Physical-depth architectural requirements for generating universal photonic cluster states

Most leading proposals for linear-optical quantum computing (LOQC) use cluster states, which act as a universal resource for measurement-based (one-way) quantum computation (MBQC). In ballistic approaches to LOQC, cluster states are generated passively from small entangled resource states using so-called fusion operations. Results from percolation theory have previously been used to argue that universal cluster states can be generated in the ballistic approach using schemes which exceed the critical threshold for percolation, but these results consider cluster states with unbounded size. Here we consider how successful percolation can be maintained using a physical architecture with fixed physical depth, assuming that the cluster state is continuously generated and measured, and therefore that only a finite portion of it is visible at any one point in time. We show that universal LOQC can be implemented using a constant-size device with modest physical depth, and that percolation can be exploited using simple pathfinding strategies without the need for high-complexity algorithms.Comment: 18 pages, 10 figure

Smeared phase transitions in percolation on real complex networks

Percolation on complex networks is used both as a model for dynamics on networks, such as network robustness or epidemic spreading, and as a benchmark for our models of networks, where our ability to predict percolation measures our ability to describe the networks themselves. In many applications, correctly identifying the phase transition of percolation on real-world networks is of critical importance. Unfortunately, this phase transition is obfuscated by the finite size of real systems, making it hard to distinguish finite size effects from the inaccuracy of a given approach that fails to capture important structural features. Here, we borrow the perspective of smeared phase transitions and argue that many observed discrepancies are due to the complex structure of real networks rather than to finite size effects only. In fact, several real networks often used as benchmarks feature a smeared phase transition where inhomogeneities in the topological distribution of the order parameter do not vanish in the thermodynamic limit. We find that these smeared transitions are sometimes better described as sequential phase transitions within correlated subsystems. Our results shed light not only on the nature of the percolation transition in complex systems, but also provide two important insights on the numerical and analytical tools we use to study them. First, we propose a measure of local susceptibility to better detect both clean and smeared phase transitions by looking at the topological variability of the order parameter. Second, we highlight a shortcoming in state-of-the-art analytical approaches such as message passing, which can detect smeared transitions but not characterize their nature.Comment: 10 pages, 8 figure

Rhythmogenesis and Bifurcation Analysis of 3-Node Neural Network Kernels

Central pattern generators (CPGs) are small neural circuits of coupled cells stably producing a range of multiphasic coordinated rhythmic activities like locomotion, heartbeat, and respiration. Rhythm generation resulting from synergistic interaction of CPG circuitry and intrinsic cellular properties remains deficiently understood and characterized. Pairing of experimental and computational studies has proven key in unlocking practical insights into operational and dynamical principles of CPGs, underlining growing consensus that the same fundamental circuitry may be shared by invertebrates and vertebrates. We explore the robustness of synchronized oscillatory patterns in small local networks, revealing universal principles of rhythmogenesis and multi-functionality in systems capable of facilitating stability in rhythm formation. Understanding principles leading to functional neural network behavior benefits future study of abnormal neurological diseases that result from perturbations of mechanisms governing normal rhythmic states. Qualitative and quantitative stability analysis of a family of reciprocally coupled neural circuits, constituted of generalized Fitzhugh–Nagumo neurons, explores symmetric and asymmetric connectivity within three-cell motifs, often forming constituent kernels within larger networks. Intrinsic mechanisms of synaptic release, escape, and post-inhibitory rebound lead to differing polyrhythmicity, where a single parameter or perturbation may trigger rhythm switching in otherwise robust networks. Bifurcation analysis and phase reduction methods elucidate qualitative changes in rhythm stability, permitting rapid identification and exploration of pivotal parameters describing biologically plausible network connectivity. Additional rhythm outcomes are elucidated, including phase-varying lags and broader cyclical behaviors, helping to characterize system capability and robustness reproducing experimentally observed outcomes. This work further develops a suite of visualization approaches and computational tools, describing robustness of network rhythmogenesis and disclosing principles for neuroscience applicable to other systems beyond motor-control. A framework for modular organization is introduced, using inhibitory and electrical synapses to couple well-characterized 3-node motifs described in this research as building blocks within larger networks to describe underlying cooperative mechanisms

Unusual percolation in simple small-world networks

We present an exact solution of percolation in a generalized class of Watts-Strogatz graphs defined on a 1-dimensional underlying lattice. We find a non-classical critical point in the limit of the number of long-range bonds in the system going to zero, with a discontinuity in the percolation probability and a divergence in the mean finite-cluster size. We show that the critical behavior falls into one of three regimes depending on the proportion of occupied long-range to unoccupied nearest-neighbor bonds, with each regime being characterized by different critical exponents. The three regimes can be united by a single scaling function around the critical point. These results can be used to identify the number of long-range links necessary to secure connectivity in a communication or transportation chain. As an example, we can resolve the communication problem in a game of "telephone".Comment: 10 pages, 4 figures, revtex

T3P: Demystifying Low-Earth Orbit Satellite Broadband

The Internet is going through a massive infrastructural revolution with the advent of low-flying satellite networks, 5/6G, WiFi7, and hollow-core fiber deployments. While these networks could unleash enhanced connectivity and new capabilities, it is critical to understand the performance characteristics to efficiently drive applications over them. Low-Earth orbit (LEO) satellite mega-constellations like SpaceX Starlink aim to offer broad coverage and low latencies at the expense of high orbital dynamics leading to continuous latency changes and frequent satellite hand-offs. This paper aims to quantify Starlink's latency and its variations and components using a real testbed spanning multiple latitudes from the North to the South of Europe. We identify tail latencies as a problem. We develop predictors for latency and throughput and show their utility in improving application performance by up to 25%. We also explore how transport protocols can be optimized for LEO networks and show that this can improve throughput by up to 115% (with only a 5% increase in latency). Also, our measurement testbed with a footprint across multiple locations offers unique trigger-based scheduling capabilities that are necessary to quantify the impact of LEO dynamics.Comment: 16 page

Inferring Geodesic Cerebrovascular Graphs: Image Processing, Topological Alignment and Biomarkers Extraction

A vectorial representation of the vascular network that embodies quantitative features - location, direction, scale, and bifurcations - has many potential neuro-vascular applications. Patient-specific models support computer-assisted surgical procedures in neurovascular interventions, while analyses on multiple subjects are essential for group-level studies on which clinical prediction and therapeutic inference ultimately depend. This first motivated the development of a variety of methods to segment the cerebrovascular system. Nonetheless, a number of limitations, ranging from data-driven inhomogeneities, the anatomical intra- and inter-subject variability, the lack of exhaustive ground-truth, the need for operator-dependent processing pipelines, and the highly non-linear vascular domain, still make the automatic inference of the cerebrovascular topology an open problem. In this thesis, brain vessels’ topology is inferred by focusing on their connectedness. With a novel framework, the brain vasculature is recovered from 3D angiographies by solving a connectivity-optimised anisotropic level-set over a voxel-wise tensor field representing the orientation of the underlying vasculature. Assuming vessels joining by minimal paths, a connectivity paradigm is formulated to automatically determine the vascular topology as an over-connected geodesic graph. Ultimately, deep-brain vascular structures are extracted with geodesic minimum spanning trees. The inferred topologies are then aligned with similar ones for labelling and propagating information over a non-linear vectorial domain, where the branching pattern of a set of vessels transcends a subject-specific quantized grid. Using a multi-source embedding of a vascular graph, the pairwise registration of topologies is performed with the state-of-the-art graph matching techniques employed in computer vision. Functional biomarkers are determined over the neurovascular graphs with two complementary approaches. Efficient approximations of blood flow and pressure drop account for autoregulation and compensation mechanisms in the whole network in presence of perturbations, using lumped-parameters analog-equivalents from clinical angiographies. Also, a localised NURBS-based parametrisation of bifurcations is introduced to model fluid-solid interactions by means of hemodynamic simulations using an isogeometric analysis framework, where both geometry and solution profile at the interface share the same homogeneous domain. Experimental results on synthetic and clinical angiographies validated the proposed formulations. Perspectives and future works are discussed for the group-wise alignment of cerebrovascular topologies over a population, towards defining cerebrovascular atlases, and for further topological optimisation strategies and risk prediction models for therapeutic inference. Most of the algorithms presented in this work are available as part of the open-source package VTrails