Random Walk Phase Research Articles

Revisiting Non-Coherent Detection of Differential PSK: A Factor Graph Perspective

For non-coherent differential modulated communications, the multiple-symbol differential detection (MSDD) may approach the coherent detection performance by jointly detecting a block of symbols. However, MSDD cannot support large-size block detection due to its complexity exponentially increasing with the block size. Moreover, MSDD assumes that the channel phase is constant over the symbols in a block, which is not realistic. In this letter, we propose to formulate the signal model of non-coherent differential modulated communications by means of a factor graph. Based on the factor graph, we develop a sum-product message-passing algorithm to enable the maximum a posteriori probability detection. Compared with MSDD, the detection complexity of our proposed scheme is linearly proportional to the block size. Simulation results show that the proposed scheme can not only achieve the performance of MSDD over the constant-phase channel, but also outperform it over the random-walk phase channel.

Advancing hybrid quantum–classical computation with real-time execution

The use of mid-circuit measurement and qubit reset within quantum programs has been introduced recently and several applications demonstrated that perform conditional branching based on these measurements. In this work, we go a step further and describe a next-generation implementation of classical computation embedded within quantum programs that enables the real-time calculation and adjustment of program variables based on the mid-circuit state of measured qubits. A full-featured Quantum Intermediate Representation (QIR) model is used to describe the quantum circuit including its embedded classical computation. This integrated approach eliminates the need to evaluate and store a potentially prohibitive volume of classical data within the quantum program in order to explore multiple solution paths. It enables a new type of quantum algorithm that requires fewer round-trips between an external classical driver program and the execution of the quantum program, significantly reducing computational latency, as much of the classical computation can be performed during the coherence time of quantum program execution. We review practical challenges to implementing this approach along with developments underway to address these challenges. An implementation of this novel and powerful quantum programming pattern, a random walk phase estimation algorithm, is demonstrated on a physical quantum computer with an analysis of its benefits and feasibility as compared to existing quantum computing methods.

Joint parameter estimation and decoding in a distributed receiver

SummaryThis paper presents an algorithm for iterative joint channel parameter (carrier phase, Doppler shift, and Doppler rate) estimation and decoding of transmission over channels affected by Doppler shift and Doppler rate using a distributed receiver. This algorithm is derived by applying the sum‐product algorithm (SPA) to a factor graph representing the joint a posteriori distribution of the information symbols and channel parameters given the channel output. In this paper, we present two methods for dealing with intractable messages of the SPA. In the first approach, we use particle filtering with sequential importance sampling for the estimation of the unknown parameters. We also propose a method for fine‐tuning of particles for improved convergence. In the second approach, we approximate our model with a random walk phase model, followed by a phase tracking algorithm and polynomial regression algorithm to estimate the unknown parameters. We derive the Weighted Bayesian Cramer‐Rao Bounds for joint carrier phase, Doppler shift, and Doppler rate estimation, which take into account the prior distribution of the estimation parameters and are accurate lower bounds for all considered signal‐to‐noise ratio values. Numerical results (of bit error rate and the mean‐square error of parameter estimation) suggest that phase tracking with the random walk model slightly outperforms particle filtering. However, particle filtering has a lower computational cost than the random walk model‐based method.

The effect of phase fluctuation and beam splitter fluctuation on two-photon quantum random walk

In the optical quantum random walk system, phase fluctuation and beam splitter fluctuation are two unavoidable decoherence factors. These two factors degrade the performance of quantum random walk by destroying coherence, and even degrade it into a classical one. We propose a scheme for the simulation of quantum random walk using phase shifters, tunable beam splitters, and photodetectors. This proposed scheme enables us to analyze the effect of phase fluctuation and beam splitter fluctuation on two-photon quantum random walk. Furthermore, it is helpful to guide the control of phase fluctuation and beam splitter fluctuation in the experiment.

Parallelizing approximate single-source personalized PageRank queries on shared memory

Given a directed graph G, a source node s, and a target node t, the personalized PageRank (PPR) $$\pi (s,t)$$ measures the importance of node t with respect to node s. In this work, we study the single-source PPR query, which takes a source node s as input and outputs the PPR values of all nodes in G with respect to s. The single-source PPR query finds many important applications, e.g., community detection and recommendation. Deriving the exact answers for single-source PPR queries is prohibitive, so most existing work focuses on approximate solutions. Nevertheless, existing approximate solutions are still inefficient, and it is challenging to compute single-source PPR queries efficiently for online applications. This motivates us to devise efficient parallel algorithms running on shared-memory multi-core systems. In this work, we present how to efficiently parallelize the state-of-the-art index-based solution FORA, and theoretically analyze the complexity of the parallel algorithms. Theoretically, we prove that our proposed algorithm achieves a time complexity of $$O(W/P+\log ^2{n})$$, where W is the time complexity of sequential FORA algorithm, P is the number of processors used, and n is the number of nodes in the graph. FORA includes a forward push phase and a random walk phase, and we present optimization techniques to both phases, including effective maintenance of active nodes, improving the efficiency of memory access, and cache-aware scheduling. Extensive experimental evaluation demonstrates that our solution achieves up to 37$$\times $$ speedup on 40 cores and 3.3$$\times $$ faster than alternatives on 40 cores. Moreover, the forward push alone can be used for local graph clustering, and our parallel algorithm for forward push is 4.8$$\times $$ faster than existing parallel alternatives.

Timing Jitter Distribution and Power Spectral Density of a Second-Order Bang–Bang Digital PLL With Transport Delay Using Fokker–Planck Equations

In this paper, a second-order bang-bang digital phase-locked loop (BBPLL) with dominant random walk phase noise and transport delay is analyzed using Fokker-Plank equations. Explicit closed-form expressions are derived for the timing error probability distribution function, jitter variance, and power spectral density (psd). For the type-II BBPLL considered in this paper, the timing error distribution is shown to be Laplacian and not Gaussian distributed as previously assumed, while the derived psd is Lorentzian, which is consistent with earlier works. The analytical solutions are valid as long as the continuous-time approximation of the BBPLL dynamics is accurate as is the case for typical operating loop bandwidths. The accuracy of the derived expressions is validated via simulation.

A Tool for Characterizing Randomness and Irregularity in Patient Respiratory Motion

Patient random irregular breathing undermines the fundamental assumption for 4DCT and radiotherapy based on it, either ITV-based or gated treatments. During patient’s 4DCT simulation, Respiratory Gating Signal Waveform (RGSW) is usually collected over a duration much longer than one breathing cycle. Therefore, RGSW may contain valuable information on irregularities in the patient breathing cycles and help to improve imaging and delivery in 4D radiation therapy. In this study, we developed a RGSW based tool for quantitatively accessing the randomness and irregularity level in patient respiratory motion. Totally 242 clinical RGSWs obtained with Varian Real-time Position Management (RPM) system were included in this study. For each RGSW, firstly we constructed its unwrapped phase φ(t) using Hilbert transform. Secondly, we computed the phase differences, i.e., φ(t+τ)-φ(t), between any two points along the waveform with a fixed time interval τ. Thirdly, we estimated the standard deviation σ of the phase differences. Finally, we calculated volatility (i.e., σ ⁄√τ) of the RGSW's phase in the given time interval τ. Sixteen intervals (i.e., τ=1s, 2s, 3s, …, 16s) were selected for volatility’s computation to examine if it was stable over different time intervals. The relative standard deviation of the acquired volatility values at all 16 time-intervals was computed for each RGSW. Fittings were performed on the histograms formed by observed volatility over a fixed time interval (e.g., 4s) and the relative standard deviation in its measured values with all 16 intervals from all patient RPM RGSWs. A stochastic random walk phase model was utilized to interpret the results. The unwrapped phase of an ideal periodic RGSW always has zero volatility. For our clinical RGSWs, the volatility is non-zero but reasonably stable over the selected time intervals. The observed volatility at 4s interval from the 242 RGSWs (∈ [0.07, 3.7] (1⁄√s), median=0.78 (1⁄√s)) could be approximated by a Gamma distribution Γ(3.0, 0.3). The population histogram of the relative standard deviation in volatility for the investigated time intervals (∈[2%, 35%], median=11.5%) could be fitted with a Gamma distribution Γ(3.5, 0.04). The stochastic random walk phase model, which yields a fixed volatility value over any given time interval, might serve as a useful tool in explaining our observations on phase volatility in patient's RGSW. We proposed a new application of patient’s RGSW for measuring the randomness and irregularity in patient respiratory motion. The volatility in RPM RGSW phase has a potential correlation to the eligibility and treatment response of a given patient to a given clinical procedure. Further studies are needed to explore its potential clinical role in patient 4D image acquisition and patient radiotherapy delivery.

Phase diagram and the pseudogap state in a linear chiral homopolymer model.

The phase structure of a single self-interacting homopolymer chain is investigated in terms of a universal theoretical model, designed to describe the chain in the infrared limit of slow spatial variations. The effects of chirality are studied and compared with the influence of a short-range attractive interaction between monomers, at various ambient temperature values. In the high-temperature limit the homopolymer chain is in the self-avoiding random walk phase. At very low temperatures two different phases are possible: When short-range attractive interactions dominate over chirality, the chain collapses into a space-filling conformation. But when the attractive interactions weaken, there is a low-temperature unfolding transition and the chain becomes like a straight rod. Between the high- and low-temperature limits, several intermediate states are observed, including the θ regime and pseudogap state, which is a novel form of phase state in the context of polymer chains. Applications to polymers and proteins, in particular collagen, are suggested.

Soliton driven relaxation dynamics and protein collapse in the villin headpiece

Protein collapse from a random chain to the native state involves a dynamical phase transition. During the process, new scales and collective variables become excited while old ones recede and fade away. The presence of different phases and many scales causes formidable computational bottle-necks in approaches that are based on full atomic scale scrutiny. Here we propose a way to describe the folding and unfolding processes effectively, using only the biologically relevant time and distance scales. We merge a coarse grained Landau theory that models the static collapsed protein in the low-temperature limit with a Glauber protocol that describes finite-temperature relaxation dynamics in a statistical system which is out of thermal equilibrium. As an example we inspect the collapse of a HP35 chicken villin headpiece subdomain, a paradigm specimen in protein folding studies. We simulate the folding and unfolding process by repeated heating and cooling cycles between a given low-temperature, i.e. bad solvent, environment where the protein is collapsed and various different high-temperature, i.e. good solvent, environments. We find that as long as the high temperature value stays below a value in the range that separates the random walk phase from the self-avoiding walk phase, we consistently recover the native state upon cooling. But, when heated to sufficiently high temperatures, the native state practically never recurs. Our result confirms Anfinsen’s thermodynamical hypothesis and estimates a temperature range for its validity, in the case of villin.

In Vivo Assessment of T Effector, T Regulatory Cell, Dendritic Cell Interaction in Lymphoid Tissue Using Intravital Imaging During Acute GvHD

Abstract 818Graft-versus-host disease (GvHD) is a complication that results from minor and/or major MHC incompatibilities between the donor and the recipient after hematopoietic stem cell transplantation (HSCT). Although the importance of donor T effector cells (Teffs) in inducing GvHD is well-established, the early events by which host antigen presenting cells (APCs) activate allogeneic T cells are not well described. In pathogen specific immunity, after T cells migrate to the lymph node, they initially form brief contacts with dendritic cells (DCs). This phase lasts for 6–8 hours, which is termed random-walk. Following this phase, T cells establish long-lasting arrest on DCs. At least 6 hours of stable T cell-DC interaction are required for na•ve T cells to undergo clonal expansion. After the phase of long-lasting contact, T cells start to proliferate and expand. At the same time (20∼24 hrs), their interactions with DCs become very short again. It is not clear if allogeneic T cells follow a similar tri-phasic activation process. In addition, studies on autoimmunity have shown that Tregs can prevent T cell activation by prolonged interaction with APCs. However, the mechanisms by which donor regulatory T cells (Tregs) regulate T effector responses in GvHD in lymphoid tissue has not described previously.In this study, we have used intravital microscopy to monitor the movement of donor na•ve T cells and Tregs within lymph nodes after bone marrow transplantation (BMT) in a C57BL/6 to BALB/c murine model (Figure 1A, DCs are green, T cells are red). We have found that donor na•ve T cells do not follow the triphasic activation process demonstrated by von Andrian’s group for pathogen-specific transgenic T cells. Instead, a substantial minority of MHC mismatched allogeneic T cells demonstrate a diminished velocity within 4 hours of adoptive transfer. These data indicate that prolonged interactions with host DCs develop rapidly post transplant. The velocity of allogeneic T cells increased at 18 hours post BMT. Peak velocity of Teff cells occurred 24 hours post BMT, consistent with the movement pattern of activated syngeneic T cells. [Display omitted] We have also observed that although the speed of donor Treg movement is very similar to na•ve T cell 4∼6 hours after BMT, the velocity of donor Tregs is much slower than the velocity of Teffs 18 hours post BMT. This slow speed persists even at 24 hours post BMT, indicating that Tregs form very stable contacts with host DCs. Interestingly, donor na•ve T cells move significantly faster when transplanted with Tregs at a 2:1 (T:Treg) ratio (Figure 1B), suggesting that Tregs interfere with interactions between na•ve T cells and DCs.We conclude that allogeneic na•ve T cells do not go through a random-walk phase in order to interact with host DCs early post HSCT. The transplantation of Tregs with donor T cells and bone marrow cells significantly increased the velocity of donor na•ve T cells, probably diminishing the interaction of Teff cells with DCs after BMT. We believe that the large number of APCs able to present antigen in the allogeneic setting allows for rapid activation of donor Teff cells and precludes the necessity of the random-walk phase characteristic of pathogen-specific T cells. Disclosures:No relevant conflicts of interest to declare.

Elastic energy and phase structure in a continuous spin Ising chain with applications to chiral homopolymers

We present a numerical Monte Carlo analysis of the phase structure in a continuous spin Ising chain that describes chiral homopolymers. We find that depending on the value of the Metropolis temperature, the model displays the three known nontrivial phases of polymers: At low temperatures the model is in a collapsed phase, at medium temperatures it is in a random walk phase, and at high temperatures it enters the self-avoiding random walk phase. By investigating the temperature dependence of the specific energy we confirm that the transition between the collapsed phase and the random walk phase is a phase transition, while the random walk phase and self-avoiding random walk phase are separated from each other by a crossover transition. We propose that the model can be applied to characterize the statistical properties of protein folding. For this we compare the predictions of the model to a phenomenological elastic energy formula, proposed by J. Lei and K. Huang [e-print arXiv:1002.5013; Europhys. Lett. 88, 68004 (2009)] to describe folded proteins.

Characterization of periodic variations in the GPS satellite clocks

The clock products of the International Global Navigation Satellite Systems (GNSS) Service (IGS) are used to characterize the timing performance of the GPS satellites. Using 5-min and 30-s observational samples and focusing only on the sub-daily regime, approximate power-law stochastic processes are found. The Block IIA Rb and Cs clocks obey predominantly random walk phase (or white frequency) noise processes. The Rb clocks are up to nearly an order of magnitude more stable and show a flicker phase noise component over intervals shorter than about 100 s. Due to the onboard Time Keeping System in the newer Block IIR and IIR-M satellites, their Rb clocks behave in a more complex way: as an apparent random walk phase process up to about 100 s and then changing to flicker phase up to a few thousand seconds. Superposed on this random background, periodic signals have been detected in all clock types at four harmonic frequencies, n × (2.0029 ± 0.0005) cycles per day (24 h coordinated universal time or UTC), for n = 1, 2, 3, and 4. The equivalent fundamental period is 11.9826 ± 0.0030 h, which surprisingly differs from the reported mean GPS orbital period of 11.9659 ± 0.0007 h by 60 ± 11 s. We cannot account for this apparent discrepancy but note that a clear relationship between the periodic signals and the orbital dynamics is evidenced for some satellites by modulations of the spectral amplitudes with eclipse season. All four harmonics are much smaller for the IIR and IIR-M satellites than for the older blocks. Awareness of the periodic variations can be used to improve the clock modeling, including for interpolation of tabulated IGS products for higher-rate GPS positioning and for predictions in real-time applications. This is especially true for high-accuracy uses, but could also benefit the standard GPS operational products. The observed stochastic properties of each satellite clock type are used to estimate the growth of interpolation and prediction errors with time interval.

Numerical modeling of optical coherent transient processes with complex configurations—III: Noisy laser source

A previously developed numerical model based on Maxwell–Bloch equations was modified to simulate optical coherent transient and spectral hole burning processes with noisy laser sources. Random walk phase noise was simulated using laser-phase sequences generated numerically according to the normal distribution of the phase shift. The noise model was tested by comparing the simulated spectral hole burning effect with the analytical solution. The noise effects on a few typical optical coherence transient processes were investigated using this numerical tool. Flicker and random walk frequency noises were considered in accumulation process.

Differential turbo-coded modulation with APP channel estimation

A serially concatenated coding system which can operate without channel state information (CSI) with use of a simple channel-estimation technique is presented. This channel-estimation technique uses the inner decoder's a posteriori probability (APP) information about the transmitted symbols to form a channel estimate for each symbol interval, and is termed "APP channel estimation." The serially concatenated code is comprised of an outer rate-2/3 binary error-control code, separated by a bit interleaver from an inner code consisting of an 8-phase-shift keying (PSK) bit mapping and differential 8-PSK modulation. Coherent decoding provides bit-error rate performance 0.6 dB from 8-PSK capacity for large interleaver sizes. APP channel-estimation decoding without initial CSI over constant and random walk phase models shows near-coherent results, with fractions of a decibel performance loss for random walk and linear phase models.

Most probable paths in homogeneous and disordered lattices at finite temperature

We determine the geometrical properties of the most probable paths at finite temperatures T, between two points separated by a distance r, in one-dimensional lattices with positive energies of interaction ε i associated with bond i. The most probable path-length t mp in a homogeneous medium ( ε i = ε, for all i) is found to undergo a phase transition, from an optimal-like form ( t mp ∼ r) at low temperatures to a random walk form ( t mp ∼ r 2) near the critical temperature T c=ε/ ln 2 . At T> T c the most probable path-length diverges, discontinuously, for all finite endpoint separations greater than a particular value r ∗(T) . In disordered lattices, with ε i homogeneously distributed between ε− δ/2 and ε+ δ/2, the random walk phase is absent, but a phase transition to diverging t mp still takes place. Different disorder configurations have different transition points. A way to characterize the whole ensemble of disorder, for a given distribution, is suggested.

On a random vibration model

A random vibration model is investigated in this paper. The model is formulated as a cosine function with a constant frequency and a random walk phase. We show that this model is second-order stationary and can be rewritten as a vector-valued AR(1) model as well as a scalar ARMA(2, 1) model. The linear innovation sequence of the AR(1) model is shown to be a martingale difference sequence while the linear innovation sequence of the ARMA(2, 1) model is only an uncorrelated sequence. A non-linear predictor is derived from the AR(1) model while a linear predictor is derived from the ARMA(2, 1) model. We deduce that the non-linear predictor of this model has less mean square error than that of the linear predictor. This has significance, for example, for predicting seasonal phenomena with this model. In addition, the limit distributions of the sample mean, the finite Fourier transforms and the autocovariance functions are derived using a martingale approach. The limit distribution of autocovariance functions differs from the classical result given by Bartlett's formula.

On a random vibration model

A random vibration model is investigated in this paper. The model is formulated as a cosine function with a constant frequency and a random walk phase. We show that this model is second-order stationary and can be rewritten as a vector-valued AR(1) model as well as a scalar ARMA(2, 1) model. The linear innovation sequence of the AR(1) model is shown to be a martingale difference sequence while the linear innovation sequence of the ARMA(2, 1) model is only an uncorrelated sequence. A non-linear predictor is derived from the AR(1) model while a linear predictor is derived from the ARMA(2, 1) model. We deduce that the non-linear predictor of this model has less mean square error than that of the linear predictor. This has significance, for example, for predicting seasonal phenomena with this model. In addition, the limit distributions of the sample mean, the finite Fourier transforms and the autocovariance functions are derived using a martingale approach. The limit distribution of autocovariance functions differs from the classical result given by Bartlett's formula.

Joint Carrier Phase Estimation and Data Detection Algorithms for Multi-h CPM Data Transmission

A dynamic programming algorithm, developed in [1]-[4] for obtaining the joint estimate of carrier phase and data, is applied to multi h continuous phase modulation. A MAP estimator detects data and jointly tracks carrier phase consisting of a normal random walk phase jitter process. Monte Carlo computer simulations are used to evaluate the probability of error performance for two receivers employed in demodulation of multi- h CPM signals. A simplified algorithm is proposed which yields up to a tenfold reduction in computation time at the expense of less than 1 dB in signal-to-noise ratio at the error rates computed, and for suitable ranges of phase jitter increments variance.

'Modelling and Properties of Modulated RF Signals Perturbed by Oscillator Phase Instabilities and Resulting Spectral Dispersion'

Abstract : This dissertation considers the problem of characterization and stochastic properties of oscillator phase instabilities. Spectral dispersion caused by such instabilities is also determined. The instabilities are modeled using white phase, random walk phase, random walk frequency random processes as well as drift phase and frequency terms. Auto-correlation functions and power spectral densities are derived for the oscillator rf output signal containing such instabilities. Furthermore, a procedure is proposed which involves the covariance matrix of the phase random process in conjunction with the characteristic function for determining the higher order moments of the rf signal. Stationarity and ergodicity properties of the rf signals containing phase instabilities are discussed. In each case, conditions for ergodicity are established for the mean, auto-correlation function, and the power spectral density. The spectral dispersion generated by oscillator phase instabilities imposes limits on dynamic range and Doppler resolution in radar signal processing. This spectral dispersion is determined for the phase instability models considered in this dissertation. Modulating waveforms considered as examples include the cw, the infinite pulse train and the finite pulse train.

Spectral Dispersion of Modulated Signals Due to Oscillator Phase Instability: White and Random Walk Phase Model

This paper considers the modeling of oscillator phase instability and the resulting spectral dispersion. A phase covariance matrix method is developed for determining the autocorrelation function and the power spectral density of the oscillator sinusoidal RF signal when corrupted by a superposition of a white phase random process and a random walk phase random process. By limiting the discussion to phase covariance matrices, it is shown that the direct use of a certain class of nonstationary phase random processes leads to stationary RF signal autocorrelation functions and associated power spectral densities. This is so despite the nonstationary phase driving force. The procedures provided here are also applied towards the determination of the average autocorrelation function and the average spectrum when the cisoidal oscillator signal undergoes modulation. Modulating waveforms used as examples include the CW, the infinite pulse train, and the finite pulse train.