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At least 55 records · Page 3

Clustering and Cliques in Preferential Attachment Random Graphs with Edge Insertion

In this paper, we investigate the global clustering coefficient (a.k.a transitivity) and clique number of graphs generated by a preferential attachment random graph model with an additional feature of allowing edge connections between existing vertices. Specifically, at each time step t, either a new vertex is added with probability f(t), or an edge is added between two existing vertices with probability 1 – f(t). We establish concentration inequalities for the global clustering and clique number of the resulting graphs under the assumption that f(t) is a regularly varying function at infinity with index of regular variation –$\gamma$, where $\gamma$ $\in$ [0, 1). Finally, we also demonstrate an inverse relation between these two statistics: the clique number is essentially the reciprocal of the global clustering coefficient.

97 MATHEMATICS AND COMPUTING↗

System characterization of positive real conditions

Necessary and sufficient conditions for positive realness in terms of state space matrices are presented under the assumption of complete controllability and complete observability of square systems with independent inputs. As an alternative to the positive real lemma and to the s-domain inequalities, these conditions provide a recursive algorithm for testing positive realness which result in a set of simple algebraic conditions. By relating the positive real property to the associated variational problem, a unified derivation of necessary and sufficient conditions for optimality of both singular and nonsingular problems is derived.

Wang, Q.↗

System characterization of positive real conditions

Necessary and sufficient conditions for positive realness in terms of state space matrices are presented under the assumption of complete controllability and complete observability of square systems with independent inputs. As an alternative to the positive real lemma and to the s-domain inequalities, these conditions provide a recursive algorithm for testing positive realness which results in a set of simple algebraic conditions. By relating the positive real property to the associated variational problem, a unified derivation of necessary and sufficient conditions for optimality of both singular and nonsingular problems is derived.

Wang, Q.↗

State-constrained booster trajectory solutions via finite elements and shooting

This paper presents an extension of a FEM formulation based on variational principles. A general formulation for handling internal boundary conditions and discontinuities in the state equations is presented, and the general formulation is modified for optimal control problems subject to state-variable inequality constraints. Solutions which only touch the state constraint and solutions which have a boundary arc of finite length are considered. Suitable shape and test functions are chosen for a FEM discretization. All element quadrature (equivalent to one-point Gaussian quadrature over each element) may be done in closed form. The final form of the algebraic equations is then derived. A simple state-constrained problem is solved. Then, for a practical application of the use of the FEM formulation, a launch vehicle subject to a dynamic pressure constraint (a first-order state inequality constraint) is solved. The results presented for the launch-vehicle trajectory have some interesting features, including a touch-point solution.

Bless, Robert R.↗

Optimization-based algorithms for nonlinear mechanics and frictional contact

An optimization-based strategy for solving nonlinear mechanics problems is proposed. In contrast to typical nonlinear equation solver algorithms that aim to find zeros in the residual force function, we minimize an energy (or energy-like) function to encourage solutions which are locally stable equilibria. These smooth and potentially non-convex objective functions are minimized using a preconditioned conjugate-gradient trust-region algorithm. Contact is formulated as an inequality constrained minimization problem, and is solved with an augmented Lagrangian algorithm. Friction is included in the approach via a regularized quasi-potential energy, and other dissipative behavior is included through the use of variational constitutive updates. Finally, to accelerate convergence rates for the Lagrange multipliers, we propose a novel multiplier update algorithm utilizing the Fischer-Burmeister function, and demonstrate super-linear solver convergence for some applications.

42 ENGINEERING↗

The near-wake structure of the Atmosphere Explorer C /AE-C/ satellite - A parametric investigation

Measurements of ion current, electron temperature, and values of space potential obtained from the cylindrical electrostatic probe on board the Atmosphere Explorer C (AE-C) satellite were used to examine, in a parametric manner, the angular distribution of charge around the satellite. Interest is focused on nighttime equatorial data in the altitude range 275-620 km, which yields a wide range for the parameter R sub D (the radius of the satellite divided by the ambient value of the Debye lengths), including R sub D greater than 100, which is of practical significance to large space platforms. The variations of normalized ion current in the wake zone of the AE-C satellite appear to display an exponential dependence on R sub D for 'constant' values of other relevant parameters. The angular variations of electron temperature and space potential in the close vicinity of the satellite's surface were examined and compared with results from the Explorer 31 satellite. The variation of the ratio of measured to computed space potential with electron temperature was examined using data from both the AE-C and Explorer 31 satellites. It was found that the ratio is greater than unity. Possible causes for the above inequality are discussed.

Samir, U.↗

On the convergence of difference approximations to scalar conservation laws

A unified treatment is given for time-explicit, two-level, second-order-resolution (SOR), total-variation-diminishing (TVD) approximations to scalar conservation laws. The schemes are assumed only to have conservation form and incremental form. A modified flux and a viscosity coefficient are introduced to obtain results in terms of the latter. The existence of a cell entropy inequality is discussed, and such an equality for all entropies is shown to imply that the scheme is an E scheme on monotone (actually more general) data, hence at most only first-order accurate in general. Convergence for TVD-SOR schemes approximating convex or concave conservation laws is shown by enforcing a single discrete entropy inequality.

Osher, Stanley↗

Inequality in the availability of residential air conditioning across 115 US metropolitan areas

Continued climate change is increasing the frequency, severity, and duration of populations’ high temperature exposures. Indoor cooling is a key adaptation, especially in urban areas, where heat extremes are intensified—the urban heat island effect (UHI)—making residential air conditioning (AC) availability critical to protecting human health. In the United States, the differences in residential AC prevalence from one metropolitan area to another is well understood, but its intra-urban variation is poorly characterized, obscuring neighborhood-scale variability in populations’ heat vulnerability and adaptive capacity. We address this gap by constructing empirically derived probabilities of residential AC for 45,995 census tracts across 115 metropolitan areas. Within cities, AC is unequally distributed, with census tracts in the urban “core” exhibiting systematically lower prevalence than their suburban counterparts. Moreover, this disparity correlates strongly with multiple indicators of social vulnerability and summer daytime surface UHI intensity, highlighting the challenges that vulnerable urban populations face in adapting to climate-change driven heat stress amplification.

54 ENVIRONMENTAL SCIENCES↗

McCormick envelopes in mixed-integer PDE-constrained optimization

McCormick envelopes are a standard tool for deriving convex relaxations of optimization problems that involve polynomial terms. Such McCormick relaxations provide lower bounds, for example, in branch-and-bound procedures for mixed-integer nonlinear programs but have not gained much attention in PDE-constrained optimization so far. This lack of attention may be due to the distributed nature of such problems, which on the one hand leads to infinitely many linear constraints (generally state constraints that may be difficult to handle) in addition to the state equation for a pointwise formulation of the McCormick envelopes and renders bound-tightening procedures that successively improve the resulting convex relaxations computationally intractable. We analyze McCormick envelopes for a model problem class that is governed by a semilinear PDE involving a bilinearity and integrality constraints. We approximate the nonlinearity and in turn the McCormick envelopes by averaging the involved terms over the cells of a partition of the computational domain on which the PDE is defined. This yields convex relaxations that underestimate the original problem up to an a priori error estimate that depends on the mesh size of the discretization. These approximate McCormick relaxations can be improved by means of an optimization-based bound-tightening procedure. We show that their minimizers converge to minimizers to a limit problem with a pointwise formulation of the McCormick envelopes when driving the mesh size to zero. We provide a computational example, for which we certify all of our imposed assumptions. The results point to both the potential of the methodology and the gaps in the research that need to be closed. Our methodology provides a framework first for obtaining pointwise underestimators for nonconvexities and second for approximating them with finitely many linear inequalities in an infinite-dimensional setting.

Approximations and Expansions↗

Global variation of the para hydrogen fraction in Jupiter's atmosphere and implications for dynamics on the outer planets

A detailed analysis of the Voyager infrared spectrometer measurements on Jupiter's atmosphere is presented, and possible implications of para hydrogen disequilibrium for the energetics and dynamics of that atmosphere are examined. The method of data analysis is described, and results for the large scale latitude variation of the para hydrogen fraction are presented. The Jovian results show pronounced latitude variation, and are compared with other parameters including wind fields, thermal structure, and various indicators of atmospheric clouds. The problem of equilibration rate is reexamined, and it is concluded that on Jupiter the equilibration time is longer than the radiative time constant at the level of emission to space, but that this inequality reverses at greater depths. A model for the interaction of fluid motions with the ortho-para conversion process is presented, and a consistent mixing length theory for the reacting ortho-para mixture is developed. Several implications of the Jovian data for atmospheric energetics and stability on the outer planets are presented.

Conrath, B. J.↗

The influence of the great inequality on the secular disturbing function of the planetary system.

This paper derives the contribution by the great inequality to the secular disturbing function of the principal planets. Andoyer's expansion of the planetary disturbing function and von Zeipel's method of eliminating the periodic terms is employed; thereby, the corrected secular disturbing function for the planetary system is derived. The conclusion is drawn that the canonicity of the equations for the secular variation of the heliocentric elements can be preserved if there be retained, in the secular disturbing function, terms only of the second and fourth order relative to the eccentricity and inclinations. The Krylov-Bogoliubov method is suggested for eliminating periodic terms, if it is desired to include the secular perturbations of the fifth and higher order in the heliocentric elements. The additional part of the secular disturbing function derived in this paper can be included in existing theories of the secular effects of principal planets.

Musen, P.↗

N-burn optimal analytic trajectories.

Derivation of N-burn analytic solutions for propellant-optimal transfer trajectories of a vehicle in a vacuum between arbitrary boundary conditions. Variational changes in the desired boundary conditions are expressed, in general, in terms of variational changes in the control vector and in the initial state vector. All coefficient matrices are computed recursively in terms of the analytic matrices established from the subarcs of the N-burn solution. The solution is applicable to shuttle ascent (exoatmospheric), rendezvous, and deorbit problems. Consideration is also given to state-variable and control-variable inequality constraints.

Jezewski, D. J.↗

Expansion and broadening of coronal loop transients - A theoretical explanation

Consequences are examined of the assumption that an observed coronal loop transient is a twisted rope of magnetic-field lines expanding and broadening in the background coronal plasma and magnetic field. It is shown that the expansion can be accounted for by the azimuthal component of the field; the observed broadening of the loop as it moves outward can be accounted for by the longitudinal component of the field. In order to have a net outward force and at the same time avoid a classical pinch (sausage) instability, the two components of the field must satisfy a certain inequality. It is predicted that, as the loop rises, the width (h) of its top portion should vary proportionally with distance (R) from the sun's center. This is in good agreement with measurements that show h is proportional to the 0.8 power of R. The prediction that the radius of curvature of the top portion of the loop should be proportional to R differs from the measured variation. The difference could be accounted for by a drag due to the background coronal field that flattens the loop's top.

Mouschovias, T. CH.↗

Quantum maximin surfaces

We formulate a quantum generalization of maximin surfaces and show that a quantum maximin surface is identical to the minimal quantum extremal surface, introduced in the EW prescription. We discuss various subtleties and complications associated to a maximinimization of the bulk von Neumann entropy due to corners and unboundedness and present arguments that nonetheless a maximinimization of the UV-finite generalized entropy should be well-defined. We give the first general proof that the EW prescription satisfies entanglement wedge nesting and the strong subadditivity inequality. In addition, we apply the quantum maximin technology to prove that recently proposed generalizations of the EW prescription to nonholographic subsystems (including the so-called “quantum extremal islands”) also satisfy entanglement wedge nesting and strong subadditivity. Our results hold in the regime where backreaction of bulk quantum fields can be treated perturbatively in G N h, but we emphasize that they are valid even when gradients of the bulk entropy are of the same order as variations in the area, a regime recently investigated in new models of black hole evaporation in AdS/CFT.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Flutter suppression using eigenspace freedoms to meet requirements

A constrained optimization methodology has been developed which allows specific use of eigensystem freedoms to meet design requirements. A subset of the available eigenvector freedoms was employed. The eigenvector freedoms associated with a particular closed-loop eigenvalue are coefficients of basis vectors which span the subspace in which that closed-loop vector must lie. Design requirements are included as a vector of inequality constraints. The procedure was successfully applied to develop an unscheduled controller which stabilizes symmetric flutter of an aeroelastic vehicle to a dynamic pressure 44 percent above the open-loop flutter point. The design process proceeded from full-state feedback to the inclusion of a full-order observer to the selection of an eighth-order controller which preserved the full-state sensitivity characteristics. Only a subset of the design freedoms was utilized (i.e., assuming full-state feedback only four out of 26 eigenvectors were used, and no variations were made in the closed-loop eigenvalues). Utilization of additional eigensystem freedoms could further improve the controller.

Adams, William M., Jr.↗

Quantifying microbial control of soil organic matter dynamics at macrosystem scales

Soil organic matter (SOM) stocks, decomposition and persistence are largely the product of controls that act locally. Yet the controls are shaped and interact at multiple spatiotemporal scales, from which macrosystem patterns in SOM emerge. Theory on SOM turnover recognizes the resulting spatial and temporal conditionality in the effect sizes of controls that play out across macrosystems, and couples them through evolutionary and community assembly processes. For example, climate history shapes plant functional traits, which in turn interact with contemporary climate to influence SOM dynamics. Selection and assembly also shape the functional traits of soil decomposer communities, but it is less clear how in turn these traits influence temporal macrosystem patterns in SOM turnover. Here, we review evidence that establishes the expectation that selection and assembly should generate decomposer communities across macrosystems that have distinct functional effects on SOM dynamics. Representation of this knowledge in soil biogeochemical models affects the magnitude and direction of projected SOM responses under global change. Yet there is high uncertainty and low confidence in these projections. To address these issues, we make the case that a coordinated set of empirical practices are required which necessitate (1) greater use of statistical approaches in biogeochemistry that are suited to causative inference; (2) long-term, macrosystem-scale, observational and experimental networks to reveal conditionality in effect sizes, and embedded correlation, in controls on SOM turnover; and (3) use of multiple measurement grains to capture local- and macroscale variation in controls and outcomes, to avoid obscuring causative understanding through data aggregation. Here, when employed together, along with process-based models to synthesize knowledge and guide further empirical work, we believe these practices will rapidly advance understanding of microbial controls on SOM and improve carbon cycle projections that guide policies on climate adaptation and mitigation.

59 BASIC BIOLOGICAL SCIENCES↗

Human papillomavirus–associated anal squamous cell carcinoma: sociodemographic, geographic, and county-level economic trends in incidence rates—United States, 2001-2019

Abstract Background Incidence of anal squamous cell carcinoma is increasing, but vaccination against human papillomavirus (HPV) and removal of precancerous anal lesions could prevent new cases. The overall HPV-associated cancer incidence is reported to be higher in rural populations and in counties with lower economic status. We assessed these differences specifically for HPV-associated anal squamous cell carcinoma and described the geographic, county-level economic, and sociodemographic variations in incidence rates and trends. Methods We analyzed data from the US Cancer Statistics to assess age-standardized incidence rates of HPV-associated squamous cell carcinomas among adults aged 18 years and older from 2001 to 2019. We calculated rate ratios and 95% confidence intervals to examine differences in incidence rates. We also quantified changes in incidence rates over time using joinpoint regression. Results From 2001 to 2019, 72 421 new cases of HPV-associated anal squamous cell carcinoma were diagnosed among women (2.8 per 100 000) and 37 147 among men (1.7 per 100 000). Age-standardized incidence rates were higher in the South compared with other census regions and in counties ranked in the bottom 25% and 25%-75% economically than in the top 25%. The overall incidence rate increased in women but remained stable in men during 2009-2019. Incidence rates increased in adults aged 50 years and older but decreased among those aged 40-44 years from 2001 to 2019 in women and from 2007 to 2019 in men. Conclusions There were inequities in HPV-associated anal squamous cell carcinoma incidence by geographic and county-level economic characteristics. Failure to improve vaccine and treatment equity may widen existing disparities.

Oncology↗

Spatial Variation of Fine Particulate Matter Levels in Nairobi Before and During the COVID-19 Curfew: Implications for Environmental Justice

The temporary decrease of fine particulate matter (PM(sub 2.5)) concentrations in many parts of the world due to the COVID-19 lockdown spurred discussions on urban air pollution and health. However there has been little focus on sub-Saharan Africa, as few African cities have air quality monitors and if they do, these data are often not publicly available. Spatial differentials of changes in PM(sub 2.5) concentrations as a result of COVID also remain largely unstudied. To address this gap, we use a serendipitous mobile air quality monitoring deployment of eight Sensirion SPS 30 sensors on motorbikes in the city of Nairobi starting on 16 March 2020, before a COVID-19 curfew was imposed on 25 March and continuing until 5 May 2020. We developed a random-forest model to estimate PM(sub 2.5) surfaces for the entire city of Nairobi before and during the COVID-19 curfew. The highest PM(sub 2.5) concentrations during both periods were observed in the poor neighborhoods of Kariobangi, Mathare, Umoja, and Dandora, located to the east of the city center. Changes in PM(sub 2.5) were heterogeneous over space. PM(sub 2.5) concentrations increased during the curfew in rapidly urbanizing, the lower-middle-class neighborhoods of Kahawa, Kasarani, and Ruaraka, likely because residents switched from LPG to biomass fuels due to loss of income. Our results indicate that COVID-19 and policies to address it may have exacerbated existing air pollution inequalities in the city of Nairobi. The quantitative results are preliminary, due to sampling limitations and measurement uncertainties, as the available data came exclusively from low-cost sensors. This research serves to highlight that spatial data that is essential for understanding structural inequalities reflected in uneven air pollution burdens and differential impacts of events like the COVID pandemic. With the help of carefully deployed low cost sensors with improved spatial sampling and at least one reference-quality monitor for calibration, we can collect data that is critical for developing targeted interventions that address environmental injustice in the African context.

Environmental justice↗