An Improved Algorithm for Incremental DFS Tree in Undirected Graphs

Depth first search (DFS) tree is one of the most well-known data structures for designing efficient graph algorithms. Given an undirected graph $G=(V,E)$ with $n$ vertices and $m$ edges, the textbook algorithm takes $O(n+m)$ time to construct a DFS tree. In this paper, we study the problem of maintaining a DFS tree when the graph is undergoing incremental updates. Formally, we show: Given an arbitrary online sequence of edge or vertex insertions, there is an algorithm that reports a DFS tree in $O(n)$ worst case time per operation, and requires $O\left(\min\{m \log n, n^2\}\right)$ preprocessing time. Our result improves the previous $O(n \log^3 n)$ worst case update time algorithm by Baswana et al. and the $O(n \log n)$ time by Nakamura and Sadakane, and matches the trivial $\Omega(n)$ lower bound when it is required to explicitly output a DFS tree. Our result builds on the framework introduced in the breakthrough work by Baswana et al., together with a novel use of a tree-partition lemma by Duan and Zhan, and the celebrated fractional cascading technique by Chazelle and Guibas

Capturing Complementarity in Set Functions by Going Beyond Submodularity/Subadditivity

We introduce two new "degree of complementarity" measures: supermodular width and superadditive width. Both are formulated based on natural witnesses of complementarity. We show that both measures are robust by proving that they, respectively, characterize the gap of monotone set functions from being submodular and subadditive. Thus, they define two new hierarchies over monotone set functions, which we will refer to as Supermodular Width (SMW) hierarchy and Superadditive Width (SAW) hierarchy, with foundations - i.e. level 0 of the hierarchies - resting exactly on submodular and subadditive functions, respectively. We present a comprehensive comparative analysis of the SMW hierarchy and the Supermodular Degree (SD) hierarchy, defined by Feige and Izsak. We prove that the SMW hierarchy is strictly more expressive than the SD hierarchy: Every monotone set function of supermodular degree d has supermodular width at most d, and there exists a supermodular-width-1 function over a ground set of m elements whose supermodular degree is m-1. We show that previous results regarding approximation guarantees for welfare and constrained maximization as well as regarding the Price of Anarchy (PoA) of simple auctions can be extended without any loss from the supermodular degree to the supermodular width. We also establish almost matching information-theoretical lower bounds for these two well-studied fundamental maximization problems over set functions. The combination of these approximation and hardness results illustrate that the SMW hierarchy provides not only a natural notion of complementarity, but also an accurate characterization of "near submodularity" needed for maximization approximation. While SD and SMW hierarchies support nontrivial bounds on the PoA of simple auctions, we show that our SAW hierarchy seems to capture more intrinsic properties needed to realize the efficiency of simple auctions. So far, the SAW hierarchy provides the best dependency for the PoA of Single-bid Auction, and is nearly as competitive as the Maximum over Positive Hypergraphs (MPH) hierarchy for Simultaneous Item First Price Auction (SIA). We also provide almost tight lower bounds for the PoA of both auctions with respect to the SAW hierarchy

Complete Submodularity Characterization in the Comparative Independent Cascade Model

Abstract. We study the propagation of comparative ideas in social network. A full characterization for submodularity in the comparative independent cascade (Com-IC) model of two-idea cascade is given, for competing ideas and complementary ideas respectively. We further introduce One-Shot model where agents show less patience toward ideas, and show that in One-Shot model, only the stronger idea spreads with submodularity

Congenital insensitivity to pain associated with PRDM12 mutation: Two case reports and a literature review

Background:PRDM12 is a newly discovered gene responsible for congenital insensitivity to pain (CIP). Its clinical manifestations are various and not widely known.Methods: The clinical data of two infants diagnosed with CIP associated with PRDM12 mutation were collected. A literature review was performed, and the clinical characteristics of 20 cases diagnosed with a mutation of PRDM12 were summarized and analyzed.Results: Two patients had pain insensitivity, tongue and lip defects, and corneal ulcers. The genomic analysis results showed that variants of PRDM12 were detected in the two families. The case 1 patient carried heterozygous variations of c.682+1G > A and c.502C > T (p.R168C), which were inherited from her father and mother, respectively. We enrolled 22 patients diagnosed with CIP through a literature review together with our cases. There were 16 male (72.7%) and 6 female (27.3%) patients. The age of onset ranged from 6 months to 57 years. The prevalence of clinic manifestation was 14 cases with insensitivity to pain (63.6%), 19 cases with self-mutilation behaviors (86.4%), 11 cases with tongue and lip defects (50%), 5 cases with mid-facial lesions (22.7%), 6 cases with distal phalanx injury (27.3%), 11 cases of recurrent infection (50%), 3 cases (13.6%) with anhidrosis, and 5 cases (22.7%) with global developmental delay. The prevalence of ocular symptoms was 11 cases (50%) with reduced tear secretion, 6 cases (27.3%) with decreased corneal sensitivity, 7 cases (31.8%) with disappeared corneal reflexes, 5.5 cases (25%, 0.5 indicated a single eye) with corneal opacity, 5 cases (22.7%) with corneal ulceration, and 1 case (4.5%) with a corneal scar.Conclusion: The syndrome caused by PRDM12 mutation is a clinically distinct and diagnosable disease that requires joint multidisciplinary management to control the development of the disease and minimize the occurrence of complications

DISQ: Dynamic Iteration Skipping for Variational Quantum Algorithms

This paper proposes DISQ to craft a stable landscape for VQA training and tackle the noise drift challenge. DISQ adopts a "drift detector" with a reference circuit to identify and skip iterations that are severely affected by noise drift errors. Specifically, the circuits from the previous training iteration are re-executed as a reference circuit in the current iteration to estimate noise drift impacts. The iteration is deemed compromised by noise drift errors and thus skipped if noise drift flips the direction of the ideal optimization gradient. To enhance noise drift detection reliability, we further propose to leverage multiple reference circuits from previous iterations to provide a well founded judge of current noise drift. Nevertheless, multiple reference circuits also introduce considerable execution overhead. To mitigate extra overhead, we propose Pauli-term subsetting (prime and minor subsets) to execute only observable circuits with large coefficient magnitudes (prime subset) during drift detection. Only this minor subset is executed when the current iteration is drift-free. Evaluations across various applications and QPUs demonstrate that DISQ can mitigate a significant portion of the noise drift impact on VQAs and achieve 1.51-2.24x fidelity improvement over the traditional baseline. DISQ's benefit is 1.1-1.9x over the best alternative approach while boosting average noise detection speed by 2.07

Role of TNF-α in vascular dysfunction

Healthy vascular function is primarily regulated by several factors including EDRF (endothelium-dependent relaxing factor), EDCF (endothelium-dependent contracting factor) and EDHF (endothelium-dependent hyperpolarizing factor). Vascular dysfunction or injury induced by aging, smoking, inflammation, trauma, hyperlipidaemia and hyperglycaemia are among a myriad of risk factors that may contribute to the pathogenesis of many cardiovascular diseases, such as hypertension, diabetes and atherosclerosis. However, the exact mechanisms underlying the impaired vascular activity remain unresolved and there is no current scientific consensus. Accumulating evidence suggests that the inflammatory cytokine TNF (tumour necrosis factor)-α plays a pivotal role in the disruption of macrovascular and microvascular circulation both in vivo and in vitro. AGEs (advanced glycation end-products)/RAGE (receptor for AGEs), LOX-1 [lectin-like oxidized low-density lipoprotein receptor-1) and NF-κB (nuclear factor κB) signalling play key roles in TNF-α expression through an increase in circulating and/or local vascular TNF-α production. The increase in TNF-α expression induces the production of ROS (reactive oxygen species), resulting in endothelial dysfunction in many pathophysiological conditions. Lipid metabolism, dietary supplements and physical activity affect TNF-α expression. The interaction between TNF-α and stem cells is also important in terms of vascular repair or regeneration. Careful scrutiny of these factors may help elucidate the mechanisms that induce vascular dysfunction. The focus of the present review is to summarize recent evidence showing the role of TNF-α in vascular dysfunction in cardiovascular disease. We believe these findings may prompt new directions for targeting inflammation in future therapies

PEO based polymer-ceramic hybrid solid electrolytes: a review

Compared with traditional lead-acid batteries, nickel–cadmium batteries and nickel-hydrogen batteries, lithium-ion batteries (LIBs) are much more environmentally friendly and much higher energy density. Besides, LIBs own the characteristics of no memory effect, high charging and discharging rate, long cycle life and high energy conversion rate. Therefore, LIBs have been widely considered as the most promising power source for mobile devices. Commonly used LIBs contain carbonate based liquid electrolytes. Such electrolytes own high ionic conductivity and excellent wetting ability. However, the use of highly flammable and volatile organic solvents in them may lead to problems like leakage, thermo runaway and parasitic interface reactions, which limit their application. Solid polymer electrolytes (SPEs) can solve these problems, while they also bring new challenges such as poor interfacial contact with electrodes and low ionic conductivity at room temperature. Many approaches have been tried to solve these problems. This article is divided into three parts to introduce polyethylene oxide (PEO) based polymer-ceramic hybrid solid electrolyte, which is one of the most efficient way to improve the performance of SPEs. The first part focuses on polymer-lithium salt (LiX) matrices, including their ionic conduction mechanism and impact factors for their ionic conductivity. In the second part, the influence of both active and passive ceramic fillers on SPEs are reviewed. In the third part, composite SPEs’ preparation methods, including solvent casting and thermocompression, are introduced and compared. Finally, we propose five key points on how to make composite SPEs with high ionic conductivity for reference

Case Report: Clinical benefit from multi-target tyrosine kinase inhibitor and PARP inhibitor in a patient with cancer of unknown primary with BRCA1 large genomic rearrangement

Background: Cancer of unknown primary (CUP), which accounts for 3%–5% of new cancer cases every year, involves the presence of a type of histologically confirmed metastatic tumors whose primary site cannot be confirmed by conventional diagnostic methods. This difficulty in identifying the primary site means that CUP patients fail to receive precisely targeted therapy. Most patients are treated with empiric chemotherapy, with a median survival of 6 months and even poorer prognosis within an unfavorable subset of CUP.Case report: An 80-year-old woman presented with masses in the abdomen. Following comprehensive imagological and immunohistochemical examinations, she was diagnosed with CUP. She emphatically declined chemotherapy; thus, anlotinib has been administered with patient consent since 02/07/2019, and stable disease (SD) was observed for 2 years. During subsequent treatment, a large genomic rearrangement in BRCA1 was identified in the patient via NGS, and SD was observed for a further 6 months following olaparib treatment. The type of LGR identified in this patient was discovered to be BRCA1 exon 17-18 inversion (inv), which has never been previously reported.Conclusion: For CUP patients, a chemo-free regimen seems to be acceptable as a first-line treatment, and NGS-guided targeted treatment could improve patient outcomes