91 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
Advanced Fabrication Method for the Preparation of MOF Thin Films: Liquid-Phase Epitaxy Approach Meets Spin Coating Method
Here,
we report a new and advanced method for the fabrication of
highly oriented/polycrystalline metalāorganic framework (MOF)
thin films. Building on the attractive features of the liquid-phase
epitaxy (LPE) approach, a facile spin coating method was implemented
to generate MOF thin films in a high-throughput fashion. Advantageously,
this approach offers a great prospective to cost-effectively construct
thin-films with a significantly shortened preparation time and a lessened
chemicals and solvents consumption, as compared to the conventional
LPE-process. Certainly, this new spin-coating approach has been implemented
successfully to construct various MOF thin films, ranging in thickness
from a few micrometers down to the nanometer scale, spanning 2-D and
3-D benchmark MOF materials including Cu<sub>2</sub>(bdc)<sub>2</sub>Ā·<i>x</i>H<sub>2</sub>O, Zn<sub>2</sub>(bdc)<sub>2</sub>Ā·<i>x</i>H<sub>2</sub>O, HKUST-1, and ZIF-8. This
method was appraised and proved effective on a variety of substrates
comprising functionalized gold, silicon, glass, porous stainless steel,
and aluminum oxide. The facile, high-throughput and cost-effective
nature of this approach, coupled with the successful thin film growth
and substrate versatility, represents the next generation of methods
for MOF thin film fabrication. Therefore, paving the way for these
unique MOF materials to address a wide range of challenges in the
areas of sensing devices and membrane technology
Supramolecular Isomers of MetalāOrganic Frameworks Derived from a Partially Flexible Ligand with Distinct Binding Motifs
Three novel metalāorganic
frameworks (MOFs) were isolated
upon reacting heterofunctional ligand 4-(pyrimidin-5-yl)Ābenzoic acid
(4,5-pmbc) with mixed valence CuĀ(I,II) under solvothermal conditions.
X-ray crystal structural analysis reveals that the first compound
is a layered structure composed of one type of inorganic building
block, dinuclear paddlewheel [Cu<sub>2</sub>(O<sub>2</sub>Cā)<sub>4</sub>], which is linked through 4,5-pmbc ligands. The two other
supramolecular isomers are composed of the same CuĀ(II) dinuclear paddlewheel
and a dinuclear Cu<sub>2</sub>I<sub>2</sub> cluster, which are linked
via the 4,5-pmbc linkers to yield two different 3-periodic frameworks
with underlying topologies related to <b>lvt</b> and <b>nbo</b>. The observed structural diversity in these structures is due to
the distinct coordination modes of the two coordinating moieties (the
carboxylate group on the phenyl ring and the N-donor atoms from the
pyrimidine moiety)
Stepwise Transformation of the Molecular Building Blocks in a Porphyrin-Encapsulating MetalāOrganic Material
When
immersed in solutions containing CuĀ(II) cations, the microporous
metalāorganic material <b>P11</b> ([Cd<sub>4</sub>(BPT)<sub>4</sub>]Ā·[CdĀ(C<sub>44</sub>H<sub>36</sub>N<sub>8</sub>)Ā(S)]Ā·[S],
BPT = biphenyl-3,4ā²,5-tricarboxylate) undergoes a transformation
of its [Cd<sub>2</sub>(COO)<sub>6</sub>]<sup>2ā</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 MetalāOrganic Material
When
immersed in solutions containing CuĀ(II) cations, the microporous
metalāorganic material <b>P11</b> ([Cd<sub>4</sub>(BPT)<sub>4</sub>]Ā·[CdĀ(C<sub>44</sub>H<sub>36</sub>N<sub>8</sub>)Ā(S)]Ā·[S],
BPT = biphenyl-3,4ā²,5-tricarboxylate) undergoes a transformation
of its [Cd<sub>2</sub>(COO)<sub>6</sub>]<sup>2ā</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 MetalāOrganic Material
When
immersed in solutions containing CuĀ(II) cations, the microporous
metalāorganic material <b>P11</b> ([Cd<sub>4</sub>(BPT)<sub>4</sub>]Ā·[CdĀ(C<sub>44</sub>H<sub>36</sub>N<sub>8</sub>)Ā(S)]Ā·[S],
BPT = biphenyl-3,4ā²,5-tricarboxylate) undergoes a transformation
of its [Cd<sub>2</sub>(COO)<sub>6</sub>]<sup>2ā</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
A Family of Porous Lonsdaleiteāe Networks Obtained through Pillaring of Decorated KagomeĢ Lattice Sheets
A new and versatile class of metalāorganic
materials (MOMs)
with augmented lonsdaleite-e (<b>lon-e</b>-a) topology is presented
herein. This family of <b>lon-e</b> nets are built by pillaring
of hexagonal two-dimensional kagomeĢ (<b>kag</b>) lattices
constructed from well-known [Zn<sub>2</sub>(CO<sub>2</sub>R)<sub>4</sub>] paddlewheel molecular building blocks (MBBs) connected by 1,3-benzenedicarboxylate
(bdc<sup>2ā</sup>) linkers. The pillars are [Cr<sub>3</sub>(Ī¼<sub>3</sub>-O)Ā(RCO<sub>2</sub>)]<sub>6</sub> trigonal prismatic
primary MBBs decorated by six pyridyl moieties (tp-PMBB-1). The three-fold
symmetry (<i>D</i><sub>3<i>h</i></sub>) of tp-PMBB-1
is complementary with the alternating orientation of the axial sites
of the paddlewheel MBBs and enables triple cross-linking of the <b>kag</b> layers by each pillar. These MOMs represent the first
examples of axial-to-axial pillared undulating <b>kag</b> layers,
and they are readily fine-tuned because the bdc<sup>2ā</sup> moieties can be varied at their 5-position without changing the
overall structure. This <b>lon-e</b> platform possesses functionalized
hexagonal channels since the <b>kag</b> lattices are necessarily
eclipsed. The effects of the substituent at the 5-positions of the
bdc<sup>2ā</sup> linkers upon gas adsorption, particularly
the heats of adsorption of carbon dioxide and methane, were studied
A Family of Porous Lonsdaleiteāe Networks Obtained through Pillaring of Decorated KagomeĢ Lattice Sheets
A new and versatile class of metalāorganic
materials (MOMs)
with augmented lonsdaleite-e (<b>lon-e</b>-a) topology is presented
herein. This family of <b>lon-e</b> nets are built by pillaring
of hexagonal two-dimensional kagomeĢ (<b>kag</b>) lattices
constructed from well-known [Zn<sub>2</sub>(CO<sub>2</sub>R)<sub>4</sub>] paddlewheel molecular building blocks (MBBs) connected by 1,3-benzenedicarboxylate
(bdc<sup>2ā</sup>) linkers. The pillars are [Cr<sub>3</sub>(Ī¼<sub>3</sub>-O)Ā(RCO<sub>2</sub>)]<sub>6</sub> trigonal prismatic
primary MBBs decorated by six pyridyl moieties (tp-PMBB-1). The three-fold
symmetry (<i>D</i><sub>3<i>h</i></sub>) of tp-PMBB-1
is complementary with the alternating orientation of the axial sites
of the paddlewheel MBBs and enables triple cross-linking of the <b>kag</b> layers by each pillar. These MOMs represent the first
examples of axial-to-axial pillared undulating <b>kag</b> layers,
and they are readily fine-tuned because the bdc<sup>2ā</sup> moieties can be varied at their 5-position without changing the
overall structure. This <b>lon-e</b> platform possesses functionalized
hexagonal channels since the <b>kag</b> lattices are necessarily
eclipsed. The effects of the substituent at the 5-positions of the
bdc<sup>2ā</sup> linkers upon gas adsorption, particularly
the heats of adsorption of carbon dioxide and methane, were studied
A Family of Porous Lonsdaleiteāe Networks Obtained through Pillaring of Decorated KagomeĢ Lattice Sheets
A new and versatile class of metalāorganic
materials (MOMs)
with augmented lonsdaleite-e (<b>lon-e</b>-a) topology is presented
herein. This family of <b>lon-e</b> nets are built by pillaring
of hexagonal two-dimensional kagomeĢ (<b>kag</b>) lattices
constructed from well-known [Zn<sub>2</sub>(CO<sub>2</sub>R)<sub>4</sub>] paddlewheel molecular building blocks (MBBs) connected by 1,3-benzenedicarboxylate
(bdc<sup>2ā</sup>) linkers. The pillars are [Cr<sub>3</sub>(Ī¼<sub>3</sub>-O)Ā(RCO<sub>2</sub>)]<sub>6</sub> trigonal prismatic
primary MBBs decorated by six pyridyl moieties (tp-PMBB-1). The three-fold
symmetry (<i>D</i><sub>3<i>h</i></sub>) of tp-PMBB-1
is complementary with the alternating orientation of the axial sites
of the paddlewheel MBBs and enables triple cross-linking of the <b>kag</b> layers by each pillar. These MOMs represent the first
examples of axial-to-axial pillared undulating <b>kag</b> layers,
and they are readily fine-tuned because the bdc<sup>2ā</sup> moieties can be varied at their 5-position without changing the
overall structure. This <b>lon-e</b> platform possesses functionalized
hexagonal channels since the <b>kag</b> lattices are necessarily
eclipsed. The effects of the substituent at the 5-positions of the
bdc<sup>2ā</sup> linkers upon gas adsorption, particularly
the heats of adsorption of carbon dioxide and methane, were studied
A Family of Porous Lonsdaleiteāe Networks Obtained through Pillaring of Decorated KagomeĢ Lattice Sheets
A new and versatile class of metalāorganic
materials (MOMs)
with augmented lonsdaleite-e (<b>lon-e</b>-a) topology is presented
herein. This family of <b>lon-e</b> nets are built by pillaring
of hexagonal two-dimensional kagomeĢ (<b>kag</b>) lattices
constructed from well-known [Zn<sub>2</sub>(CO<sub>2</sub>R)<sub>4</sub>] paddlewheel molecular building blocks (MBBs) connected by 1,3-benzenedicarboxylate
(bdc<sup>2ā</sup>) linkers. The pillars are [Cr<sub>3</sub>(Ī¼<sub>3</sub>-O)Ā(RCO<sub>2</sub>)]<sub>6</sub> trigonal prismatic
primary MBBs decorated by six pyridyl moieties (tp-PMBB-1). The three-fold
symmetry (<i>D</i><sub>3<i>h</i></sub>) of tp-PMBB-1
is complementary with the alternating orientation of the axial sites
of the paddlewheel MBBs and enables triple cross-linking of the <b>kag</b> layers by each pillar. These MOMs represent the first
examples of axial-to-axial pillared undulating <b>kag</b> layers,
and they are readily fine-tuned because the bdc<sup>2ā</sup> moieties can be varied at their 5-position without changing the
overall structure. This <b>lon-e</b> platform possesses functionalized
hexagonal channels since the <b>kag</b> lattices are necessarily
eclipsed. The effects of the substituent at the 5-positions of the
bdc<sup>2ā</sup> linkers upon gas adsorption, particularly
the heats of adsorption of carbon dioxide and methane, were studied
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