Relative Distance Measurements Research Articles

Dynamics of ‘quantumness’ measures in the decohering harmonic oscillator

We studied the behaviour under decoherence of four different measures of the distance between quantum states and classical states for the harmonic oscillator coupled to a linear Markovian bath. Three of these are relative measures, using different definitions of the distance between the given quantum states and the set of all classical states. The fourth measure is an absolute one, the negative volume of the Wigner function of the state. All four measures are found to agree, in general, with each other. When applied to the eigenstates |n〉, all four measures behave non-trivially as a function of time during dynamical decoherence. First, we find that the first set of classical states to which the set of eigenstate evolves is (by all measures used) closest to the initial set. That is, all the states decohere to classicality along the ‘shortest path’. Finding this closest classical set of states helps improve the behaviour of all the relative distance measures. Second, at each point in time before becoming classical, all measures have a state n ∗ with maximal quantum-classical distance; the value n ∗ decreases as a function of time. Finally, we explore the dynamics of these non-classicality measures for more general states.

Dilution of Precision Analysis for GNSS Collaborative Positioning

Performance analysis of Global Navigation Satellite Systems (GNSS) collaborative positioning accuracy is a challenging task since there are too many impact factors. To simplify the analysis, the collaborative dilution of precision (CDOP) model is proposed to specify the multiplicative effect of various factors on the accuracy of collaborative positioning. Based on this CDOP model, the theoretical analysis and simulation tests are performed, and the results are compared with GNSS standalone positioning. The impacts of the number of users and their distribution and of relative distance measurement accuracy are also analyzed and verified under this CDOP model. Experiments are carried out with several real-time GNSS receivers in actual outdoor and partially blockage scenarios, respectively, and the results are consistent with theoretical analysis.

Genetically Encoding Single-Molecule Fluorophores into Ion Channels in Living Cells

We have developed a new approach to track protein dynamics in living cells on a single-molecule level with genetically encoded fluorescent non-canonical amino acids (ncAAs). The probes are based on amino acids with free primary amines that are chemically coupled to commercially available fluorophores, such as Cy3 and Cy5. Specific incorporation of fluorescent ncAAs was achieved by nonsense suppression in Xenopus laevis oocytes and confirmed by two-electrode voltage clamp of rescued ionic currents as well as by total internal reflection fluorescence microscopy detecting single fluorophores in the plasma membrane. Overall, the data show that these fluorescent ncAA were accepted as substrates for the X. laevis translation machinery. To date, we have encoded five fluorescent ncAAs into intracellular, extracellular and transmembrane regions of a CLC chloride channel or a voltage-gated sodium channel. Moreover, the variation in the linker length between the alpha carbon atom and the fluorescent moiety of the ncAA was explored by coupling to para-amino-phenylalanine, lysine and diaminopropionic acid and shows that linker length does not significantly affect the incorporation efficiency. This approach overcomes limitations of existing methods to study protein dynamics in living cells and is applicable to virtually any membrane protein. New applications include the detection of stoichiometry of macromolecular complexes by photo-bleaching of diffraction-limited puncta or the acquisition of relative distance measurements resulting from dynamic conformational changes within a membrane protein by Forster resonance energy transfer, both on a single-molecule level.

Joint inversion of Rayleigh-wave dispersion data and vertical electric sounding data: synthetic tests on characteristic sub-surface models

In the traditional inversion of the Rayleigh dispersion curve, layer thickness, which is the second most sensitive parameter of modelling the Rayleigh dispersion curve, is usually assumed as correct and is used as fixed a priori information. Because the knowledge of the layer thickness is typically not precise, the use of such a priori information may result in the traditional Rayleigh dispersion curve inversions getting trapped in some local minima and may show results that are far from the real solution. In this study, we try to avoid this issue by using a joint inversion of the Rayleigh dispersion curve data with vertical electric sounding data, where we use the common-layer thickness to couple the two methods. The key idea of the proposed joint inversion scheme is to combine methods in one joint Jacobian matrix and to invert for layer S-wave velocity, resistivity, and layer thickness as an additional parameter, in contrast with a traditional Rayleigh dispersion curve inversion. The proposed joint inversion approach is tested with noise-free and Gaussian noise data on six characteristic, synthetic sub-surface models: a model with a typical dispersion; a low-velocity, half-space model; a model with particularly stiff and soft layers, respectively; and a model reproduced from the stiff and soft layers for different layer-resistivity propagation. In the joint inversion process, the non-linear damped least squares method is used together with the singular value decomposition approach to find a proper damping value for each iteration. The proposed joint inversion scheme tests many damping values, and it chooses the one that best approximates the observed data in the current iteration. The quality of the joint inversion is checked with the relative distance measure. In addition, a sensitivity analysis is performed for the typical dispersive sub-surface model to illustrate the benefits of the proposed joint scheme. The results of synthetic models revealed that the combination of the Rayleigh dispersion curve and vertical electric sounding methods in a joint scheme allows to provide reliable sub-surface models even in complex and challenging situations and without using any a priori information.

Mixing times towards demographic equilibrium in insect populations with temperature variable age structures

In this study, we use entropy related mixing rate modules to measure the effects of temperature on insect population stability and demographic breakdown. The uncertainty in the age of the mother of a randomly chosen newborn, and how it is moved after a finite act of time steps, is modeled using a stochastic transformation of the Leslie matrix. Age classes are represented as a cycle graph and its transitions towards the stable age distribution are brought forth as an exact Markov chain. The dynamics of divergence, from a non equilibrium state towards equilibrium, are evaluated using the Kolmogorov–Sinai entropy. Moreover, Kullback–Leibler distance is applied as information-theoretic measure to estimate exact mixing times of age transitions probabilities towards equilibrium.Using empirically data, we show that on the initial conditions and simulated projection’s trough time, that population entropy can effectively be applied to detect demographic variability towards equilibrium under different temperature conditions. Changes in entropy are correlated with the fluctuations of the insect population decay rates (i.e. demographic stability towards equilibrium). Moreover, shorter mixing times are directly linked to lower entropy rates and vice versa. This may be linked to the properties of the insect model system, which in contrast to warm blooded animals has the ability to greatly change its metabolic and demographic rates. Moreover, population entropy and the related distance measures that are applied, provide a means to measure these rates. The current results and model projections provide clear biological evidence why dynamic population entropy may be useful to measure population stability.

Pulsed Eddy Current Detection of Cracks in Multilayer Aluminum Lap Joints

Aging aircraft is susceptible to cyclic fatigue cracks around ferrous fasteners in multilayer aluminum wing lap joints, as found on Canadian Military aircraft CP-140 Aurora and CC-130 Hercules. Current methods of crack detection utilize bolt hole eddy current, requiring fastener removal, a time consuming process that also has the potential to result in collateral damage. In this paper, pulsed eddy currents (PECs) are induced in the aluminum wing structure by a probe centered over a ferrous fastener. The response signals are analyzed using a modified principal components analysis (PCA) and cluster analysis to show separation of groups of PCA scores from fasteners with and without notches in the bore hole. The Mahalanobis distance (MD), a cluster analysis method, is used to obtain a relative distance measurement between scores associated with cracks from those without cracks. The MD evaluation provides confidence intervals for detection of cracks, which range in extent from fastener holes from 0.9 to 5.5 mm, and a means of potentially sizing larger (>3 mm) second layer cracks. In this paper, 100% of the cracks in the sample were detectable. The results demonstrate PEC as a viable technique for second layer crack detection with ferrous fasteners present.

Disk of the Small Magellanic Cloud as traced by Cepheids

The structure and evolution of the disk of the Small Magellanic Cloud (SMC) are traced by studying the Cepheids. We aim to estimate the orientation measurements of the disk, such as the inclination and the position angle of the line of nodes, and the depth of the disk. We used the V and I band photometric data of the fundamental and first-overtone Cepheids from the Optical Gravitational Lensing Experiment survey. The period-luminosity relations were used to estimate the relative distance and reddening of each Cepheid. A weighted least-square plane fitting method was then applied to estimate the structural parameters. The line-of-sight depth and then the orientation corrected depth or thickness of the disk were estimated from the relative distance measurements. The period-age-colour relation of Cepheids were used to derive the age of the Cepheids. A break in the PL relations of the fundamental-mode and first-overtone Cepheids at P ~ 2.95 days and P ~ 1 day are observed. An inclination of 64$^o$.4$\pm$0$^o$.7 and a PA$_{lon}$=155$^o$.3$\pm$6$^o$.3 are obtained from the full sample. A reddening map of the SMC disk is also presented. The orientation-corrected depth or thickness of the SMC disk is found to be 1.76 $\pm$ 0.6 kpc. The scale height is estimated to be 0.82 $\pm$ 0.3 kpc. The age distribution of Cepheids matches the SMC cluster age distribution. The radial variation of the disk parameters mildly indicate structures/disturbances in the inner SMC (0.5 $<$ r $<$ 2.5 degree). Some of the Cepheids found in front of the fitted plane in the eastern regions are possibly the youngest tidally stripped counterpart of the H {{\sc i}} gas of the Magellanic Bridge. The Cepheids behind the fitted plane are most likely the population in the Counter Bridge predicted in recent numerical simulations. Different scenarios for the origin of the extra-planar Cepheids are also discussed.

Single range observability for cooperative underactuated underwater vehicles

The paper addresses the single range observability analysis of a kinematics model of cooperating underactuated underwater vehicles. Teams of underwater vehicles that communicate with each other may be able to access and exchange their relative distances through, by example, acoustic signal time-of-flight measurements. Such relative distance measurements together with vehicle’s attitude and velocity information may be used onboard to implement a navigation filter to estimate the vehicle’s relative positions and orientations. A pre-requisite for successfully designing such navigation filters is to assess the systems observability properties. Contrary to the majority of existing studies on single range observability, the paper considers a more realistic underactuated kinematics model for slender body autonomous underwater vehicles rather than a simple point mass model. The paper extends previous results building on an augmented state technique allowing to reformulate the nonlinear observability problem in terms of a linear time varying one. As a result, all possible (globally) unobservable motions are characterized in terms of the systems’ initial conditions and velocity commands within the class of interest. The fundamental results reported are also illustrated by numerical simulations providing evidence of different motions generating the same output, namely lacking observability.

Multi-resonator System for Contactless Measurement of Relative Distances

A precise measurement of two relative distances requires more sophisticated measurement schemes, which often demand two channels and consequently additional technical effort. Based on our current research on multi-resonator systems, we can demonstrate a novel method using two passive structures and a single transceiver. This presented method does not require an optical connection and is therefore robust against dust or other iron-free surroundings.

A Barycentric Coordinate Based Distributed Localization Algorithm for Sensor Networks

This paper studies the problem of determining the sensor locations in a large sensor network using only relative distance (range) measurements. Based on a generalized barycentric coordinate representation, our work generalizes the DILOC algorithm to the localization problem under arbitrary deployments of sensor nodes and anchor nodes. First, a criterion and algorithm are developed to determine a generalized barycentric coordinate of a node with respect to its neighboring nodes, which do not require the node to be inside the convex hull of its neighbors. Next, for the localization problem based on the generalized barycentric coordinate representation, a necessary and sufficient condition for the localizability of a sensor network with a generic configuration is obtained. Finally, a new linear iterative algorithm is proposed to ensure distributed implementation as well as global convergence to the true coordinates.

Use of the SAFE Index to Evaluate the Status of a Summer Aggregation of Atlantic Sturgeon in Minas Basin, Canada, and the Implication of the Index for the USA Endangered Species Designation of Atlantic and Shortnose Sturgeons

Sturgeon species worldwide have undergone population declines due to habitat alteration and overexploitation and many are listed by the International Union for Conservation of Nature (IUCN) and national agencies. Atlantic and shortnose sturgeon on the east coast of North America are listed as “endangered” or “threatened” over most of their ranges. It has been proposed, however, that IUCN risk categories are ambiguous and do not consider the threat status of a species in relation to a minimum viable population level. Here, we examine the Species Ability to Forestall Extinction (SAFE) Index, which is a heuristic measure of a species relative distance from extinction, and other available information on Atlantic and shortnose sturgeon with regard to the risk status of the two species. To move beyond a ‘tipping point’ designation of threatened, the SAFE Index requires a species abundance of 5000 adults (SAFE Index = 0.0). DNA and mark-recapture data for Atlantic sturgeon in Minas Basin, Canada indicates a USA/Canada mixed stock of ∼10,000 fish aggregate there in summer. The SAFE Index for this population is 0.28 indicating abundance is within the “vulnerable” threshold range for the Index although it includes but a small portion of the Atlantic sturgeon in the western Atlantic. Estimates for the east coast of North America suggest the Atlantic sturgeon population could consist of ∼177,000 sub adults and adults for a SAFE Index of 1.55. Additionally, the present spawning range of Atlantic sturgeon in North America is ∼99% of the historically known range and the number of stocks is near the historic level (33+) which means the species does not meet IUCN criteria for listing. Similarly, shortnose sturgeon has an Atlantic coast population of ∼96,800 adults (SAFE Index of 1.29) and a species range and number of stocks (26+) that has not changed substantially from the historical situation. Since the abundance of Atlantic and shortnose sturgeon are well above the SAFE threshold for “threatened” and they lack other accepted criteria for endangered or threatened designation, we conclude that the risk status of both species should be reconsidered.

A Distributed Multi-Robot Map Fusion Algorithm

This paper proposes a new approach to the multi-robot map fusion algorithm that enables a team of robots to build a joint map without initial knowledge of their relative pose. First, the relative distance and bearing measurements between two robots are fused together by the covariance intersection method after they detect each other. Second, the transformation equations among multi robots coordinates are derived based on their relative distance and bearing measurements. Third, all the multi robots local maps are merged into one global map by unscented transform based on the transformation equations. Fourth, the possible duplicate features are filtered out by the robots maximal detection area and the features coordinate range, then the Mahalanobis distance is computed to decide the duplicate features correspondence through unscented transform, and the Kalman Filter is used while fusing the duplicate features information. As a means of validation for the proposed method, experimental results obtained from the two robots are presented.

Gossip-Based Centroid and Common Reference Frame Estimation in Multiagent Systems

In this study, the decentralized common reference frame estimation problem for multiagent systems in the absence of any common coordinate system is investigated. Each agent is deployed in a 2-D space and can only measure the relative distance of neighboring agents and the angle of their line of sight in its local reference frame; no relative attitude measurement is available. Only asynchronous and random pairwise communications are allowed between neighboring agents. The convergence properties of the proposed algorithm are characterized, and its sensitiveness against additive noise on the relative distance measurements is investigated. An experimental validation of the effectiveness of the proposed algorithm is provided.

Using self-location to calibrate the errors of observer positions for source localization

The uncertainty of observers' positions can lead to significantly degrading in source localization accuracy. This paper proposes a method of using self-location for calibrating the positions of observer stations in source localization to reduce the errors of the observer positions and improve the accuracy of the source localization. The relative distance measurements of the two coordinative observers are used for the linear minimum mean square error (LMMSE) estimator. The results of computer simulations prove the feasibility and effectiveness of the proposed method. With the general estimation errors of observers' positions, the MSE of the source localization with self-location calibration, which is significantly lower than that without self-location calibration, is approximating to the Cramer-Rao lower bound (CRLB).

Cooperative Localization of Multi-UAVs via Dynamic Nonparametric Belief Propagation under GPS Signal Loss Condition

Self-localization is critical for many unmanned aerial vehicles (UAVs) tasks such as formation flight, path planning, and activity coordination. Traditionally, UAV can locate itself using GPS combined with some inertial sensors. However, due to the complex flight environment or failure of the GPS receiver, the UAV may lose its GPS signal and fail to locate itself, resulting in devastating consequence. In this paper, we will consider the problem of cooperative localization among multiple UAVs, in which the UAVs with failure of GPS receiver can help each other to locate themselves through mutual information exchanged based on the relative distance measurements. Specifically, we propose a dynamic Nonparametric Belief Propagation (dNBP) algorithm to calculate the posterior distribution of UAV's position conditioned on all observations made in the whole UAVs group. The dNBP is a natural combination of NBP with particle filtering, suitable for treating with the nonlinear model and highly non-Gaussian distributions arising in our application. Furthermore, dNBP provides the basis for distributed algorithm in which messages are exchanges between neighboring UAVs. Thus, the computational burden is distributed across UAVs. Simulations in Matlab environment show the effectiveness of our method.

Noisy Range Network Localization based on Distributed Multidimensional Scaling

This paper considers the noisy range-only network localization problem in which measurements of relative distances between agents are used to estimate their positions in networked systems. When distance information is noisy, existence and uniqueness of location solution are usually not guaranteed. It is well known that in presence of distance measurement noise, a node may have discontinuous deformations (e.g., flip ambiguities and discontinuous flex ambiguities). Thus, there are two issues that we consider in the noisy localization problem. The first one is the location estimate error propagated from distance measurement noise. We compare two kinds of analytical location error computation methods by assuming that each distance is corrupted with independent Gaussian random noise. These analytical results help us to understand effects of the measurement noises on the position estimation accuracy. After that, based on multidimensional scaling theory, we propose a distributed localization algorithm to solve the noisy range network localization problem. Our approach is robust to distance measurement noise, and it can be implemented in any random case without considering the network setup constraints. Moreover, a refined version of distributed noisy range localization method is developed, which achieves a good tradeoff between computational effort and global convergence especially in large-scale networks.

Metroglyph analysis of maize (Zea mays L.) inbreds for preliminary classification and group constellation

When a large number of accessions are available it is often useful to represent them on two dimensional graph and form preliminary groups which are subsequently subjected to more detailed stratification for specific breeding purposes. In the present investigation inbreds were grouped in to clusters using metroglyph analysis. Index scores were assigned to each glyph to arrive at conclusions about the agronomic potential of the inbreds. The group constellation deviated from the one derived through D2 analysis. However, pictorial representation of inbreds as brought about by metroglyph analysis can be used as a measure of relative genetic distance among the inbreds. Key words: D2 statistic, genetic divergence, group constellation, metroglyph analysis.

Distributed formation control of mobile autonomous agents using relative position measurements

In this study, we consider an acyclic rigid formation with a group of mobile autonomous agents moving in a two-dimensional space. The formation is generated via a Henneberg sequence construction in which there is one global leader that does not follow any other agents, one first-follower that only follows the global leader, and each of other agents has two leaders, which is added by a vertex addition or an edge splitting operation. The entire formation moves with the leadership of the global leader. Every follower agent tries to maintain distances towards its leaders. Under the constraint of the acceleration for the global leader, the distributed formation control laws are proposed for the followers that only use the locally relative distance measurement. The control law of the first-follower is proposed, which needs to know the velocity of the global leader and the relative distance between the global leader and itself. The global asymptotic stability of the expected formation is proved via a Lyapunov-based technique for the considered multi-agent system. Moreover, the stable rigidity problem of a formation is investigated for the proposed distributed relative position-only formation control law. Necessary and sufficient conditions are provided that must be satisfied by the architecture of the underlying graph. Simulation results illustrate the effectiveness of the proposed formation control approach.

A Second Look at the Logic of Explanatory Power (with Two Novel Representation Theorems)

We discuss the probabilistic analysis of explanatory power and prove a representation theorem for posterior ratio measures recently advocated by Schupbach and Sprenger. We then prove a representation theorem for an alternative class of measures that rely on the notion of relative probability distance. We end up endorsing the latter, as relative distance measures share the properties of posterior ratio measures that are genuinely appealing, while overcoming a feature that we consider undesirable. They also yield a telling result concerning formal accounts of explanatory power versus inductive confirmation, thereby bridging our discussion to a so-called no-miracle argument.

Relative Distance Measure Model for the Fuzzy Synthetic Evaluation of Subgrade Stability in Seasonal Frozen Area

Based on the fuzziness and uncertainty of the subgrade stability in seasonal frozen area, the relative distance measure model with evaluation indexes and weights in the form of interval numbers is presented for the fuzzy synthetic evaluation of the subgrade stability. Firstly, the relative distance measure of each single index between the evaluated subgrade stability and the grading standards is defined. Then, the fuzzy synthetic evaluation model, which considers the functionality and proportionality of evaluation indexes, is established to calculate the comprehensive relative distance measure by using the Monte Carlo simulation method and the sequential relation analysis. Finally, a new decision index of the comprehensive relative distance measure is defined considering the concept of structural reliability, and the stability grade of seasonal frost soil subgrade can be determined by the minimum decision index from the corresponding grading standards. A practical example is given to demonstrate the feasibility and practicability of the proposed model.