Open Cone Research Articles

Sharp weighted log-Sobolev inequalities: Characterization of equality cases and applications

By using optimal mass transport theory, we provide a direct proof to the sharp L p L^p -log-Sobolev inequality ( p ≥ 1 ) (p\geq 1) involving a log-concave homogeneous weight on an open convex cone E ⊆ R n E\subseteq \mathbb R^n . The perk of this proof is that it allows to characterize the extremal functions realizing the equality cases in the L p L^p -log-Sobolev inequality. The characterization of the equality cases is new for p ≥ n p\geq n even in the unweighted setting and E = R n E=\mathbb R^n . As an application, we provide a sharp weighted hypercontractivity estimate for the Hopf-Lax semigroup related to the Hamilton-Jacobi equation, characterizing also the equality cases.

Low-severity fires in the boreal region: reproductive implications for black spruce stands in between stand-replacing fire events.

Stand-replacing crown fires are the most prevalent type of fire regime in boreal forests in North America. However, a substantial proportion of low-severity fires are found within fire perimeters. Here we aimed to investigate the effects of low-severity fires on the reproductive potential and seedling recruitment in boreal forests stands in between stand-replacing fire events. We recorded site and tree characteristics from 149 trees within twelve sites dominated by mature black spruce [Picea mariana (Mill.) B.S.P.] trees in the Northwest Territories, Canada. The presence of fire-scarred trees supported classification of sites as unburned or affected by low-severity fires in recent history. We used non-parametric tests to evaluate differences in site conditions between unburned and low-severity sites, and mixed effect models to evaluate differences in tree age, size, and reproductive traits among unburned trees and trees from low-severity sites. Results showed significantly higher density of dead black spruce trees in low-severity sites, and marginally significant higher presence of permafrost. Trees from low-severity fire sites were significantly older, exhibited significantly lower tree growth, and showed a tendency towards a higher probability of cone presence and percentage of open cones compared to trees from unburned sites. Surviving fire-scarred trees affected by more recent low-severity fires showed a tendency towards higher probability of cone presence and cone production. Density of black spruce seedlings significantly increased with recent low-severity fires. Trees in low-severity sites appeared to have escaped mortality from up to three fires, as indicated by fire scar records and their older ages. Shallow permafrost at low-severity sites may cause lower flammability, allowing areas to act as fire refugia. Low-severity surface fires temporarily enhanced the reproductive capacity of surviving trees and the density of seedlings, likely as a stress response to the fire event.

Ordered locales

We extend the Stone duality between topological spaces and locales to include order: there is an adjunction between the category of preordered topological spaces satisfying the so-called open cone condition, and the newly defined category of ordered locales. The adjunction restricts to an equivalence of categories between spatial ordered locales and sober T0-ordered spaces with open cones.

Stochastic modelling of symmetric positive definite material tensors

Spatial symmetries and invariances play an important role in the behaviour of materials and should be respected in the description and modelling of material properties. The focus here is the class of physically symmetric and positive definite tensors, as they appear often in the description of materials, and one wants to be able to prescribe certain classes of spatial symmetries and invariances for each member of the whole ensemble, while at the same time demanding that the mean or expected value of the ensemble be subject to a possibly ‘higher’ spatial invariance class. We formulate a modelling framework which not only respects these two requirements—positive definiteness and invariance—but also allows a fine control over orientation on one hand, and strength / size on the other. As the set of positive definite tensors is not a linear space, but rather an open convex cone in the linear space of physically symmetric tensors, we consider it advantageous to widen the notion of mean to the so-called Fréchet mean on a metric space, which is based on distance measures or metrics between positive definite tensors other than the usual Euclidean one. It is shown how the random ensemble can be modelled and generated, independently in its scaling and orientational or directional aspects, with a Lie algebra representation via a memoryless transformation. The parameters which describe the elements in this Lie algebra are then to be considered as random fields on the domain of interest. As an example, a 2D and a 3D model of steady-state heat conduction in a human proximal femur, a bone with high material anisotropy, is modelled with a random thermal conductivity tensor, and the numerical results show the distinct impact of incorporating into the constitutive model different material uncertainties—scaling, orientation, and prescribed material symmetry—on the desired quantities of interest.

Maximum principles and consequences for γ$\gamma$‐translators in Rn+1${\mathbb {R}}^{n+1}$

AbstractIn this paper, we obtain several properties of translating solitons for a general class of extrinsic geometric curvature flow, where the deformation speed is given by a homogeneous smooth symmetric positive function defined in a symmetric open cone. The main result of this paper is about the uniqueness of ‐translators in the class of complete graphs defined on a ball.

Is resource specialization the key?: some, but not all Red Crossbill call types associate with their key conifers in a diverse North American landscape

Red Crossbills (Fringillidae: Loxia curvirostra) are finches specialized to pry open cones and extract seeds of coniferous trees. Within the species, variable bill morphology may provide more efficient foraging on some species of conifers than others. Subgroups also have distinctly different contact calls often given in flight (hereafter, call types). Variable morphology and discrete call types suggest the existence of distinct evolutionary lineages. Because coniferous trees produce seeds on irregular and unpredictable schedules, crossbills wander widely in search of food. The key conifer hypothesis suggests that each call type diverged by specializing on a single conifer species to maximize foraging efficiency, while other hypotheses have emphasized geographic isolation as a driver of lineage divergence. To quantify the degree to which call types occur with specific conifer species, we surveyed Red Crossbills in five ecoregions of western and central Oregon, USA, an area with high conifer diversity. Two of five call types (Types 5 and 10) were encountered in only one ecoregion and associated with their hypothesized key conifers. Three others (Types 2, 3, and 4) were found to wander widely and did not exclusively align geographically with their presumed key conifer species. Whereas types 2 and 3 were sometimes associated with their proposed key conifers, they wandered widely during our 2-year study and occurred with a wide variety of conifers. Type 4 was not significantly associated with its key conifer and also wandered widely during our study. Relationships of call types with key conifers were weaker in the winter and spring, when Types 3 and 4 were frequently encountered in hard-coned pines rather than their soft-coned key conifer species. In our study area, the key conifer hypothesis was strongly supported only for call type 10 as that call type was not encountered away from the coastal range of Sitka Spruce (Picea sitchensis). We found mixed support for the key conifer hypothesis based on our measure of geographic associations of crossbills with a diverse array of coniferous tree species. In most cases we observed, crossbills wandered widely and associated with multiple species of conifers.

Geometry effects on energy selective focusing of laser-driven protons with open and closed hemisphere-cone targets

Relativistically intense laser light interacting with solid density targets can accelerate protons to multi-MeV energies via the target normal sheath acceleration process. The use of hollow hemisphere targets with a hollow conical region to focus protons of selected energies, for applications such as isochoric heating of matter and for the fast ignition approach to inertial confinement fusion, is explored for laser intensity Wcm−2. Specifically, the effects of having the cone tip open or closed is investigated experimentally and via a programme of scaled particle-in-cell simulations. The open cone configuration is found to result in proton focusing in the energy range of 9 to 24 MeV, and produce an annular profile for higher energy components, up to 55 MeV, while the spatial distribution of lower energy components remains unchanged. By contrast, for the closed cone case, the focusing effect is diminished by the fields present on the inner wall of the cone tip. Simulations reveal that strong electrostatic and magnetic fields present on the inner surfaces of the target induce the focusing effect with the open cone, but also result in proton divergence in the case of the closed cone. Additionally, the simulations demonstrate the possibility to tailor the cone geometry to select the energy range over which the focusing occurs.

Decomposing the Spectrum of Ultraluminous X-Ray Pulsar NGC 300 ULX-1

A phase-resolved analysis on the X-ray spectrum of ultraluminous X-ray pulsar (ULXP) NGC 300 ULX-1 is performed with data taken with XMM-Newton and NuSTAR on 2016 December 16. In addition to the classical phase-restricting analysis, a method developed in active galactic nuclei studies is newly employed for ULXP. It has revealed that the pulsation cycle of the source can be divided into two intervals in terms of X-ray variability. This suggests the rotating flow consists of at least two representative emission regions. Furthermore, the new method successfully decomposed the spectrum into an independent pair in each interval. One is an unchanging-component spectrum that can be reproduced by a standard disk model with a km inner radius and a 0.25 ± 0.03 keV peak temperature. The other is the spectrum of the component that coincides with the pulsation. This was explained with a Comptonization of a keV blackbody and exhibited a harder photon index in the brighter phase interval of two. The results are consistent with a picture that the pulsating emission originates from a funnel-like flow formed within the magnetosphere, and the inner flow exhibiting a harder continuum is observed exclusively when the opening cone points to the observer.

Non-homogeneous Riemannian gradient equations for sum of squares of Bures–Wasserstein metric

We investigate Riemannian gradient equations on the open convex cone Pm of all m×m positive definite Hermitian matrices, for the function WA(X)=∑j=1nwjdW2(X,Aj)where dW denotes the Bures–Wasserstein metric. On the special case where the gradient of the weighted sum of squares of the Bures–Wasserstein metrics vanishes, its unique solution is known as the Wasserstein mean of A1,…,An. We discuss the existence and uniqueness of solutions for non-homogeneous Riemannian gradient equations at which vector fields are constant and congruence transformations. Furthermore, we establish some bounds for these solutions.

Forest resilience and regeneration dynamics following wildfire disturbance

AbstractSpecies that are adapted to specific disturbance regimes may be sensitive to changes such as severity, frequency, and extent of ecosystem perturbation. Along range margins, these sensitivities may be exacerbated by concurrent changes in climate resulting in loss of resilience and shifts to alternative ecosystem states. Pinus banksiana (jack pine) is a serotinous species dependent on fire disturbance to open cones, release seed, reduce understory competition, and expose mineral soil. The Altona Flat Rock in northern New York is a globally rare sandstone pine barrens, at the southern edge of jack pine's range. In the summer of 2018, a wildfire burned approximately 200 ha of the Flat Rock barrens, providing the opportunity to study post‐disturbance jack pine and understory resilience. We aimed to establish if jack pine regeneration would occur, and if so, would it be influenced by fire severity, pre‐fire stand characteristics, and competition. We predicted that higher seedling densities would be associated with higher burn severity, higher pre‐fire jack pine stand density, and lesser understory competition. We collected seedling density and understory composition data annually from 2019 to 2022 across 45 plots spanning the disturbed and adjacent undisturbed barrens. In 2021 and 2022, seedling heights were also collected. Seedling densities following the disturbance ranged from 275,385 to 390,513 ha−1; = 357,821 ha−1. Jack pine seedling density was positively associated with fire severity and moss abundance for all years. Pre‐fire stand density along with ericaceous shrub, grass, and duff abundance were also positively associated with seedling density in some years. Seedling height was positively associated with fire severity along with grass and blueberry abundance. These factors, for both establishment/survival and growth, point to the importance of seed supply, microsite conditions, and facilitation in jack pine regeneration success. At this point, it does not appear that the interaction of disturbance with changing climate has shifted enough to prevent the recovery of this ecosystem to its pre‐disturbance jack pine‐dominated state. However, ongoing climate change may still have an impact on seedlings/saplings as this forest continues to mature.

IMPROVEMENT OF THE SECURITY SYSTEM AGAINST POLLUTANTS USING A CIRCULAR CONE

This study focuses on the improvement of a security system against the pollutants dispersing from Industrial chimneys. In order to simulate the system, we study numerically a turbulent flow generated by a heated open cone at the extremities. Different control parameters were used to improve the thermal and dynamic behavior of the considered flow. In this study, the interaction of pollutants with its surrounding environment simulated by the cone walls was investigated. This study was focused on convection, which is natural, turbulent, steady, 2-D, incompressible flow passing through a vertical conical channel with a heated source at the center of the cone inlet that performed uniform heating at a constant temperature. The interior of the conical wall channel was reheated via the thermal radiation emitted by the hot source. The studied system was mathematically presented by the continuity, Navier stokes, energy and K-epsilon equations. The computational fluid dynamics analysisand ANSYS-FLUENT software were used. The optimal cone can provide further control of the pollutants velocity at the exit. The thermal and dynamic profiles exhibitedgood stability and homogeneity at the cone exit.

Deep Domain Adaptation Using Cascaded Learning Networks and Metric Learning

How can we bridge efficiently distribution difference between the source and target domains in an isomorphic latent feature space by using metric learning. This study introduces metric learning on manifolds which combine a cascaded learning network and a metric learning model to form a Unified Domain Adaptation Model. Our approach is based on formulating a transfer from the source to the target as a geometric mean metric learning problem on manifolds. The solution of symmetric positive definite covariance matrices not only reduces the statistical differences between the source and target domains, but also the underlying geometry of the source and target domains using diffusions on the underlying source and target manifolds. By retaining both the nonlinear structure of the Riemannian geometry of the open cone of symmetric positive definite matrices and cascaded learning networks, we improve the state-of-the-art results on the Amazon (A), Caltech256 (C), DSLR (D), Webcam (W) and VisDA benchmark datasets by knowledge transfer, while achieving comparable performances to competing methods on domain adaptation modeling.

A note on the real support of Silva–Hasumi–Morimoto ultrahyperfunctions

Recently, we have studied the relation between the singular spectrum of a class of tempered ultrahyperfunctions corresponding to proper convex cones and their expressions as boundary values of holomorphic functions. In this note, we added some more results on the singular spectrum of the tempered ultrahyperfunctions. More specifically, the “microlocalization” of a Silva–Hasumi–Morimoto ultrahyperfunction corresponding to an open proper convex cone is addressed. Following Nishiwada’s approach to the analytic wave front set, we introduce the real singular spectrum of such an ultrahyperfunction and prove that it canonically projects onto Silva’s real support.

Mixture and interpolation of the parameterized ordered means

Loewner partial order plays a very important role in metric topology and operator inequality on the open convex cone of positive invertible operators. In this paper, we consider a family of the ordered means for positive invertible operators equipped with homogeneity and properties related to the Loewner partial order such as the monotonicity, joint concavity, and arithmetic-G-harmonic weighted mean inequalities. Similar to the resolvent average, we construct a parameterized ordered mean and compare two types of mixtures of parameterized ordered means in terms of the Loewner order. We also show a relation between two families of parameterized ordered means associated with the power mean monotonic interpolating given two parameterized ordered means.

Smooth dependence of fixed points of Hamiltonians

We consider the Lie semigroup of symplectic Hamiltonians acting on the open convex cone of positive definite matrices via linear fractional transformations. Each member of its interior contracts strictly the invariant Finsler metric, the Thompson metric on the cone, and has a unique positive definite fixed point. We show that the fixed point map is smooth. As applications, we obtain the smooth dependence of the solutions of discrete algebraic Riccati equations and a family of smooth maps from the Siegel upper half-plane over the cone of positive definite matrices into its imaginary part.

Validation of Monte Carlo-based calculations for megavolt electron beams for IORT and FLASH-IORT

In Intra-Operative Radiation Therapy (IORT) the tumour site is surgically exposed and normal tissue located around the tumour may be avoided. Electron applicators would require large surgical incisions; therefore, the preferred mechanism for beam collimation is the IORT cone system. FLASH radiotherapy (FLASH-RT) involves the treatment of tumours at ultra-high dose rates and the IORT cone system can also be used. This study validates the Monte Carlo-based calculations for these small electron beams to accurately determine the dose characteristics of each possible cone-energy combination as well as custom-built alloy cutouts attached to the end of the IORT cone. This will contribute to accurate dose distribution and output factor calculations that are essential to all radiation therapy treatments. A Monte Carlo (MC) model was modelled for electron beams produced by a Siemens Primus LINAC and the IORT cones. The accelerator was built with the component modules available in the BEAMnrc code. The phase-space file generated by the BEAM simulation was used as the source input for the subsequent DOSXYZnrc simulations. Percentage Depth Dose (PDD) data and profiles were extracted from the dose distributions obtained with the DOSXYZnrc simulations. These beam characteristics were compared with measured data for 6, 12, and 18 MeV electron beams for the IORT open cones of diameters 19, 45, and 64 mm and irregularly shaped cutouts. The MC simulations could replicate electron beams within a criterion of 3%/3 mm. Applicator factors were within 0.7%, and cone factors showed good agreement, except for the 9 mm cone size.Based on the successful comparisons between measurement and MC-calculated dose distributions, output factors for the open cones and for small irregularly shaped IORT beams, it may be concluded that the Monte Carlo based dose calculation could replicate electron beams used for IORT and FLASH-IORT.

Catalytic Performance of Cobalt(II) Polyethylene Catalysts with Sterically Hindered Dibenzopyranyl Substituents Studied by Experimental and MLR Methods.

Given the great importance of cobalt catalysts supported by benchmark bis(imino)pyridine in the (oligo)polymerization, a series of dibenzopyran-incorporated symmetrical 2,6-bis(imino) pyridyl cobalt complexes (Co1–Co5) are designed and prepared using a one-pot template approach. The structures of the resulting complexes are well characterized by a number of techniques. After activation with either methylaluminoxane (MAO) or modified MAO (MMAO), the complexes Co1–Co4 are highly active for ethylene polymerization with a maximum activity of up to 7.36 × 106 g (PE) mol−1 (Co) h−1 and produced highly linear polyethylene with narrow molecular weight distributions, while Co5 is completely inactive under the standard conditions. Particularly, complex Co3 affords polyethylene with high molecular weights of 85.02 and 79.85 kg mol−1 in the presence of MAO and MMAO, respectively. The 1H and 13C NMR spectroscopy revealed the existence of vinyl end groups in the resulting polyethylene, highlighting the predominant involvement of the β-H elimination reaction in the chain-termination process. To investigate the mechanism underlying the variation of catalytic activities as a function of substituents, multiple linear regression (MLR) analysis was performed, showing the key role of open cone angle (θ) and effective net charge (Q) on catalytic activity.

Generalized Vector-Valued Hardy Functions

We consider analytic functions in tubes Rn+iB⊂Cn with values in Banach space or Hilbert space. The base of the tube B will be a proper open connected subset of Rn, an open connected cone in Rn, an open convex cone in Rn, and a regular cone in Rn, with this latter cone being an open convex cone which does not contain any entire straight lines. The analytic functions satisfy several different growth conditions in Lp norm, and all of the resulting spaces of analytic functions generalize the vector valued Hardy space Hp in Cn. The analytic functions are represented as the Fourier–Laplace transform of certain vector valued Lp functions which are characterized in the analysis. We give a characterization of the spaces of analytic functions in which the spaces are in fact subsets of the Hardy functions Hp. We obtain boundary value results on the distinguished boundary Rn+i{0¯} and on the topological boundary Rn+i∂B of the tube for the analytic functions in the Lp and vector valued tempered distribution topologies. Suggestions for associated future research are given.

Morphological variability of Douglas fir (Pseudotsuga menziesii (Mirb.) Franco) cones in the context of seed extraction

In the paper generating curves given by fourth-degree polynomials were used to model the shape of Douglas fir (Pseudotsuga menziesii (Mirb.) Franco) cones from the Polish Forest Districts of Kołaczyce (one batch) and Opole (two batches), and to calculate the surface area and volume of individual cones. However, it was not possible to construct generalized equations for the surface area and volume of Douglas fir cones due to the high variability of empirical coefficients. The surface area and volume of the cones were also calculated from their length and diameter based on formulas for a cylinder and a barrel corrected by constants k1 and k2. The mean surface area of closed Douglas fir cones determined for the first, second, and third batch using the generating function was 4,348.4 mm2, 3,857.0 mm2, and 2,844.7 mm2, and the volume was 27,212.4 mm3, 21,012.9 mm3, and 12,844.4 mm3, respectively. The corresponding values calculated from the geometric formulas for solids were 4,332.0 mm2, 3,838.0 mm2, and 2,862.9 mm2 for the surface area and 27,366.0 mm3, 20,648.9 mm3, and 13,375.3 mm3 for the volume. The evaporation area of open cones was found to be five times greater than that of closed cones, with the difference being statistically significant. The outer and inner surfaces of scales taken from the middle segment of Douglas fir cones were photographed using a Quanta 200 scanning microscope (FEIC). The characteristic elements of scale morphology were evaluated by means of MultiScan Base software package. The outer and inner surfaces of Douglas fir scales were found to differ in some important ways, similarly as it has been reported in the literature for the Scots pine, silver fir, European larch, and black alder. The outer surface of scales is formed by thick-walled cells with marked protrusions, while the inner surface reveals cells with thin, frayed walls in the region adjacent to the seeds and wings. Knowledge of the geometry of Douglas fir cones and the morphology of their scales may be helpful in optimizing seed extraction parameters for those cones. Key words: seed extraction, model, shape curve, surface area, volume, scanning electron microscope

Weakly binary expansions of dense meet‐trees

AbstractWe compute the domination monoid in the theory of dense meet‐trees. In order to show that this monoid is well‐defined, we prove weak binarity of and, more generally, of certain expansions of it by binary relations on sets of open cones, a special case being the theory from [7]. We then describe the domination monoids of such expansions in terms of those of the expanding relations.