Solver-based gradual type migration

Gradually typed languages allow programmers to mix statically and dynamically typed code, enabling them to incrementally reap the benefits of static typing as they add type annotations to their code. However, this type migration process is typically a manual effort with limited tool support. This paper examines the problem of automated type migration: given a dynamic program, infer additional or improved type annotations. Existing type migration algorithms prioritize different goals, such as maximizing type precision, maintaining compatibility with unmigrated code, and preserving the semantics of the original program. We argue that the type migration problem involves fundamental compromises: optimizing for a single goal often comes at the expense of others. Ideally, a type migration tool would flexibly accommodate a range of user priorities. We present TypeWhich, a new approach to automated type migration for the gradually-typed lambda calculus with some extensions. Unlike prior work, which relies on custom solvers, TypeWhich produces constraints for an off-the-shelf MaxSMT solver. This allows us to easily express objectives, such as minimizing the number of necessary syntactic coercions, and constraining the type of the migration to be compatible with unmigrated code. We present the first comprehensive evaluation of GTLC type migration algorithms, and compare TypeWhich to four other tools from the literature. Our evaluation uses prior benchmarks, and a new set of "challenge problems." Moreover, we design a new evaluation methodology that highlights the subtleties of gradual type migration. In addition, we apply TypeWhich to a suite of benchmarks for Grift, a programming language based on the GTLC. TypeWhich is able to reconstruct all human-written annotations on all but one program.

THE EFFECTIVENESS GEOGEBRA ON SOFTWARE IN TEACHING

This study aimed to clarify the Effectiveness GeoGebra on Software in Teaching " Space Geometry in the Development of Spatial Abilities and Achievement of Eleventh Grade and tried to answer the following two questions: 1. What is the Effectiveness of using GeoGebra Software in Teaching " Space Geometry of eleventh-grade students? To answer these questions, a sample of (52) eleventh-grade students was chosen and divided into two groups: an experimental group with (25) students, studied using GeoGebra Software, and a control group with (27) students, studied using the usual way. To attain the purpose of the study, an educational material for the unit of " Space Geometry " of grade eleven was prepared according to GeoGebra Software Also, GeoGebra Software Achievement test The study result showed statistically significant differences at the level (α=0,05) between the mean score of the experimental group and the mean score of the control group in the GeoGebra Software Achievement test group who studied using GeoGebra Software. In light of these results, the study recommended the importance to enter the GeoGebra of anther dynamic program in the math , to study Space Geometry and providing appropriate and encouraging study environment to improve students. Keywords: Geogebra, Space Engineering, Software

Dynamic pricing with finite price sets: a non-parametric approach

We study price optimization of perishable inventory over multiple, consecutive selling seasons in the presence of demand uncertainty. Each selling season consists of a finite number of discrete time periods, and demand per time period is Bernoulli distributed with price-dependent parameter. The set of feasible prices is finite, and the expected demand corresponding to each price is unknown to the seller, whose objective is to maximize cumulative expected revenue. We propose an algorithm that estimates the unknown parameters in a learning phase, and in each subsequent season applies a policy determined as the solution to a sample dynamic program, which modifies the underlying dynamic program by replacing the unknown parameters by the estimate. Revenue performance is measured by the regret: the expected revenue loss relative to the optimal attainable revenue under full information. For a given number of seasons n, we show that if the number of seasons allocated to learning is asymptotic to $$(n^2\log n)^{1/3}$$ ( n 2 log n ) 1 / 3 , then the regret is of the same order, uniformly over all unknown demand parameters. An extensive numerical study that compares our algorithm to six benchmarks adapted from the literature demonstrates the effectiveness of our approach.

Assessment and Optimization of Water Division Pattern in Sampean Baru Irrigation Area

Recently, agricultural production in the Sampean Baru Irrigation area has not shown optimal cropping production. The average percentage of planted areas in the first (November-February),second (March-June), and third (July-October) planting seasons for the upstream area was 93.67%; 98.02%, and 76.76%, and for the downstream area was 83.54%; 80.81%; and 89.36%. This research aims to optimize the water distribution system based on the calculation of water requirements for plants and the availability of channels to obtain the maximum planting area and amount of agricultural production. This optimization method uses a Dynamic Program with three scenarios. This calculation is based on effective rainfall, crop water requirements, and water discharge availability. Percentage of planted area obtained from the calculation in the dry year for the first, second, and third planting seasons respectively were 100%, 100%, and 90.36%. Based on the existing condition, potential profit obtained for a year is Rp. 170.08 billion. After optimization using Dynamic Program, potential profit in the dry year, normal year, and wet year are IDR 213.52 billion, IDR 215.92 billion, and IDR 228.50 billion, respectively.

Reliability analysis for a multi-stack solid oxide fuel cell system subject to operation condition-dependent degradation

PurposeA reliability analysis of a solid oxide fuel cell (SOFC) system is presented for applications with strict constant power supply requirements, such as data centers. The purpose is to demonstrate the effect when moving from a module-level to a system-level in terms of reliability, also considering effects during start-up and degradation.Design/methodology/approachIn-house experimental data on a system-level are used to capture the behavior during start-up and normal operation, including drifts of the operation point due to degradation. The system is assumed to allow replacement of stacks during operation, but a minimum number of stacks in operation is needed to avoid complete shutdown. Experimental data are used in conjunction with a physics-based performance model to construct the failure probability function. A dynamic program then solves the optimization problem in terms of time and replacement requirements to minimize the total negative deviation from a given target reliability.FindingsResults show that multi-stack SOFC systems face challenges which are only revealed on a system- and not on a module-level. The main finding is that the reliability of multi-stack SOFC systems is not sufficient to serve as sole power source for critical applications such as data center.Practical implicationsThe principal methodology may be applicable to other modular systems which include multiple critical components (of the same kind). These systems comprise other electrochemical systems such as further fuel cell types.Originality/valueThe novelty of this work is the combination of mathematical modeling to solve a real-world problem, rather than assuming idealized input which lead to more benign system conditions. Furthermore, the necessity to use a mathematical model, which captures sufficient physics of the SOFC system as well as stochasticity elements of its environment, is of critical importance. Some simplifications are, however, necessary because the use of a detailed model directly in the dynamic program would have led to a combinatorial explosion of the numerical solution space.

Individualized Pricing for a Cloud Provider Hosting Interactive Applications

We consider a cloud provider that hosts interactive applications, such as mobile apps and online games. Depending on the traffic of users for an application, the provider commits a subset of its resources (hardware capacity) to serve the application. The provider must choose a dynamic pricing mechanism to indirectly select the applications hosted and maximize revenue. We model the provider’s pricing problem as a large-scale stochastic dynamic program. To approach this problem, we propose a tractable approach to enable decomposing the multidimensional stochastic dynamic program into single-dimensional subproblems. We then extend the proposed framework to define an individualized dynamic pricing mechanism for the cloud provider. We present novel upper bounds on the optimal revenue to evaluate the performance of our pricing mechanism. The computational results show that a contract-based model of selling interactive cloud services achieves significantly greater revenue than the prevalent alternative and that our pricing scheme attains near-optimal revenue.