We propose a flexible convex relaxation for the phase retrieval problem that operates in the natural domain of the signal. Therefore, we avoid the prohibitive computational cost associated with “lifting” and semidefinite programming (SDP) in methods such as PhaseLift and compete with recently developed non-convex techniques for phase retrieval. We relax the quadratic equations for phaseless mea...

Scale-discretised wavelets yield a directional wavelet framework on the sphere where a signal can be probed not only in scale and position but also in orientation. Furthermore, a signal can be synthesised from its wavelet coefficients exactly, in theory and practice (to machine precision). Scale-discretised wavelets are closely related to spherical needlets (both were developed independently at...

Verification of temporal logic properties plays a crucial role in proving the desired behaviors of continuous systems. In this paper, we propose an interval method that verifies the properties described by a bounded signal temporal logic. We relax the problem so that if the verification process cannot succeed at the prescribed precision, it outputs an inconclusive result. The problem is solved ...

In a recent paper [16], one of us identified all of the quasi-stationary distributions for a non-explosive, evanescent birth-death process for which absorption is certain, and established conditions for the existence of the corresponding limiting conditional distributions. Our purpose is to extend these results in a number of directions. We shall consider separately two cases depending on wheth...

Capacity regulation system by controlling suction valve is useful for large scale reciprocating compressor in petrochemical engineering field. The dynamic performance of adjustment device influences the stability and accurancy of this system. In this paper, a mathematical model of adjustment device coupled with the motion of suction valve is built, and the dynamic performances of valve plate ar...

An analog CMOS peak detect and hold (PDH) circuit, which combines high speed and accuracy, rail-to-rail sensing and driving, low power, and buffering is presented. It is based on a configuration that cancels the major error sources of the classical CMOS PDH, including offset and common mode gain, by re-using the same amplifier for tracking, peak sensing, and output buffering. By virtue of its h...

The ability to hold stool (called continence) requires the rectum, anus and nervous system to be working normally. Two groups of muscles in the wall of the anus and rectum are responsible for holding the stool in the rectum, the outer muscle group (external anal sphincter) and the inner muscle group (internal anal sphincter). Your ability to sense the presence of stool in the rectum (called rec...

We tested the hypothesis that vasoregulatory mechanisms completely counteract the effects of sudden changes in arterial perfusion pressure on exercising muscle blood flow. Twelve healthy young subjects (7 female, 5 male) lay supine and performed rhythmic isometric handgrip contractions (2 s contraction/ 2 s relaxation 30% maximal voluntary contraction). Forearm blood flow (FBF; echo and Doppler...

Verification of temporal logic properties plays a crucial role in proving the desired behaviors of hybrid systems. In this paper, we propose an interval method for verifying the properties described by a bounded linear temporal logic. We relax the problem to allow outputting an inconclusive result when verification process cannot succeed with a prescribed precision, and present an efficient and...

This paper considers the problem of online graph colouring. An algorithm for vertex-colouring graphs is said to be online if each vertex is irrevocably assigned a colour before later vertices are considered. We first introduce the problem formally and define a perfomance metric to evaluate the success of an online colouring algorithm. Then, several upper and lower bounds are presented on the pe...