Explicit Characterization Research Articles

Characterizing canopy complexity of natural and restored intertidal oyster reefs (Crassostrea virginica) with a novel laser‐scanning method

The structural complexity of oyster reef canopy plays a major role in promoting biodiversity, balancing the sediment budget, and modulating hydrodynamics in estuarine systems. Although oyster canopy structure is both spatially and temporally heterogeneous, oyster canopies are generally characterized using simple first‐order quantities, like oyster density, which may lack the ability to sufficiently parameterize reef roughness. In this study, a novel laser‐scan approach was used to map the surface of intact reference and restored reefs (restoration age: 1–4 years) during low tide, when the oyster canopy was fully exposed. Measurements were used to estimate hydrodynamically relevant roughness characteristics over the entire reef surface (>140 m2; 0.50 m resolution), providing estimates of the canopy height (hc), standard deviation (), rugosity index (R), and fractal dimension (D). Average canopy heights ranged from 3.6 to 4.9 cm, with canopy height standard deviations between 1.4 and 2.0 cm. Mean rugosity indices and fractal dimensions were relatively low on the youngest (1 year) restored reef (R = 1.28;D = 2.67), with substantial increases observed for more mature reef canopies (4 years:R = 1.56;D = 2.71). Structural complexity was consistently greater on reef margins than in reef interiors. Increases in complexity were linked to restoration age, with older reefs exhibiting more complex oyster canopies. The highest fractal dimension was observed on the intact reference reef, highlighting the importance of sustained reef growth for maintaining higher‐order structural complexity. Results provide spatially explicit surface roughness characterizations for healthy, intertidal oyster reefs, with applications in both restoration science and natural and nature‐based feature design.

Non-commutative disintegrations: Existence and uniqueness in finite dimensions

Motivated by advances in categorical probability, we introduce non-commutative almost everywhere (a.e.) equivalence and disintegrations in the setting of C^* -algebras. We show that C^* -algebras (resp. W^* -algebras) and a.e. equivalence classes of 2-positive (resp. positive) unital maps form a category. We prove that non-commutative disintegrations are a.e. unique whenever they exist. We provide an explicit characterization for when disintegrations exist in the setting of finite-dimensional C^* -algebras, and we give formulas for the associated disintegrations.

Characterization of nitrogen emissions for freshwater eutrophication modelling in life cycle impact assessment at the damage level and urban scale

Human interventions mobilize massive nitrogen (N) emissions to freshwater and result in serious eutrophication impacts. Life cycle impact assessment (LCIA) provides a reliable quantitative tool to address the challenges of potential ecological impact induced by increasing nutrient inputs. However, characterization procedures that relate N emissions to ecological damage in freshwater ecosystems in LCIA methodology are still lacking. This study aims to propose a spatially explicit characterization model (1 km × 1 km) for N-induced freshwater eutrophication. A complete cause-effect chains linking the N emission with species loss endpoint impact was constructed, in which the site-specific fate factor modelling contained transfer and removal processes in terrestrial and freshwater compartments, and the mechanistic modelling of ecosystem exposure and damage effect were quantified with species loss. The eutrophication characterization was conducted with a case study in Guangzhou, China, and 1 km × 1 km spatial differentiation of eutrophication susceptibility was intuitively demonstrated, with higher values in the Pearl River Estuary area. Method comparisons and further improvements were discussed in support of model generalization and further application.

Potential and limitations of quantum extreme learning machines

Quantum extreme learning machines (QELMs) aim to efficiently post-process the outcome of fixed — generally uncalibrated — quantum devices to solve tasks such as the estimation of the properties of quantum states. The characterisation of their potential and limitations, which is currently lacking, will enable the full deployment of such approaches to problems of system identification, device performance optimization, and state or process reconstruction. We present a framework to model QELMs, showing that they can be concisely described via single effective measurements, and provide an explicit characterisation of the information exactly retrievable with such protocols. We furthermore find a close analogy between the training process of QELMs and that of reconstructing the effective measurement characterising the given device. Our analysis paves the way to a more thorough understanding of the capabilities and limitations of QELMs, and has the potential to become a powerful measurement paradigm for quantum state estimation that is more resilient to noise and imperfections.

The corona theorem for bounded analytic functions in Q K type spaces

ABSTRACT For 1 < p < ∞ and a nondecreasing function K on [ 0 , ∞ ) , we give an explicit derivative-free characterization of Q K type space, denoted by Q K p and characterize the boundary version of Q K p . By using these results, we prove the corona theorems both for Q K p ∩ H ∞ and for the multiplier algebra of Q K p under some assumptions of the weight function K.

Structural Properties of Gibbsian Point Processes in Abstract Spaces

In the language of random counting measures, many structural properties of the Poisson process can be studied in arbitrary measurable spaces. We provide a similarly general treatise of Gibbs processes. With the GNZ equations as a definition of these objects, Gibbs processes can be introduced in abstract spaces without any topological structure. In this general setting, partition functions, Janossy densities, and correlation functions are studied. While the definition covers finite and infinite Gibbs processes alike, the finite case allows, even in abstract spaces, for an equivalent and more explicit characterization via a familiar series expansion. Recent generalizations of factorial measures to arbitrary measurable spaces, where counting measures cannot be written as sums of Dirac measures, likewise allow to generalize the concept of Hamiltonians. The DLR equations, which completely characterize a Gibbs process, as well as basic results for the local convergence topology, are also formulated in full generality. We prove a new theorem on the extraction of locally convergent subsequences from a sequence of point processes and use this statement to provide existence results for Gibbs processes in general spaces with potentially infinite range of interaction. These results are used to guarantee the existence of Gibbs processes with cluster-dependent interactions and to prove a recent conjecture concerning the existence of Gibbsian particle processes.

Parking Functions, Multi-shuffle, and Asymptotic Phenomena

Given a positive integer-valued vector $${\textbf{u}}=(u_1, \dots , u_m)$$ with $$u_1<\cdots <u_m$$ , a $${\textbf{u}}$$ -parking function of length m is a sequence $$\varvec{\pi }=(\pi _1, \dots , \pi _m)$$ of positive integers whose non-decreasing rearrangement $$(\lambda _1, \dots , \lambda _m)$$ satisfies $$\lambda _i\le u_i$$ for all $$1\le i\le m$$ . We introduce a combinatorial construction termed a parking function multi-shuffle to generic $${\textbf{u}}$$ -parking functions and obtain an explicit characterization of multiple parking coordinates. As an application, we derive various asymptotic probabilistic properties of a uniform $${\textbf{u}}$$ -parking function of length m when $$u_i=cm+ib$$ . The asymptotic scenario in the generic situation $$c>0$$ is in sharp contrast with that of the special situation $$c=0$$ .

N-Doped Carbon Dots and ZnO Conglomerated Electrodes for Optically Responsive Supercapacitor Applications

The over-dependence of human society on fossil fuels for energy is exhausting the level of such non-renewable energy sources. Alternative energy storage systems have gained more popularity recently to counter this issue. In this context, we report the fabrication of N-doped carbon dot (N-CD)-decorated ZnO-based electrodes for supercapacitor applications. Due to the light-responsive nature of the N-CDs and ZnO, the electrode was also responsive under the influence of UV light. After the experimental tests, it was found that the areal capacitance value of the supercapacitor increased upto ∼58.9% when illuminated compared to that under the dark conditions. Moreover, the device showed a maximum areal capacitance of 2.6 mF/cm2 after photocharging and galvanostatically discharging at a current density value of 1.6 μA/cm2, which is quite comparable with the previously reported data. The doping of N-CDs with ZnO showed a significant improvement in the areal capacitance value under both illuminated (∼58.64%) and dark conditions (∼22.08%) compared to the case of pristine ZnO, which justifies the purpose of attaching N-CDs with ZnO. Therefore, in brief, we have fabricated a photoresponsive electrode material for supercapacitor application by combining N-CDs and ZnO. An explicit electrochemical characterization of the electrode was also done to identify the contribution from diffusion-controlled capacitance and double layer capacitance, and it was observed that the diffusion-controlled capacitance gets reduced from 59.1 to 33.6% when the scan rate is increased from 2 to 75 mV/s. Moreover, a detailed study has also been done to understand the reaction mechanism. It was confirmed that the defects in the electrode material played a vital role in the intercalation of K+ ions.

On Several Parameters of Super Line Graph L2(G)

The super line graph of index r, denoted by Lr(G), is defined for any graph G with at least r edges. Its vertices are the sets of r edges of G, and two such sets are adjacent if an edge of one is adjacent to an edge of the other. In this paper, we give an explicit characterization for all graphs G with L2(G) being a complete graph. We present lower bounds for the clique number and chromatic number of L2(G) for several classes of graphs. In addition, bounds for the domination number of L2(G) are established in terms of the domination number of the line graph L(G) of a graph. A number of related problems on L2(G) are proposed for a further study.

Adversarial Robustness via Fisher-Rao Regularization.

Adversarial robustness has become a topic of growing interest in machine learning since it was observed that neural networks tend to be brittle. We propose an information-geometric formulation of adversarial defense and introduce Fire, a new Fisher-Rao regularization for the categorical cross-entropy loss, which is based on the geodesic distance between the softmax outputs corresponding to natural and perturbed input features. Based on the information-geometric properties of the class of softmax distributions, we derive an explicit characterization of the Fisher-Rao Distance (FRD) for the binary and multiclass cases, and draw some interesting properties as well as connections with standard regularization metrics. Furthermore, we verify on a simple linear and Gaussian model, that all Pareto-optimal points in the accuracy-robustness region can be reached by Fire while other state-of-the-art methods fail. Empirically, we evaluate the performance of various classifiers trained with the proposed loss on standard datasets, showing up to a simultaneous 1% of improvement in terms of clean and robust performances while reducing the training time by 20% over the best-performing methods.

Risk-sharing and optimal contracts with large exogenous risks

We consider a dynamic principal–agent model that naturally extends the classical Holmström–Milgrom setting to include a risk capable of stopping production completely. We obtain an explicit characterization of the optimal wage along with the optimal action provided by the agent. The optimal contract is linear by offering both a fixed share of the output which is similar to the standard Holmström–Milgrom model and a linear prevention mechanism that is proportional to the random lifetime of the contract. We then extend the model by allowing insurable risks where the agent can control the intensity of the failure by exerting an additional costly effort.

An explicit characterization of isochordal-viewed multihedgehogs with circular isoptics

A curve α is called (ϕ,ℓ)-isochordal viewed if a straight segment of constant length ℓ can slide with its endpoints on α and such that their tangents to α at these endpoints make a constant angle ϕ. These tangents determine the so-called ϕ-isoptic curve of α. In this paper, an explicit characterization of all (ϕ,ℓ)-isochordal-viewed multihedgehogs with circular ϕ-isoptics is provided by their support functions, which are obtained as the solutions of a differential equation. This allows to construct any example of these curves in a very simple way from some free parameters. In addition, it is shown that a regular polygon of side length ℓ can slide smoothly along these multihedgehogs.

Gas-Phase Characterization of Hypervalent Carbon Compounds Bearing 7-6-7-Ring Skeleton: Penta- versus Tetra-Coordinate Isomers.

In this study, we afford explicit characterizations of the electronic and geometrical structures of recently reported hypervalent penta-coordinate carbon compounds by using gas-phase characterization techniques: photodissociation spectroscopy (PDS) and ion mobility-mass spectrometry (IM-MS). In particular for a compound with moderately electron-donating ligands, bearing p-methylthiophenyl substituents, the coexistence of tetra- and penta-coordinate isomers is confirmed, consistent with solution characterizations. It is in sharp contrast to the exclusive tetra-coordinate form (with normal valence of the central carbon atom) in the single crystal. This suggests that a non-polar environment makes the penta-coordinate structure thermodynamically most stable. This delicate difference between the tetra- and penta-coordinate structures, which depends on the environment, is a close reflection of the lower activation barrier of the SN 2 reaction found in neutral solvent or gas-phase reactions.

A quantitative enhanced assessment for ancient landslide reactivation risk considering cross-time scale joint response mechanism

Ancient landslide has strong concealment and disturbance sensitivity due to its special geotechnical mechanical characteristics, and it is the potential hazard that cannot be ignored in human activities and major engineering planning. The quantitative assessment of ancient landslide reactivation risk has become more necessary for pre-disaster scientific warning. However, because the mechanisms of deformation and damage during the evolution of ancient landslides are quite complex, traditional landslide risk assessment methods only select the single-time scale and relatively stable environmental factors for analysis, lacking consideration of dynamic triggering factors such as rainfall. Focusing on the complexity, a quantitative enhanced assessment for ancient landslide reactivation risk considering cross-time scale joint response mechanism is proposed. First, on the basis of systematic analysis of the implicit genesis mechanism and explicit characterization, an evaluation system of the cross-time scale joint characteristics of ancient landslide reactivation is constructed. Then, XGBoost algorithm and SBAS-InSAR are used to establish the long-time scale developmental evolution mechanism model and the short-time scale dynamical trigger model, respectively. Subsequently, we propose a cross-time scale joint response mechanism. The information entropy weight method is applied to calculate the contribution degree of long-short time scale assessment models for ancient landslide reactivation based on the constraints of quantitative interval thresholds, and the assessment processes of different time scales are dynamically and quantitatively correlated. Finally, the updated optimization of the assessment of ancient landslide reactivation risk is achieved. In this research, experimental analysis was carried out for ancient landslide groups in a geological hazard-prone area in Fengjie County, Chongqing, a typical mountainous region of China. The results of the comparative analysis validate the superiority of the method in this paper. It helps to accurately assess the ancient landslide potential hazard in advance, providing scientific basis and technical support for the risk assessment of mountainous watershed geological hazards and major engineering projects.

Determination and Sensitivity Analysis of the Specular Reflection Point in GNSS Reflectometry

In applying Global Navigation Satellite System Reflectometry (GNSS-R) techniques for the remote sensing of surface properties of the Earth, it is imperative to determine the specular reflection point and provide a quantitative characterization of the associated errors. In this article, a rigorous formulation of the problem with respect to ellipsoidal Earth is provided for the determination and error analysis of the specular reflection point. A polynomial equation approach is developed to characterize the specular reflection point. This explicit characterization is beneficial in the GNSS-R receiver operation. The sensitivity analysis is further performed to assess the errors in the presence of uncertainties.

Remark on complements on surfaces

Abstract We give an explicit characterization on the singularities of exceptional pairs in any dimension. In particular, we show that any exceptional Fano surface is $\frac {1}{42}$ -lc. As corollaries, we show that any $\mathbb R$ -complementary surface X has an n-complement for some integer $n\leq 192\cdot 84^{128\cdot 42^5}\approx 10^{10^{10.5}}$ , and Tian’s alpha invariant for any surface is $\leq 3\sqrt {2}\cdot 84^{64\cdot 42^5}\approx 10^{10^{10.2}}$ . Although the latter two values are expected to be far from being optimal, they are the first explicit upper bounds of these two algebraic invariants for surfaces.

Rank-one transformations, odometers, and finite factors

In this paper we give explicit characterizations, based on the cutting and spacer parameters, of (a) which rank-one transformations factor onto a given finite cyclic permutation, (b) which rank-one transformations factor onto a given odometer, and (c) which rank-one transformations are isomorphic to a given odometer. These naturally yield characterizations of (d) which rank-one transformations factor onto some (unspecified) finite cyclic permutation, (d′) which rank-one transformations are totally ergodic, (e) which rank-one transformations factor onto some (unspecified) odometer, and (f) which rank-one transformations are isomorphic to some (unspecified) odometer.

Understanding the complex interplay of persistent and antipersistent regimes in animal movement trajectories as a prominent characteristic of their behavioral pattern profiles: Towards an automated and robust model based quantification of anxiety test data

Rapid advancement in computer vision technologies provides increasing opportunities for the quantitative characterization of animal behavior, although reduction of their analysis to several scalar metrics appears a common limitation for the representation of complex behavioral patterns. Here we suggest an alternative approach to the quantitative assessment of animal behavioral patterns by parameterization of a generalized scalable model based on fractional Brownian motion using detrended fluctuation analysis of the observational movement trajectories and validate it using novel tank test data. In a zebrafish model representative movement patterns are characterized by two asymptotic regimes, with persistent increments at small scales and antipersistent increments at large scales. A single crossover between these asymptotic regimes that appears a single free parameter of the animal movement model acts as a complementary behavioral indicator leading to a more explicit characterization of both stimulative and sedative effects. We show explicitly that the model can be also used for a robust estimation of interpretable scalar metrics commonly used in behavioral analysis leading to the emphasized differences between experimental groups. We believe that this approach, due to its universality, robustness and clear physical interpretation, is a perspective tool for the analysis of animal behavior complexity under various experimental and natural conditions.

A characterization of Thurston’s Master Teapot

AbstractWe prove an explicit characterization of the points in Thurston’s Master Teapot, which can be implemented algorithmically to test whether a point in$\mathbb {C}\times \mathbb {R}$belongs to the complement of the Master Teapot. As an application, we show that the intersection of the Master Teapot with the unit cylinder is not symmetrical under reflection through the plane that is the product of the imaginary axis of$\mathbb {C}$and$\mathbb {R}$.

A characterization of the zero-free region of the Riemann zeta function and its applications

We characterize the zero-free regions of a class of functions (including the Riemann zeta function) in half-planes in terms of closures of ranges of the corresponding multiplication operators on Hardy spaces. We give an explicit characterization of these closures. As applications, we obtain a weaker version of the Nyman–Beurling–Báez-Duarte criterion, and provide some investigations on a problem relating to the Riemann hypothesis proposed by Báez-Duarte et al. [Adv. Math. 149 (2000) 130-144].