We study the Tricomi problem for a differential–difference equation with the Lavrent’ev–Bitsadze operator in the main part and with parallel type change lines in an unbounded domain. Uniqueness and ...existence theorems for a twice continuously differentiable solution are proved.
•Frustrations are described in the Ising chain with the third-neighbors interactions.•Criteria for the emergence of magnetic frustrations are formulated.•Nonzero residual entropy values of a ...frustrated system were found.•The heat capacity shows two-peak structure in the vicinity of the frustration point.
We study the frustration properties of the Ising model on a one-dimensional monoatomic equidistant lattice, taking into account the exchange interactions of atomic spins at the sites of the nearest, next-nearest, and third neighbors. The exact analytical expressions for the thermodynamic functions of the system are obtained using the Kramers-Wannier transfer matrix technique. Criteria for the emergence of magnetic frustrations in the presence of competition between the energies of exchange interactions are formulated. The points and intervals of the existence of frustrations, which depend on the values and signs of the exchange interactions, are found. The features of the entropy and heat capacity of this model in the frustration regime and its vicinity are investigated. Non-zero entropy values of the ground state of a frustrated system, as well as a two-peak temperature structure of the heat capacity in the vicinity of the frustration point, are found.
We study the Dirichlet problem for a nonlocal integro-functional-differential equation of the composite type. Theorems on the existence and uniqueness of a twice continuously differentiable solution ...are proved.
We study the Tricomi problem for an advance–delay mixed type equation. Theorems on the uniqueness and existence of a twice continuously differentiable solution are proved.
We study the Tricomi boundary value problem for the Lavrent'ev–Bitsadze advanced-retarded equation of the mixed type. This problem is uniquely solvable.
Frustration Properties of the 1D Ising Model Zarubin, A. V.; Kassan-Ogly, F. A.; Proshkin, A. I. ...
Journal of experimental and theoretical physics,
05/2019, Letnik:
128, Številka:
5
Journal Article
Recenzirano
We analyze frustration properties of the Ising model for a 1D monatomic equidistant lattice in an external uniform magnetic field considering exchange interactions of atomic spins at the sites of the ...first (nearest) and second neighbors. Exact analytic expressions for thermodynamic and magnetic characteristics of the system, as well as for the Fourier transform of the pair spin–spin correlation function and magnetic diffused scattering wavevectors, were obtained by the method of the Kramers–Wannier transfer matrix considering the exchange interaction between spins at the nearest-neighbor sites in an external magnetic field, as well as the exchange interaction between spins at the second-neighbor sites in zero magnetic field. The criteria for the emergence of magnetic frustration in the presence of competition not only between exchange-interaction energies, but also between these energies and the external magnetic field energy are formulated. The frustration points and the values of frustration magnetic fields depending on the magnitudes and signs of the exchange interaction are determined. The distinguishing features of this model in the frustration regime and its vicinity are analyzed. The set of characteristic features inherent in observables for systems with magnetic frustrations is considered and analyzed. It is shown that the inclusion of competing exchange interactions at the first- and second-neighbor sites makes it possible to describe the behavior of the magnetic diffused scattering wavevector for commensurate, incommensurate, and lock-in structures.
Introduction
aCGH determines pathogenic copy number variations (CNVs) in about 10% of patients with intellectual disability (ID). In another 20% of patients, probably pathogenic CNVs or variants with ...uncertain clinical significance are detected. It may be variants that do not fully explain the patient’s symptoms, aberrations with reduced penetrance or inherited from healthy parents. The use of a sequencing method for such cases is advisable.
Objectives
Improvement of diagnosis of intellectual disability.
Methods
aCGH with 60K Agilent microarrays, qPCR, targeted sequencing, whole exome sequencing (WES).
Results
Six patients with ID and inherited deletions/duplications detected by aCGH and their parents if available were further examined by sequencing. Four patients had maternal CNVs: (1) del1q41 (
SPATA17, LINC00210, RRP15
), (2) del7q35 (
TCAF2
, exon 8), (3) dup8p22p21.3 (
PSD3,
exons 1-11), and (4) del12p11.1 (
SYT10,
exons 1-2). Two patients had paternal CNVs: (5) dup1q44 (
SMYD3
, exons 2-5) and (6) del15q11.2 (
TUBGCP5, CYFIP1, NIPA1, NIPA2, LOC283683
). The severe phenotype of patient (5) with dup1q44 could not be explained by the paternally inherited disruption of the single
SMYD3
gene. WES determined probably pathogenic SNV in the
MID1
gene associated with Opitz GBBB syndrome (OMIM 300000), which corresponds better to the patient’s phenotype and is likely to be the cause of the disease. Although del1q41 is included in the region of chromosome 1q41-q42 deletion syndrome (OMIM 612530) the phenotype of the patient (1) is much milder; WES in the patient detected two pathogenic (
MPO, MAN2C1
) and one probably pathogenic (
ARID1B
) SNVs. In patient (6) with del15q11.2 pat WES detected additional pathogenic SNV in exon 7 of the
ARSE
gene. In patient (3) with dup8p22p21.3 WES determined two SNVs with uncertain significance in the
KIDINS220, FOXG1
genes. No SNVs were detected by WES in patient (2) with del7q35. For patient (4) with del12p11.1 targeted
SYT10
sequencing revealed no pathogenic SNVs as well.
Conclusions
Sometimes aCGH-analysis is sufficient to identify the causes of ID, however, in the case of detection of CNVs with uncertain clinical significance and/or inherited from healthy parents, it may be necessary to further examine the patient using sequencing methods. So, the accurate diagnosis was made by WES for one patient of eight. For another two patients the combination of CNVs and SNPs should be considered. For the last three patients the described aberrations could not explain the phenotype and whole genome sequencing may be the solution.This study was supported by the Russian Science Foundation, grant 21-65-00017, https://rscf.ru/project/21-65-00017/
Disclosure of Interest
None Declared
Background
Squamous cell lung cancer (SCLC) arises from bronchial changes: basal cell hyperplasia (BCH), squamous metaplasia (SM), and dysplasia. However, the premalignant process preceding SCLC is ...not inevitable; it can stop at any of the bronchial lesions. Previously, we hypothesized that combinations of premalignant lesions observed in the small bronchi of SCLC patients can reflect the different “scenarios” of the premalignant process: BCH
i
—the stoppage at the stage of hyperplasia and BCH
SM
—the progression of hyperplasia to metaplasia.
Methods and Results
In this study, using whole-genome bisulfite sequencing we analyzed the DNA methylome of two forms of BCH: isolated BCH (BCH
i
) and BCH co-occurred with SM (BCH
SM
) in the small bronchi of SCLC patients. It was shown that BCH
i
harbored differentially methylated regions (DMRs) affecting genes associated with regulating phosphatase activity. In BCH
SM
, DMRs were found in genes involved in PI3K-Akt and AMPK signaling pathways. DMRs were also found to affect specific miRNA genes: miR-34a and miR-3648 in BCH
i
and miR-924 and miR-100 in BCH
SM
.
Conclusions
Thus, this study demonstrated the significant changes in DNA methylome between the isolated BCH and BCH combined with SM. The identified epigenetic alterations may underlie different “scenarios” of the premalignant process in the bronchial epithelium.
Increasing evidence suggests that both coding and non-coding regions of sarcomeric protein genes can contribute to hypertrophic cardiomyopathy (HCM). Here, we introduce an experimental workflow ...(tested on four patients) for complete sequencing of the most common HCM genes (
,
,
,
and
) via long-range PCR, Oxford Nanopore Technology (ONT) sequencing, and bioinformatic analysis. We applied Illumina and Sanger sequencing to validate the results, FastQC, Qualimap, and MultiQC for quality evaluations, MiniMap2 to align data, Clair3 to call and phase variants, and Annovar's tools and CADD to assess pathogenicity of variants. We could not amplify the region encompassing exons 6-12 of
. A higher sequencing error rate was observed with ONT (6.86-6.92%) than with Illumina technology (1.14-1.35%), mostly for small indels. Pathogenic variant p.Gln1233Ter and benign polymorphism p.Arg326Gln in
in a heterozygous state were found in one patient. We demonstrated the ability of ONT to phase single-nucleotide variants, enabling direct haplotype determination for genes
and
. These findings highlight the importance of long-range PCR efficiency, as well as lower accuracy of variant calling by ONT than by Illumina technology; these differences should be clarified prior to clinical application of the ONT method.
The Tricomi problem for a mixed-composite equation involving a product of multiple functional advance-delay operators is studied. The problem is shown to be uniquely solvable.
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