Linear matrix inequalities

The purpose of the paper is a popularisation of linear matrix inequalities

UPOREDNOPRAVNI PRIKAZ BRAKA U ŠERIJATSKOM PRAVU I POZITIVNOM PRAVU REPUBLIKE SRBIJE

Comparative legal analysis of natural and positive law has provoked various disagreements and discussions on the topic from the earliest periods of history. Proponents of natural law believed that such a comparison could not be made because natural law is true, irreplaceable and comes from God, while positive law has been regulated by man, following the example of all other rights that exist on earth. Positive law defines marriage as a community of life governed by legal norms, which is an expression of the undoubted interest of society to make marriage a legal institution, and the Qur’an, as a main source of Sharia law, categorizes the institution of marriage on a very precise system based on the strongest and safest principles that guarantee happiness to spouses, peace and morality to communities and society. The aim of the research is to present the understandings of natural-legal and positive-legal theory of law through a comparative analysis of the institute of marriage in Sharia law and law of the Republic of Serbia where the focus on this and similar issues should not be the “compatibility” of Sharia with “universal human rights norms” or vice versa, the focus should be on explanation and approaching of norms in order to make it easier to overcome, understand and accept differences.Uporednopravna analiza prirodnog i pozitivnog prava je od najranijih vremena izazivala različita neslaganja i diskusije na temu. Zagovornici prirodnog prava su smatrali da se ne može vršiti ovakvo poređenje jer je prirodno pravo istinsko, nezamjenljivo i dolazi od boga, dok je pozitivno pravo uredio i uređuje čovjek, po uzoru na sva ostala prava koja postoje na zemlji. Pozitivno pravo definiše brak kao zajednicu života koja se uređuje pravnim normama, što je izraz nesumnjivog interesa društvene zajednice da brak bude pravni institut, isto tako Kur’an kao glavni izvor šerijatskog prava kategorizuje instituciju braka na vrlo preciznom sistemu koji počiva na najčvršćim i najsigurnijim načelima koja garantuju sreću supružnicima, a mir i moral zajednici i društvu. Cilj ovog rada je predstavljanje osnovnih shvatanja prirodnopravne i pozitivnopravne teorije prava kroz uporednu analizu instituta braka u šerijatskom pravu i pravu Republike Srbije gde fokus istraživanja neće biti na kompatibilnosti šerijatskog prava sa univerzalnim normama ljudskih prava, ili suprotno, već će fokus biti na pojašnjenjima ovih normi u cilju lakšeg razumevanja i prihvatanja različitih učenja i shvatanja

The arithmetic-geometric-harmonic-mean and related matrix inequalities

AbstractRecently, Sagae and Tanabe defined a geometric mean of positive definite matrices and proved the harmonic-geometric-arithmetic-mean inequality. Here, we give a reversal of these results

On the geometric-arithmetic mean inequality for matrices

In this paper refinements and converses of matrix forms of the geometric-arithmetic mean inequality are given

Diferencijacija stanica u primarnoj kulturi neurona iz dva soja transgeničnih miševa

Matične stanice mogu se diferencirati u različite vrste stanica i nailaze na široku eksperimentalnu primjenu. Iz tog su razloga istraživanja matičnih stanica u posljednjih petnaestak godina u velikom porastu. Cilj je ovog istraživanja usporedba diferencijacije neurona podrijetlom iz dvaju različitih transgeničnih sojeva miša u svrhu prikaza njihovih osobitosti za daljnju primjenu u istraživanjima matičnih stanica. U ovom je radu uzgojena primarna kultura neurona iz dvaju mišjih sojeva, ubikvitarnog GFP-LUC i Thy1-YFP. Uzgojeni neuroni analizirani su 7. i 14. dan, opisan je uzorak izražaja bjelančevina te su međusobno uspoređeni neuroni podrijetlom iz dvaju navedenih mišjih sojeva. Stanice mišjega soja GFP-LUC tijekom 7. dana diferencirale su se u potpunosti u zrele neurone i astrocite. U 100 % stanica pozitivan je GFP. U ovoj su skupini stanica biljezi neurona (MAP2, ß3-tubulin i NeuN) pozitivni u 90 % diferenciranih stanica, a biljeg astrocita (GFAP) samo u 10 % stanica. Tijekom 14. dana stanice su razvijenije, na što upućuju deblji nastavci koji su prisutni u većem broju. Biljezi neurona pozitivni su u 80 % diferenciranih stanica, a biljeg astrocita pozitivan je u 20 % stanica. Stanice mišjega soja Thy1-YFP tijekom 7. dana također su se diferencirale u zrele neu- rone i astrocite, međutim samo je 20 % neurona YFP-pozitivno. Kao i u GFP-LUC mišjeg soja, 7. dan diferencijacije prisutno je 90 % neurona i 10 % astrocita, a 14. dan 80 % neurona i 20 % astrocita

The teaching practices with GIS in Hyogo Prefecture, Japan

This study aims to quantify the heterogeneity of tumour enhancement in dynamic contrast-enhanced MRI (DCE-MRI) using texture analysis methods. The suitability of the coherence and the fractal dimension to monitor tumour response was evaluated in 18 patients with limb sarcomas imaged by DCE-MRI pre- and post-treatment. According to the histopathology, tumours were classified into responders and non-responders. Pharmacokinetic (K(trans)) and heuristic model-based parametric maps (slope, max enhancement, AUC) were computed from the DCE-MRI data. A substantial correlation was found between the pharmacokinetic and heuristic model-based parametric maps: ρ = 0.56 for the slope, ρ = 0.44 for maximum enhancement, and ρ = 0.61 for AUC. From all four parametric maps, the enhancing fraction, and the heterogeneity features (i.e. coherence and fractal dimension) were determined. In terms of monitoring tumour response, using both pre- and post-treatment DCE-MRI, the enhancing fraction and the coherence showed significant differences between the response group and the non-response group (i.e. the highest sensitivity (91%) for K(trans), and the highest specificity (83%) for max enhancement). In terms of treatment prediction, using solely the pre-treatment DCE-MRI, the enhancing fraction and coherence discriminated between responders and non-responders. For prediction, the highest sensitivity (91%) was shared by K(trans), slope and max enhancement, and the highest specificity (71%) was achieved by K(trans). On average, tumours that responded showed a high enhancing fraction and high coherence on the pre-treatment scan. These results suggest that specific heterogeneity features, computed from both pharmacokinetic and heuristic model-based parametric maps, show potential as a biomarker for monitoring tumour response

Patient-specific Alzheimer-like pathology in trisomy 21 cerebral organoids reveals BACE2 as a gene dose-sensitive AD suppressor in human brain

A population of >6 million people worldwide at high risk of Alzheimer’s disease (AD) are those with Down Syndrome (DS, caused by trisomy 21 (T21)), 70% of whom develop dementia during lifetime, caused by an extra copy of β-amyloid-(Aβ)-precursor-protein gene. We report AD-like pathology in cerebral organoids grown in vitro from non-invasively sampled strands of hair from 71% of DS donors. The pathology consisted of extracellular diffuse and fibrillar Aβ deposits, hyperphosphorylated/pathologically conformed Tau, and premature neuronal loss. Presence/absence of AD-like pathology was donor-specific (reproducible between individual organoids/iPSC lines/experiments). Pathology could be triggered in pathology-negative T21 organoids by CRISPR/Cas9-mediated elimination of the third copy of chromosome-21-gene BACE2, but prevented by combined chemical β and γ-secretase inhibition. We found that T21-organoids secrete increased proportions of Aβ-preventing (Aβ1-19) and Aβ-degradation products (Aβ1-20 and Aβ1-34). We show these profiles mirror in cerebrospinal fluid of people with DS. We demonstrate that this protective mechanism is mediated by BACE2-trisomy and cross-inhibited by clinically trialled BACE1-inhibitors. Combined, our data prove the physiological role of BACE2 as a dose-sensitive AD-suppressor gene, potentially explaining the dementia delay in ~30% of people with DS. We also show that DS cerebral organoids could be explored as pre-morbid AD-risk population detector and a system for hypothesis-free drug screens as well as identification of natural suppressor genes for neurodegenerative diseases

Linear matrix inequalities

The purpose of the paper is a popularisation of linear matrix inequalities