Non-homogeneous Set Research Articles

Choosing a Proper Control Strategy for Multipath Transmission in Industry 4.0 Applications

The industrial applications, especially in the context of communication-intensive Industry 4.0, require high throughput, good robustness, and low latency in the data exchange among the system components. These objectives can be achieved through multipath transfer. In order to overcome the restrictions of the primary networking protocols with respect to engaging multiple network interfaces, a new version of transmission control protocol (TCP) has recently been standardized—multipath TCP (MPTCP). Still though, only one type of congestion control algorithm is used to manage the flow of data despite various choices available in the modern operating systems, which leads to nonoptimal transfer dynamics. In this article, the influence of TCP congestion control algorithms, operating at the path and MPTCP level, on the transmission quality in industrial applications is examined. The conducted experiments involving physical devices and real, public networks lead to a set of recommendations for the algorithm selection so that the premises of robustness and efficiency are met. The default algorithm configuration is found ill-suited, yielding priority to nonhomogeneous settings. Only a few algorithms can maintain the benefits of multiplicity for an on-going transmission when the transfer conditions at one or more paths deteriorate. Motivated by the deficiency of common solutions, a new MPTCP congestion control algorithm has been developed. While retaining their good properties in the general networking context, this new–robust–algorithm yields improved performance in the uncertain, industrial communication environment.

High-resolution global map of smallholder and industrial closed-canopy oil palm plantations

Abstract. Oil seed crops, especially oil palm, are among the most rapidly expanding agricultural land uses, and their expansion is known to cause significant environmental damage. Accordingly, these crops often feature in public and policy debates which are hampered or biased by a lack of accurate information on environmental impacts. In particular, the lack of accurate global crop maps remains a concern. Recent advances in deep-learning and remotely sensed data access make it possible to address this gap. We present a map of closed-canopy oil palm (Elaeis guineensis) plantations by typology (industrial versus smallholder plantations) at the global scale and with unprecedented detail (10 m resolution) for the year 2019. The DeepLabv3+ model, a convolutional neural network (CNN) for semantic segmentation, was trained to classify Sentinel-1 and Sentinel-2 images onto an oil palm land cover map. The characteristic backscatter response of closed-canopy oil palm stands in Sentinel-1 and the ability of CNN to learn spatial patterns, such as the harvest road networks, allowed the distinction between industrial and smallholder plantations globally (overall accuracy =98.52±0.20 %), outperforming the accuracy of existing regional oil palm datasets that used conventional machine-learning algorithms. The user's accuracy, reflecting commission error, in industrial and smallholders was 88.22 ± 2.73 % and 76.56 ± 4.53 %, and the producer's accuracy, reflecting omission error, was 75.78 ± 3.55 % and 86.92 ± 5.12 %, respectively. The global oil palm layer reveals that closed-canopy oil palm plantations are found in 49 countries, covering a mapped area of 19.60 Mha; the area estimate was 21.00 ± 0.42 Mha (72.7 % industrial and 27.3 % smallholder plantations). Southeast Asia ranks as the main producing region with an oil palm area estimate of 18.69 ± 0.33 Mha or 89 % of global closed-canopy plantations. Our analysis confirms significant regional variation in the ratio of industrial versus smallholder growers, but it also confirms that, from a typical land development perspective, large areas of legally defined smallholder oil palm resemble industrial-scale plantings. Since our study identified only closed-canopy oil palm stands, our area estimate was lower than the harvested area reported by the Food and Agriculture Organization (FAO), particularly in West Africa, due to the omission of young and sparse oil palm stands, oil palm in nonhomogeneous settings, and semi-wild oil palm plantations. An accurate global map of planted oil palm can help to shape the ongoing debate about the environmental impacts of oil seed crop expansion, especially if other crops can be mapped to the same level of accuracy. As our model can be regularly rerun as new images become available, it can be used to monitor the expansion of the crop in monocultural settings. The global oil palm layer for the second half of 2019 at a spatial resolution of 10 m can be found at https://doi.org/10.5281/zenodo.4473715 (Descals et al., 2021).

Музей русской космософии: «философия действия» В.Н. Муравьева

The article deals with a part of scientific and philosophical heritage of Valerian Nikolaevich Muravyov (1885‒1930), a thinker and a representative of Russian cosmism. The author of the article undertakes an attempt to explicate the major notions of the philosophy of action as the active principle of the common cause project by N.F. Fyodorov. In the theoretical system of Muravyov action is a uni­versal notion which unites various connections and relations among objects of different nature. Basing on philosophy of Parmenides and mathematical set theo­ry of G. Cantor Muravyov believes a possibility of action to be determined by the structure of the system: to possess the action capacity the system has to be a non-homogeneous set. The article reviews the general scheme of interaction of the active system elements which are defined as hypostases in the philosophy of action. The work also reveals the hierarchy of rational action points. Time is in­separably connected with set and action in the philosophical concept of Mu­ravyov. The paper observes Mouraviov’s logical approach to understanding time genesis and structure resting on the ideas of H. Bergson. Defining time as an ac­tion subject, its obligatory output the philosophy of action sets a task of time takeover.

Affine connections on 3-Sasakian and manifolds

The space of invariant affine connections on every 3-Sasakian homogeneous manifold of dimension at least seven is described. In particular, the subspace of invariant affine metric connections and the subclass with skew torsion are also determined. To this aim, an explicit construction of all 3-Sasakian homogeneous manifolds is exhibited. It is shown that the 3-Sasakian homogeneous manifolds which admit nontrivial Einstein with skew torsion invariant affine connections are those of dimension seven, that is, $${\mathbb {S}}^7$$, $${\mathbb {R}}P^7$$ and the Aloff–Wallach space $${\mathfrak {W}}^{7}_{1,1}$$. On $${\mathbb {S}}^7$$ and $${\mathbb {R}}P^7$$, the set of such connections is bijective to two copies of the conformal linear transformation group of the Euclidean space, while it is strictly bigger on $${\mathfrak {W}}^{7}_{1,1}$$. The set of invariant connections with skew torsion whose Ricci tensor satisfies that its eigenspaces are the canonical vertical and horizontal distributions, is fully described on 3-Sasakian homogeneous manifolds. An affine connection satisfying these conditions is distinguished, by parallelizing all the Reeb vector fields associated with the 3-Sasakian structure, which is also Einstein with skew torsion on the 7-dimensional examples. The invariant metric affine connections on 3-Sasakian homogeneous manifolds with parallel skew torsion have been found. Finally, some results have been adapted to the non-homogeneous setting.

An Endpoint Weak-Type Estimate for Multilinear Calderón–Zygmund Operators

The purpose of this article is to provide an alternative proof of the weak-type $\left(1,\ldots,1;\frac{1}{m}\right)$ estimate for $m$-multilinear Calder\'on-Zygmund operators on $\mathbb{R}^n$ first proved by Grafakos and Torres. Subsequent proofs in the bilinear setting have been given by Maldonado and Naibo and also by P\'erez and Torres. The proof given here is motivated by the proof of the weak-type $(1,1)$ estimate for Calder\'on-Zygmund operators in the nonhomogeneous setting by Nazarov, Treil, and Volberg.

Potential estimates for elliptic systems with subquadratic growth

We prove gradient Riesz potential estimates for nonlinear elliptic systems with subquadratic growth of the form−div(A(x,Du))=f, adopting ε-regularity criteria to the non-homogeneous setting. Assuming Dini type continuity in the first variable of the vector field A, we obtain partial C1-regularity of solutions to such problems via Riesz potentials whenever f∈L(n,1).

Robust Estimation of the Normal-Distribution Parameters by Use of Structural Partitioning-Perobls D Method

Quite many authors have dealt with the estimation of the parameters of normal distribution on the basis of non-homogeneous sets: Hald A. 1949 [1], Arango-Castillo L. and Takahara G. 2018 [2]. All the robust methods are based on the assumption that the results affected by gross errors can be found to the left and/or to the right of censoring, or truncated, points. However, as a rule, the (intrinsic) distribution of observations is complex (mixed) consisting of two or more distributions. Then the existing methods, such as ML, Huber’s, etc., yield enlarged estimates for the normal-distribution variance. By studying better estimates the present author has invented new method, called PEROBLS D, based on the Tukeyan mixed-distribution model in which both the contamination rate (percentage) and the parameters of both distributions, forming the mixed one, are estimated, and for the parameters of the basic normal distribution better estimates are obtained than by the existing methods.

From the sinh-Gordon field theory to the one-dimensional Bose gas: exact local correlations and full counting statistics

We derive exact formulas for the expectation value of local observables in a one-dimensional gas of bosons with point-wise repulsive interactions (Lieb–Liniger model). Starting from a recently conjectured expression for the expectation value of vertex operators in the sinh-Gordon field theory, we derive explicit analytic expressions for the one-point K-body correlation functions in the Lieb–Liniger gas, for arbitrary integer K. These are valid for all excited states in the thermodynamic limit, including thermal states, generalized Gibbs ensembles and non-equilibrium steady states arising in transport settings. Our formulas display several physically interesting applications: most prominently, they allow us to compute the full counting statistics for the particle-number fluctuations in a short interval. Furthermore, combining our findings with the recently introduced generalized hydrodynamics, we are able to study multi-point correlation functions at the Eulerian scale in non-homogeneous settings. Our results complement previous studies in the literature and provide a full solution to the problem of computing one-point functions in the Lieb–Liniger model.

The semantic roots of positive polarity: epistemic modal verbs and adverbs in English, Greek and Italian

Epistemic modal verbs and adverbs of necessity are claimed to be positive polarity items. We study their behavior by examining modal spread, a phenomenon that appears redundant or even anomalous, since it involves two apparent modal operators being interpreted as a single modality. We propose an analysis in which the modal adverb is an argument of the MUST modal, providing a meta-evaluation $$\mathcal {O}$$ which ranks the Ideal, stereotypical worlds in the modal base as better possibilities than the Non-Ideal worlds in it. MUST and possibility modals differ in that the latter have an empty $$\mathcal {O}$$ , a default that can be negotiated. Languages vary in the malleability of this parameter. Positive polarity is derived as a conflict between the ranking imposed by $$\mathcal {O}$$ —which requires that the Ideal worlds be better possibilities than Non-Ideal worlds—and the effect of higher negation which renders the Ideal set non-homogenous. Applying the ordering over such a non-homogeneous set would express preference towards both p and $$\lnot p $$ worlds thus rendering the sentence uninformative. Negative polarity MUST and possibility modals, on the other hand, contain an empty $$\mathcal {O}$$ , application of higher negation therefore poses no problem. This account is the first to connect modal spread to positive polarity of necessity modals, and captures the properties of both in a unified analysis.

The Minimal Free Resolution of Fat Almost Complete Intersections in ℙ1 × ℙ1

AbstractA current research theme is to compare symbolic powers of an ideal I with the regular powers of I. In this paper, we focus on the case where I = IX is an ideal deûning an almost complete intersection (ACI) set of points X in ℙ1 × ℙ1. In particular, we describe a minimal free bigraded resolution of a non-arithmetically Cohen-Macaulay (also non-homogeneous) set 𝒵 of fat points whose support is an ACI, generalizing an earlier result of Cooper et al. for homogeneous sets of triple points. We call 𝒵 a fat ACI.We also show that its symbolic and ordinary powers are equal, i.e, .

Two weight Lp estimates for paraproducts in non-homogeneous settings

We give a necessary and sufficient condition for the two weight Lp-estimates for paraproducts in non-homogeneous settings, 1<p<∞. We are mainly interested in the case p≠2, since the case p=2 is a well-known and easy corollary of the Carleson embedding theorem. The necessary and sufficient condition is given in terms of testing conditions of Sawyer type: for p≤2 only one (“direct”) testing condition is required, but for p>2 both “direct” and “adjoint” testing conditions are needed. An interesting feature is that the “adjoint” testing condition is that it is a testing condition not for the adjoint of the paraproduct, but for some auxiliary operator.

Mean-field analysis of the convergence time of message-passing computation of harmonic influence in social networks

The concept of harmonic influence has been recently proposed as a metric for the importance of nodes in a social network. A distributed message passing algorithm for its computation has been proposed by Vassio et al. (2014) and proved to converge on general graphs by Rossi and Frasca (2016a). In this paper, we want to evaluate the convergence time of this algorithm by using a mean-field approach. The mean-field dynamics is first introduced in a “homogeneous” setting, where it is exact, then heuristically extended to a non-homogeneous setting. The rigorous analysis of the mean-field dynamics is complemented by numerical examples and simulations that demonstrate the validity of the approach.

Scattering and Radiation by Perturbed Spherical Metallic Bodies of Revolution

A general theory, based on asymptotic expansions, for the electromagnetic scattering by rotationally symmetric bodies, whose boundary is considered as a shape perturbation of the sphere, is constructed in this work. The parametric expression of the arc that generates the body by rotation is asymptotically expanded applying Maclaurin series. Next, the fields are expressed in asymptotic expansions using the spherical vector wave functions (SVWFs). The boundary conditions are then satisfied and lead to infinite nonhomogeneous sets for the evaluation of the unknown expansion coefficients. Depending on the body of revolution (BoR), these sets are solved analytically, in asymptotic closed form, and finally the whole procedure enables a closed-form evaluation of the scattering quantities. An application of the general theory for the scattering by a body of revolution is presented.

Weighted martingale multipliers in the non-homogeneous setting and outer measure spaces

We investigate the unconditional basis property of martingale differences in weighted spaces L2(wdν) in the non-homogeneous situation, that is when the reference measure ν is not doubling. Specifically, we prove that finiteness of the quantity [w]A2=supI⁡〈w〉I〈w−1〉I, defined through averages 〈⋅〉I relative to the reference measure ν, implies that Haar subspaces form an unconditional basis in the weighted space L2(wdν). Moreover, we prove that the unconditional basis constant of this system grows at most linearly in [w]A2. The problem is reduced to the sharp weighted estimates of the so-called Haar multipliers. Even in the classical case of the standard dyadic lattice in Rd with Lebesgue reference measure our result is new in that our estimates are independent of the dimension n. Our approach combines the technique of outer measure spaces with the Bellman function argument.

Capacity Results for Binary Fading Interference Channels With Delayed CSIT

To study the effect of lack of up-to-date channel state information at the transmitters (CSITs), we consider two-user binary fading interference channels with Delayed-CSIT. We characterize the capacity region for such channels under homogeneous assumption, where channel gains have identical and independent distributions across time and space, eliminating the possibility of exploiting time/space correlation. We introduce and discuss several novel coding opportunities created by outdated CSIT that can enlarge the achievable rate region. The capacity-achieving scheme relies on accurate combination, concatenation, and merging of these opportunities, depending on the channel statistics. The outer-bounds are based on an extremal inequality we develop for a binary broadcast channel with delayed-CSIT. We further extend the results and characterize the capacity region when output feedback links are available from the receivers to the transmitters in addition to the delayed knowledge of the channel state information. We also discuss the extension of our results to the nonhomogeneous setting.

Spatial point processes and moment dynamics in the life sciences: a parsimonious derivation and some extensions.

Mathematical models of dynamical systems in the life sciences typically assume that biological systems are spatially well mixed (the mean-field assumption). Even spatially explicit differential equation models typically make a local mean-field assumption. In effect, the assumption is that diffusive movement is strong enough to destroy spatial structure or that interactions between individuals are sufficiently long-range that the effects of spatial structure are weak. However, many important biophysical processes, such as chemical reactions of biomolecules within cells, disease transmission among humans, and dispersal of plants, have characteristic spatial scales that can generate strong spatial structure at the scale of individuals, with important effects on the behaviour of biological systems. This calls for mathematical methods that incorporate spatial structure. Here, we focus on one method, spatial-moment dynamics, which is based on the idea that important information about a spatial point process is held in its low-order spatial moments. The method goes beyond the dynamics of the first moment, i.e. the mean density or concentration of agents in space, in which no information about spatial structure is retained. By including the dynamics of at least the second moment, the method retains some information about spatial structure. Whereas mean-field models effectively use a closure assumption for the second moment, spatial-moment models use a closure assumption for the third (or a higher-order) moment. The aim of the paper was to provide a parsimonious and intuitive derivation of spatial-moment dynamic equations that is accessible to non-specialists. The derivation builds naturally from the first moment to the second, and we show how it can be extended to higher-order moments. Rather than tying the model to a specific biological example, we formulate a general model of movement, birth, and death of multiple types of interacting agents. This model can be applied to problems from a range of disciplines, some of which we discuss. The derivation is performed in a spatially non-homogeneous setting, to facilitate future investigations of biological scenarios, such as invasions, in which the spatial patterns are non-stationary over space.

Complemented Brunn–Minkowski inequalities and isoperimetry for homogeneous and non-homogeneous measures

Elementary proofs of sharp isoperimetric inequalities on a normed space (Rn,‖⋅‖) equipped with a measure μ=w(x)dx so that wp is homogeneous are provided, along with a characterization of the corresponding equality cases. When p∈(0,∞] and in addition wp is assumed concave, the result is an immediate corollary of the Borell–Brascamp–Lieb extension of the classical Brunn–Minkowski inequality, providing a new elementary proof of a recent Cabré–Ros-Oton–Serra result. When p∈(−1/n,0), the relevant property turns out to be a novel “q-complemented Brunn–Minkowski” inequality:∀λ∈(0,1)∀ Borel sets A,B⊂Rnsuch thatμ(Rn∖A),μ(Rn∖B)<∞,μ⁎(Rn∖(λA+(1−λ)B))≤(λμ(Rn∖A)q+(1−λ)μ(Rn∖B)q)1/q, which we show is always satisfied by μ when wp is homogeneous with 1q=1p+n; in particular, this is satisfied by the Lebesgue measure with q=1/n. This gives rise to a new class of measures, which are “complemented” analogues of the class of convex measures introduced by Borell, but which have vastly different properties. The resulting isoperimetric inequality and characterization of isoperimetric minimizers extends beyond the recent results of Cañete–Rosales and Howe. The isoperimetric and Brunn–Minkowski type inequalities also extend to the non-homogeneous setting, under a certain log-convexity assumption on the density. Finally, we obtain functional, Sobolev and Nash-type versions of the studied inequalities.

Warped product Einstein metrics on homogeneous spaces and homogeneous Ricci solitons

Abstract In this paper we consider connections between Ricci solitons and Einstein metrics on homogeneous spaces. We show that a semi-algebraic Ricci soliton admits an Einstein one-dimensional extension if the soliton derivation can be chosen to be normal. Using our previous work on warped product Einstein metrics, we show that every normal semi-algebraic Ricci soliton also admits a k-dimensional Einstein extension for any k ≥ 2. We also prove converse theorems for these constructions and some geometric and topological structure results for homogeneous warped product Einstein metrics. In the appendix we give an alternative approach to semi-algebraic Ricci solitons which naturally leads to a definition of semi-algebraic Ricci solitons in the non-homogeneous setting.

Local mass non-equilibrium dynamics in multi-layered porous media: application to the drug-eluting stent

A solution for a model of mass diffusion from a drug-eluting stent to the arterial wall is addressed. The coating layer is described as a porous reservoir where the drug is initially loaded in polymer-encapsulated solid-phase, and then released both to the coating and to the arterial tissue in a liquid-phase. The endothelium, intima, internal elastic lamina and media are all treated as homogeneous porous media and the drug transfer through them is modelled by a non-homogeneous set of coupled partial differential equations that describe a local mass non-equilibrium diffusion problem. Drug concentration levels and mass profiles in each layer at various times are computed as a spectral decomposition: numerical results show a delayed release depending on the physico-chemical drug properties combined with the microstructure of the polymeric-coated stents.

Filtering Procedures for Reliable Outdoor Temperature Coefficients in Different Photovoltaic Technologies

Power temperature coefficients δ (TCo) measured indoor at standard test conditions (STC) (as given on products datasheet) always present a negative sign; an increase in temperature leads to a reduced power output. Interestingly, the magnitude of the TCo is not always confirmed outdoor with significant differences between technologies with even change in signs in some cases (e.g., a-Si). It is important to investigate if the reported outdoor behavior is a true effect or if it is the result of a choice of nonhomogeneous sets of data (e.g., either irradiance sensor or modules shaded). In this work, the importance of filtering procedures is discussed in order to work with a reliable set of data and to establish a method that allows comparison with indoor data.