Galoisove reprezentacije pridružene eliptičkim krivuljama

U prvom poglavlju definirali smo pojam endomorfizma na eliptičkoj krivulji $C$ i dokazali osnovna svojstva. Uveli smo pojam izogenije te pokazali kako se svojstva endomorfizama lako proširuju na izogenije. Spomenuli smo Frobeniusov endomorfizam i dali nekoliko primjera izogenija. U drugom poglavlju definirali smo pojam visine te iskazali neka njezina bitna svojstva. Iskazali smo teorem spusta te iskazali Mordellov teorem. U trećem poglavlju razvili smo osnove teorije djelidbenih polinoma te pokazali da je $C[n] \simeq \mathbb{Z}/n \mathbb{Z} \bigoplus \mathbb{Z}/n \mathbb{Z}$. Četvrto poglavlje je glavni dio ovog rada. Definirali smo djelovanje elemenata Galoisove grupe $Gal(K/\mathbb{Q})$ na točke iz $C$ te pokazali osnovne rezultate koji slijede iz djelovanja. Pokazali smo da su koordinate točaka konačnog reda algebarske nad $\mathbb{Q}$ te da je proširenje od $\mathbb{Q}$ inducirano $x$ i $y$ koordinatama točaka nekog fiksnog reda $n$ Galoisovo. Definirali smo mod $n$ Galoisovu reprezentaciju pridruženu krivulji $C$ i pokazali da je to preslikavanje monomorfizam. Definirali smo Borelovu i Cartanovu podgrupu od $GL(\mathbb{F}_p)$ i pokazali osnovna svojstva. Odredili smo u kojim se maksimalnim podgrupama od $GL(\mathbb{F}_p)$ može nalaziti slika nesurjektivne mod $p$ Galoisove reprezentacije. Definirali smo Weilovo sparivanje i pokazali u teoremu 4.15. kakva svojstva mora imati slika mod $p$ Galoisove reprezentacije.In the first chapter we defined endomorphisms of the elliptic curve $C$ and proved their basic properties. We introduced isogenies and showed how properties of endomorphisms hold for isogenies. We mentioned the Frobenius endomorphism and give a few examples of isogenies. In the second chapter we defined the height function and showed some important properties. We also introduced the Descent theorem and stated Mordell's theorem. In the third chapter we developed basic division polynomials theory and we showed that $C[n] \simeq \mathbb{Z}/n \mathbb{Z} \bigoplus \mathbb{Z}/n \mathbb{Z}$. The fourth chapter is the main part of this work. We defined the action of the Galois group $Gal(K/\mathbb{Q})$ on points on $C$ and showed basic properties. We showed that coordinates of points of finite order are algebraic over $\mathbb{Q}$ and that the field extension induced by the $x$ and $y$ coordinates of points that are of finite order $n$ is Galois. We defined the mod $n$ Galois representation attached to the curve $C$ and showed that it is a monomorphism. We defined the Borel and Cartan subgroup of $GL(\mathbb{F}_p)$ and showed some basic properties. We determined in which maximal subgroups of $GL(\mathbb{F}_p)$ can the image of non-surjective mod $p$ Galois representation be. We defined the Weil pairing and showed in theorem 4.15 some properties of mod $p$ Galois representation

Odnos kreativnosti i školskog postignuća gluve i nagluve i dece tipičnog razvoja

Креативност представља способност особe да пронађe нова решења, да сагледа проблеме из новог угла, да створи нове идеје. Она подразумева и слободно изражавање ученика, њихово усавршавање и оплемењивање индивидуалности. Подстицање креативности је важан задатак родитеља, школе и друштва, а само образовање и васпитање треба да пруже различите могућости да би их креативна деца искористила на најбољи начин. Циљ овог истраживања је утврдити разлике и специфичности односа кеативности и школског постигнућа код глуве и наглуве и деце типичног развоја. На основу дефинисаног основног циља истраживања, постављени су и посебни циљеви којима је потребно утврдити разлике у креативности глуве и наглуве деце и деце типичног развоја у односу на узраст, пол, интересовање деце, општи школски успех, као и успех из предмета: српски језик, математика и ликовно васпитање, и потребно је утврдити специфичности у креативности глуве и наглуве деце у односу на аудитивни статус. Истраживањем је обухваћено 72 ученика, 32 глува и наглува ученика из Основне школе за оштећене слухом – наглуве „ Стефан Дечански“ у Београду и 40 ученика типичног развоја из Основне школе „ Краљ Александар Карађорђевић“ из Мачванског Прњавора. Узорак су чинили ученици оба пола, узраста од 7 до 14 година. За истраживање је коришћен Урбан-Јеленов тест за креативно мишљење које се мери цртањем(Test for Creative Thinking-Drawing Production - TCT-DP). Анализом података добијено је да постоје разлике у односу креативности и школског постигнућа између глуве и наглуве и деце типичног развоја у односу на узраст, успех из ликовног васпитања, успех из математике и интересовања ученика.Creativity is the ability of a person to find new solutions, to look at problems from a new angle, to create new ideas. It also involves the free expression of students, their improvement and the improvement of individuality. Encouraging creativity is an important task for parents, school and society, education and education alone should provide different opportunities for them to use them creatively in the best way possible. The aim of the research is to determine the differences and specifics of the raltionships between creativity and school achievement for deaf and hard of hearing and children of typical development. Based on the defined primary goal of the research, special goals have been set to determine the differences in the creativity of deaf and hard of hearing children and children of typical development in relation to age, gender, interests of children, general school success and the success in the subjects like : serbian language, mathematics and art education, and it is necessary to determine the specifics in the creativity of deaf and hard of hearing children in relation to the auditory status. The study included 72 students, 32 deaf and hard of hearing students from the Elementary School for deaf children „Stefan Dečanski“ in Belgrade and 40 students of typical development from Elementary School „Kralj Aleksandar Karađorđević“ from Mačvanski Prnjavor. The sample was made by students of both gender, ages 7 to 14. For the research Test for Creativity Thinking- Drawing Production (TCT-DP) have been used for data gathering. Data analysis has revealed that there are diffrences in the relation between creativity and school achievement between deaf and hard of hearing children and children of typical development in relation to age, success in art education, success in mathematics and students interests

Galoisove reprezentacije pridružene eliptičkim krivuljama

U prvom poglavlju definirali smo pojam endomorfizma na eliptičkoj krivulji $C$ i dokazali osnovna svojstva. Uveli smo pojam izogenije te pokazali kako se svojstva endomorfizama lako proširuju na izogenije. Spomenuli smo Frobeniusov endomorfizam i dali nekoliko primjera izogenija. U drugom poglavlju definirali smo pojam visine te iskazali neka njezina bitna svojstva. Iskazali smo teorem spusta te iskazali Mordellov teorem. U trećem poglavlju razvili smo osnove teorije djelidbenih polinoma te pokazali da je $C[n] \simeq \mathbb{Z}/n \mathbb{Z} \bigoplus \mathbb{Z}/n \mathbb{Z}$. Četvrto poglavlje je glavni dio ovog rada. Definirali smo djelovanje elemenata Galoisove grupe $Gal(K/\mathbb{Q})$ na točke iz $C$ te pokazali osnovne rezultate koji slijede iz djelovanja. Pokazali smo da su koordinate točaka konačnog reda algebarske nad $\mathbb{Q}$ te da je proširenje od $\mathbb{Q}$ inducirano $x$ i $y$ koordinatama točaka nekog fiksnog reda $n$ Galoisovo. Definirali smo mod $n$ Galoisovu reprezentaciju pridruženu krivulji $C$ i pokazali da je to preslikavanje monomorfizam. Definirali smo Borelovu i Cartanovu podgrupu od $GL(\mathbb{F}_p)$ i pokazali osnovna svojstva. Odredili smo u kojim se maksimalnim podgrupama od $GL(\mathbb{F}_p)$ može nalaziti slika nesurjektivne mod $p$ Galoisove reprezentacije. Definirali smo Weilovo sparivanje i pokazali u teoremu 4.15. kakva svojstva mora imati slika mod $p$ Galoisove reprezentacije.In the first chapter we defined endomorphisms of the elliptic curve $C$ and proved their basic properties. We introduced isogenies and showed how properties of endomorphisms hold for isogenies. We mentioned the Frobenius endomorphism and give a few examples of isogenies. In the second chapter we defined the height function and showed some important properties. We also introduced the Descent theorem and stated Mordell's theorem. In the third chapter we developed basic division polynomials theory and we showed that $C[n] \simeq \mathbb{Z}/n \mathbb{Z} \bigoplus \mathbb{Z}/n \mathbb{Z}$. The fourth chapter is the main part of this work. We defined the action of the Galois group $Gal(K/\mathbb{Q})$ on points on $C$ and showed basic properties. We showed that coordinates of points of finite order are algebraic over $\mathbb{Q}$ and that the field extension induced by the $x$ and $y$ coordinates of points that are of finite order $n$ is Galois. We defined the mod $n$ Galois representation attached to the curve $C$ and showed that it is a monomorphism. We defined the Borel and Cartan subgroup of $GL(\mathbb{F}_p)$ and showed some basic properties. We determined in which maximal subgroups of $GL(\mathbb{F}_p)$ can the image of non-surjective mod $p$ Galois representation be. We defined the Weil pairing and showed in theorem 4.15 some properties of mod $p$ Galois representation

Association of HLA class I and II with occurrence of uveitis in Eastern Croatia

Cilj istraživanja: Odrediti učestalost genskih varijanti lokusa HLA razreda I (HLA-A, -B) i II (HLA-DRB1, -DQB1) oboljelih od uveitisa u populaciji istočne Hrvatske i rezultate usporediti s podacima za kontrolnu zdravu populaciju Hrvatske. Ispitanici i metode: Skupina ispitanika sastojala se od 38 bolesnika (20 M, 18 Ž) s uputnom dijagnozom uveitisa kojima je molekularna tipizacija HLA učinjena u periodu od 2007. do 2017. godine metodom PCR-SSP niskog razlučivanja. Kontrolnu skupinu predstavljali su ranije objavljeni podaci molekularne tipizacije HLA zdravih nesrodnih osoba iz populacije Hrvatske. Rezultati: Povećana učestalost u skupini oboljelih u odnosu na kontrolnu skupinu nađena je za gene: HLA-A*29 (OR 1,48), -A*11 (OR 1,41), -A*32 (OR 1,39), -A*25 (OR 1,3), -A*03 (OR 1,23), -A*02 (OR 1,18), HLA-B*52 (OR 2,77), -B*50 (OR 2,75), -B*27 (2,03), -B*44 (OR 1,83), -B*57 (OR 1,50), -B*56 (OR 1,34), -B*08 (OR 1,21), HLA-DRB1*16 (OR 1,58), -DRB1*15 (OR 1,50), -DRB1*11 (OR 1,11) i HLA-DQB1*03(DQ9) (OR 3,22). Razlika u učestalosti navedenih gena HLA nije bila statistički značajna osim za HLA-B*27 (p=0,054) i -B*44 (p=0,071). Gen HLA-A*68 bio je statistički značajno učestaliji u kontrolnoj skupini (p=0,049, OR 0,14). Zaključak: Geni HLA-B*27 i HLA-B*44 u ovom su se istraživanju pokazali susceptibilni, a gen HLA-A*68 zaštitni za razvoj uveitisa u populaciji istočne Hrvatske. Dobiveni rezultati za gene HLA-A*29, HLA-B*27, HLA-B*44 i HLA-B*57 u skladu su s izvješćima istraživanja provedenih u europskim, blisko-istočnim, azijskim i američkim populacijama.Objectives: The aim of this study was to detrmine HLA class I (HLA-A, -B) and II (HLA-DRB1, -DQB1) gene frequencies in a group of patients affected with uveitis in the population of Eastern Croatia and to compare results with data from healthy population of Croatia. Participants and methods: A total of 38 patients (20 M, 18 F) were HLA typed at low resolution leel using PCR-SSP method in the period 2007-2017. The control group represents previously published data of molecular typing of HLA for healthy unrelated persons from the Croatian population. Results: Increased frequencies in tested group compared to control group were found for: HLA-A*29 (OR 1,48), -A*11 (OR 1,41), -A*32 (OR 1,39), -A*25 (OR 1,3), -A*03 (OR 1,23), -A*02 (OR 1,18), HLA-B*52 (OR 2,77), -B*50 (OR 2,75), -B*27 (2,03), -B*44 (OR 1,83), -B*57 (OR 1,50), -B*56 (OR 1,34), -B*08 (OR 1,21), HLA-DRB1*16 (OR 1,58), -DRB1*15 (OR 1,50), -DRB1*11 (OR 1,11) and HLA-DQB1*03(DQ9) (OR 3,22). The difference in the frequency of these HLA genes was not statistically significant except for HLA-B*27 (p=0,054) and -B*44 (p=0,071). HLA-A*68 was more frequent in the control group (p=0,049, OR 0,14). Conclusion: In this study the HLA-B*27 and HLA-B*44 were positively associated with uveitis unlike the HLA-B*68 which was protective for development of uveitis in population of Eastern Croatia. The results obtained for HLA-A*29, HLA-B*27, HLA-B*44 and HLA-B*57 are in concordance with research eports conducted in European, Middle East, Asian and American populations

Stromal upregulation of lateral epithelial adhesions: Gene expression analysis of signalling pathways in prostate epithelium

BACKGROUND: Stromal signalling increases the lateral cell adhesions of prostate epithelial cells grown in 3D culture. The aim of this study was to use microarray analysis to identify significant epithelial signalling pathways and genes in this process. METHODS: Microarray analysis was used to identify genes that were differentially expressed when epithelial cells were grown in 3D Matrigel culture with stromal co-culture compared to without stroma. Two culture models were employed: primary epithelial cells (ten samples) and an epithelial cell line (three experiments). A separate microarray analysis was performed on each model system and then compared to identify tissue-relevant genes in a cell line model. RESULTS: TGF beta signalling was significantly ranked for both model systems and in both models the TGF beta signalling gene SOX4 was significantly down regulated. Analysis of all differentially expressed genes to identify genes that were common to both models found several morphology related gene clusters; actin binding (DIAPH2, FHOD3, ABLIM1, TMOD4, MYH10), GTPase activator activity (BCR, MYH10), cytoskeleton (MAP2, MYH10, TMOD4, FHOD3), protein binding (ITGA6, CD44), proteinaceous extracellular matrix (NID2, CILP2), ion channel/ ion transporter activity (CACNA1C, CACNB2, KCNH2, SLC8A1, SLC39A9) and genes associated with developmental pathways (POFUT1, FZD2, HOXA5, IRX2, FGF11, SOX4, SMARCC1). CONCLUSIONS: In 3D prostate cultures, stromal cells increase lateral epithelial cell adhesions. We show that this morphological effect is associated with gene expression changes to TGF beta signalling, cytoskeleton and anion activity

Mice produced by mitotic reprogramming of sperm injected into haploid parthenogenotes

Sperm are highly differentiated and the activities that reprogram them for embryonic development during fertilization have historically been considered unique to the oocyte. We here challenge this view and demonstrate that mouse embryos in the mitotic cell cycle can also directly reprogram sperm for full-term development. Developmentally incompetent haploid embryos (parthenogenotes) injected with sperm developed to produce healthy offspring at up to 24% of control rates, depending when in the embryonic cell cycle injection took place. This implies that most of the first embryonic cell cycle can be bypassed in sperm genome reprogramming for full development. Remodelling of histones and genomic 5′-methylcytosine and 5′-hydroxymethylcytosine following embryo injection were distinct from remodelling in fertilization and the resulting 2-cell embryos consistently possessed abnormal transcriptomes. These studies demonstrate plasticity in the reprogramming of terminally differentiated sperm nuclei and suggest that different epigenetic pathways or kinetics can establish totipotency

Body Composition of Patients Undergoing Radical Cystectomy for Bladder Cancer: Sarcopenia, Low Psoas Muscle Index, and Myosteatosis Are Independent Risk Factors for Mortality

Abstract: Background: We assessed a wide array of body composition parameters to identify those most relevant as prognostic tools for patients undergoing radical cystectomy (RC) due to bladder cancer (BC). Methods: In this retrospective, single-center study, preoperative computed tomography (CT) scans of 657 patients were measured at the level of the 3rd lumbar vertebra (L3) to determine common body composition indices including sarcopenia, myosteatosis, psoas muscle index (PMI), subcutaneous and visceral fat index (SFI and VFI), visceral-to-subcutaneous fat ratio (VSR), and visceral obesity. Predictors of overall survival (OS) and cancer-specific survival (CSS) were identified in univariate and multivariate survival analysis. Results: Sarcopenia and a low PMI were independently associated with shorter OS (Sarcopenia: HR 1.30; 95% CI 1.02–1.66; p = 0.04 and a low PMI: HR 1.32; 95% CI 1.02–1.70; p = 0.03) and CSS (Sarcopenia: HR 1.64; 95% CI 1.19–2.25; p < 0.01 and a low PMI: HR 1.41; 95% CI 1.02–1.96; p = 0.04). Myosteatosis, measured as decreasing average Hounsfield units of skeletal muscle, was an independent risk factor for OS (HR 0.98; 95% CI 0.97–1.00; p = 0.01) and CSS (HR 0.98; 95% CI 0.96–1.00; p < 0.05). The assessed adipose tissue indices were not significant predictors for OS and CSS. Conclusions: Sarcopenia, a low PMI, and myosteatosis are independent predictors for OS and CSS in patients undergoing radical cystectomy for bladder cancer

Body Composition as a Comorbidity-Independent Predictor of Survival following Nephroureterectomy for Urothelial Cancer of the Upper Urinary Tract

Radical nephroureterectomy (NUE) is the gold standard treatment for high-risk urothelial cancer of the upper urinary tract (UTUC). Besides sarcopenia and frailty, fat distribution is moving increasingly into focus. Components of body composition were assessed in patients undergoing NUE due to UTUC. The study cohort included 142 patients. By using CT-based measurements, the skeletal muscle index (SMI), subcutaneous adipose tissue index (SATI), and visceral adipose tissue index (VATI) were measured at the height of the third lumbar vertebra. Overall survival (OS) and cancer-specific survival (CSS) were estimated using univariable und multivariable Cox regression models. The prevalence of sarcopenia in the study population (n = 142) was 37%. OS and CSS were significantly reduced in sarcopenic patients. In the multivariable cox regression analysis, including age, ACE-27, T-stage, R-stage, LVI and necrosis, sarcopenia remained a significant risk factor of OS (HR, 1.77; 95% CI 1.02–3.07; p = 0.042) and CSS (HR, 2.17; 95% CI 1.18–3.99; p = 0.012). High visceral adipose tissue seems to be protective, although not statistically significant. Sarcopenia is a comorbidity-independent risk factor in patients who underwent NUE due to UTUC. Visceral fat represents a potentially protective factor. These results suggest that specific factors of body composition can be used for better risk stratification