Abstract The angular synchronization problem of estimating a set unknown angles from their known noisy pairwise differences arises in various applications. It can be reformulated as an optimization on graphs involving the graph Laplacian matrix. We consider general, weighted version this problem, where impact noise differs between different pairs entries and some are erased completely; for exam...

Neural networks have become standard tools in the analysis of data, but they lack comprehensive mathematical theories. For example, there are very few statistical guarantees for learning neural from especially classes estimators that used practice or at least similar to such. In this paper, we develop a general guarantee consist least-squares term and regularizer. We then exemplify with ?1-regu...

Abstract Neural networks are becoming increasingly popular in applications, but our mathematical understanding of their potential and limitations is still limited. In this paper, we further by developing statistical guarantees for sparse deep learning. contrast to previous work, consider different types sparsity, such as few active connections, nodes, other norm-based sparsity. Moreover, theori...

We present our on-going efforts to guarantee the timing behavior of a program targeted for the precision timed architecture. We extend both the ISA and the hardware to support a set of timing instructions that allow programmers to control the execution time of a sequence of instructions. Programs written using these timing instructions specify deadlines within the program specification itself, ...

One goal in network design is the construction of sparse networks that guarantee short distances with respect to some given distance requirements. By this, it can be guaranteed, for example, that delays that are incurred by link faults are bounded. An appropriate graph-theoretic model for this is the concept of k–spanners: Given a graph G, a k–spanner of G is a spanning subgraph S, such that th...

Electronic Commerce over the Internet is one of the most rapidly growing areas in todays business. However, considering the most important phase of Electronic Commerce, the payment, it has to be noted that in most currently exploited approaches support for at least one of the participants is limited. From a general point of view, a couple of requirements for correct payment interactions exist, ...