Intersection Graph of a Module

Let $V$ be a left $R$-module where $R$ is a (not necessarily commutative) ring with unit. The intersection graph \cG(V) of proper $R$-submodules of $V$ is an undirected graph without loops and multiple edges defined as follows: the vertex set is the set of all proper $R$-submodules of $V,$ and there is an edge between two distinct vertices $U$ and $W$ if and only if $U\cap W\neq 0.$ We study these graphs to relate the combinatorial properties of \cG(V) to the algebraic properties of the $R$-module $V.$ We study connectedness, domination, finiteness, coloring, and planarity for \cG (V). For instance, we find the domination number of \cG (V). We also find the chromatic number of \cG(V) in some cases. Furthermore, we study cycles in \cG(V), and complete subgraphs in \cG (V) determining the structure of $V$ for which \cG(V) is planar

Earlier emergence of a temperature response to mitigation by filtering annual variability

The rate of global surface warming is crucial for tracking progress towards global climate targets, but is strongly influenced by interannual-to-decadal variability, which precludes rapid detection of the temperature response to emission mitigation. Here we use a physics based Green's function approach to filter out modulations to global mean surface temperature from sea-surface temperature (SST) patterns, and show that it results in an earlier emergence of a response to strong emissions mitigation. For observed temperatures, we find a filtered 2011-2020 surface warming rate of 0.24 °C per decade, consistent with long-term trends. Unfiltered observations show 0.35 °C per decade, partly due to the El Nino of 2015-2016. Pattern filtered warming rates can become a strong tool for the climate community to inform policy makers and stakeholder communities about the ongoing and expected climate responses to emission reductions, provided an effort is made to improve and validate standardized Green's functions. © 2022. The Author(s)

A Survey on Approximation Mechanism Design without Money for Facility Games

In a facility game one or more facilities are placed in a metric space to serve a set of selfish agents whose addresses are their private information. In a classical facility game, each agent wants to be as close to a facility as possible, and the cost of an agent can be defined as the distance between her location and the closest facility. In an obnoxious facility game, each agent wants to be far away from all facilities, and her utility is the distance from her location to the facility set. The objective of each agent is to minimize her cost or maximize her utility. An agent may lie if, by doing so, more benefit can be obtained. We are interested in social choice mechanisms that do not utilize payments. The game designer aims at a mechanism that is strategy-proof, in the sense that any agent cannot benefit by misreporting her address, or, even better, group strategy-proof, in the sense that any coalition of agents cannot all benefit by lying. Meanwhile, it is desirable to have the mechanism to be approximately optimal with respect to a chosen objective function. Several models for such approximation mechanism design without money for facility games have been proposed. In this paper we briefly review these models and related results for both deterministic and randomized mechanisms, and meanwhile we present a general framework for approximation mechanism design without money for facility games

Do evolutionary algorithms indeed require random numbers? Extended study

An inherent part of evolutionary algorithms, that are based on Darwin theory of evolution and Mendel theory of genetic heritage, are random processes. In this participation, we discuss whether are random processes really needed in evolutionary algorithms. We use n periodic deterministic processes instead of random number generators and compare performance of evolutionary algorithms powered by those processes and by pseudo-random number generators. Deterministic processes used in this participation are based on deterministic chaos and are used to generate periodical series with different length. Results presented here are numerical demonstration rather than mathematical proofs. We propose that a certain class of deterministic processes can be used instead of random number generators without lowering of evolutionary algorithms performance. © Springer International Publishing Switzerland 2013

Theory of differential inclusions and its application in mechanics

The following chapter deals with systems of differential equations with discontinuous right-hand sides. The key question is how to define the solutions of such systems. The most adequate approach is to treat discontinuous systems as systems with multivalued right-hand sides (differential inclusions). In this work three well-known definitions of solution of discontinuous system are considered. We will demonstrate the difference between these definitions and their application to different mechanical problems. Mathematical models of drilling systems with discontinuous friction torque characteristics are considered. Here, opposite to classical Coulomb symmetric friction law, the friction torque characteristic is asymmetrical. Problem of sudden load change is studied. Analytical methods of investigation of systems with such asymmetrical friction based on the use of Lyapunov functions are demonstrated. The Watt governor and Chua system are considered to show different aspects of computer modeling of discontinuous systems

A large ozone-circulation feedback and its implications for global warming assessments.

State-of-the-art climate models now include more climate processes which are simulated at higher spatial resolution than ever1. Nevertheless, some processes, such as atmospheric chemical feedbacks, are still computationally expensive and are often ignored in climate simulations1,2. Here we present evidence that how stratospheric ozone is represented in climate models can have a first order impact on estimates of effective climate sensitivity. Using a comprehensive atmosphere-ocean chemistry-climate model, we find an increase in global mean surface warming of around 1°C (~20%) after 75 years when ozone is prescribed at pre-industrial levels compared with when it is allowed to evolve self-consistently in response to an abrupt 4×CO2 forcing. The difference is primarily attributed to changes in longwave radiative feedbacks associated with circulation-driven decreases in tropical lower stratospheric ozone and related stratospheric water vapour and cirrus cloud changes. This has important implications for global model intercomparison studies1,2 in which participating models often use simplified treatments of atmospheric composition changes that are neither consistent with the specified greenhouse gas forcing scenario nor with the associated atmospheric circulation feedbacks3-5.We thank the European Research Council for funding through the ACCI project, project number 267760. The model development was part of the QESM-ESM project supported by the UK Natural Environment Research Council (NERC) under contract numbers RH/H10/19 and R8/H12/124. We acknowledge use of the MONSooN system, a collaborative facility supplied under the Joint Weather and Climate Research Programme, which is a strategic partnership between the UK Met Office and NERC. A.C.M. acknowledges support from an AXA Postdoctoral Research Fellowship.This is the accepted manuscript. The final version is available from Nature Publishing at http://www.nature.com/nclimate/journal/v5/n1/full/nclimate2451.html

An Integrated TCGA Pan-Cancer Clinical Data Resource to Drive High-Quality Survival Outcome Analytics

For a decade, The Cancer Genome Atlas (TCGA) program collected clinicopathologic annotation data along with multi-platform molecular profiles of more than 11,000 human tumors across 33 different cancer types. TCGA clinical data contain key features representing the democratized nature of the data collection process. To ensure proper use of this large clinical dataset associated with genomic features, we developed a standardized dataset named the TCGA Pan-Cancer Clinical Data Resource (TCGA-CDR), which includes four major clinical outcome endpoints. In addition to detailing major challenges and statistical limitations encountered during the effort of integrating the acquired clinical data, we present a summary that includes endpoint usage recommendations for each cancer type. These TCGA-CDR findings appear to be consistent with cancer genomics studies independent of the TCGA effort and provide opportunities for investigating cancer biology using clinical correlates at an unprecedented scale. Analysis of clinicopathologic annotations for over 11,000 cancer patients in the TCGA program leads to the generation of TCGA Clinical Data Resource, which provides recommendations of clinical outcome endpoint usage for 33 cancer types