Minimal Separation Research Articles

Statistical analysis of achievable resolution limit in the near field source localization context

In this fast communication, we derive the statistical resolution limit (SRL), characterizing the minimal parameter separation, to resolve two closely spaced known near-field sources impinging on a linear array. Toward this goal, we conduct on the first-order Taylor expansion of the observation model a Generalized Likelihood Ratio Test (GLRT) based on a Constrained Maximum Likelihood Estimator (CMLE) of the SRL. More precisely, the minimum separation between two near-field sources, that is detectable for a given probability of false alarm and a given probability of detection, is derived herein. Finally, numerical simulations are done to quantify the impact of the array geometry of the signal sources power distribution and of the array aperture on the statistical resolution limit.

Comparing trees characteristic to chordal and dually chordal graphs

Abstract Chordal and dually chordal graphs possess characteristic tree representations, namely, clique trees and compatible trees, respectively. The following problem is studied: given a chordal graph G, it has to be determined if the clique trees of G are exactly the compatible trees of K ( G ) . This does not always happen. A necessary and sufficient condition so that it is true, in terms of the minimal vertex separators of the graph, is found.

Extensions and Improvements to the Chordal Graph Approach to the Multistate Perfect Phylogeny Problem

The multistate perfect phylogeny problem is a classic problem in computational biology. When no perfect phylogeny exists, it is of interest to find a set of characters to remove in order to obtain a perfect phylogeny in the remaining data. This is known as the character removal problem. We show how to use chordal graphs and triangulations to solve the character removal problem for an arbitrary number of states, which was previously unsolved. We outline a preprocessing technique that speeds up the computation of the minimal separators of a graph. Minimal separators are used in our solution to the missing data character removal problem and to Gusfield's solution of the perfect phylogeny problem with missing data.

A 60 GHz Tunable Output Profile Power Amplifier in 65 nm CMOS

A fully integrated three-stage 60 GHz power amplifier with amplitude/phase compensation is realized in 65 nm CMOS. An adaptive feedback bias scheme with three control knobs is proposed to extend the linear operating region. At a supply voltage of 1 V, the fully differential amplifier achieves a linear gain of 15 dB and occupies a compact area of 0.056 mm2. It achieves a minimal Psat-P1dB separation of 0.6 dB by extending the P1dB by 8.5 dB. To our best knowledge, this is the smallest Psat-P1dB separation reported to date. With on-chip phase compensation, the output phase variation is reduced by 57%.

Statistical resolution limit for the multidimensional harmonic retrieval model: hypothesis test and Cramér-Rao Bound approaches

The statistical resolution limit (SRL), which is defined as the minimal separation between parameters to allow a correct resolvability, is an important statistical tool to quantify the ultimate performance for parametric estimation problems. In this article, we generalize the concept of the SRL to the multidimensional SRL (MSRL) applied to the multidimensional harmonic retrieval model. In this article, we derive the SRL for the so-called multidimensional harmonic retrieval model using a generalization of the previously introduced SRL concepts that we call multidimensional SRL (MSRL). We first derive the MSRL using an hypothesis test approach. This statistical test is shown to be asymptotically an uniformly most powerful test which is the strongest optimality statement that one could expect to obtain. Second, we link the proposed asymptotic MSRL based on the hypothesis test approach to a new extension of the SRL based on the Cramér-Rao Bound approach. Thus, a closed-form expression of the asymptotic MSRL is given and analyzed in the framework of the multidimensional harmonic retrieval model. Particularly, it is proved that the optimal MSRL is obtained for equi-powered sources and/or an equi-distributed number of sensors on each multi-way array.

Minimal Encounter Time and Separation Determine Ligand-Receptor Binding in Cell Adhesion

The binding properties of biomolecules play a crucial role in many biological phenomena, especially cell adhesion. Whereas the attachment kinetics of soluble proteins is considered well known, complex behavior arises when protein molecules are bound to the cell membrane. We probe the hidden kinetics of ligand-receptor bond formation using single-molecule flow chamber assays and Brownian dynamics simulations. We show that, consistent with our recently proposed hypothesis, association requires a minimum duration of contact between the reactive species. In our experiments, ICAM-1 anchored on a flat substrate binds to anti-ICAM-1 coated onto flowing microbeads. The interaction potential between bead and substrate is measured by microinterferometry and is used as an ingredient to simulate bead movement. Our simulation calculates the duration of ligand-receptor contacts imposed by the bead movement. We quantitatively predict the reduction of adhesion probability measured for shorter tether length of the ligand or if a repulsive hyaluronan layer is added onto the surface. To account for our results, we propose that bond formation may occur in our system by crossing of a diffusive plateau in the energy landscape, on the timescale of 5 ms and an energy barrier of 5 kBT, before reaching the first detectable bound state. Our results show how to relate cell-scale behavior to the combined information of molecular reactivity and biomolecule submicron-scale environment.

Experiment on the production and separation of the pulsed reflective discharge gas-metal plasma

A proprietary way of introducing a working substance to be separated into a reflective-discharge magnetoplasma separator is experimentally verified. The efficiency of working substance delivery using this sputtering mechanism providing a plasma density on the order of 1014 cm−3 is demonstrated. The sputtering yield of the substance being separated achieves (2.6–2.8) × 10−2 atoms/ion depending on the amount of particles in the discharge. Simultaneously, the minimal separation coefficient for light and heavy particles in a rotating plasma subjected to E × H crossed fields is estimated.

Channel Spectral Separation Narrowing for Spectral Beam Combining by Apodisation of the Reflecting Volume Bragg Grating

The sidelobe in diffraction efficiency of reflecting volume Bragg grating (RVBG) limits the wavelength channel spectral separation, which determines the combining power output in spectral beam combining (SBC) systems. A novel SBC system based on the apodised RVBG has been proposed to suppress the sidelobe. Several apodised RVBGs have been compared and the optimal apodised RVBG is obtained by using the chain-matrix approach. Numerical results show that the sidelobe could be suppressed excellently with Blackman apodised RVBG. In the numerical example, the minimal channel spectral separation was 1.0 nm for SBC system based on the RVBG and it decreased to 0.6 nm for the novel SBC system based on the Blackman apodised RVBG when the spectral combining efficiency of both systems achieves the same maximum value. Defence Science Journal, 2011, 61(3), pp.201-205 , DOI:http://dx.doi.org/10.14429/dsj.61.528

Fast minimal triangulation algorithm using minimum degree criterion

We propose an algorithm for minimal triangulation which, using simple and efficient strategy, subdivides the input graph in different, almost non-overlapping, subgraphs. Using the technique of matrix multiplication for saturating the minimal separators, we show that the partition of the graph can be computed in time O ( n α ) where n α is the time required by the binary matrix multiplication. After saturating the minimal separators, the same procedure is recursively applied on each subgraphs. We also present a variant of the algorithm in which the minimum degree criterion is used. In this way, we obtain an algorithm that uses minimum degree criterion and at the same time produces a minimal triangulation, thus shedding new light on the effectiveness of the minimum degree heuristics.

Coupling of Plasmon Resonances in Tunable Layered Arrays of Gold Nanoparticles

Using bottom-up and self-assembly processes, large scale layered arrays of strongly coupled gold nanoparticles with controllable dimensions were fabricated. By carefully adjusting the distance between adjacent gold nanoparticle arrays, it is possible to control the coupling of the localized surface plasmon polariton resonance as sustained by individual gold nanoparticles. A greater interaction is observed at smaller separations, leading to a well pronounced shift in the spectral position of resonances that can be adjusted with high precision. Simulations showed good agreement with experimental observations in an in-depth investigation of such structures, suggesting minimal separations of only one nanometer are achieved.

Elements of Analytical Measurement in Brewing

A successful analytical method must measure an analyte of interest in a suitable matrix with adequate sensitivity, accuracy, and precision. This requires an appropriate combination of detector specificity and component resolution. Highly specific detectors require little or no separation of the analyte from other constituents. Specificity can often be achieved using a chemical reaction. Detectors with low specificity need a high degree of separation of components before they can be applied. Minimal separation into two fractions can be achieved with distillation, filtration, sedimentation, or extraction. Multivariate analysis applied to multiple measurements (e.g., NIR spectra) can achieve mathematical rather than physical separation. The degrees of specificity and separation in brewing analytical methods are discussed.

Democracy promotion in Africa: the institutional context

Democracy is seen by many as a viable means to rebuild the legitimacy of African states. However, African democracy is often based on a particular set of institutions which tend to concentrate power in the executive. A powerful president operates in a context of a minimal separation of powers, with few possibilities to restrain the executive, and a highly majoritarian party-political landscape. Democratic reforms and democracy assistance policies were first directed primarily at multiparty elections and political parties. Later donors have shifted to a broader approach of good governance and human rights. However, both the narrow electoral and the broader good governance and human rights approaches do not address sufficiently the institutional context of multi-party competition, which is characterized by the fusion of powers and a powerful presidency. This is a serious flaw which also limits the impact of current democracy promotion policies. This contribution suggests that democracy promoters could address this institutional gap by advocating for institutional reforms through which accountability in Africa may be increased, notably through greater inclusion of parliament and interest groups and of civil society actors in policy-making. Moreover, donors can set an example by introducing such reforms in the donor–recipient policy dialogue process they themselves conduct.

Performance Bounds and Angular Resolution Limit for the Moving Colocated MIMO Radar

To identify a target, the moving noncoherent colocated multiple-input multiple-output (MIMO) radar system takes advantage of multiple antennas in transmission and reception which are close in space. In this paper, we study the estimation performance and the resolution limit for this scheme in which each array geometry is described by the sample-variance of the sensor distribution. So, our analysis encompasses any sensor distributions, including varying intersensors distances or/and lacunar (missing sensors) configuration. As in the space-time MIMO model considered here the radar is moving, the target Doppler frequency cannot be assumed invariant to the target position/angle. The first part of this paper derives and analyzes closed form (nonmatrix) expressions of the deterministic Cramer-Rao lower bound (CRB) for the direction and the velocity of a moving target contaminated by a structured noise (clutter echoes) and a background noise, including the cases of the clutter-free environment and the high signal-to-noise ratio (SNR) regime. The analysis of the proposed expressions of the CRB allows to better understand the characterization of the target. In particular, we prove the coupling between the direction parameter and the velocity of the target is linear with the radar velocity. In the second part, we focus our study on the analytical (closed form) derivation and the analysis of the angular resolution limit (ARL). Based on the resolution of an equation involving the CRB, the ARL can be interpreted as the minimal separation to resolve two closely spaced targets. Consequently, the ARL is a key quantity to evaluate the performance of a radar system. We show that the ARL is in fact quasi-invariant to the movement of the MIMO radar.

A simple algorithm to generate the minimal separators and the maximal cliques of a chordal graph

We present a simple unified algorithmic process which uses either LexBFS or MCS on a chordal graph to generate the minimal separators and the maximal cliques in linear time in a single pass.

Statistical Resolution Limit of the Uniform Linear Cocentered Orthogonal Loop and Dipole Array

Among the family of polarization sensitive arrays, we can find the so-called cocentered orthogonal loop and dipole uniform linear array (COLD-ULA). The COLD-ULA exhibits some interesting properties, e.g., the insensibility of the polarization vector with respect to the source localization in the plan of the array. In this correspondence, we derive the statistical resolution limit (SRL) characterizing the minimal separation, in terms of direction-of-arrivals, to resolve two closely spaced known polarized sources impinging on a COLD-ULA. Toward this end, nonmatrix closed form expressions of the deterministic Cramer-Rao bound (CRB) are derived and thus, the SRL is deduced. A comparison between the SRL of the COLD-ULA and the classical ULA are given. Particularly, it is shown that, in the case of orthogonal known signal sources, the SRL of the COLD-ULA is equal to the SRL of the ULA, meaning that it is not a function of polarization parameters. Furthermore, due to the derived SRL, it is shown that, under some general conditions, the SRL of the COLD-ULA is smaller than the one of the ULA.

Surface swabbing technique for the rapid screening for pesticides using ambient pressure desorption ionization with high‐resolution mass spectrometry

A rapid screening method for pesticides has been developed to promote more efficient processing of produce entering the United States. Foam swabs were used to recover a multiclass mixture of 132 pesticides from the surfaces of grapes, apples, and oranges. The swabs were analyzed using direct analysis in real time (DART) ionization coupled with a high-resolution Exactive Orbitrap™ mass spectrometer. By using a DART helium temperature gradient from 100-350°C over 3 min, a minimal separation of analytes based on volatility differences was achieved. This, combined with the Exactive's mass resolution of 100,00, allowed the chromatographic step, along with the typical compositing and extraction steps associated with gas chromatography/mass spectrometry (GC/MS) or liquid chromatography/mass spectrometry (LC/MS) approaches, to be eliminated. Detection of 86% of the analytes present was consistently achieved at levels of 2 ng/g (per each apple or orange) and 10 ng/g (per grape). A resolution study was conducted with four pairs of isobaric compounds analyzed at a mass resolution of 100 000. Baseline separation was achieved with analyte ions differing in mass by 25 ppm and analyte ions with a mass difference of 10 ppm were partially resolved. In addition, field samples that had undergone traditional sample preparation using QuEChERS (quick, easy, cheap, rugged, and safe) were analyzed using both LC/MS and DART-MS and the results from the two techniques were found to be comparable in terms of identification of the pesticides present. The use of swabs greatly increased sample throughput by reducing sample preparation and analysis time.

Relationship between the particle size distribution of commercial fully porous and superficially porous high-performance liquid chromatography column packings and their chromatographic performance

The separation efficiency and kinetics of several commercial HPLC particle types (both fully porous and superficially porous) have been investigated using a pharmaceutical weakly basic N-containing compound as a test molecule. A strong trend between the particle size distribution (PSD) of the particles and the typically employed “goodness of packing”-parameters was observed. The relative standard deviation of the PSD of the tested particles ranged between 0.05 and 0.2, and in this range, a near linear relationship between the A-term constant, the h min-value and the minimal separation impedance was found. The experimental findings hence confirm the recent observations regarding the relationship between the narrow PSD of the recently commercialized porous-shell particles and their superior efficiency and kinetic performance. The outcome also suggests that the performance of the current generation of fully porous particle columns could be significantly improved if the PSD of these particles could be reduced.

Separators of fat points in Pn

Abstract In this paper we extend the definition of a separator of a point P in P n to a fat point P of multiplicity m. The key idea in our definition is to compare the fat point schemes Z = m 1 P 1 + ⋯ + m i P i + ⋯ + m s P s ⊆ P n and Z ′ = m 1 P 1 + ⋯ + ( m i − 1 ) P i + ⋯ + m s P s . We associate to P i a tuple of positive integers of length ν = deg Z − deg Z ′ . We call this tuple the degree of the minimal separators of P i of multiplicity m i , and we denote it by deg Z ( P i ) = ( d 1 , … , d ν ) . We show that if one knows deg Z ( P i ) and the Hilbert function of Z, one will also know the Hilbert function of Z ′ . We also show that the entries of deg Z ( P i ) are related to the shifts in the last syzygy module of I Z . Both results generalize well-known results about reduced sets of points and their separators.

Space-optimal, backtracking algorithms to list the minimal vertex separators of a graph

For a graph G in read-only memory on n vertices and m edges and a write-only output buffer, we give two algorithms using only O ( n ) rewritable space. The first algorithm lists all minimal a − b separators of G with a polynomial delay of O ( n m ) . The second lists all minimal vertex separators of G with a cumulative polynomial delay of O ( n 3 m ) . One consequence is that the algorithms can list the minimal a − b separators (and minimal vertex separators) spending O ( n m ) time (respectively, O ( n 3 m ) time) per object output.

An Introduction to Clique Minimal Separator Decomposition

This paper is a review which presents and explains the decomposition of graphs by clique minimal separators. The pace is leisurely, we give many examples and figures. Easy algorithms are provided to implement this decomposition. The historical and theoretical background is given, as well as sketches of proofs of the structural results involved.