Sharif Digital Repository

The notion of compressibility of a random measure is a rather general concept which find applications in many contexts from data compression, to signal quantization, and parameter estimation. While compressibility for discrete and continuous measures is generally well understood, the case of discrete-continuous measures is quite subtle. In this paper, we focus on a class of multi-dimensional random measures that have singularities on affine lower-dimensional subsets. We refer to this class of random variables as affinely singular. Affinely singular random vectors naturally arises when considering linear transformation of component-wise independent discrete-continuous random variables. To... 

The emerging trend of distribution generation with existing power system network leads uncertainty factor. To handle this uncertainty, it is a provocation for the power system control, planning, and operation engineers. Although there are numerous techniques to model and evaluate these uncertainties, but in this paper the integration of Copula theory with Improved Latin-hypercube Sampling (ILHS) are incorporated for Probabilistic load Flow (PLF) evaluation. In probabilistic research approaches, the dominant interest is to achieve appropriate modelling of input random variables and reduce the computational burden. To address the said problem, Copula theory is applied to execute the modelling... 

In this article, a novel cooperative secondary voltage/frequency control considering time-varying delays and noises in fading channels is presented for an autonomous alternating current (AC) voltage sourced-based converter (VSC)-based microgrid (MG), including inverter-interfaced distributed generations (DGs). Fading phenomenon makes complex random fluctuations on the voltage and frequency of every DG received from its neighbor DGs. In multi-agent cooperative systems, in addition to the total additive noise and time-variant delay, a multiplicative complex random variable is considered to model the main received signal and its replicas due to multipath propagation. The proposed... 

A coding scheme for transmission of a bit maps a given bit to a sequence of channel inputs (called the codeword associated with the transmitted bit). In this paper, we study the problem of designing the best code for a discrete Poisson channel with memory (under peak-power and total-power constraints). The outputs of a discrete Poisson channel with memory are Poisson distributed random variables with a mean comprising of a fixed additive noise and a linear combination of past input symbols. Assuming a maximum-likelihood (ML) decoder, we search for a codebook that has the smallest possible error probability. This problem is challenging because error probability of a code does not have a... 

A coding scheme for transmission of a bit maps a given bit to a sequence of channel inputs (called the codeword associated to the transmitted bit). In this paper, we study the problem of designing the best code for a discrete Poisson channel with memory (under peak-power and total-power constraints). The outputs of a discrete Poisson channel with memory are Poisson distributed random variables with a mean comprising a fixed additive noise and a linear combination of past input symbols. Assuming a maximum-likelihood (ML) decoder, we find the best codebook design by minimizing the error probability of the decoder over all codebooks. For the case of having only a total-power constraint, the... 

A coding scheme for transmission of a bit maps a given bit to a sequence of channel inputs (called the codeword associated with the transmitted bit). In this paper, we study the problem of designing the best code for a discrete Poisson channel with memory (under peak-power and total-power constraints). The outputs of a discrete Poisson channel with memory are Poisson distributed random variables with a mean comprising of a fixed additive noise and a linear combination of past input symbols. Assuming a maximum-likelihood (ML) decoder, we search for a codebook that has the smallest possible error probability. This problem is challenging because error probability of a code does not have a... 

A coding scheme for transmission of a bit maps a given bit to a sequence of channel inputs (called the codeword associated to the transmitted bit). In this paper, we study the problem of designing the best code for a discrete Poisson channel with memory (under peak-power and total-power constraints). The outputs of a discrete Poisson channel with memory are Poisson distributed random variables with a mean comprising a fixed additive noise and a linear combination of past input symbols. Assuming a maximum-likelihood (ML) decoder, we find the best codebook design by minimizing the error probability of the decoder over all codebooks. For the case of having only a total-power constraint, the... 

Blockchain technology brings about an opportunity to maintain decentralization in several applications, such as cryptocurrency. With the agents of a decentralized system operating independently, it calls for a consensus protocol that helps all nodes to agree on the state of the ledger. Most of the existing blockchains rely on Proof of Work (PoW) as the underlying consensus algorithm, resulting in a significant amount of electricity power consumption. Furthermore, it demands the miner to buy specific computation devices. Besides, a protocol to gather the society-related taxes such as public education funding and charities is lacking in existing consensus algorithms. In response, this paper... 

A group-characterizable (GC) random variable is induced by a finite group, called main group, and a collection of its subgroups. The notion extends directly to secret sharing schemes (SSSs). It is known that linear and abelian SSSs can be equivalently described in terms of GC SSSs. In this paper, we present a necessary and sufficient condition for a SSS to be equivalent to a GC one. Using this result, we show that homomorphic SSSs (HSSSs) are equivalent to GC SSSs whose subgroups are normal in the main group. We also present two applications for this equivalent description of HSSSs. One concerns lower bounding the information ratio of access structures for the class of HSSSs, and the other... 

The Renyi's information dimension (RID) of an n-dimensional random vector (RV) is the average dimension of the vector when accounting for non-zero probability measures over lower-dimensional subsets. From an information-theoretical perspective, the RID can be interpreted as a measure of compressibility of a probability distribution. While the RID for continuous and discrete measures is well understood, the case of a discrete-continuous measures presents a number of interesting subtleties. In this paper, we investigate the RID for a class of multi-dimensional discrete-continuous random measures with singularities on affine lower dimensional subsets. This class of RVs, which we term affinely... 

The reliability analysis of defective pipes, which operate under creep-fatigue loading conditions has been studied. An austenitic stainless steel pipe containing an axially external semi-elliptical surface crack, subjected to variable internal pressure at elevated temperature has been considered as the benchmark problem. Different parameters in material behavior, geometry parameters, and operational condition have been assumed as random variables in the probabilistic assessments. The reliability of the cracked pipes have been evaluated at various operation times, using different reliability methods. Sensitivity analyses have been conducted to investigate the importance measure of the random... 

In this paper, we argue that in many basic algorithms for machine learning, including support vector machine (SVM) for classification, principal component analysis (PCA) for dimensionality reduction, and regression for dependency estimation, we need the inner products of the data samples, rather than the data samples themselves.Motivated by the above observation, we introduce the problem of private inner product retrieval for distributed machine learning, where we have a system including a database of some files, duplicated across some non-colluding servers. A user intends to retrieve a subset of specific size of the set of the inner product of every pair of data items in the database with... 

Marton's inner bound is the best known achievable rate region for a general two-receiver discrete memoryless broadcast channel. In this paper, we establish improved bounds on the cardinalities of the auxiliary random variables appearing in this inner bound to the true rate region. We combine a perturbation technique, along with a representation using concave envelopes of information-theoretic functions that involve the use of auxiliary random variables, to achieve this improvement. The new cardinality bounds lead to a proof that a randomized-time-division strategy achieves every rate triple in Marton's region for binary input broadcast channels. This extends the result by Hajek and Pursley... 

Discrete Phase-Type (DPH) distributions have one property that is not shared by Continuous Phase-Type (CPH) distributions, i.e., representing a deterministic value as a DPH random variable. This property distinguishes the application of DPH in stochastic modeling of real-life problems, such as stochastic scheduling, in which service time random variables should be compared with a deadline that is usually a constant value. In this paper, we consider a restricted class of DPH distributions, called Mixed Shifted Negative Binomial (MSNB), and show its flexibility in producing a wide range of variances as well as its adequacy in fitting fat-tailed distributions. These properties render MSNB... 

Discrete Phase-Type (DPH) distributions have one property that is not shared by Continuous Phase-Type (CPH) distributions, i.e., representing a deterministic value as a DPH random variable. This property distinguishes the application of DPH in stochastic modeling of real-life problems, such as stochastic scheduling, in which service time random variables should be compared with a deadline that is usually a constant value. In this paper, we consider a restricted class of DPH distributions, called Mixed Shifted Negative Binomial (MSNB), and show its flexibility in producing a wide range of variances as well as its adequacy in fitting fat-tailed distributions. These properties render MSNB... 

This study investigates the effects of uncertainties in the prediction of creep-fatigue crack propagation in 316L(N) austenitic stainless steel plates containing a semi-elliptical surface defect. Different parameters in geometry, material behavior and test condition are considered as random variables in probabilistic assessments. Monte-Carlo sampling method is employed to estimate the probability distribution of desired outputs such as propagated crack sizes, stress intensity factors and creep rupture life. It is shown that, the standard deviation of the predicted crack sizes in both through-wall direction and along the surface of the plate will be increased by increasing the time (hence the... 

The sparsity and compressibility of finite-dimensional signals are of great interest in fields, such as compressed sensing. The notion of compressibility is also extended to infinite sequences of independent identically distributed or ergodic random variables based on the observed error in their nonlinear $k$ -term approximation. In this paper, we use the entropy measure to study the compressibility of continuous-domain innovation processes (alternatively known as white noise). Specifically, we define such a measure as the entropy limit of the doubly quantized (time and amplitude) process. This provides a tool to compare the compressibility of various innovation processes. It also allows us... 

In this paper, the optimal sampling strategies (uniform or nonuniform) and distortion tradeoffs for Gaussian bandlimited periodic signals with additive white Gaussian noise are studied. Our emphasis is on characterizing the optimal sampling locations as well as the optimal presampling filter to minimize the reconstruction distortion. We first show that to achieve the optimal distortion, no presampling filter is necessary for any arbitrary sampling rate. Then, we provide a complete characterization of optimal distortion for low and high sampling rates (with respect to the signal bandwidth). We also provide bounds on the reconstruction distortion for rates in the intermediate region. It is... 

Expanding the electricity market into the retail domain calls for inexpensive mass-produced smart devices that enable the small customers to participate in local energy transactions by managing the energy production/consumption and submitting buy/sell bids to the market. In this context, this paper presents a mathematically proven as well as practical approach for bidding of an autonomous smart transactive agent in local energy markets. To reach this goal, behaviors of both riskneutral and risk-averse agents selling energy to the market are modeled taking into account expected profit and risk criteria. Based on this modeling procedure, an optimal multi-step quantity-price bidding strategy is... 

Marton’s inner bound is the best known achievable rate region for a general two-receiver discrete memoryless broadcast channel. In this paper, we establish improved bounds on the cardinalities of the auxiliary random variables appearing in this inner bound to the true rate region. We combine a perturbation technique, along with a representation using concave envelopes of information-theoretic functions that involve the use of auxiliary random variables, to achieve this improvement. The new cardinality bounds lead to a proof that a randomized time-division strategy achieves every rate triple in Marton’s region for binary input broadcast channels. This extends the result by Hajek and Pursley...