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1. Recent Advances in Dual Triplet Ketone/Transition-Metal Catalysis

   https://doi.org/10.1055/s-0042-1751444  

   Iziumchenko, Valeriia; Gevorgyan, Vladimir (July 2023, Synlett)

   Abstract Dual light-excited ketone/transition-metal catalysis is a rapidly developing field of photochemistry. It allows for versatile functionalizations of C–H or C–X bonds enabled by triplet ketone acting as a hydrogen-atom-abstracting agent, a single-electron acceptor, or a photosensitizer. This review summarizes recent developments of synthetically useful transformations promoted by the synergy between triplet ketone and transition-metal catalysis. 1 Introduction 2 Triplet Ketone Catalysis via Hydrogen Atom Transfer 2.1 Triplet Ketones with Nickel Catalysis 2.2 Triplet Ketones with Copper Catalysis 2.3 Triplet Ketones with Other Transition-Metal Catalysis 3 Triplet Ketone Catalysis via Single-Electron Transfer 4 Triplet Ketone Catalysis via Energy Transfer 5 Conclusions 

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2. Averages Along the Primes: Improving and Sparse Bounds

   https://doi.org/10.1515/conop-2020-0003  

   Han, Rui; Krause, Ben; Lacey, Michael T.; Yang, Fan (February 2020, Concrete Operators)

   Abstract Consider averages along the prime integers ℙ given by {\mathcal{A}_N}f(x) = {N^{ - 1}}\sum\limits_{p \in \mathbb{P}:p \le N} {(\log p)f(x - p).} These averages satisfy a uniform scale-free ℓ p -improving estimate. For all 1 < p < 2, there is a constant C p so that for all integer N and functions f supported on [0, N ], there holds {N^{ - 1/p'}}{\left\| {{\mathcal{A}_N}f} \right\|_{\ell p'}} \le {C_p}{N^{ - 1/p}}{\left\| f \right\|_{\ell p}}. The maximal function 𝒜 * f = sup N |𝒜 N f | satisfies ( p , p ) sparse bounds for all 1 < p < 2. The latter are the natural variants of the scale-free bounds. As a corollary, 𝒜 * is bounded on ℓ p ( w ), for all weights w in the Muckenhoupt 𝒜 p class. No prior weighted inequalities for 𝒜 * were known. 

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3. Advances in Selected Heterocyclization Methods

   https://doi.org/10.1055/s-0042-1751429  

   Rivas, Mónica; Gevorgyan, Vladimir (July 2023, Synlett)

   Abstract This Account summarizes efforts in our group toward synthesis of heterocycles in the past decade. Selected examples of transannulative heterocyclizations, intermediate construction of reactive compounds en route to these important motifs, and newer developments of a radical approach are outlined. 1 Introduction 2 Transannulative Heterocyclization 2.1 Rhodium-Catalyzed Transannulative Heterocyclization 2.2 Copper-Catalyzed Transannulative Heterocyclization 3 Synthesis of Heterocycles from Reactive Precursors 3.1 Synthesis of Heterocycles from Diazo Compounds 3.2 Synthesis of Heterocycles from Alkynones 4 Radical Heterocyclization 4.1 Light-Induced Radical Heterocyclization 4.2 Light-Free Radical Heterocyclization 7 Conclusion 

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4. Ni- and Pd-Catalyzed Enantioselective 1,2-Dicarbofunctionalization of Alkenes

   https://doi.org/10.1055/a-2108-9549  

   Kang, Taeho; Apolinar, Omar; Engle, Keary M (December 2023, Synthesis)

   Abstract Catalytic enantioselective 1,2-dicarbofunctionalization (1,2-DCF) of alkenes is a powerful transformation of growing importance in organic synthesis for constructing chiral building blocks, bioactive molecules, and agrochemicals. Both in a two- and three-component context, this family of reactions generates densely functionalized, structurally complex products in a single step. Across several distinct mechanistic pathways at play in these transformations with nickel or palladium catalysts, stereocontrol can be obtained through tailored chiral ligands. In this Review we discuss the various strategies, mechanisms, and catalysts that have been applied to achieve enantioinduction in alkene 1,2-DCF. 1 Introduction 2 Two-Component Enantioselective 1,2-DCF via Migratory Insertion 3 Two-Component Enantioselective 1,2-DCF via Radical Capture 4 Three-Component Enantioselective 1,2-DCF via Radical Capture 5 Three-Component Enantioselective 1,2-DCF via Migratory Insertion 6 Miscellaneous Mechanisms 7 Conclusion 

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5. A deterministic near-linear time approximation scheme for geometric transportation

   https://doi.org/10.1109/FOCS57990.2023.00078  

   Fox, Emily; Lu, Jiashuai (November 2023, IEEE)

   Given a set of points $$P = (P^+ \sqcup P^-) \subset \mathbb{R}^d$$ for some constant $$d$$ and a supply function $$\mu:P\to \mathbb{R}$$ such that $$\mu(p) > 0~\forall p \in P^+$$, $$\mu(p) < 0~\forall p \in P^-$$, and $$\sum_{p\in P}{\mu(p)} = 0$$, the geometric transportation problem asks one to find a transportation map $$\tau: P^+\times P^-\to \mathbb{R}_{\ge 0}$$ such that $$\sum_{q\in P^-}{\tau(p, q)} = \mu(p)~\forall p \in P^+$$, $$\sum_{p\in P^+}{\tau(p, q)} = -\mu(q) \forall q \in P^-$$, and the weighted sum of Euclidean distances for the pairs $$\sum_{(p,q)\in P^+\times P^-}\tau(p, q)\cdot ||q-p||_2$$ is minimized. We present the first deterministic algorithm that computes, in near-linear time, a transportation map whose cost is within a $$(1 + \varepsilon)$$ factor of optimal. More precisely, our algorithm runs in $$O(n\varepsilon^{-(d+2)}\log^5{n}\log{\log{n}})$$ time for any constant $$\varepsilon > 0$$. While a randomized $$n\varepsilon^{-O(d)}\log^{O(d)}{n}$$ time algorithm for this problem was discovered in the last few years, all previously known deterministic $$(1 + \varepsilon)$$-approximation algorithms run in~$$\Omega(n^{3/2})$$ time. A similar situation existed for geometric bipartite matching, the special case of geometric transportation where all supplies are unit, until a deterministic $$n\varepsilon^{-O(d)}\log^{O(d)}{n}$$ time $$(1 + \varepsilon)$$-approximation algorithm was presented at STOC 2022. Surprisingly, our result is not only a generalization of the bipartite matching one to arbitrary instances of geometric transportation, but it also reduces the running time for all previously known $$(1 + \varepsilon)$$-approximation algorithms, randomized or deterministic, even for geometric bipartite matching. In particular, we give the first $$(1 + \varepsilon)$$-approximate deterministic algorithm for geometric bipartite matching and the first $$(1 + \varepsilon)$$-approximate deterministic or randomized algorithm for geometric transportation with no dependence on $$d$$ in the exponent of the running time's polylog. As an additional application of our main ideas, we also give the first randomized near-linear $$O(\varepsilon^{-2} m \log^{O(1)} n)$$ time $$(1 + \varepsilon)$$-approximation algorithm for the uncapacitated minimum cost flow (transshipment) problem in undirected graphs with arbitrary \emph{real} edge costs. 

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