Streaming Complexity of Spanning Tree Computation

The semi-streaming model is a variant of the streaming model frequently used for the computation of graph problems. It allows the edges of an n-node input graph to be read sequentially in p passes using Õ(n) space. If the list of edges includes deletions, then the model is called the turnstile model; otherwise it is called the insertion-only model. In both models, some graph problems, such as spanning trees, k-connectivity, densest subgraph, degeneracy, cut-sparsifier, and (Δ+1)-coloring, can be exactly solved or (1+ε)-approximated in a single pass; while other graph problems, such as triangle detection and unweighted all-pairs shortest paths, are known to require Ω̃(n) passes to compute. For many fundamental graph problems, the tractability in these models is open. In this paper, we study the tractability of computing some standard spanning trees, including BFS, DFS, and maximum-leaf spanning trees. Our results, in both the insertion-only and the turnstile models, are as follows. Maximum-Leaf Spanning Trees: This problem is known to be APX-complete with inapproximability constant ρ ∈ [245/244, 2). By constructing an ε-MLST sparsifier, we show that for every constant ε > 0, MLST can be approximated in a single pass to within a factor of 1+ε w.h.p. (albeit in super-polynomial time for ε ≤ ρ-1 assuming P ≠ NP) and can be approximated in polynomial time in a single pass to within a factor of ρ_n+ε w.h.p., where ρ_n is the supremum constant that MLST cannot be approximated to within using polynomial time and Õ(n) space. In the insertion-only model, these algorithms can be deterministic. BFS Trees: It is known that BFS trees require ω(1) passes to compute, but the naïve approach needs O(n) passes. We devise a new randomized algorithm that reduces the pass complexity to O(√n), and it offers a smooth tradeoff between pass complexity and space usage. This gives a polynomial separation between single-source and all-pairs shortest paths for unweighted graphs. DFS Trees: It is unknown whether DFS trees require more than one pass. The current best algorithm by Khan and Mehta [STACS 2019] takes Õ(h) passes, where h is the height of computed DFS trees. Note that h can be as large as Ω(m/n) for n-node m-edge graphs. Our contribution is twofold. First, we provide a simple alternative proof of this result, via a new connection to sparse certificates for k-node-connectivity. Second, we present a randomized algorithm that reduces the pass complexity to O(√n), and it also offers a smooth tradeoff between pass complexity and space usage.ISSN:1868-896

Bis{1-[(E)-(2-methyl­phen­yl)diazen­yl]-2-naphtho­lato}palladium(II)

In the title compound, [Pd(C17H13N2O)2], the PdII atom is tetra­coordinated by two N atoms and two O atoms from two bidentate methylphenyl­diazenylnaphtolate ligands, forming a square-planar complex. The two N atoms and two O atoms around the PdII atom are trans to each other (as the PdII atom lies on a crystallographic inversion centre) with O—Pd—N bond angles of 89.60 (11) and 90.40 (11)°. The distances between the PdII atom and the coordinated O and N atoms are 1.966 (3) and 2.009 (3) Å, respectively

Assessing suitability of Co@Au core/shell nanoparticle geometry for improved theranostics in colon carcinoma

The interactions between cells and nanomaterials at the nanoscale play a pivotal role in controlling cellular behavior and ample evidence links cell intercommunication to nanomaterial size. However, little is known about the effect of nanomaterial geometry on cell behavior. To elucidate this and to extend the application in cancer theranostics, we have engineered core–shell cobalt–gold nanoparticles with spherical (Co@Au NPs) and elliptical morphology (Co@Au NEs). Our results show that owing to superparamagnetism, Co@Au NPs can generate hyperthermia upon magnetic field stimulation. In contrast, due to the geometric difference, Co@Au NEs can be optically excited to generate hyperthermia upon photostimulation and elevate the medium temperature to 45 °C. Both nanomaterial geometries can be employed as prospective contrast agents; however, at identical concentration, Co@Au NPs exhibited 4-fold higher cytotoxicity to L929 fibroblasts as compared to Co@Au NEs, confirming the effect of nanomaterial geometry on cell fate. Furthermore, photostimulation-generated hyperthermia prompted detachment of anti-cancer drug, Methotrexate (MTX), from Co@Au NEs-MTX complex and which triggered 90% decrease in SW620 colon carcinoma cell viability, confirming their application in cancer theranostics. The geometry-based perturbation of cell fate can have a profound impact on our understanding of interactions at nano-bio interface which can be exploited for engineering materials with optimized geometries for superior theranostic applications

Evaluation of Laser-Assisted Trans-Nail Drug Delivery with Optical Coherence Tomography

The nail provides a functional protection to the fingertips and surrounding tissue from external injuries. The nail plate consists of three layers including dorsal, intermediate, and ventral layers. The dorsal layer consists of compact, hard keratins, limiting topical drug delivery through the nail. In this study, we investigate the application of fractional CO2 laser that produces arrays of microthermal ablation zones (MAZs) to facilitate drug delivery in the nails. We utilized optical coherence tomography (OCT) for real-time monitoring of the laser–skin tissue interaction, sparing the patient from an invasive surgical sampling procedure. The time-dependent OCT intensity variance was used to observe drug diffusion through an induced MAZ array. Subsequently, nails were treated with cream and liquid topical drugs to investigate the feasibility and diffusion efficacy of laser-assisted drug delivery. Our results show that fractional CO2 laser improves the effectiveness of topical drug delivery in the nail plate and that OCT could potentially be used for in vivo monitoring of the depth of laser penetration as well as real-time observations of drug delivery

Two-Level Optical Coherence Tomography Scheme for Suppressing Spectral Saturation Artifacts

We demonstrate a novel method for reducing saturation artifacts in spectral-domain optical coherence tomography (SD-OCT) systems. This method is based on a two-level SD-OCT system with a dual-line charge-coupled device (CCD) camera. We compensate the saturated signal detected by the first line using the unsaturated signal detected by the second line. The Fourier transform of the compensated spectrum shows effective suppression of saturation artifacts. This method was also successfully performed on phantom material and skin on a human finger. Our method causes neither back-scattering power loss nor signal-to-noise ratio (SNR) degradation. The only difference between the traditional system and our two-level system is our utilization of the dual-line CCD camera; no additional devices or complex designs are needed