Exercising Control When Confronted by a (Brownian) Spider

We consider the Brownian "spider," a construct introduced in \cite{Dubins} and in \cite{Pitman}. In this note, the author proves the "spider" bounds by using the dynamic programming strategy of guessing the optimal reward function and subsequently establishing its optimality by proving its excessiveness.Comment: Final version. Operations Research Letters (2016); 8 pages, 1 figur

Monte Carlo Bounding Techniques for Determining Solution Quality in Stochastic Programs

Operations Research Letters, 24, pp. 47-56

Algebraic properties of structured context-free languages: old approaches and novel developments

The historical research line on the algebraic properties of structured CF languages initiated by McNaughton's Parenthesis Languages has recently attracted much renewed interest with the Balanced Languages, the Visibly Pushdown Automata languages (VPDA), the Synchronized Languages, and the Height-deterministic ones. Such families preserve to a varying degree the basic algebraic properties of Regular languages: boolean closure, closure under reversal, under concatenation, and Kleene star. We prove that the VPDA family is strictly contained within the Floyd Grammars (FG) family historically known as operator precedence. Languages over the same precedence matrix are known to be closed under boolean operations, and are recognized by a machine whose pop or push operations on the stack are purely determined by terminal letters. We characterize VPDA's as the subclass of FG having a peculiarly structured set of precedence relations, and balanced grammars as a further restricted case. The non-counting invariance property of FG has a direct implication for VPDA too.Comment: Extended version of paper presented at WORDS2009, Salerno,Italy, September 200

Improved Approximation Algorithms for the Min-Max Selecting Items Problem

We give a simple deterministic $O(\log K / \log\log K)$ approximation algorithm for the Min-Max Selecting Items problem, where $K$ is the number of scenarios. While our main goal is simplicity, this result also improves over the previous best approximation ratio of $O(\log K)$ due to Kasperski, Kurpisz, and Zieli\'nski (Information Processing Letters (2013)). Despite using the method of pessimistic estimators, the algorithm has a polynomial runtime also in the RAM model of computation. We also show that the LP formulation for this problem by Kasperski and Zieli\'nski (Annals of Operations Research (2009)), which is the basis for the previous work and ours, has an integrality gap of at least $\Omega(\log K / \log\log K)$

THINNING STENTIFORD ALGORITHM FOR KINTAMANI INSCRIPTION IMAGE SEGMENTATION

In the copper, inscription contained writing strokes that have high historical value. Age and environmental factors cause damage to the inscription surface and also reduce the appearance of images and letters. One way to preserve it is to carry out the process of converting it into digital format. The use of the morphological operation method is very suitable to be used to improve the shape of the letters in the copper inscription. The morphological operations performed in this study were the Thinning Stentiford algorithm. Based on research that has been done, it was concluded that the Thinning Stentiford algorithm has succeeded in segmenting the letters that exist in the Kintamani copper inscription. However, there are some letters are not well segmented. This is due to the inscription background color and carved letter colors that don't have significant differences. Testing the time it was concluded that the greater the size of the image and the more letters will be segmented, the longer the processing computing

On graphs with representation number 3

A graph $G=(V,E)$ is word-representable if there exists a word $w$ over the alphabet $V$ such that letters $x$ and $y$ alternate in $w$ if and only if $(x,y)$ is an edge in $E$. A graph is word-representable if and only if it is $k$-word-representable for some $k$, that is, if there exists a word containing $k$ copies of each letter that represents the graph. Also, being $k$-word-representable implies being $(k+1)$-word-representable. The minimum $k$ such that a word-representable graph is $k$-word-representable, is called graph's representation number. Graphs with representation number 1 are complete graphs, while graphs with representation number 2 are circle graphs. The only fact known before this paper on the class of graphs with representation number 3, denoted by $\mathcal{R}_3$, is that the Petersen graph and triangular prism belong to this class. In this paper, we show that any prism belongs to $\mathcal{R}_3$, and that two particular operations of extending graphs preserve the property of being in $\mathcal{R}_3$. Further, we show that $\mathcal{R}_3$ is not included in a class of $c$-colorable graphs for a constant $c$. To this end, we extend three known results related to operations on graphs. We also show that ladder graphs used in the study of prisms are $2$-word-representable, and thus each ladder graph is a circle graph. Finally, we discuss $k$-word-representing comparability graphs via consideration of crown graphs, where we state some problems for further research

EFFICIENCY COMPARISON OF NETWORKS IN HANDWRITTEN LATIN CHARACTERS RECOGNITION WITH DIACRITICS

The aim of the article is to analyze and compare the performance and accuracy of architectures with a different number of parameters on the example of a set of handwritten Latin characters from the Polish Handwritten Characters Database (PHCD). It is a database of handwriting scans containing letters of the Latin alphabet as well as diacritics characteristic of the Polish language. Each class in the PHCD dataset contains 6,000 scans for each character. The research was carried out on six proposed architectures and compared with the architecture from the literature. Each of the models was trained for 50 epochs, and then the accuracy of prediction was measured on a separate test set. The experiment thus constructed was repeated 20 times for each model. Accuracy, number of parameters and number of floating-point operations performed by the network were compared. The research was conducted on subsets such as uppercase letters, lowercase letters, lowercase letters with diacritics, and a subset of all available characters. The relationship between the number of parameters and the accuracy of the model was indicated. Among the examined architectures, those that significantly improved the prediction accuracy at the expense of a larger network size were selected, and a network with a similar prediction accuracy as the base one, but with twice as many model parameters was selected