SDP Algorithm Research Articles

V2V-ESP: Vehicle-to-Vehicle Energy Sharing Privacy Protection Scheme Based on SDP Algorithm

V2V-ESP: Vehicle-to-Vehicle Energy Sharing Privacy Protection Scheme Based on SDP Algorithm

Differential privacy scheme using Laplace mechanism and statistical method computation in deep neural network for privacy preservation

Mountainous amounts of information are now available in hospitals, finance, counter-terrorism, education and many other sectors. Those information can offer a rich source for analysis and decision making. Such information contains user's sensitive and personal data as well. This emanates direct conflict with the user's privacy. Individual's privacy is their right. The existing privacy preserving algorithms works mainly on the numerical data and doesn't care about the categorical data. In addition, there is a heavy trade-off between privacy preservation and data utility. To overcome these issues, a deep neural network - statistical differential privacy (DNN−SDP) algorithm is proposed as the solution to disguise the individual's private and sensitive data. Both the numerical and categorical based human-specific data are considered and fed to the input layer of the neural network. The statistical methods weight of evidence and information value is applied in the hidden layer along with the random weight (wi) to get the initial perturbed data. This initially perturbed data is taken by Laplace computation based differential privacy mechanism as the input and provides the final perturbed data. Census income, bank marketing and heart disease datasets are used for experimentation. While comparing with the state-of-the-art methods, DNN−SDP algorithm provides 97.4% of accuracy with 98.2% of precision, 99% of recall rate and 98.7% of F-measure value. In addition, the fall-out rate, miss rate and false omission rate of the proposed algorithm are less than 4.1%. The DNN−SDP algorithm guarantees the privacy preservation along with data utility.

Study on the Optimal Operation of a Hydropower Plant Group Based on the Stochastic Dynamic Programming with Consideration for Runoff Uncertainty

Hydropower plant operation reorganizes the temporal and spatial distribution of water resources to promote the comprehensive utilization of water resources in the basin. However, a lot of uncertainties were brought to light concerning cascade hydropower plant operation with the introduction of the stochastic process of incoming runoff. Therefore, it is of guiding significance for the practice operation to investigate the stochastic operation of cascade hydropower plants while considering runoff uncertainty. The runoff simulation model was constructed by taking the cascade hydropower plants in the lower reaches of the Lancang River as the research object, and combining their data with the copula joint function and Gibbs method, and a Markov chain was adopted to construct the transfer matrix of runoff between adjacent months. With consideration for the uncertainty of inflow runoff, the stochastic optimal operation model of cascade hydropower plants was constructed and solved by the SDP algorithm. The results showed that 71.12% of the simulated monthly inflow of 5000 groups in the Nuozhadu hydropower plant drop into the reasonable range. Due to the insufficiency of measured runoff, there were too many 0 values in the derived transfer probability, but after the simulated runoff series were introduced, the results significantly improved. Taking the transfer probability matrix of simulated runoff as the input of the stochastic optimal operation model of the cascade hydropower plants, the operation diagram containing the future-period incoming water information was obtained, which could directly provide a reference for the optimal operation of the Nuozhadu hydropower plant. In addition, taking the incoming runoff process in a normal year as the standard, the annual mean power generation based on stochastic dynamic programming was similar to that based on dynamic programming (respectively 305.97 × 108 kW⋅h and 306.91 × 108 kW⋅h), which proved that the operation diagram constructed in this study was reasonable.

Bounds on the Sum-Rate of MIMO Causal Source Coding Systems with Memory under Spatio-Temporal Distortion Constraints.

In this paper, we derive lower and upper bounds on the OPTA of a two-user multi-input multi-output (MIMO) causal encoding and causal decoding problem. Each user’s source model is described by a multidimensional Markov source driven by additive noise process subject to three classes of spatio-temporal distortion constraints. To characterize the lower bounds, we use state augmentation techniques and a data processing theorem, which recovers a variant of rate distortion function as an information measure known in the literature as nonanticipatory -entropy, sequential or nonanticipative RDF. We derive lower bound characterizations for a system driven by an Gaussian noise process, which we solve using the SDP algorithm for all three classes of distortion constraints. We obtain closed form solutions when the system’s noise is possibly non-Gaussian for both users and when only one of the users is described by a source model driven by a Gaussian noise process. To obtain the upper bounds, we use the best linear forward test channel realization that corresponds to the optimal test channel realization when the system is driven by a Gaussian noise process and apply a sequential causal DPCM-based scheme with a feedback loop followed by a scaled ECDQ scheme that leads to upper bounds with certain performance guarantees. Then, we use the linear forward test channel as a benchmark to obtain upper bounds on the OPTA, when the system is driven by an additive non-Gaussian noise process. We support our framework with various simulation studies.

Stochastic Dynamic Pricing for EV Charging Stations With Renewable Integration and Energy Storage

This paper studies the problem of stochastic dynamic pricing and energy management policy for electric vehicle (EV) charging service providers. In the presence of renewable energy integration and energy storage system, EV charging service providers must deal with multiple uncertainties-charging demand volatility, inherent intermittency of renewable energy generation, and wholesale electricity price fluctuation. The motivation behind our work is to offer guidelines for charging service providers to determine proper charging prices and manage electricity to balance the competing objectives of improving profitability, enhancing customer satisfaction, and reducing impact on power grid in spite of these uncertainties. We propose a new metric to assess the impact on power grid without solving complete power flow equations. To protect service providers from severe financial losses, a safeguard of profit is incorporated in the model. Two algorithms-stochastic dynamic programming (SDP) algorithm and greedy algorithm (benchmark algorithm)-are applied to derive the pricing and electricity procurement policy. A Pareto front of the multi-objective optimization is derived. Simulation results show that using SDP algorithm can achieve up to 7% profit gain over using greedy algorithm. Additionally, we observe that the charging service provider is able to reshape spatial-temporal charging demands to reduce the impact on power grid via pricing signals.

Minimum error discrimination for an ensemble of linearly independent pure states

Inspired by the work done by Belavkin (1975 Stochastics 1 315) and independently by Mochon, (2006 Phys. Rev. A 73 032328), we formulate the problem of minimum error discrimination (MED) of any ensemble of n linearly independent pure states by stripping the problem of its rotational covariance and retaining only the rotationally invariant aspect of the problem. This is done by embedding the optimal conditions in a matrix equality as well as matrix inequality. Employing the implicit function theorem in these conditions we get a set of first-order coupled ordinary nonlinear differential equations which can be used to drag the solution from an initial point (where solution is known) to another point (whose solution is sought). This way of obtaining the solution can be done through a simple Taylor series expansion and analytic continuation when required. Thus, we complete the work done by Belavkin and Mochon by ultimately leading their theory to a solution for the MED problem of linearly independent pure state ensembles. We also compare the computational complexity of our technique with the barrier-type interior point method of SDP and show that our technique is computationally as efficient as (actually, a bit more than) the SDP algorithm, with the added advantage of being much simpler to implement.

Estimating quantum chromatic numbers

We develop further the new versions of quantum chromatic numbers of graphs introduced by the first and fourth authors. We prove that the problem of computation of the commuting quantum chromatic number of a graph is solvable by an SDP algorithm and describe an hierarchy of variants of the commuting quantum chromatic number which converge to it. We introduce the tracial rank of a graph, a parameter that gives a lower bound for the commuting quantum chromatic number and parallels the projective rank, and prove that it is multiplicative. We describe the tracial rank, the projective rank and the fractional chromatic numbers in a unified manner that clarifies their connection with the commuting quantum chromatic number, the quantum chromatic number and the classical chromatic number, respectively. Finally, we present a new SDP algorithm that yields a parameter larger than the Lov\'asz number and is yet a lower bound for the tracial rank of the graph. We determine the precise value of the tracial rank of an odd cycle.

Simple linear time approximation algorithm for betweenness

We study the Betweenness problem. We are given a set of vertices and betweenness constraints. Each betweenness constraint of the form x⇝{y,z} requires that vertex x lies between vertices y and z. Our goal is to find a vertex ordering that maximizes the number of satisfied constraints. In 1995, Chor and Sudan designed an SDP algorithm that satisfies half of all constraints in a satisfiable instance. We present a simple combinatorial linear time algorithm with the same approximation guarantee.

An evaluation of the multi-state node networks reliability using the traditional binary-state networks reliability algorithm

Abstract A system where the components and system itself are allowed to have a number of performance levels is called the Multi-state system (MSS). A multi-state node network (MNN) is a generalization of the MSS without satisfying the flow conservation law. Evaluating the MNN reliability arises at the design and exploitation stage of many types of technical systems. Up to now, the known existing methods can only evaluate a special MNN reliability called the multi-state node acyclic network (MNAN) in which no cyclic is allowed. However, no method exists for evaluating the general MNN reliability. The main purpose of this article is to show first that each MNN reliability can be solved using any the traditional binary-state networks (TBSN) reliability algorithm with a special code for the state probability. A simple heuristic SDP algorithm based on minimal cuts (MC) for estimating the MNN reliability is presented as an example to show how the TBSN reliability algorithm is revised to solve the MNN reliability problem. To the author's knowledge, this study is the first to discuss the relationships between MNN and TBSN and also the first to present methods to solve the exact and approximated MNN reliability. One example is illustrated to show how the exact MNN reliability is obtained using the proposed algorithm.

A sequence alignment algorithm with an arbitrary gap penalty function.

An algorithm for aligning biological sequences is presented that is an adaptation of the sequence generating function approach used in the statistical mechanics of biopolymers. This algorithm uses recursion relationships developed from a partition function formalism of alignment probabilities. It is implemented within a dynamic programming format that closely resembles the forward algorithm used in hidden Markov models (HMM). The algorithm aligns sequences or structures according to the statistically dominant alignment path and will be referred to as the SDP algorithm. An advantage of this method over previous ones is that it allows more complicated and physically realistic gap penalty functions to be incorporated into the algorithm in a facile manner. The performance of this algorithm in a case study of aligning the heavy and light chain from the variable region of an immunoglobulin is investigated.

An efficient minimizing algorithm for sum of disjoint products

This paper presents an efficient algorithm for calculating system reliability by sum of disjoint products (sdp). Abraham and his successors yield relatively short system reliability formula. This new algorithm follows the philosophy of Abraham, but uses new rules to arrange the initial ordering of minipaths in outer loop and the ordering of terms in inner loop, and adopts multiple-variable inversion. The algorithm generates a shorter system reliability formula than any known sdp algorithm.

A Minimizing Algorithm for Sum of Disjoint Products

This paper describes a minimizing version of the Abraham sum-of-disjoint products (sdp) algorithm, called the Abraham-Locks-Revised (ALR) method, as an improved technique for obtaining a disjoint system-reliability formula. The principal changes are: 1) Boolean minimization and rapid inversion are substituted for time-consuming search operations of the inner loop. 2) Paths and terms are ordered both according to size and alphanumerically. ALR reduces the computing cost and data processing effort required to generate the disjoint system formula compared to the seminal 1979 Abraham paper, and obtains a shorter formula than any other known sdp method. Very substantial savings are achieved in processing large paths of complex networks.