We present in this paper several results concerning a simple model of interaction between an inviscid fluid, modeled by the Burgers equation, and a particle, assumed to be point-wise. It is composed by a first-order partial differential equation which involves a singular source term and by an ordinary differential equation. Though this model can be considered simple, its mathematical analysis i...

We present an implementation of the LPDual Active Set Algorithm (LP DASA) based on a quadratic proximal approximation, a strategy for dropping inactive equations from the constraints, and recently developed algorithms for updating a sparse Cholesky factorization after a low-rank change. Although our main focus is linear programming, the first and second-order proximal techniques that we develop...

In this note we provide proofs of various expressions for expectation values symmetric polynomials in \beta ? -deformed eigenvalue models with quadratic, linear, and logarithmic potentials. The relations derive are also referred to as superintegrability. Our work completes superintegrability st...

This paper presents an accelerated variant of the hybrid proximal extragradient (HPE) method for convex optimization, referred to as the accelerated HPE (A-HPE) framework. Iterationcomplexity results are established for the A-HPE framework, as well as a special version of it, where a large stepsize condition is imposed. Two specific implementations of the A-HPE framework are described in the co...

We study finite-time horizon continuous-time linear-quadratic reinforcement learning problems in an episodic setting, where both the state and control coefficients are unknown to controller. first propose a least-squares algorithm based on observations controls, establish logarithmic regret bound of order $O((\ln M)(\ln\ln M))$, with $M$ being number episodes. The analysis consists two parts: p...

To determine the timing of peak bone mass and density, we conducted a cross-sectional study of bone mass measurements in 265 premenopausal Caucasian females, aged 8-50 yr. Bone mass and bone mineral density were measured using dual X-ray absorptiometry and single-photon absorptiometry at the spine (anteroposterior, lateral), proximal femur, radius shaft, distal forearm, and the whole body. Bone...

Recent studies have shown that proximal gradient (PG) method and accelerated gradient method (APG) with restarting can enjoy a linear convergence under a weaker condition than strong convexity, namely a quadratic growth condition (QGC). However, the faster convergence of restarting APG method relies on the potentially unknown constant in QGC to appropriately restart APG, which restricts its app...

Logarithmic signatures for finite groups are the essential constituent of public key cryptosystems MST1 and MST3. Especially they form the main component of the private key of MST3. Constructing new classes of logarithmic signatures having features that do not share with the well-known class of transversal or fused transversal logarithmic signatures, has become a vital issue regarding the use o...