A survey on the inverse integrating factor

The relation between limit cycles of planar differential systems and the inverse integrating factor was first shown in an article of Giacomini, Llibre and Viano appeared in 1996. From that moment on, many research articles are devoted to the study of the properties of the inverse integrating factor and its relationwith limit cycles and their bifurcations. This paper is a summary of all the results about this topic. We include a list of references together with the corresponding related results aiming at being as much exhaustive as possible. The paper is, nonetheless, self-contained in such a way that all the main results on the inverse integrating factor are stated and a complete overview of the subject is given. Each section contains a different issue to which the inverse integrating factor plays a role: the integrability problem, relation with Lie symmetries, the center problem, vanishing set of an inverse integrating factor, bifurcation of limit cycles from either a period annulus or from a monodromic ω-limit set and some generalizations.

Defining the Effect of the 16p11.2 Duplication on Cognition, Behavior, and Medical Comorbidities.

IMPORTANCE: The 16p11.2 BP4-BP5 duplication is the copy number variant most frequently associated with autism spectrum disorder (ASD), schizophrenia, and comorbidities such as decreased body mass index (BMI). OBJECTIVES: To characterize the effects of the 16p11.2 duplication on cognitive, behavioral, medical, and anthropometric traits and to understand the specificity of these effects by systematically comparing results in duplication carriers and reciprocal deletion carriers, who are also at risk for ASD. DESIGN, SETTING, AND PARTICIPANTS: This international cohort study of 1006 study participants compared 270 duplication carriers with their 102 intrafamilial control individuals, 390 reciprocal deletion carriers, and 244 deletion controls from European and North American cohorts. Data were collected from August 1, 2010, to May 31, 2015 and analyzed from January 1 to August 14, 2015. Linear mixed models were used to estimate the effect of the duplication and deletion on clinical traits by comparison with noncarrier relatives. MAIN OUTCOMES AND MEASURES: Findings on the Full-Scale IQ (FSIQ), Nonverbal IQ, and Verbal IQ; the presence of ASD or other DSM-IV diagnoses; BMI; head circumference; and medical data. RESULTS: Among the 1006 study participants, the duplication was associated with a mean FSIQ score that was lower by 26.3 points between proband carriers and noncarrier relatives and a lower mean FSIQ score (16.2-11.4 points) in nonproband carriers. The mean overall effect of the deletion was similar (-22.1 points; P < .001). However, broad variation in FSIQ was found, with a 19.4- and 2.0-fold increase in the proportion of FSIQ scores that were very low (≤40) and higher than the mean (>100) compared with the deletion group (P < .001). Parental FSIQ predicted part of this variation (approximately 36.0% in hereditary probands). Although the frequency of ASD was similar in deletion and duplication proband carriers (16.0% and 20.0%, respectively), the FSIQ was significantly lower (by 26.3 points) in the duplication probands with ASD. There also were lower head circumference and BMI measurements among duplication carriers, which is consistent with the findings of previous studies. CONCLUSIONS AND RELEVANCE: The mean effect of the duplication on cognition is similar to that of the reciprocal deletion, but the variance in the duplication is significantly higher, with severe and mild subgroups not observed with the deletion. These results suggest that additional genetic and familial factors contribute to this variability. Additional studies will be necessary to characterize the predictors of cognitive deficits.

Repeated Whole-Genome Duplication, Karyotype Reshuffling, and Biased Retention of Stress-Responding Genes in Buckler Mustard.

Whole-genome duplication (WGD) is usually followed by gene loss and karyotype repatterning. Despite evidence of new adaptive traits associated with WGD, the underpinnings and evolutionary significance of such genome fractionation remain elusive. Here, we use Buckler mustard (Biscutella laevigata) to infer processes that have driven the retention of duplicated genes after recurrent WGDs. In addition to the β- and α-WGD events shared by all Brassicaceae, cytogenetic and transcriptome analyses revealed two younger WGD events that occurred at times of environmental changes in the clade of Buckler mustard (Biscutelleae): a mesopolyploidy event from the late Miocene that was followed by considerable karyotype reshuffling and chromosome number reduction and a neopolyploidy event during the Pleistocene. Although a considerable number of the older duplicates presented signatures of retention under positive selection, the majority of retained duplicates arising from the younger mesopolyploidy WGD event matched predictions of the gene balance hypothesis and showed evidence of strong purifying selection as well as enrichment in gene categories responding to abiotic stressors. Retention of large stretches of chromosomes for both genomic copies supported the hypothesis that cycles of WGD and biased fractionation shaped the genome of this stress-tolerant polypolyloid, promoting the adaptive recruitment of stress-responding genes in the face of environmental challenges.

Reciprocal Effects on Neurocognitive and Metabolic Phenotypes in Mouse Models of 16p11.2 Deletion and Duplication Syndromes.

The 16p11.2 600 kb BP4-BP5 deletion and duplication syndromes have been associated with developmental delay; autism spectrum disorders; and reciprocal effects on the body mass index, head circumference and brain volumes. Here, we explored these relationships using novel engineered mouse models carrying a deletion (Del/+) or a duplication (Dup/+) of the Sult1a1-Spn region homologous to the human 16p11.2 BP4-BP5 locus. On a C57BL/6N inbred genetic background, Del/+ mice exhibited reduced weight and impaired adipogenesis, hyperactivity, repetitive behaviors, and recognition memory deficits. In contrast, Dup/+ mice showed largely opposite phenotypes. On a F1 C57BL/6N × C3B hybrid genetic background, we also observed alterations in social interaction in the Del/+ and the Dup/+ animals, with other robust phenotypes affecting recognition memory and weight. To explore the dosage effect of the 16p11.2 genes on metabolism, Del/+ and Dup/+ models were challenged with high fat and high sugar diet, which revealed opposite energy imbalance. Transcriptomic analysis revealed that the majority of the genes located in the Sult1a1-Spn region were sensitive to dosage with a major effect on several pathways associated with neurocognitive and metabolic phenotypes. Whereas the behavioral consequence of the 16p11 region genetic dosage was similar in mice and humans with activity and memory alterations, the metabolic defects were opposite: adult Del/+ mice are lean in comparison to the human obese phenotype and the Dup/+ mice are overweight in comparison to the human underweight phenotype. Together, these data indicate that the dosage imbalance at the 16p11.2 locus perturbs the expression of modifiers outside the CNV that can modulate the penetrance, expressivity and direction of effects in both humans and mice.

Retrieval of kinetic rates in reactions with semi batch liquid phase using ill-posed inverse problem theory

A neural network procedure to solve inverse chemical kinetic problems is discussed in this work. Rate constants are calculated from the product concentration of an irreversible consecutive reaction: the hydrogenation of Citral molecule, a process with industrial interest. Simulated and experimental data are considered. Errors in the simulated data, up to 7% in the concentrations, were assumed to investigate the robustness of the inverse procedure. Also, the proposed method is compared with two common methods in nonlinear analysis; the Simplex and Levenberg-Marquardt approaches. In all situations investigated, the neural network approach was numerically stable and robust with respect to deviations in the initial conditions or experimental noises.

Methane combustion kinetic rate constants determination: an ill-posed inverse problem analysis

Methane combustion was studied by the Westbrook and Dryer model. This well-established simplified mechanism is very useful in combustion science, for computational effort can be notably reduced. In the inversion procedure to be studied, rate constants are obtained from [CO] concentration data. However, when inherent experimental errors in chemical concentrations are considered, an ill-conditioned inverse problem must be solved for which appropriate mathematical algorithms are needed. A recurrent neural network was chosen due to its numerical stability and robustness. The proposed methodology was compared against Simplex and Levenberg-Marquardt, the most used methods for optimization problems.

Multidata inverse problems and Bayesian solution methods in astronomy

Statistical analyses of measurements that can be described by statistical models are of essence in astronomy and in scientific inquiry in general. The sensitivity of such analyses, modelling approaches, and the consequent predictions, is sometimes highly dependent on the exact techniques applied, and improvements therein can result in significantly better understanding of the observed system of interest. Particularly, optimising the sensitivity of statistical techniques in detecting the faint signatures of low-mass planets orbiting the nearby stars is, together with improvements in instrumentation, essential in estimating the properties of the population of such planets, and in the race to detect Earth-analogs, i.e. planets that could support liquid water and, perhaps, life on their surfaces. We review the developments in Bayesian statistical techniques applicable to detections planets orbiting nearby stars and astronomical data analysis problems in general. We also discuss these techniques and demonstrate their usefulness by using various examples and detailed descriptions of the respective mathematics involved. We demonstrate the practical aspects of Bayesian statistical techniques by describing several algorithms and numerical techniques, as well as theoretical constructions, in the estimation of model parameters and in hypothesis testing. We also apply these algorithms to Doppler measurements of nearby stars to show how they can be used in practice to obtain as much information from the noisy data as possible. Bayesian statistical techniques are powerful tools in analysing and interpreting noisy data and should be preferred in practice whenever computational limitations are not too restrictive.

Inverse convection problem of simultaneous estimation of two boundary heat fluxes in parallel plate channels

This paper deals with the use of the conjugate gradient method of function estimation for the simultaneous identification of two unknown boundary heat fluxes in parallel plate channels. The fluid flow is assumed to be laminar and hydrodynamically developed. Temperature measurements taken inside the channel are used in the inverse analysis. The accuracy of the present solution approach is examined by using simulated measurements containing random errors, for strict cases involving functional forms with discontinuities and sharp-corners for the unknown functions. Three different types of inverse problems are addressed in the paper, involving the estimation of: (i) Spatially dependent heat fluxes; (ii) Time-dependent heat fluxes; and (iii) Time and spatially dependent heat fluxes.

Heat Source Estimation with the Conjugate Gradient Method in Inverse Linear Diffusive Problems

In this work, we present the solution of a class of linear inverse heat conduction problems for the estimation of unknown heat source terms, with no prior information of the functional forms of timewise and spatial dependence of the source strength, using the conjugate gradient method with an adjoint problem. After describing the mathematical formulation of a general direct problem and the procedure for the solution of the inverse problem, we show applications to three transient heat transfer problems: a one-dimensional cylindrical problem; a two-dimensional cylindrical problem; and a one-dimensional problem with two plates.

On-site calibration of a phase fraction meter by an inverse technique

The formal calibration procedure of a phase fraction meter is based on registering the outputs resulting from imposed phase fractions at known flow regimes. This can be straightforwardly done in laboratory conditions, but is rarely the case in industrial conditions, and particularly for on-site applications. Thus, there is a clear need for less restrictive calibration methods regarding to the prior knowledge of the complete set of inlet conditions. A new procedure is proposed in this work for the on-site construction of the calibration curve from total flown mass values of the homogeneous dispersed phase. The solution is obtained by minimizing a convenient error functional, assembled with data from redundant tests to handle the intrinsic ill-conditioned nature of the problem. Numerical simulations performed for increasing error levels demonstrate that acceptable calibration curves can be reconstructed, even from total mass measured within a precision of up to 2%. Consequently, the method can readily be applied, especially in on-site calibration problems in which classical procedures fail due to the impossibility of having a strict control of all the input/output parameters.

Too many copies: confusion between duplication and versioning

Presentation at Open Repositories 2014, Helsinki, Finland, June 9-13, 2014

Thr(118)Met amino acid substitution in the peripheral myelin protein 22 does not influence the clinical phenotype of Charcot-Marie-Tooth disease type 1A due to the 17p11.2-p12 duplication

The Thr(118)Met substitution in the peripheral myelin protein 22 (PMP22) gene has been detected in a number of families with demyelinating Charcot-Marie-Tooth (CMT1) neuropathy or with the hereditary neuropathy with liability to pressure palsy, but in none of them has it consistently segregated with the peripheral neuropathy. We describe here a CMT1 family (a 63-year-old man, his brother and his niece) in which two mutations on different chromosomes were found in the PMP22 gene, the 17p duplication, detected by fluorescent semiquantitative polymerase chain reaction (PCR) of microsatellite markers localized within the duplicated region on chromosome 17p11.2-p12, and the Thr(118)Met substitution, detected by direct sequencing the four coding exons of the PMP22 gene. A genotype/phenotype correlation study showed that the neuropathy segregates with the duplication and that the amino acid substitution does not seem to modify the clinical characteristics or the severity of the peripheral neuropathy. We did not find any evidence to characterize this substitution as a polymorphism in the population studied and we propose that the high frequency reported for this point mutation in the literature suggests that the Thr(118)Met substitution may be a hotspot for mutations in the PMP22 gene.

A search for RNA insertions and NS3 gene duplication in the genome of cytopathic isolates of bovine viral diarrhea virus

Calves born persistently infected with non-cytopathic bovine viral diarrhea virus (ncpBVDV) frequently develop a fatal gastroenteric illness called mucosal disease. Both the original virus (ncpBVDV) and an antigenically identical but cytopathic virus (cpBVDV) can be isolated from animals affected by mucosal disease. Cytopathic BVDVs originate from their ncp counterparts by diverse genetic mechanisms, all leading to the expression of the non-structural polypeptide NS3 as a discrete protein. In contrast, ncpBVDVs express only the large precursor polypeptide, NS2-3, which contains the NS3 sequence within its carboxy-terminal half. We report here the investigation of the mechanism leading to NS3 expression in 41 cpBVDV isolates. An RT-PCR strategy was employed to detect RNA insertions within the NS2-3 gene and/or duplication of the NS3 gene, two common mechanisms of NS3 expression. RT-PCR amplification revealed insertions in the NS2-3 gene of three cp isolates, with the inserts being similar in size to that present in the cpBVDV NADL strain. Sequencing of one such insert revealed a 296-nucleotide sequence with a central core of 270 nucleotides coding for an amino acid sequence highly homologous (98%) to the NADL insert, a sequence corresponding to part of the cellular J-Domain gene. One cpBVDV isolate contained a duplication of the NS3 gene downstream from the original locus. In contrast, no detectable NS2-3 insertions or NS3 gene duplications were observed in the genome of 37 cp isolates. These results demonstrate that processing of NS2-3 without bulk mRNA insertions or NS3 gene duplications seems to be a frequent mechanism leading to NS3 expression and BVDV cytopathology.