55 research outputs found
Robust Stackelberg Equilibria in Extensive-Form Games and Extension to Limited Lookahead
Stackelberg equilibria have become increasingly important as a solution
concept in computational game theory, largely inspired by practical problems
such as security settings. In practice, however, there is typically uncertainty
regarding the model about the opponent. This paper is, to our knowledge, the
first to investigate Stackelberg equilibria under uncertainty in extensive-form
games, one of the broadest classes of game. We introduce robust Stackelberg
equilibria, where the uncertainty is about the opponent's payoffs, as well as
ones where the opponent has limited lookahead and the uncertainty is about the
opponent's node evaluation function. We develop a new mixed-integer program for
the deterministic limited-lookahead setting. We then extend the program to the
robust setting for Stackelberg equilibrium under unlimited and under limited
lookahead by the opponent. We show that for the specific case of interval
uncertainty about the opponent's payoffs (or about the opponent's node
evaluations in the case of limited lookahead), robust Stackelberg equilibria
can be computed with a mixed-integer program that is of the same asymptotic
size as that for the deterministic setting.Comment: Published at AAAI1
Mimic Carbonic Anhydrase Using Metal–Organic Frameworks for CO<sub>2</sub> Capture and Conversion
Carbonic anhydrase
(CA) is a zinc-containing metalloprotein, in which the Zn active center
plays the key role to transform CO<sub>2</sub> into carbonate. Inspired
by nature, herein we used metal–organic frameworks (MOFs) to
mimic CA for CO<sub>2</sub> conversion, on the basis of the structural
similarity between the Zn coordination in MOFs and CA active center.
The biomimetic activity of MOFs was investigated by detecting the
hydrolysis of <i>para</i>-nitrophenyl acetate, which is
a model reaction used to evaluate CA activity. The biomimetic materials
(e.g., CFA-1) showed good catalytic activity, and excellent reusability,
and solvent and thermal stability, which is very important for practical
applications. In addition, ZIF-100 and CFA-1 were used to mimic CA
to convert CO<sub>2</sub> gas, and exhibited good efficiency on CO<sub>2</sub> conversion compared with those of other porous materials
(e.g., MCM-41, active carbon). This biomimetic study revealed a novel
CO<sub>2</sub> treatment method. Instead of simply using MOFs to absorb
CO<sub>2</sub>, ZIF-100 and CFA-1 were used to mimic CA for in situ
CO<sub>2</sub> conversion, which provides a new prospect in the biological
and industrial applications of MOFs
Three Porphyrin-Encapsulating Metal–Organic Materials with Ordered Metalloporphyrin Moieties
1,3,5-benzenetricarboxylate, biphenyl-3,4′,5-tricarboxylate,
and [1,1′:3′,1″-terphenyl]-4,4″,5′-tricarboxylate
react with CdÂ(II) cations in the presence of meso-tetraÂ(<i>N</i>-methyl-4-pyridyl) porphine cations to afford three metalloporphyrin-encapsulating
metal–organic materials, <b>porph@MOM-11</b>, <b>-12</b> and <b>-13</b>, respectively. The metalloporphyrin moieties
are ordered within channels and closely fit hexagonal or rectangular
cavities, thereby facilitating a better understanding of the structure-directing
effect that can be promoted by metalloporphyrins. <b>Porph@MOM-12</b> is noteworthy because it exhibits two distinct types of hexagonal
channels and it represents the first example of a net that exhibits <b>mzz</b> topology
Toward “metalloMOFzymes”: Metal–Organic Frameworks with Single-Site Metal Catalysts for Small-Molecule Transformations
Metal–organic frameworks (MOFs)
are being increasingly studied
as scaffolds and supports for catalysis. The solid-state structures
of MOFs, combined with their high porosity, suggest that MOFs may
possess advantages shared by both heterogeneous and homogeneous catalysts,
with few of the shortcomings of either. Herein, efforts to create
single-site catalytic metal centers appended to the organic ligand
struts of MOFs will be discussed. Reactions important for advanced
energy applications, such as H<sub>2</sub> production and CO<sub>2</sub> reduction, will be highlighted. Examining how these active sites
can be introduced, their performance, and their existing limitations
should provide direction for design of the next generation of MOF-based
catalysts for energy-relevant, small-molecule transformations. Finally,
the introduction of second-sphere interactions (e.g., hydrogen bonding
via squaramide groups) as a possible route to enhancing the activity
of these metal centers is reported
Stepwise Transformation of the Molecular Building Blocks in a Porphyrin-Encapsulating Metal–Organic Material
When
immersed in solutions containing CuÂ(II) cations, the microporous
metal–organic material <b>P11</b> ([Cd<sub>4</sub>(BPT)<sub>4</sub>]·[CdÂ(C<sub>44</sub>H<sub>36</sub>N<sub>8</sub>)Â(S)]·[S],
BPT = biphenyl-3,4′,5-tricarboxylate) undergoes a transformation
of its [Cd<sub>2</sub>(COO)<sub>6</sub>]<sup>2–</sup> molecular
building blocks (MBBs) into novel tetranuclear [Cu<sub>4</sub>X<sub>2</sub>(COO)<sub>6</sub>(S)<sub>2</sub>] MBBs to form <b>P11-Cu</b>. The transformation occurs in single-crystal to single-crystal fashion,
and its stepwise mechanism was studied by varying the Cd<sup>2+</sup>/Cu<sup>2+</sup> ratio of the solution in which crystals of <b>P11</b> were immersed. <b>P11-16/1</b> (Cd in framework
retained, Cd in encapsulated porphyrins exchanged) and other intermediate
phases were thereby isolated and structurally characterized. <b>P11-16/1</b> and <b>P11-Cu</b> retain the microporosity
of <b>P11</b>, and the relatively larger MBBs in <b>P11-Cu</b> permit a 20% unit cell expansion and afford a higher surface area
and a larger pore size
Stepwise Transformation of the Molecular Building Blocks in a Porphyrin-Encapsulating Metal–Organic Material
When
immersed in solutions containing CuÂ(II) cations, the microporous
metal–organic material <b>P11</b> ([Cd<sub>4</sub>(BPT)<sub>4</sub>]·[CdÂ(C<sub>44</sub>H<sub>36</sub>N<sub>8</sub>)Â(S)]·[S],
BPT = biphenyl-3,4′,5-tricarboxylate) undergoes a transformation
of its [Cd<sub>2</sub>(COO)<sub>6</sub>]<sup>2–</sup> molecular
building blocks (MBBs) into novel tetranuclear [Cu<sub>4</sub>X<sub>2</sub>(COO)<sub>6</sub>(S)<sub>2</sub>] MBBs to form <b>P11-Cu</b>. The transformation occurs in single-crystal to single-crystal fashion,
and its stepwise mechanism was studied by varying the Cd<sup>2+</sup>/Cu<sup>2+</sup> ratio of the solution in which crystals of <b>P11</b> were immersed. <b>P11-16/1</b> (Cd in framework
retained, Cd in encapsulated porphyrins exchanged) and other intermediate
phases were thereby isolated and structurally characterized. <b>P11-16/1</b> and <b>P11-Cu</b> retain the microporosity
of <b>P11</b>, and the relatively larger MBBs in <b>P11-Cu</b> permit a 20% unit cell expansion and afford a higher surface area
and a larger pore size
Stepwise Transformation of the Molecular Building Blocks in a Porphyrin-Encapsulating Metal–Organic Material
When
immersed in solutions containing CuÂ(II) cations, the microporous
metal–organic material <b>P11</b> ([Cd<sub>4</sub>(BPT)<sub>4</sub>]·[CdÂ(C<sub>44</sub>H<sub>36</sub>N<sub>8</sub>)Â(S)]·[S],
BPT = biphenyl-3,4′,5-tricarboxylate) undergoes a transformation
of its [Cd<sub>2</sub>(COO)<sub>6</sub>]<sup>2–</sup> molecular
building blocks (MBBs) into novel tetranuclear [Cu<sub>4</sub>X<sub>2</sub>(COO)<sub>6</sub>(S)<sub>2</sub>] MBBs to form <b>P11-Cu</b>. The transformation occurs in single-crystal to single-crystal fashion,
and its stepwise mechanism was studied by varying the Cd<sup>2+</sup>/Cu<sup>2+</sup> ratio of the solution in which crystals of <b>P11</b> were immersed. <b>P11-16/1</b> (Cd in framework
retained, Cd in encapsulated porphyrins exchanged) and other intermediate
phases were thereby isolated and structurally characterized. <b>P11-16/1</b> and <b>P11-Cu</b> retain the microporosity
of <b>P11</b>, and the relatively larger MBBs in <b>P11-Cu</b> permit a 20% unit cell expansion and afford a higher surface area
and a larger pore size
Template-Directed Synthesis of Nets Based upon Octahemioctahedral Cages That Encapsulate Catalytically Active Metalloporphyrins
<i>meso</i>-TetraÂ(<i>N</i>-methyl-4-pyridyl)Âporphine
tetratosylate (TMPyP) templates the synthesis of six new metal–organic
materials by the reaction of benzene-1,3,5-tricarboxylate with transition
metals, five of which exhibit HKUST-1 or <b>tbo</b> topology
(M = Fe, Mn, Co, Ni, Mg). The resulting materials, <b>porph@MOMs</b>, selectively encapsulate the corresponding metalloporphyrins in
octahemioctahedral cages and can serve as size-selective heterogeneous
catalysts for oxidation of olefins
Template-Directed Synthesis of Nets Based upon Octahemioctahedral Cages That Encapsulate Catalytically Active Metalloporphyrins
<i>meso</i>-TetraÂ(<i>N</i>-methyl-4-pyridyl)Âporphine
tetratosylate (TMPyP) templates the synthesis of six new metal–organic
materials by the reaction of benzene-1,3,5-tricarboxylate with transition
metals, five of which exhibit HKUST-1 or <b>tbo</b> topology
(M = Fe, Mn, Co, Ni, Mg). The resulting materials, <b>porph@MOMs</b>, selectively encapsulate the corresponding metalloporphyrins in
octahemioctahedral cages and can serve as size-selective heterogeneous
catalysts for oxidation of olefins
Template-Directed Synthesis of Nets Based upon Octahemioctahedral Cages That Encapsulate Catalytically Active Metalloporphyrins
<i>meso</i>-TetraÂ(<i>N</i>-methyl-4-pyridyl)Âporphine
tetratosylate (TMPyP) templates the synthesis of six new metal–organic
materials by the reaction of benzene-1,3,5-tricarboxylate with transition
metals, five of which exhibit HKUST-1 or <b>tbo</b> topology
(M = Fe, Mn, Co, Ni, Mg). The resulting materials, <b>porph@MOMs</b>, selectively encapsulate the corresponding metalloporphyrins in
octahemioctahedral cages and can serve as size-selective heterogeneous
catalysts for oxidation of olefins
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