Sidechains are among the most promising scalability and extended functionality solutions for blockchains. Application of zero knowledge techniques (Latus, Mina) allows reaching high level security general throughput, though it brings new challenges on keeping decentralization where significant effort is required robust computation zk-proofs. We consider a simultaneous decentralized creation var...

The first hunt took a long time. The existence of a highly sensitive calciumsensing receptor (CaSR) was postulated more than 30 years ago based on the exquisite ability of the parathyroid cell to respond to small changes in serum ionized calcium concentration (1). The gene encoding CaSR was finally cloned in 1993 (2). Shortly thereafter it was found that inactivating mutations in CaSR were resp...

Most of the physiological and metabolic processes in any organism are controlled by a regulatory factor network, which includes a lot of protein kinases, protein phosphatases and transcription factors. Protein kinases and phosphatases are key regulators of the majority of transcription factors which control metabolism both in normal and in different pathological conditions; it is a circadian ty...

In this note we construct two infinite snark families which have high oddness and low circumference compared to the number of vertices. Using this construction, we also give a counterexample to a suggested strengthening of Fulkerson’s conjecture by showing that the Petersen graph is not the only cyclically 4-edge connected cubic graph which require at least five perfect matchings to cover its e...

Elliptic curves have become key ingredients for instantiating zero-knowledge proofs and more generally proof systems. Recently, there been many tailored constructions of these that aim at efficiently implementing different kinds In this survey we provide the reader with a comprehensive overview on existing work revisit contributions in terms efficiency security. We present an three stages proce...

from the paper). Non-interactive zero-knowledge proofs (NIZKs) are a powerful cryptographic tool, with numerous potential applications. However, succinct NIZKs (e.g., zk-SNARK schemes) necessitate a trusted party to generate and publish some public parameters, to be used by all provers and verifiers. This party is trusted to correctly run a probabilistic algorithm (specified by the the proof sy...

A snark is a cubic cyclically 4–edge connected graph with edge chromatic number four and girth at least five. We say that a graph G is odd 2–factored if for each 2–factor F of G each cycle of F is odd. In this paper, we present a method for constructing odd 2–factored snarks. In particular, we construct two new odd 2–factored snarks that disprove a conjecture by some of the authors. Moreover, w...

A permutation snark is a cubic graph with no 3-edge-colouring that contains a 2-factor consisting of two induced circuits. In the talk we analyse the basic properties of permutation snarks, focusing on the structure of edge-cuts of size 4 and 5. As an application of our knowledge we provide rich families of cyclically 4edge-connected and 5-edge-connected permutation snarks of order 8n+2 for eac...

BACKGROUND As biologists increasingly rely upon computational tools, it is imperative that they be able to appropriately apply these tools and clearly understand the methods the tools employ. Such tools must have access to all the relevant data and knowledge and, in some sense, "understand" biology so that they can serve biologists' goals appropriately and "explain" in biological terms how resu...