Fuzzy relation equations and reduction of fuzzy automata

We show that the state reduction problem for fuzzy automata is related to the problem of finding a solution to a particular system of fuzzy relation equations in the set of all fuzzy equivalences on its set of states. This system may consist of infinitely many equations, and finding its non-trivial solutions may be a very difficult task. For that reason we aim our attention to some instances of this system which consist of finitely many equations and are easier to solve. First, we study right invariant fuzzy equivalences, and their duals, the left invariant ones. We prove that each fuzzy automaton possesses the greatest right (resp. left) invariant fuzzy equivalence, which provides the best reduction by means of fuzzy equivalences of this type, and we give an effective procedure for computing this fuzzy equivalence, which works if the underlying structure of truth values is a locally finite residuated lattice. Moreover, we show that even better reductions can be achieved alternating reductions by means of right and left invariant fuzzy equivalences. We also study strongly right and left invariant fuzzy equivalences, which give worse reductions than right and left invariant ones, but whose computing is much easier. We give an effective procedure for computing the greatest strongly right (resp. left) invariant fuzzy equivalence, which is applicable to fuzzy automata over an arbitrary complete residuated lattice.     

Trees with minimal Laplacian coefficients

Let $G$ be a simple undirected graph with the characteristic polynomial of its Laplacian matrix $L\left(G\right)$, $P(G,\mu )={\sum }_{k=0}^n{(?1)}^k{c}_k{\mu }^{n?k}$. It is well known that for trees the Laplacian coefficient $c_{n?2}$ is equal to the Wiener index of $G$, while $c_{n?3}$ is equal to the modified hyper-Wiener index of the graph. In this paper, we characterize $n$-vertex trees with given matching number $m$ which simultaneously minimize all Laplacian coefficients. The extremal tree $A(n,m)$ is a spur, obtained from the star graph $S_{n?m+1}$ with $n?m+1$ vertices by attaching a pendant edge to each of certain $m?1$ non-central vertices of $S_{n?m+1}$. In particular, $A(n,m)$ minimizes the Wiener index, the modified hyper-Wiener index and the recently introduced Incidence energy of trees, defined as $IE\left(G\right)={\sum }_{k=0}^n\sqrt{{\mu }_k}$, where ${\mu }_k$ are the eigenvalues of signless Laplacian matrix $Q\left(G\right)=D\left(G\right)+A\left(G\right)$. We introduced a general $\rho$ transformation which decreases all Laplacian coefficients simultaneously. In conclusion, we illustrate on examples of Wiener index and Incidence energy that the opposite problem of simultaneously maximizing all Laplacian coefficients has no solution.     

Why deep neural nets cannot ever match biological intelligence and what to do about it?

The recently introduced theory of practopoiesis offers an account on how adaptive intelligent systems are organized. According to that theory, biological agents adapt at three levels of organization and this structure applies also to our brains. This is referred to as tri-traversal theory of the organization of mind or for short, a T3-structure. To implement a similar T3-organization in an artificially intelligent agent, it is necessary to have multiple policies, as usually used as a concept in the theory of reinforcement learning. These policies have to form a hierarchy. We define adaptive practopoietic systems in terms of hierarchy of policies and calculate whether the total variety of behavior required by real-life conditions of an adult human can be satisfactorily accounted for by a traditional approach to artificial intelligence based on T2-agents, or whether a T3-agent is needed instead. We conclude that the complexity of real life can be dealt with appropriately only by a T3-agent. This means that the current approaches to artificial intelligence, such as deep architectures of neural networks, will not suffice with fixed network architectures. Rather, they will need to be equipped with intelligent mechanisms that rapidly alter the architectures of those networks.     

A continuation‐based task programming model for C++: design of the Causeway library

There is a big class of problems that requires writing programs in an asynchronous manner. Cloud computing, service‐oriented architectures, multi‐core and heterogeneous systems all require programs to be written with asynchronous components. The necessity of concurrency and asynchronous execution brings in the added complexity of the inversion of control into the system, either through message passing or through event processing. In this paper, we introduce explicit programming language support for asynchronous programming that completely hides inversion of control. The presented programming model defines a common abstraction of the different types of tasks, both synchronous and asynchronous. It defines common imperative control constructs equivalent to those of the host programming language, along with a few more advanced ones for transactional and parallel execution that can universally work for any task type. It allows the programmer to implement the logic of an asynchronous system in a natural way by writing simple, seemingly, synchronous imperative code. We will show that the programs written using this approach are easier to understand by programmers. They are also easier to design automated tests for, and for performing computer‐based static analysis of the program logic. The principles behind this approach were tested in a couple of real‐world systems with worldwide user base. Our experience shows that it makes the complex code with a lot of interdependencies between asynchronously executed tasks easy to write and reason about. Copyright © 2016 John Wiley & Sons, Ltd.     

Hubness-aware shared neighbor distances for high-dimensional k-nearest neighbor classification

Learning from high-dimensional data is usually quite challenging, as captured by the well-known phrase curse of dimensionality. Data analysis often involves measuring the similarity between different examples. This sometimes becomes a problem, as many widely used metrics tend to concentrate in high-dimensional feature spaces. The reduced contrast makes it more difficult to distinguish between close and distant points, which renders many traditional distance-based learning methods ineffective. Secondary distances based on shared neighbor similarities have recently been proposed as one possible solution to this problem. However, these initial metrics failed to take hubness into account. Hubness is a recently described aspect of the dimensionality curse, and it affects all sorts of $k$ -nearest neighbor learning methods in severely negative ways. This paper is the first to discuss the impact of hubs on forming the shared neighbor similarity scores. We propose a novel, hubness-aware secondary similarity measure $simhub_s$ and an extensive experimental evaluation shows it to be much more appropriate for high-dimensional data classification than the standard $simcos_s$ measure. The proposed similarity changes the underlying $k$ NN graph in such a way that it reduces the overall frequency of label mismatches in $k$ -neighbor sets and increases the purity of occurrence profiles, which improves classifier performance. It is a hybrid measure, which takes into account both the supervised and the unsupervised hubness information. The analysis shows that both components are useful in their own ways and that the measure is therefore properly defined. This new similarity does not increase the overall computational cost, and the improvement is essentially ‘free’.     

RMS Detector of Multiharmonic Signals

This paper presents a new realization of the implicit root‐mean‐square (RMS) detector, employing three second‐generation current conveyors and MOS transistors. The proposed circuit can be applied in measuring the RMS value of complex, periodic signals, represented in the form of the Fourier series. To verify the theoretical analysis, circuit Simulation Program with Integrated Circuit Emphasis simulations and experiment results are included, showing agreement with the theory.     

Croatia

Abstract

When we speak about early photography in Yugoslavia, we must bear in mind the geographical and political situation of the country at the time when photography appeared. In the 19th century, Croatia, today one of the six Yugoslav federal republics, was a part of the Austro-Hungarian monarchy. So was Slovenia and, in the latter part of the century, Bosnia and Hercegovina, while Serbia and Montenegro had emerged from the disintegration of the Ottoman empire as small independent states. In this survey we shall consider the beginnings of photography in Croatia, not just because that aspect has been studied the most, but because Croatia's special position within the boundaries of Austria-Hungary led to a correspondingly rapid development of photography in this area, as compared with other Slav lands in the south.