Convex regularizers is popular for sparse and low-rank learning, mainly due to their nice statistical and optimization guarantee. However, they often lead to bias estimation, thus the sparsity and accuracy is not as good as desired. This motivates replacement of convex regularizers with nonconvex one, and recently many nonconvex regularizers have been proposed and indeed better performance than...

A homomorphism from an oriented graph G to an oriented graph H is a mapping φ from the set of vertices of G to the set of vertices of H such that −−−−−−→ φ(u)φ(v) is an arc in H whenever −→ uv is an arc in G. The oriented chromatic index of an oriented graph G is the minimum number of vertices in an oriented graph H such that there exists a homomorphism from the line digraph LD(G) of G to H (th...

One thousand five hundred and forty Hybro HI-YR broilers were used in the study. One-day-old chickens were allocated to four groups; in the pen trial each group comprised 5 replications with 56 birds, in the digestibility trial there were 7 replications with 15 birds. The dietary treatments were as follows: unsupplemented control wheat-barley diet or the same diet supplemented with 10 ppm avila...

Peripheral blood progenitor cell mobilization with intermediate-dose cyclophosphamide (ID-CY) and granulocyte colony-stimulating factor (G-CSF) has been shown to be more efficacious, albeit more toxic, than low-dose cyclophosphamide (LD-CY) mobilization regimens in patients with multiple myeloma treated with conventional therapies. However, the relative importance of cyclophosphamide dose inten...

This paper is a continuation of our previous (Liu and Pagès, 2020). In this paper, we establish the monotone convex order (see further (1.1)) between two R-valued McKean–Vlasov processes X=(Xt)t∈[0,T] Y=(Yt)t∈[0,T] defined on filtered probability space (Ω,F,(Ft)t≥0,P) by dXt=b(t,Xt,μt)dt+σ(t,Xt,μt)dBt,X0∈Lp(P)withp≥2,dYt=β(t,Yt,νt)dt+θ(t,Yt,νt)dBt,Y0∈Lp(P),where∀t∈[0,T],μt=P∘Xt−1,νt=P∘Yt−1.If m...

Given a real valued and time-inhomogeneous martingale diffusion X , we investigate the properties of functions defined by the conditional expectation f(t,Xt) = E [g(XT )|Ft]. We show that whenever g is monotonic or Lipschitz continuous then f(t, x) will also be monotonic or Lipschitz continuous in x. If g is convex then f(t, x) will be convex in x and decreasing in t. We also define the margina...

Consider the standard, one dimensional, nonlinear filtering problem for diffusion processes observed in small additive white noise: dXt = b(Xt)dt + dBt , dY ε t = γ(Xt)dt + εdVt , where B·, V· are standard independent Brownian motions. Denote by qε 1(·) the density of the law of Ξ1 conditioned on σ(Y ε t : 0 ≤ t ≤ 1). We provide “quenched” large deviation estimates for the random family of meas...

Let LD(G) denote the minimum cardinality of a locating-dominating set for graph G. If T is a tree of order n with l leaf vertices and s support vertices, then a known lower bound of Blidia, Chellali, Maffray, Moncel and Semri [Australas. J. Combin. 39 (2007), 219–232] is LD(T ) ≥ (n+ 1 + l − s)/3 . In this paper, we show that LD(T ) ≥ (n+ 1 + 2(l − s))/3 and these bounds are sharp. We construct...