Classical Resolution Research Articles

A heuristic derivation of the uncertainty for frequency determination in time series data

Context. Several approaches to estimating frequency, phase, and amplitude errors in time-series analyse have been reported in the literature, but they are either time-consuming to compute, grossly overestimating the error, or are based on empirically determined criteria.Aims. A simple, but realistic estimate of the frequency uncertainty in time-series analyses is our goal here.Methods. Synthetic data sets with mono- and multi-periodic harmonic signals and with randomly distributed amplitude, frequency, and phase were generated and white noise added. We tried to recover the input parameters with classical Fourier techniques and investigated the error as a function of the relative level of noise, signal, and frequency difference.Results. We present simple formulas for the upper limit of the amplitude, frequency, and phase uncertainties in time-serie analyses. We also demonstrate the possibility of detecting frequencies that are separated by less than the classical frequency resolution and of finding that the realistic frequency error is at least 4 times smaller than the classical frequency resolution.

SAT graph-based representation: A new perspective

In this paper a new graph based representation of Boolean formulas in conjunctive normal form (CNF) is proposed. It extends the well-known graph representation of binary CNF formulas (2-SAT) to the general case. Every clause is represented as a set of (conditional) implications and encoded with different edges labeled with a set of literals, called context. This representation admits many interesting features. For example, a path from the node labeled with a literal ¬ x to the node labeled with a literal x gives us an original way to compute the condition under which the literal x is implied. Using this representation, we show that classical resolution can be reformulated as a transitive closure on the generated graph. Interestingly enough, using the SAT graph-based representation three original applications are then derived. The first one deals with the 2-SAT strong backdoor set computation problem, whereas in the second one the underlying representation is used to derive hard SAT instances with respect to the state-of-the-art satisfiability solvers. Finally, a new preprocessing technique of CNF formulas which extends the well-known hyper-resolution rule is proposed. Experimental results show interesting improvements on many classes of SAT instances taken from the last SAT competitions.

Moment inference from tomograms

Time‐lapse geophysical tomography can provide valuable qualitative insights into hydrologic transport phenomena associated with aquifer dynamics, tracer experiments, and engineered remediation. Increasingly, tomograms are used to infer the spatial and/or temporal moments of solute plumes; these moments provide quantitative information about transport processes (e.g., advection, dispersion, and rate‐limited mass transfer) and controlling parameters (e.g., permeability, dispersivity, and rate coefficients). The reliability of moments calculated from tomograms is, however, poorly understood because classic approaches to image appraisal (e.g., the model resolution matrix) are not directly applicable to moment inference. Here, we present a semi‐analytical approach to construct a moment resolution matrix based on (1) the classic model resolution matrix and (2) image reconstruction from orthogonal moments. Numerical results for radar and electrical‐resistivity imaging of solute plumes demonstrate that moment values calculated from tomograms depend strongly on plume location within the tomogram, survey geometry, regularization criteria, and measurement error.

Long-range three-dimensional active imaging with superresolution depth mapping

We present a technique to overcome the depth resolution limitation for 3D active imaging. Applying microsecond laser pulses and sensor gate width, a scene of several hundred meters is illuminated and recorded in a single image. The trapezoid-shaped range intensity profile is analyzed to obtain both the reflectivity and the depth of scene. We demonstrate a 3D scene reconstruction in a depth of 650 to 1550 m from only three images with an accuracy of <30 m. This depth accuracy is 10 times better than estimated from the classical resolution limit obtained for depth scanning active imaging with a similar number of images. Therefore, this technique enables superresolution depth mapping with a reduction of image data processing.

Design of a high speed logic engine for distributed decision support systems

The paper provides a new approach to designing a massively parallel logic engine for automated reasoning in a distributed decision support system. The design includes extension of classical linear resolution of first order logic clauses by multi-reso

Synthesis and Resolution of Planar‐Chiral Derivatives of 4‐(Dimethylamino)pyridine

AbstractA safer and more efficient method for the synthesis of planar‐chiral 4‐(dimethylamino)pyridine (DMAP) derivatives has been developed. Racemic mixtures of the complexes can be resolved via classical resolution with commercially available tartaric acids.

Asymmetric Baeyer–Villiger Biooxidation of α‐Substituted Cyanocyclohexanones: Influence of the Substituent Length on Regio‐ and Enantioselectivity

AbstractCells of Escherichia coli expressing cyclohexanone monooxygenase catalyzed a highly enantioselective Baeyer–Villiger oxidation of α‐substituted cyanocyclohexanones, leading to the corresponding enantiopure caprolactones (ees &gt;97 %). Classical kinetic resolution and regiodivergent parallel kinetic resolution patterns were observed, depending on the length of the linear chain at the alpha position. Regioselectivity was compared with that of chemical BV oxidations. Cells revealed an outstanding stability since 50 % of the specific BV activity was retained after 42 days of storage, which facilitates their use in biotransformations.

BLM is required for faithful chromosome segregation and its localization defines a class of ultrafine anaphase bridges

Mutations in BLM cause Bloom's syndrome, a disorder associated with cancer predisposition and chromosomal instability. We investigated whether BLM plays a role in ensuring the faithful chromosome segregation in human cells. We show that BLM-defective cells display a higher frequency of anaphase bridges and lagging chromatin than do isogenic corrected derivatives that eptopically express the BLM protein. In normal cells undergoing mitosis, BLM protein localizes to anaphase bridges, where it colocalizes with its cellular partners, topoisomerase IIIalpha and hRMI1 (BLAP75). Using BLM staining as a marker, we have identified a class of ultrafine DNA bridges in anaphase that are surprisingly prevalent in the anaphase population of normal human cells. These so-called BLM-DNA bridges, which also stain for the PICH protein, frequently link centromeric loci, and are present at an elevated frequency in cells lacking BLM. On the basis of these results, we propose that sister-chromatid disjunction is often incomplete in human cells even after the onset of anaphase. We present a model for the action of BLM in ensuring complete sister chromatid decatenation in anaphase.

A Facile Preparation of an Octahydropyrrolo[2,3-c]pyridine Enantiomer

A facile synthesis of octahydro-pyrrolo[2,3-c]pyridine 1 using an intramolecular [3+2]-cycloaddition of an azomethine ylide as the key step and employing DW-therm heat-transfer fluid as a solvent is disclosed. Enantiomerically pure 1 was obtained either via a chromatographic separation of the diastereoisomers 12 and 13 resulting from the cycloaddition with a chiral appendage or by a classical resolution of racemate 19.

A generalized spectral decomposition technique to solve a class of linear stochastic partial differential equations

We propose a new robust technique for solving a class of linear stochastic partial differential equations. The solution is approximated by a series of terms, each of which being the product of a scalar stochastic function by a deterministic function. None of these functions are fixed a priori but determined by solving a problem which can be interpreted as an “extended” eigenvalue problem. This technique generalizes the classical spectral decomposition, namely the Karhunen–Loève expansion. Ad hoc iterative techniques to build the approximation, inspired by the power method for classical eigenproblems, then transform the problem into the resolution of a few uncoupled deterministic problems and stochastic equations. This method drastically reduces the calculation costs and memory requirements of classical resolution techniques used in the context of Galerkin stochastic finite element methods. Finally, this technique is particularly suitable to non-linear and evolution problems since it enables the construction of a relevant reduced basis of deterministic functions which can be efficiently reused for subsequent resolutions.

Synthetic aperture microscopy using off-axis illumination and polarization coding

A new method to improve the resolution of optical imaging systems beyond the classical Rayleigh resolution limit is presented. The technique relies on synthetic aperture generation in three stages. The first one (encoding stage) uses an illumination procedure that combines both on-axis and off-axis illumination beams with different polarization states onto the object. After the imaging system, a second stage (decoding stage) allows the recovering of the encoded spatial-frequency object information by means of an interferometric configuration based on the polarization coding carried out in the previous stage. Finally, a third stage (digital post-processing stage) is used to generate a synthetic aperture that is three times larger than the conventional aperture of the imaging system. The whole process allows us to obtain a superresolved image of the object. Experimental implementation of the approach for a commercial microscope objective is presented.

Practical Tactics in Resolution of Racemates via Diastereomeric Salt Formation

AbstractA practical tactics in the classical resolutions was illustrated for affording the desired isomers in maximum yields. According to the practical tactics resolution of racemic ethyl nipecotate, Corey lactone and huperzine A intermediate was successfully practiced. The basis of this practicability is the well‐known Marckwald principle.

Resolution of 2-substituted 1,4-benzodioxanes by entrainment

The methyl ester of 1,4-benzodioxane-2-carboxylic acid 1 and the mesylate of 2-hydroxymethyl-1,4-benzodioxane 2 are synthetic intermediates whose enantiomers can be advantageously used to prepare a number of enantiopure 2-substituted 1,4-benzodioxanes from readily accessible (±)-1,4-benzodioxane-2-carboxilic acid. We have previously demonstrated the conglomerate nature of the enantiomeric systems of 1 and 2. Herein, we report the resolution of their racemates by preferential crystallization according to an entrainment procedure. In particular, the entrainment resolution of 1 showed good efficiency, which makes the present method a competitive alternative to the classical resolutions of 1,4-benzodioxane-2-carboxylic acid with dehydroabietylamine and para-substituted 1-phenylethylamines that we have recently reported.

Nuclear Magnetic Resonance Spectroscopy of Lipids in Cancer

Analytical methods often benefit from progress in other fields of science. One of the best-illustrated and most spectacular examples is NMR technology and its numerous improvements that have resulted from new applications in biology and medicine. These techniques came under the term MRI during the mid 1970s, and then in vivo MRS since the early 1980s. Biomedical NMR of lipids is presently emerging as an exciting topic in onco-biology. However, for various reasons, biochemists up to quite recently showed more interest in proteins than in lipids. This is probably because proteins are “active” reactant molecules and lipids are often still considered as merely nutritional or structurally more “passive” components. While classical biochemistry quantifies molecules independently from each other, biophysical methods, including NMR, also take into account the multi-molecular structure and the resulting “visibility” of each component, which is itself related to mobility. Results from numerous studies concerning lipids in cancer mainly focused on blood plasma using high resolution in vitro NMR, cells using both classical high resolution ex-vivo NMR and high-resolution Magic Angle Spinning NMR and, more recently, in vivo tumours by single-voxel spectroscopy or by Chemical Shift Imaging. Keywords: blood plasma lipoproteins, Malignancy Associated Lipoprotein, HDL, tetraphenylphosphonium chloride (TPP), Multidrug Resistance

Apodized apertures for solar coronagraphy

Aims. We propose the principle of a new solar telescope that makes it possible to observe the solar corona very close to the solar limb, without the help of a Lyot coronagraph. The result is obtained using a strongly apodized aperture. Methods. We obtain the theoretical form of the diffraction halo produced by the solar disk at the level of the corona for a perfect diffraction-limited telescope, for raw and apodized apertures. The problem is first solved at one dimension for which a complete set of analytical expressions can be derived, including the effect of the center-to-limb solar variation. Formal equations are written for the two-dimensional case, and it is shown that the expression may take the form of a 1D integral. Nevertheless, the problem is difficult to solve. An analytic expression can be worked out using the line spread function, which is shown to give a valid approximation of the problem, in excellent agreement with a numerical computation that uses the exact integral. Results. We show for the raw aperture that the diffraction halo is very strong and decreases slowly as p -1 . We propose as a solution to this problem an apodized aperture based on the generalized prolate spheroidal functions (GPSF). Such an apodized aperture may reduce the diffraction halo enough to permit a direct observation of the solar corona very close to the solar limb. A signal-to-noise ratio analysis is given. Conclusions. Different strengths of apodization may be used, but very strong apodizations are indeed mandatory. A good choice seems to be a GPSF aperture with the prolate coefficient c on the order of 10. It could reduce the halo of diffraction by a factor 10 5 (at the cost of an intensity throughput of 10% and a reduction in the classical resolution by a factor of about 1.6) and permit observation of the corona very close to the solar limb.

An Efficient Synthesis of (R)-2-Butyl-3-hydroxypropionic Acid

An efficient synthesis of (R)-2-butyl-3-hydroxypropionic acid (1) via a classical resolution of (±)-2-butyl-3-hydroxypropionic acid (7) with (R)-α-methylbenzylamine is described. (±)-2-Butyl-3-hydroxypropionic acid (7) was readily available from diethyl butylmalonate (2) in two steps. Results on the enantioselective enzymatic hydrolysis of 2 with pig liver esterase and α-chymotrypsin towards 1 are also described.

Identifying Pathways Linking Child Abuse to Psychological Outcome

ABSTRACT Child abuse has been linked to pathogenic parenting, and each has been associated with long-term psychological impairment. This study seeks to contribute to the growing volume of investigations concerned with the identification of possible pathways linking child abuse to symptoms by exploring the mediating role of perceived parental failure of empathy in this association. Child abuse and deficient parental empathy were strongly related to one another and separately predictive of symptoms in a sample of 437 female students. Whereas parental empathic failure was found to mediate the long-term effects of physical and extrafamilial sexual abuse, neither it nor incest were capable of predicting most measures of adjustment independently of the other. Findings are discussed in the context of classic developmental psychopathology and trauma resolution theories, and implications for treatment are outlined.

Predicting Survival within the Lung Cancer Histopathological Hierarchy Using a Multi-Scale Genomic Model of Development

BackgroundThe histopathologic heterogeneity of lung cancer remains a significant confounding factor in its diagnosis and prognosis—spurring numerous recent efforts to find a molecular classification of the disease that has clinical relevance.Methods and FindingsMolecular profiles of tumors from 186 patients representing four different lung cancer subtypes (and 17 normal lung tissue samples) were compared with a mouse lung development model using principal component analysis in both temporal and genomic domains. An algorithm for the classification of lung cancers using a multi-scale developmental framework was developed. Kaplan–Meier survival analysis was conducted for lung adenocarcinoma patient subgroups identified via their developmental association. We found multi-scale genomic similarities between four human lung cancer subtypes and the developing mouse lung that are prognostically meaningful. Significant association was observed between the localization of human lung cancer cases along the principal mouse lung development trajectory and the corresponding patient survival rate at three distinct levels of classical histopathologic resolution: among different lung cancer subtypes, among patients within the adenocarcinoma subtype, and within the stage I adenocarcinoma subclass. The earlier the genomic association between a human tumor profile and the mouse lung development sequence, the poorer the patient's prognosis. Furthermore, decomposing this principal lung development trajectory identified a gene set that was significantly enriched for pyrimidine metabolism and cell-adhesion functions specific to lung development and oncogenesis.ConclusionsFrom a multi-scale disease modeling perspective, the molecular dynamics of murine lung development provide an effective framework that is not only data driven but also informed by the biology of development for elucidating the mechanisms of human lung cancer biology and its clinical outcome.

Fluorination-Free Synthesis of a 4,4-Difluoro-3,3-Dimethylproline Derivative

A Claisen rearrangement/iodolactamization sequence starting from commercially available trifluoroacetaldehyde methyl hemiacetal, followed by a classical chemical resolution, provided enantiomerically pure 4,4-difluoro-3,3-dimethylproline (S)-1. No hazardous fluorination reagents were used, and the overall yield over 12 steps was greater than 28%.

Azedaralide: total synthesis, relative and absolute stereochemical assignment

Azedaralide, a potentially advanced intermediate for the total synthesis of various tetranortriterpenes, was constructed utilising the Fernandez-Mateos protocol and assigned both relative and absolute stereochemistries. Both asymmetric aldol and classical chiral resolution attempts failed to deliver pure enantiomers whereas preparative chiral chromatography resolved racemic azedaralide with ease.