Theranostic Nanoplatforms for MRSA Detection and Destruction from Whole Blood

Bloodstream infection with methicillin‐resistant Staphylococcus aureus (MRSA) and other drug‐resistant bacteria kill several million people in the world every year. Detection of drug‐resistant bacteria in the blood stream is clinically important to save lives. Driven by this need, multifunctional theranostic nanoplatforms have been developed for simultaneous targeted imaging and multimodal photodestruction of MRSA in a whole‐blood sample. Experimental data for the whole‐blood sample spiked with MRSA show that the theranostic nanoplatform can be used for fluorescence imaging after magnetic separation even in a 10^?5:1 ratio. A targeted photodynamic and photothermal combined treatment shows that the multimodal treatment regime can dramatically enhance the possibility of destroying MRSA in vitro. Therefore, our developed theranostic nanoplatform have a great potential as a fluorescent marker and as a light absorber for combined therapy in clinical settings. The possible mechanisms and operating principles are discussed for targeted imaging and combined therapeutic actions using theranostic nanoplatform.     

Start‐up demonstration tests: models,methods and applications,with some unifications

Start‐up demonstration tests were first discussed in the quality/reliability literature about three decades ago. Since then, many variations of these tests have been introduced, and the corresponding distributional characteristics and inferential methods have also been studied. All these developments, based on independent and identically distributed binary trials, have been further generalized to some other forms of trials such as Markov‐dependent trials, exchangeable trials and multistate trials. In this paper, we provide a comprehensive review of all these results and highlight some unifications of the results. We also describe a general estimation method and then present several numerical examples to illustrate some of the models and methods described here. Finally, a number of open issues in this area of research are pointed out. Copyright © 2014 John Wiley & Sons, Ltd.     

Galois structure and de Rham invariants of elliptic curves

Let K be a number field with ring of integers OK. Suppose a finite group G acts numerically tamely on a regular scheme X over OK. One can then define a de Rham invariant class in the class group Cl(OK[G]), which is a refined Euler characteristic of the de Rham complex of X. Our results concern the classification of numerically tame actions and the de Rham invariant classes. We first describe how all Galois étale G-covers of a K-variety may be built up from finite Galois extensions of K and from geometric covers. When X is a curve of positive genus, we show that a given étale action of G on X extends to a numerically tame action on a regular model if and only if this is possible on the minimal model. Finally, we characterize the classes in Cl(OK[G]) which are realizable as the de Rham invariants for minimal models of elliptic curves when G has prime order.     

Large sets of <Emphasis Type="Italic">t</Emphasis>-designs from groups

This paper addresses questions related to the existence and construction of large sets of t-(v, k, λ) designs. It contains material from my talk in the Combinatorial Designs Conference in honor of Alex Rosa’s 70th birthday, which took place in beautiful Bratislava, in July, 2007. Naturally, only a small number of “highlight” topics could be included, and for the most part these involve the use of symmetry, that is, it is assumed that the particular designs or large sets of designs, are invariant under a prescribed group of automorphisms. I present almost no proofs, but give references so that the reader can find a much wider repertory of theorems and constructions in the literature. For completeness, I include the statement of a few recursive constructions. The latter are extremely important on their own right, and deserve extensive attention elsewhere. I hope the reader becomes interested in the intriguing open problems posed at the end of the paper and succeeds in solving some of them. (Communicated by Peter Horák)     

On the asymptotic existence of cocyclic Hadamard matrices

Let q be an odd natural number. We prove there is a cocyclic Hadamard matrix of order ²10+tq whenever . We also show that if the binary expansion of q contains N ones, then there is a cocyclic Hadamard matrix of order ²4N−2q.     

The equivariant LS-category of polar actions

We will provide a lower bound for arbitrary proper actions in terms of the stratification by orbit types, and an upper bound for proper polar actions in terms of the equivariant LS-category of its generalized Weyl group. As an application we reprove a theorem of Singhof that determines the classical Lusternik-Schnirelmann category for U(n) and SU(n).     

On the topological entropy of the free semigroup action generated by proper maps

In this paper, we introduce the topological entropy of a free semigroup action generated by proper maps, which extends the notions of the topological entropy of the free semigroup actions defined by Bufetov in 1999 and topological entropy of the proper maps defined by Patrão in 2010. We then give some properties of these notions and discuss the relations between them. We also give a partial variational principle for locally compact separable metric spaces. Moreover, the relationship between topological entropy of the free semigroup generated by proper maps and topological entropy of a skew-product transformation is given. These results extend the results obtained by Patrão, Bufetov and Lin, Ma and Wang in 2018.     

Reconstructing under Group Actions

We give a bound on the reconstructibility of an action GX in terms of the reconstructibility of a the action NX, where N is a normal subgroup of G, and the reconstructibility of the quotient G/N. We also show that if the action GX is locally finite, in the sense that every point is either in an orbit by itself or has finite stabilizer, then the reconstructibility of GX is at most the reconstructibility of G. Finally, we give some applications to geometric reconstruction problems.     

FUNDAMENTAL GROUPS OF CLOSED POSITIVELY CURVED MANIFOLDS WITH ALMOST DISCRETE ABELIAN GROUP ACTIONS

Let M be a closed n-manifold of positive sectional curvature.Assume that M admits an effiective isometrical T 1×Zkp-action with p prime.The main result of the article is that if k=1 for n=3 or k (n+1)/4 for n≥5,then there exists a positive constant p(n),depending only on n,such that π1(M) is cyclic if p≥p(n).