High-grade metamorphic soles in NE Bosnia and Herzegovina make part of the Krivaja-Konjuh ophiolite complex (KKOC), which is one of the most important constituents of the Jurassic ophiolite melange of the Central Dinarides. Several rock types were distinguished within the investigated metamorphic suite - sapphirine and corundum amphibolites, garnet-clinopyroxene±orthopyroxene amphibolites, clinopyroxene±garnet amphibolites, amphibolites per se and clinopyroxene+plagoclase±garnet gneisses.Peak temperature and pressure conditions calculated from different mineral pairs were estimated to range between 850 and 1100°C at 1.1 to 1.3 GPa. A prograde multi-stage metamorphic history of analyzed rocks was followed by the post-peak relaxation witnessed in decomposing porphyroblasts of garnet and ubiquitous formation of amphibole and orthopyroxene rims around clinopyroxene. The whole-rock chemical composition of magmatic protoliths largely defines it as cumulates from supra-subduction zones and scarcely as MORB-like tholeiitic mafic extrusives. Their origin is linked to near-ridge crust generation of a back-arc basin. Following the Middle Jurassic contraction of Neotethyan a portion of these rocks was likely entrained in an incipient subduction/thrusting system characteristic for the formation of metamorphic soles. According to geological evidences, and most notably, the age of radiolarians taken from KKOC basalts, the formation of metamorphic sole rocks must have followed a rapid transition in the Dinaridic Neotethys geotectonic setting before its final obduction onto the Adria margins in the next 15 Ma before the end of Jurassic.

In this paper we explore a way of securing a secret inside a graph by observing pieces of the secret as colors assigned to the graph vertices. If a graph allows a highly (a, b)-resistant k-multicoloring then a secret can be divided into k parts and sets of those parts distributed to the vertices of the graph so that no a attackers can steal the secret, and when a attackers and b malfuntioning vertices leave the graph, the secret is still whole in the remaining graph. In this paper we explore how many vertices a graph must have in order to allow a highly (3, 1)-resistant k-multicoloring, and what is the minimal number of colors, for graphs that do allow such multicoloring.

. Complex networks are often used to model objects and their relations. Network descriptors are graph-theoretical invariants assigned to graphs that correspond to complex networks. Transmission and betweenness centrality are well known network descriptors and networkness and network surplus have been recently analyzed. All these four descriptors are based on the unrealistic assumption about equal communication between all vertices. Here, we amend this by assuming that vertices on the distance larger then one communicate less than those that are neighbors. We analyze network descriptors for all possible values of the factor α that measures reduction in the communication of the vertices that are not neighbors. We term these descriptors one-alpha descriptors and determine their extremal values.

Networks (or graphs) appear as dominant structures in different domains, including sociology, biology, neuroscience and computing. In most cases, these graphs are directed which changes the semantics of the edges that are no longer symmetrical in the sense that the beginning vertex transfers some property or value to the end vertex, but not vice versa. Detecting community structure in complex networks is an interdisciplinary topic with many relevant areas of application. In order to detect communities in directed acyclic networks, apart from the direction of the edge, the requirement for topological ordering of the vertices should be taken into account. In other words, if the vertices are topologically order is such a way that x1 < x2 < ... < xn we are interested in dividing the network into communities C1, C2, ..., Ck in such a way that: if xi < xj , xi ∈ Ci, xj ∈ Cj then Ci < Cj or Ci = Cj We present an algorithm derived from LPA algorithms which are commonly used in network detection, mostly because of their quick computational time and fairly good results. They were originally developed for undirected networks, but have been modified for this purpose.

antineutrophil cytoplasmic autoantibody (anca)-associated vasculitis (aav) is a small-vessel vasculitis, characterized by necrotizing inflammation of small vessels and positive ancas. cancas are directed against proteinase-3 (Pr-3) and are specific for granulomatosis with polyangiitis (GPa, formerly known as Wegener’s disease), although their role in the immunopathology of the disease is still unclear. This is why the european medicines agency suggested that canca positivity, in addition to the clinical picture, can be enough for the diagnosis of GPa. Granulomatosis with polyangiitis is characterized by granulomatous inflammation that usually involves the upper and lower respiratory tract, necrotizing vasculitis that affects small and medium-sized vessels, and often rapidly progressive glomerulonephritis. We present a patient with an unusual presentation of canca-associated vasculitis, who presented with arthritis, palpable purpura on legs, and pauci-immune necrotizing glomerulonephritis with highly positive canca antibodies, without any signs or symptoms of airway involvement. although renal-limited anca vasculitis is recognized as a separate entity, our patient also had signs of skin and joint involvement and prominent constitutional symptoms that contributed to the diagnosis of systemic disease. in this paper, we present a patient with an atypical course of GPa, which can also be called a limited form of the disease. an atypical course or limited form belongs to the group of sine syndromes in inflammatory rheumatic diseases, which are not very common, but should be considered in the differential diagnosis. to our knowledge, there are only a few described case reports with a similar presentation.