Some Integrals for Molecular Properties and Relativistic Effects over Hermite-Gaussian Functions

Formulas for some integrals over Hermite-Gaussian functions occurring in the calculations of the molecular first and second order properties as well as relativistic corrections arising in the Breit hamiltonian are discussed. It is shown that all these molecular properties integrals can be reduced to the integrals already encountered in the minimum energy calculations. More specifically, the one-electron and two-electron integrals involving (l/r1 j)" operator, where j denotes either the coordinates of a nucleus or the coordinates of the electron 2 and n is an integer, are expressed in terms of nuclear attraction and Coulomb repulsion integrals, respectively. Therefore the electric and magnetic properties of molecules can be computed with little additional effort if the Hermite-Gaussian basis set is employed. The same conclusion holds for the matrix elements arising in the pseudo-potential calculations involving the Bonifacic- Huzinaga model potential which in turn give a fair description of the heavy atoms inner-shell electrons. Since the Hermite- Gaussian functions are particularly advantageous for atomic orbitals with higher angular momentum quantum numbers (f, g, h etc.) their use is expected to be preferable in molecules involving heavy atoms. The relativistic effects are of great importance for the latter and it is gratifying that the corresponding integrals over Hermite-Gaussians can be expressed in a closed form

GRB 081024B and GRB 140402A: two additional short GRBs from binary neutron star mergers

Theoretical and observational evidences have been recently gained for a two-fold classification of short bursts: 1) short gamma-ray flashes (S-GRFs), with isotropic energy $E_{iso}<10^{52}$~erg and no BH formation, and 2) the authentic short gamma-ray bursts (S-GRBs), with isotropic energy $E_{iso}>10^{52}$~erg evidencing a BH formation in the binary neutron star merging process. The signature for the BH formation consists in the on-set of the high energy ($0.1$--$100$~GeV) emission, coeval to the prompt emission, in all S-GRBs. No GeV emission is expected nor observed in the S-GRFs. In this paper we present two additional S-GRBs, GRB 081024B and GRB 140402A, following the already identified S-GRBs, i.e., GRB 090227B, GRB 090510 and GRB 140619B. We also return on the absence of the GeV emission of the S-GRB 090227B, at an angle of $71^{\rm{o}}$ from the \textit{Fermi}-LAT boresight. All the correctly identified S-GRBs correlate to the high energy emission, implying no significant presence of beaming in the GeV emission. The existence of a common power-law behavior in the GeV luminosities, following the BH formation, when measured in the source rest-frame, points to a commonality in the mass and spin of the newly-formed BH in all S-GRBs.Comment: 16 pages, submitted to ApJ, second version addressing the comments by the refere

Croatian genetic heritage: Y-chromosome story

The aim of this article is to offer a concise interpretation of the scientific data about the topic of Croatian genetic heritage that was obtained over the past 10 years. We made a short overview of previously published articles by our and other groups, based mostly on Y-chromosome results. The data demonstrate that Croatian human population, as almost any other European population, represents remarkable genetic mixture. More than 3/4 of the contemporary Croatian men are most probably the offspring of Old Europeans who came here before and after the Last Glacial Maximum. The rest of the population is the offspring of the people who were arriving in this part of Europe through the southeastern route in the last 10 000 years, mostly during the neolithization process. We believe that the latest discoveries made with the techniques for whole-genome typing using the array technology, will help us understand the structure of Croatian population in more detail, as well as the aspects of its demographic history

GRB 170817A-GW170817-AT 2017gfo and the observations of NS-NS, NS-WD and WD-WD mergers

The LIGO-Virgo Collaboration has announced the detection of GW170817 and has associated it with GRB 170817A. These signals have been followed after 11 hours by the optical and infrared emission of AT 2017gfo. The origin of this complex phenomenon has been attributed to a neutron star-neutron star (NS-NS) merger. In order to probe this association we confront our current understanding of the gravitational waves and associated electromagnetic radiation with four observed GRBs originating in binaries composed of different combinations NSs and white dwarfs (WDs). We consider 1) GRB 090510 the prototype of NS-NS merger leading to a black hole (BH); 2) GRB 130603B the prototype of a NS-NS merger leading to massive NS (MNS) with an associated kilonova; 3) GRB 060614 the prototype of a NS-WD merger leading to a MNS with an associated kilonova candidate; 4) GRB 170817A the prototype of a WD-WD merger leading to massive WD with an associated AT 2017gfo-like emission. None of these systems support the above mentioned association. The clear association between GRB 170817A and AT 2017gfo has led to introduce a new model based on on a new subfamily of GRBs originating from WD-WD mergers. We show how this novel model is in agreement with the exceptional observations in the optical, infrared, X- and gamma-rays of GRB 170817A-AT 2017gfo.Comment: version accepted for publication in JCAP. Missing references adde

BubR1 promotes Bub3-dependent APC/C inhibition during Spindle Assembly Checkpoint signaling.

The spindle assembly checkpoint (SAC) prevents premature sister chromatid separation during mitosis. Phosphorylation of unattached kinetochores by the Mps1 kinase promotes recruitment of SAC machinery that catalyzes assembly of the SAC effector mitotic checkpoint complex (MCC). The SAC protein Bub3 is a phospho-amino acid adaptor that forms structurally related stable complexes with functionally distinct paralogs named Bub1 and BubR1. A short motif ("loop") of Bub1, but not the equivalent loop of BubR1, enhances binding of Bub3 to kinetochore phospho-targets. Here, we asked whether the BubR1 loop directs Bub3 to different phospho-targets. The BubR1 loop is essential for SAC function and cannot be removed or replaced with the Bub1 loop. BubR1 loop mutants bind Bub3 and are normally incorporated in MCC in vitro but have reduced ability to inhibit the MCC target anaphase-promoting complex (APC/C), suggesting that BubR1:Bub3 recognition and inhibition of APC/C requires phosphorylation. Thus, small sequence differences in Bub1 and BubR1 direct Bub3 to different phosphorylated targets in the SAC signaling cascade

The microscopic structure of cold aqueous methanol mixtures

The evolution of the micro-segregated structure of aqueous methanol mixtures, in the temperature range 300 K-120 K, is studied with computer simulations, from the static structural point of view. The structural heterogeneity of water is reinforced at lower temperatures, as witnessed by a pre-peak in the oxygen-oxygen structure factor. Water tends to form predominantly chain-like clusters at lower temperatures and smaller concentrations. Methanol domains have essentially the same chain-like cluster structure as the pure liquid at high concentrations and becomes mono- meric at smaller ones. Concentration uctuations decrease with temperature, leading to quasi-ideal Kirkwood-Bu integrals, despite the enhanced molecular interactions, which we interpret as the signature of non-interacting segregated water and methanol clusters. This study throws a new light on the nature of the micro-heterogeneous structure of this mixture: the domain segregation is essentially based on the appearance of linear water clusters, unlike other alcohol aqueous mixtures, such as with propanol or butanol, where the water domains are more bulky.

Osteogenesis imperfecta: pregled suvremenih spoznaja o radiologiji koštanoga sustava i nove genetske spoznaje

Osteogenesis imperfecta is a genetically and clinically heterogeneous disorder of bone and connective tissue characterized by osteoporosis, fragile bones, hyperextensible joints, dentinogenesis imperfecta, bluish coloration of the sclerae, and adult-onset hearing loss. Medical history, careful physical examination, radiographic features of fractures, and biochemical analysis of skin collagen are the four cornerstones of accurate diagnosis. As osteogenesis imperfecta affects the whole skeleton, radiologic diagnostic features could be seen on any bone at any age of the patient. A radiology specialist should be aware of subtle changes seen on radiographs of axial skeleton (i.e. skull, spine and pelvic bones) and appendicular skeleton (i.e. long and short bones of extremities) as well as of specific osteogenesis features (i.e. “popcorn” calcifications) and difficult differential diagnosis (i.e. hypertrophic callus formation versus osteosarcoma; child abuse fractures versus true osteogenesis imperfecta). About 300 different mutations have been identified within COL1A1 and COL1A2 genes that encode the chains of type I collagen. More than 90% of these are heterozygous single base pair mutations unique to the affected individuals within families. Depending on the location of the mutation within the collagen gene, these produce a variety of clinical pictures which range from mild (OI type 1), lethal (OI type 2) to severely deforming (OI type 3) and mildly deforming (OI type 4). Each of the four types has a common radiologic appearance that helps in establishing the diagnosis. However, recent findings have confirmed that new genes other than type I collagen could be responsible for three new types of OI (OI type 5; OI type 6 and rhizomelic OI). Here we describe the complexity of the phenotype-genotype correlation in OI, and the recently proposed new classification.Osteogenesis imperfecta (OI) je genetski i klinički heterogena bolest kosti i vezivnoga tkiva s odrednicama: osteoporoza; lomljivost kostiju; labavost zglobova, dentinogenesis imperfecta; plavičaste bjeloočnice i nagluhost u odrasloj dobi. Ključ točne dijagnoze su četiri bitna postupka: precizna anamneza; pažljiv fizikalni pregled; uočavanje radioloških značajka prijeloma i promjena kostiju i biokemijska analiza kolagena kože. Uobičajena je podjela na četiri tipa OI: od blagog (tip 1), letalnog (tip 2) do teško deformirajućeg (tip 3) i umjereno deformirajućeg oblika (tip 4). Svaki od četiri tipa ima zasebne radiološke značajke koje pomažu kod postavljanja točne dijagnoze i klasificiranja. Dijagnostičko-radiološki znaci postoje na cijelom mišićno koštanom sustavu od novorođenačke do kasne životne dobi. Za radiologa je važno prepoznati brojne sićušne i specifične promjene na rendgenogramima aksijalnog (lubanja, kralješnica, zdjelica) i apendikularnog (kosti udova) skeleta. Znaci korisni u diferenciranju osteosarkoma prema stvaranju hipertrofičnog koštanog kalusa kod OI i drugi posebni znaci bolesti, primjerice metafizne “popcorn” kalcifikacije, prepoznaju se dobrom radiološkom obradom. Dosad je otkriveno oko 300 različitih mutacija na COL1A1 i COL1A2 genima odgovornima za oblikovanje lanaca kolagena tip I. Klinička slika OI razlikuje se prema mjestu mutacije na genu za kolagen. Nedavni nalazi su potvrdili da i drugi geni, uz kolagen tip 1, mogu biti odgovorni za nastanak tri nova tipa OI: tip 5; tip 6 i rizomelični tip OI. Nadalje, u tekstu je opisana složenost fenotipske i genotipske korelacije, kao i nedavno predložena nova klasifikacija OI

Osteogenesis imperfecta: pregled suvremenih spoznaja o radiologiji koštanoga sustava i nove genetske spoznaje

Osteogenesis imperfecta is a genetically and clinically heterogeneous disorder of bone and connective tissue characterized by osteoporosis, fragile bones, hyperextensible joints, dentinogenesis imperfecta, bluish coloration of the sclerae, and adult-onset hearing loss. Medical history, careful physical examination, radiographic features of fractures, and biochemical analysis of skin collagen are the four cornerstones of accurate diagnosis. As osteogenesis imperfecta affects the whole skeleton, radiologic diagnostic features could be seen on any bone at any age of the patient. A radiology specialist should be aware of subtle changes seen on radiographs of axial skeleton (i.e. skull, spine and pelvic bones) and appendicular skeleton (i.e. long and short bones of extremities) as well as of specific osteogenesis features (i.e. “popcorn” calcifications) and difficult differential diagnosis (i.e. hypertrophic callus formation versus osteosarcoma; child abuse fractures versus true osteogenesis imperfecta). About 300 different mutations have been identified within COL1A1 and COL1A2 genes that encode the chains of type I collagen. More than 90% of these are heterozygous single base pair mutations unique to the affected individuals within families. Depending on the location of the mutation within the collagen gene, these produce a variety of clinical pictures which range from mild (OI type 1), lethal (OI type 2) to severely deforming (OI type 3) and mildly deforming (OI type 4). Each of the four types has a common radiologic appearance that helps in establishing the diagnosis. However, recent findings have confirmed that new genes other than type I collagen could be responsible for three new types of OI (OI type 5; OI type 6 and rhizomelic OI). Here we describe the complexity of the phenotype-genotype correlation in OI, and the recently proposed new classification.Osteogenesis imperfecta (OI) je genetski i klinički heterogena bolest kosti i vezivnoga tkiva s odrednicama: osteoporoza; lomljivost kostiju; labavost zglobova, dentinogenesis imperfecta; plavičaste bjeloočnice i nagluhost u odrasloj dobi. Ključ točne dijagnoze su četiri bitna postupka: precizna anamneza; pažljiv fizikalni pregled; uočavanje radioloških značajka prijeloma i promjena kostiju i biokemijska analiza kolagena kože. Uobičajena je podjela na četiri tipa OI: od blagog (tip 1), letalnog (tip 2) do teško deformirajućeg (tip 3) i umjereno deformirajućeg oblika (tip 4). Svaki od četiri tipa ima zasebne radiološke značajke koje pomažu kod postavljanja točne dijagnoze i klasificiranja. Dijagnostičko-radiološki znaci postoje na cijelom mišićno koštanom sustavu od novorođenačke do kasne životne dobi. Za radiologa je važno prepoznati brojne sićušne i specifične promjene na rendgenogramima aksijalnog (lubanja, kralješnica, zdjelica) i apendikularnog (kosti udova) skeleta. Znaci korisni u diferenciranju osteosarkoma prema stvaranju hipertrofičnog koštanog kalusa kod OI i drugi posebni znaci bolesti, primjerice metafizne “popcorn” kalcifikacije, prepoznaju se dobrom radiološkom obradom. Dosad je otkriveno oko 300 različitih mutacija na COL1A1 i COL1A2 genima odgovornima za oblikovanje lanaca kolagena tip I. Klinička slika OI razlikuje se prema mjestu mutacije na genu za kolagen. Nedavni nalazi su potvrdili da i drugi geni, uz kolagen tip 1, mogu biti odgovorni za nastanak tri nova tipa OI: tip 5; tip 6 i rizomelični tip OI. Nadalje, u tekstu je opisana složenost fenotipske i genotipske korelacije, kao i nedavno predložena nova klasifikacija OI