Decay Conditions Research Articles

Dimension-Free Empirical Entropy Estimation

We seek an entropy estimator for discrete distributions with fully empirical accuracy bounds. As stated, this goal is infeasible without some prior assumptions on the distribution. We discover that a certain information moment assumption renders the problem feasible. We argue that the moment assumption is natural and, in some sense, {\em minimalistic} -- weaker than finite support or tail decay conditions. Under the moment assumption, we provide the first finite-sample entropy estimates for infinite alphabets, nearly recovering the known minimax rates. Moreover, we demonstrate that our empirical bounds are significantly sharper than the state-of-the-art bounds, for various natural distributions and non-trivial sample regimes. Along the way, we give a dimension-free analogue of the Cover-Thomas result on entropy continuity (with respect to total variation distance) for finite alphabets, which may be of independent interest.

Long-range scattering for a critical homogeneous type nonlinear Schrödinger equation with time-decaying harmonic potentials

This paper is concerned with the final state problem for the homogeneous type nonlinear Schrödinger equation with time-decaying harmonic potentials. The nonlinearity has the critical order and is not necessarily the form of a polynomial. In the case of the gauge-invariant power-type nonlinearity, the first author proves that the equation admits a nontrivial solution that behaves like a free solution with a logarithmic phase correction in [22]. In this paper, we extend his result into the case with the general homogeneous nonlinearity by the technique due to the Fourier series expansion introduced by Masaki and the second author [26]. To adapt the argument in the aforementioned paper, we develop a factorization identity for the propagator and require a little stronger decay condition for the Fourier coefficients arising from the harmonic potential. Moreover, in two or three dimensions, we improve the regularity condition of the final data in [26,29].

Climate and air pollution impacts of generating biopower from forest management residues in California

California faces crisis conditions on its forested landscapes. A century of aggressive logging and fire suppression in combination with conditions exacerbated by climate change have created an ongoing ecological, economic, and public health emergency. Between commercial harvests on California’s working forestlands and the increasing number of acres the state treats each year for fire risk reduction and carbon sequestration, California forests generate millions of tons of woody residues annually—residues that are typically left or burned in the field. State policymakers have turned to biomass electricity generation as a key market for woody biomass in the hope that it can support sustainable forest management activities while also providing low-carbon renewable electricity. However, open questions surrounding the climate and air pollution performance of electricity generation from woody biomass have made it difficult to determine how best to manage the risks and opportunities posed by forest residues. The California Biomass Residue Emissions Characterization (C-BREC) model offers a spatially-explicit life cycle assessment framework to rigorously and transparently establish the climate and air pollution impacts of biopower from forest residues in California under current conditions. The C-BREC model characterizes the variable emissions from different biomass supply chains as well as the counterfactual emissions from prescribed burn, wildfire, and decay avoided by residue mobilization. We find that the life cycle ‘carbon footprint’ of biopower from woody residues generated by recent forest treatments in California ranges widely—from comparable with solar photovoltaic on the low end to comparable with natural gas on the high end. This variation stems largely from the heterogeneity in the fire and decay conditions these residues would encounter if left in the field, with utilization of residue that would otherwise have been burned in place offering the best climate and air quality performance. California’s energy and forest management policies should account for this variation to ensure desired climate benefits are achieved.

Anisotropic Triebel–Lizorkin spaces and wavelet coefficient decay over one-parameter dilation groups, I

This paper provides maximal function characterizations of anisotropic Triebel–Lizorkin spaces associated to general expansive matrices for the full range of parameters p in (0,infty ), q in (0,infty ] and alpha in {mathbb {R}}. The equivalent norm is defined in terms of the decay of wavelet coefficients, quantified by a Peetre-type space over a one-parameter dilation group. As an application, the existence of dual molecular frames and Riesz sequences is obtained; the wavelet systems are generated by translations and anisotropic dilations of a single function, where neither the translation nor dilation parameters are required to belong to a discrete subgroup. Explicit criteria for molecules are given in terms of mild decay, moment, and smoothness conditions.

SU(2)^2-Invariant Gauge Theory on Asymptotically Conical Calabi–Yau 3-Folds

We give a complete description of the behaviour of Calabi–Yau instantons and monopoles with an SU(2)^2-symmetry, on Calabi–Yau 3-folds with asymptotically conical geometry and SU(2)^2 acting with co-homogeneity one. We consider gauge theory on the smoothing and small resolution of the conifold, and on the canonical bundle of mathbb{C}mathbb{P}^1 times mathbb{C}mathbb{P}^1, with their known asymptotically conical co-homogeneity one Calabi–Yau metrics, and find new one-parameter families of invariant instantons. We also entirely classify the relevant moduli-spaces of instantons and monopoles satisfying a natural curvature decay condition, and show that the expected bubbling phenomena occur in these families of instantons.

Relationship between the hadley circulation and tropical SST meridional structures under different thermal conditions in the indo-pacific warm pool

The Hadley circulation (HC), as a thermally driven large-scale meridional circulation, acts a significant role in the changes of global climate. The modulation of Indo-Pacific warm pool (IPWP) thermal conditions on the relationship between the HC and different tropical sea surface temperature (SST) meridional structures was investigated. Based on the two components of HC and SST, one equatorially asymmetric component (HEA for HC, SEA for SST) and one equatorially symmetric component (HES for HC, SES for SST), the connections of HC to different SST variations in the warm and cold IPWP are explored. The result demonstrates that the relationship of the HC to tropical SST is suppressed in the cold IPWP conditions, whereas it is equivalent to the climatology in the warm IPWP conditions. The plausible mechanism is that the cold (warm) IPWP events are in concordance with the La Niña (El Niño) decay phase. The La Niña decay phase are associated with significant equatorially asymmetric SST anomalies within the IPWP, generating an anomalous meridional circulation and favoring a strengthened equatorially asymmetric anomalous meridional circulation. By contrast, the SST anomalies associated with El Niño decay phase are insignificant. The role of La Niña decay conditions in determining the suppressed connection between SST and HC is further verified by exploring the result after 1979. A similar suppressed response contrast has been detected. Therefore, the results demonstrate that warm and cold ENSO events have impacts on the interannual thermal conditions of IPWP, whereby it plays considerable role in impacting the relationship between the HC and tropical SST. Particularly, with the rapid warming, the interconnection between ENSO events and thermal conditions of IPWP under different timescales could be altered, the influence of which on the responses of the HC to tropical SST remains uncertain and is worthy further researching.

Information fusion of stationary, mobile, and wearable consumer-grade sensors to confidently estimate bedroom ventilation rates

This study adds to the body of research investigating ventilation rates measured in residential dwellings. Using open-source Consumer-Grade Sensors (CGS), we measure Carbon Dioxide (CO2) to estimate ventilation rates under one of three conditions: CO2build-up when bedrooms were initially occupied, steady-state CO2 during the latter half of participants’ sleep episodes, and CO2decay after participants wake and vacate their bedroom. We do not ask participants to record their bedroom occupancy, but use information fusion to identify nightly occupied periods by cross-referencing home addresses to GPS measurements provided by their smartphones during sleep episodes identified by Fitbit wearable fitness trackers. We estimate 106 ventilation rates during build-up conditions which ranged from 0.04–1.36 h−1, 242 ventilation rates under steady-state conditions spanning 0.17–2.49 h−1, and 39 ventilation rates from decay conditions over a range of 0.06–1.05 h−1. In addition, we used occupied periods alongside times when GPS confirmed participants were away from home to label Indoor Air Quality (IAQ) data, and to train a Multi-Layer Perceptron (MLP) to classify occupancy based on CO2 and Total Volatile Organic Compound (TVOC) measurements. Using periods classified as occupied with at least 90% confidence, we estimated 116 additional steady-state ventilation rates spanning 0.25–2.49 h−1. Our results are consistent with more traditional and costly sensing approaches, and we conclude that information fusion of CGS is effective in measuring IAQ, detecting occupancy, and estimating ventilation rates.

The common range of co-analytic Toeplitz operators on the Drury-Arveson space

We characterize the common range of the adjoints of cyclic multiplication operators on the Drury-Arveson space. We show that a function belongs to this common range if and only if its Taylor coefficients satisfy a simple decay condition. To achieve this, we introduce the uniform Smirnov class on the ball and determine its dual space. We show that the dual space of the uniform Smirnov class equals the dual space of the strictly smaller Smirnov class of the Drury-Arveson space, and that this in turn equals the common range of the adjoints of cyclic multiplication operators.

A nonexistence result of positive stable solutions to a weighted elliptic equation

We investigate the following weighted elliptic equation ??u + b(x) ? ?u = (1 + |x|2)?2 up in RN, where ? ? 0, p > 1, N ? 3 and the advection term b(x) is a smooth vector field satisfying certain decay condition. We establish a Liouville-type theorem for possible stable solutions of the equation above.

Diffusing-Horizon Model Predictive Control

We analyze a time-coarsening strategy for model predictive control (MPC) that we call diffusing-horizon MPC. This strategy seeks to overcome the computational challenges associated with optimal control problems that span multiple timescales. The coarsening approach uses a time discretization grid that becomes exponentially more sparse as one moves forward in time. This design is motivated by a recently established property of optimal control problems that is known as exponential decay of sensitivity (EDS). This property states that the impact of a parametric perturbation at a future time decays exponentially as one moves backward in time. We establish conditions under which this property holds for a constrained MPC formulation with linear dynamics and costs. Moreover, we show that the proposed coarsening scheme can be cast as a parametric perturbation of the MPC problem and, thus, the exponential decay condition holds. We use a HVAC plant case study with real data to demonstrate the proposed approach. Specifically, we show that computational times can be reduced by two orders of magnitude while increasing the closed-loop cost by only 3%.

On global classical solutions of the three dimensional non-relativistic Vlasov–Darwin System

We are concerned with the global well-posedness of the non-relativistic Vlasov–Darwin system with generalized variables approach in three dimensions. We obtain the global existence and uniqueness of classical solutions for the perturbation of global solutions with specified decay conditions. And generalizing the result of the quasi-spherical-symmetry case, we prove the existence and uniqueness of the global classical solution of the system when initial data sufficiently closes to a fixed spherically symmetric function. Moreover, we obtain asymptotic behavior for the Darwin potentials in both cases.

The marble envelope of the Casa delle Armi by Luigi Moretti: documentary and experimental knowledge finalized to digital modeling

The application of digital modeling for safeguarding the built heritage is a consolidated research field and carries substantial operational interest. The methodological aspects of this application are theoretically outlined but far from being commonly applied. In the perspective of delineating a more straightforward method for implementing these practices among the built heritage, modern Italian architectural production constitutes an ideal field of investigation, both for the significance of the built heritage and for the construction problems that characterize them. Indeed, in the case of stone cladding – which is typical of the Fascist period – the decay conditions and the peculiarity of the material make the investigation specific and paradigmatic of the implementation of the above-mentioned digital methodologies. The Casa delle Armi built heritage by Luigi Moretti in Rome, which has been the research subject of the Authors for years, features a marbled envelope detailed by the designer in every aspect, not only during the design phase but also during construction. This uniqueness makes the recovery of the envelope extremely challenging, as it should not alter its extremely complex nature, while today, the marble envelope is profoundly degraded by natural and anthropogenic factors. Digital modeling appears to be an optimal operational solution for guiding the recovery, but it presents many issues illustrated in this article and to which we have begun to give answers in this contribution. In particular, we delineate the knowledge of the case mentioned above study-built heritage, pursued through documentary analysis integrated by direct and instrumental observation on site.

MULTI-SENSOR SURVEYS FOR THE CHURCH OF SANT'AGNELLO ABATE. 3D MODELS AND VIRTUAL FRUITION

Abstract. The proposed contribution outlines the study conducted on the Church of Sant’Agnello Abate, located in the ancient center of the city of Maddaloni. The church is characterized by severe decay conditions and has been inaccessible and unusable for decades. To recover the memory of a place that was habitually used until 1980, survey activities were performed on the building body. Specifically, multi-sensor surveys have been performed and allowed the complete 3D documentation of the building. Various goals were set: documenting the current condition and configuration of the church: creating virtual fruition systems, since the place is closed and characterized by poor safety conditions; establishing communication models, aligned with contemporary iconographic culture, for the appearance of the places before 1980. Both for survey technologies and fruition modalities, low-cost systems were employed and tested.

Metastatic calcification and nephrosclerosis in an adult sloth (Choloepus hoffmani)

Clinical History: Multiple fragments of various organs from the necropsy of an adult sloth (Choloepus hoffmani) were received. The animal, prior to its death, had presented decay and poor general body condition, which is why it was euthanized. Necropsy Findings: According to the referring veterinarian, at necropsy, irregular and locally extensive hard yellowish lesions, were observed in the subcutaneous tissue of the thorax and abdomen. Similar lesions were observed in the tunica media of the aorta.

Upper and lower bounds of convergence rates for strong solutions of the generalized Newtonian fluids with non-standard growth conditions

We consider the motion of an incompressible shear-thickening power-law-like non-Newtonian fluid in $R^3$ with a variable power-law index. This system of nonlinear partial differential equations arises in mathematical models of electrorheological fluids. The aim of this paper is to investigate the large-time behaviour of the difference $u-\tilde{u}$ where $u$ is a strong solution of the given equations with the initial data $u_0$ and $\tilde{u}$ is the strong solution of the same equations with perturbed initial data $u_0+w_0$. The initial perturbation $w_0$ is not required to be small, but is assumed to satisfy certain decay condition. In particular, we can show that $(1+t)^{-\frac{\gamma}{2}}\lesssim \|u(t)-\tilde{u}(t)\|_2\lesssim(1+t)^{-\frac{\gamma}{2}}$, for sufficiently large $t>0$, where $\gamma\in(2,\frac{5}{2})$. The proof is based on the observation that the solution of the linear heat equation describes the asymptotic behaviour of the solutions of the electrorheological fluids well for sufficiently large time $t>0$, and the generalized Fourier splitting method with an iterative argument. Furthermore, it will also be discussed that the argument used in the present paper can improve the previous results for the generalized Newtonian fluids with a constant power-law index.

Triviality results for quasi k-Yamabe solitons

In this paper, we show that any compact quasi k-Yamabe gradient soliton must have constant \(\sigma _{k}\)-curvature. Moreover, we provide a certain condition for a compact quasi k-Yamabe soliton to be gradient, and for noncompact solitons, we present a geometric rigidity under a decay condition on the norm of the soliton field.

Random sampling and reconstruction in reproducing kernel subspace of mixed Lebesgue spaces

In this article, we consider the random sampling in the image space of an idempotent integral operator on mixed Lebesgue space . We assume some decay and regularity conditions on the integral kernel and show that the bounded functions in can be approximated by an element in a finite‐dimensional subspace of on . Consequently, we show that the set of bounded functions concentrated on is totally bounded and prove with an overwhelming probability that the random sample set uniformly distributed over is a stable set of sampling for the set of concentrated functions on . Further, we propose an iterative scheme to reconstruct the concentrated functions from their random measurements.

Asymptotic behavior in a forager-exploiter model with nonlinear resource consumption with/without general logistic sources

This work is concerned with a forager-exploiter model with nonlinear resource consumption with/without general logistic sources{ut=Δu−χ∇⋅(u∇w)+a1u−b1uα,x∈Ω,t>0,vt=Δv−ξ∇⋅(v∇u)+a2v−b2vβ,x∈Ω,t>0,wt=Δw−u+v(1+u+v)γw−μw+r(x,t),x∈Ω,t>0 in a bounded smooth domain Ω⊂Rn (n≥2) with homogeneous Neumann boundary conditions, where the parameters ai,bi≥0 (i=1,2), and χ,ξ,γ,μ are some given positive constants, and α,β>1, r∈C2(Ω¯×[0,∞))∩L∞(Ω×(0,∞)) is a given nonnegative function. The present work shows that, if α,β,γ satisfy{α,β>(n+2)(1−γ)2,if0<γ<nn+2,α,β>1,ifγ≥nn+2, then the corresponding initial-boundary value problem admits a unique global bounded classical solution. Furthermore, the paper also establishes the large time behavior of the classical solution to the above model with/without general logistic sources in the case of the function r is a positive constant or has suitable decay conditions.

Preliminary Study on an Integrated System Composed of a Floating Offshore Wind Turbine and an Octagonal Fishing Cage

To maximize the utilization of ocean resources, shorten the return period of investment and directly supply energy to the fishing cage, this paper performs a preliminary study for a state-of-the-art concept integrating a floating offshore wind turbine with a fishing cage. An octagonal semisubmersible rigid fishing cage with a slack catenary mooring system is designed to match the NREL 5 MW offshore baseline wind turbine. Combined with the blade pitch controller, fully coupled aero-hydro-elastic-servo-mooring simulations are performed through FAST and AQWA to explore the dynamic performance of the integrated system. Free decay conditions, uniform wind with irregular and regular waves, and turbulent wind with irregular waves are tested. The results showed that the integrated system works normally at the operating conditions and exhibits different dynamic characteristics for various scenarios. Additionally, the study on the influence of mooring line length indicates that the increasing line length can significantly affect the cage surge motion and the maximum and mean values of the upwind line tension at fairlead. Specifically, the maximum surge motion with a 924-m-long line is 404.8% larger than that with an 880-m-long line. When the line length increases by 5%, the maximum and mean line tensions decrease by 45.7% and 47.7%, respectively, while when the line length increases by 10%, the maximum and mean line tension decrease by 52.9% and 54.2%, respectively. It should be noted that the main purpose of this work is to conduct a preliminary study on this integrated system, aiming to provide an idea for the conceptual design, modeling and simulation analysis of this integrated system.

Mesofauna community influences litter chemical trajectories during early-stage litter decay

Decomposition of organic material is moderated by both litter chemistry and decomposer communities. Chemical alteration of the litter occurs throughout decomposition, yet our understanding of the nature of chemical change during decomposition is limited, particularly beyond carbon (C) and nitrogen (N). The decomposer food web likely interacts with these chemical changes in their basal resource to alter the trajectories of chemical changes during decay. To investigate how decomposer mesofauna influence patterns of litter chemical change throughout early stages of decay, we tracked mass loss, macro- and micronutrient elements, and fiber chemistry dynamics in Arizona sycamore (Platanus wrightii) leaves decomposed in a mesocosm of optimal decay conditions in a biotically diverse compost pile. By using litterbags of two different mesh sizes to manipulate the mesofauna gaining access to the litter, we identify how the complexity of the soil mesofauna community changes the trajectory of litter chemistry, beyond the typical focus on mass loss and N dynamics. Counter to many examples in the literature, the more abundant and complex arthropod community slowed mass loss and enhanced nutrient immobilization, perhaps due to competition and grazing pressure on the microbial community to immobilize N, P, and Ca sooner from the surrounding compost.