We present a measurement study on compositions of Decentralized Finance (DeFi) protocols, which aim to disrupt traditional finance and offer services top distributed ledgers, such as Ethereum. Understanding DeFi is great importance, they may impact the development ecosystem interoperability, are increasingly integrated with web technologies, introduce risks through complexity. Starting from dat...

Abstract. Recently, the authors established a number of inequalities involving integer powers of the Hadamard product of two positive de nite Hermitian matrices. Here these results are extended in two ways. First, the restriction to integer powers is relaxed to include all real numbers not in the open interval ( 1; 1). Second, the results are extended to the Hadamard product of any nite number ...

Abstract In this viewpoint article, we provide an analysis of the value proposition decentralized finance (DeFi) and its limitations using a simple stylized model collateralized lending. DeFi uses ledger to run smart contracts that automatically enforce terms lending contract safeguard collateral. can lower costs associated with intermediated improve financial inclusion. Limitations are volatil...

Perspectives T he lack of a " gold standard " defi nition for severe malaria has been a longstanding problem for both clinicians and researchers. The defi nitions currently used comprise a set of clinical and laboratory parameters associated with an increased risk of death [1,2], combined with the presence of Plasmodium falciparum parasitemia [2,3]. In young children, these criteria are predomi...

Many of the currently popular \block algorithms" are scalar algorithms in which the operations have been grouped and reordered into matrix operations. One genuine block algorithm in practical use is block LU factorization, and this has recently been shown by Demmel and Higham to be unstable in general. It is shown here that block LU factorization is stable if A is block diagonally dominant by c...

We derive a cell-centered 3-D di usion di erencing scheme for arbitrary hexahedral meshes using the local support-operators method. Our method is said to be local because it yields a sparse matrix representation for the di usion equation, whereas the traditional support-operators method yields a dense matrix representation. The di usion discretization scheme that we have developed o ers several...

We give a sharp estimate for the eigenvectors of a positive deenite Hermitian matrix under a oating-point perturbation. The proof is elementary. Recently there have been a number of papers on eigenvector perturbation bounds that involve a perturbation of the matrix which is small in some relative sense, including the typical rounding errors in matrix elements ((1], 2], 10], 8], 4], 5]). The pro...

The Riemannian metric on the manifold of positive de nite matrices is de ned by a kernel function in the form K D(H;K) = P i;j ( i; j) 1TrPiHPjK when P i iPi is the spectral decomposition of the foot point D and the Hermitian matrices H;K are tangent vectors. For such kernel metrics the tangent space has an orthogonal decomposition. The pull-back of a kernel metric under a mapping D 7! G(D) is ...

Positive and conditionally positive deenite functions, especially radial basis functions and similar functions for spheres, tori, and even Riemannian manifolds, are of interest because of the their well-known ability to synthesize a good surface t from scattered data. More recently, positive deenite basis functions have been employed to analyze scattered data. The methods used to do this involv...