A Novel, Fast, Reliable, and Data-Driven Method for Simultaneous Single-Trial Mining and Amplitude—Latency Estimation Based on Proximity Graphs and Network Analysis

Both amplitude and latency of single-trial EEG/MEG recordings provide valuable information regarding functionality of the human brain. In this article, we provided a data-driven graph and network-based framework for mining information from multi-trial event-related brain recordings. In the first part, we provide the general outline of the proposed methodological approach. In the second part, we provide a more detailed illustration, and present the obtained results on every step of the algorithmic procedure. To justify the proposed framework instead of presenting the analytic data mining and graph-based steps, we address the problem of response variability, a prerequisite to reliable estimates for both the amplitude and latency on specific N/P components linked to the nature of the stimuli. The major question addressed in this study is the selection of representative single-trials with the aim of uncovering a less noisey averaged waveform elicited from the stimuli. This graph and network-based algorithmic procedure increases the signal-to-noise (SNR) of the brain response, a key pre-processing step to reveal significant and reliable amplitude and latency at a specific time after the onset of the stimulus and with the right polarity (N or P). We demonstrated the whole approach using electroencephalography (EEG) auditory mismatch negativity (MMN) recordings from 42 young healthy controls. The method is novel, fast and data-driven succeeding first to reveal the true waveform elicited by MMN on different conditions (frequency, intensity, duration, etc.). The proposed graph-oriented algorithmic pipeline increased the SNR of the characteristic waveforms and the reliability of amplitude and latency within the adopted cohort. We also demonstrated how different EEG reference schemes (REST vs. average) can influence amplitude-latency estimation. Simulation results revealed robust amplitude-latency estimations under different SNR and amplitude-latency variations with the proposed algorithm

Photoemission spectra of many-polaron systems

The cross over from low to high carrier densities in a many-polaron system is studied in the framework of the one-dimensional spinless Holstein model, using unbiased numerical methods. Combining a novel quantum Monte Carlo approach and exact diagonalization, accurate results for the single-particle spectrum and the electronic kinetic energy on fairly large systems are obtained. A detailed investigation of the quality of the Monte Carlo data is presented. In the physically most important adiabatic intermediate electron-phonon coupling regime, for which no analytical results are available, we observe a dissociation of polarons with increasing band filling, leading to normal metallic behavior, while for parameters favoring small polarons, no such density-driven changes occur. The present work points towards the inadequacy of single-polaron theories for a number of polaronic materials such as the manganites.Comment: 15 pages, 13 figures; final version, accepted for publication in Phys. Rev.

Entanglement capabilities of non-local Hamiltonians

We quantify the capability of creating entanglement for a general physical interaction acting on two qubits. We give a procedure for optimizing the generation of entanglement. We also show that a Hamiltonian can create more entanglement if one uses auxiliary systems.Comment: replaced with published version, 4 pages, no figure

Optimal simulation of two-qubit Hamiltonians using general local operations

We consider the simulation of the dynamics of one nonlocal Hamiltonian by another, allowing arbitrary local resources but no entanglement nor classical communication. We characterize notions of simulation, and proceed to focus on deterministic simulation involving one copy of the system. More specifically, two otherwise isolated systems $A$ and $B$ interact by a nonlocal Hamiltonian $H \neq H_A+H_B$. We consider the achievable space of Hamiltonians $H'$ such that the evolution $e^{-iH't}$ can be simulated by the interaction $H$ interspersed with local operations. For any dimensions of $A$ and $B$, and any nonlocal Hamiltonians $H$ and $H'$, there exists a scale factor $s$ such that for all times $t$ the evolution $e^{-iH'st}$ can be simulated by $H$ acting for time $t$ interspersed with local operations. For 2-qubit Hamiltonians $H$ and $H'$, we calculate the optimal $s$ and give protocols achieving it. The optimal protocols do not require local ancillas, and can be understood geometrically in terms of a polyhedron defined by a partial order on the set of 2-qubit Hamiltonians.Comment: (1) References to related work, (2) protocol to simulate one two-qudit Hamiltonian with another, and (3) other related results added. Some proofs are simplifie

Temperature- and quantum phonon effects on Holstein-Hubbard bipolarons

The one-dimensional Holstein-Hubbard model with two electrons of opposite spin is studied using an extension of a recently developed quantum Monte Carlo method, and a very simple yet rewarding variational approach, both based on a canonically transformed Hamiltonian. The quantum Monte Carlo method yields very accurate results in the regime of small but finite phonon frequencies, characteristic of many strongly correlated materials such as, e.g., the cuprates and the manganites. The influence of electron-electron repulsion, phonon frequency and temperature on the bipolaron state is investigated. Thermal dissociation of the intersite bipolaron is observed at high temperatures, and its relation to an existing theory of the manganites is discussed.Comment: 12 pages, 7 figures; final version, accepted for publication in Phys. Rev.

Constraining the initial temperature and shear viscosity in a hybrid hydrodynamic model of sNN\sqrt{s_{NN}}=200 GeV Au+Au collisions using pion spectra, elliptic flow, and femtoscopic radii

A new framework for evaluating hydrodynamic models of relativistic heavy ion collisions has been developed. This framework, a Comprehesive Heavy Ion Model Evaluation and Reporting Algorithm (CHIMERA) has been implemented by augmenting UVH 2+1D viscous hydrodynamic model with eccentricity fluctuations, pre-equilibrium flow, and the Ultra-relativistic Quantum Molecular Dynamic (UrQMD) hadronic cascade. A range of initial temperatures and shear viscosity to entropy ratios were evaluated for four initial profiles, $N_{part}$ and $N_{coll}$ scaling with and without pre-equilibrium flow. The model results were compared to pion spectra, elliptic flow, and femtoscopic radii from 200 GeV Au+Au collisions for the 0--20% centrality range.Two sets of initial density profiles, $N_{part}$ scaling with pre-equilibrium flow and $N_{coll}$ scaling without were shown to provide a consistent description of all three measurements.Comment: 21 pages, 32 figures, version 3 includes additional text for clarification, division of figures into more manageable units, and placement of chi-squared values in tables for ease of viewin