On the Fine-Grained Complexity of Small-Size Geometric Set Cover and Discrete k-Center for Small k

We study the time complexity of the discrete k-center problem and related (exact) geometric set cover problems when k or the size of the cover is small. We obtain a plethora of new results: - We give the first subquadratic algorithm for rectilinear discrete 3-center in 2D, running in O?(n^{3/2}) time. - We prove a lower bound of ?(n^{4/3-?}) for rectilinear discrete 3-center in 4D, for any constant ? > 0, under a standard hypothesis about triangle detection in sparse graphs. - Given n points and n weighted axis-aligned unit squares in 2D, we give the first subquadratic algorithm for finding a minimum-weight cover of the points by 3 unit squares, running in O?(n^{8/5}) time. We also prove a lower bound of ?(n^{3/2-?}) for the same problem in 2D, under the well-known APSP Hypothesis. For arbitrary axis-aligned rectangles in 2D, our upper bound is O?(n^{7/4}). - We prove a lower bound of ?(n^{2-?}) for Euclidean discrete 2-center in 13D, under the Hyperclique Hypothesis. This lower bound nearly matches the straightforward upper bound of O?(n^?), if the matrix multiplication exponent ? is equal to 2. - We similarly prove an ?(n^{k-?}) lower bound for Euclidean discrete k-center in O(k) dimensions for any constant k ? 3, under the Hyperclique Hypothesis. This lower bound again nearly matches known upper bounds if ? = 2. - We also prove an ?(n^{2-?}) lower bound for the problem of finding 2 boxes to cover the largest number of points, given n points and n boxes in 12D . This matches the straightforward near-quadratic upper bound

Multivariate Mendelian randomization provides no evidence for causal associations among both psoriasis and psoriatic arthritis, and skin cancer

BackgroundSome retrospective studies reported that psoriasis (PsO) and psoriatic arthritis (PsA) may have been associated with an elevated risk of skin cancer. The causal associations among them remain unclear.ObjectivesTo evaluate the causal association of among both PsO and PsA, and skin cancer.MethodsWe performed large-scale two-sample and Multivariate Mendelian randomization analyses to examine whether there is a causal relationship between PsO and PsA, and skin cancer, encompassing basal cell carcinoma (BCC), cutaneous squamous cell carcinoma (cSCC), and cutaneous melanoma (CM).ResultsGenetically predicted PsO, per log-odds ratio increase, showed no significant association with the risk of BCC, cSCC, and CM. The odds ratios (with corresponding 95% confidence intervals) for BCC, cSCC, and CM were 1.00 (0.99,1.01) (PIvw = 0.990), 0.94(0.89, 1.00) (PIvw = 0.065), and 0.99 (0.98, 1.01) (PIvw = 0.239), respectively. PsA showed a significant association with a decreased risk of BCC, with odds ratios (with corresponding 95% confidence intervals) of 1.00 (1.00, 1.00) (PIvw = 0.214) and 1.00 (1.00, 1.00) (PIvw = 0.477), respectively. Univariate analysis of the FinnGen database demonstrated PsA did exhibit a significant association with the decrease risk of BCC, with an odds ratio of 0.94(0.90,0.99) (PIvw = 0.016). However, this association disappeared after other risk factors were adjusted.ConclusionsOur findings suggest no causal association between PsO and PsA and the genetic risk of skin cancer. Further observational studies are required to elucidate the relationship among PsO, PsA, and skin cancer

Approximation Algorithms for Min-Distance Problems

We study fundamental graph parameters such as the Diameter and Radius in directed graphs, when distances are measured using a somewhat unorthodox but natural measure: the distance between u and v is the minimum of the shortest path distances from u to v and from v to u. The center node in a graph under this measure can for instance represent the optimal location for a hospital to ensure the fastest medical care for everyone, as one can either go to the hospital, or a doctor can be sent to help. By computing All-Pairs Shortest Paths, all pairwise distances and thus the parameters we study can be computed exactly in O~(mn) time for directed graphs on n vertices, m edges and nonnegative edge weights. Furthermore, this time bound is tight under the Strong Exponential Time Hypothesis [Roditty-Vassilevska W. STOC 2013] so it is natural to study how well these parameters can be approximated in O(mn^{1-epsilon}) time for constant epsilon>0. Abboud, Vassilevska Williams, and Wang [SODA 2016] gave a polynomial factor approximation for Diameter and Radius, as well as a constant factor approximation for both problems in the special case where the graph is a DAG. We greatly improve upon these bounds by providing the first constant factor approximations for Diameter, Radius and the related Eccentricities problem in general graphs. Additionally, we provide a hierarchy of algorithms for Diameter that gives a time/accuracy trade-off

Nearly Optimal Separation Between Partially and Fully Retroactive Data Structures

Since the introduction of retroactive data structures at SODA 2004, a major unsolved problem has been to bound the gap between the best partially retroactive data structure (where changes can be made to the past, but only the present can be queried) and the best fully retroactive data structure (where the past can also be queried) for any problem. It was proved in 2004 that any partially retroactive data structure with operation time T_{op}(n,m) can be transformed into a fully retroactive data structure with operation time O(sqrt{m} * T_{op}(n,m)), where n is the size of the data structure and m is the number of operations in the timeline [Demaine et al., 2004]. But it has been open for 14 years whether such a gap is necessary. In this paper, we prove nearly matching upper and lower bounds on this gap for all n and m. We improve the upper bound for n << sqrt m by showing a new transformation with multiplicative overhead n log m. We then prove a lower bound of min {n log m, sqrt m}^{1-o(1)} assuming any of the following conjectures: - Conjecture I: Circuit SAT requires 2^{n - o(n)} time on n-input circuits of size 2^{o(n)}. This conjecture is far weaker than the well-believed SETH conjecture from complexity theory, which asserts that CNF SAT with n variables and O(n) clauses already requires 2^{n-o(n)} time. - Conjecture II: Online (min,+) product between an integer n x n matrix and n vectors requires n^{3 - o(1)} time. This conjecture is weaker than the APSP conjectures widely used in fine-grained complexity. - Conjecture III (3-SUM Conjecture): Given three sets A,B,C of integers, each of size n, deciding whether there exist a in A, b in B, c in C such that a + b + c = 0 requires n^{2 - o(1)} time. This 1995 conjecture [Anka Gajentaan and Mark H. Overmars, 1995] was the first conjecture in fine-grained complexity. Our lower bound construction illustrates an interesting power of fully retroactive queries: they can be used to quickly solve batched pair evaluation. We believe this technique can prove useful for other data structure lower bounds, especially dynamic ones

Thoracic CT radiomics analysis for predicting synchronous brain metastasis in patients with lung cancer

PURPOSE:We aimed to assess the feasibility of radiomics analysis based on non-contrast-enhanced thoracic CT images in predicting synchronous brain metastasis (SBM) in lung cancer patients at initial diagnosis.METHODS:This retrospective study enrolled 371 lung cancer patients (with SBM n=147, without SBM n=224) confirmed by histopathology. Patients were allocated to the training set (n=258) and testing set (n=113). The optimal radiomics features were selected by using the least absolute shrinkage and selection operator (LASSO) algorithm. The radiomics, clinicoradiologic, and combined models were developed to predict SBM using multivariable logistic regression. Then the discrimination ability of the models was assessed. Furthermore, the prediction performance of the abovementioned three models for oligometastatic (1-3 lesions) or multiple (>3 lesions) brain metastases in SBM, metachronous brain metastasis (MBM), and total (SBM and MBM) groups were investigated.RESULTS:Six radiomics features and two clinicoradiologic characteristics were chosen for predicting SBM. Both the radiomics model (area under the receiver operating characteristic curve [AUC] = 0.870 and 0.824 in the training and testing sets, respectively) and the combined model (AUC = 0.912 and 0.859, respectively) presented better predictive ability for SBM than the clinicoradiologic model (AUC = 0.712 and 0.692, respectively). The decision curve analysis (DCA) demonstrated the clinical usefulness of the radiomics-based models. The radiomics model can also be used to predict oligometastatic or multiple brain metastases in SBM, MBM, and total groups (P = .045, P = .022, and P = .030, respectively).CONCLUSION:The radiomics model and the combined model we presented can be used as valuable imaging markers for predicting patients at high risk of SBM at the initial diagnosis of lung cancer. Furthermore, the radiomics model can also be utilized as an indicator for identifying oligometastatic or multiple brain metastases

Broadband enhanced transmission through the stacked metallic multi-layers perforated with coaxial annular apertures

This paper theoretically and experimentally presents a first report on broadband enhanced transmission through stacked metallic multi-layers perforated with coaxial annular apertures (CAAs). Different from previous studies on extraordinary transmission that occurs at a single frequency, the enhanced transmission of our system with two or three metallic layers can span a wide frequency range with a bandwidth about 60% of the central frequency. The phenomena arise from the excitation and hybridization of guided resonance modes in CAAs among different layers. Measured transmission spectra are in good agreement with calculations semi-analytically resolved by modal expansion method.Comment: 9 pages,4 figure

The utility of high-frequency 18 MHz ultrasonography for preoperative evaluation of acral melanoma thickness in Chinese patients

BackgroundDespite the increasing use of preoperative ultrasound evaluation for melanoma, there is limited research on the use of this technique for Acral Melanoma (AM).MethodsThis retrospective study analyzed the electronic medical records of patients who underwent preoperative evaluation for cutaneous melanoma maximum thickness using an 18 MHz probe and histopathological examination between December 2017 and March 2021 at the Department of Dermatology in Xiangya Hospital, Central South University.ResultsA total of 105 patients were included in the study. The mean tumor thickness was 3.9 mm (s.d., 2.3), with 63% of the specimens showing ulceration and 44 patients showing lymph node metastasis. The results showed a good correlation between the high-frequency ultrasonography (HFUS) and histopathological thickness measurements, with a Spearman’s correlation coefficient of 0.83 [(95% CI 0.73–0.90) (P &lt; 0.001)]. The positive predictive value (PPV) of sonography in identifying tumor thickness was also found to be high.ConclusionOur study suggests that high-frequency 18 MHz ultrasonography is an effective tool for the preoperative evaluation of AM thickness. The HFUS measurements correlated well with the histopathological thickness measurements, making it a valuable and reliable method for clinicians to assess the thickness of melanoma lesions preoperatively

<i>Trans</i>-vaccenic acid reprograms CD8⁺ T cells and anti-tumour immunity

Diet-derived nutrients are inextricably linked to human physiology by providing energy and biosynthetic building blocks and by functioning as regulatory molecules. However, the mechanisms by which circulating nutrients in the human body influence specific physiological processes remain largely unknown. Here we use a blood nutrient compound library-based screening approach to demonstrate that dietary trans-vaccenic acid (TVA) directly promotes effector CD8+ T cell function and anti-tumour immunity in vivo. TVA is the predominant form of trans-fatty acids enriched in human milk, but the human body cannot produce TVA endogenously. Circulating TVA in humans is mainly from ruminant-derived foods including beef, lamb and dairy products such as milk and butter, but only around 19% or 12% of dietary TVA is converted to rumenic acid by humans or mice, respectively. Mechanistically, TVA inactivates the cell-surface receptor GPR43, an immunomodulatory G protein-coupled receptor activated by its short-chain fatty acid ligands. TVA thus antagonizes the short-chain fatty acid agonists of GPR43, leading to activation of the cAMP–PKA–CREB axis for enhanced CD8+ T cell function. These findings reveal that diet-derived TVA represents a mechanism for host-extrinsic reprogramming of CD8+ T cells as opposed to the intrahost gut microbiota-derived short-chain fatty acids. TVA thus has translational potential for the treatment of tumours

High-Dimensional Smoothed Entropy Estimation via Dimensionality Reduction

We study the problem of overcoming exponential sample complexity in differential entropy estimation under Gaussian convolutions. Specifically, we consider the estimation of the differential entropy $h(X+Z)$ via $n$ independently and identically distributed samples of $X$, where $X$ and $Z$ are independent $D$-dimensional random variables with $X$ sub-Gaussian with bounded second moment and $Z\sim\mathcal{N}(0,\sigma^2I_D)$. Under the absolute-error loss, the above problem has a parametric estimation rate of $\frac{c^D}{\sqrt{n}}$, which is exponential in data dimension $D$ and often problematic for applications. We overcome this exponential sample complexity by projecting $X$ to a low-dimensional space via principal component analysis (PCA) before the entropy estimation, and show that the asymptotic error overhead vanishes as the unexplained variance of the PCA vanishes. This implies near-optimal performance for inherently low-dimensional structures embedded in high-dimensional spaces, including hidden-layer outputs of deep neural networks (DNN), which can be used to estimate mutual information (MI) in DNNs. We provide numerical results verifying the performance of our PCA approach on Gaussian and spiral data. We also apply our method to analysis of information flow through neural network layers (c.f. information bottleneck), with results measuring mutual information in a noisy fully connected network and a noisy convolutional neural network (CNN) for MNIST classification.Comment: To appear in ISIT 202