Deterministic Impartial Selection with Weights

In the impartial selection problem, a subset of agents up to a fixed size $k$ among a group of $n$ is to be chosen based on votes cast by the agents themselves. A selection mechanism is impartial if no agent can influence its own chance of being selected by changing its vote. It is $\alpha$-optimal if, for every instance, the ratio between the votes received by the selected subset is at least a fraction of $\alpha$ of the votes received by the subset of size $k$ with the highest number of votes. We study deterministic impartial mechanisms in a more general setting with arbitrarily weighted votes and provide the first approximation guarantee, roughly $1/\lceil 2n/k\rceil$. When the number of agents to select is large enough compared to the total number of agents, this yields an improvement on the previously best known approximation ratio of $1/k$ for the unweighted setting. We further show that our mechanism can be adapted to the impartial assignment problem, in which multiple sets of up to $k$ agents are to be selected, with a loss in the approximation ratio of $1/2$.Comment: To appear in the Proceedings of the 19th Conference on Web and Internet Economics (WINE 2023

Improved Approximation Algorithms for the Expanding Search Problem

A searcher faces a graph with edge lengths and vertex weights, initially having explored only a given starting vertex. In each step, the searcher adds an edge to the solution that connects an unexplored vertex to an explored vertex. This requires an amount of time equal to the edge length. The goal is to minimize the weighted sum of the exploration times over all vertices. We show that this problem is hard to approximate and provide algorithms with improved approximation guarantees. For the general case, we give a (2e+?)-approximation for any ? > 0. For the case that all vertices have unit weight, we provide a 2e-approximation. Finally, we provide a PTAS for the case of a Euclidean graph. Previously, for all cases only an 8-approximation was known

Book Embeddings of Nonplanar Graphs with Small Faces in Few Pages

An embedding of a graph in a book, called book embedding, consists of a linear ordering of its vertices along the spine of the book and an assignment of its edges to the pages of the book, so that no two edges on the same page cross. The book thickness of a graph is the minimum number of pages over all its book embeddings. For planar graphs, a fundamental result is due to Yannakakis, who proposed an algorithm to compute embeddings of planar graphs in books with four pages. Our main contribution is a technique that generalizes this result to a much wider family of nonplanar graphs, which is characterized by a biconnected skeleton of crossing-free edges whose faces have bounded degree. Notably, this family includes all 1-planar and all optimal 2-planar graphs as subgraphs. We prove that this family of graphs has bounded book thickness, and as a corollary, we obtain the first constant upper bound for the book thickness of optimal 2-planar graphs

A Chemical and Genetic Approach to the Mode of Action of Fumagillin

SummaryPrevious mode of action studies identified methionine aminopeptidase 2 (MetAP-2) as the target of the antiangiogenic natural product fumagillin and its drug candidate analog, TNP-470. We report here that TNP-470-mediated MetAP-2 inhibition blocks noncanonical Wnt signaling, which plays a critical role in development, cell differentiation, and tumorigenesis. Consistent with this finding, antisense MetAP-2 morpholino oligonucleotide injection in zebrafish embryos phenocopies gastrulation defects seen in noncanonical Wnt5 loss-of-function zebrafish mutants. MetAP-2 inhibition or depletion blocks signaling downstream of the Wnt receptor Frizzled, but upstream of Calmodulin-dependent Kinase II, RhoA, and c-Jun N-terminal Kinase. Moreover, we demonstrate that TNP-470 does not block the canonical Wnt/β-catenin pathway. Thus, TNP-470 selectively regulates noncanonical over canonical Wnt signaling and provides a unique means to explore and dissect the biological systems mediated by these pathways

Enhanced firing of locus coeruleus neurons and SK channel dysfunction are conserved in distinct models of prodromal Parkinson's disease

Parkinson’s disease (PD) is clinically defined by the presence of the cardinal motor symptoms, which are associated with a loss of dopaminergic nigrostriatal neurons in the substantia nigra pars compacta (SNpc). While SNpc neurons serve as the prototypical cell-type to study cellular vulnerability in PD, there is an unmet need to extent our efforts to other neurons at risk. The noradrenergic locus coeruleus (LC) represents one of the first brain structures affected in Parkinson’s disease (PD) and plays not only a crucial role for the evolving non-motor symptomatology, but it is also believed to contribute to disease progression by efferent noradrenergic deficiency. Therefore, we sought to characterize the electrophysiological properties of LC neurons in two distinct PD models: (1) in an in vivo mouse model of focal α-synuclein overexpression; and (2) in an in vitro rotenone-induced PD model. Despite the fundamental differences of these two PD models, α-synuclein overexpression as well as rotenone exposure led to an accelerated autonomous pacemaker frequency of LC neurons, accompanied by severe alterations of the afterhyperpolarization amplitude. On the mechanistic side, we suggest that Ca(2+)-activated K(+) (SK) channels are mediators of the increased LC neuronal excitability, as pharmacological activation of these channels is sufficient to prevent increased LC pacemaking and subsequent neuronal loss in the LC following in vitro rotenone exposure. These findings suggest a role of SK channels in PD by linking α-synuclein- and rotenone-induced changes in LC firing rate to SK channel dysfunction

Neprilysin Is Required for Angiotensin-(1-7)'s Ability to Enhance Insulin Secretion via Its Proteolytic Activity to Generate Angiotensin-(1-2)

Recent work has renewed interest in therapies targeting the renin-angiotensin system (RAS) to improve β-cell function in type 2 diabetes. Studies show that generation of angiotensin-(1–7) by ACE2 and its binding to the Mas receptor (MasR) improves glucose homeostasis, partly by enhancing glucose-stimulated insulin secretion (GSIS). Thus, islet ACE2 upregulation is viewed as a desirable therapeutic goal. Here, we show that, although endogenous islet ACE2 expression is sparse, its inhibition abrogates angiotensin-(1–7)–mediated GSIS. However, a more widely expressed islet peptidase, neprilysin, degrades angiotensin-(1–7) into several peptides. In neprilysin-deficient mouse islets, angiotensin-(1–7) and neprilysin-derived degradation products angiotensin-(1–4), angiotensin-(5–7), and angiotensin-(3–4) failed to enhance GSIS. Conversely, angiotensin-(1–2) enhanced GSIS in both neprilysin-deficient and wild-type islets. Rather than mediating this effect via activation of the G-protein–coupled receptor (GPCR) MasR, angiotensin-(1–2) was found to signal via another GPCR, namely GPCR family C group 6 member A (GPRC6A). In conclusion, in islets, intact angiotensin-(1–7) is not the primary mediator of beneficial effects ascribed to the ACE2/angiotensin-(1–7)/MasR axis. Our findings warrant caution for the concurrent use of angiotensin-(1–7) compounds and neprilysin inhibitors as therapies for diabetes