Functional sample path properties of subsequence's C-R increments for a Wiener process in Hlder norm

In this paper, with the aid of large deviation formulas established in strong topology of functional space generated by HSlder norm, we discuss the functional sample path properties of subsequence＇s C-R increments for a Wiener process in HSlder norm. The obtained results, generalize the corresponding results of Chen and the classic Strassen＇s law of iterated logarithm for a Wiener process.

A GENERAL FORM OF THE INCREMENTS OF A TWO-PARAMETER WIENER PROCESS

In this paper, we consider a general form of the increments for a two-parameter Wiener process. Both the Csorgo-Revesz's increments and a class of the lag increments are the special cases of this general form of increments. Our results imply the theorem that have been given by Csorgo and Revesz (1978), and some of their conditions are removed.

A LIMINF RESULT FOR HANSON-RUSSO TYPE INCREMENTS OF FRACTIONAL BROWNIAN MOTION

Let {X(t), t greater than or equal to 0} be a fractional Brownian motion of order 2 alpha with 0 < alpha < 1,beta > 0 be a real number, alpha(T) be a function of T and 0 < alpha(T), [GRAPHICS] (log T/alpha(T))/log T = r, (0 less than or equal to r less than or equal to infinity). In this paper, we proved that [GRAPHICS] where c(1), c(2) are two positive constants depending only on alpha,beta.

On the Increments of Stable Subordinators

Let be a stable subordinator defined on a probability space and let at for t>0?be a non-negative valued function. In this paper, it is shown that under varying conditions on at, there exists a function such that where , , and .

SOME LIMINF RESULTS ON INCREMENTS OF THE PRIMITIVES OF BROWNIAN MOTION

Let { W(t);t≥0 } be a standard Brownian motion.For a positive integer m ,define a Gaussian processX m(t)=1m!∫ t 0(t-s) m d W(s).In this paper the liminf behavior of the increments of this process is discussed by establishing some probability inequalities.Some previous results are extended and improved.

Disentangling the factors that contribute to variation in forest biomass increments in the mid-subtropical forests of China

Mid-subtropical forests are the main vegetation type of global terrestrial biomes, and are critical for maintaining the global carbon balance. However, estimates of forest biomass increment in mid-subtropical forests remain highly uncertain. It is critically important to determine the relative importance of different biotic and abiotic factors between plants and soil, particularly with respect to their influence on plant regrowth. Consequently,it is necessary to quantitatively characterize the dynamicspatiotemporal distribution of forest carbon sinks at a regional scale. This study used a large, long-term dataset in a boosted regression tree（BRT） model to determine the major components that quantitatively control forest biomass increments in a mid-subtropical forested region（Wuyishan National Nature Reserve, China）. Long-term,stand-level data were used to derive the forest biomass increment, with the BRT model being applied to quantify the relative contributions of various biotic and abiotic variables to forest biomass increment. Our data show that total biomass（t） increased from 4.62 9 106 to 5.30 9 106 t between 1988 and 2010, and that the mean biomass increased from 80.19 ± 0.39 t ha-1（mean ± standard error） to 94.33 ± 0.41 t ha-1in the study region. The major factors that controlled biomass（in decreasing order of importance） were the stand, topography, and soil. Stand density was initially the most important stand factor, while elevation was the most important topographic factor. Soil factors were important for forest biomass increment but have a much weaker influence compared to the other two controlling factors. These results provide baseline information about the practical utility of spatial interpolationmethods for mapping forest biomass increments at regional scales.

A GENERAL FORM OF THE INCREMENTS OF TWO-PARAMETER FRACTIONAL WIENER PROCESS

A general form of the increments of two-parameter fractional Wiener process is given. The results of Csoergo-Révész increments are a special case,and it also implies the results of the increments of the two-parameter Wiener process.

SOME RESULTSON LAG INCREMENTSOF PRINCIPAL VALUE OF BROWNIAN LOCAL TIME

Let W be a standard Brownian motion,and define Y(t) =∫t 0 ds W(s) as Cauchy' s principal value related to the local time of W.We study some limitresults on lag increments of Y(t) and obtain various results all of which are related to earlier work by Hanson and Russo in 1 983

ON THE INCREMENTS DISTRIBUTION OF STOCK PRICES

In this paper,the models of increment distributions of stock price are constructed with two approaches. The first approach is based on limit theorems of random summation. The second approach is based on the statistical analysis of the increment distribution of the logarithms of stock prices.

Quantum and Non-Quantum Formulation of Eye’s Adaptation to Light’s Intensity Increments

Context and background: A quantum formulation of vision in vertebrates was proposed in the early 1940s. The number of quanta useful for enabling vision was found. The time interval required for their absorption, however, was never specified. In the early 1950s, experimental data on the effects of light’s intensity increment on vision indicated that the quantum formulation is true only at low light’s intensities. In this case, a vaguely described signaling adaptation mechanism was invoked to explain the separation between vision at low and high intensities, accompanied by the switch from rod to cones as photoreceptors. Motivation: In this article, we want to prove the validity of the non-totally-quantum formulation and unveil the nature of the signaling adaptation mechanism. Hypothesis: To accomplish our proof, we hypothesize that the amount of energy transferred and conserved in light’s interaction with the eyes is given by the product of light’s intensity (or power) times its period. Method: We construct and use the plots of the trends of light’s intensity increments and the corresponding changes in the axon’s membrane capacitance versus adapting intensity. Results: We find that 1) the average solar light’s intensity is the critical value that separates low from high light’s intensity regimes in vision, and 2) changes in the capacitance of the axon’s membrane enable the signaling adaptation of vision when light’s intensity changes. Conclusions: We prove the validity of the non-totally-quantum formulation and unveil the nature of the signaling adaptation mechanism. Our proof is supported by the model based on light’s intensity times period as being the energy conserved in light-matter interaction This model suggests that 1) all the waves in the electromagnetic spectrum, at the correct intensity for each frequency, could be used to produce the effects of optogenetics in diagnostics and therapy, and 2) it takes seconds to minutes to see details in the dark when light is switched off.

No effect of invasive tree species on aboveground biomass increments of oaks and pines in temperate forests

Prunus serotina and Robinia pseudoacacia are the most widespread invasive trees in Central Europe.In addition,according to climate models,decreased growth of many economically and ecologically important native trees will likely be observed in the future.We aimed to assess the impact of these two neophytes,which differ in the biomass range and nitrogen-fixing abilities observed in Central European conditions,on the relative aboveground biomass increments of native oaks Qucrcus robur and Q.petraea and Scots pine Pinus sylvestris.We aimed to increase our understanding of the relationship between facilitation and competition between woody alien species and overstory native trees.We established 72 circular plots(0.05 ha)in two different forest habitat types and stands varying in age in western Poland.We chose plots with different abundances of the studied neophytes to determine how effects scaled along the quantitative invasion gradient.Furthermore,we collected growth cores of the studied native species,and we calculated aboveground biomass increments at the tree and stand levels.Then,we used generalized linear mixed-effects models to assess the impact of invasive species abundances on relative aboveground biomass increments of native tree species.We did not find a biologically or statistically significant impact of invasive R.pseudoacacia or P.serotina on the relative aboveground,biomass increments of native oaks and pines along the quantitative gradient of invader biomass or on the proportion of total stand biomass accounted for by invaders.The neophytes did not act as native tree growth stimulators but also did not compete with them for resources,which would escalate the negative impact of climate change on pines and oaks.The neophytes should not significantly modify the carbon sequestration capacity of the native species.Our work combines elements of the per capita effect of invasion with research on mixed forest management.

Continual learning fault diagnosis:A dual-branch adaptive aggregation residual network for fault diagnosis with machine increments

As a data-driven approach, Deep Learning(DL)-based fault diagnosis methods need to collect the relatively comprehensive data on machine fault types to achieve satisfactory performance. A mechanical system may include multiple submachines in the real-world. During condition monitoring of a mechanical system, fault data are distributed in a continuous flow of constantly generated information and new faults will inevitably occur in unconsidered submachines, which are also called machine increments. Therefore, adequately collecting fault data in advance is difficult. Limited by the characteristics of DL, training existing models directly with new fault data of new submachines leads to catastrophic forgetting of old tasks, while the cost of collecting all known data to retrain the models is excessively high. DL-based fault diagnosis methods cannot learn continually and adaptively in dynamic environments. A new Continual Learning Fault Diagnosis method(CLFD) is proposed in this paper to solve a series of fault diagnosis tasks with machine increments. The stability–plasticity dilemma is an intrinsic issue in continual learning. The core of CLFD is the proposed Dual-branch Adaptive Aggregation Residual Network(DAARN).Two types of residual blocks are created in each block layer of DAARN: steady and dynamic blocks. The stability–plasticity dilemma is solved by assigning them with adaptive aggregation weights to balance stability and plasticity, and a bi-level optimization program is used to optimize adaptive aggregation weights and model parameters. In addition, a feature-level knowledge distillation loss function is proposed to further overcome catastrophic forgetting. CLFD is then applied to the fault diagnosis case with machine increments. Results demonstrate that CLFD outperforms other continual learning methods and has satisfactory robustness.

Functional Limit Theorems for C-R Increments of k-Dimensional Brownian Motion in Holder Norm

In this paper. based on large deviation formulas established in stronger topology generated by Hlder norm, we obtain the functional limit theorems for C-R increments of k-dimensional Brownian motion in Hlder norm

Functional Limit Theorems for C-R Increments of lp-Valued Wiener Processes in the Norm

In this paper, based on accurately large deviation formulae established in strong topology generated by the Holder norm for l^2-valued Wiener processes, we obtain the functional limit theorems for C-R increments of l^p-valued Wiener processes in the Holder norm.

Studentized Increments of Partial Sums

Using suitable self-normalization for partial sums of i.i.d.random variables,Griffin and Kuelbs established the law of the iterated logarithm for all distributions in the domain of attraction of a normal law.We obtain the corresponding results for Studentized increments of partial sums under thesame condition.

Effect of external magnetic field on the instability of THz plasma waves in nanoscale graphene field-effect transistors

The instability of plasma waves in the channel of field-effect transistors will cause the electromagnetic waves with THz frequency.Based on a self-consistent quantum hydrodynamic model,the instability of THz plasmas waves in the channel of graphene field-effect transistors has been investigated with external magnetic field and quantum effects.We analyzed the influence of weak magnetic fields,quantum effects,device size,and temperature on the instability of plasma waves under asymmetric boundary conditions numerically.The results show that the magnetic fields,quantum effects,and the thickness of the dielectric layer between the gate and the channel can increase the radiation frequency.Additionally,we observed that increase in temperature leads to a decrease in both oscillation frequency and instability increment.The numerical results and accompanying images obtained from our simulations provide support for the above conclusions.

Effects of baffle position in serpentine flow channel on the performance of proton exchange membrane fuel cells

This study used a three-dimensional numerical model of a proton exchange membrane fuel cell with five types of channels:a smooth channel(Case 1);eight rectangular baffles were arranged in the upstream(Case 2),midstream(Case 3),downstream(Case 4),and the entire cathode flow channel(Case 5)to study the effects of baffle position on mass transport,power density,net power,etc.Moreover,the effects of back pressure and humidity on the voltage were investigated.Results showed that compared to smooth channels,the oxygen and water transport facilitation at the diffusion layer-channel interface were added 11.53%-20.60%and 7.81%-9.80%at 1.68 A·cm^(-2)by adding baffles.The closer the baffles were to upstream,the higher the total oxygen flux,but the lower the flux uniformity the worse the water removal.The oxygen flux of upstream baffles was 8.14%higher than that of downstream baffles,but oxygen flux uniformity decreased by 18.96%at 1.68 A·cm^(-2).The order of water removal and voltage improvement was Case 4>Case 5>Case 3>Case 2>Case 1.Net power of Case 4 was 9.87%higher than that of the smooth channel.To the Case 4,when the cell worked under low back pressure or high humidity,the voltage increments were higher.The potential increment for the back pressure of 0 atm was 0.9%higher than that of 2 atm(1 atm=101.325 kPa).The potential increment for the humidity of 100%was 7.89%higher than that of 50%.

Grouping tree species to estimate basal area increment in temperate multispecies forests in Durango,Mexico

Multispecies forests have received increased scientific attention,driven by the hypothesis that biodiversity improves ecological resilience.However,a greater species diversity presents challenges for forest management and research.Our study aims to develop basal area growth models for tree species cohorts.The analysis is based on a dataset of 423 permanent plots(2,500 m^(2))located in temperate forests in Durango,Mexico.First,we define tree species cohorts based on individual and neighborhood-based variables using a combination of principal component and cluster analyses.Then,we estimate the basal area increment of each cohort through the generalized additive model to describe the effect of tree size,competition,stand density and site quality.The principal component and cluster analyses assign a total of 37 tree species to eight cohorts that differed primarily with regard to the distribution of tree size and vertical position within the community.The generalized additive models provide satisfactory estimates of tree growth for the species cohorts,explaining between 19 and 53 percent of the total variation of basal area increment,and highlight the following results:i)most cohorts show a"rise-and-fall"effect of tree size on tree growth;ii)surprisingly,the competition index"basal area of larger trees"had showed a positive effect in four of the eight cohorts;iii)stand density had a negative effect on basal area increment,though the effect was minor in medium-and high-density stands,and iv)basal area growth was positively correlated with site quality except for an oak cohort.The developed species cohorts and growth models provide insight into their particular ecological features and growth patterns that may support the development of sustainable management strategies for temperate multispecies forests.

Ethical Decision-Making Framework Based on Incremental ILP Considering Conflicts

Humans are experiencing the inclusion of artificial agents in their lives,such as unmanned vehicles,service robots,voice assistants,and intelligent medical care.If the artificial agents cannot align with social values or make ethical decisions,they may not meet the expectations of humans.Traditionally,an ethical decision-making framework is constructed by rule-based or statistical approaches.In this paper,we propose an ethical decision-making framework based on incremental ILP(Inductive Logic Programming),which can overcome the brittleness of rule-based approaches and little interpretability of statistical approaches.As the current incremental ILP makes it difficult to solve conflicts,we propose a novel ethical decision-making framework considering conflicts in this paper,which adopts our proposed incremental ILP system.The framework consists of two processes:the learning process and the deduction process.The first process records bottom clauses with their score functions and learns rules guided by the entailment and the score function.The second process obtains an ethical decision based on the rules.In an ethical scenario about chatbots for teenagers’mental health,we verify that our framework can learn ethical rules and make ethical decisions.Besides,we extract incremental ILP from the framework and compare it with the state-of-the-art ILP systems based on ASP(Answer Set Programming)focusing on conflict resolution.The results of comparisons show that our proposed system can generate better-quality rules than most other systems.

Selective and Adaptive Incremental Transfer Learning with Multiple Datasets for Machine Fault Diagnosis

The visions of Industry 4.0 and 5.0 have reinforced the industrial environment.They have also made artificial intelligence incorporated as a major facilitator.Diagnosing machine faults has become a solid foundation for automatically recognizing machine failure,and thus timely maintenance can ensure safe operations.Transfer learning is a promising solution that can enhance the machine fault diagnosis model by borrowing pre-trained knowledge from the source model and applying it to the target model,which typically involves two datasets.In response to the availability of multiple datasets,this paper proposes using selective and adaptive incremental transfer learning(SA-ITL),which fuses three algorithms,namely,the hybrid selective algorithm,the transferability enhancement algorithm,and the incremental transfer learning algorithm.It is a selective algorithm that enables selecting and ordering appropriate datasets for transfer learning and selecting useful knowledge to avoid negative transfer.The algorithm also adaptively adjusts the portion of training data to balance the learning rate and training time.The proposed algorithm is evaluated and analyzed using ten benchmark datasets.Compared with other algorithms from existing works,SA-ITL improves the accuracy of all datasets.Ablation studies present the accuracy enhancements of the SA-ITL,including the hybrid selective algorithm(1.22%-3.82%),transferability enhancement algorithm(1.91%-4.15%),and incremental transfer learning algorithm(0.605%-2.68%).These also show the benefits of enhancing the target model with heterogeneous image datasets that widen the range of domain selection between source and target domains.