Making Change in 2048

The 2048 game involves tiles labeled with powers of two that can be merged to form bigger powers of two; variants of the same puzzle involve similar merges of other tile values. We analyze the maximum score achievable in these games by proving a min-max theorem equating this maximum score (in an abstract generalized variation of 2048 that allows all the moves of the original game) with the minimum value that causes a greedy change-making algorithm to use a given number of coins. A widely-followed strategy in 2048 maintains tiles that represent the move number in binary notation, and a similar strategy in the Fibonacci number variant of the game (987) maintains the Zeckendorf representation of the move number as a sum of the fewest possible Fibonacci numbers; our analysis shows that the ability to follow these strategies is intimately connected with the fact that greedy change-making is optimal for binary and Fibonacci coinage. For variants of 2048 using tile values for which greedy change-making is suboptimal, it is the greedy strategy, not the optimal representation as sums of tile values, that controls the length of the game. In particular, the game will always terminate whenever the sequence of allowable tile values has arbitrarily large gaps between consecutive values

Computer Aided Verification

This open access two-volume set LNCS 13371 and 13372 constitutes the refereed proceedings of the 34rd International Conference on Computer Aided Verification, CAV 2022, which was held in Haifa, Israel, in August 2022. The 40 full papers presented together with 9 tool papers and 2 case studies were carefully reviewed and selected from 209 submissions. The papers were organized in the following topical sections: Part I: Invited papers; formal methods for probabilistic programs; formal methods for neural networks; software Verification and model checking; hyperproperties and security; formal methods for hardware, cyber-physical, and hybrid systems. Part II: Probabilistic techniques; automata and logic; deductive verification and decision procedures; machine learning; synthesis and concurrency. This is an open access book

Video Abstracting at a Semantical Level

One the most common form of a video abstract is the movie trailer. Contemporary movie trailers share a common structure across genres which allows for an automatic generation and also reflects the corresponding moviea s composition. In this thesis a system for the automatic generation of trailers is presented. In addition to action trailers, the system is able to deal with further genres such as Horror and comedy trailers, which were first manually analyzed in order to identify their basic structures. To simplify the modeling of trailers and the abstract generation itself a new video abstracting application was developed. This application is capable of performing all steps of the abstract generation automatically and allows for previews and manual optimizations. Based on this system, new abstracting models for horror and comedy trailers were created and the corresponding trailers have been automatically generated using the new abstracting models. In an evaluation the automatic trailers were compared to the original Trailers and showed a similar structure. However, the automatically generated trailers still do not exhibit the full perfection of the Hollywood originals as they lack intentional storylines across shots

Using MapReduce Streaming for Distributed Life Simulation on the Cloud

Distributed software simulations are indispensable in the study of large-scale life models but often require the use of technically complex lower-level distributed computing frameworks, such as MPI. We propose to overcome the complexity challenge by applying the emerging MapReduce (MR) model to distributed life simulations and by running such simulations on the cloud. Technically, we design optimized MR streaming algorithms for discrete and continuous versions of Conway’s life according to a general MR streaming pattern. We chose life because it is simple enough as a testbed for MR’s applicability to a-life simulations and general enough to make our results applicable to various lattice-based a-life models. We implement and empirically evaluate our algorithms’ performance on Amazon’s Elastic MR cloud. Our experiments demonstrate that a single MR optimization technique called strip partitioning can reduce the execution time of continuous life simulations by 64%. To the best of our knowledge, we are the first to propose and evaluate MR streaming algorithms for lattice-based simulations. Our algorithms can serve as prototypes in the development of novel MR simulation algorithms for large-scale lattice-based a-life models.https://digitalcommons.chapman.edu/scs_books/1014/thumbnail.jp

Automated retinal layer segmentation and pre-apoptotic monitoring for three-dimensional optical coherence tomography

The aim of this PhD thesis was to develop segmentation algorithm adapted and optimized to retinal OCT data that will provide objective 3D layer thickness which might be used to improve diagnosis and monitoring of retinal pathologies. Additionally, a 3D stack registration method was produced by modifying an existing algorithm. A related project was to develop a pre-apoptotic retinal monitoring based on the changes in texture parameters of the OCT scans in order to enable treatment before the changes become irreversible; apoptosis refers to the programmed cell death that can occur in retinal tissue and lead to blindness. These issues can be critical for the examination of tissues within the central nervous system. A novel statistical model for segmentation has been created and successfully applied to a large data set. A broad range of future research possibilities into advanced pathologies has been created by the results obtained. A separate model has been created for choroid segmentation located deep in retina, as the appearance of choroid is very different from the top retinal layers. Choroid thickness and structure is an important index of various pathologies (diabetes etc.). As part of the pre-apoptotic monitoring project it was shown that an increase in proportion of apoptotic cells in vitro can be accurately quantified. Moreover, the data obtained indicates a similar increase in neuronal scatter in retinal explants following axotomy (removal of retinas from the eye), suggesting that UHR-OCT can be a novel non-invasive technique for the in vivo assessment of neuronal health. Additionally, an independent project within the computer science department in collaboration with the school of psychology has been successfully carried out, improving analysis of facial dynamics and behaviour transfer between individuals. Also, important improvements to a general signal processing algorithm, dynamic time warping (DTW), have been made, allowing potential application in a broad signal processing field.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Software for Exascale Computing - SPPEXA 2016-2019

This open access book summarizes the research done and results obtained in the second funding phase of the Priority Program 1648 "Software for Exascale Computing" (SPPEXA) of the German Research Foundation (DFG) presented at the SPPEXA Symposium in Dresden during October 21-23, 2019. In that respect, it both represents a continuation of Vol. 113 in Springer’s series Lecture Notes in Computational Science and Engineering, the corresponding report of SPPEXA’s first funding phase, and provides an overview of SPPEXA’s contributions towards exascale computing in today's sumpercomputer technology. The individual chapters address one or more of the research directions (1) computational algorithms, (2) system software, (3) application software, (4) data management and exploration, (5) programming, and (6) software tools. The book has an interdisciplinary appeal: scholars from computational sub-fields in computer science, mathematics, physics, or engineering will find it of particular interest