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PubMed2001

Type of inversion problem in physics: an inverse emissivity problem.

Inversion problems have recently drawn vast amounts of attention from the physics community due to their potential widespread applications. In this Rapid Communication, a different type of inversion problem in physics is proposed: an inverse emissivity problem, which aims to determine the emissivity g(nu) by measuring only the total radiated power J(T). Like other inverse problems, this one has potential for important practical applications. An exact solution is obtained for the proposed inverse problem. A unique existence theorem and techniques for eliminating divergences are also presented. A universal function set (UFS) suggested for numerical calculations is shown to be very useful in a numerical example. The UFS makes this inversion method practical and convenient for realistic calculations.

Journal Article↗

PubMed2005

Inverse melting and inverse freezing: a spin model.

Systems of highly degenerate ordered or frozen state may exhibit inverse melting (reversible crystallization upon heating) or inverse freezing (reversible glass transition upon heating). This phenomenon is reviewed, and a list of experimental demonstrations and theoretical models is presented. A simple spin model for inverse melting is introduced and solved analytically for infinite range, constant paramagnetic exchange interaction. The random exchange analogue of this model yields inverse freezing, as implied by the analytic solution based on the replica trick. The qualitative features of this system (generalized Blume-Capel spin model) are shown to resemble a large class of inverse melting phenomena. The appearance of inverse melting is related to an exact rescaling of one of the interaction parameters that measures the entropy of the system. For the case of almost degenerate spin states, perturbative expansion is presented, and the first three terms correspond to the empiric formula for the Flory-Huggins chi parameter in the theory of polymer melts. The possible microscopic origin of this chi parameter and the limitations of the Flory-Huggins theory where the state degeneracy is associated with the different conformations of a single polymer or with the spatial structures of two interacting molecules are discussed.

Journal Article↗

PubMed2005

Feasibility of a fast inverse dose optimization algorithm for IMRT via matrix inversion without negative beamlet intensities.

A fast optimization algorithm is very important for inverse planning of intensity modulated radiation therapy (IMRT), and for adaptive radiotherapy of the future. Conventional numerical search algorithms such as the conjugate gradient search, with positive beam weight constraints, generally require numerous iterations and may produce suboptimal dose results due to trapping in local minima. A direct solution of the inverse problem using conventional quadratic objective functions without positive beam constraints is more efficient but will result in unrealistic negative beam weights. We present here a direct solution of the inverse problem that does not yield unphysical negative beam weights. The objective function for the optimization of a large number of beamlets is reformulated such that the optimization problem is reduced to a linear set of equations. The optimal set of intensities is found through a matrix inversion, and negative beamlet intensities are avoided without the need for externally imposed ad-hoc constraints. The method has been demonstrated with a test phantom and a few clinical radiotherapy cases, using primary dose calculations. We achieve highly conformal primary dose distributions with very rapid optimization times. Typical optimization times for a single anatomical slice (two dimensional) (head and neck) using a LAPACK matrix inversion routine in a single processor desktop computer, are: 0.03 s for 500 beamlets; 0.28 s for 1000 beamlets; 3.1 s for 2000 beamlets; and 12 s for 3000 beamlets. Clinical implementation will require the additional time of a one-time precomputation of scattered radiation for all beamlets, but will not impact the optimization speed. In conclusion, the new method provides a fast and robust technique to find a global minimum that yields excellent results for the inverse planning of IMRT.

Algorithms↗

PubMed1998

Cloning of inversion breakpoints in the Anopheles gambiae complex traces a transposable element at the inversion junction.

Anopheles arabiensis, one of the two most potent malaria vectors of the gambiae complex, is characterized by the presence of chromosomal paracentric inversions. Elucidation of the nature and the dynamics of these inversions is of paramount importance for the understanding of the population genetics and evolutionary biology of this mosquito and of the impact on malaria epidemiology. We report here the cloning of the breakpoints of the naturally occurring polymorphic inversion 2Rd' of A. arabiensis. A cDNA clone that cytologically mapped on the proximal breakpoint was the starting material for the isolation of a cosmid clone that spanned the breakpoint. Analysis of the surrounding sequences demonstrated that adjacent to the distal breakpoint lies a repetitive element that exhibits distinct distribution in different A. arabiensis strains. Sequencing analysis of that area revealed elements characteristic of transposable element terminal repeats. We called this presumed transposable element Odysseus. The presence of Odysseus at the junction of the naturally occuring inversion 2Rd' suggests that the inversion may be the result of the transposable element's activity. Characteristics of Odysseus' terminal region as well as its cytological distribution in different strains may indicate a relatively recent activity of Odysseus.

Animals↗

PubMed1997

Molecular analysis of deletion (17)(p11.2p11.2) in a family segregating a 17p paracentric inversion: implications for carriers of paracentric inversions.

A male child with multiple congenital anomalies initially was clinically diagnosed as having Smith-Lemli-Opitz syndrome (SLOS). Subsequent cytogenetic studies revealed an interstitial deletion of 17p11.2, which is associated with Smith-Magenis syndrome (SMS). Biochemical studies were not supportive of a diagnosis of SLOS, and the child did not display the typical SMS phenotype. The father's karyotype showed a paracentric inversion of 17p, with breakpoints in p11.2 and p13.3, and the same inversion was also found in two of the father's sisters. FISH analyses of the deleted and inverted 17p chromosomes indicated that the deletion was similar to that typically seen in SMS patients and was found to bracket the proximal inversion breakpoint. Available family members were genotyped at 33 polymorphic DNA loci in 17p. These studies determined that the deletion was of paternal origin and that the inversion was of grandpaternal origin. Haplotype analysis demonstrated that the 17p11.2 deletion arose following a recombination event involving the father's normal and inverted chromosome 17 homologues. A mechanism is proposed to explain the simultaneous deletion and apparent "reinversion" of the recombinant paternal chromosome. These findings have implications for prenatal counseling of carriers of paracentric inversions, who typically are considered to bear minimal reproductive risk.

Abnormalities, Multiple↗

PubMed1984

Amine inversion in proteins. A 13C-NMR study of proton exchange and nitrogen inversion rates in N epsilon,N epsilon,N alpha,N alpha-[13C]tetramethyllysine,N epsilon,N epsilon,N alpha,N alpha-[13C]tetramethyllysine methyl ester, and reductively methylated concanavalin A.

Exchange rates were calculated as a function of pH from line widths of methylamine resonances in 13C-NMR spectra of N epsilon,N epsilon,N alpha,N alpha-[13C]tetramethyllysine (TML) and N epsilon,N epsilon,N alpha,N alpha-tetramethyllysine methyl ester (TMLME). The pH dependence of the dimethyl alpha-amine exchange rate could be adequately described by assuming base-catalyzed chemical exchange between two diastereotopic methyl populations related by nitrogen inversion. Deprotonation of the alpha-amine was assumed to occur by proton transfer to (1) OH-, (2) water, (3) a deprotonated amine or (4) RCO2-. Microscopic rate constants characterizing each of these transfer processes (k1, k2, k3 and k4, respectively) were determined by fitting the rates calculated from line width analysis to a steady-state kinetic model. Using this procedure it was determined that for both TML and TMLME k2 approximately equal to 1-10 M-1 s-1, k3 approximately equal to 10(6) M-1 s-1 and ki, the rate constant for nitrogen inversion was about 10(8)-10(9) s-1. Upper limits of 10(12) and 10(3) M-1 s-1 could be determined for k1 and k4, respectively. A similar kinetic analysis was used to explain pH-dependent line-broadening effects observed for the N-terminal dimethylalanyl resonance in 13C-NMR spectra of concanavalin A, reductively methylated using 90% [13C]formaldehyde. From exchange data below pH 4 it could be determined that amine inversion was limited by the proton transfer rate to the solvent, with a rate constant estimated at 20 M-1 s-1. Above pH 4, exchange was limited by proton transfer to other titrating groups in the protein structure. Based upon their proximity, the carboxylate side chains of Asp-2 and Asp-218 appear to be likely candidates. The apparent first-order microscopic rate constant characterizing proton transfer to these groups was estimated to be about 1 X 10(4) s-1. Rate constants characterizing nitrogen inversion (ki), proton transfer to OH- (k1) and proton transfer to the solvent (k2) were estimated to be of the same order of magnitude as those determined for the model compounds. On the basis of our results, it is proposed that chemical exchange processes associated with base-catalyzed nitrogen inversion may contribute to 15N or 13C spin-lattice relaxation times in reductively methylated peptides or proteins.

Concanavalin A↗

PubMed2001

Best estimated inverse versus inverse of the best estimator.

The construction of a feed-forward controller frequently requires the estimation of an inverse function. Two possible methods to achieve this are: (i) learning the best estimated inverse (BEI), a method that is sometimes referred to as direct inverse learning and (ii) learning the inverse of the best estimator (IBE), a method that is sometimes referred to as indirect inverse learning. We analyze a general control problem, in the presence of noise, and show analytically that these two methods are asymptotically significantly different, even for simple linear non-redundant systems. We further demonstrate that the IBE method is typically superior for control purposes.

Artifacts↗

PubMed2001

Regular and inverse secondary kinetic enthalpy effects (KHE) for the rate of inversion of thioether and 1,1'-biisoquinoline complexes of ruthenium and osmium.

Thioether complexes with the formula Delta/Lambda-chloro(thioether)bis(2,2'-bipyridine)metal(II) (M = Ru, Os; thioether = dimethyl sulfide (3a(+)), diethyl sulfide (3b(+)), and tetrahydrothiophene (3c(+))) have been synthesized. The rates of inversion at the sulfur atom of the thioether ligands have been measured by spin-inversion transfer and line-shape NMR methods. In every case, the ruthenium derivative exhibits a faster inversion frequency at a given temperature than the corresponding osmium derivative. In contrast, similar complexes with the formula chloro(delta/lambda-1,1'-biisoquinoline)(2,2':6',2"-terpyridine)metal(II), 4(M=Ru,Os)(+), undergo atropisomerization of the misdirected 1,1'-biisoquinoline (1,1'-biiq) ligand with rates that are faster for osmium than ruthenium. As a result of the lanthanide contraction effect and the similar metric parameters associated with the structures of second-row and third-row transition metal derivatives, steric factors associated with the isomerizations are presumably similar for the Ru and Os derivatives of these compounds. Since third-row transition metal complexes tend to have larger bond dissociation enthalpies (BDE) than their second-row congeners, we conclude the difference in reactivities of 3(M=Ru)(+) versus 3(M=Os)(+) and 4(M=Ru)(+) versus 4(M=Os)(+) are attributed to electronic effects. For 3, the S3p lone pair of the thioether, the principal sigma donor orbital, is orthogonal to the metal sigma acceptor orbital in the transition state of inversion at sulfur and the S 3s orbital is an ineffective sigma donor. Thus, a regular relationship between the kinetic and thermodynamic stabilities of 3(M=Ru)(+) and 3(M=Os)(+) is observed for the directed <==> [misdirected] <==> directed (DMD) isomerization (the more thermodynamically stable bond is less reactive). In contrast, atropisomerization of 4(+) involves redirecting (strengthening) the M-N bonds of the misdirected 1,1'-biiq ligand in the transition state. Therefore, an inverse relationship between the kinetic and thermodynamic stabilities of 4(M=Ru)(+) and 4(M=Os)(+) is observed for the misdirected <==> [directed] <==> misdirected (MDM) isomerization (the more thermodynamically stable bond is more reactive). The rates obtained for 4(+) are consistent with the rates of atropisomerization of Delta/Lambda-(delta/lambda-1,1'-biisoquinoline)bis(2,2'-bipyridine)metal(II), 1(M=Ru,Os)(2+), and (eta(6)-benzene) Delta/Lambda-(delta/lambda-1,1'-biisoquinoline)halometal(II), 2(M=Ru,Os;halo=Cl,I)(+), that we reported previously. We term the relative rates of reaction of second-row versus third-row transition metal derivatives kinetic element effects (KEE = k(second)/k(third)). While the KEE appears to be generally useful when comparing reactions of isostructural species (e.g. the relative rates of 1(M=Ru)(2+), 1(M=Os)(2+), and 1(M=Ir)(3+)), different temperature dependencies of reactions prevent the comparison of related reactions between species that have different structures (e.g., the 1,1'-biiq atropisomerization reactions of 1(M=Ru,Os)(2+) versus 2(M=Ru,Os;halo=Cl,I)(+) versus 4(M=Ru,Os)(+)). This problem is overcome by comparing entropies of activation and kinetic enthalpy effects (KHE = DeltaH(third)/DeltaH(second)). For a given class of 1,1'-biiq complexes, we observe a structure/reactivity relationship between DeltaH and the torsional twist of the 1,1'-biiq ligands that are measured in the solid state.

Journal Article↗

PubMed2000

Exact solution of the specific-heat-phonon spectrum inversion from the Mobius inverse formula

The application of the Mobius inversion formula to the specific-heat-phonon spectrum inversion problem (SPI) initially appeared promising [N.X. Chen, Phys. Rev. Lett. 64, 1193 (1990); J. Maddox, Nature (London) 344, 377 (1990)]. However, no one has previously been able to obtain the exact Debye spectrum with the correct cut-off factor and frequency dependence from the Mobius formula. The main difficulty arises from the fact that the Mobius function &mgr;(n) is not completely known for large n in practice. In this paper, some exact solutions of SPI are obtained by using the Mobius inversion formula, most importantly the Debye spectrum as a special case, and the problem of the unknown Mobius function &mgr;(n) for large n is avoided. It is shown that the Mobius inversion formula can be useful for exact solutions to spectral inversion problems.

Journal Article↗

PubMed1997

Peak passive resistive torque at maximum inversion range of motion in subjects with recurrent ankle inversion sprains.

Although a number of mechanical and neuromuscular processes have been identified, the primary mechanisms underlying residual functional instability of the ankle remain unclear. Understanding such mechanisms will help physical therapists identify where to focus treatment efforts, ultimately leading to more effective rehabilitation. In the present investigation, resistive torque at maximum ankle inversion was evaluated to determine if lateral ankle structures demonstrated mechanical laxity. Thirty subjects with a history of unilateral recurrent inversion sprains were tested bilaterally. A custom-made apparatus provided a stress to the lateral ankle in a method that was similar to the inversion stress test. Two measures of laxity were used: maximum passive inversion range of motion and peak passive resistive torque. Differences between the involved and uninvolved ankles were determined using analysis of covariance procedures. There were no significant differences between involved and uninvolved ankles for maximum inversion range of motion and for peak passive resistive torque. Post hoc testing confirmed adequate statistical power. The results support previous investigations, which suggest that functional instability can exist in the absence of mechanical lateral ankle laxity.

Adult↗

PubMed1995

Paracentric inversions in humans: a review of 446 paracentric inversions with presentation of 120 new cases.

We present a large review of 446 cases of paracentric inversions (PAI), including 120 new cases, to assess their incidence, distribution, inheritance, modes of ascertainment, interchromosomal effects, viable recombinant offspring, and clinical relevance. All 23 autosomes and sex chromosomes had inversions. However, none were identified in chromosome arms 18p, 19q, 20q, and Yp. PAI were most commonly reported in chromosomes 1, 3, 5, 6, 7, 11, and 14 and less frequently in chromosomes 4, 16, 17, 18, 19, 20, 21, 22, and Y. Inversions were most common in chromosome arms 6p, 7q, 11q, and 14q and observed least in chromosome arms 2p, 2q, 3q, 4q, and 6q. Frequently encountered breakpoints included 3(p13p25), 6(p12p23), 6(p12p25), 7(q11q22), and 11(q21q23). Ascertainment was primarily incidental (54.5%), mental retardation and/or congenital anomalies (22.2%), spontaneous abortions (11.4%), associations with syndromes (3.0%), and infertility (2.0%) accounted for the remainder. Ascertainment was neither related to the length of the inverted segment nor to specific inversions except for PAI of Xq which often presented with manifestations of Ullrich-Turner syndrome. Sixty-six percent of PAI were inherited while 8.5% were de novo. Recombination was observed in 17 cases, 15 of which resulted in a monocentric chromosomal deletion or duplication. No common factors were identified that suggested a tendency towards recombination. The incidence of viable recombinants was estimated to be 3.8%. This review documents that PAI are perhaps more commonly identified than suggested in previous reviews. Despite the possible bias of ascertainment in some cases, there may be associated risks with PAI that require further examination. Our data suggest that PAI carriers do not appear to be free of risks of abnormalities or abnormal progeny and caution is recommended when counseling.

Chromosome Inversion↗

PubMed1983

[Inversion polymorphism of the malarial mosquito Anopheles messeae. V. The interaction of different chromosomal inversions in the spatial area].

The relations between inversions of chromosome XL, 2R, 3R, 3L from 8 populations of the central part and periphery of the species area were studied. 2-, 3- and 4-factor analysis was carried out. Interaction of inversions XL1, 2R1, 3R1 in central populations (Riga, Moscow, Tomsk) was observed. The nonrandom association of definite inversional genotypes was stationary in spatial - temporary. The phylogenetic initial sequences XL0, 2R0, 3R0 display "+" interaction. The 3-factor analysis of populations of Tomsk shows: 1) interaction of inversions is more essential in males than in females; 2) the statistically significant interaction of 3-4 inversions is not always determined by the effect of 2-factor analysis; 3) the chromosome 3R has a dominance influence on the pattern of association of the multiinversional complex. These data support the hypothesis that differential selection for chromosomes with certain combinations of arrangements is mainly responsible for this phenomenon. In peripheral area populations (Syctyvkar, Irkutsk, Chita), no associations were observed (2R and 3R). When they do take place, their character is changed (Kiev - XL and 3R). This phenomenon may be explained by the influence of frequency-dependent selection.

Animals↗

PubMed1997

A model of the inversion process in an arterial inversion experiment.

A model of the behavior of spins moving through spatially varying gradient and B1 fields is presented. The model simulates the adiabatic behavior of flowing arterial water during a two-coil arterial inversion experiment. Predictions of the degree of inversion generated by the model are compared with flow phantom results for a wide range of gradient magnitudes, nominal B1 magnitudes, and flow velocities. The high level of agreement between the model and the flow phantom results indicates that the model can be used to help select efficient pulse sequence parameters when setting up an in vivo arterial inversion experiment. In addition, the model provides valuable insights into the adiabatic behavior of arterial spins. These insights could be useful in selecting an efficient surface coil geometry which achieves maximum inversion with a minimum B1 magnitude.

Arteries↗

PubMed2003

Magnetic resonance imaging of normal and osteomyelitis in the mandible: assessment of short inversion time inversion recovery sequence.

OBJECTIVE: We sought to determine the suitable magnetic resonance imaging conditions for the short inversion time inversion recovery (STIR) sequence through the use of phantoms; to describe the signal characteristics of normal structures in the mandible; and to evaluate the usefulness of STIR images in enabling the identification of mandibular osteomyelitis on conventional T1- and T2-weighted spin-echo images. STUDY DESIGN: Suitable mandibular STIR imaging conditions were determined by varying inversion time and repetition time in each sequence. STIR magnetic resonance images of 162 healthy subjects and STIR and T1- and T2-weighted spin-echo images of 21 subjects with mandibular osteomyelitis were evaluated. RESULTS: In STIR imaging, the signal of oil was suppressed at an inversion time equaling 100 milliseconds and a repetition time equaling 1500 to 3000 milliseconds. In healthy subjects, the mandibular marrow was revealed to have high signal intensities (100%) and cortical bone had no signal intensities (100%) on STIR images. In surrounding soft tissue in these healthy subjects, the submandibular glands were shown to have high signal intensities (100%); the parotid glands had intermediate to high signal intensities (100%); the sublingual glands had high (88.9%) and intermediate to high (11.1%) signal intensities; lymph nodes had high signal intensities (100%); and the masseter muscles had intermediate signal intensities (100%) on STIR images. The lesions in bone marrow had low (75%) and low to intermediate (25%) signal intensities on T1-weighted images and high (54%), intermediate to high (29%), and intermediate (17%) signal intensities on T2-weighted images. On STIR images, the signal intensities resulted in high (75%), intermediate to high (21%), and intermediate (4%) signal intensities. CONCLUSIONS: STIR imaging is highly effective for the evaluation of bone marrow and surrounding soft tissue in terms of the detection of osteomyelitis in the mandible and the identification of inflammation spreading to soft tissue.

Adult↗

PubMed1980

Inversions of specific DNA segments in flagellar phase variation of Salmonella and inversion systems of bacteriophages P1 and Mu.

Prophages P1 and Mu produces a trans-acting factor possessing the din+ activity which catalyzes the inversion of the specific DNA segment responsible for flagellar phase variation of Salmonella, din mutants were isolated from PICMclr100 phage by selecting phages that did not suppress the yh2 mutation of Salmonella in prophage state. No inversion loop structure was detected among DNA forms arising after denaturation and rehybridization of DNAs extracted from the din mutants. The DNA fragment containing C region of P1 was cloned on a plasmid vector, pCR1. The resulting hybrid plasmid, pKK2, was shown to possess the din+ activity: the vh2 mutant of Salmonella harboring the plasmid changed the flagellar phase. From analysis of the plasmid by use of BamHI and Bgl II, the din gene specifying the din+ activity was located near or within the C region of P1. It is highly plausible that the din gene of P1 was also involved in the inversion of the C region. Similarly, the DNA fragment containing the G and beta segments of Mu was cloned on pCR1. The resulting hybrid plasmid, pII101, also possessed the din+ activity.

Bacterial Proteins↗

PubMed1985

[Inversion polymorphism in the malaria mosquito Anopheles messeae. VI. Local selection and 3-dimensional differentiation of the inversion gene complexes for fertility].

A field experiment was carried on with the view of compulsory change of the frequency of chromosomal inversion (2R1) in the population of Anopheles messeae from the centre of the area. Quick return of the population to the original structure was observed. This confirmed that the local differentiation of chromosomal polymorphism is supported by natural selection. The fertility of the females was shown to be connected with the inversion polymorphism. The females with inversion complexes of genes of the "northern" type (with homozygotes 2R1) had higher fertility and lower dispersion of the fertility, in comparison with those having gene complexes which prevailed in the south part of the area.

Animals↗

PubMed1983

[Inversion polymorphism of the malarial mosquito Anopheles messeae. IV. The stability of the frequency distribution of the inversions by species area].

Distribution of the frequencies of inversions XL1, 2R1, 3R1, 3L1, from geographically widely separated 8 populations had been studied during a long period of time. The geographical inclines of distribution of inversions XL1, 3R1 (a longitudinal) and 2R1 (a latitudinal) are stable in time. Stationarity of inversional polymorphism is not connected with superdominance of heterozygotes. It is supposed that the stable equilibrium of the frequencies of inversions is supported by variable selection.

Animals↗

PubMed1998

An Alternative Scheme for 13C Chemical-Shift Imaging via Inverse Detection of Protons through an MILS (or Inverse SLIM) Technique

An alternative scheme in acquiring 13C spectroscopic images using inverse detection via polarization transfer through protons was proposed and experimentally verified by a phantom using a heteronuclear multiple-quantum coherence technique. This scheme has some features that, in special circumstances, can be exploited to one's advantages. These features are: (1) signal enhancement, a feat realizable under favorable conditions; (2) spectroscopic encoding via constant time; and (3) improvement of the time efficiency of the constant-time method via optimization by singular-value decomposition analysis. Features (1) and (2) can, in some cases, yield better sensitivity than the conventional 3DFT technique without sacrificing the most important attribute of 13C, the enormity of the chemical shifts. Such is the case because spectroscopic images acquired by the technique proposed are based on the chemical shifts of carbon, in contrast to the other more prevalent inverse-detection schemes. Feature (2) can also offer higher spatial resolution by shifting the emphasis of signal encoding from a spectral-resolution-first viewpoint to one that favors spatial resolution. Feature (3) was adopted from a method previously known as MILS (metabolite imaging of lines in a spectrum), or the inverse of SLIM, an economical scheme originally proposed by Hu et al. (1988, Magn. Reson. Med. 8, 314) for obtaining a compartmentalized NMR spectrum. Copyright 1998 Academic Press. Copyright 1998 Academic Press

Journal Article↗