Exchangeability Research Articles

On the characterization of exchangeable sequences through reverse-martingale empirical distributions

On the characterization of exchangeable sequences through reverse-martingale empirical distributions

Effects of the ion-exchange sequence on the CO2 uptake and CO2–over–N2 selectivity of zeolite NaKA

The CO2 and N2 adsorption on small-pore zeolite |Na12-xKx|-A was hypothesized to be affected by the ion exchange sequence used for the zeolite preparation. Zeolites were prepared by ion exchange of a commercially available zeolite |Na12|-A (4A) and a zeolite |K12|-A (3A) composition prepared from zeolite 4A. The CO2 and N2 adsorption properties were studied experimentally, and the binary CO2-over-N2 selectivity was estimated from single-component adsorption data using the apparent Henry's law coefficients. It was observed that the level of CO2 adsorption was reduced by increasing the K content for both series of zeolite NaKA. Zeolite |Na12-xKx|-A-from-4A had the highest CO2 adsorption capacity (at 1 atm and 273 K) for a given K content. At low K content, zeolite |Na12-xKx|-A-from-3A had the highest CO2-over-N2 selectivity. At an intermediate K content, the zeolites prepared from 4A had the highest selectivity. These differences show that non-equilibrium processes during the ion exchange are important for the CO2 and N2 adsorption properties of the derived zeolites. As of now, we refrain from speculating whether they relate to the detailed positioning of K+ and Na+ cations in the local structure of the zeolite or to mass-transport-related concentration gradients of the cations in the structure. Irrespectively, it was observed that the ion-exchange sequence affects the CO2 and N2 adsorption properties of the zeolites, which could be of general importance when it comes to the tuning of the properties of cation-rich zeolites.

Deformations of cluster mutations and invariant presymplectic forms

We consider deformations of sequences of cluster mutations in finite type cluster algebras, which destroy the Laurent property but preserve the presymplectic structure defined by the exchange matrix. The simplest example is the Lyness 5-cycle, arising from the cluster algebra of type A_2: this deforms to the Lyness family of integrable symplectic maps in the plane. For types A_3 and A_4, we find suitable conditions such that the deformation produces a two-parameter family of Liouville integrable maps (in dimensions two and four, respectively). We also perform Laurentification for these maps, by lifting them to a higher-dimensional space of tau functions with a cluster algebra structure, where the Laurent property is restored. More general types of deformed mutations associated with affine Dynkin quivers are shown to correspond to four-dimensional symplectic maps arising as reductions in the discrete sine-Gordon equation.

Exchangeable min-id sequences: Characterization, exponent measures and non-decreasing id-processes

We establish a one-to-one correspondence between (i) exchangeable sequences of random variables whose finite-dimensional distributions are minimum (or maximum) infinitely divisible and (ii) non-negative, non-decreasing, infinitely divisible stochastic processes. The exponent measure of an exchangeable minimum infinitely divisible sequence is shown to be the sum of a very simple “drift measure” and a mixture of product probability measures, which uniquely corresponds to the Lévy measure of a non-negative and non-decreasing infinitely divisible process. The latter is shown to be supported on non-negative and non-decreasing functions. In probabilistic terms, the aforementioned infinitely divisible process is equal to the conditional cumulative hazard process associated with the exchangeable sequence of random variables with minimum (or maximum) infinitely divisible marginals. Our results provide an analytic umbrella which embeds the de Finetti subfamilies of many interesting classes of multivariate distributions, such as exogenous shock models, exponential and geometric laws with lack-of-memory property, min-stable multivariate exponential and extreme-value distributions, as well as reciprocal Archimedean copulas with completely monotone generator and Archimedean copulas with log-completely monotone generator.

Sharp Estimates for Proximity of Geometric and Related Sums Distributions to Limit Laws

The convergence rate in the famous Rényi theorem is studied by means of the Stein method refinement. Namely, it is demonstrated that the new estimate of the convergence rate of the normalized geometric sums to exponential law involving the ideal probability metric of the second order is sharp. Some recent results concerning the convergence rates in Kolmogorov and Kantorovich metrics are extended as well. In contrast to many previous works, there are no assumptions that the summands of geometric sums are positive and have the same distribution. For the first time, an analogue of the Rényi theorem is established for the model of exchangeable random variables. Also within this model, a sharp estimate of convergence rate to a specified mixture of distributions is provided. The convergence rate of the appropriately normalized random sums of random summands to the generalized gamma distribution is estimated. Here, the number of summands follows the generalized negative binomial law. The sharp estimates of the proximity of random sums of random summands distributions to the limit law are established for independent summands and for the model of exchangeable ones. The inverse to the equilibrium transformation of the probability measures is introduced, and in this way a new approximation of the Pareto distributions by exponential laws is proposed. The integral probability metrics and the techniques of integration with respect to sign measures are essentially employed.

Highly stable natural zeolite/montmorillonite hybrid microspheres with green preparation process for efficient adsorption of ammonia nitrogen in wastewater

Adsorption technology has attracted increasing attention for the remediation of ammonia nitrogen pollutions from landfill leachate. However, developing effective adsorbing materials with low cost, outstanding activities and long-term stabilities in the aqueous environment remains a significant challenge. Zeolite with high ability of cation exchange is significantly preferable for the removal of ammonia nitrogen. Herein, a novel polyvinyl alcohol (PVA) thin membrane modified natural zeolite and Na-montmorillonite (NaMt) hybrid microspheres (denoted as PVA-(zeolite/Na-Mt)) adsorbent is successfully synthesized by a facile granulation and impregnation method. The adsorption experiments reveal that the multicomponent PVA-(zeolite/Na-Mt) microspheres show higher removal efficiency (98.16%) for ammonia nitrogen within 40 h even at a wide pH (3.0–11.0) and temperature (10–30 °C) range. Meanwhile, the spent PVA-(zeolite/Na-Mt) microspheres with high stability in aqueous environment for more than 20 days originates from the modification of the PVA molecule and enhanced adsorption performance that is beneficial for practical applications in the wastewater remediation field.

Application of virtual reality for peritoneal dialysis exchange learning in patients with end-stage renal disease and cognitive impairment.

Cognitive impairment is not uncommon in patients with end-stage renal disease and can make it more difficult for these patients to carry out peritoneal dialysis (PD) on their own. Their attempts to do so may result in adverse consequences such as peritonitis. PD exchange is a complex procedure demanding knowledge and skill which requires close supervision and guidance by a renal nurse specialist. In this study, a non-immersive virtual reality (VR) training program using a Leap motion hand tracking device was developed to facilitate patients' understanding and learning of the PD exchange procedure before attempting real task practice. This study was a two-center single-blinded randomized controlled trial on 23 incident PD patients. Patients in the experimental group received 8 sessions of VR training, while patients in the control were provided with printed educational materials. The results showed that there were significant differences between the two groups in performance of the overall PD exchange sequence, especially on the crucial steps. VR had a patient satisfaction rate of 89%, and all patients preferred to have the VR aid incorporated in PD training. Our findings conclude VR can be a useful aid in the training and reinforcement of PD exchange procedures, with distinct merits of being free from restrictions of time, space, and manpower.

Toxicity of hexadecylamine modified nano-montmorillonite

• Montmorillonite (Mnt) modified by hexadecylamine (HDA) is no toxic to mouse. • The interlayer distance of Mnt modified by HDA (OMnt) increases to 2.80 nm. • OMnt exhibits good dispersity and layer structure and high ion exchange ability. • Mnt and OMnt can enter and excrete the organs of mouse without causing jeopardy. Montmorillonite (Mnt) can be widely used in pharmacy for its good ion exchange, and organics modified Mnt (OMnt) has a wider range of applications. Therefore, it is crucial to explore whether OMnt is toxic or not. Herein, the toxicity of hexadecylamine (HDA) modified nano-Mnt was investigated by a mouse gavage, an in vivo bioluminescence imaging test and H&E staining section experiment. In the FTIR spectra of OMnt labeled suflo Cy5 NHS (Cy5), the peaks around 1660, 1469 and 1387, and 1321 cm −1 can be assigned to the bending vibration of N H, stretching vibration of C N and C O bond, respectively, this indicates that Cy5 was labeled onto OMnt. The in vivo bioluminescence images showed that Mnt and OMnt firstly accumulated in the stomach of mice for digestion, portions of them was directly excreted, and the other entered the heart, liver, spleen, lung and kidney of mice through blood circulation and finally excreted out of the body of mice. H&E staining section results showed that no tumor or abnormality can be seen in the organs of mice. These imply that OMnt is no toxic to mouse and can be found more applications in medicine and biomaterials, etc.

Multiple‐input multiple‐output sonar adaptive beamforming using transmission diversity smoothing and backward processing

AbstractBenefit from the transmission diversity smoothing (TDS) effect upon coherent targets decorrelation, the kind of adaptive beamformers can be directly applied for multiple‐input multiple‐output (MIMO) sonar applications. Increasing the number of transmitted signals helps improve the TDS‐based decorrelation performance. However, a large number of transmitters is not feasible for those sonar systems mounted on small platforms with limited space. To address the lack of TDS‐based degrees of freedom for smoothing, an improved TDS decorrelation method is proposed for MIMO sonar in this study. With the conjugated MIMO data covariance matrix being left‐multiplied and right‐multiplied, respectively, by the exchange matrix, the authors obtain a backward‐smoothed data covariance matrix. Afterwards, the authors average it with the original MIMO receiving data covariance matrix to reconstruct a new data covariance matrix. Compared with TDS, the improved TDS strengthens the decorrelation performance by increasing the number of covariance matrix for smoothing and thus enables the new rank restored signal covariance matrix to have better non‐singularity. Without increasing any aperture loss and system complexity, a lower correlation between echoes is obtained, and the performance of the minimum variance distortionless response beamformer is hence improved in the presence of coherent targets. The effectiveness of the proposed decorrelation method is verified by numerical simulations and real data from a water tank experiment.

Fast Exchange with Gaussian Basis Set Using Robust Pseudospectral Method.

In this article, we present an algorithm to efficiently evaluate the exchange matrix in periodic systems when a Gaussian basis set with pseudopotentials is used. The usual algorithm for evaluating exchange matrix scales cubically with the system size because one has to perform O(N2) fast Fourier transform (FFT). Here, we introduce an algorithm that retains the cubic scaling but reduces the prefactor significantly by eliminating the need to do FFTs during each exchange build. This is accomplished by representing the products of Gaussian basis function using a linear combination of an auxiliary basis the number of which scales linearly with the size of the system. We store the potential due to these auxiliary functions in memory, which allows us to obtain the exchange matrix without the need to do FFT, albeit at the cost of additional memory requirement. Although the basic idea of using auxiliary functions is not new, our algorithm is cheaper due to a combination of three ingredients: (a) we use a robust pseudospectral method that allows us to use a relatively small number of auxiliary basis to obtain high accuracy; (b) we use occ-RI exchange, which eliminates the need to construct the full exchange matrix; and (c) we use the (interpolative separable density fitting) ISDF algorithm to construct these auxiliary basis sets that are used in the robust pseudospectral method. The resulting algorithm is accurate, and we note that the error in the final energy decreases exponentially rapidly with the number of auxiliary functions.

On the Jajte weak law of large numbers for exchangeable random variables

In this paper, we prove an extension of the Jajte weak law of large numbers for exchangeable random variables. We make a simulation to illustrate the asymptotic behavior in the sense of convergence in probability for weighted sums of exchangeable weighted random variables.

Distributions of runs and scans in multistate Markov exchangeable sequences

In this paper, we look at the distributions of runs and scans in multistate Markov exchangeable sequences. The joint distributions of runs of several lengths under four types of enumeration schemes are analyzed. We evaluate the upper tail probabilities for ratchet scan statistics exactly. By utilizing the expansion of the generating functions, we propose effective computational tools for the derivation of probability functions. The results presented here provide approaches for the evaluation of the exact distributions of runs and scans in a wide class of practical problems. Finally, we discuss several applications and numerical examples to show how our theoretical results are applied to the investigation of runs and scans, as well as a parameter estimation problem.

An Adaptive Sinusoidal-Disturbance-Strategy Sparrow Search Algorithm and Its Application.

In light of the problems of slow convergence speed, insufficient optimization accuracy and easy falling into local optima in the sparrow search algorithm, this paper proposes an adaptive sinusoidal-disturbance-strategy sparrow search algorithm (ASDSSA) and its mathematical equation. Firstly, the initial population quality of the algorithm is improved by fusing cubic chaos mapping and perturbation compensation factors; secondly, the sinusoidal-disturbance-strategy is introduced to update the mathematical equation of the discoverer's position to improve the information exchange ability of the population and the global search performance of the algorithm; finally, the adaptive Cauchy mutation strategy is used to improve the ability of the algorithm to jump out of the local optimal solutions. Through the optimization experiments on eight benchmark functions and CEC2017 test functions, as well as the Wilcoxon rank-sum test and time complexity analysis, the results show that the improved algorithm has better optimization performance and convergence efficiency. Further, the improved algorithm was applied to optimize the parameters of the long short term memory network (LSTM) model for passenger flow prediction on selected metro passenger flow datasets. The effectiveness and feasibility of the improved algorithm were verified by experiments.

Rhizosphere effect of nanoscale zero-valent iron on mycorrhiza-dependent maize assimilation.

Rhizosphere effect of nanoscale zero-valent iron (nZVI) is crucial but little reported. Maize seeds were dressed with four nZVI concentrations (0, 1.0, 1.5, 2 g kg-1 ) and inoculated with arbuscular mycorrhizal fungus (AMF) (Funneliformis mosseae). The SEM images illuminated that excessive nZVI particles (2 g kg-1 ) were agglomerated on the surface of hyphae and spore, causing severe deformation and inactivation of AMF symbionts and thereafter inhibiting water uptake in maize seedlings. This restrained the scavenging effects of enzymatic (superoxide dismutase, peroxidase) and non-enzymatic compounds (proline & malondialdehyde) on ROS, and leaf photoreduction activity andgas exchange ability (p < 0.05). Interestingly, the inoculation with AMF effectively alleviated above negative effects. In contrast, appropriate dose of nZVI, that is, ≤1.5 g kg-1 , can be evenly distributed on the hyphae surface and form the ordered symbionts with AMF. This help massively to enhance hyphae growth and water and nutrient uptake. The enhanced mycorrhizal infection turned to promote rhizosphere symbiont activity and leaf Rubisco and Rubisco activase activity. Light compensation point was massively lowered, which increased photosynthetic carbon supply for AMF symbionts. Particularly, such priming effects were evidently enhanced by drought stress. Our findings provided a novel insight into functional role of nZVI in agriculture and AMF-led green production.

Synthesis of NaA zeolite via the mesoscale reorganization of submolten salt depolymerized kaolin: A mechanistic study

Deep understanding of the formation mechanism is crucial to the rational design and controllable synthesis of zeolites with desired pore architecture and acidity. Herein, we take the synthesis of NaA zeolite from a submolten salt depolymerized kaolin (SMS-K) as an example to elucidate the formation mechanism of NaA zeolite. By using SMS-K as sole Si and Al sources, a highly pure and crystalline NaA zeolite with superior ion exchange ability was synthesized. By using various ex-situ and in-situ characterizations and studying the crystallization kinetics, a plausible formation mechanism of NaA zeolite via the mesoscale reorganization of SMS-K was proposed. The results indicate that the reorganization of SMS-K into NaA zeolite follows the solid-phase transformation route. Upon being mixed with H2O, SMS-K that is mainly composed of silicate monomers and chain/ring microstructures is in-situ transformed rapidly into mesoscale intermediates containing double four-membered rings and β cages, sufficient stirring during aging generates more mesoscale intermediates. During the subsequent crystallization process, the mesoscale intermediates are further self-assembled into NaA nanoparticles when theirs amount reaches a maximum, and finally the nanoparticles grow into well-shaped cubic NaA zeolite particles with smooth surfaces through layer spreading. Our work provides the theoretical foundation for the design and green synthesis of zeolites directly from the natural minerals.

Adsorption of ammonium ions in aqueous solution using raw and treated peat soil

Peat exists in abundance in many parts of the world, but has low economic value. The presence of active functional groups, in the form of carboxyl and phenolic groups, makes peat an alternative sorbent having high porosity and ion exchange ability. Washing peat soil prior to adsorption has been reported to be effective in increasing its ion exchange capacity. In this study, the effect of peat washing using NaOH on its adsorption capacity for ammonium ions was investigated. The FTIR analysis indicated decreases in -OH absorption at 3300-3600 cm-1, C=O (carboxylate) at 1625 cm-1 and C-O at 1300-1000 cm-1 possibly due to the replacement of H+ by Na+ upon peat washing using NaOH. SEM analyses of peat samples showed a more homogeneous surface morphology upon washing. BET analysis results showed a reduction in surface area, pore size, and pore volume. However, the adsorption study conducted in batch mode indicated that the adsorption capacities of washed and raw peats were 28.08 mg/g and 14.48 mg/g, respectively. It can be concluded that washing peat soil using NaOH solution may alter its surface properties and may be beneficial in improving its adsorption capacity towards ammonium ions in aqueous solution.

Technical details and long-term outcomes of P.A.D.U.A. for congenital urethral narrowing; a case series and review of the literature

The P.A.D.U.A. technique is a method of addressing congenital urethral narrowing. It involves passive dilation with a series of progressively larger indwelling catheters. Utilization is limited by scant literature, particularly regarding technical details and long-term durability. Tools for achieving safe and reliable urinary drainage are critical in these patients, who require careful stewardship of their kidney and bladder function. To describe long-term urethral patency and urinary function following P.A.D.U.A., and to provide sufficient technical detail to reproduce the technique. Patients with congenital urethral narrowing managed with P.A.D.U.A. were identified and chart review was performed. Details of catheter exchange sequences were compiled and described. The primary outcome was the attainment of adequate urethral caliber by successful completion of P.A.D.U.A., and the secondary outcome was voiding per urethra at most recent follow-up. P.A.D.U.A. achieved adequate urethral caliber in 9/11 (82%) of patients. This included seven patients with Prune Belly Syndrome, one with isolated urethral atresia, and one with a cloacal anomaly. P.A.D.U.A. failed to achieve urethral patency in one patient with urethral duplication, who was unable to progress through the catheter sequence, and one patient with Prune Belly Syndrome, who completed P.A.D.U.A. but developed recurrent narrowing one week later. There were no delayed failures of urethral patency. Patients who achieved patency underwent a median of seven catheter placements over 92 days. Median (range) initial and final catheter sizes were 3.5F (1.9-8F) and 14F (8-16F). While 82% achieved patency, only 3/11 (27%) were voiding spontaneously per native urethra at most recent follow-up. This series of patients undergoing P.A.D.U.A. for primary treatment of congenital urethral narrowing is the largest to date and provides granular technical details. It aligns with prior reports suggesting that P.A.D.U.A. achieves urethral patency in most patients with Prune Belly Syndrome or isolated urethral atresia, but has limited application in the hypoplastic duplicated urethra. Despite high rates of urethral patency in this select population, many patients will not achieve and maintain spontaneous voiding without catheterization. This is likely due to ongoing deterioration of bladder function caused by the prenatal developmental insult, paralleling the phenomenon seen in posterior urethral valves. P.A.D.U.A. is an effective and durable technique for achieving urethral patency. However, due to complicating factors such as the underlying bladder pathology present in many patients, urethral patency achieved with P.A.D.U.A. does not guarantee long-term safe and reliable spontaneous emptying per urethra.

Research on Subjective-Cultural Ecological Design System of Vernacular Architecture

With the impact of urbanization and other factors, the vernacular architectural heritage faces the problem of how to carry on and innovate for sustainable development with originality and authenticity in the process of redesigning and planning. Therefore, this study uses the visualization method of quantitative analysis to analyze the research trends and hot spots of domestic vernacular architecture and explore new ways of coexistence between vernacular architecture, subject perception and cultural ecology. The critical challenge of this study is to analyze the theoretical coupling action rule between the socio-cultural structure of emotions and the cultural ecosystem of vernacular architecture, drawing on the concept of cultural ecology and the reasoning method of transmission relations in logical deduction. The main contribution of this study is to propose the concept of a subjective-cultural ecological design system for the sustainable development of vernacular architecture, to establish a three-dimensional structural analysis design paradigm and an evaluation analysis matrix, and to make vernacular architecture present the self-renewal ability of continuous exchange and revision in the dynamic cycle of this design system. This study aims to provide a standardized and flexible design research framework for contemporary vernacular architecture’s innovation and sustainable development.

Resident training in psychopathology and uncertainty in a clinical situation.

The central theme of this article is the way in which psychiatry physicians-in-training deal with uncertainty in the discussion of clinical cases in Mexico. Methodologically, it is approached from the field of clinical ethnography and the narrative interpretation of plots in performative actions where there are sequences of communicative exchanges. In this way, it focuses on a detailed description of situations where clinical cases are reviewed to decipher, explain, and understand intersubjective meanings in the face of the emergence of uncertainty, its management, and the implications on decisions and actions. The study finds that limitations within the field of psychiatry lie in the nosographic construction of disease and its translation into the diagnostic hypotheses made by clinicians, where there are wide margins of ambiguity. The strategies implemented in the face of uncertainty are use of drugs, the collegiate review of the case, and utilization of intuition as a spontaneous, preconscious daily practice. The specific case described here provides a microscopic observation of the complex scenarios in which uncertainty occurs in educational and teaching processes, clearly revealing how patient care is articulated. The narratives and their interpretation are materials for training/curriculum and psychiatric clinical practice.

Solidification of uranium tailings using alkali-activated slag mixed with natural zeolite

Cemented uranium tailings backfill created from alkali-activated slag (CUTB) is an effective method of disposing of uranium tailings. Using some environmental functional minerals with ion exchange, adsorption, and solidification abilities as backfill modified materials may improve the leaching resistance of the CUTB. Natural zeolite, which has good ion exchange and adsorption characteristics, is selected as the backfill modified material, and it is added to the backfill materials with cementitious material proportions of 4%, 8%, 12%, and 16% to prepare CUTB mixtures with environmental functional minerals. After the addition of natural zeolite, the uniaxial compressive strength (UCS) of the CUTB decreases, but the leaching resistance of the CUTB increases. When the natural zeolite content is 12%, the UCS reaches the minimum value of 8.95 MPa, and the concentration of uranium in the leaching solution is 0.28–8.07 μg/L, the leaching rate R42 is 9.61 × 10−7 cm/d, and cumulative leaching fraction P42 is 8.53 × 10−4 cm, which shows that the alkali-activated slag cementitious material has a good curing effect on the CUTB, and the addition of environmental functional minerals helps to further improve the leaching resistance of the CUTB, but it reduces the UCS to an extent.