Cumulative Subtraction Research Articles

Discrete Richman-bidding scoring games

We study zero-sum combinatorial games within the framework of so-called Richman auctions (Lazarus et al., in Games No Chance 29:439–449, 1996). We modify the alternating play scoring ruleset Cumulative Subtraction (Cohensius et al., in Electron J Combin 26(P4):52, 2019), to a discrete bidding scheme, similar to Develin and Payne (Electron J Combin 17(1):85, 2010). Players bid to move, and the player with the highest bid wins the move and hands over the winning bid amount to the other player. The new game is dubbed Bidding Cumulative Subtraction. In so-called unitary games, players remove exactly one item out of a single heap of identical items, until the heap is empty, and their actions contribute to a common score, which increases or decreases by one unit depending on whether the maximizing player wins the turn or not. We show that there is a unique bidding equilibrium for a much larger class of games that generalize standard scoring play. We prove that for all sufficiently large heap sizes, the equilibrium outcomes of unitary games are eventually periodic, with period 2. We show that the periodicity appears at the latest for heaps of sizes quadratic in the total budget.

Cumulative Subtraction Games

We study a variation of Nim-type subtraction games, called Cumulative Subtraction (CS). Two players alternate in removing pebbles out of a joint pile, and their actions add or remove points to a common score. We prove that the zero-sum outcome in optimal play of a CS with a finite number of possible actions is eventually periodic, with period $2s$, where $s$ is the size of the largest available action. This settles a conjecture by Stewart in his Ph.D. thesis (2011). Specifically, we find a quadratic bound, in the size of $s$, on when the outcome function must have become periodic. In case of exactly two possible actions, we give an explicit description of optimal play.

Dry Electrode-Based Fully Isolated EEG/fNIRS Hybrid Brain-Monitoring System.

A portable hybrid brain monitoring system is proposed to perform simultaneous 16-channel electroencephalogram (EEG) and 8-channel functional near-infrared spectroscopy (fNIRS) measurements. Architecture-optimized analog frontend integrated circuits (Texas Instruments ADS1299 and ADS8688A) were used to simultaneously achieve 24-bit EEG resolution and reliable latency-less (<0.85 μs) bio-optical measurements. Suppression of the noise and crosstalk generated by the digital circuit components and flashing NIR light sources was maximized through linear regulator-based fully isolated circuit design. Gel-less EEG measurements were enabled by using spring-loaded dry electrodes. Several evaluations were carried out by conducting an EEG phantom test and an arterial occlusion experiment. An alpha rhythm detection test (eye-closing task) and a mental arithmetic experiment (cumulative subtraction task) were conducted to determine whether the system is applicable to human subject studies. The evaluation results show that the proposed system is sufficiently capable of detecting microvoltage EEG signals and hemodynamic responses. The results of the studies on human subjects enabled us to verify that the proposed system is able to detect task-related EEG spectral features such as eye-closed event-related synchronization and mental-arithmetic event-related desynchronization in the alpha and beta rhythm ranges. An analysis of the fNIRS measurements with an arithmetic operation task also revealed a decreasing trend in oxyhemoglobin concentration.

HPV guided object tracking: Theoretical advances on fast pattern matching technique

Summary Pattern matching is a fundamental machine vision problem that deals with searching an object in a comparatively large scene. It can use to solve many vision problems ranging from typical human detection to searching defective parts in industrial automation. This paper reports a fast pattern matching technique which makes use of cumulative subtraction and cumulative division operations based on Image Integral model. The idea is to use both the cumulative subtraction and division operations to evaluate the image values on a very small rectangular region of the image scene as well as on the input pattern to be searched for. Image values are transformed to Haar Projection Values (HPVs) using Haar transform in order to achieve pattern matching on sliding window of the image scene. Computation of HPV needs seven arithmetic operations, including two addition and five subtraction operations, which are found to be same as that of Image Integral technique. Besides, the proposed pattern matching technique is identified as computationally effective in terms of both time and memory.

Real‐time functional MRI using pseudo‐continuous arterial spin labeling

The first implementation of real-time acquisition and analysis of arterial spin labeling-based functional magnetic resonance imaging time series is presented in this article. The implementation uses a pseudo-continuous labeling scheme followed by a spiral k-space acquisition trajectory. Real-time reconstruction of the images, preprocessing, and regression analysis of the functional magnetic resonance imaging data were implemented on a laptop computer interfaced with the MRI scanner. The method allows the user to track the current raw data, subtraction images, and the cumulative t-statistic map overlaid on a cumulative subtraction image. The user is also able to track the time course of individual time courses and interactively selects a region of interest as a nuisance covariate. The pulse sequence allows the user to adjust acquisition and labeling parameters while observing their effect on the image within two successive pulse repetition times. This method is demonstrated by two functional imaging experiments: a simultaneous finger-tapping and visual stimulation paradigm, and a bimanual finger-tapping task.

VLAD. Un sistema gráfico de expresión continua de efectividad asistencial aplicado en medicina intensiva

Introduction Different methods for estimating and expressing effectiveness of the care of critically ill patients are described. Among them, especial interest is placed on VLAD methodology, which allows continuous and sequential expression of the variable under study through a graphic display that is easy to use and understand. The aim of this article was not to describe a new methodology, but rather to present a little-known method not previously used in critically-ill patients in Spain. Material and method We describe the procedure for calculating VLAD as the result of the cumulative subtraction of real mortality from predicted mortality, irrespective of the methodology used for prediction. In the present article, SAPS 2 was used. Results The method was applied in 7,448 patients consecutively admitted to a medical–surgical ICU from 1999 to 2004 (inclusive). Graphs depicting the use of VLAD in the whole sample and in homogeneous subgroups (type of admission or certain admission diagnoses) were obtained. Discussion We provide a critical view of techniques for expressing effectiveness, from the perspective of clinical management, as well as of the possible uses of these techniques in healthcare management, quality evaluation, teaching, and research.