Pastur Distribution Research Articles

Drivers of human–tiger conflict risk and potential mitigation approaches

AbstractHuman–wildlife conflict has become a significant challenge for conservationists, particularly in areas where endangered species, such as large carnivores, are recovering. If we fail to keep a balance between the interests of humans and wildlife, the human–wildlife conflict can have adverse outcomes. However, the drivers of human–wildlife conflict, and how to mitigate conflict, are often poorly understood. In this study, we aimed to explore the possible causes for and potential mitigating approaches to human–tiger conflict risks through spatiotemporal niche partitioning. Based on data from the reports of Amur tiger (Panthera tigris altaica) preying on cattle and camera trap detection data from 2014 to 2019 in Hunchun, Northeast China, we predicted Amur tiger occurrence and created risk maps of human–tiger potential encounters. We found that Amur tiger occurrence was positively driven by prey distribution and negatively by the distribution of pastures used for domestic cattle grazing. Livestock was increasingly predated in areas with limited preferred prey, that is, wild pig (Sus scrofa) and sika (Cervus nippon), and in closer proximity to cattle‐grazing land. On the basis of our models, we divided areas utilized by human and Amur tigers into low‐, medium‐, and high‐risk areas across multiple spatiotemporal scales. We suppose that multiple spatiotemporal scale niche partitioning management might effectively reduce the risk of human–tiger encounters, prompt harmonized coexistence between humans and tigers, and provide new solutions to other areas experiencing human–wildlife conflicts.

A Dyson Brownian Motion Model for Weak Measurements in Chaotic Quantum Systems

We consider a toy model for the study of monitored dynamics in many-body quantum systems. We study the stochastic Schrödinger equation resulting from continuous monitoring with a rate Γ of a random Hermitian operator, drawn from the Gaussian unitary ensemble (GUE) at every time t. Due to invariance by unitary transformations, the dynamics of the eigenvalues {λα}α=1n of the density matrix decouples from that of the eigenvectors, and is exactly described by stochastic equations that we derive. We consider two regimes: in the presence of an extra dephasing term, which can be generated by imperfect quantum measurements, the density matrix has a stationary distribution, and we show that in the limit of large size n→∞ it matches with the inverse-Marchenko–Pastur distribution. In the case of perfect measurements, instead, purification eventually occurs and we focus on finite-time dynamics. In this case, remarkably, we find an exact solution for the joint probability distribution of λ’s at each time t and for each size n. Two relevant regimes emerge: at short times tΓ=O(1), the spectrum is in a Coulomb gas regime, with a well-defined continuous spectral distribution in the n→∞ limit. In that case, all moments of the density matrix become self-averaging and it is possible to exactly characterize the entanglement spectrum. In the limit of large times tΓ=O(n), one enters instead a regime in which the eigenvalues are exponentially separated log(λα/λβ)=O(Γt/n), but fluctuations ∼O(Γt/n) play an essential role. We are still able to characterize the asymptotic behaviors of the entanglement entropy in this regime.

Random Tensor Networks with Non-trivial Links

Random tensor networks are a powerful toy model for understanding the entanglement structure of holographic quantum gravity. However, unlike holographic quantum gravity, their entanglement spectra are flat. It has therefore been argued that a better model consists of random tensor networks with link states that are not maximally entangled, i.e., have non-trivial spectra. In this work, we initiate a systematic study of the entanglement properties of these networks. We employ tools from free probability, random matrix theory, and one-shot quantum information theory to study random tensor networks with bounded and unbounded variation in link spectra, and in cases where a subsystem has one or multiple minimal cuts. If the link states have bounded spectral variation, the limiting entanglement spectrum of a subsystem with two minimal cuts can be expressed as a free product of the entanglement spectra of each cut, along with a Marchenko–Pastur distribution. For a class of states with unbounded spectral variation, analogous to semiclassical states in quantum gravity, we relate the limiting entanglement spectrum of a subsystem with two minimal cuts to the distribution of the minimal entanglement across the two cuts. In doing so, we draw connections to previous work on split transfer protocols, entanglement negativity in random tensor networks, and Euclidean path integrals in quantum gravity.

Decomposing cryptocurrency high-frequency price dynamics into recurring and noisy components

This paper investigates the temporal patterns of activity in the cryptocurrency market with a focus on Bitcoin, Ethereum, Dogecoin, and WINkLink from January 2020 to December 2022. Market activity measures—logarithmic returns, volume, and transaction number, sampled every 10 s, were divided into intraday and intraweek periods and then further decomposed into recurring and noise components via correlation matrix formalism. The key findings include the distinctive market behavior from traditional stock markets due to the nonexistence of trade opening and closing. This was manifested in three enhanced-activity phases aligning with Asian, European, and U.S. trading sessions. An intriguing pattern of activity surge in 15-min intervals, particularly at full hours, was also noticed, implying the potential role of algorithmic trading. Most notably, recurring bursts of activity in bitcoin and ether were identified to coincide with the release times of significant U.S. macroeconomic reports, such as Nonfarm payrolls, Consumer Price Index data, and Federal Reserve statements. The most correlated daily patterns of activity occurred in 2022, possibly reflecting the documented correlations with U.S. stock indices in the same period. Factors that are external to the inner market dynamics are found to be responsible for the repeatable components of the market dynamics, while the internal factors appear to be substantially random, which manifests itself in a good agreement between the empirical eigenvalue distributions in their bulk and the random-matrix theory predictions expressed by the Marchenko–Pastur distribution. The findings reported support the growing integration of cryptocurrencies into the global financial markets.

National-Territorial Delimitation in Central Asia in the 1920s: the Emergence of Border Disputes

The formation of the administrative borders of the Central Asian republics is connected with the historical events of the 1920s, the Bolshevik policy of division, or national-territorial demarcation of this vast Islamized region in the center of Eurasia. The Central Asian states that existed during the imperial period (Bukhara Emirate, Khiva and Kokand khanates), as well as during the initial period of Sovietization of the region (Turkestan ASSR, Bukhara NSR and Khorezm NSR) were not national entities. After the end of the Civil War, the Bolsheviks, within the framework of the "policy of self-determination of peoples", assumed that each state was to unite the population within a single nation, defined primarily by ethnicity. However, the implementation of these guidelines ran up against the lack of clear ethnic boundaries and the multiculturalism of the region; conflicts over the distribution of water, pasture, and minerals were not uncommon in the delimitation of borders. The territorial delimitation in the Fergana Valley, perceived by the Bolsheviks as a stronghold of the antiSoviet movement in Central Asia under the slogans of Pan-Islamism and Pan-Turkism, was especially difficult. It is no coincidence that the Fergana Valley, which was a single economic, cultural and historical complex, turned out to be divided between three state formations, the border disputes between which have not yet been finally resolved.

CORRELATION MATRIX OF EQUI-CORRELATED NORMAL POPULATION: FLUCTUATION OF THE LARGEST EIGENVALUE, SCALING OF THE BULK EIGENVALUES, AND STOCK MARKET

Given an N-dimensional sample of size [Formula: see text] form a sample correlation matrix [Formula: see text]. Suppose that N and T tend to infinity with [Formula: see text] converging to a fixed finite constant [Formula: see text]. If the population is a factor model, then the eigenvalue distribution of [Formula: see text] almost surely converges weakly to Marčenko–Pastur distribution such that the index is Q and the scale parameter is the limiting ratio of the specific variance to the ith variable [Formula: see text]. For an N-dimensional normal population with equi-correlation coefficient [Formula: see text], which is a one-factor model, for the largest eigenvalue [Formula: see text] of [Formula: see text], we prove that [Formula: see text] converges to the equi-correlation coefficient [Formula: see text] almost surely. These results suggest an important role of an equi-correlated normal population and a factor model in Laloux et al. [(2000) Random matrix theory and financial correlations, International Journal of Theoretical and Applied Finance3 (3), 391–397]: the histogram of the eigenvalue of sample correlation matrix of the returns of stock prices fits the density of Marčenko–Pastur distribution of index [Formula: see text] and scale parameter [Formula: see text]. Moreover, we provide the limiting distribution of the largest eigenvalue of a sample covariance matrix of an equi-correlated normal population. We discuss the phase transition as to the decay rate of the equi-correlation coefficient in N.

Distribution of Wood Pastures in Slovakia—Constraints and Potentials for Restoration of Multifunctional Traditional Land Use Form

Wood pastures represent specific ecosystems across Europe with diverse ecological, agricultural, and socioeconomic roles. Land-use changes and the cessation of traditional management in conjunction with socioeconomic changes led to shifts in their spatiotemporal distribution. Despite a recent increase in scientific interest, data on historical patterns of wood pastures in many European locations remain insufficient. This study presents wood-pasture habitat continuity and analyzes changes in their distribution over space and time in selected parts of Slovakia. Simultaneously, we analyzed the relation of wood pastures to selected environmental and landscape features. To achieve this, we examined the historical distribution of wood pastures using aerial imagery from the 1950s. We thoroughly examined an area of 16,209 km2 to identify preserved wood pastures. To identify the present conditions and the spatial distribution of wood-pasture habitats, we compared the historical data with recent ortophotomaps. Based on landscape–ecological analyses of historical distribution, we determined prevailing environmental conditions of wood-pasture locations. The findings reveal that over 90% of wood pastures from the first half of the 20th century have now been lost or encroached and preserved in the form of a closed-canopy forest. In most of the encroached sites, we identified the presence of vital core veteran trees. For the identification of wood pastures and further analyses of the environmental variables, the ArcGIS 10.3 program was used; the R software was used for all statistical evaluations. The results show that the studied wood pastures were not established randomly, but were rather set within a certain landscape context, characterized by elevation, soil quality, and distance from settlements.

On the eigenvectors of large-dimensional sample spatial sign covariance matrices

To investigate the limiting behavior of eigenvectors of the sample spatial sign covariance matrix (SSCM), the eigenvector empirical spectral distribution (VESD) is defined with weights depending on the eigenvectors. In this paper, we first show that the VESD of a large-dimensional sample SSCM converges to a generalized Marčenko–Pastur distribution when both the dimension p of observations and the sample size n tend to infinity proportionally. Further, the central limit theorem of linear spectral statistics of VESD is established, which suggests that the eigenmatrix of sample SSCM and the classical sample covariance matrix are asymptotically the same.

The Influence of Landscape Structure on Wildlife–Vehicle Collisions: Geostatistical Analysis on Hot Spot and Habitat Proximity Relations

Vehicle collisions with animals pose serious issues in countries with well-developed highway networks. Both expanding wildlife populations and the development of urbanised areas reduce the potential contact distance between wildlife species and vehicles. Many recent studies have been conducted to better understand the factors that influence wildlife–vehicle collisions (WVCs) and provide mitigation methods. Most of these studies examined road density, traffic volume, seasonal fluctuations, etc. However, in analysing the distribution of WVC, few studies have considered a spatial and significant distance geostatistical analysis approach that includes how different land-use categories are associated with the distance to WVCs. Our study investigated the spatial distribution of agricultural land, meadows and pastures, forests, built-up areas, rivers, lakes, and ponds, to highlight the most dangerous sections of roadways where WVCs occur. We examined six potential ‘hot spot’ distances (5–10–25–50–100–200 m) to evaluate the role different landscape elements play in the occurrence of WVC. The near analysis tool showed that a distance of 10–25 m to different landscape elements provided the most sensitive results. Hot spots associated with agricultural land, forests, as well as meadows and pastures, peaked on roadways in close proximity (10 m), while hot spots associated with built-up areas, rivers, lakes, and ponds peaked on roadways farther (200 m) from these land-use types. We found that the order of habitat importance in WVC hot spots was agricultural land < forests < meadows and pastures < built-up areas < rivers < lakes and ponds. This methodological approach includes general hot-spot analysis as well as differentiated distance analysis which helps to better reveal the influence of landscape structure on WVCs.

On the asymptotic behavior of the eigenvalue distribution of block correlation matrices of high-dimensional time series

We consider linear spectral statistics built from the block-normalized correlation matrix of a set of M mutually independent scalar time series. This matrix is composed of [Formula: see text] blocks. Each block has size [Formula: see text] and contains the sample cross-correlation measured at L consecutive time lags between each pair of time series. Let N denote the total number of consecutively observed windows that are used to estimate these correlation matrices. We analyze the asymptotic regime where [Formula: see text] while [Formula: see text], [Formula: see text]. We study the behavior of linear statistics of the eigenvalues of this block correlation matrix under these asymptotic conditions and show that the empirical eigenvalue distribution converges to a Marcenko–Pastur distribution. Our results are potentially useful in order to address the problem of testing whether a large number of time series are uncorrelated or not.

The role of accessibility for land use and land cover change in the Brazilian Amazon

Roads and infrastructure are fundamental preconditions for the large-scale conversion of natural forests into agricultural landscapes. Therefore, geographic differences in accessibility are critical for understanding land use and land cover change (LULCC) dynamics. As one of the most dynamic agricultural frontiers globally, the Amazon has much attention in LULCC research. While most studies account for roads and infrastructure, LULCC research often relies on one-dimensional measures of accessibility (e.g., Euclidean distances), which may not optimally represent the underlying latent variable concept. In this study, we demonstrate how alternative concepts and measures of accessibility (specifically travel time maps) can have considerably different explanatory value in the prediction of LULCC. We adopt a panel-data model to explain the geographical distribution of pasture and crop expansion in the Brazilian Amazon using land cover data and travel time maps generated with high-quality representations of existing official and non-official road infrastructure. Our approach's novelty consists of comparing travel time to different markets during the wet- and the dry season and their effect on the allocation of LULCC within a macro scale modeling approach. Our results suggest that (1) pronounced differences between wet- and rainy season accessibility (due to road quality) increase the likelihood of pasture expansion and reduce the likelihood for crops, and (2) that alternative measures of infrastructure access (e.g., to markets versus towns or processing facilities) can explain different socio-economic aspects of LULCC. Our findings suggest that bad infrastructure quality might severely limit the possibility of establishing a less land-intensive agricultural model in the Amazon and that LULCC research can significantly benefit from improved and context-specific measures of accessibility.

Timing of Protein/energy Supplementation in Late Gestating Bos Indicus-influenced Beef Cows Influences Postnatal Growth, Immunity and Carcass Characteristics of Their Offspring

Abstract This 2-yr study investigated the timing of dried distillers grains (DDG) supplementation of Bos indicus-influenced cows during late gestation and its impacts on offspring performance. On d 0, 84 Brangus cows/yr were stratified by BW (482 ± 75 kg) and BCS (5.3 ± 0.8) and randomly assigned to bahiagrass pastures (14 cows/pasture). Treatments were randomly assigned to pastures (2 pastures/treatment/yr) and consisted of no prepartum supplementation (CON), 2 kg/d of DDG from d 0 to 42 (LATE42), or 1 kg/d of DDG from d 0 to 84 (LATE84). At weaning (d 347), 38 steers/yr were vaccinated against bovine respiratory disease, transported for 720 mi to the feedlot, penned according to prepartum pasture distribution, and fed the same corn silage-based diet until harvest. Data were analyzed using SAS GLIMMIX procedure. Cow BCS at calving was greater (P ≤ 0.05) for LATE84 and LATE42 vs. CON cows and did not differ (P = 0.16) between LATE84 and LATE 42 cows. Cows offered LATE42 supplementation had greater (P ≤ 0.05) calving percentage from wk 2 to 6 of the subsequent calving season than CON and LATE84 cows. Calf BW at weaning was greater (P ≤ 0.05) for LATE 84 vs. LATE42 calves, and the latter greater than CON calves (269, 261, and 255 ± 2.6 kg, respectively). Seroconversion against parainfluenza-3 virus at weaning was greater (P ≤ 0.05) for LATE42 vs. CON steers, with LATE84 being intermediate. Feedlot BW and carcass weight did not differ (P ≥ 0.36) among treatments, but marbling scores and carcasses grading choice tended (P ≤ 0.10) to be greater for LATE42 vs. CON steers, with LATE84 being intermediate. Therefore, timing of DDG supplementation during late gestation in Bos indicus-influenced cows enhanced calf weaning weight, humoral immunity, and carcass characteristics at different magnitudes than cohorts born from non-supplemented cows.

Effects of Winter vs. Year-round Supplementation of Multiparous Bos Indicus-influenced Beef Cows on Offspring Postnatal Growth, Immunity, and Carcass Characteristics

Abstract This 2-yr study evaluated the effects of winter vs. year-round supplementation of Bos indicus-influenced beef cows on offspring feedlot performance. Brangus cows (82–84 cows/yr) were stratified by BW and BCS (475 ± 67 kg; 4.85 ± 0.73) and randomly assigned to bahiagrass pastures (13–14 cows/pasture). Treatments were randomly assigned to pastures (2 pastures/treatment/yr) and consisted of winter supplementation with molasses (MOL-W), or year-round supplementation with molasses (MOL-Y) or cubes (CUB-Y). Supplements were isocaloric and isonitrogenous (75% TDN, 20% CP; DM basis). Total yearly supplement DM amount was 272 kg/cow for all treatments. At weaning (d 421), 33–35 steers/yr were vaccinated against bovine respiratory disease, transported for 720 miles to the feedlot, penned according to prepartum pasture distribution, and fed the same corn silage-based diet until harvest. Data were analyzed using SAS GLIMMIX procedure. Cow BCS at calving was greater (P < 0.01) for MOL-Y and CUB-Y vs. CON cows. Calving rate, calving date, calf birth weight, and calf preweaning BW did not differ (P ≥ 0.22) among treatments. Steer feedlot BW did not differ (P ≥ 0.36) at time of feedlot entry but was greater (P ≤ 0.05) for MOL-Y and MOL-W steers vs. CUB-Y steers at feedlot exit. Plasma haptoglobin concentrations at feedlot entry were greater (P = 0.05) for CUB-Y vs. CON steers, with MOL-Y steers being intermediate, whereas plasma cortisol concentrations at feedlot entry were greater (P ≤ 0.05) for CUB-Y vs. MOL-Y and MOL-W steers. Marbling score, yield grade, and carcass weight did not differ (P ≥ 0.14), but CON steers had greater fat thickness at the 12th rib than MOL-Y and CUB-Y steers. Hence, year-round supplementation (molasses or cubes) of beef cows increased cow BCS at calving but had minor effects on offspring post-weaning growth and immunity compared to winter supplementation of molasses.

Estimating biological capacity for grass-finished ruminant meat production in New England and New York

The Northeastern United States contributes a small share to national meat production. However, increasing interest in local food production and on-going challenges posed by drought and fire on Western rangelands give reason to believe that the importance of Northeastern grass-based ruminant meat could grow in the near future. Using an integrated modeling approach, the present study quantifies current and potential biological capacity for grass-based ruminant meat production in New York and New England. We used the Cropland Data Layer (CDL) to establish the area and spatial distribution of hay and pasture, with area estimates validated against the USDA Census of Agriculture. Potential forage productivity was modeled using ordinary least squares linear regression of SSURGO non-irrigated crop yield values for pasture against NICC classes and subclasses, drainage classes, slope, air temperature, and quintiles of depth to restrictive soil layers, using ordinary least squares linear regression. Forage yield gaps were calculated by comparing potential productivity to annual crop survey data from the USDA. The potential production of grass-finished cattle based on either current or potential forage yields based on models of feed needs for spring- and fall-calving herds produced using the Large Ruminant Nutritional System. We show that more than half of agricultural land cover currently appears to be pasture, but that only some of this land is actively used for grazing, with actual yields just 54% or 47% of economic yields for hay and pasture respectively. Overall, we estimate the potential to increase the regional beef herd size by 90% to 270% by increasing yields, expanding production into unutilized grassland area, or both. We conclude that up to 3% of U.S. beef could be produced in the region, on less than 0.5% of U.S. agricultural land area, pointing to high potential for sustainable intensification of beef production in the Northeastern United States. Realizing this potential, however, requires closing of yield gaps and intensification of the use of land in agricultural cover. The amount of biophysical productivity that is economically attainable remains highly uncertain.

Extreme-value statistics of stochastic transport processes

We derive exact expressions for the finite-time statistics of extrema (maximum and minimum) of the spatial displacement and the fluctuating entropy flow of biased random walks. Our approach captures key features of extreme events in molecular motor motion along linear filaments. For one-dimensional biased random walks, we derive exact results which tighten bounds for entropy production extrema obtained with martingale theory and reveal a symmetry between the distribution of the maxima and minima of entropy production. Furthermore, we show that the relaxation spectrum of the full generating function, and hence of any moment, of the finite-time extrema distributions can be written in terms of the Marčenko–Pastur distribution of random-matrix theory. Using this result, we obtain efficient estimates for the extreme-value statistics of stochastic transport processes from the eigenvalue distributions of suitable Wishart and Laguerre random matrices. We confirm our results with numerical simulations of stochastic models of molecular motors.

71 Effects of timing of supplementation during late gestation in Bos indicus-influenced beef cows on post-weaning growth, immunity, and carcass characteristics of steer progeny

Abstract This study evaluated the growth, immunity, and carcass characteristics of beef steers born to cows offered dried distillers grains (DDG) at different timing during late gestation. Approximately 84 d before calving (d 0), 84 mature Brangus cows were stratified by BW and BCS (422 ± 42 kg; 5.0 ± 0.14) and allocated into 1 of 6 bahiagrass pastures (14 cows/pasture). Treatments were randomly assigned to pastures: 1) no prepartum supplementation (CON); 2) 1 kg/d DDG from d 0 to 84 (LATE84); or 3) 2 kg/d from d 0 to 42 (LATE42). Calves were weaned at 261 ± 23 d of age. At weaning, 38 steers were vaccinated against bovine viral diarrhea virus (BVDV-1) and parainfluenza-3 (PI-3) and transported to a feedlot facility. Steers were penned according to cow prepartum pasture distribution and fed a similar diet until slaughter (d 587). Data were analyzed as complete randomized design using MIXED procedure of SAS, pasture as the experimental unit, treatment as fixed effect, and pasture(treatment) and steer(pasture) as random effects. Steer feedlot BW, ADG, DMI, and G:F did not differ (P ≥ 0.12) among treatments. Plasma haptoglobin concentrations were greater (P ≤ 0.03) for LATE42 and LATE84 vs. CON steers 2 d after feedlot entry. Plasma cortisol and seroconversion for BVDV-1 and PI-3 did not differ (P ≥ 0.15) among treatments. The percentage of carcasses grading Choice did not differ (P = 0.13), but carcasses grading low Choice were greater (P = 0.03) for CON vs. LATE42, with LATE84 being intermediate (91, 40, and 58%, respectively). Thus, prepartum dried distillers grain supplementation to B. indicus-influenced cows did not enhance feedlot growth but had subtle positive impacts on carcass quality and innate immunity in steer progeny. In addition, timing of dried distillers grain supplementation (last 84 d vs. first 42 d of late gestation) did not impact steer post-weaning feedlot performance and carcass quality.

190 Winter vs. year-round supplementation of mature beef cows on feedlot performance and carcass characteristics of steer progeny

Abstract This study evaluated the effects of year-round supplementation of molasses/urea or wheat middlings-based range cubes to mature cows on subsequent feedlot growth, immunity, and carcass characteristics of their steer progeny. On d 0, 82 mature Brangus cows were stratified by BW and BCS (433 ± 47 kg; 4.6 ± 0.77) and randomly allocated into 1 of 6 bahiagrass pastures (13–14 cows/pasture). Treatments were randomly assigned to 2 pastures/treatment and consisted of supplementation with molasses/urea during winter (MOL-W), or year-round supplementation with molasses/urea (MOL-Y) or range cubes (CUB-Y). Supplements were isocaloric and isonitrogenous (75% TDN, 20% CP; DM basis) and offered at a total yearly supplement DM amount of 272 kg/cow. On d 423, all calves were weaned, and 33 steers were randomly selected for the feedlot phase. Steers were penned based on cow prepartum pasture distribution and managed similarly until slaughter (d 661). Data were analyzed as complete randomized design using MIXED procedure of SAS, pasture as the experimental unit, treatment as fixed effect, and pasture(treatment) and steer(pasture) as random effects. Dry matter intake did not differ (P ≥ 0.70), but MOL-Y and MOL-W steers had greater (P = 0.05) overall ADG vs. CUB-Y steers. Plasma haptoglobin concentrations tended (P = 0.06) to be greater for CUB-Y vs. MOL-W, and intermediate for MOL-Y. Serum titers against bovine viral diarrhea virus-1 and parainfluenza-3, hot carcass weight, REA, and YG did not differ (P ≥ 0.16) among treatments, but back fat thickness was greater (P = 0.03) for MOL-W vs. MOL-Y and CUB-Y. The percentage of carcasses grading Choice did not differ (P = 0.35) among treatments, but more carcasses tended (P = 0.08) to grade low Choice for MOL-W vs. CUB-Y and MOL-Y. Therefore, providing molasses/urea supplementation to mature beef cows during winter only or year-round increased steer post-weaning feedlot performance and carcass quality compared to steers born from cows offered year-round supplementation with range cubes.

A Non-Hermitian Generalisation of the Marchenko–Pastur Distribution: From the Circular Law to Multi-criticality

We consider the complex eigenvalues of a Wishart type random matrix model $X=X_1 X_2^*$, where two rectangular complex Ginibre matrices $X_{1,2}$ of size $N\times (N+\nu)$ are correlated through a non-Hermiticity parameter $\tau\in[0,1]$. For general $\nu=O(N)$ and $\tau$ we obtain the global limiting density and its support, given by a shifted ellipse. It provides a non-Hermitian generalisation of the Marchenko-Pastur distribution, which is recovered at maximal correlation $X_1=X_2$ when $\tau=1$. The square root of the complex Wishart eigenvalues, corresponding to the non-zero complex eigenvalues of the Dirac matrix $\mathcal{D}=\begin{pmatrix} 0 & X_1 \\ X_2^* & 0 \end{pmatrix},$ are supported in a domain parametrised by a quartic equation. It displays a lemniscate type transition at a critical value $\tau_c,$ where the interior of the spectrum splits into two connected components. At multi-criticality we obtain the limiting local kernel given by the edge kernel of the Ginibre ensemble in squared variables. For the global statistics, we apply Frostman's equilibrium problem to the 2D Coulomb gas, whereas the local statistics follows from a saddle point analysis of the kernel of orthogonal Laguerre polynomials in the complex plane.

A multi-proxy magnetic approach for monitoring large-scale airborne pollution impact

The interpretive utility of environmental magnetic proxies for investigating airborne particulate matter (PM) pollution impact is restricted by differences in soil composition, land cover and land use. For soil magnetic applications, land use strongly influences magnetic particle distribution down the soil profile, even in homogeneous soil environments. Here, an adaptive approach is engineered to provide accurate magnetic proxy information for pollution monitoring across different land use types. In an 81-km2 area between two industrial harbours, the irregular distribution of forests, arable lands, pasture and residential areas prevented robustly relating topsoil magnetic susceptibility data to known pollution impacts. Although normalized topsoil susceptibility values showed improved potential for deriving airborne pollution impacts, optimal results were obtained by depth-integrating magnetic susceptibility logs, revealing long-term impacts of both active and decommissioned industrial facilities. Complementing soil magnetic observations, active and passive (bio)magnetic monitoring allowed discriminating short-term pollution patterns and evaluating changes in PM impact across the study area. Hereby, active PM receptors (strawberry leaves and plastic coated cardboards (PCCs)) provided promising results, yet passive receptors allowed estimating pollution impacts more efficiently. For the latter, species-independent grass leaf sampling reflected airborne PM depositional patterns most accurately, whereas wiped anthropogenic surfaces proved too sensitive to wash-off.

Efficient fault-tolerant routing in IoT wireless sensor networks based on path graph flow modeling with Marchenko–Pastur distribution (EFT-PMD)

In the internet of things (IoT) based wireless sensor network (WSN), the nodes are scattered to segregate the rapt data in the relevant field of application. In general, sensor nodes of IoT possess heterogeneous property and display cluster-based routing to transmit the data as it is considered as an efficient routing method. When one or more cluster heads (CHs) fail, the sensed data of sensor nodes that are currently serving cannot be forwarded by the faulty CHs. Consequently, data of the IoT application will not be sufficiently sensed by the sink node (gateway). As a result, information processing of this field will be affected profusely. This paper focuses on the development of a paired cluster fault-tolerant disjoint path routing in a path graph and a novel approach to solve this dilemma in polynomial time of the degree of the graph. The objective of this proposed IoT–WSN architecture is to diminish the latency, end-to-end delay as well as energy consumption and thereby improving the performance in terms of throughput and packet delivery ratio. The performance of this proposed method in IoT–WSN network is measured and affirmed using benchmark network simulator.