The Exact Query Complexity of Yes-No Permutation Mastermind

Mastermind is famous two-player game. The first player (codemaker) chooses a secret code which the second player (codebreaker) is supposed to crack within a minimum number of code guesses (queries). Therefore, the codemaker’s duty is to help the codebreaker by providing a well-defined error measure between the secret code and the guessed code after each query. We consider a variant, called Yes-No AB-Mastermind, where both secret code and queries must be repetition-free and the provided information by the codemaker only indicates if a query contains any correct position at all. For this Mastermind version with n positions and k ≥ n colors and ` := k + 1 − n, we prove a lower bound of ∑ k j=` log 2 j and an upper bound of n log 2 n + k on the number of queries necessary to break the secret code. For the important case k = n, where both secret code and queries represent permutations, our results imply an exact asymptotic complexity of Θ (n log n) queries

Solving Static Permutation Mastermind using O(nlog⁡n)O(n \log n) Queries

Permutation Mastermind is a version of the classical mastermind game in which the number of positions $n$ is equal to the number of colors $k$, and repetition of colors is not allowed, neither in the codeword nor in the queries. In this paper we solve the main open question from Glazik, J\"ager, Schiemann and Srivastav (2021), who asked whether their bound of $O(n^{1.525})$ for the static version can be improved to $O(n \log n)$, which would be best possible. By using a simple probabilistic argument we show that this is indeed the case.Comment: 6 page

Optimal Strategies for Static Black-Peg AB Game With Two and Three Pegs

The AB~Game is a game similar to the popular game Mastermind. We study a version of this game called Static Black-Peg AB~Game. It is played by two players, the codemaker and the codebreaker. The codemaker creates a so-called secret by placing a color from a set of $c$ colors on each of $p \le c$ pegs, subject to the condition that every color is used at most once. The codebreaker tries to determine the secret by asking questions, where all questions are given at once and each question is a possible secret. As an answer the codemaker reveals the number of correctly placed colors for each of the questions. After that, the codebreaker only has one more try to determine the secret and thus to win the game. For given $p$ and $c$, our goal is to find the smallest number $k$ of questions the codebreaker needs to win, regardless of the secret, and the corresponding list of questions, called a $(k+1)$-strategy. We present a $\lceil 4c/3 \rceil-1)$-strategy for $p=2$ for all $c \ge 2$, and a $\lfloor (3c-1)/2 \rfloor$-strategy for $p=3$ for all $c \ge 4$ and show the optimality of both strategies, i.e., we prove that no $(k+1)$-strategy for a smaller $k$ exists

Positions- und Detektionsspiele

When it comes to the interaction of two ore more parties with individual aims, it’s all about finding an appropriate strategy. In most cases, the individual aim boils down to detection of information about the general situation or about your opponents and improvement of your own position. This goal becomes most clear and specific in the field of recreational games. In games like chess or tic-tac-toe, every player has complete information and the player’s position decides over win and loss. On the contrary, in games like poker every player tries to find out the value of the other players’ hands to play accordingly. This uncertainty of the opponent’s hand is the factor that makes the game interesting. Since all results of this thesis are connected to the field of game theory, it seems important to mention that this research field is not about having fun with different kinds of games, but, in the contrary, it’s about analysis of these games. The crucial difference between casual games and formal combinatorial games is that a combinatorial game is always assumed to be played by two players of infinite computational power. If the considered game is of complete information, the outcome of the game is already determined before it even started. The variety of games that are analyzed in this work ranges from popular recreational games as Mastermind over network-formation games to purely abstract games on graphs or hypergraph

AN UPDATED REVIEW ON THE APPLICATION OF DENDRIMERS AS SUCCESSFUL NANOCARRIERS FOR BRAIN DELIVERY OF THERAPEUTIC MOIETIES

It’s been nearly 100 y of effort to study the organization and role of the blood brain-barrier and still, we strive to find better techniques to overcome this barrier to deliver the drugs to the brain effectively with reduced systemic side effects. The advances in nanotechnology have given newer horizons in achieving this goal since the nano-scaled systems can modify an existing drug to have a high degree of sensitivity to the physiological conditions and specificity to reach the target organ. Among the various nanocarriers, dendrimers owing to their unique physical and chemical characteristics, represent a potential therapeutic tool in biomedical and pharmaceutical science. Dendrimers, an established polymeric nanocarrier system of the time, can deliver both drugs and genetic material and are being extensively studied to target the brain. The surface modification of dendrimers can reduce their innate toxicity problems and increase the therapeutic efficacy of brain disorders. This review article is an attempt to update on the potential of dendrimers explored in the past five years as a drug delivery avenue that can be considered as a promising solution in the management of a wide range of disorders affecting the central nervous system, including neoplastic, degenerative, and ischemic conditions. The following search criteria were used to expand the review article with the keywords dendrimers, novel drug delivery, nanoparticles, site-specific drug delivery etc

The Chronicle [March 20, 1981]

The Chronicle, March 20, 1981https://repository.stcloudstate.edu/chron/3233/thumbnail.jp

Detection and Evaluation of Clusters within Sequential Data

Motivated by theoretical advancements in dimensionality reduction techniques we use a recent model, called Block Markov Chains, to conduct a practical study of clustering in real-world sequential data. Clustering algorithms for Block Markov Chains possess theoretical optimality guarantees and can be deployed in sparse data regimes. Despite these favorable theoretical properties, a thorough evaluation of these algorithms in realistic settings has been lacking. We address this issue and investigate the suitability of these clustering algorithms in exploratory data analysis of real-world sequential data. In particular, our sequential data is derived from human DNA, written text, animal movement data and financial markets. In order to evaluate the determined clusters, and the associated Block Markov Chain model, we further develop a set of evaluation tools. These tools include benchmarking, spectral noise analysis and statistical model selection tools. An efficient implementation of the clustering algorithm and the new evaluation tools is made available together with this paper. Practical challenges associated to real-world data are encountered and discussed. It is ultimately found that the Block Markov Chain model assumption, together with the tools developed here, can indeed produce meaningful insights in exploratory data analyses despite the complexity and sparsity of real-world data.Comment: 37 pages, 12 figure