Interference Minimization in Asymmetric Sensor Networks

A fundamental problem in wireless sensor networks is to connect a given set of sensors while minimizing the \emph{receiver interference}. This is modeled as follows: each sensor node corresponds to a point in $\mathbb{R}^d$ and each \emph{transmission range} corresponds to a ball. The receiver interference of a sensor node is defined as the number of transmission ranges it lies in. Our goal is to choose transmission radii that minimize the maximum interference while maintaining a strongly connected asymmetric communication graph. For the two-dimensional case, we show that it is NP-complete to decide whether one can achieve a receiver interference of at most $5$. In the one-dimensional case, we prove that there are optimal solutions with nontrivial structural properties. These properties can be exploited to obtain an exact algorithm that runs in quasi-polynomial time. This generalizes a result by Tan et al. to the asymmetric case.Comment: 15 pages, 5 figure

Ring -expansion carbonylation of epoxides: development of new catalysts for improved regio- and stereocontrol

Carbon monoxide is arguably one of the most important feedstocks in organic synthesis because it enables the introduction of valuable functional groups in often a mild, efficient, and economical manner. Utilization of this building block in hydroformylation reactions or ring-expansion carbonylation reactions of heterocycles gives rise to value added-products. One transformation of particular importance is the carbonylation of epoxides to ?-lactones. ?-Lactones are a highly versatile set of compounds that can undergo numerous reactions in often a benign and economical fashion, thus giving rise to small molecules such as aldol-type compounds, and polymers such as polyesters. The use of catalysts of the form [Lewis acid]+[Co(CO)4]- have streamlined the synthesis of ?-lactones to a point where implementation on an industrial scale seems feasible. Nonetheless, challenges remain in the conversion of epoxides to ?-lactones using these catalysts. Regioselectivity in the carbonylation of cis- or trans-disubstituted epoxides, and enantioselectivity in general are two largely unsolved synthetic hurdles in this regard and await further exploration. The work presented herein introduces new catalyst design strategies, and implements them in an effort to address these remaining challenges. The result are four new carbonylation catalysts that enable the highly regioselective synthesis of ?-lactones starting from cis- or trans-disubstituted epoxides. The value of the resulting products, and the fact that regioselective ring-opening reactions of disubstituted epoxides have been a long-standing challenge in the field of organic synthesis make this study relevant on both a practical as well as an academic level. In addition to the four catalysts introduced for improved regioselectivity, two more catalysts were synthesized and found to be competent for the formation of highly enantioenriched ?-lactones starting from meso or racemic epoxides. Given the scarcity of catalysts that can affect similar transformations with equally high selectivities, this represents another important step forward in the field of ring-expansion carbonylation reactions. Lastly, the use of carbon monoxide in a more streamlined synthesis of a pharmaceutically relevant class of compounds called ampakines is explored. This new methodology underlines once more the synthetic potential that rests in this building block

Long Plane Trees

In the longest plane spanning tree problem, we are given a finite planar point set ?, and our task is to find a plane (i.e., noncrossing) spanning tree T_OPT for ? with maximum total Euclidean edge length |T_OPT|. Despite more than two decades of research, it remains open if this problem is NP-hard. Thus, previous efforts have focused on polynomial-time algorithms that produce plane trees whose total edge length approximates |T_OPT|. The approximate trees in these algorithms all have small unweighted diameter, typically three or four. It is natural to ask whether this is a common feature of longest plane spanning trees, or an artifact of the specific approximation algorithms. We provide three results to elucidate the interplay between the approximation guarantee and the unweighted diameter of the approximate trees. First, we describe a polynomial-time algorithm to construct a plane tree T_ALG with diameter at most four and |T_ALG| ? 0.546 ? |T_OPT|. This constitutes a substantial improvement over the state of the art. Second, we show that a longest plane tree among those with diameter at most three can be found in polynomial time. Third, for any candidate diameter d ? 3, we provide upper bounds on the approximation factor that can be achieved by a longest plane tree with diameter at most d (compared to a longest plane tree without constraints)

Carbonylation of <i>cis</i>-Disubstituted Epoxides to <i>trans</i>-β-Lactones: Catalysts Displaying Steric and Contrasteric Regioselectivity

<i>trans</i>-β-Lactones are a versatile and useful class of compounds, but reliable methods for their direct synthesis are still limited. Addressing this problem, we present herein two catalysts for the regioselective carbonylation of <i>cis</i>-disubstituted epoxides. The two catalysts show high activities and opposing regioselectivities so that either one of the two possible β-lactone regioisomers can be obtained selectively

Long Plane Trees

In the longest plane spanning tree problem, we are given a finite planar point set P, and our task is to find a plane (i.e., noncrossing) spanning tree TOPT for P with maximum total Euclidean edge length |TOPT|. Despite more than two decades of research, it remains open if this problem is NP-hard. Thus, previous efforts have focused on polynomial-time algorithms that produce plane trees whose total edge length approximates |TOPT|. The approximate trees in these algorithms all have small unweighted diameter, typically three or four. It is natural to ask whether this is a common feature of longest plane spanning trees, or an artifact of the specific approximation algorithms. We provide three results to elucidate the interplay between the approximation guarantee and the unweighted diameter of the approximate trees. First, we describe a polynomial-time algorithm to construct a plane tree TALG with diameter at most four and |TALG| = 0.546 · |TOPT|. This constitutes a substantial improvement over the state of the art. Second, we show that a longest plane tree among those with diameter at most three can be found in polynomial time. Third, for any candidate diameter d = 3, we provide upper bounds on the approximation factor that can be achieved by a longest plane tree with diameter at most d (compared to a longest plane tree without constraints).ISSN:1868-896

Regioselective Carbonylation of <i>trans</i>-Disubstituted Epoxides to β‑Lactones: A Viable Entry into <i>syn</i>-Aldol-Type Products

Two new catalysts are reported for the regioselective carbonylation of <i>trans</i>-disubstituted epoxides to <i>cis</i>-β-lactones. The two catalysts display high and opposing selectivities, which generally are difficult to achieve for this class of epoxides. The resulting β-lactones are well-defined precursors for a wide variety of aldol-type compounds. Altogether, carbonylation of disubstituted epoxides is established as a viable and economical entry into <i>syn</i>- and <i>anti</i>-aldol products

Copolymerization of CO2 and meso epoxides using enantioselective β-diiminate catalysts: a route to highly isotactic polycarbonates

We report a new class of catalysts for the enantioselective copolymerization of CO2 and alicyclic meso epoxides. C1-Symmetric β-diiminate zinc catalysts were designed on the basis of mechanistic information and subsequently optimized using structure–activity relationships and iterative ligand design. The optimized catalysts yield highly isotactic poly(cyclohexene carbonate) and poly(cyclopentene carbonate) with units of up to 94% ee under mild conditions. A diblock copolymer of CO2/cyclohexene oxide and CO2/cyclopentene oxide was synthesized, demonstrating the controlled behaviour of the catalyst. Solid-state structures and solution-state dynamics of the catalyst were studied to explain trends in enantioselectivities and turnover frequencies. A strong correlation between the isotacticity of the polymer and its melting temperature was observed. X-ray powder diffraction was used to measure crystallinity and study the changes in morphology observed upon annealing

Synthesis of Adipic Aldehyde by <i>n</i>‑Selective Hydroformylation of 4‑Pentenal

Several phosphine and phosphite ligands were tested in the hydroformylation of 4-pentenal to adipic aldehyde, a versatile starting material for industrially very relevant compounds. By varying the ligand structure we were able to increase the selectivity toward adipic aldehyde to >95%. Additionally, two molecular structures of important catalytic intermediates [(bisphosphite)­RhH­(CO)₂] and one structure of a previously unknown catalyst decomposition product were obtained

Total Synthesis of Tetrahydrolipstatin and Stereoisomers via a Highly Regio- and Diastereoselective Carbonylation of Epoxyhomoallylic Alcohols

A concise enantioselective synthesis of tetrahydrolipstatin (THL) and seven stereoisomers has been achieved. The synthesis of THL was accomplished in 10 steps and 31% overall yield from an achiral ynone. Key to the success of the approach is the use of a bimetallic [Lewis acid]⁺[Co­(CO)₄]⁻ catalyst for a late-stage regioselective carbonylation of an enantiomerically pure <i>cis</i>-epoxide to a <i>trans</i>-β-lactone. The success of this route to THL and its stereoisomers also demonstrated the practicality of the carbonylation catalyst for complex molecule synthesis as well as its functional group compatibility