Some remarks to the Jacobian Conjecture

This work is related to the Jacobian Conjecture. It contains the formulas concerning algebraic dependence of the polynomial mappings having two zeros at infinity and the constant Jacobian. These relations mean that such mappings are non-invertible. They reduce the Jacobian Conjecture only to the case of mappings having one zero at infinity. This case is already solved by Abhyankar. The formulas presented in the paper were illustrated by the large example

Validation of exophthalmos magnetic resonance imaging measurements in patients with Graves’ orbitopathy, compared to ophthalmometry results

Purpose: Although assessment of the orbital structures using magnetic resonance imaging (MRI) is well described in the literature, there is no consensus as to which measurement method is the most useful in exophthalmos assessment. The aim of the study was to correlate 2 MRI methods of exophthalmos measurement with exophthalmometry results and to determine a proper technique of exophthalmos measurement. Material and methods: Fifty-four patients (108 orbits) with exophthalmos in the course of Graves’ orbitopathy were enrolled in the study. Two measurements on axial T2W orbital MRI images were performed by 2 independent radiologists: the distance from the interzygomatic line to the anterior surface of the globe (AD) and the distance from the interzygomatic line to the posterior sclera (PD). Within 4 weeks, an exophthalmometry was performed by an ophthalmologist using a Hertel exophthalmometer. The inter-observer variation was assessed using the Pearson correlation coefficient. Values were presented as mean and standard deviation, and the differences in values were explored with Student’s t-test. Results: The mean AD measured on MRI by the first observer was 20.6 ± 3 mm, and 20.6 ± 2.9 mm by the second observer. PD values were 2.9 ± 2.8 mm and 3.4 ± 2.8 mm, respectively. The mean exophthalmometry result was 21 ± 3.3 mm. The correlation was very high between observers for AD measurements (r = 0.98, p = 0.01) and high for PD measurements (r = 0.95, p = 0.01). AD measurements on MRI and exophthalmometry results were strongly correlated (r = 0.9, p = 0.01). Conclusions: The AD measurement has better reproducibility and is directly correlated with Hertel exophthalmometry. This method could be sufficient in routine practice

A second example of non-Keller mapping

In the article the next nontrivial example of non-Keller mapping having two zeros at infinity is analyzed. The rare mapping of two complex variables having two zeros at infinity is considered. In the article it has been proved that if the Jacobian of the considered mapping is constant, then it is zero

Genetic variants in transforming growth factor-β gene (TGFB1) affect susceptibility to schizophrenia

Immense body of evidence indicates that dysfunction of immune system is implicated in the etiology of schizophrenia. The immune theory of schizophrenia is supported by alterations in cytokine profile in the brain and peripheral blood. Given the strong genetic background of schizophrenia, it might be assumed that aberrant production of cytokines might be the consequence of genetic factors. This study aimed at investigating the association between schizophrenia susceptibility and selected functional polymorphisms in genes encoding cytokines including: interleukin-2 (IL2 −330T>G, rs2069756), interleukin-6 (IL-6 −174G>C, rs1800795), interferon-γ (IFNG +874T>A, rs2430561) as well as for the first time transforming growth factor-β1 (TGFB1 +869T>C, rs1800470 and +916G>C, rs1800471). We recruited 151 subjects with schizophrenia and 279 controls. There was a significant difference in the genotype distribution and allelic frequency of the TGFB1 +869T>C between patients with schizophrenia and healthy controls (p < 0.05). The risk of schizophrenia was more than two-fold higher in carriers of T allele (CT+TT genotypes) than individuals with CC genotype. Given documented gender differences in incidence of schizophrenia, we conducted separate analyses of male and female participants. We have shown that the association was significant in females, while in males it reached a trend toward statistical significance. To the best of our knowledge, it is the first report showing the association between TGFB1 +869T>C polymorphism and schizophrenia

Effects of interactions between variation in dopaminergic genes, traumatic life events, and anomalous self-experiences on psychosis proneness : results from a cross-sectional study in a nonclinical sample

Background: there is a growing number of studies showing interactions between genetic polymorphisms associated with dopaminergic neurotransmission and traumatic life events (TLEs) on a risk of psychotic-like experiences (PLEs). Anomalous self-experiences (ASEs) have been associated both with TLEs as well as with PLEs. However, it remains unknown what is the role of ASEs in the complexity of gene - environment interactions on the emergence of PLEs. Patients and methods: we included 445 young adults - university students from three big cities in Poland. We used the Traumatic Events Checklist to assess TLEs, the Inventory of Psychotic-Like anomalous self-experiences in order to measure ASEs, and the Prodromal Questionnaire (PQ16) to record the level of PLEs. The following gene polymorphisms, related to dopaminergic neurotransmission, were determined: the catechol-O-methyltransferase (COMT) rs4680 polymorphism, the dopamine D2 receptor (DRD2) rs6277 polymorphism, and the dopamine transporter 1 (DAT1) rs28363170 polymorphism. Results: there was a significant effect of the interaction between the DAT1 polymorphism, a severity of ASEs, and a history of TLEs on the level of PLEs. Among the DAT1 10R/10R homozygotes with low level of ASEs, a severity of PLEs was significantly higher in individuals with a history of any TLEs. Higher scores of the PQ16 were associated with a greater severity of ASEs both in the DAT1 9R allele carriers and the DAT1 10R/10R homozygotes. Conclusion: our findings imply that genetic liability related to aberrant dopamine transport might impact the association between TLEs and PLEs in subjects with high levels of ASEs

Variations in Suppressor Molecule CTLA-4 Gene Are Related to Susceptibility to Multiple Myeloma in a Polish Population

Various phenotype and functional T-cell abnormalities are observed in multiple myeloma (MM) patients. The aim of this study was to investigate the association between polymorphisms in the gene encoding cytotoxic T-lymphocyte antigen-4 (CTLA-4), a negative regulator of the T-lymphocyte immune response and susceptibility to multiple myeloma in a Polish population. Two hundred MM patients and 380 healthy subjects were genotyped for the following polymorphisms: CTLA-4c.49A>G, CTLA-4g.319C>T, CTLA-4g.*642AT(8_33), CT60 (CTLA-4g.*6230G>A), Jo31 (CTLA-4g.*10223G>T). Our study is the largest and most comprehensive evaluation to date of the association between genetic polymorphisms in the CTLA-4 molecule and multiple myeloma. It was found that CTLA-4c.49A>G[G], CT60[G], and Jo31[G] alleles were more frequently observed in MM patients than in controls (0.50 vs. 0.44, p = 0.03, 0.65 vs. 0.58, p = 0.04, and 0.63 vs. 0.57, p = 0.03, respectively). Moreover, the haplotype CTLA-4c.49A>G[G], CTLA-4g.319C>T[C], CTLA-4g.*642AT(8_33) [8], CT60[G], Jo31[G] including all susceptibility alleles increases the risk of MM about fourfold (OR: 3.79, 95%CI: 2.08–6.89, p = 0.00001). These findings indicate that genetic variations in the CTLA-4 gene play role in susceptibility to multiple myeloma and warrant further investigation through replication studies

Comparison of reorganized versus unaltered cardiology departments during the COVID-19 era: a subanalysis of the COV-HF-SIRIO 6 study

Background: Since the beginning of the coronavirus disease-2019 (COVID-19) pandemic, numerous cardiology departments were reorganized to provide care for COVID-19 patients. We aimed to compare the impact of the COVID-19 pandemic on hospital admissions and in-hospital mortality in reorganized vs. unaltered cardiology departments. Methods: The present subanalysis is a multicenter retrospective COV-HF-SIRIO 6 study that includes all patients (n = 101,433) hospitalized in 24 cardiology departments in Poland between January 1, 2019 and December 31, 2020, with a focus on patients with acute heart failure (AHF). Results: Reduction of all-cause hospitalizations was 50.6% vs. 21.3% for reorganized vs. unaltered cardiology departments in 2020 vs. 2019, respectively (p &lt; 0.0001). Considering AHF alone respective reductions by 46.5% and 15.2% were registered (p &lt; 0.0001). A higher percentage of patients was brought in by ambulance to reorganized vs. unaltered cardiology departments (51.7% vs. 34.6%; p &lt; 0.0001) alongside with a lower rate of self-referrals (45.7% vs. 58.4%; p &lt; 0.0001). The rate of all-cause in-hospital mortality in AHF patients was higher in reorganized than unaltered cardiology departments (10.9% vs. 6.4%; p &lt; 0.0001). After the exclusion of patients with concomitant COVID-19, the mortality rates did not differ significantly (6.9% vs. 6.4%; p = 0.55). Conclusions: In cardiology departments reorganized to provide care for COVID-19 patients vs. unaltered ones, observed: i) a greater reduction in hospital admissions in 2020 vs. 2019; ii) higher rates of patients brought by ambulance and lower rates of self-referrals; and iii) higher all-cause in-hospital mortality for AHF due to COVID-19 related deaths

The determinants of the block band matrices based on the n-dimensional Fourier equation.

Abstract. This work is a continuation of the considerations concerning the determinants of the band block matrices on the example of the n-dimensional Fourier equation (work Part 1). The discussion will concern the special case called the three-dimensional Fourier equation