Explicit Estimates Research Articles

Explicit averages of square-free supported functions: to the edge of the convolution method

We give a general statement of the convolution method so that one can provide explicit asymptotic estimations for all averages of square-free supported arithmetic functions that have a sufficiently regular behavior on the prime numbers and observe how the

ATMConvGRU for Weather Forecasting

Weather forecasting, which is challenging due to the complex atmospheric correlation, focuses on providing explicit meteorological estimations as accurate as possible. Recently, techniques based upon convolutional-recurrent networks have shown dramatic performance in domains including radar echo prediction and precipitation forecasting, indicating that deep learning models have great potential in this area. However, existing methods concentrate on adding extra paralleled memory cells to the inner recurrent unit, where the information is mutually independent. To extract spatial–temporal features with stronger correlation, this letter introduced an axial attention memory module with quasi state-in-state cascaded manner. Benefitting from this unit, the spatial–temporal features can be aggregated and embedded into standard ConvGRU formulating Axial aTtention Memory Cascaded ConvGRU (ATMConvGRU) for sequential weather prediction. Experimental results compared with many state-of-the-art methods on four types of weather forecasting related datasets, including temperature, relative humidity, wind, and radar echo, demonstrate the effectiveness and superiority of the proposed ATMConvGRU.

Spatially explicit population trend estimates of owls in the Maritime provinces of Canada and the influence of call playback

Ethier, D. M., R. Torrenta, and A.-L. Kouwenberg. 2022. Spatially explicit population trend estimates of owls in the Maritime provinces of Canada and the influence of call playback. Avian Conservation and Ecology 17(1):12. https://doi.org/10.5751/ACE-02075-170112

Weak convergence of delay SDEs with applications to Carathéodory approximation

<p style='text-indent:20px;'>In this paper, we consider a fundamental class of stochastic differential equations with time delays. Our aim is to investigate the weak convergence with respect to delay parameter of the solutions. Based on the techniques of Malliavin calculus, we obtain an explicit estimate for the rate of convergence. An application to the Carathéodory approximation scheme of stochastic differential equations is provided as well.</p>

On the exponential time-decay for the one-dimensional wave equation with variable coefficients

<p style='text-indent:20px;'>We consider the initial-value problem for the one-dimensional, time-dependent wave equation with positive, Lipschitz continuous coefficients, which are constant outside a bounded region. Under the assumption of compact support of the initial data, we prove that the local energy decays exponentially fast in time, and provide the explicit constant to which the solution converges for large times. We give explicit estimates of the rate of this exponential decay by two different techniques. The first one is based on the definition of a modified, weighted local energy, with suitably constructed weights. The second one is based on the integral formulation of the problem and, under a more restrictive assumption on the variation of the coefficients, allows us to obtain improved decay rates.</p>

Łojasiewicz exponents of certain analytic functions

We consider the exponent of Łojasiewicz inequality ‖∂f(z)‖≥c|f(z|θ for two classes of analytic functions and we will give an explicit estimation for θ. First we consider certain non-degenerate functions which is not convenient. In §3.4, we give an example of a polynomial for which θ0(f) is not constant on the moduli space and in §3.5, we show that the behaviors of the Łojasiewicz exponents are not similar as the Milnor numbers by an example.In the last section (§4), we give also an estimation for product functions f(z)=f1(z)⋯fk(z) associated to a family of a certain convenient non-degenerate complete intersection varieties. In either class, the singularity is not isolated. We will give explicit estimations of the Łojasiewicz exponent θ0(f) using combinatorial data of the Newton boundary of f. We generalize this estimation for non-reduced function g=f1m1⋯fkmk.

Body schema plasticity is altered in Developmental Coordination Disorder

Developmental Coordination Disorder (DCD) is a pathological condition characterized by impaired motor skills. Current theories advance that a deficit of the internal models is mainly responsible for DCD children's altered behavior. Yet, accurate movement execution requires not only correct movement planning, but also integration of sensory feedback into body representation for action (Body Schema) to update the state of the body. Here we advance and test the hypothesis that the plasticity of this body representation is altered in DCD. To probe Body Schema (BS) plasticity, we submitted a well-established tool-use paradigm to seventeen DCD children, required to reach for an object with their hand before and after tool use, and compared their movement kinematics to that of a control group of Typically Developing (TD) peers. We also asked both groups to provide explicit estimates of their arm length to probe plasticity of their Body Image (BI). Results revealed that DCD children explicitly judged their arm shorter after tool use, showing changes in their BI comparable to their TD peers. Unlike them, though, DCD did not update their implicit BS estimate: kinematics showed that tool use affected their peak amplitudes, but not their latencies. Remarkably, the kinematics of tool use showed that the motor control of the tool was comparable between groups, both improving with practice, confirming that motor learning abilities are preserved in DCD. This study thus brings evidence in favor of an alternative theoretical account of the DCD etiology. Our findings point to a deficit in the plasticity of the body representation used to plan and execute movements. Though not mutually exclusive, this widens the theoretical perspective under which DCD should be considered: DCD may not be limited to a problem affecting the internal models and their motor functions, but may concern the state of the effector they have to use.

Projecting the compound effects of climate change and white-nose syndrome on North American bat species

Climate change and disease are threats to biodiversity that may compound and interact with one another in ways that are difficult to predict. White-nose syndrome (WNS), caused by a cold-loving fungus (Pseudogymnoascus destructans), has had devastating impacts on North American hibernating bats, and impact severity has been linked to hibernaculum microclimate conditions. As WNS spreads across the continent and climate conditions change, anticipating these stressors’ combined impacts may improve conservation outcomes for bats. We build on the recent development of winter species distribution models for five North American bat species, which used a hybrid correlative-mechanistic approach to integrate spatially explicit winter survivorship estimates from a bioenergetic model of hibernation physiology. We apply this bioenergetic model given the presence of P. destructans, including parameters capturing its climate-dependent growth as well as its climate-dependent effects on host physiology, under both current climate conditions and scenarios of future climate change. We then update species distribution models with the resulting survivorship estimates to predict changes in winter hibernacula suitability under future conditions. Exposure to P. destructans is generally projected to decrease bats’ winter occurrence probability, but in many areas, changes in climate are projected to lessen the detrimental impacts of WNS. This rescue effect is not predicted for all species or geographies and may arrive too late to benefit many hibernacula. However, our findings offer hope that proactive conservation strategies to minimize other sources of mortality could allow bat populations exposed to P. destructans to persist long enough for conditions to improve.

Tail distribution estimates of the mixed-fractional CEV model

The aim of this paper is to study the tail distribution of the CEV model driven by Brownian motion and fractional Brownian motion. Based on the techniques of Malliavin calculus and a result established recently in [<a href="#1">1</a>], we obtain an explicit estimate for tail distributions.

Numerical scheme and stability analysis of stochastic Fitzhugh–Nagumo model

This article deals with the Fitzhugh–Nagumo equation in the presence of stochastic function. A numerical scheme has been developed for the solution of such equations which preserves the certain structure of the unknown functions, also we have given the stability analysis, consistency of the problem, and explicitly optimal a priori estimates for the existence of solutions of such equations. A unique solution has been guaranteed. The corresponding explicit estimates in the function spaces are formulated in the form of theorems. Lastly, one important feature of the article is the simulation of the proposed numerical scheme in the form of the 2D and 3D plots which shows the efficacy of the stochastic analysis of such nonlinear partial differential equations.

Assessing Soil Organic Carbon Stock Dynamics under Future Climate Change Scenarios in the Middle Qilian Mountains

Soil organic carbon (SOC) simply cannot be managed if its amounts, changes and locations are not well known. Thus, evaluations of the spatio-temporal dynamics of SOC stock under future climate change are crucial for the adaptive management of regional carbon sequestration. Here, we evaluated the dynamics of SOC stock to a 60 cm depth in the middle Qilian Mountains (1755–5051 m a.s.l.) by combining systematic measurements from 138 sampling sites with a machine learning model. Our results reveal that the combination of systematic measurements with the machine learning model allowed spatially explicit estimates of SOC change to be made. The average SOC stock in the middle Qilian Mountains was expected to decrease under future climate change, while the size and direction of SOC stock changes seemed to be elevation-dependent. Specifically, in comparison with the 2000s, the mean annual precipitation was projected to increase by 18.37, 19.80 and 30.80 mm, and the mean annual temperature was projected to increase by 1.9, 2.4 and 2.9 °C under the Representative Concentration Pathway (RCP) 2.6 (low-emissions pathway), RCP4.5 (low-to-moderate-emissions pathway), and RCP8.5 (high-emissions pathway) scenarios by the 2050s, respectively. Accordingly, the area-weighted SOC stock and total storage for the whole study area were estimated to decrease by 0.43, 0.63 and 1.01 kg m–2 and 4.55, 6.66 and 10.62 Tg under the RCP2.6, RCP4.5 and RCP8.5 scenarios, respectively. In addition, the mid-elevation zones (3100–3900 m), especially the subalpine shrub-meadow Mollic Leptosols, were projected to experience the most intense carbon loss. However, the higher elevation zones (>3900 m), especially the alpine desert zone, were characterized by significant carbon accumulation. As for the low-elevation zones (<2900 m), SOC was projected to be less varied under future climate change scenarios. Thus, the mid-elevation zones, especially the subalpine shrub-meadows and Mollic Leptosols, should be given priority in terms of reducing CO2 emissions in the Qilian Mountains.

On the Number of Sum-Free Triplets of Sets

We count the ordered sum-free triplets of subsets in the group $\mathbb{Z}/p\mathbb{Z}$, i.e., the triplets $(A,B,C)$ of sets $A,B,C \subset \mathbb{Z}/p\mathbb{Z}$ for which the equation $a+b=c$ has no solution with $a\in A$, $b \in B$ and $c \in C$. Our main theorem improves on a recent result by Semchankau, Shabanov, and Shkredov using a different and simpler method. Our proof relates previous results on the number of independent sets of regular graphs by Kahn; Perarnau and Perkins; and Csikvári to produce explicit estimates on smaller order terms. We also obtain estimates for the number of sum-free triplets of subsets in a general abelian group.

On incidence bounds with Möbius hyperbolae in positive characteristic

We prove new incidence bounds between a plane point set, which is a Cartesian product, and a set of translates H of the hyperbola xy=λ≠0, over a field of asymptotically large positive characteristic p. They improve recent bounds by Shkredov, which are based on using explicit incidence estimates in the early terminated procedure of repeated applications of the Cauchy-Schwarz inequality, underlying many qualitative results related to growth and expansion in groups. The improvement – both quantitative, plus we are able to deal with a general H, rather than a Cartesian product – is mostly due to a non-trivial “intermediate” bound on the number of k-rich Möbius hyperbolae in positive characteristic. In addition, we make an observation that a certain energy-type quantity in the context of H can be bounded via the L2-moment of the Minkowski distance in H and can therefore fetch the corresponding estimates apropos of the Erdős distinct distance problem.

The LOFAR Two-metre Sky Survey Deep Fields

We have exploited LOFAR deep observations of the Lockman Hole field at 150 MHz to investigate the relation between the radio luminosity of star-forming galaxies (SFGs) and their star-formation rates (SFRs), as well as its dependence on stellar mass and redshift. The adopted source classification, SFRs, and stellar masses are consensus estimates based on a combination of four different spectral energy distribution fitting methods. We note a flattening of the radio spectra of a substantial minority of sources below ∼1.4 GHz. Such sources have thus a lower ‘radio-loudness’ level at 150 MHz than expected from extrapolations from 1.4 GHz using the average spectral index. We found a weak trend towards a lower SFR/L150 MHzratio for higher stellar mass,M⋆. We argue that such a trend may account for most of the apparent redshift evolution of theL150 MHz/SFR ratio, in line with previous work. Our data indicate a weaker evolution than found by some previous analyses. We also find a weaker evolution with redshift of the specific SFR than found by several (but not all) previous studies. Our radio selection provides a view of the distribution of galaxies in the SFR–M⋆plane complementary to that of optical and near-IR selection. It suggests a higher uniformity of the star-formation history of galaxies than implied by some analyses of optical and near-IR data. We have derived luminosity functions at 150 MHz of both SFGs and radio-quiet (RQ) AGN at various redshifts. Our results are in very good agreement with the T-RECS simulations and with literature estimates. We also present explicit estimates of SFR functions of SFGs and RQ AGN at several redshifts derived from our radio survey data.

Dynamic modelling shows substantial contribution of ecosystem restoration to climate change mitigation

Limiting global warming to a 1.5°C temperature rise requires drastic emissions reductions and removal of carbon-dioxide from the atmosphere. Most modelled pathways for 1.5°C assume substantial removals in the form of biomass energy with carbon capture and storage, which brings with it increasing risks to biodiversity and food security via extensive land-use change. Recently, multiple efforts to describe and quantify potential removals via ecosystem-based approaches have gained traction in the climate policy discourse. However, these options have yet to be evaluated in a systematic and scientifically robust way. We provide spatially explicit estimates of ecosystem restoration potential quantified with a Dynamic Global Vegetation Model. Simulations covering forest restoration, reforestation, reduced harvest, agroforestry and silvopasture were combined and found to sequester an additional 93 Gt C by 2100, reducing mean global temperature increase by ∼0.12°C (5%–95% range 0.06°C–0.21°C) relative to a baseline mitigation pathway. Ultimately, pathways to achieving the 1.5°C goal garner broader public support when they include land management options that can bring about multiple benefits, including ecosystem restoration, biodiversity protection, and resilient agricultural practices.

Accuracy and Predictive Power of Sell-Side Target Prices for Global Clean Energy Companies

Target prices are often provided as a support for stock recommendations by sell-side analysts which represent an explicit estimate of the expected future value of a company’s stock. This research focuses on mean target prices for stocks contained in the Standard and Poor’s Global Clean Energy Index during the time period from 2009 to 2020. The accuracy of mean target prices for these global clean energy stocks at any point during a 12-month period (Year-Highest) is 68.1% and only 46.6% after exactly 12 months (Year-End). A random forest and an SVM classification model were trained for both a Year-End and a Year-Highest target and compared to a random model. The random forest demonstrates the best results with an average accuracy of 73.24% for the Year-End target and 81.15% for the Year-Highest target. The analysis of the variables shows that for all models the mean target price is the most relevant variable, whereas the number of target prices appears to be highly relevant as well. Moreover, the results indicate that following the rare positive predictions of the random forest for the highest target return groups (“30% to 70%” and “Above 70%”) may potentially represent attractive investment opportunities.

Soil acidification and factors controlling topsoil pH shift of cropland in central China from 2008 to 2018

Soil acidification can negatively impact the sustainability of agricultural systems. Spatially explicit estimations of soil acidification and the identification of local factors driving soil pH change are prerequisites for formulating and implementing site-specific measures to prevent and mitigate cropland soil acidification. Based on pairwise comparisons between 1443 pairs of topsoil pH observations at colocated sites in 2008 and 2018, this study revealed the spatial variability of cropland soil acidification and its influencing factors across Henan Province, central China. The results showed that the topsoil pH of cropland in Henan Province decreased by an average of 0.36 units, and more than 94% of the cropland in the study region suffered from varying degrees of topsoil pH decline from 2008 to 2018, demonstrating a large range in soil acidification. The most serious soil acidification of croplands occurred in the southern part of the province, while in the northern part of the province, the topsoil pH decreased to a lesser extent or even slightly increased. The topsoil pH shift of cropland was found to be closely associated with the N fertilizer application rate, base cation removal by crops, and factors influencing the soil response to acidification, i.e., soil calcareousness, initial acidity, clay content, moisture regimes and temperature regimes. Among the various factors, the N fertilizer application rate was identified as the most important factor related to soil acidification. Croplands face the risk of accelerating soil acidification due to continuous excessive nitrogen application, increasing the removal of base cations while promoting crop yield, and decreasing or even disappearing carbonate material in the soil.

Land Use Increases the Correlation between Tree Cover and Biomass Carbon Stocks in the Global Tropics

Tree cover (TC) and biomass carbon stocks (CS) are key parameters for characterizing vegetation and are indispensable for assessing the role of terrestrial ecosystems in the global climate system. Land use, through land cover change and land management, affects both parameters. In this study, we quantify the empirical relationship between TC and CS and demonstrate the impacts of land use by combining spatially explicit estimates of TC and CS in actual and potential vegetation (i.e., in the hypothetical absence of land use) across the global tropics (~23.4° N to 23.4° S). We find that land use strongly alters both TC and CS, with stronger effects on CS than on TC across tropical biomes, especially in tropical moist forests. In comparison to the TC-CS correlation observed in the potential vegetation (biome-level R based on tropical ecozones = 0.56–0.90), land use strongly increases this correlation (biome-level R based on tropical ecozones = 0.87–0.94) in the actual vegetation. Increased correlations are not only the effects of land cover change. We additionally identify land management impacts in closed forests, which cause CS reductions. Our large-scale assessment of the TC-CS relationship can inform upcoming remote sensing efforts to map ecosystem structure in high spatio-temporal detail and highlights the need for an explicit focus on land management impacts in the tropics.

A Riemann–von Mangoldt-Type Formula for the Distribution of Beurling Primes

In this paper we work out a Riemann–von Mangoldt type formula for the summatory function := , where is an arithmetical semigroup (a Beurling generalized system of integers) and is the corresponding von Mangoldt function attaining with a prime element and zero otherwise. On the way towards this formula, we prove explicit estimates on the Beurling zeta function , belonging to , to the number of zeroes of in various regions, in particular within the critical strip where the analytic continuation exists, and to the magnitude of the logarithmic derivative of , under the sole additional assumption that Knopfmacher’s Axiom A is satisfied. We also construct a technically useful broken line contour to which the technic of integral transformation can be well applied. The whole work serves as a first step towards a further study of the distribution of zeros of the Beurling zeta function, providing appropriate zero density and zero clustering estimates, to be presented in the continuation of this paper.

Magnetized Dusty Black Holes and Wormholes

We consider the generalized Tolman solution of general relativity, describing the evolution of a spherical dust cloud in the presence of an external electric or magnetic field. The solution contains three arbitrary functions f(R), F(R) and τ0(R), where R is a radial coordinate in the comoving reference frame. The solution splits into three branches corresponding to hyperbolic (f>0), parabolic (f=0) and elliptic (f<0) types of motion. In such models, we study the possible existence of wormhole throats defined as spheres of minimum radius at a fixed time instant, and prove the existence of throats in the elliptic branch under certain conditions imposed on the arbitrary functions. It is further shown that the normal to a throat is a timelike vector (except for the instant of maximum expansion, when this vector is null), hence a throat is in general located in a T-region of space-time. Thus, if such a dust cloud is placed between two empty (Reissner–Nordström or Schwarzschild) space-time regions, the whole configuration is a black hole rather than a wormhole. However, dust clouds with throats can be inscribed into closed isotropic cosmological models filled with dust to form wormholes which exist for a finite period of time and experience expansion and contraction together with the corresponding cosmology. Explicit examples and numerical estimates are presented. The possible traversability of wormhole-like evolving dust layers is established by a numerical study of radial null geodesics.