A continuous model for dynamic pricing under costly price modifications

This paper presents a heuristic method to solve a dynamic pricing problem under costly price modifications. This is a remarkably difficult problem that is solvable only under very few special cases. The method is applied to a more general form of the problem and is numerically tested for a variety of demand functions in the literature. The results show that the method is quite accurate, approximating the optimal profit within usually much less than 1\%. A more important result is that the accuracy tend to be much greater as the number of price changes increases, precisely when the underlying optimization problem becomes much harder, which makes this approach particularly desirable

Reinventing discovery learning: a field-wide research program

© 2017, Springer Science+Business Media B.V., part of Springer Nature. Whereas some educational designers believe that students should learn new concepts through explorative problem solving within dedicated environments that constrain key parameters of their search and then support their progressive appropriation of empowering disciplinary forms, others are critical of the ultimate efficacy of this discovery-based pedagogical philosophy, citing an inherent structural challenge of students constructing historically achieved conceptual structures from their ingenuous notions. This special issue presents six educational research projects that, while adhering to principles of discovery-based learning, are motivated by complementary philosophical stances and theoretical constructs. The editorial introduction frames the set of projects as collectively exemplifying the viability and breadth of discovery-based learning, even as these projects: (a) put to work a span of design heuristics, such as productive failure, surfacing implicit know-how, playing epistemic games, problem posing, or participatory simulation activities; (b) vary in their target content and skills, including building electric circuits, solving algebra problems, driving safely in traffic jams, and performing martial-arts maneuvers; and (c) employ different media, such as interactive computer-based modules for constructing models of scientific phenomena or mathematical problem situations, networked classroom collective “video games,” and intercorporeal master–student training practices. The authors of these papers consider the potential generativity of their design heuristics across domains and contexts

Probabilistic Bisimulation: Naturally on Distributions

In contrast to the usual understanding of probabilistic systems as stochastic processes, recently these systems have also been regarded as transformers of probabilities. In this paper, we give a natural definition of strong bisimulation for probabilistic systems corresponding to this view that treats probability distributions as first-class citizens. Our definition applies in the same way to discrete systems as well as to systems with uncountable state and action spaces. Several examples demonstrate that our definition refines the understanding of behavioural equivalences of probabilistic systems. In particular, it solves a long-standing open problem concerning the representation of memoryless continuous time by memory-full continuous time. Finally, we give algorithms for computing this bisimulation not only for finite but also for classes of uncountably infinite systems

Asynchronous Channel Training in Multi-Cell Massive MIMO

Pilot contamination has been regarded as the main bottleneck in time division duplexing (TDD) multi-cell massive multiple-input multiple-output (MIMO) systems. The pilot contamination problem cannot be addressed with large-scale antenna arrays. We provide a novel asynchronous channel training scheme to obtain precise channel matrices without the cooperation of base stations. The scheme takes advantage of sampling diversity by inducing intentional timing mismatch. Then, the linear minimum mean square error (LMMSE) estimator and the zero-forcing (ZF) estimator are designed. Moreover, we derive the minimum square error (MSE) upper bound of the ZF estimator. In addition, we propose the equally-divided delay scheme which under certain conditions is the optimal solution to minimize the MSE of the ZF estimator employing the identity matrix as pilot matrix. We calculate the uplink achievable rate using maximum ratio combining (MRC) to compare asynchronous and synchronous channel training schemes. Finally, simulation results demonstrate that the asynchronous channel estimation scheme can greatly reduce the harmful effect of pilot contamination

Invariant Generation for Multi-Path Loops with Polynomial Assignments

Program analysis requires the generation of program properties expressing conditions to hold at intermediate program locations. When it comes to programs with loops, these properties are typically expressed as loop invariants. In this paper we study a class of multi-path program loops with numeric variables, in particular nested loops with conditionals, where assignments to program variables are polynomial expressions over program variables. We call this class of loops extended P-solvable and introduce an algorithm for generating all polynomial invariants of such loops. By an iterative procedure employing Gr\"obner basis computation, our approach computes the polynomial ideal of the polynomial invariants of each program path and combines these ideals sequentially until a fixed point is reached. This fixed point represents the polynomial ideal of all polynomial invariants of the given extended P-solvable loop. We prove termination of our method and show that the maximal number of iterations for reaching the fixed point depends linearly on the number of program variables and the number of inner loops. In particular, for a loop with m program variables and r conditional branches we prove an upper bound of m*r iterations. We implemented our approach in the Aligator software package. Furthermore, we evaluated it on 18 programs with polynomial arithmetic and compared it to existing methods in invariant generation. The results show the efficiency of our approach