectrum available in millimeter wave band cannot solve the challenge by its own due to the severe path loss and other limitations. Since it is economically challenging to deploy wired backhaul every few hundred meters, relays (e.g., wireless access points) have been proposed to extend the coverage of a base station which has wired connection to the core network. These relays, deployed every few hundred meters, serve the users in their vicinity and are backhauled to the base station through wireless connections. In this work, the wireless relayed backhaul design has been formulated as a topology-bandwidth-power joint optimization problem, and the influence of path loss, angular spread, array size, and RF power limitation on the user rate has been evaluated. It has been shown that for a linear network deployed along the street at 28 GHz, when high joint directional gain (50 dBi) is available, 1 Gbps user rate within cell range of 1 km can be delivered using 1.5 GHz of bandwidth (using single polarization antennas). The user rates drop precipitously when joint directional gain is reduced, or when the path loss is much more severe. When the number of RF chains is limited, the benefit of larger arrays will eventually be surpassed by the increased channel estimation penalty as the effective beamforming gain saturates owing to the channel angular spread.

cs.IT↗

arXiv2017

Projected Power Iteration for Network Alignment

The network alignment problem asks for the best correspondence between two given graphs, so that the largest possible number of edges are matched. This problem appears in many scientific problems (like the study of protein-protein interactions) and it is very closely related to the quadratic assignment problem which has graph isomorphism, traveling salesman and minimum bisection problems as particular cases. The graph matching problem is NP-hard in general. However, under some restrictive models for the graphs, algorithms can approximate the alignment efficiently. In that spirit the recent work by Feizi and collaborators introduce EigenAlign, a fast spectral method with convergence guarantees for Erdős-Renyí graphs. In this work we propose the algorithm Projected Power Alignment, which is a projected power iteration version of EigenAlign. We numerically show it improves the recovery rates of EigenAlign and we describe the theory that may be used to provide performance guarantees for Projected Power Alignment.

stat.CO↗

arXiv2016

Optimal De-Anonymization in Random Graphs with Community Structure

Anonymized social network graphs published for academic or advertisement purposes are subject to de-anonymization attacks by leveraging side information in the form of a second, public social network graph correlated with the anonymized graph. This is because the two are from the same underlying graph of true social relationships. In this paper, we (i) characterize the maximum a posteriori (MAP) estimates of user identities for the anonymized graph and (ii) provide sufficient conditions for successful de-anonymization for underlying graphs with community structure. Our results generalize prior work that assumed underlying graphs of Erdős-Rényi type, in addition to proving the optimality of the attack strategy adopted in the prior work.

cs.SI↗