A Nearly Tight Sum-of-Squares Lower Bound for the Planted Clique Problem

We prove that with high probability over the choice of a random graph $G$ from the Erd\H{o}s-R\'enyi distribution $G(n,1/2)$, the $n^{O(d)}$-time degree $d$ Sum-of-Squares semidefinite programming relaxation for the clique problem will give a value of at least $n^{1/2-c(d/\log n)^{1/2}}$ for some constant $c>0$. This yields a nearly tight $n^{1/2 - o(1)}$ bound on the value of this program for any degree $d = o(\log n)$. Moreover we introduce a new framework that we call \emph{pseudo-calibration} to construct Sum of Squares lower bounds. This framework is inspired by taking a computational analog of Bayesian probability theory. It yields a general recipe for constructing good pseudo-distributions (i.e., dual certificates for the Sum-of-Squares semidefinite program), and sheds further light on the ways in which this hierarchy differs from others.Comment: 55 page

A Common Fixed Point of Integral Type Contraction in Generalized Metric Spacess

In this paper, we present a common fixed point theorem for two self-mappings satisfying a contractive condition of integral type in G- metric spaces. Our result generalizes some well-known results

A Fixed Point Theorem for Weakly C - Contraction Mappings of Integral Type

In the present paper, we shall prove a fixed point theorem by using generalized weak C- contraction of integral type. Our result is generalization of  very known results. Key words: Metric space, fixed point, weak C- contraction. AMS Subject Classification: 54H2

Coupled Fixed Point Theorem in Partially Ordered Metric Spaces

The present paper deals with some Coupled fixed point theorem for mapping having mixed monotone property in Partially Ordered Metric space. AMS Subject Classification: 47H10, 54H25. Keywords: fixed point, mixed monotone property,coupled fixed point

[Demo] Low-latency spark queries on updatable data

As data science gets deployed more and more into operational applications, it becomes important for data science frameworks to be able to perform computations in interactive, sub-second time. Indexing and caching are two key techniques that can make interactive query processing on large datasets possible. In this demo, we show the design, implementation and performance of a new indexing abstraction in Apache Spark, called the Indexed DataFrame. This is a cached DataFrame that incorporates an index to support fast lookup and join operations, and supports updates with multi-version concurrency. We demonstrate the Indexed Dataframe on a social network dataset using microbench-marks and real-world graph processing queries, in datasets that are continuously growing

Staged Pullout Testing of Extensible and Inextensible Reinforcements

Disposal of waste material like pond ash is a major concern to environment. One of the possible applications of this type of waste material is to utilize them as backfill material in reinforced earth structures. To proper design of any reinforced earth structure, soil reinforcement interactions are important where shear and pullout are the most common internal failure modes. Pullout parameters have an important role in design of reinforced earth structure and to determine these parameters pullout test has been carried out at different samples. In this study it is proposed to use pond ash and sand as a backfill material so, this study is carried out to determine the axial pullout resistance of smooth metal strip reinforcement and geogrids. Pond ash from Narla Tarato thermal plant, Vijaywada, Andhra Pradesh has been used. Here, a new test method has been developed named as staged pullout test (SPOT) where a model ground can be tested for two or more than two normal stress conditions. SPOT has advantage over conventional pullout test (CPOT) because CPOT requires three or more model ground to get the pullout properties and it is very difficult to maintain same properties for each model ground while for SPOT only one ground has been used to get the pullout properties. In the SPOT, normal loads are in staged condition or changing the normal load after stopping the test when pullout displacement reaches to 20 mm. In order to investigate the SPOT method, both CPOT and SPOT have been performed on the same model ground and results have been compared. From the comparison, SPOT results of smooth metal strip reinforcement were found to be closer with CPOT results for 17 kPa and 52 kPa while for 87 kPa SPOT results can be used with a factor of safety of 1.2. It has been also observed that SPOT results produce comparable results with CPOT for first 20 mm displacement irrespective of the reinforcement. For geogrids, logarithmic fitted test results are differ by less than 10% for first 20 mm displacement and 15-20% for remaining displacement up to 60 mm. The percentage change for logarithmic fitted results is going to higher when moving to higher normal stress conditions. So, SPOT method could be used instead of CPOT with a factor of safety of 1.2 to 1.3. From the results, SPOT has a probability to be used as a new pullout test method instead of CPOT

Sexual Identity Continuity and Change in a U.S. National Probability Sample of Sexual Minority Adults: Associations With Mental Health and Problematic Substance Use

OBJECTIVE: Sexual minority disparities in behavioral health (e.g., mental health and substance use) are well-established. However, sexual identity is dynamic, and changes are common across the life course (e.g., identifying with a monosexual [lesbian or gay] label and later with a plurisexual [queer, pansexual, etc.] label). This study assessed whether behavioral health risks coincide with sexual identity change among sexual minority people. METHODS: Associations in a 3-year U.S. national probability sample of sexual minority adults were assessed between sexual minority identity change (consistently monosexual [N=400; 44.3% weighted], consistently plurisexual [N=239; 46.7% weighted], monosexual to plurisexual [N=19; 4.2% weighted], and plurisexual to monosexual [N=25; 4.8% weighted]) and five behavioral health indicators (psychological distress, social well-being, number of poor mental health days in the past month, problematic alcohol use, and problematic use of other drugs), controlling for demographic characteristics and baseline behavioral health. RESULTS: Among female participants, monosexual-to-plurisexual identity change (vs. consistently monosexual identity) was associated with greater psychological distress (B=3.41, SE=1.13), lower social well-being (B=-0.61, SE=0.25), and more days of poor mental health in the past month (B=0.69 [Bexp=1.99], SE=0.23). Among male participants, plurisexual-to-monosexual identity change (vs. consistently plurisexual identity) was associated with lower social well-being (B=-0.56, SE=0.25), and identity change (regardless of type) was generally associated with increased problematic use of alcohol and other drugs. CONCLUSIONS: Sexual identity change is an important consideration for sexual minority behavioral health research, with changes (vs. consistency) in identity being an important risk factor for compromised behavioral health. Prevention and treatment interventions may need to tailor messaging to sexual minority men and women differently

Equivariant Neural Networks Utilizing Molecular Clusters for Accurate Molecular Crystal Lattice Energy Predictions

Equivariant neural networks have emerged as prominent models in advancing the construction of interatomic potentials due to their remarkable data efficiency and generalization capabilities for out-of-distribution data. Here, we expand the utility of these networks to the prediction of crystal structures consisting of organic molecules. Traditional methods for computing crystal structure properties, such as plane-wave quantum chemical methods based on density functional theory (DFT), are prohibitively resource-intensive, often necessitating compromises in accuracy and the choice of exchange-correlation functional. We present an approach that leverages the efficiency, and transferability of equivariant neural networks, specifically Allegro, to predict molecular crystal structure energies at a reduced computational cost. Our neural network is trained on molecular clusters using a highly accurate Gaussian-type orbital (GTO)-based method as the target level of theory, eliminating the need for costly periodic DFT calculations, while providing access to all families of exchange-corelation functionals and post-Hartree-Fock methods. The trained model exhibits remarkable accuracy in predicting lattice energies, aligning closely with those computed by plane-wave based DFT methods, thus representing significant cost reductions. Furthermore, the Allegro network was seamlessly integrated with the USPEX framework, accelerating the discovery of low-energy crystal structures during crystal structure prediction

CryoEM structure of the Vibrio cholerae Type IV competence pilus secretin PilQ

Natural transformation is the process by which bacteria take up genetic material from their environment and integrate it into their genome by homologous recombination. It represents one mode of horizontal gene transfer and contributes to the spread of traits like antibiotic resistance. In Vibrio cholerae, the Type IV competence pilus is thought to facilitate natural transformation by extending from the cell surface, binding to exogenous DNA, and retracting to thread this DNA through the outer membrane secretin, PilQ. A lack of structural information has hindered our understanding of this process, however. Here, we solved the first ever high-resolution structure of a Type IV competence pilus secretin. A functional tagged allele of VcPilQ purified from native V. cholerae cells was used to determine the cryoEM structure of the PilQ secretin in amphipol to ~2.7 Å. This structure highlights for the first time key differences in the architecture of the Type IV competence pilus secretin from the Type II and Type III Secretin System secretins. Based on our cryoEM structure, we designed a series of mutants to interrogate the mechanism of PilQ. These experiments provide insight into the channel that DNA likely traverses to promote the spread of antibiotic resistance via horizontal gene transfer by natural transformation. We prove that it is possible to reduce pilus biogenesis and natural transformation by sealing the gate, suggesting VcPilQ as a new drug target