Optimal Probability Research Articles

General lower and upper bounds under minimum-error quantum state discrimination

For the optimal success probability under minimum-error discrimination between $r\geq2$ arbitrary quantum states prepared with any a priori probabilities, we find new general analytical lower and upper bounds and specify the relations between these new general bounds and the general bounds known in the literature. We also present the example where the new general analytical bounds, lower and upper, on the optimal success probability are tighter than most of the general analytical bounds known in the literature. The new upper bound on the optimal success probability explicitly generalizes to $r>2$ the form of the Helstrom bound. For $r=2$, each of our new bounds, lower and upper, reduces to the Helstrom bound.

UAV-Assisted Cooperative & Cognitive NOMA: Deployment, Clustering, and Resource Allocation

Cooperative and cognitive non-orthogonal multiple access (CCR-NOMA) has been recognized as a promising technique to overcome issues of spectrum scarcity and support massive connectivity envisioned in next-generation wireless networks. In this paper, we investigate the deployment of an unmanned aerial vehicle (UAV) as a relay that fairly serves a large number of secondary users in a hot-spot region. The UAV deployment algorithm must jointly account for user clustering, channel assignment, and resource allocation sub-problems. We propose a solution methodology that obtains user clustering and channel assignment based on the optimal resource allocations for a given UAV location. To this end, we derive closed-form optimal power and time allocations and show it delivers optimal max-min fair throughput by consuming less energy and time than geometric programming. Based on optimal resource allocation, the optimal coverage probability is also provided in closed-form, which takes channel estimation errors, hardware impairments, and primary network interference into account. The optimal coverage probabilities are used by the proposed max-min fair user clustering and channel assignment approaches. The results show that the proposed method achieves 100% accuracy in more than five orders of magnitude less time than the optimal benchmark.

Securing localization-free underwater routing protocols against depth-spoofing attacks

Localization-free depth-based opportunistic routing protocols are an energy efficient choice for underwater wireless sensor networks (UWSNs). However, most depth-based routing protocols are vulnerable to sinkhole attacks caused by depth spoofing. In this paper, we propose an energy-efficient depth-based probabilistic routing protocol (DPR) that is resilient against depth spoofing. By encouraging unqualified (suboptimal) relay nodes to randomly forward data packets, the adversarial effects of depth-spoofing can be mitigated. As the randomized forwarding probability increases, a better packet delivery ratio can be achieved when under depth-spoofing attacks. To keep energy consumption in check, we propose a simulation-based methodology for finding the optimal forwarding probability. By adjusting the unqualified node forwarding probability, the proposed DPR protocol can effectively resist depth-spoofing attacks with a reasonably efficient energy overhead. A delivery ratio exceeding 90% can be achieved under attack with energy overhead as low as 35% under normal conditions. In comparison with relevant existing protocols, the proposed protocol achieves better energy efficiency, resilience efficiency, and scalability.

Bayesian Basket Trial Design Accounting for Multiple Cutoffs of an Ambiguous Biomarker

Basket trial designs enroll patients with different cancer types but the same genetic mutation or biomarker to evaluate the treatment effect of targeted therapy. However, the explicit biomarker sometimes may not be clearly identified. In this article, we propose a Bayesian basket trial design to account for multiple cutoffs of ambiguous biomarkers and select the optimal cutoff window to maximize the beneficial subpopulation. A two-stage design is proposed for the estimation. Second, we propose threshold calibration and sample size determination to facilitate the design. Extensive simulations are conducted to demonstrate the operating characteristics of the two estimation methods in terms of probability of correct selection of optimal cutoff window and probability of efficacy.

Matching Learning-Based Relay Selection for Substation Power Internet of Things

Wireless sensor network (WSN) can effectively solve the problems of weak coverage, blind coverage, and low survivability of smart substation communication networks by deploying multiple relay nodes and adopting multihop transmission. However, there are still some challenges in the traditional relay selection strategy of WSN in substation, including incomplete information and the selection conflicts among multisource nodes. In this paper, we propose a matching learning-based relay selection mechanism for WSN-based substation power Internet of things (SPIoT). Firstly, considering the electromagnetic interference caused by the operation of high-voltage equipment, a multihop transmission model of SPIoT is built. Furthermore, based on the upper confidence bound (UCB) algorithm and matching theory, a matching learning-based relay selection (MLRS) algorithm is proposed to minimize the energy consumption of SPIoT devices. Simulation results demonstrate that MLRS outperforms existing algorithms in terms of energy consumption and optimal selection probability.

Effects of multi-temporal scale drought on vegetation dynamics in Inner Mongolia from 1982 to 2015, China

Climate change is causing severe changes in the ecosystem, thus understanding how plants respond to drought is essential to protecting ecosystems in Inner Mongolia. Multi-temporal variations of drought in Inner Mongolia were studied using the Standardized Precipitation Evapotranspiration Index (SPEI), and the vegetation growth was analyzed using the Normalized Difference Vegetation Index (NDVI). Moreover, the correlation between droughts of different lengths and NDVI was studied. Subsequently, we developed an optimal binary probability model to calculate the probability of vegetation productivity loss at different drought levels using the copula method. The results showed: (1) a weak aridification in the western parts and significant wetness in the central and eastern parts of Inner Mongolia; (2) a significant decreasing trend of NDVI from 1982 to 2009 and a significant increasing trend from 2010 to 2015; (3) a strong positive correlation between NDVI and SPEI and a difference between their related time scales based on soil textures; and (4) a higher probability of vegetation productivity loss with increasing drought at different drought levels.

A SIMPLE AND NEARLY OPTIMAL INVESTMENT STRATEGY TO MINIMIZE THE PROBABILITY OF LIFETIME RUIN

AbstractWe study the optimal investment strategy to minimize the probability of lifetime ruin under a general mortality hazard rate. We explore the error between the minimum probability of lifetime ruin and the achieved probability of lifetime ruin if one follows a simple investment strategy inspired by earlier work in this area. We also include numerical examples to illustrate the estimation. We show that the nearly optimal probability of lifetime ruin under the simplified investment strategy is quite close to the original minimum probability of lifetime ruin under reasonable parameter values.

An intelligent optimization method of reload core loading pattern and its application

Reload core loading pattern design is the key content related to safety, economy and flexibility of the operation after refueling in nuclear power plant. The optimization design of the reload loading pattern is a very short time requirements, great difficulty, high experience requirements and repeatable work. According to these above rigorous requirements, based on statistical learning and random sampling, this study proposes an intelligent method of reload core loading pattern optimization——Probability Sampling Loading Pattern Optimization (PSLPO). This method intelligently extracts the characteristic law in the optimization space of the reload core loading pattern by statistical learning method to establish the probability model. And the probability model is embedded into PSLPO by the random sampling method. Finally, PSLPO method is constantly updated and evolved in the optimization process by intelligent means such as dynamic adjustment weight factor, probability model adaptive adjustment mechanism and combined simulated annealing design, which realizes the improvement of the optimization ability of the algorithm continuously. According to the actual reload design verification for cycle 5 of Hainan nuclear power plant unit 2, it is shown that the recommended pattern of PSLPO is better than manual search pattern in the aspect of cycle length and power distribution, and the method can intelligently give multiple design patterns, which users can have many choices. Through the optimization evaluation with a single computer core, the optimization efficiency of the method can meet the needs of core reload design. The global optimization ability can be further improved through parallelization and algorithm parameter optimization.

Research on Dynamic Cooperative Replenishment Optimization of Shipbuilding Enterprise Inventory Control under Uncertainty

Aiming at the problem of high inventory control costs of shipbuilding enterprises under uncertain conditions, this paper constructs and optimizes a dynamic collaborative replenishment model of shipbuilding enterprises inventory control. This model adopts integrated supply chain management theory and collaborative theory to analyze the inventory control principle in shipbuilding enterprises, and its goal is to minimize the cost and maximize the service level. The dynamic replenishment strategy from two types of suppliers is given by using mathematical knowledge, such as optimization theory, probability theory, and mathematical statistics to solve the model. Finally, shipbuilding enterprises take paint inventory control as an example to test and verify the validity and correctness of the model by using numerical simulation and sensitivity analysis. The results show that the dynamic collaborative replenishment model of shipbuilding enterprises inventory control can make full use of the advantages of two types of suppliers. Additionally, it cannot only quickly respond to demand changes, but can also maintain low operating costs. Therefore, the dynamic collaborative replenishment model could effectively solve the problem of high inventory control costs of shipbuilding enterprises under uncertain conditions and has great application value and practical significance.

Integrative Analysis of Peripheral Blood Indices for the Renal Sinus Invasion Prediction of T1 Renal Cell Carcinoma: An Ensemble Study Using Machine Learning-Assisted Decision-Support Models.

PurposeRenal sinus invasion is an attributive factor affecting the prognosis of renal cell carcinoma (RCC). This study aimed to construct a risk prediction model that could stratify patients with RCC and predict renal sinus invasion with the help of a machine learning (ML) algorithm.Patients and MethodsWe retrospectively recruited 1229 patients diagnosed with T1 stage RCC at the Baotou Cancer Hospital between November 2013 and August 2021. Iterative analysis was used to screen out predictors related to renal sinus invasion, after which ML-based models were developed to predict renal sinus invasion in patients with T1 stage RCC. The receiver operating characteristic curve (ROC), decision curve analysis (DCA), and clinical impact curve (CIC) were performed to evaluate the robustness and clinical practicability of each model.ResultsA total of 21 candidate variables were shortlisted for model building. Iterative analysis screened that neutrophil to albumin ratio (NAR), hemoglobin level * albumin level * lymphocyte count/platelet count ratio (HALP), prognostic nutrition index (PNI), body mass index*serum albumin/neutrophil-lymphocyte ratio (AKI), NAR, and fibrinogen (FIB) concentration (NARFIB), platelet to lymphocyte ratio (PLR), and R.E.N.A.L score was related to renal sinus invasion and contributed significantly to ML-based algorithm. The areas under the ROC curve (AUCs) of the random forest classifier (RFC) model, support vector machine (SVM), eXtreme gradient boosting (XGBoost), artificial neural network (ANN), and decision tree (DT) ranged from 0.797 to 0.924. The optimal risk probability of renal sinus invasion predicted was RFC (AUC = 0.924, 95% confidence interval [CI]: 0.414–1.434), which showed robust discrimination for identifying high-risk patients.ConclusionWe successfully develop practical models for renal sinus invasion prediction, particularly the RFC, which could contribute to early detection via integrating systemic inflammatory factors and nutritional parameters.

Qubit state discrimination using post-measurement information

We consider the optimal discrimination of nonorthogonal qubit states with post-measurement information and provide an analytic structure of the optimal measurements. We also show that there is always a null optimal measurement when post-measurement information is given. Further, in discriminating four states using post-measurement information, we analytically provide the optimal probability of correct guessing and show that the uniqueness of optimal measurement is equivalent to the non-existence of non-null optimal measurement with post-measurement information.

Novel Secure Outsourcing of Modular Inversion for Arbitrary and Variable Modulus

In cryptography and algorithmic number theory, modular inversion is viewed as one of the most common and time-consuming operations. It is hard to be directly accomplished on resource-constrained clients (e.g., mobile devices and IC cards) since modular inversion involves a great amount of operations on large numbers in practice. To address the above problem, this paper proposes a novel unimodular matrix transformation technique to realize secure outsourcing of modular inversion. This technique makes our algorithm achieve several amazing properties. First, to the best of our knowledge, it is the first secure outsourcing computation algorithm that supports arbitrary and variable modulus, which eliminates the restriction in previous work that the protected modulus has to be a fixed composite number. Second, our algorithm is based on the single untrusted program model, which avoids the non-collusion assumption between multiple servers. Third, for each given instance of modular inversion, it only needs one round interaction between the client and the cloud server, and enables the client to verify the correctness of the results returned from the cloud server with the (optimal) probability 1. Furthermore, we propose an extended secure outsourcing algorithm that can solve modular inversion in multi-variable case. Theoretical analysis and experimental results show that our proposed algorithms achieve remarkable local-client’s computational savings. At last, as two important and helpful applications of our algorithms, the outsourced implementations of the key generation of RSA algorithm and the Chinese Reminder Theorem are given.

An Adaptive Offloading Mechanism for Mobile Cloud Computing: A Niching Genetic Algorithm Perspective

The fast evolution of mobile applications demonstrates the growing need for more resources and processing power on mobile devices. Mobile Cloud Computing (MCC) combines cloud computing with mobile devices, enabling sophisticated and resource-intensive applications to operate on mobile devices regardless of their performance limits (e.g., battery life, memory utilization, and computation). Overcoming these constraints is accomplished using a well-known technique called computation offloading, which entails offloading heavy processing to resourceful servers and getting the results from these servers. Many studies have been done on mobile code offloading, with the goal of avoiding the stated limits and reducing execution time or battery consumption through single- or multiple-site offloading, so that people can use their phones and tablets more. However, the majority of existing techniques make offloading choices based on profile data, which implies a stable network environment and forces an object to be offloaded to the same site. As a consequence of these challenges, this research proposes a novel strategy for enhancing the multisite offloading mechanism by combining a Niching Genetic Algorithm (NGA) with a Markov Decision Process (MDP). MDP is used to determine the most optimal location for each application’s modules to be executed. GA was used to determine the optimal transition probability for components operating on several sites. To aid in initial population selection, the proposed model employs a niche model in the form of a context-based clearing (CBC) technique to improve the variability of the genes inside the chromosome in order to minimize their association. The simulation results reveal that the proposed technique consumes little power and executes quickly while determining the optimal offloading decision with lower generation numbers.

Request Control of Web Service-Based Sampling System With Multiple Smart Sensors

In a Web service-based sampling system (WSSS) with multiple smart sensors, where the smart sensors request the sampling-commands (SCs) from the Web server with polling mechanism, and the Web server picks up the targeted estimates (TEs) from all the estimates received, higher polling frequency and more estimate-submissions enable the Web server to obtain all TEs (ATE) with larger probability, enjoying less delays, while suffering more network traffic. Therefore, how to minimize the network traffic while satisfying the acceptable delays and probability of the server obtaining ATE arises as an interesting issue. To address this issue, this paper first proposes a Markov decision process (MDP) framework to formulate the request process of WSSS, then explores out the optimal polling frequency and probability in the polynomial time for the smart sensors' requests, and finally proposes a probability threshold-based algorithm to guide the smart sensors to decide the polling frequency and whether to request the SCs. Theoretical results, simulations, and field experiments document and illustrate its performance.

Effect of parameter correlation on risk analysis of wellbore instability in deep igneous formations

A Permian igneous formation in the Sichuan Basin typically exhibits complex lithology, strong heterogeneity, and strong uncertainty; consequently, there is a very high risk of wellbore collapse during drilling and completion, which would seriously affect the safety, efficiency, and cost of drilling operations. Therefore, to prevent wellbore collapse in Permian igneous rock formations, a risk assessment method of wellbore instability based on reliability theory was proposed, and the effects of parameter correlation on the reliability of wellbore stability were considered. First, profiles of the rock mechanical parameters, formation pore pressure, and in-situ stresses were established by logging interpretation. Second, the optimal probability distribution of each parameter was determined for three typical igneous formations, and the correlation coefficient matrix was obtained using correlation analysis. Third, the effect of parameter correlation was involved to propose a risk analysis method of wellbore instability, where the Monte Carlo method was used for random sampling. Finally, the safe mud weight window of each igneous formation was determined, and the sensitivity of wellbore stability to the parameter mean values and correlation coefficients was analyzed. The results indicate that significant uncertainty and parameter correlation exist for the igneous formations, which clearly affect wellbore stability. The effect is greatest for the breccia formation, followed by the tuff and basalt formations. The correlations between cohesion and internal friction angle and between cohesion and maximum horizontal principal stress are the most important factors affecting collapse pressure, whereas the correlation between the two horizontal stresses is most important for fracture pressure. The results suggest that the effect of parameter correlation on the reliability of wellbore stability in strongly heterogeneous settings cannot be ignored.

Optimization of international road transportation of cargoes in the management of enterprises of agricultural sector and road transport enterprises

To enhance the efficiency of management of enterprises in the agricultural sector, it is necessary to improve logistic processes of delivery of livestock and crop production in the implementation of international road transportation. Delivery of cargo "just in time" is very important, so transportation time planning is relevant and allows reducing costs. The process of planning the delivery of perishable goods was described. The spread of the required time is presented for transportation with a varied degree of stochasticity. It was found that the specifics of customs clearance affect the availability of a certain minimum time required for such a procedure. The time of customs clearance of cargo and delay time affect the deadline for cargo registration in international road transportation. The widest spread of time is observed by the procedure of customs clearance of cargoes that takes from 12 to 25 hours, and the probability of customs clearance is only 0.435. Accordingly, this affects a decrease in indicators of "just in time" delivery. The functional dependence of the probability of transit time not exceeding the planned time was compared, depending on the data of the specified route. Based on probabilistic analysis, the possibility of unplanned deviations from the estimated terms of each stage was taken into account and the optimal set of time intervals, which allow obtaining the optimal probability of "just in time" delivery, was proposed. The total cargo delivery time does not change. The recommendations on formulating the requirements for road transport enterprises were given. Namely, to strengthen the requirements for the time of cargo transit. These requirements include the average speed of motion, the choice of appropriate transport, planning the route in terms of the speed mode of highways, etc.

Unambiguous State Discrimination with Intrinsic Coherence.

We investigate the discrimination of pure-mixed (quantum filtering) and mixed-mixed states and compare their optimal success probability with the one for discriminating other pairs of pure states superposed by the vectors included in the mixed states. We prove that under the equal-fidelity condition, the pure-pure state discrimination scheme is superior to the pure-mixed (mixed-mixed) one. With respect to quantum filtering, the coherence exists only in one pure state and is detrimental to the state discrimination for lower dimensional systems; while it is the opposite for the mixed-mixed case with symmetrically distributed coherence. Making an extension to infinite-dimensional systems, we find that the coherence which is detrimental to state discrimination may become helpful and vice versa.

Optimising Pedestrian Flow Around Large Stadiums

This study proposes a method that combines the cellular automaton model and the differential evolution algorithm for optimising pedestrian flow around large stadiums. A miniature version of a large stadium and its surrounding areas is constructed via the cellular automaton model. Special mechanisms are applied to influence the behaviour of an agent that leaves from a certain stadium gate. The agent may be attracted to a nearby business facility and/or guided to uncongested areas. The differential evolution algorithm is then used to determine the optimal probabilities of the influencing agents for each stadium gate. The main goal is to reduce the evacuation time, and other goals such as reducing the costs for the influencing agents’ behaviours and the individual evacuation time are also considered. We found that, although they worked differently in different scenarios, the attraction and guidance of agents significantly reduced the evacuation time. The optimal evacuation time was achieved with moderate attraction to the business facilities and strong guidance to the detouring route. The results demonstrate that the proposed method can provide a goal-dependent, exit-specific strategy that is otherwise hard to acquire for optimising pedestrian flow.

The postdoc variant of the secretary problem

The classical secretary problem involves sequentially interviewing a pool of n applicants with the aim of hiring exactly the best one in the pool—nothing less is good enough. The optimal decision strategy is easy to describe and the probability of success is 1/e. In this paper, we consider a minor variant of this classical problem. We wish to pick not the best but the second-best (the best is going to Harvard). In this case, an explicit solution can be given both for the optimal strategy and the associated optimal success probability. As n goes to infinity, the probability of success tends to 1/4. Apparently, it is easier to pick the best than the second best.

Application of Spectral Index-Based Logistic Regression to Detect Inland Water in the South Caucasus

The Caucasus is a diverse region with many climate zones that range from subtropical lowlands to mountainous alpine areas. The region is marked by irrigated croplands fed by irrigation canals, heavily vegetated wetlands, lakes, and reservoirs. In this study, we demonstrate the development of an improved surface water map based on a global water dataset to get a better understanding of the spatial distribution of small water bodies. First, we used the global water product from the European Commission Joint Research Center (JRC) to generate training data points by stratified random sampling. Next, we applied the optimal probability cut-off logistic regression model to develop surface water datasets for the entire Caucasus region, covering 19 Landsat tiles from May to October 2019. Finally, we used 6745 manually classified points (3261 non-water, 3484 water) to validate both the newly developed water dataset and the JRC global surface water dataset using an estimated proportion of area error matrix to evaluate accuracy. Our approach produced surface water extent maps with higher accuracy (89.2%) and detected 392 km2 more water than the global product (86.7% accuracy). We demonstrate that the newly developed method enables surface water detection of small ponds and lakes, flooded agricultural fields, and narrow irrigation channels, which are particularly important for mosquito-borne diseases.