κ\kappa-Deformations and Extended κ\kappa-Minkowski Spacetimes

We extend our previous study of Hopf-algebraic $\kappa$-deformations of all inhomogeneous orthogonal Lie algebras ${\rm iso}(g)$ as written in a tensorial and unified form. Such deformations are determined by a vector $\tau$ which for Lorentzian signature can be taken time-, light- or space-like. We focus on some mathematical aspects related to this subject. Firstly, we describe real forms with connection to the metric's signatures and their compatibility with the reality condition for the corresponding $\kappa$-Minkowski (Hopf) module algebras. Secondly, $h$-adic vs $q$-analog (polynomial) versions of deformed algebras including specialization of the formal deformation parameter $\kappa$ to some numerical value are considered. In the latter the general covariance is lost and one deals with an orthogonal decomposition. The last topic treated in this paper concerns twisted extensions of $\kappa$-deformations as well as the description of resulting noncommutative spacetime algebras in terms of solvable Lie algebras. We found that if the type of the algebra does not depend on deformation parameters then specialization is possible.Comment: new extended version with new material added and with title change

κ\kappa-Minkowski Spacetimes and DSR Algebras: Fresh Look and Old Problems

Some classes of Deformed Special Relativity (DSR) theories are reconsidered within the Hopf algebraic formulation. For this purpose we shall explore a minimal framework of deformed Weyl-Heisenberg algebras provided by a smash product construction of DSR algebra. It is proved that this DSR algebra, which uniquely unifies $\kappa$-Minkowski spacetime coordinates with Poincar\'e generators, can be obtained by nonlinear change of generators from undeformed one. Its various realizations in terms of the standard (undeformed) Weyl-Heisenberg algebra opens the way for quantum mechanical interpretation of DSR theories in terms of relativistic (St\"uckelberg version) Quantum Mechanics. On this basis we review some recent results concerning twist realization of $\kappa$-Minkowski spacetime described as a quantum covariant algebra determining a deformation quantization of the corresponding linear Poisson structure. Formal and conceptual issues concerning quantum $\kappa$-Poincar\'e and $\kappa$-Minkowski algebras as well as DSR theories are discussed. Particularly, the so-called "$q$-analog" version of DSR algebra is introduced. Is deformed special relativity quantization of doubly special relativity remains an open question. Finally, possible physical applications of DSR algebra to description of some aspects of Planck scale physics are shortly recalled

Dispersion Relations in κ\kappa-Noncommutative Cosmology

We study noncommutative deformations of the wave equation in curved backgrounds and discuss the modification of the dispersion relations due to noncommutativity combined with curvature of spacetime. Our noncommutative differential geometry approach is based on Drinfeld twist deformation, and can be implemented for any twist and any curved background. We discuss in detail the Jordanian twist $-$giving $\kappa$-Minkowski spacetime in flat space$-$ in the presence of a Friedman-Lema\^{i}tre-Robertson-Walker (FLRW) cosmological background. We obtain a new expression for the variation of the speed of light, depending linearly on the ratio $E_{ph}/E_{LV}$ (photon energy / Lorentz violation scale), but also linearly on the cosmological time, the Hubble parameter and inversely proportional to the scale factor.Comment: 20 pages. New version: 23 pages, added 4-dim. dispersion relations and numerical estimate

Bicrossproduct construction versus Weyl-Heisenberg algebra

We are focused on detailed analysis of the Weyl-Heisenberg algebra in the framework of bicrossproduct construction. We argue that however it is not possible to introduce full bialgebra structure in this case, it is possible to introduce non-counital bialgebra counterpart of this construction. Some remarks concerning bicrossproduct basis for kappa-Poincare Hopf algebra are also presented.Comment: 11 pages, contribution to the proceedings of the 7th International Conference on Quantum Theory and Symmetries (QTS7), 7-13 August 2011, Prague, Czech Republi

Metabolic syndrome in a teenager as a clinical picture of R482W LMNA mutation

Metabolic Syndrome (MS) can be diagnosed from the age of 10 years, when the coexistence of abdominal obesity, glucose metabolism disorders, dyslipidemia, and hypertension is observed. A binding part of MS is insulin resistance. Severe insulin resistance may be caused by a mutation in lamin (LMNA) gene. A teenager with MS due to mutation in LMNA gene is presented. A 17.5-yr-old Caucasian girl was admitted to the hospital with the suspicion of diabetes mellitus due to causal blood glucose 393 mg/dl (21.8 mmol/l), without typical diabetic symptoms. Since the age of 13 years she had been presented with excessive weight gain, hirsutism, and oligomenorrhoea. Her family history was positive for diabetes and partial lipodystrophy in three generations. Physical examination revealed abdominal obesity (waist-circumference 86 cm, BMI 27 kg/m2), android/cushingoidal habitus, acanthosis nigricans in axillae and neck, hirsutism, enlarged liver, and pseudohypertrophy of muscles of limbs with partial lipodystrophy. Based on oral glucose tolerance test diabetes was diagnosed (HOMA-IR 14). HbA1c was 9.2% (78 mmol/mol). Diabetes autoantibodies were negative. Lab tests revealed also dyslipidemia (total cholesterol 6.42 mmol/l, triglicerydes 7.42 mmol/l, HDL cholesterol 0.73 mmol/l) and elevated liver enzymes. Ultrasonography revealed steatosis hepatis and polycystic ovaries. Genetic tests confirmed that she is a carrier of heterozygous missense mutation (c.1444C>T; R482W) in the LMNA gene. Lifestyle changes, metformin dosage 500 mg three times a day and ursodeoxycholic acid were introduced as her therapy. After 4 months of this treatment HbA1c levels dropped 5.8% (40 mmol/mol). Moreover an improvement of lipid profile, liver tests and 2 kg body weight loss were observed. Diabetes mellitus as a component of MS in a young obese patient should be diagnosed individually. When other nontypical for diabetes mellitus clinical signs and symptoms exist with positive, multigenerational family history, genetic causes of MS should be taken into consideration

Atypowe cechy fenotypowe u nosicieli nowej mutacji nonsens Q248X w genie HNF1B

Introduction: Hepatocyte transforming factor 1B-maturity onset diabetes mellitus of the young (HNF1B-MODY) is an autosomal dominant type of monogenic diabetes caused by a mutation in the gene encoding hepatocyte nuclear factor 1beta (HNF-1beta). The aim of this study was to determine if a HNF1B gene mutation was responsible for a dominantly inherited form of diabetes mellitus among the members of a three-generation Polish family. Material and methods: The index subject was a 13-year-old boy with metabolic syndrome, spina bifida occulta, posterior urethral valves, congenital ureteropelvic junction obstruction, and a family history of diabetes of autosomal dominant trait of inheritance. We performed clinical and laboratory examinations of his family and sequenced the HNF1B gene. Results: A novel Q248X mutation (nucleotide C to T transition at position 742 of the exon 3 of HNF1B gene, resulting in stop codon formation) was identified. Phenotypes of family members sharing this mutation are highly variable, and include previously known abnormalities of the urinary system and pancreas, diabetes mellitus of variable onset and severity, hyperinsulinaemia, insulin resistance, metabolic syndrome, elevated aminotransferases, hyperbilirubinemia, hyperamylasemia, short stature and cataracts. To the best of our knowledge, spina bifida occulta, pectus carinatum, and splenomegaly have not been previously reported. Conclusions: Our results broaden the spectrum of HNF1B gene mutations and HNF1B-MODY-related phenotypes. Wstęp: Cukrzyca HNF1B-MODY dziedziczona w sposób autosomalnie dominujący jest rodzajem cukrzycy monogenowej, którą powoduje mutacja w genie HNF1B (hepatocyte transforming factor 1B). Celem pracy było zbadanie czy mutacja w HNF1B jest przyczyną występowania cukrzycy w trzech pokoleniach polskiej rodziny. Materiał i metody: Przeprowadzono ocenę kliniczną i laboratoryjną oraz sekwencjonowanie genu HNF1B trzynastoletniego chłopca z zespołem metabolicznym, rozszczepem kręgosłupa, zastawkami cewki tylnej i wrodzonym zwężeniem moczowodu oraz obciążonym wywiadem rodzinnym w kierunku cukrzycy. Ze względu na wywiad rodzinny o autosomalnie dominującym sposobie dziedziczenia cukrzycy zbadano również członków jego rodziny. Wyniki: Stwierdzono obecność nowej mutacji Q248X będącej skutkiem przeniesienia nukleotydu C na miejsce T w pozycji 742 eksonu 3 genu HNF1B i powstaniem kodonu stop. Cechy fenotypowe członków rodziny będących nosicielami tej mutacji okazały być się bardzo zróżnicowane, a niektóre z nich takie jak spina bifida occulta, pectus carinatum i splenomegalia nie były dotychczas opisywane. Wnioski: Wyniki poszerzają spectrum mutacji genu HNF1B oraz związanych z nimi cech fenotypowych cukrzycy HNF1B-MODY

Tumour necrosis factor-alpha polymorphism as one of the complex inherited factors in pemphigus.

The aim of our study was to analyse a significance of tumour necrosis factor (TNF)-alpha promoter gene polymorphisms in relation to the HLA-DR locus in genetic predisposition to pemphigus. TNF-alpha gene polymorphisms in position -238 and -308 were identified using a modified polymerase chain reaction-restriction fragment length polymorphism method in 53 patients with pemphigus (38 with pemphigus vulgaris, 15 with pemphigus foliaceus) and 87 healthy controls. The HLA-DRB1 locus was typed using the polymerase chain reaction SSO method in all the patients and 152 population controls. Carriers of the TNF-alpha polymorphic -308 A allele were found to be more frequent in the pemphigus foliaceus group in comparison with the control group (odds ratio (OR) = 8.12; p = 0.0005). A significant association between HLA-DRB1*04 (OR = 3.86; pcor = 0.0001) and DRB1*14 (OR = 8.4; pcor = 0.0001) and pemphigus vulgaris was found. In this group of patients a decreased frequency of HLA-DRB1*07 (OR = 0.08; pcor = 0.006) was also identified. We have shown for the first time a positive association of TNF-alpha polymorphism in position -308 with pemphigus foliaceus