Fuzzy forecasting and decision making in short dynamic time series

This paper focuses on the usage of fuzzy set theory in forecasting and decision-making. The primary area of concern is on those decisions with dynamically short time series

Fourier transform over finite groups for error detection and error correction in computation channels

We consider the methods of error detection and correction in devices and programs calculating functions f: G → K where G is a finite group and K is a field. For error detection and correction we use linear checks generated by convolutions in the field K of the original function f and some checking idempotent function δ: G → , 1 For the construction of the optimal checking function δ we use methods of harmonic analysis over the group G in the field K. Since these methods will be the main tools for the construction of optimal checks, we consider the algorithms for the fast computation of Fourier Transforms over the group G in the field K. We solve the problem of error detecting and correcting capability for our methods for two important classes of decoding procedures (memoryless and memory-aided decoding) and consider the question of syndrome computation for these methods. We describe also properties of error correcting codes generated by convolution checks

On two variations of identifying codes

Identifying codes have been introduced in 1998 to model fault-detection in multiprocessor systems. In this paper, we introduce two variations of identifying codes: weak codes and light codes. They correspond to fault-detection by successive rounds. We give exact bounds for those two definitions for the family of cycles

Characterizing extremal digraphs for identifying codes and extremal cases of Bondy's theorem on induced subsets

An identifying code of a (di)graph $G$ is a dominating subset $C$ of the vertices of $G$ such that all distinct vertices of $G$ have distinct (in)neighbourhoods within $C$. In this paper, we classify all finite digraphs which only admit their whole vertex set in any identifying code. We also classify all such infinite oriented graphs. Furthermore, by relating this concept to a well known theorem of A. Bondy on set systems we classify the extremal cases for this theorem

Exhaustive testing of combinatorial circuits

We present a method for the construction of s-surjective arrays, which allows exhaustive testing of any set of s inputs in a combinatorial device . The method is based upon the use of linear codes, which implies simplicity of implementation. The size (number of tests) of the obtained arrays is close to the minimum f (n, s) for values of th e parameters n (total number of inputs) and s useful in practice .Nous présentons une méthode de construction de tableaux dits s-surjectifs qui permettent de tester exhaustivement tout ensemble de s entrées d'un circuit combinatoire . La méthode est basée sur l'emploi de codes linéaires, c e qui assure la simplicité de sa mise en œuvre. La taille (nombre de tests) des tableaux obtenus se rapproche d u minimum f(n, s) pour certaines valeurs des paramètres n (nombre total d'entrées du circuit) et s utiles en pratique

On the size of identifying codes in triangle-free graphs

In an undirected graph $G$, a subset $C\subseteq V(G)$ such that $C$ is a dominating set of $G$, and each vertex in $V(G)$ is dominated by a distinct subset of vertices from $C$, is called an identifying code of $G$. The concept of identifying codes was introduced by Karpovsky, Chakrabarty and Levitin in 1998. For a given identifiable graph $G$, let \M(G) be the minimum cardinality of an identifying code in $G$. In this paper, we show that for any connected identifiable triangle-free graph $G$ on $n$ vertices having maximum degree $\Delta\geq 3$, \M(G)\le n-\tfrac{n}{\Delta+o(\Delta)}. This bound is asymptotically tight up to constants due to various classes of graphs including $(\Delta-1)$-ary trees, which are known to have their minimum identifying code of size $n-\tfrac{n}{\Delta-1+o(1)}$. We also provide improved bounds for restricted subfamilies of triangle-free graphs, and conjecture that there exists some constant $c$ such that the bound \M(G)\le n-\tfrac{n}{\Delta}+c holds for any nontrivial connected identifiable graph $G$

An improved lower bound for (1,<=2)-identifying codes in the king grid

We call a subset $C$ of vertices of a graph $G$ a $(1,\leq \ell)$-identifying code if for all subsets $X$ of vertices with size at most $\ell$, the sets $\{c\in C |\exists u \in X, d(u,c)\leq 1\}$ are distinct. The concept of identifying codes was introduced in 1998 by Karpovsky, Chakrabarty and Levitin. Identifying codes have been studied in various grids. In particular, it has been shown that there exists a $(1,\leq 2)$-identifying code in the king grid with density 3/7 and that there are no such identifying codes with density smaller than 5/12. Using a suitable frame and a discharging procedure, we improve the lower bound by showing that any $(1,\leq 2)$-identifying code of the king grid has density at least 47/111

Роль основних характеристик коркових процесів у регуляції обміну Купруму

Cortical mechanisms of regulation of the content of Cuprum in the blood of cows are presented in the article. Experiments were carried out on cows of Ukrainian black-and-rumped breed of second-third lactation period of different types of higher nervous activity. The conducted researches have established that the content of Cuprum in blood of cows of strong types of higher nervous activity does not differ significantly. The content of this trace element in the blood of cows of a strong, balanced, mobile type of higher nervous activity is 12.81–13.35 μmol/dm3. In the blood of weak cows, Cuprum content is 12.22 ± 0.37 μmol/dm3, which is significantly lower by 8.0% (P &lt; 0.05) and 8.5% (P &lt; 0.05) than the indicators of strong animals balanced, mobile and strong balanced inert type of higher nervous activity. It is established that the strength and balance of cortical processes have the same significant effect on the content of Cuprum in the blood of cows – ղ²ᵪ = 0.21 (P &lt; 0.051). Then, as the effect of the motility of the cortical processes on the content of Cuprumum in the blood is unreliable – ղ²ᵪ = 0.06. The conducted regression analysis shows that the balance and mobility of cortical processes are not interrelated with the content of Cuprum in the blood of cows (b = 0.31–0.38). Then, as with the reduction of the strength of the cortical processes per unit, the content of Cuprum in the blood of cows significantly changes in the same direction by 0.53 μmol/dm3 (P &lt; 0.05). The determination coefficient of the strength of the cortical processes and the content of Cuprum in the blood of cows is – 0.258 (P &lt; 0.05), and, consequently, up to 26% of variations in the content of Cuprum in the blood of cows are due to the variability of the strength of the cortical processes. The correlation analysis of the connection of the content of Cuprum in the blood of cows with the main indicators of cortical processes has shown that there is no correlation between the equilibrium and the mobility of the cortical processes with the metal content. Only the tendency for direct correlation connections of the characteristics of cortical processes with the content of Cuprum in blood of cows is established – r = 0.31–0.39. Then, as the strength of cortical processes is significantly correlated with the content of Cuprum in the blood of cows (r = 0.51; P&nbsp;&lt; 0.05). Consequently, the content of Cuprum in the blood of cows of high types of higher nervous activity depends on the main characteristics of cortical processes.У статті наведено кортикальні механізми регуляції вмісту Купруму в крові корів. Досліди проводили на коровах української чорно-рябої породи другої–третьої лактації різних типів вищої нервової діяльності. Проведеними дослідженнями встановлено, що вміст Купруму в крові корів сильних типів вищої нервової діяльності достовірно не відрізняється. Вміст даного мікроелементу в крові корів сильного врівноваженого рухливого типу вищої нервової діяльності становить 12,81–13,35 мкмоль/дм3. У крові корів слабкого типу вміст Купруму становить 12,22 ± 0,37 мкмоль/дм3, що достовірно нижче на 8,0% (Р &lt; 0,05) та 8,5% (Р &lt; 0,05) від показників тварин сильного врівноваженого рухливого та сильного врівноваженого інертного типу вищої нервової діяльності. Встановлено, що сила і врівноваженість коркових процесів чинять однаково достовірний вплив на вміст Купруму в крові корів – ղ²ᵪ = 0,21 (Р &lt; 0,051), Тимчасом як вплив рухливості коркових процесів на вміст Купруму в крові недостовірний – ղ²ᵪ = 0,06. Проведений регресійний аналіз свідчить, що врівноваженість та рухливість коркових процесів не взаємопов’язана із вмістом Купруму в крові корів (b = 0,31–0,38), тимчасом як при зменшенні сили коркових процесів на одну одиницю вміст Купруму в крові корів достовірно змінюється у тому ж напрямку на 0,53 мкмоль/дм3 (Р &lt; 0,05). Коефіцієнт детермінації сили коркових процесів та вмісту Купруму в крові корів становить – 0,258 (Р &lt; 0,05), отже, до 26% варіацій вмісту Купруму в крові корів зумовлені варіабельністю сили коркових процесів. Проведений кореляційний аналіз зв’язку вмісту Купруму в крові корів з основними показниками коркових процесів свідчать про відсутність взаємозалежності врівноваженості та рухливості коркових процесів з умістом металу. Встановлено лише тенденцію щодо прямих кореляційних зв’язків даних характеристик коркових процесів зі вмістом Купруму в крові корів – r = 0,31–0,39, тимчасом як сила коркових процесів достовірно прямо корелює з вмістом Купруму в крові корів (r = 0,51; Р &lt; 0,05). Отже, вміст Купруму в крові корів сильних типів вищої нервової діяльності залежить від основних характеристик коркових процесів

Generalized iterated wreath products of symmetric groups and generalized rooted trees correspondence

Consider the generalized iterated wreath product $S_{r_1}\wr \ldots \wr S_{r_k}$ of symmetric groups. We give a complete description of the traversal for the generalized iterated wreath product. We also prove an existence of a bijection between the equivalence classes of ordinary irreducible representations of the generalized iterated wreath product and orbits of labels on certain rooted trees. We find a recursion for the number of these labels and the degrees of irreducible representations of the generalized iterated wreath product. Finally, we give rough upper bound estimates for fast Fourier transforms.Comment: 18 pages, to appear in Advances in the Mathematical Sciences. arXiv admin note: text overlap with arXiv:1409.060