Coinvariant algebras and fake degrees for spin Weyl groups of classical type

The coinvariant algebra of a Weyl group plays a fundamental role in several areas of mathematics. The fake degrees are the graded multiplicities of the irreducible modules of a Weyl group in its coinvariant algebra, and they were computed by Steinberg, Lusztig and Beynon-Lusztig. In this paper we formulate a notion of spin coinvariant algebra for every Weyl group. Then we compute all the spin fake degrees for each classical Weyl group, which are by definition the graded multiplicities of the simple modules of a spin Weyl group in the spin coinvariant algebra. The spin fake degrees for the exceptional Weyl groups are given in a sequel.Comment: v2, 39 pages, title modified (with "of classical type" added), the original version was split into two parts following editor's suggestion; this v2 is the part one (to appear in Math. Proc. Cambridge Philos. Soc.), with a sequel dealing with the exceptional typ

Nucleases isolated from Chelidonium majus L. milky sap can induce apoptosis in human cervical carcinoma HeLa cells but not in Chinese Hamster Ovary CHO cells.

Milky sap isolated from Chelidonium majus L. (Greater Celandine) serves as a rich source of various biologically active substances such as alkaloids, flavonoids and phenolic acids. Previous research showed that the activity of Ch. majus milky sap may depend also on the presence of biologically active proteins. The goal of this study was to evaluate the biological effect of two nucleases isolated from Ch. majus milk sap, CMN1 of 20 kDa and CMN2 of 36 kDa, on HeLa and CHO tumour cell lines. Both studied nucleases together with other proteins in the sap of the plant are involved in stress and defence reactions against different pathogens. After 48 h incubation of CMN1 and CMN2 only with HeLa cells, the dependence between the number of apoptotic lesions and the concentration of applied nuclease was observed. The highest proapoptotic activity was induced by 13.3 ng/ml concentration of CMN2 collected in May (62 +/- 3% HeLa cells were apoptotic). Moreover, the proportion of necrotic cells in all concentrations of the nucleases and both cell lines was relatively low (1-8 +/- 0.5%). In summary, results of this study show that purified nucleases CMN1 and CMN2 isolated from Ch. majus milky sap exhibit apoptotic activity in HeLa tumour cell line, but not in CHO cells, without inflammatory reaction

The peak algebra and the Hecke-Clifford algebras at q=0q=0

Using the formalism of noncommutative symmetric functions, we derive the basic theory of the peak algebra of symmetric groups and of its graded Hopf dual. Our main result is to provide a representation theoretical interpretation of the peak algebra and its graded dual as Grothendieck rings of the tower of Hecke-Clifford algebras at $q=0$.Comment: Final version, 17 pages, LaTex, 1 PDF figure, graphic

Parafermionic algebras, their modules and cohomologies

We explore the Fock spaces of the parafermionic algebra introduced by H.S. Green. Each parafermionic Fock space allows for a free minimal resolution by graded modules of the graded 2-step nilpotent subalgebra of the parafermionic creation operators. Such a free resolution is constructed with the help of a classical Kostant's theorem computing Lie algebra cohomologies of the nilpotent subalgebra with values in the parafermionic Fock space. The Euler-Poincar\'e characteristics of the parafermionic Fock space free resolution yields some interesting identities between Schur polynomials. Finally we briefly comment on parabosonic and general parastatistics Fock spaces.Comment: 10 pages, talk presented at the International Workshop "Lie theory and its applications in Physics" (17-23 June 2013, Varna, Bulgaria

FDA Approves Omaveloxolone based on Successful Moxie Trial Results for Friedreich's Ataxia - Review

Introduction: In recent years, the medical community has witnessed a significant breakthrough in the treatment of Friedreich's Ataxia (FRDA), a rare and debilitating genetic disorder affecting the nervous system. This neurological condition, characterized by progressive muscle weakness, impaired coordination, and cardiomyopathy, has long posed challenges for both patients and healthcare professionals alike. However, there is newfound hope with the recent approval of Omaveloxolone by the U.S. Food and Drug Administration (FDA).Aim of the study: This review article aims to present a detailed summary of the FDA's approval of Omaveloxolone as a therapeutic option for Friedreich's Ataxia (FRDA), focusing on the positive results obtained from the MOXIe trial. It covers various aspects of FRDA and explains how Omaveloxolone works as an activator of NRF2, a transcription factor that helps reduce oxidative stress. The MOXIe trial, which examined the safety and effectiveness of Omaveloxolone in FRDA patients, is discussed in detail, including its methodology, primary and secondary goals, and results. Materials and methods: This review was based on available data collected in the PubMed and Google Scholar database, using the key words: FRDA, Friedreich’s Ataxia, Omaveloxolone, RTA 408, NRF2, MOXIe trail.Conclusion: Omaveloxolone has shown significant efficacy in improving neurological function and mFARS scores compared to a placebo in the MOXIe trial. It is well-tolerated with minimal adverse events. Early intervention with Omaveloxolone offers enhanced benefits for managing Friedreich's ataxia progression

The KRASG12C inhibitors in lung cancer therapy

Introduction: Lung cancer is characterized by the highest mortality among cancers and is the second most frequently diagnosed type of cancer in the world. Targeted therapies are a promising therapeutic option for patients with this disease, however, one of the most common and most malignant mutations (KRAS) remains a challenge. Purpose: The aim of this study is to bring closer the problem of the KRAS mutation, in particular KRASG12C, and to present the most important information about the compounds created for therapies targeted at it.For a better understanding of the issue, the study contains information about the mechanisms of both mutation and drugs, as well as the most important statistical data and research results. Materials and methods: The review was based on articles available in the PubMed database. Conclusions: Two drugs targeting KRASG12C (sotorasib and adagrasib) have proven their clinical effectiveness and represent a milestone in the development of targeted therapies for lung cancer with this mutation. However, they are not without side effects, and the emerging resistance and presence of commutations that reduce drug potency continue to challenge the scientific community. Research is underway to refine therapies using existing inhibitors as well as to develop further compounds targeting KRASG12C

Pruritus. Pathomechanism, management and novel treatment

Introduction Itching is an unpleasant sensation that is commonly experienced in the general population. It accompanies many diseases. This sensory experience is burdensome and significantly reduces the quality of life. The mechanism of itching is complex. It involves receptors, the histaminergic and non-histaminergic pathways, cytokines, neuropeptides, neurotransmitters, proteases, and enzymes. External factors such as temperature or capsaicin also influence itching. Aim of the study This review presents the current state of knowledge regarding therapy in the treatment of itching. Also aims to show that it is a complicated process. Pruritus is a very bothersome sensory sensation and is a common symptom.  Material and methods This review was based on scientific books on human physiology and dermatology were used, which are listed in the bibliography and available data collected in the PubMed and Google Scholar database. Using key words:  itch, management, pathogenesis, pathophysiology, pruritus, therapeutics, treatments. Conclusion The latest research on itching has led to a better understanding of this complex mechanism. As a result, there is a possibility of discovering new, innovative treatment methods that are targeted at specific elements of this process or work systemically. Understanding the broad etiology assists in identifying the cause and in implementing an appropriate therapeutic strategy. Further research will enable improvements in treatment and enhance patient comfort