Machine Learning is the study of methods for programming computers to learn. Computers are applied to a wide range of tasks, and for most of these it is relatively easy for programmers to design and implement the necessary software. However, there are many tasks for which this is difficult or impossible. These can be divided into four general categories. First, there are problems for which there exist no human experts. For example, in modern automated manufacturing facilities, there is a need to predict machine failures before they occur by analyzing sensor readings. Because the machines are new, there are no human experts who can be interviewed by a programmer to provide the knowledge necessary to build a computer system. A machine learning system can study recorded data and subsequent machine failures and learn prediction rules. Second, there are problems where human experts exist, but where they are unable to explain their expertise. This is the case in many perceptual tasks, such as speech recognition, hand-writing recognition, and natural language understanding. Virtually all humans exhibit expert-level abilities on these tasks, but none of them can describe the detailed steps that they follow as they perform them. Fortunately, humans can provide machines with examples of the inputs and correct outputs for these tasks, so machine learning algorithms can learn to map the inputs to the outputs. Third, there are problems where phenomena are changing rapidly. In finance, for example, people would like to predict the future behavior of the stock market, of consumer purchases, or of exchange rates. These behaviors change frequently, so that even if a programmer could construct a good predictive computer program, it would need to be rewritten frequently. A learning program can relieve the programmer of this burden by constantly modifying and tuning a set of learned prediction rules. Fourth, there are applications that need to be customized for each computer user separately. Consider, for example, a program to filter unwanted electronic mail messages. Different users will need different filters. It is unreasonable to expect each user to program his or her own rules, and it is infeasible to provide every user with a software engineer to keep the rules up-to-date. A machine learning system can learn which mail messages the user rejects and maintain the filtering rules automatically. Machine learning addresses many of the same research questions as the fields of statistics, data mining, and psychology, but with differences of emphasis. Statistics focuses on understanding the phenomena that have generated the data, often with the goal of testing different hypotheses about those phenomena. Data mining seeks to find patterns in the data that are understandable by people. Psychological studies of human learning aspire to understand the mechanisms underlying the various learning behaviors exhibited by people (concept learning, skill acquisition, strategy change, etc.).

Machine learning

I. Introduction: Transcending Nationalism: The European Community 1958-2000

A signed graph is a graph whose edges are labeled by signs. This is a bibliography of signed graphs and related mathematics. Several kinds of labelled graph have been called "signed" yet are mathematically very different. I distinguish four types: Group-signed graphs: the edge labels are elements of a 2-element group and are multiplied around a polygon (or along any walk). Among the natural generalizations are larger groups and vertex signs. Sign-colored graphs, in which the edges are labelled from a two-element set that is acted upon by the sign group: - interchanges labels, + leaves them unchanged. This is the kind of "signed graph" found in knot theory. The natural generalization is to more colors and more general groups —  or no group. Weighted graphs, in which the edge labels are the elements +1 and -1 of the integers or another additive domain. Weights behave like numbers, not signs; thus I regard work on weighted graphs as outside the scope of the bibliography — ex cept (to some extent) when the author calls the weights "signs". Labelled graphs where the labels have no structure or properties but are called "signs" for any or no reason.

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A Mathematical Bibliography of Signed and Gain Graphs and Allied Areas

On computable numbers

We brie y present (basic ideas, some examples, classes of spiking neural P systems, some results concerning their power, research topics) a recently initiated branch of membrane computing with motivation from neural computing. Further details can be found at the web page of membrane computing, from http://psystems.disco.unimib.it. 1 The General Framework The most intuitive way to introduce spiking neural P systems (in short, SN P systems) is by watching the movie available at http://www.igi.tugraz. at/tnatschl/spike_trains_eng.html, in the web page of Wofgang Maass, Graz, Austria: neurons are sending to each others spikes, electrical impulses of identical shape (duration, voltage, etc.), with the information encoded in the frequency of these impulses, hence in the time passes between consecutive spikes. For neurologists, this is nothing new, related drawings already appears in papers by Ramon y Cajal, a pioneer of neuroscience at the beginning of the last century, but in the recent years computing by spiking is a vivid research area, with the hope to lead to a neural computing of the third generation see [12], [21], etc. For membrane computing it is somehow natural to incorporate the idea of spiking neurons (already neural-like P systems exist, based on di erent ingredients see [23], e orts to compute with a small number of objects were recently made in several papers see, e.g., [2], using the time as a support of information, for instance, taking the time between two events as the result of a computation, was also considered see [3]), but still important di erences exist between the general way of working with multisets of objects in the compartments of a cell-like membrane structure as in membrane computing and the way the neurons communicate by spikes. A way to answer this challenge was proposed in [18]: neurons as single membranes, placed in the nodes of a graph corresponding to synapses, only one type of objects present

Spiking Neural P Systems: A Tutorial.

P systems are parallel molecular computing models based on processing multisets of objects in cell-like membrane structures. Recently, Petr Sosik has shown that a semi-uniform family of P systems with active membranes and 2-division is able to solve the PSPACE-complete problem QBF-SAT in linear time; he has also conjectured that the membrane dissolving rules of the (d) type may be omitted, but probably not the (f) type rules for non-elementary membrane division. In this paper, we partially confirm the conjecture proving that dissolving rules are not necessary. Moreover, the construction is now uniform. It still remains open whether or not non-elementary membrane division is needed.

Solving a PSPACE-complete problem by recognizing P systems with restricted active membranes

This paper addresses the problem of removing the polarization of membranes from P systems with active membranes - and this is achieved by allowing the change of membrane labels by means of communication rules or by membrane dividing rules. As consequences of these results, we obtain the universality of P systems with active membranes which are allowed to change the labels of membranes, but do not use polarizations. Universality results are easily obtained also by direct proofs. By direct constructions, we also prove that SAT can be solved in linear time by systems without polarizations and with label changing possibilities. If non-elementary membranes can be divided, then SAT can be solved in linear time without using polarizations and label changing. Several open problems are also formulated.

http://psystems.disco.unimib.it/download/Polar.pdf

Trading polarizations for labels in P systems with active membranes

The P systems (or membrane systems) are a class of distributed parallel computing devices of a biochemical type, where membrane division is the frequently investigated way for obtaining an exponential working space in a linear time, and on this basis solving hard problems, typically NP-complete problems, in polynomial (often, linear) time. In this paper, using another way to obtain exponential working space --- membrane separation, it was shown that Satisfiability Problem and Hamiltonian Path Problem can be deterministically solved in linear or polynomial time by a uniform family of P systems with separation rules, where separation rules are not changing labels, but polarizations are used. Some related open problems are mentioned.

Solving HPP and SAT by P Systems with Active Membranes and Separation Rules

It is known that the satisfiability problem (SAT) can be solved with a semi-uniform family of deterministic polarizationless P systems with active membranes with non-elementary membrane division. We present a double improvement of this result by showing that the satisfiability of a quantified Boolean formula (QSAT) can be solved by a uniform family of P systems of the same kind.

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Artiom Alhazov

Papers

Solving a PSPACE-complete problem by recognizing P systems with restricted active membranes

Trading polarizations for labels in P systems with active membranes

Solving HPP and SAT by P Systems with Active Membranes and Separation Rules

Uniform solution of QSAT using polarizationless active membranes

Uniform Solution of.