Strong Variants Research Articles

Assessment of the evidence yield for the calibrated PP3/BP4 computational recommendations

PurposeTo investigate the number of rare missense variants observed in human genome sequences by ACMG/AMP PP3/BP4 evidence strength, following the ClinGen-calibrated PP3/BP4 computational recommendations. MethodsMissense variants from the genome sequences of 300 probands from the Rare Genomes Project with suspected rare disease were analyzed using computational prediction tools that were able to reach PP3_Strong and BP4_Moderate evidence strengths (BayesDel, MutPred2, REVEL, and VEST4). The numbers of variants at each evidence strength were analyzed across disease-associated genes and genome-wide. ResultsFrom a median of 75.5 rare (≤1% allele frequency) missense variants in disease-associated genes per proband, a median of one reached PP3_Strong, 3-5 PP3_Moderate, and 3-5 PP3_Supporting. Most were allocated BP4 evidence (median 41-49 per proband) or were indeterminate (median 17.5-19 per proband). Extending the analysis to all protein-coding genes genome-wide, the number of variants reaching PP3_Strong score thresholds increased approximately 2.6-fold compared with disease-associated genes, with a median per proband of 1-3 PP3_Strong, 8-16 PP3_Moderate, and 10-17 PP3_Supporting. ConclusionA small number of variants per proband reached PP3_Strong and PP3_Moderate in 3424 disease-associated genes. Although not the intended use of the recommendations, this was also observed genome-wide. Use of PP3/BP4 evidence as recommended from calibrated computational prediction tools in the clinical diagnostic laboratory is unlikely to inappropriately contribute to the classification of an excessive number of variants as pathogenic or likely pathogenic by ACMG/AMP rules.

Statin persistence and adherence among older initiators: A nationwide cohort study using the national health insurance claims database in Japan.

This study clarifies the reality of persistence and adherence to statins in older Japanese people who initiated statin use and compares it between primary and secondary prevention cohorts. The nationwide study using the national claims database targeted statin initiators aged ≥55 years from FY2014 to FY2017 in Japan. Persistence and adherence to statins were analyzed overall and according to subgroups based on sex, age stratum, and prevention cohorts. Permissible gap of median days that statins were supplied per prescription to an individual was employed. Persistence rates were estimated as Kaplan-Meier estimates. Poor adherence during persistence was evaluated and defined as <0.8 of the proportion of days covered. Of 3 675 949 initiators, approximately 80% initiated statin use with strong variants. The persistence rate at 1 year was 0.61. Poor adherence to statins during persistence was 8.0% in all patients and this value gradually improved with increasing age. Persistence rate and adherence were lower for the primary prevention cohort than for the secondary prevention cohort, and a notable sex difference was observed for the secondary prevention cohort, which was lower in females but was almost never and slightly observed in the primary prevention cohorts without and with high-risk factors, respectively. Many statin initiators discontinued statins shortly following statin initiation but adherence while on statin therapy was good. Attentively watching older patients not to discontinue statins and listening to their reasons for discontinuation are required, especially for initiators in primary prevention and females in secondary prevention.

Comparative analysis of atmospheric parameters from high-resolution spectroscopic sky surveys: APOGEE, GALAH, Gaia-ESO

Context. SDSS-IV APOGEE-2, GALAH, and Gaia-ESO are high-resolution, ground-based, multi-object spectroscopic surveys providing fundamental stellar atmospheric parameters and multiple elemental abundance ratios for hundreds of thousands of stars of the Milky Way. Data from these and other surveys contribute to investigations of the history and evolution of the Galaxy. Aims. We undertake a comparison between the most recent data releases of these surveys to investigate the accuracy and precision of derived parameters by placing the abundances on an absolute scale. We also discuss the correlations in parameter and abundance differences as a function of main parameters. Uncovering the variants provides a basis to continue the efforts of future sky surveys. Methods. Quality samples from the APOGEE−GALAH (15 537 stars), APOGEE−GES (804 stars), and GALAH−GES (441 stars) overlapping catalogs were collected. We investigated the mean variants between the surveys, and linear trends were also investigated. We compared the slope of correlations and mean differences with the reported uncertainties. Results. The average and scatter of vrad, Teff, log g, [M/H], and vmicro, along with numerous species of elemental abundances in the combined catalogs, show that in general there is a good agreement between the surveys. We find large radial velocity scatters ranging from 1.3 km s−1 to 4.4 km s−1 when comparing the three surveys. We observe some weak trends (e.g., in ΔTeff vs. Δlog g for the APOGEE−GES stars) and a clear correlation in the vmicro − Δvmicro planes in the APOGEE−GALAH common sample. For [α/H], [Ti/H] (APOGEE−GALAH giants), and [Al/H] (APOGEE−GALAH dwarfs) potential strong correlations are discovered as a function of the differences in the main atmospheric parameters, and we also find weak trends for other elements. Conclusions. In general we find good agreement between the three surveys within their respective uncertainties. However, there are certain regimes in which strong variants exist, which we discuss. There are still offsets larger than 0.1 dex in the absolute abundance scales.

Prediction of the SARS-CoV-2 Derived T-Cell Epitopes’ Response Against COVID Variants

The COVID-19 outbreak began in December 2019 and was declared a global health emergency by the World Health Organization. The four most dominating variants are Beta, Gamma, Delta, and Omicron. After the administration of vaccine doses, an eminent decline in new cases has been observed. The COVID-19 vaccine induces neutralizing antibodies and T-cells in our bodies. However, strong variants like Delta and Omicron tend to escape these neutralizing antibodies elicited by COVID-19 vaccination. Therefore, it is indispensable to study, analyze and most importantly, predict the response of SARS-CoV-2-derived t-cell epitopes against Covid variants in vaccinated and unvaccinated persons. In this regard, machine learning can be effectively utilized for predicting the response of COVID-derived t-cell epitopes. In this study, prediction of T-cells Epitopes’ response was conducted for vaccinated and unvaccinated people for Beta, Gamma, Delta, and Omicron variants. The dataset was divided into two classes, i.e., vaccinated and unvaccinated, and the predicted response of T-cell Epitopes was divided into three categories, i.e., Strong, Impaired, and Over-activated. For the aforementioned prediction purposes, a self-proposed Bayesian neural network has been designed by combining variational inference and flow normalization optimizers. Furthermore, the Hidden Markov Model has also been trained on the same dataset to compare the results of the self-proposed Bayesian neural network with this state-of-the-art statistical approach. Extensive experimentation and results demonstrate the efficacy of the proposed network in terms of accurate prediction and reduced error.

Genotypes and phenotypes heterogeneity in PIK3CA-related overgrowth spectrum and overlapping conditions: 150 novel patients and systematic review of 1007 patients with PIK3CA pathogenetic variants

BackgroundPostzygotic activating PIK3CA variants cause several phenotypes within the PIK3CA-related overgrowth spectrum (PROS). Variant strength, mosaicism level, specific tissue involvement and overlapping disorders are responsible for disease heterogeneity. We explored...

An experimental approach to iconicity in Dutch strong and weak verb morphology

In Dutch, some verbs can vary in their preterite and past participle form. These verbs can either take the strong inflection (using ablaut, e.g. schuilen-school-gescholen ‘hide-hid-hidden’) or the weak inflection (adding a dental suffix, e.g. schuilen-schuilde-geschuild ‘hide-hid-hidden’). In a diachronic corpus study, De Smet and Van de Velde (2020) show that this variation can be exapted to express aspect in an iconic manner. Their results indicate that weak preterites are used more often in durative contexts, while the shorter strong variants are used more often in punctual contexts. For the past participles, this pattern is reversed: the longer strong variants are used more often in durative contexts, while the shorter weak variants are used more often in punctual contexts. In this paper, we seek experimental validation of these results. Furthermore, we also distinguish between preterite singulars and preterite plurals, as we expect the iconicity effect to be less obvious for the latter, given that the difference in length between the strong and weak preterite plural is negligible (e.g. schuilden vs. scholen). Participants were presented with a forced choice task where they had to choose between weak or strong preterites and past participles of nonce verbs in sentences suggesting either a durative or a punctual context. Though no general effect of aspect on verb inflection was found, results indicate a trend for a particular group of verbs that supports the corpus results from De Smet and Van de Velde (2020). Furthermore, the durative-punctual distinction was also found to be portrayed in yet another iconic manner: verb forms with vowels that are sound symbolically associated with slow long movements were used more often in durative contexts, while verb forms with vowels that are associated with quick, short movements were used more often in punctual contexts.

Molecular Diagnosis of Hereditary Neuropathies by Whole Exome Sequencing and Expanding the Phenotype Spectrum.

Inherited peripheral neuropathies (IPNs) are a group of neuropathies affecting peripheral motor and sensory neurons. Charcot-Marie-Tooth (CMT) disease is the most common disease in this group. With recent advances in next-generation sequencing (NGS) technologies, more than 100 genes have been implicated for different types of CMT and other clinically and genetically inherited neuropathies. There are also a number of genes where neuropathy is a major feature of the disease such as spinocerebellar ataxia (SCA) and hereditary spastic paraplegia (HSP). We aimed to determine the genetic causes underlying IPNs in Iranian families. We performed whole exome sequencing (WES) for 58 PMP22 deletion-/duplication-negative unrelated Iranian patients with a spectrum of phenotypes and with a preliminary diagnosis of hereditary neuropathies. Twenty-seven (46.6%) of the cases were genetically diagnosed with pathogenic or likely pathogenic variants. In this study, we identified genetically strong variants within genes not previously linked to any established disease phenotype in five (8.6%) patients. Our results highlight the advantage of using WES for genetic diagnosis in highly heterogeneous diseases such as IPNs. Moreover, functional analysis is required for novel and uncertain variants.

Abstract P5-10-04: Exome sequencing in high breast and ovarian cancer incidence families which lack detectable mutations in established cancer susceptibility genes

Abstract At our center, a standard 25 gene panel has proved useful for the identification of pathogenic germline mutations in many families with a high penetrance of breast and ovarian cancer, yet there remain several families with very high cancer incidence but from whom these assays have not identified pathogenic alleles. To attempt to define the genetic mechanism of susceptibility in such cases, are conducting germline whole exome sequencing in affected individuals. Here we describe the identification of strong candidate susceptibility variants in two such families. Both variants cause loss-of-function of DNA repair genes not previously implicated in breast cancer, but which share properties with genes with known roles in maintenance of genome integrity. In one individual, with a personal history of ovarian cancer and two independent breast tumors, we identified a novel point mutation in POLD2 which introduces a mutation at a residue which is biochemically conserved in all animal species thus far sequenced. In the second individual, a frameshift mutation was detected in ERCC4. In both cases, the variants found have not been observed in large exome datasets (e.g. ExAC) or reported in ClinVar. Our study highlights the potential utility of whole exome sequencing as a discovery tool in those families with high cancer incidence yet which lack mutations in known hereditary cancer predisposition genes. Citation Format: Kenny PA, Girtman MA, Deviley JA, Meier DR, Vos CR, Richmond CS, Lofgren KA. Exome sequencing in high breast and ovarian cancer incidence families which lack detectable mutations in established cancer susceptibility genes [abstract]. In: Proceedings of the 2018 San Antonio Breast Cancer Symposium; 2018 Dec 4-8; San Antonio, TX. Philadelphia (PA): AACR; Cancer Res 2019;79(4 Suppl):Abstract nr P5-10-04.

Chronic lifestyle diseases display seasonal sensitive comorbid trend in human population evidence from Google Trends.

Seasonal and human physiological changes are important factors in the development of many diseases. But, the study of genuine seasonal impact on these diseases is difficult to measure due to many other environment and lifestyle factors which directly affect these diseases. However, several clinical studies have been conducted in different parts of the world, and it has clearly indicated that certain groups of population are highly subjected to seasonal changes, and their maladaptation can possibly lead to several disorders/diseases. Thus, it is crucial to study the significant seasonal sensitive diseases spread across the human population. To narrow down these disorders/diseases, the study hypothesized that high altitude (HA) associated diseases and disorders are of the strong variants of seasonal physiologic changes. It is because, HA is the only geographical condition for which humans can develop very efficient physiological adaptation mechanism called acclimatization. To study this hypothesis, PubMed was used to collect the HA associated symptoms and disorders. Disease Ontology based semantic similarity network (DSN) and disease-drug networks were constructed to narrow down the benchmark diseases and disorders of HA. The DSN which was further subjected to different community structure analysis uncovered the highly associated or possible comorbid diseases of HA. The predicted 12 lifestyle diseases were assumed to be “seasonal (sensitive) comorbid lifestyle diseases (SCLD)”. A time series analyses on Google Search data of the world from 2004–2016 was conducted to investigate whether the 12 lifestyle diseases have seasonal patterns. Because, the trends were sensitive to the term used as benchmark; the temporal relationships among the 12 disease search volumes and their temporal sequences similarity by dynamic time warping analyses was used to predict the comorbid diseases. Among the 12 lifestyle diseases, the study provides an indirect evidence in the existence of severe seasonal comorbidity among hypertension, obesity, asthma and fibrosis diseases, which is widespread in the world population. Thus, the present study has successfully addressed this issue by predicting the SCLD, and indirectly verified them among the world population using Google Search Trend. Furthermore, based on the SCLD seasonal trend, the study also classified them as severe, moderate, and mild. Interestingly, seasonal trends of the severe seasonal comorbid diseases displayed an inverse pattern between USA (Northern hemisphere) and New Zealand (Southern hemisphere). Further, knowledge in the so called “seasonal sensitive populations” physiological response to seasonal triggers such as winter, summer, spring, and autumn become crucial to modulate disease incidence, disease course, or clinical prevention.

Noncommutative topology and Jordan operator algebras

AbstractJordan operator algebras are norm‐closed spaces of operators on a Hilbert space with for all . We study noncommutative topology, noncommutative peak sets and peak interpolation, and hereditary subalgebras of Jordan operator algebras. We show that Jordan operator algebras present perhaps the most general setting for a “full” noncommutative topology in the ‐algebraic sense of Akemann, L. G. Brown, Pedersen, etc, and as modified for not necessarily selfadjoint algebras by the authors with Read, Hay and other coauthors. Our breakthrough relies in part on establishing several strong variants of ‐algebraic results of Brown relating to hereditary subalgebras, proximinality, deeper facts about for a left ideal L in a ‐algebra, noncommutative Urysohn lemmas, etc. We also prove several other approximation results in ‐algebras and various subspaces of ‐algebras, related to open and closed projections and technical ‐algebraic results of Brown.

Heat shock protein 104 (Hsp104)-mediated curing of [PSI+] yeast prions depends on both [PSI+] conformation and the properties of the Hsp104 homologs

Prions arise from proteins that have two possible conformations: properly folded and non-infectious or misfolded and infectious. The [PSI+] yeast prion, which is the misfolded and self-propagating form of the translation termination factor eRF3 (Sup35), can be cured of its infectious conformation by overexpression of Hsp104, which helps dissolve the prion seeds. This dissolution depends on the trimming activity of Hsp104, which reduces the size of the prion seeds without increasing their number. To further understand the relationship between trimming and curing, trimming was followed by measuring the loss of GFP-labeled Sup35 foci from both strong and weak [PSI+] variants; the former variant has more seeds and less soluble Sup35 than the latter. Overexpression of Saccharomyces cerevisiae Hsp104 (Sc-Hsp104) trimmed the weak [PSI+] variants much faster than the strong variants and cured the weak variants an order of magnitude faster than the strong variants. Overexpression of the fungal Hsp104 homologs from Schizosaccharomyces pombe (Sp-Hsp104) or Candida albicans (Ca-Hsp104) also trimmed and cured the weak variants, but interestingly, it neither trimmed nor cured the strong variants. These results show that, because Sc-Hsp104 has greater trimming activity than either Ca-Hsp104 or Sp-Hsp104, it cures both the weak and strong variants, whereas Ca-Hsp104 and Sp-Hsp104 only cure the weak variants. Therefore, curing by Hsp104 overexpression depends on both the trimming ability of the fungal Hsp104 homolog and the strength of the [PSI+] variant: the greater the trimming activity of the Hsp104 homolog and the weaker the variant, the greater the curing.

Variant‐specific and reciprocal Hsp40 functions in Hsp104‐mediated prion elimination: A potential role for the ‘Anti‐prion J‐protein 1’ (Apj1)

The prions of Saccharomyces cerevisiae are heritable aggregates of misfolded yeast proteins. Yeast prions are incorporated into daughter cells through the fragmentation of these aggregates by molecular chaperone proteins, including J‐proteins (Hsp40s), Hsp70s, and Hsp104. Previous studies have shown that the overexpression of Hsp104 cures the prion [PSI+], but not other prions, a phenomenon which has promoted the exploration of Hsp104 as a potential therapeutic agent for neurodegenerative diseases, despite the fact that the mechanism of [PSI+] elimination by Hsp104 overabundance is currently the subject of significant debate. We recently reported that the human homolog of Sis1, Hdj1, was capable of substituting for Sis1 in the propagation of strong but not weak [PSI+] variants and was deficient in substituting for Sis1 in the elimination of [PSI+] by Hsp104 overexpression. The objective of this study was to extend that investigation to the Sis1‐domain requirements for Hsp104‐mediated [PSI+] curing, expanding upon another prior investigation by extending the analysis to multiple [PSI+] variants and genetic backgrounds. We also asked whether any of the other 12 J‐proteins located in the S. cerevisiae cytosol are also necessary for Hsp104‐induced [PSI+] curing and if prion amyloid structure (variant identity) affects experimental outcomes. The primary method used in this study was complementation by plasmid‐shuffling in the budding yeast S. cerevisiae.Summary of ResultsOur investigation revealed that at least two weak [PSI+] variants can be maintained in the absence of any of 12 non‐essential J‐proteins, ruling out essential roles for any of these J‐proteins in weak [PSI+] prion propagation. Likewise, elimination of these weak [PSI+] variants by Hsp104 overexpression was ubiquitous, demonstrating that no J‐protein other than Sis1 is necessary for the elimination of weak [PSI+] variants by overexpression of Hsp104. In sharp contrast however, we found that strong variants of [PSI+] exhibited exceptional resistance to Hsp104‐mediated elimination only in strains lacking the J‐protein Apj1 (originally named: Anti‐Yeast Prion J‐protein 1) and conversely Apj1 overexpression accelerates prion elimination. Apj1 has been implicated in prion biology several times; often acting similarly to Ydj1 in prion biology. Here we find a novel genetic interaction for Apj1 and prions that is distinct from Ydj1 function. Additional mutation and truncation experiments revealed domains required for Apj1 function in Hsp104‐mediated [PSI+] curing and may ultimately help to explain the prion‐specificity of this curing mechanism.Support or Funding InformationThis work was supported by the National Institute of General Medical Sciences of the National Institutes of Health under Award Number R15GM110606. The content is solely the responsibility of the authors and does not necessarily represent the official views of the National Institutes of Health. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.

Human J-protein DnaJB6b Cures a Subset of Saccharomyces cerevisiae Prions and Selectively Blocks Assembly of Structurally Related Amyloids

Human chaperone DnaJB6, an Hsp70 co-chaperone whose defects cause myopathies, protects cells from polyglutamine toxicity and prevents purified polyglutamine and Aβ peptides from forming amyloid. Yeast prions [URE3] and [PSI(+)] propagate as amyloid forms of Ure2 and Sup35 proteins, respectively. Here we find DnaJB6-protected yeast cells from polyglutamine toxicity and cured yeast of both [URE3] prions and weak variants of [PSI(+)] prions but not strong [PSI(+)] prions. Weak and strong variants of [PSI(+)] differ only in the structural conformation of their amyloid cores. In line with its anti-prion effects, DnaJB6 prevented purified Sup35NM from forming amyloids at 37 °C, which produce predominantly weak [PSI(+)] variants when used to infect yeast, but not at 4 °C, which produces mostly strong [PSI(+)] variants. Thus, structurally distinct amyloids composed of the same protein were differentially sensitive to the anti-amyloid activity of DnaJB6 both in vitro and in vivo. These findings have important implications for strategies using DnaJB6 as a target for therapy in amyloid disorders.

Some derivative-free solvers for numerical solution of SODEs

In this paper, some variants of stochastic solvers free from derivatives for It\(\hat{\text {o}}\) stochastic ordinary differential equations (SODEs) are given. The derived strong variants are convergent and explicit. Then, some implicit solvers are also proposed. Numerical results are reported for confirming convergence properties and for comparing the behavior of these methods for pathwise approximation of SODEs.

$R_z$-supercontinuous functions

A new class of functions called “$R_{z}$-supercontinuous functions” is introduced. Their basic properties are studied and their place in the hierarchy of strong variants of continuity that already exist in the literature is elaborated. The class of $R_{z}$-supercontinuous functions properly includes the class of $R_{\rm cl}$-supercontinuous functions, Tyagi, Kohli, Singh (2013), which in its turn contains the class of $\rm cl$-supercontinuous ($\equiv $ clopen continuous) functions, Singh (2007), Reilly, Vamanamurthy (1983), and is strictly contained in the class of $R_{\delta }$-supercontinuous, Kohli, Tyagi, Singh, Aggarwal (2014), which in its turn is properly contained in the class of $R$-supercontinuous functions, Kohli, Singh, Aggarwal (2010).

Choice functions and bounded rationality

Bounded rationality assumes a utility function but not maximization. Simon’s version is satisficing. Another, attributable to Luce, is maximization to within a threshold of discrimination. Framed as conditions on a choice function, each with weak and strong variants, the two versions of bounded rationality have been shown to be equivalent, weak variant to weak variant, strong to strong. A finding of this paper is that, unlike classical rationality, bounded rationality does not depend on (or vary in strength with) the ordering properties of the underlying preference relation. Weak bounded rationality has been shown to be equivalent to a simple relaxation of Chernoff’s Axiom, got by changing “everyx∈C(X)” to “somex∈C(X)”. Another finding of this paper is that exactly the same change turns the Weak Axiom of Revealed Preference into an equivalent of strong bounded rationality.

Upper and lower cl-supercontinuous multifunctions

The notion of cl-supercontinuity ( clopen continuity) of functions is extended to the realm of multifunctions. Basic properties of upper(lower) cl-supercontinuous multifunctions are studied and their place in the hierarchy of strong variants of continuity of multifunctions is discussed. Examples are included to reflect upon the distinctiveness of upper (lower) cl-supercontinuity of multifunctions from that of othe rstrong variants of continuity of multifunctions which already exist in the literature.

R cl-supercontinuous functions

Abstract A new class of functions called ‘R cl-supercontinuous functions’ is introduced. Their basic properties are studied and their place in the hierarchy of strong variants of continuity that already exist in the literature is elaborated. The class of R cl-supercontinuous functions properly contains the class of cl-supercontinuous (≡ clopen continuous) functions (Applied Gen. Topology 8(2) (2007), 293–300; Indian J. Pure Appl. Math. 14(6) (1983), 767–772) and is strictly contained in the class of Rδ -supercontinuous functions which in its turn, is properly contained in the class of R-supercontinuous functions (Demonstratio Math. 43(3) (2010), 703–723).

On Strong Simulation and Composable Point Obfuscation

The Virtual Black Box (VBB) property for program obfuscators provides a strong guarantee: anything computable by an efficient adversary, given the obfuscated program, can also be computed by an efficient simulator, with only oracle access to the program. However, we know how to achieve this notion only for very restricted classes of programs. This work studies a simple relaxation of VBB: allow the simulator unbounded computation time, while still allowing only polynomially many queries to the oracle. We demonstrate the viability of this relaxed notion, which we call Virtual Grey Box (VGB), in the context of composable obfuscators for point programs: it is known that, with respect to VBB, if such obfuscators exist, then there exist multi-bit point obfuscators (also known as “digital lockers”) and subsequently also very strong variants of encryption that are resilient to various attacks, such as key leakage and key-dependent-messages. However, no composable VBB-obfuscators for point programs have been shown. We show composable VGB-obfuscators for point programs under a strong variant of the Decision Diffie–Hellman assumption. We show that VGB (instead of VBB) obfuscation still suffices for the above applications, as well as for new applications. This includes extensions to the public key setting and to encryption schemes with resistance to certain related key attacks (RKA).

Propertiesandfor Bounded Linear Operators

We shall consider properties which are related to Weyl type theorem for bounded linear operators , defined on a complex Banach space . These properties, that we callproperty, means that the set of all poles of the resolvent of of finite rank in the usual spectrum are exactly those points of the spectrum for which is an upper semi-Fredholm with index less than or equal to 0 and we callproperty, means that the set of all poles of the resolvent of in the usual spectrum are exactly those points of the spectrum for which is an upper semi--Fredholm with index less than or equal to 0. Properties and are related to a strong variants of classical Weyl’s theorem, the so-called property and property We shall characterize properties and in several ways and we shall also describe the relationships of it with the other variants of Weyl type theorems. Our main tool is localized version of the single valued extension property. Also, we consider the properties and in the frame of polaroid type operators.