Sharif Digital Repository

We study the problem of fair allocation for indivisible goods. We use the maxmin share paradigm introduced by Budish [16] as a measure for fairness. Kurokawa, Procaccia, and Wang [36] were the first to investigate this fundamental problem in the additive setting. They show that a maxmin guarantee (1-MMS allocation) is not always possible even when the number of agents is limited to 3. While the existence of an approximation solution (e.g. a 1/2-MMS allocation) is quite straightforward, improving the guarantee becomes subtler for larger constants. Kurokawa et al. [36] provide a proof for the existence of a 2/3-MMS allocation and leave the question open for better guarantees. Our main... 

Edit distance and longest common subsequence are among the most fundamental problems in combinatorial optimization. Recent developments have proven strong lower bounds against subquadratic time solutions for both problems. Moreover, the best approximation factors for subquadratic time solutions have been limited to 3 for edit distance and super constant for longest common subsequence. Improved approximation algorithms for these problems1 are some of the biggest open questions in combinatorial optimization. In this work, we present improved algorithms for both edit distance and longest common subsequence. The running times are truly subquadratic, though we obtain 1 + o(1) approximate... 

Given a terrain and a query point p on or above it, we want to count the number of triangles of terrain that are visible from p. We present an approximation algorithm to solve this problem. We implement the algorithm and then we run it on the real data sets. The experimental results show that our approximation solution is very close to the real solution and compare to the other similar works, the running time of our algorithm is better than their algorithm. The analysis of time complexity of algorithm is also presented. Also, we consider visibility testing problem, where the goal is to test whether p and a given triangle of train are visible or not. We propose an algorithm for this problem... 

Deformation of single stranded DNA in a translocation process before reaching the pore is investigated. By solving the Laplace equation in a suitable coordinate system and with appropriate boundary conditions, an approximate solution for the electric field inside and outside a narrow pore is obtained. With an analysis based on the "electrohydrodynamic equivalence" we determine the possibility of the extension of a charged polymer due to the presence of an electric field gradient in the vicinity of the pore entrance. With a multi-scale hybrid simulation (LB-MD), it is shown that an effective deformation before reaching the pore occurs, which facilitates the process of finding the entrance for... 

This paper considers a repair-replacement strategy for a special class of discretely degrading and repairable products under renewing free replacement warranty. Each product may experience N different working states with different exponential hazard functions, before the warranty contract expires. Once the item enters working state i (i = 1,2, ⋯ ,N), it can either fail or move to any of the subsequent working states with different probabilities, given that a transition has been made. In the former case, the best rectification action, replacement or minimal repair, regarding the failure status, i.e., the product degradation level at the failure time and the remaining warranty time, should be... 

In recent decades, multistate two-terminal reliability problem has attracted several researchers, and accordingly many exact and approximation approaches have been proposed in the literature in terms of minimal cuts (MCs) or minimal paths (MPs) to address this problem. Here, an MP-based approximation approach is developed based on exact algorithms. With all the MPs at hand, the approach rearranges the MPs ascendingly with respect to their lengths and then sets the flow on some MPs to be zero which turns to reduce the computing cost in solving the problem. We provide the complexity results, and by employing some benchmarks and one thousand randomly generated networks illustrate that not only... 

Submodularity is a discrete domain functional property that can be interpreted as mimicking the role of well-known convexity/concavity properties in the continuous domain. Submodular functions exhibit strong structure that lead to efficient optimization algorithms with provable near-optimality guarantees. These characteristics, namely, efficiency and provable performance bounds, are of particular interest for signal processing (SP) and machine learning (ML) practitioners, as a variety of discrete optimization problems are encountered in a wide range of applications. Conventionally, two general approaches exist to solve discrete problems: 1) relaxation into the continuous domain to obtain an... 

We first establish some necessary and sufficient conditions for solvability of fuzzy LR linear systems. We then propose a concept for an approximate solution when a fuzzy LR linear system lacks a solution. Recently, we have proposed an approximate solution for a fuzzy LR linear system under the condition that a corresponding crisp linear system was solvable. Here, we remove this condition by presenting a more general concept of an approximate solution based on a least squares model. We also develop the conditions for the uniqueness of the approximate solution. To compute an approximate solution, we propose an algorithm based on a quadratic programming model with bound constraints on some... 

Approximate solutions for vibrations of flexible beam-type appendages subjected to tip mass are studied while uniform and exponential profiles for arm deployment are simulated. Applying an equivalent dynamical system and following Lagrangian approach, the equations of motion of the system are derived as nonlinear ordinary differential equations (ODEs) (with time-varying coefficients), in which the effect of the tip mass can be considered as some nonlinearity added to the 'no tip mass' case dynamics. The approximate closed-form solutions are obtained through a novel methodology using a computer algorithm, in which the solutions of the 'no tip mass' case are expanded by imposing quadratic... 

Thermally developing mixed electroosmotically and pressure-driven flow in a parallel plate microchannel with a step change in wall temperature is considered in the framework of an extended Graetz problem. Both Joule heating and viscous dissipation effects are taken into consideration. Expressions for the dimensionless temperature and Nusselt number in the form of infinite series are presented. In general, the associated eigenvalue problem is solved numerically. Nevertheless, an analytical solution is also presented for axial locations close to the entrance. Comparisons are made between the present results and those obtained by approximating the electroosmotic velocity with the... 

The present investigation considers the fully developed electro-osmotic flow of power-law fluids in a planar microchannel subject to constant wall heat fluxes. Using an approximate velocity distribution, closed form expressions are obtained for the transverse distribution of temperature and Nusselt number. The approximate solution is found to be quite accurate, especially for the values of higher than ten for the dimensionless Debye-Huckel parameter where the exact values of Nusselt number are predicted. The results demonstrate that a higher value of the dimensionless Debye-Huckel parameter is accompanied by a higher Nusselt number for wall cooling, whereas the opposite is true for wall... 

Applying integrated variational principles on fluid and deck plate to the large deflection analysis of floating roofs, this paper investigates the significance of the flexural and membrane components in the formulations of the deck plate. Integrated variational principles facilitate the treatment of the compatibility of deformation between floating roof and supporting liquid. Analysis results show that different assumptions about deck plate formulation commonly used in the literature, results in considerably different deflection and stress patterns on the floating roof. The results show that modeling of the deck plate as a flexural element rather than the membrane, by eliminating the need... 

In this work, we implement a relatively new analytical technique, the exp-function method, for solving nonlinear special form of generalized nonlinear (2 + 1) dimensional Broer-Kaup-Kupershmidt equation, which may contain high nonlinear terms. This method can be used as an alternative to obtain analytic and approximate solutions of different types of fractional differential equations which applied in engineering mathematics. Some numerical examples are presented to illustrate the efficiency and reliability of exp method. It is predicted that exp-function method can be found widely applicable in engineering  

This paper is concerned with a distributed model predictive control (DMPC) method that is based on a distributed optimisation method with two-level architecture for communication. Feasibility (constraints satisfaction by the approximated solution), convergence and optimality of this distributed optimisation method are mathematically proved. For an automated irrigation channel, the satisfactory performance of the proposed DMPC method in attenuation of the undesired upstream transient error propagation and amplification phenomenon is illustrated and compared with the performance of another DMPC method that exploits a single-level architecture for communication. It is illustrated that the DMPC... 

In this article, the effects of the changes in the mass of the floating wind turbine (as a multi-body system) on its nonlinear vertical vibrations are investigated. The fluctuations of the hydrodynamic added mass of the floating platform and the mass of the vibration absorbers, which added to the structure to mitigate the lateral vibrations, change the mass and consequently the dynamics of the vertical vibrations. In this regard, first, the governing equations of the vertical vibrations of the floating wind turbine are derived. The FAST code is used to validate the proposed model of the dynamics of the vertical vibrations through numerical simulations. Then, derived equations are solved... 

In the present investigation, design of integrated numerical computing through Levenberg-Marquardt backpropagation neural network (LMBNN) is presented to examine the fluid mechanics problems governing the dynamics of expanding and contracting cylinder for Cross magneto-nanofluid flow (ECCCMNF) model in the presence of time dependent non-uniform magnetic force and permeability of the cylinder. The original system model ECCCMNF in terms of PDEs is converted to nonlinear ODEs by introducing the similarity transformations. Reference dataset of the designed LMBNN methodology is formulated with Adam numerical technique for scenarios of ECCCMNF by variation of thermophoresis temperature ratio... 

One of the main challenges in diffusion-based molecular communication is dealing with the non-linearity of reaction-diffusion chemical equations. While numerical methods can be used to solve these equations, a change in the input signals or the parameters of the medium requires one to redo the simulations. This makes it difficult to design modulation schemes and practically impossible to prove the optimality of a given transmission strategy. In this paper, we provide an analytical technique for modeling the non-linearity of chemical reaction equations based on the perturbation method. The perturbation method expresses the solution in terms of an infinite power series. An approximate solution... 

One of the main challenges in diffusion-based molecular communication is dealing with the non-linearity of reaction-diffusion chemical equations. While numerical methods can be used to solve these equations, a change in the input signals or the parameters of the medium requires one to redo the simulations. This makes it difficult to design modulation schemes and practically impossible to prove the optimality of a given transmission strategy. In this paper, we provide an analytical technique for modeling the non-linearity of chemical reaction equations based on the perturbation method. The perturbation method expresses the solution in terms of an infinite power series. An approximate solution... 

Multiple sequence alignment (MSA) is one of the basic and important problems in molecular biology. MSA can be used for different purposes including finding the conserved motifs and structurally important regions in protein sequences and determine evolutionary distance between sequences. Aligning several sequences cannot be done in polynomial time and therefore heuristic methods such as genetic algorithms can be used to find approximate solutions of MSA problems. Several algorithms based on genetic algorithms have been developed for this problem in recent years. Most of these algorithms use very complicated, problem specific and time consuming mutation operators. In this paper, we propose a...