Sensitive biomarkers are needed to detect kidney injury at the earliest stages. The objective of this study was to determine whether the appearance of kidney injury molecule-1 (Kim-1) protein ectodomain in urine and kidney injury molecule-1/hepatitis A viral cellular receptor-1 (Kim-1/ Havcr1) gene expression in kidney tissue may be more predictive of renal injury after exposure to nephrotoxicants when compared to traditionally used biomarkers. Male Sprague-Dawley rats were injected with a range of doses of gentamicin, mercury (Hg; HgCl 2 ), or chromium (Cr; K 2 Cr 2 O 7 ). The results showed that increases in urinary Kim-1 and kidney Kim-1/Havcr1 gene expression paralleled the degree of severity of renal histopathology and were detected at lower doses of nephrotoxicants when compared to blood urea nitrogen (BUN), serum creatinine, and urinary Nacetyl-β-D-glucosaminidase (NAG). In a time course study, urinary Kim-1 was elevated within 24 h after exposure to gentamicin (100 mg/kg), Hg (0.25 mg/kg), or Cr (5 mg/kg) and remained elevated through 72 h. NAG responses were nephrotoxicant dependent with elevations occurring early (gentamicin), late (Cr), or no change (Hg). At 72 h, after treatment with any of the three nephrotoxicants, there was increased Kim-1 immunoreactivity and necrosis involving ∼50% of the proximal tubules; however, only urinary Kim-1 was significantly increased, while BUN, serum creatinine, and NAG were not different from controls. In rats treated with the hepatotoxicant galactosamine (1.1 mg/kg), serum alanine aminotransferase was increased, but no increase in urinary Kim-1 was observed. Urinary Kim-1 and kidney Kim-1/Havcr1 expression appear to be sensitive and tissue-specific biomarkers that will improve detection of early acute kidney injury following exposure to nephrotoxic chemicals and drugs. Keywordsacute kidney injury; nephrotoxicity biomarkers; kidney injury molecule-1; mercury; chromium; gentamicin 1To whom correspondence should be addressed at Center for Devices and Radiological Health, U.S. Food and Drug Administration, White Oak Life Sciences Laboratory, WO64-4064, 10903 New Hampshire Avenue, Silver Spring, MD 20993-0002. Fax: 301-796-9826. E-mail: peter.goering@fda.hhs.gov.. NIH Public Access NIH-PA Author ManuscriptNIH-PA Author Manuscript NIH-PA Author ManuscriptRenal insufficiency, in some form, has been reported to occur in ∼11% of the U.S. population (Nally, 2002). Acute kidney injury (AKI) or acute renal failure (ARF) occurs in 2-5% of patients admitted to general hospitals in the United States, and AKI is associated with a high rate (up to 50%) of mortality (Chertow et al., 2005;Nally, 2002). The annual health care expenditures attributable to hospital-acquired AKI based on conservative assumptions are estimated to exceed $10 billion (Chertow et al., 2005). Patients with subclinical renal injury may be more sensitive to AKI following exposure to potentially nephrotoxic drugs and/or compounds released unintentionally from medical device materials (e.g., residues, le...

High‐performance graphene microwave absorption materials are highly desirable in daily life and some extreme situations. A simple technique for the direct growth of graphene as absorption fillers in wave‐transmitting matrices is of paramount importance to bring it to real‐world application. Herein, a simple chemical vapor deposition (CVD) route for the direct growth of edge‐rich graphene (ERG) with tailored structures and tunable dielectric properties in porous Si3N4 ceramics using only methyl alcohol (CH3OH) as precursor is reported. The large O/C atomic ratio of CH3OH helps to build a mild oxidizing atmosphere and leads to a unique structure featuring open graphite nanosteps and freestanding nanoplanes, endowing the ERG/Si3N4 hybrid with an appropriate balance between good impedance matching and strong loss capacity. Accordingly, the prepared materials exhibit superior electromagnetic wave absorption, far surpassing that of traditional CVD graphene and reduced graphene oxide‐based materials, achieving an effective absorption bandwidth of 4.2 GHz covering the entire X band, with a thickness of 3.75 mm and a negligibly low loading content of absorbents. The results provide new insights for developing novel microwave absorption materials with strong reflection loss and wide absorption frequency range.

In this paper, the authors characterize, in terms of pointwise inequalities, the classical Besov spacesḂ s p, q and Triebel-Lizorkin spacesḞ s p, q for all s ∈ (0, 1) and p, q ∈ (n/(n+ s), ∞], both in R n and in the metric measure spaces enjoying the doubling and reverse doubling properties. Applying this characterization, the authors prove that quasiconformal mappings preserveḞ s n/s, q on R n for all s ∈ (0, 1) and q ∈ (n/(n + s), ∞]. A metric measure space version of the above morphism property is also established.

We study the computational complexity of approximating the 2-toq norm of linear operators (defined as A 2→q = max v 0 Av| q / v 2 ) for q > 2, as well as connections between this question and issues arising in quantum information theory and the study of Khot's Unique Games Conjecture (UGC). We show the following:1. For any constant even integer q 4, a graph G is a smallset expander if and only if the projector into the span of the top eigenvectors of G's adjacency matrix has bounded 2 → q norm. As a corollary, a good approximation to the 2 → q norm will refute the Small-Set Expansion Conjecture -a close variant of the UGC. We also show that such a good approximation can be obtained in exp(n 2/q ) time, thus obtaining a different proof of the known subexponential algorithm for Small-Set Expansion.2. Constant rounds of the "Sum of Squares" semidefinite programing hierarchy certify an upper bound on the 2 → 4 norm of the projector to low degree polynomials over the Boolean cube, as well certify the unsatisfiability of the "noisy cube" and "short code" based instances of Unique Games considered by prior works. This improves on the previous upper bound of exp(log O(1) n) rounds (for the "short code"), as well as separates the "Sum of Squares"/"Lasserre" hierarchy from weaker hierarchies that were known to require ω(1) rounds.3. We show reductions between computing the 2 → 4 norm and computing the injective tensor norm of a tensor, a problem with connections to quantum information theory. Three corollaries are: (i) the 2 → 4 norm is NP-hard to approximate to precision inverse-polynomial in the dimension, (ii) the 2 → 4 norm does not have a good approximation (in the sense above) unless 3-SAT can be solved in time exp( √ n poly log(n)), and (iii) known algorithms for the quantum separability problem imply a non-trivial additive approximation for the 2 → 4 norm.

Abstract. Let X be an RD-space, which means that X is a space of homogenous type in the sense of Coifman and Weiss with the additional property that a reverse doubling property holds in X . In this paper, the authors first introduce the notion of admissible functions ρ and then develop a theory of localized Hardy spaces H 1 ρ (X ) associated with ρ, which includes several maximal function characterizations of H 1 ρ (X ), the relations between H 1 ρ (X ) and the classical Hardy space H 1 (X ) via constructing a kernel function related to ρ, the atomic decomposition characterization of H 1 ρ (X ), and the boundedness of certain localized singular integrals on H 1 ρ (X ) via a finite atomic decomposition characterization of some dense subspace of H 1 ρ (X ). This theory has a wide range of applications. Even when this theory is applied, respectively, to the Schrödinger operator or the degenerate Schrödinger operator on R n , or to the sub-Laplace Schrödinger operator on Heisenberg groups or connected and simply connected nilpotent Lie groups, some new results are also obtained. The Schrödinger operators considered here are associated with nonnegative potentials satisfying the reverse Hölder inequality.

We say that an algorithm robustly decides a constraint satisfaction problem Π if it distinguishes at-least-(1 − )-satisfiable instances from less-than-(1 − r( ))-satisfiable instances for some function r( ) with r( ) → 0 as → 0. In this paper we show that the canonical linear programming relaxation robustly decides Π if and only if Π has "width 1" (in the sense of Feder and Vardi).

An RD-space X is a space of homogeneous type in the sense of Coifman and Weiss with the additional property that a reverse doubling property holds in X . In this paper, the authors first give several equivalent characterizations of RD-spaces and show that the definitions of spaces of test functions on X are independent of the choice of the regularity ǫ ∈ (0, 1); as a result of this, the Besov and Triebel-Lizorkin spaces on X are also independent of the choice of the underlying distribution space. Then the authors characterize the norms of inhomogeneous Besov and Triebel-Lizorkin spaces by the norms of homogeneous Besov and Triebel-Lizorkin spaces together with the norm of local Hardy spaces in the sense of Goldberg. Also, the authors obtain the sharp locally integrability of elements in Besov and Triebel-Lizorkin spaces.Comparing Corollary 5.1 with the corresponding conclusions of Besov and Triebel-Lizorkin spaces on R n in [16, Theorem 3.3.2], the corresponding conclusions for X when p ∈ (n/(n+s), 1) are missed. To obtain these cases, the method in [16] strongly depends on the embedding theorems for different metrics on R n in [17, p. 129]. However, such embedding conclusions are not available for X due to the fact that for an RD-space X , its "local"

In this paper, we establish the equivalence between the Hajłasz-Sobolev spaces or classical TriebelLizorkin spaces and a class of grand Triebel-Lizorkin spaces on Euclidean spaces and also on metric spaces that are both doubling and reverse doubling. In particular, when p ∈ (n/(n + 1), ∞), we give a new characterization of the Hajłasz-Sobolev spacesṀ 1,p (R n ) via a grand Littlewood-Paley function.