Fault-tolerant additive weighted geometric spanners

Let S be a set of n points and let w be a function that assigns non-negative weights to points in S. The additive weighted distance d_w(p, q) between two points p,q belonging to S is defined as w(p) + d(p, q) + w(q) if p \ne q and it is zero if p = q. Here, d(p, q) denotes the (geodesic) Euclidean distance between p and q. A graph G(S, E) is called a t-spanner for the additive weighted set S of points if for any two points p and q in S the distance between p and q in graph G is at most t.d_w(p, q) for a real number t > 1. Here, d_w(p,q) is the additive weighted distance between p and q. For some integer k \geq 1, a t-spanner G for the set S is a (k, t)-vertex fault-tolerant additive weighted spanner, denoted with (k, t)-VFTAWS, if for any set S' \subset S with cardinality at most k, the graph G \ S' is a t-spanner for the points in S \ S'. For any given real number \epsilon > 0, we obtain the following results: - When the points in S belong to Euclidean space R^d, an algorithm to compute a (k,(2 + \epsilon))-VFTAWS with O(kn) edges for the metric space (S, d_w). Here, for any two points p, q \in S, d(p, q) is the Euclidean distance between p and q in R^d. - When the points in S belong to a simple polygon P, for the metric space (S, d_w), one algorithm to compute a geodesic (k, (2 + \epsilon))-VFTAWS with O(\frac{k n}{\epsilon^{2}}\lg{n}) edges and another algorithm to compute a geodesic (k, (\sqrt{10} + \epsilon))-VFTAWS with O(kn(\lg{n})^2) edges. Here, for any two points p, q \in S, d(p, q) is the geodesic Euclidean distance along the shortest path between p and q in P. - When the points in $S$ lie on a terrain T, an algorithm to compute a geodesic (k, (2 + \epsilon))-VFTAWS with O(\frac{k n}{\epsilon^{2}}\lg{n}) edges.Comment: a few update

Synthetic, Structural, and Biochemical Studies of Organotin(IV) With Schiff Bases Having Nitrogen and Sulphur Donor Ligands

Three bidentate Schiff bases having nitrogen and sulphur donor sequences were prepared by condensing S-benzyldithiocarbazate (NH(2)NHCS(2)CH(2)C(6)H(5)) with heterocyclic aldehydes. The reaction of diphenyltin dichloride with Schiff bases leads to the formation of a new series of organotin(IV) complexes. An attempt has been made to prove their structures on the basis of elemental analyses, conductance measurements, molecular weights determinations, UV, infrared, and multinuclear magnetic resonance ((1)H, (13)C, and (119)Sn) spectral studies. Organotin(IV) complexes were five- and six-coordinate. Schiff bases and their corresponding organotin complexes have also been screened for their antibacterial and antifungal activities and found to be quite active in this respect

PENGARUH PENGGUNAAN MINYAK KELAPA SAWIT SEBAGAI BAHAN PEMINYAKAN TERHADAP KUALITAS KULIT SAMAK IKAN BANDENG (Chanos chanos Forsk.)

Peminyakan merupakan bagian dari proses penyamakan kulit yang bertujuan untuk menempatkan molekul minyak pada ruang yang terdapat di antara serat-serat kulit dan dapat berfungsi sebagai pelumas sehingga kulit lebih lemas, lunak dan mudah dilekuk-lekukkan. Peminyakan dapat menggunakan berbagai macam minyak, salah satunya yaitu minyak kelapa sawit. Minyak kelapa sawit mampu mengubah kulit yang kasar dan keras menjadi kulit yang lebih lembut. Tujuan dari penelitian ini adalah untuk mengetahui pengaruh penggunaan minyak kelapa sawit terhadap kualitas dari kulit samak ikan Bandeng. Penelitian dilakukan menggunakan konsentrasi minyak 4%, 8% dan 12% dengan tiga kali pengulangan. Hasil penelitian menunjukkan bahwa minyak kelapa sawit dengan konsentrasi berbeda berpengaruh nyata (p<0,05) terhadap kekuatan tarik, kemuluran, kekuatan sobek, dan kadar lemak. Kulit samak ikan Bandeng dengan konsentrasi minyak kelapa sawit 4% merupakan produk yang terbaik dengan kriteria mutu: kekuatan tarik (2003,59 N/cm2 ), kekuatan sobek (325,87 N/cm2 ), kadar lemak (2,97%) dan uji fotomikrograf

Approximate Minimum Diameter

We study the minimum diameter problem for a set of inexact points. By inexact, we mean that the precise location of the points is not known. Instead, the location of each point is restricted to a contineus region (\impre model) or a finite set of points (\indec model). Given a set of inexact points in one of \impre or \indec models, we wish to provide a lower-bound on the diameter of the real points. In the first part of the paper, we focus on \indec model. We present an $O(2^{\frac{1}{\epsilon^d}} \cdot \epsilon^{-2d} \cdot n^3 )$ time approximation algorithm of factor $(1+\epsilon)$ for finding minimum diameter of a set of points in $d$ dimensions. This improves the previously proposed algorithms for this problem substantially. Next, we consider the problem in \impre model. In $d$-dimensional space, we propose a polynomial time $\sqrt{d}$-approximation algorithm. In addition, for $d=2$, we define the notion of $\alpha$-separability and use our algorithm for \indec model to obtain $(1+\epsilon)$-approximation algorithm for a set of $\alpha$-separable regions in time $O(2^{\frac{1}{\epsilon^2}}\allowbreak . \frac{n^3}{\epsilon^{10} .\sin(\alpha/2)^3} )$

A spanner for the day after

We show how to construct (1+ε)-spanner over a set P of n points in Rd that is resilient to a catastrophic failure of nodes. Specifically, for prescribed parameters ϑ,ε∈(0,1), the computed spanner G has O(ε−cϑ−6nlogn(loglogn)6) edges, where c=O(d). Furthermore, for any k, and any deleted set B⊆P of k points, the residual graph G∖B is (1+ε)-spanner for all the points of P except for (1+ϑ)k of them. No previous constructions, beyond the trivial clique with O(n2) edges, were known such that only a tiny additional fraction (i.e., ϑ) lose their distance preserving connectivity.Our construction works by first solving the exact problem in one dimension, and then showing a surprisingly simple and elegant construction in higher dimensions, that uses the one-dimensional construction in a black box fashion

Computing the Similarity Between Moving Curves

In this paper we study similarity measures for moving curves which can, for example, model changing coastlines or retreating glacier termini. Points on a moving curve have two parameters, namely the position along the curve as well as time. We therefore focus on similarity measures for surfaces, specifically the Fr\'echet distance between surfaces. While the Fr\'echet distance between surfaces is not even known to be computable, we show for variants arising in the context of moving curves that they are polynomial-time solvable or NP-complete depending on the restrictions imposed on how the moving curves are matched. We achieve the polynomial-time solutions by a novel approach for computing a surface in the so-called free-space diagram based on max-flow min-cut duality

Magnetic resonance spectroscopy demonstrates neuronal loss and altered glutamatergic neurotransmission in Alzheimer's Disease

BACKGROUND: The role of the anterior cingulate cortex (ACC) is involved in the default mode network during resting state, and is dysfunctional in ageing and Alzheimer’s disease (AD). We used magnetic resonance spectroscopy (MRS) to study the biochemical and metabolite profile in patients with AD, and compared with cognitive-normal healthy controls (HC) with no cognitive complaints …published_or_final_versio

Metabolism of profenofos to 4-bromo-2-chlorophenol, a specific and sensitive exposure biomarker.

Profenofos is a direct acting phosphorothioate organophosphorus (OP) pesticide capable of inhibiting β-esterases such as acetylcholinesterase, butyrylcholinesterase, and carboxylesterase. Profenofos is known to be detoxified to the biologically inactive metabolite, 4-bromo-2-chlorophenol (BCP); however, limited data are available regarding the use of urinary BCP as an exposure biomarker in humans. A pilot study conducted in Egyptian agriculture workers, demonstrated that urinary BCP levels prior to application (3.3-30.0 μg/g creatinine) were elevated to 34.5-3,566 μg/g creatinine during the time workers were applying profenofos to cotton fields. Subsequently, the in vitro enzymatic formation of BCP was examined using pooled human liver microsomes and recombinant human cytochrome P-450s (CYPs) incubated with profenofos. Of the nine human CYPs studied, only CYPs 3A4, 2B6, and 2C19 were able to metabolize profenofos to BCP. Kinetic studies indicated that CYP 2C19 has the lowest Km, 0.516 μM followed by 2B6 (Km=1.02 μM) and 3A4 (Km=18.9μM). The Vmax for BCP formation was 47.9, 25.1, and 19.2 nmol/min/nmol CYP for CYP2B6, 2C19, and 3A4, respectively. Intrinsic clearance (Vmax/Km) values of 48.8, 46.9, and 1.02 ml/min/nmol CYP 2C19, 2B6, and 3A4, respectively, indicate that CYP2C19 and CYP2B6 are primarily responsible for the detoxification of profenofos. These findings support the use of urinary BCP as a biomarker of exposure to profenofos in humans and suggest polymorphisms in CYP 2C19 and CYP 2B6 as potential biomarkers of susceptibility

Fast Locality-Sensitive Hashing Frameworks for Approximate Near Neighbor Search

The Indyk-Motwani Locality-Sensitive Hashing (LSH) framework (STOC 1998) is a general technique for constructing a data structure to answer approximate near neighbor queries by using a distribution $\mathcal{H}$ over locality-sensitive hash functions that partition space. For a collection of $n$ points, after preprocessing, the query time is dominated by $O(n^{\rho} \log n)$ evaluations of hash functions from $\mathcal{H}$ and $O(n^{\rho})$ hash table lookups and distance computations where $\rho \in (0,1)$ is determined by the locality-sensitivity properties of $\mathcal{H}$. It follows from a recent result by Dahlgaard et al. (FOCS 2017) that the number of locality-sensitive hash functions can be reduced to $O(\log^2 n)$, leaving the query time to be dominated by $O(n^{\rho})$ distance computations and $O(n^{\rho} \log n)$ additional word-RAM operations. We state this result as a general framework and provide a simpler analysis showing that the number of lookups and distance computations closely match the Indyk-Motwani framework, making it a viable replacement in practice. Using ideas from another locality-sensitive hashing framework by Andoni and Indyk (SODA 2006) we are able to reduce the number of additional word-RAM operations to $O(n^\rho)$.Comment: 15 pages, 3 figure