Defect Group Research Articles

Decomposition Matrix for the projective Characters S_28, p=11

In this work, we compute the decomposition matrix to the spin characteristics of S_28 for a given field of characteristic p=11, the connections between the irreducible modular spin characters and the irreducible spin characters of S_28. The technique employed in this study is (r,r ̅ )-inducing, which creates projective characters for S_28 by using the projective characters of S_27. Maple was used to seeing all available columns and then choosing the potentially appropriate columns of them. In order to explore irreducible modular spin characteristics, general correlations and theorems will be discovered as a result of this research.

Classification of LED Packages for Quality Control by Discriminant Analysis, Neural Network and Decision Tree.

This study investigates supervised learning to improve LED classification. A hardware system for testing was built. The data for learning were acquired and then analyzed to show their characteristics. An LED was tested, and the results were categorized into three defective LED groups and one normal LED group. Before classification, electrical and optical data were examined to identify their characteristics. To find out the best way for quality control, an ensemble of methods was used. First, the discriminant analysis using the validation data achieved a 77.9% true positive rate for normal products, inadequate for quality control. Second, neural network-based learning boosted this rate to 97.8%, but the 2.2% false negative rate remained problematic. Finally, a binary decision tree was constructed, achieving a 99.4% true positive rate from just 14 splits, proving highly effective in product classification. The training time was measured as 8.1, 18.2 and 8.2 s for discriminant analysis, neural network and decision tree, respectively. This work has found the binary decision tree is advantageous considering both learning and classification efficiencies.

In vitro hemodynamic performance of a blood pump for self-powered venous assist in univentricular hearts

Univentricular heart anomalies represent a group of severe congenital heart defects necessitating early surgical intervention in infancy. The Fontan procedure, the final stage of single-ventricle palliation, establishes a serial connection between systemic and pulmonary circulation by channeling venous return to the lungs. The absence of the subpulmonary ventricle in this peculiar circulation progressively eventuates in failure, primarily due to chronic elevation in inferior vena cava (IVC) pressure. This study experimentally validates the effectiveness of an intracorporeally-powered venous ejector pump (VEP) in reducing IVC pressure in Fontan patients. The VEP exploits a fraction of aortic flow to create a jet-venturi effect for the IVC, negating the external power requirement and driveline infections. An invitro Fontan mock-up circulation loop is developed and the impact of VEP design parameters and physiological conditions is assessed using both idealized and patient-specific total cavopulmonary connection (TCPC) phantoms. The VEP performance in reducing IVC pressure exhibited an inverse relationship with the cardiac output and extra-cardiac conduit (ECC) size and a proportional relationship with the transpulmonary pressure gradient (TPG) and mean arterial pressure (MAP). The ideal VEP with fail-safe features provided an IVC pressure drop of 1.82 ± 0.49, 2.45 ± 0.54, and 3.12 ± 0.43 mm Hg for TPG values of 6, 8, and 10 mm Hg, respectively, averaged over all ECC sizes and cardiac outputs. Furthermore, the arterial oxygen saturation was consistently maintained above 85% during full-assist mode. These results emphasize the potential utility of the VEP to mitigate elevated venous pressure in Fontan patients.

Predicting Long-Term Childhood Survival of Newborns with Congenital Heart Defects: A Population-Based, Prospective Cohort Study (EPICARD).

Backgroud: Congenital heart defects (CHDs) are the most frequent group of major congenital anomalies, accounting for almost 1% of all births. They comprise a very heterogeneous group of birth defects in terms of their severity, clinical management, epidemiology, and embryologic origins. Taking this heterogeneity into account is an important imperative to provide reliable prognostic information to patients and their caregivers, as well as to compare results between centers or to assess alternative diagnostic and treatment strategies. The Anatomic and Clinical Classification of CHD (ACC-CHD) aims to facilitate both the CHD coding process and data analysis in clinical and epidemiological studies. The objectives of the study were to (1) Describe the long-term childhood survival of newborns with CHD, and (2) Develop and validate predictive models of infant mortality based on the ACC-CHD. Methods: This study wasbased on data from a population-based, prospective cohort study: Epidemiological Study of Children with Congenital Heart Defects (EPICARD). The final study population comprised 1881 newborns with CHDs after excluding cases that were associated with chromosomal and other anomalies. Statistical analysis included non-parametric survival analysis and flexible parametric survival models. The predictive performance of models was assessed by Harrell's C index and the Royston-Sauerbrei RD2, with internal validation by bootstrap. Results: The overall 8-year survival rate for newborns with isolated CHDs was 0.96 [0.93-0.95]. There was a substantial difference between the survival rate of the categories of ACC-CHD. The highest and lowest 8-year survival rates were 0.995 [0.989-0.997] and 0.34 [0.21-0.50] for "interatrial communication abnormalities and ventricular septal defects" and "functionally univentricular heart", respectively. Model discrimination, as measured by Harrell's C, was 87% and 89% for the model with ACC-CHD alone and the full model, which included other known predictors of infant mortality, respectively. The predictive performance, as measured by RD2, was 45% and 50% for the ACC-CHD alone and the full model. These measures were essentially the same after internal validation by bootstrap. Conclusions: The ACC-CHD classification provided the basis of a highly discriminant survival model with good predictive ability for the 8-year survival of newborns with CHDs. Prediction of individual outcomes remains an important clinical and statistical challenge.

Tensor Categories for Vertex Operator Superalgebra Extensions

Let V V be a vertex operator algebra with a category C \mathcal {C} of (generalized) modules that has vertex tensor category structure, and thus braided tensor category structure, and let A A be a vertex operator (super)algebra extension of V V . We employ tensor categories to study untwisted (also called local) A A -modules in C \mathcal {C} , using results of Huang-Kirillov-Lepowsky that show that A A is a (super)algebra object in C \mathcal {C} and that generalized A A -modules in C \mathcal {C} correspond exactly to local modules for the corresponding (super)algebra object. Both categories, of local modules for a C \mathcal {C} -algebra and (under suitable conditions) of generalized A A -modules, have natural braided monoidal category structure, given in the first case by Pareigis and Kirillov-Ostrik and in the second case by Huang-Lepowsky-Zhang. Our main result is that the Huang-Kirillov-Lepowsky isomorphism of categories between local (super)algebra modules and extended vertex operator (super)algebra modules is also an isomorphism of braided monoidal (super)categories. Using this result, we show that induction from a suitable subcategory of V V -modules to A A -modules is a vertex tensor functor. Two applications are given: First, we derive Verlinde formulae for regular vertex operator superalgebras and regular 1 2 Z \frac {1}{2}\mathbb {Z} -graded vertex operator algebras by realizing them as (super)algebra objects in the vertex tensor categories of their even and Z \mathbb {Z} -graded components, respectively. Second, we analyze parafermionic cosets C = C o m ( V L , V ) C=\mathrm {Com}(V_L,V) where L L is a positive definite even lattice and V V is regular. If the vertex tensor category of either V V -modules or C C -modules is understood, then our results classify all inequivalent simple modules for the other algebra and determine their fusion rules and modular character transformations. We illustrate both directions with several examples.

Cores of Partitions in Rectangles

For a positive integer $t \geq 2$, the $t$-core of a partition plays an important role in modular representation theory and combinatorics. We initiate the study of $t$-cores of partitions contained in an {$r\times s$} rectangle. Our main results are as follows. We first give a simple formula for the number of partitions in the rectangle that are themselves $t$-cores and compute its asymptotics for large $r,s$. We then prove that the number of partitions inside the rectangle whose $t$-cores are a fixed partition $\rho$ is given by a product of binomial coefficients. Finally, we use this formula to compute the distribution of the $t$-core of a uniformly random partition inside the rectangle extending our previous work on all partitions of a fixed integer $n$ (Ann. Appl. Prob. 2023). In particular, we show that in the limit as $r,s \to \infty$ maintaining a fixed aspect ratio, we again obtain a Gamma distribution with the same shape parameter $\alpha = (t-1)/2$ and rate parameter $\beta$ that depends on the aspect ratio.

Combinatorial biosynthesis in yeast leads to over 200 diterpenoids

Diterpenoids form a diverse group of natural products, many of which are or could become pharmaceuticals or industrial chemicals. The modular character of diterpene biosynthesis and the promiscuity of the enzymes involved make combinatorial biosynthesis a promising approach to generate libraries of diverse diterpenoids. Here, we report on the combinatorial assembly in yeast of ten diterpene synthases producing (+)-copalyl diphosphate-derived backbones and four cytochrome P450 oxygenases (CYPs) in diverse combinations. This resulted in the production of over 200 diterpenoids. Based on literature and chemical database searches, 162 of these compounds can be considered new-to-Nature. The CYPs accepted most substrates they were given but remained regioselective with few exceptions. Our results provide the basis for the systematic exploration of the diterpenoid chemical space in yeast using sequence databases.

Supratrochlear Rim Is Correlated With Isolated Patellar Chondromalacia on Magnetic Resonance Imaging of the Knee

To investigate the relationship between the supratrochlear rim and isolated patellar chondromalacia (PC) using magnetic resonance imaging (MRI) scans of the knee. Patients without patellofemoral pain (control group) and patients with patellofemoral pain and diagnosed with stage III or IV PC based on MRI (defect group) were retrospectively identified. Patients with a history of patellar subluxation were excluded. We used patient MRI scans to perform 20 anatomical measurements of the patellofemoral joint. We also performed 2 measurements of the anterior femoral curvature. A total of 30 patients (29 ± 8.7 years) were in the control group, and 20 patients were in the defect group (29.4 ± 9.7 years). The maximum curvature (P < .001) and mean curvature (P < .001) of the anterior femoral condyle were found statistically significantly different between the groups. Patellotrochlear index (P= .03) and Insall-Salvati index (P < .001) were also found statistically significantly different between the 2 groups. Patella type III and trochlear dysplasia grade B were found more common in the defect group. In this Level III prognostic, case-control study, we have shown through MRI knee measurements that the isolated patellar chondromalacia in patients without a history of patellar subluxation and dislocation is correlated with the increased anterior femoral curvature in combination with patella alta.

Genetic susceptibility to Tuberculosis in an infant with BCG-osis

Mendelian susceptibility to mycobacterial diseases (MSMD) is a group of innate immunity defects characterized by inborn susceptibility to intracellular pathogens. These are due to defects in the interleukin 12-23-interferon gamma y axis. Twenty-three genetic mutations have been identified in this axis, of which mutation in the IL12RB1 gene is the most common genetic defect of MSMD identified. An 11-month-old infant presented with features of axillary lymphadenitis and skin lesions both of which were positive for acid-fast bacilli on Ziehl– Neelsen stain and GeneXpert. Keeping a high index of suspicion of primary immunodeficiency, the child was evaluated further and was diagnosed as a case of MSMD with IL12RB1 gene mutation.

On a theorem of Knörr

Knörr has constructed an ideal, in the center of the p-modular group algebra of a finite group G, whose dimension is the number of p-blocks of defect zero in G/Q; here p is a prime and Q is a normal p-subgroup of G. We generalize his construction to symmetric algebras.

Enriched Ti3+ in TiONC electrocatalyst for efficient H2O2 generation via 2-electron oxygen reduction reaction

The 2-electron electrochemical oxygen reduction reaction (ORR) is considered a viable method for synthesizing H2O2 because of its efficiency and environmental friendliness. However, conventional catalysts for this reaction predominantly rely on high-cost metals and require complex preparation procedures. Herein, we synthesized an electrocatalyst containing TiN and N-doped carbon via the pyrolysis of melamine and MIL125(Ti)–NH2. The effects of melamine and pyrolysis temperature on the chemical composition and defect site formation were investigated. Importantly, the obtained results suggest that the generated Ti3+ sites are more important in enhancing the performance of the 2-electron ORR, surpassing defective carbon and oxygen functional groups. In particular, the resulting TiONC-MA-1000 catalyst prepared through pyrolysis at 1,000 °C contained abundant Ti3+ sites, resulting in high 2-electron ORR activity with a molar selectivity exceeding 91 % and high stability over a 12 h testing period. The electrochemical H2O2 generation experiments conducted in an H-cell configuration employing TiONC-MA-1000 as the electrocatalyst yielded 6.99 mol⋅gcatalyst−1⋅h−1 H2O2. Therefore, the present study proposes a facile approach for fabricating highly active electrocatalysts suitable for large-scale H2O2 production.

Non-induced modular representations of cyclic groups

We compute the ring of non-induced representations for a cyclic group, Cn , over an arbitrary field and show that it has rank φ ( n ) , where φ is Euler’s totient function—independent of the characteristic of the field. Along the way, we obtain a “pick-a-number” trick; expressing an integer n as a sum of products of p-adic digits of related integers.

Intermediate defect groups, polarization pairs, and noninvertible duality defects

Within the framework of relative and absolute quantum field theories (QFTs), we present a general formalism for understanding polarizations of the intermediate defect group and constructing noninvertible duality defects in theories in 2k spacetime dimensions with self-dual gauge fields. We introduce the polarization pair, which fully specifies absolute QFTs as far as their (k−1)-form defect groups are concerned, including their (k−1)-form symmetries, global structures (including discrete θ-angle), and local counterterms. Using the associated symmetry topological field theory (TFT), we show that the polarization pair is capable of succinctly describing topological manipulations, e.g., gauging (k−1)-form global symmetries and stacking counterterms, of absolute QFTs. Furthermore, automorphisms of the (k−1)-form charge lattice naturally act on polarization pairs via their action on the defect group; they can be viewed as dualities between absolute QFTs descending from the same relative QFT. Using this formalism, we present a prescription for building noninvertible symmetries of absolute QFTs. A large class of known examples, e.g., noninvertible defects in 4D N=4 super-Yang-Mills, can be reformulated via this prescription. As another class of examples, we identify and investigate in detail a family of noninvertible duality defects in 6D superconformal field theories (SCFTs), including from the perspective of the symmetry TFT derived from type IIB string theory. Published by the American Physical Society 2024

Modular representations in type A with a two-row nilpotent central character

We study the category of representations of slm+2n over a field of characteristic p with p≫0, whose p-character is a nilpotent whose Jordan type is the two-row partition (m+n,n). In a previous paper with Anno, we used Bezrukavnikov-Mirkovic-Rumynin's theory of positive characteristic localization and exotic t-structures to give a geometric parametrization of the simples using annular crossingless matchings. Building on this, here we give combinatorial dimension formulae for the simple objects, and compute the Jordan-Hölder multiplicities of the simples inside the baby Vermas. We use Cautis-Kamnitzer's geometric categorification of the tangle calculus to study the images of the simple objects under the BMR equivalence. Our results generalize Jantzen's formulae in the subregular nilpotent case (i.e. when n=1), and may be viewed as a positive characteristic analogue of the combinatorial description for Kazhdan-Lusztig polynomials of Grassmannian permutations due to Lascoux and Schutzenberger.

The group of splendid Morita equivalences of principal 2-blocks with dihedral and generalised quaternion defect groups

Let $k$ be an algebraically closed field of characteristic $2$, let $G$ be a finite group and let $B$ be the principal $2$-block of $kG$ with a dihedral or a generalised quaternion defect group $P$. Let also $\calT(B)$ denote the group of splendid Morita auto-equivalences of $B$. We show that \begin{align*} \calT(B)\cong \Out_P(A)\rtimes \Out(P,\calF), \end{align*} where $\Out(P,\calF)$ is the group of outer automorphisms of $P$ which stabilize the fusion system $\calF$ of $G$ on $P$ and $\Out_P(A)$ is the group of algebra automorphisms of a source algebra $A$ of $B$ fixing $P$ modulo inner automorphisms induced by $(A^P)^\times$.

Expression and function of the urea cycle in widely-used hepatic cellular models.

The group of rare metabolic defects termed urea cycle disorders (UCDs) occur within the ammonia elimination pathway and lead to significant neurocognitive sequelae for patients surviving decompensation episodes. Besides orthotopic liver transplantation, curative options are lacking for UCDs, with dietary management being the gold clinical standard. Novel therapeutic approaches are essential for UCDs; however, such effort presupposes preclinical testing in cellular models that effectively capture disease manifestation. Several cellular and animal models exist and aim to recapitulate the broad phenotypic spectrum of UCDs; however, the majority of those lack extensive molecular and biochemical characterization. The development of cellular models is emerging since animal models are extremely time and cost consuming, and subject to ethical considerations, including the 3R principle that endorses animal welfare over unchecked preclinical testing. The aim of this study was to compare the extent of expression and functionality of the urea cycle in two commercial hepatoma-derived cell lines, induced pluripotent stem cell hepatocytes (iPSC-Heps), primary human hepatocytes (PHHs) and human liver cell preparations. Using immunoblotting, immunocytochemistry, and stable isotope tracing of the urea cycle metabolites, we identified that the hepatoma-derived, 2-week differentiated HepaRG cells are urea cycle proficient and behave as cellular alternatives to PHHs. Furthermore, HepaRG cells were superior to iPSC-Heps, which are known to exhibit batch-to-batch variabilities in terms of hepatic maturity and enzyme expression. Finally, HepG2 cells lack the urea cycle enzymes ornithine transcarbamylase and arginase 1, the transporter ORNT1, which limits their suitability as model for the study of UCDs.

Chromatinopathies: insight in clinical aspects and underlying epigenetic changes.

Chromatinopathies (CPs), a group of rare inborn defects characterized by chromatin state imbalance, have evolved from initially resembling Cornelia de Lange syndrome to encompass a wide array of genetic diseases with diverse clinical presentations. The CPs classification now includes human developmental disorders caused by germline mutations in epigenes, genes that regulate the epigenome. Recent advances in next-generation sequencing have enabled the association of 154 epigenes with CPs, revealing distinctive DNA methylation patterns known as episignatures.It has been shown that episignatures are unique for a particular CP or share similarities among specific CP subgroup. Consequently, these episignatures have emerged as promising biomarkers for diagnosing and treating CPs, differentiating subtypes, evaluating variants of unknown significance, and facilitating targeted therapies tailored to the underlying epigenetic dysregulation.The following review was conducted to collect, summarize, and analyze data regarding CPs in such aspects as clinical evaluation encompassing long-term patient care, underlying epigenetic changes, and innovative molecular and bioinformatic methodologies that have been devised for the assessment of CPs. We have also shed light on promising novel treatment options that have surfaced in recent research and presented a synthesis of ongoing clinical trials, contributing to the current understanding of the dynamic and evolving nature of CPs investigation.

Smith theory and cyclic base change functoriality

Abstract Lafforgue and Genestier-Lafforgue have constructed the global and (semisimplified) local Langlands correspondences for arbitrary reductive groups over function fields. We establish various properties of these correspondences regarding functoriality for cyclic base change: For $\mathbf {Z}/p\mathbf {Z}$ -extensions of global function fields, we prove the existence of base change for mod p automorphic forms on arbitrary reductive groups. For $\mathbf {Z}/p\mathbf {Z}$ -extensions of local function fields, we construct a base change homomorphism for the mod p Bernstein center of any reductive group. We then use this to prove existence of local base change for mod p irreducible representation along $\mathbf {Z}/p\mathbf {Z}$ -extensions, and that Tate cohomology realizes base change descent, verifying a function field version of a conjecture of Treumann-Venkatesh. The proofs are based on equivariant localization arguments for the moduli spaces of shtukas. They also draw upon new tools from modular representation theory, including parity sheaves and Smith-Treumann theory. In particular, we use these to establish a categorification of the base change homomorphism for mod p spherical Hecke algebras, in a joint appendix with Gus Lonergan.

Ectopia Cordis with Omphalocele in First Trimester Pregnancy: A Case Report of Incomplete Type of Pentalogy of Cantrell

Ectopia Cordis (EC) is a rare congenital malformation in which the heart is located partially or totally outside the thoracic cavity. It results from the failure of migration of the lateral mesoderm into the midline. The four main ectopic positions are cervical, thoracic, thoracoabdominal and abdominal. EC can manifest as an isolated deformity or as part of a broader group of ventral body wall defects affecting the abdomen, thorax, or both. Pentalogy of Cantrell is a well known association that comprises EC, omphalocele (typically supraumbilical), congenital diaphragmatic hernia, sternal cleft and congenital heart disease. A 27-year-old primigravida came for a routine antenatal ultrasound at 13 weeks of gestation. There was no family history of congenital anomalies, genetic abnormalities, or exposure to teratogenic agents. The ultrasound showed a single foetus corresponding to 13 weeks of gestation with an anterior thoracic defect and an extrathoracic heart, along with partial herniation of the liver near the midline in the epigastric region. These findings were confirmed by foetal Magnetic Resonance Imaging (MRI). An unfavourable prognosis for the foetus was explained to the parents, and medical termination of pregnancy was performed. Therefore, prenatal ultrasonographic diagnosis of EC should be followed by a thorough search for associated defects, as the prognosis may vary.

ЭКСПЕРТИЗА КАЧЕСТВА ОНКОЛОГИЧЕСКОЙ ПОМОЩИ КАК ИНСТРУМЕНТ ПРИНЯТИЯ УПРАВЛЕНЧЕСКИХ РЕШЕНИЙ

Significance. Objective data, including results of quality assessment and expertise carried out by health insurance organizations as part of monitoring over volumes, service periods, quality and conditions of medical care delivery within the compulsory health insurance system are needed to make management decisions on organizing appropriate quality care delivery at the regional and institutional levels. The subject of study: quality of medical care provided to patients with cancer. The purpose of the study: to evaluate results of medical and economic expertise and quality assessment of cancer care, carried out by health insurance organizations in the Arkhangelsk region in 2018 –first half of 2023 (25,012 expert opinions). Material and methods. The study used depersonalized results of medical-economic expertise and quality assessment of medical care (25,012 expert opinions). Methods: retrospective analysis, statistical (calculation of extensive and intensive coefficients and their comparison), analytical method. Results. In general, the frequency of cancer care defects during the period under study equaled to 29.1 per 100 assessed cases. The leading group of defects included a failure, untimely or improper implementation of diagnostic and (or) treatment activities necessary for the patient (49.3%). The study has identified significant differences in the frequency and structure of the identified defects of medical care under different conditions of its provision, in medical organizations of different levels and in different nosological groups. Conclusion. The study shows a decline in the total number of defects in cancer care delivery with the same frequency of medical-economic expertise and quality assessment in the Arkhangelsk region in 2018 - first half of 2023. To identify causes of the leading groups of defects in the provision of medical care according to code 3.2. (failure, untimely or improper implementation of diagnostic and (or) treatment activities necessary for the patient), it is necessary to conduct a sociological survey (questionnaire) of doctors involved in cancer care delivery. Scope of application: management decision-making aimed to improving access to and quality of cancer care at the regional and institutional levels.