Competitive Algorithms for Online Multidimensional Knapsack Problems

In this paper, we study the online multidimensional knapsack problem (called OMdKP) in which there is a knapsack whose capacity is represented in m dimensions, each dimension could have a different capacity. Then, n items with different scalar profit values and m-dimensional weights arrive in an online manner and the goal is to admit or decline items upon their arrival such that the total profit obtained by admitted items is maximized and the capacity of knapsack across all dimensions is respected. This is a natural generalization of the classic single-dimension knapsack problem and finds several relevant applications such as in virtual machine allocation, job scheduling, and all-or-nothing flow maximization over a graph. We develop two algorithms for OMdKP that use linear and exponential reservation functions to make online admission decisions. Our competitive analysis shows that the linear and exponential algorithms achieve the competitive ratios of O(θα ) and O(łogł(θα)), respectively, where α is the ratio between the aggregate knapsack capacity and the minimum capacity over a single dimension and θ is the ratio between the maximum and minimum item unit values. We also characterize a lower bound for the competitive ratio of any online algorithm solving OMdKP and show that the competitive ratio of our algorithm with exponential reservation function matches the lower bound up to a constant factor.

Surveying the Landscape of Numbers in U.S. News

The news arguably serves to inform the quantitative reasoning (QR) of news audiences. Before one can contemplate how well the news serves this function, we first need to determine how much QR typical news stories require from readers. This paper assesses the amount of quantitative content present in a wide array of media sources, and the types of QR required for audiences to make sense of the information presented. We build a corpus of 230 US news reports across four topic areas (health, science, economy, and politics) in February 2020. After classifying reports for QR required at both the conceptual and phrase levels, we find that the news stories in our sample can largely be classified along a single dimension: The amount of quantitative information they contain. There were two main types of quantitative clauses: those reporting on magnitude and those reporting on comparisons. While economy and health reporting required significantly more QR than science or politics reporting, we could not reliably differentiate the topic area based on story-level requirements for quantitative knowledge and clause-level quantitative content. Instead, we find three reliable clusters of stories based on the amounts and types of quantitative information in the news stories.

An An Integrated Automatic-Grading and Quality Measure for Assessing Programming Assignment

Programming teachers very often assess their students' submissions solely from their correctness, sometimes with the help of an automated-grading platform. This approach is arguably effective and efficient at the same time. Unfortunately, this single-dimension assessment approach narrows the students' perspective on a high-quality solution to just a working solution. In the real world setting, a solution should be maintainable with minimal cost. Maintainability is closely related to code quality. In this paper, we present a web-based tool that would help the teachers to assess the students' submissions from both correctness and quality in one place. In this tool, we integrate GitHub Classroom and SonarQube.

Model-Free-Based Single-Dimension Fuzzy SMC Design for Underactuated Quadrotor UAV

The underactuated quadrotor unmanned aerial vehicle (UAV) is one of the nonlinear systems that have few actuators as compared to the degree of freedom (DOF); thus, it is a strenuous task to stabilize its attitude and positions. Moreover, an induction of unmodelled dynamic factors and uncertainties make it more difficult to control its maneuverability. In this paper, a model-free based single-dimension fuzzy sliding mode control (MFSDF-SMC) is proposed to control the attitude and positions of underactuated quadrotor UAV. The paper discusses the kinematic and dynamic models with unmodelled dynamic factors and unknown external disturbances. These unmodelled factors and disturbances may lead the quadrotor towards failure in tracking specific trajectory and may also generate some serious transient and steady-state issues. Furthermore, to avoid the problem of gimbal lock, the model is amalgamated with hyperbolic function to resolve the singularity issues dully developed due to Newton Euler’s dynamic modeling. The simulation results performed for MFSDF-SMC using MATLAB software R2020a are compared with conventional sliding mode control, fuzzy-based sliding control and single-dimension fuzzy-based sliding mode control without a model-free approach. The design and implementation of the model-free single dimension-based fuzzy sliding mode control (MFSDF-SMC) with an updated Lyapunov stability theorem is presented in this work. It is observed that MFSDF-SMC produces robust trajectory performance therefore, and the manuscript suggests the experimental setup to test the proposed algorithm in a noisy environment keeping the same conditions. The verification of the equipment used and its effective demonstration is also available for the reader within the manuscript.

The meaning of an infinitely great velocity

An instantaneous velocity where a moment of the clock only corresponds to an arbitrary distance or position in space cannot be implied in Axiom 1, but it indicates that there is only one dimensional existence, space or time, where a certain moment only corresponds to itself specifically, not to any other time or any given length of space. Further , a definition of velocity that consists of two dimensions representing the relationship between space and time is not valid and there is only one-dimensional space or time that is independent of each other in Axiom 1. As a result, the principle of relativity and the principle of the constant velocity of light are replaced by the principle of an inertial system and the principle of universal invariant velocity in Axiom 1. Unlike two dimensions whose magnitude is determined by the ratio, the magnitude of a single dimension is determined by the unit values of one dimension, which indicates that an infinitely great velocity is meaningless. Further, if the two inertial systems are infinite versus finite in Axiom 3, then this extension of the infinitely great velocity can be defined as inextensible.

Information-Efficient, Off-Center Sampling Results in Improved Precision in 3D Single-Particle Tracking Microscopy

In this work, we present a 3D single-particle tracking system that can apply tailored sampling patterns to selectively extract photons that yield the most information for particle localization. We demonstrate that off-center sampling at locations predicted by Fisher information utilizes photons most efficiently. When performing localization in a single dimension, optimized off-center sampling patterns gave doubled precision compared to uniform sampling. A ~20% increase in precision compared to uniform sampling can be achieved when a similar off-center pattern is used in 3D localization. Here, we systematically investigated the photon efficiency of different emission patterns in a diffraction-limited system and achieved higher precision than uniform sampling. The ability to maximize information from the limited number of photons demonstrated here is critical for particle tracking applications in biological samples, where photons may be limited.

Information-Efficient, Off-Center Sampling Results in Improved Precision in 3D Single Particle Tracking Microscopy

In this work, we present a 3D single-particle tracking system that can apply tailored sampling patterns to selectively extract photons that yield the most information for particle localization. We demonstrate that off-center sampling at locations predicted by Fisher information utilizes photons most efficiently. When performing localization in a single dimension, optimized off-center sampling patterns gave doubled precision compared to uniform sampling. A ~20% increase in precision compared to uniform sampling can be achieved when a similar off-center pattern is used in 3D localization. This work is the first to thoroughly investigate the photon efficiency of different emission patterns in a diffraction-limited system and achieve higher precision than uniform sampling. The ability to maximize information from the limited number of photons demonstrated here is critical for particle tracking applications in biological samples, where photons may be limited.

Sterner Response toward Rape in line with Islamic Law: Special Reference to Pakistan

This paper tends to examine the nature of rape crime under Islamic law in order to take sterner action against this crime in line with Islamic law. As the Holy Quran does not directly deal with rape crime, for this reason, there is a wide range of disagreement among jurists regarding the issue of rape crime. Rape is not a single dimension issue, therefore, this paper is meant to shed light on issues related to rape such as whether or not rape is a separate crime? When does sexual intercourse amount to rape? What does Islam prescribe punishment for a person who is coerced to commit rape? Does Islam permit abortion for raped women? Why marital rape does not exist in Islam? Whether rapists may be awarded the punishment of lashes, Imprisonment or death as t‘azir or syasah? This paper finds out what Zina (fornication) is under Islamic law because in Islamic jurisprudence only coerced Zina is regarded as rape. Thus, this paper is classifying rape in the same category as Zina. By classifying rape as a subset of Zina can only sort out the juridical issues that are emanating from coerced Zina. However, Some modern scholars put rape in a category of Hirabbah crime in order to circumvent the strict evidentiary procedure of Zina(fornication) crime. This paper depicts that there is no need to put rape in the domain of Hirabah because Islamic law permits the ruler or legislation to award punishment of lashes or death as Tazir or Syasah without waiting for the four pious Muslim male eye witness and inflicting Hadd of Qadaf(slander) to the complainant. Finally, this paper is exploring the options that may be taken in order to nip this crime in the bud.