Restricted Boltzmann Machine representation for the groundstate and excited states of Kitaev Honeycomb model

In this work, the capability of restricted Boltzmann machines (RBMs) to find solutions for the Kitaev honeycomb model with periodic boundary conditions is investigated. The measured groundstate (GS) energy of the system is compared and, for small lattice sizes (e.g. 3×3 with 18 spinors), shown to agree with the analytically derived value of the energy up to a deviation of 0.09 %. Moreover, the wave-functions we find have 99.89 % overlap with the exact ground state wave-functions. Furthermore, the possibility of realizing anyons in the RBM is discussed and an algorithm is given to build these anyonic excitations and braid them for possible future applications in quantum computation. Using the correspondence between topological field theories in (2+1)d and 2d CFTs, we propose an identification between our RBM states with the Moore-Read state and conformal blocks of the 2 d Ising model.

Computational Abstraction

Representation and abstraction are two of the fundamental concepts of computer science. Together they enable “high-level” programming: without abstraction programming would be tied to machine code; without a machine representation, it would be a pure mathematical exercise. Representation begins with an abstract structure and seeks to find a more concrete one. Abstraction does the reverse: it starts with concrete structures and abstracts away. While formal accounts of representation are easy to find, abstraction is a different matter. In this paper, we provide an analysis of data abstraction based upon some contemporary work in the philosophy of mathematics. The paper contains a mathematical account of how Frege’s approach to abstraction may be interpreted, modified, extended and imported into type theory. We argue that representation and abstraction, while mathematical siblings, are philosophically quite different. A case of special interest concerns the abstract/physical interface which houses both the physical representation of abstract structures and the abstraction of physical systems.

Data Driven Modelling of Nuclear Power Plant Performance Data as Finite State Machines

Accurate modelling and simulation of a nuclear power plant are important factors in the strategic planning and maintenance of the plant. Several nonlinearities and multivariable couplings are associated with real-world plants. Therefore, it is quite challenging to model such cyberphysical systems using conventional mathematical equations. A visual analytics approach which addresses these limitations and models both short term as well as long term behaviour of the system is introduced. Principal Component Analysis (PCA) followed by Linear Discriminant Analysis (LDA) is used to extract features from the data, k-means clustering is applied to label the data instances. Finite state machine representation formulated from the clustered data is then used to model the behaviour of cyberphysical systems using system states and state transitions. In this paper, the indicated methodology is deployed over time-series data collected from a nuclear power plant for nine years. It is observed that this approach of combining the machine learning principles with the finite state machine capabilities facilitates feature exploration, visual analysis, pattern discovery, and effective modelling of nuclear power plant data. In addition, finite state machine representation supports identification of normal and abnormal operation of the plant, thereby suggesting that the given approach captures the anomalous behaviour of the plant.

Railway photography and technology: analysis of the photographic record of Brazilian railway in the 19th century

ABSTRACT The purpose of this text is to examine some sets of photographs about railway companies in Brazil, in order to highlight the potential of this type of iconographic material, not as artistic documentation but also technological documentation. We deal in particular with a collection of 6,000 photographs gathered by companies such as Companhia Paulista, Companhia Mogiana and Estrada de Ferro Sorocabana, which was deposited in the Museu da Companhia Paulista, in Jundiaí. These images were cataloged in 2014 by the RFFSA Inventory and IPHAN - within the attributions established to them by Law 11483/2007 - and then transferred to the Public Archive of the State of São Paulo. Although some images eventually had aesthetic quality, our first hypothesis is that the main reason for its production seems to have been technical: record of rolling stock or the evolution of construction work; therefore, this would be a routine activity in the companies that would explain the great volume of photographic material still existing. Secondly, we believe that the same material could be dealt with from the historical perspective of the technique and technology as an expression of technical-scientific knowledge and, often, by rules of machine representation and geographical space - although the pictorial tradition is not absent. This would demonstrate a potential for analysis of this type of iconographic material, where an interpretation proposed by the history of technology may not only enrich or complement studies of the history of photography, but also explore the importance of visual representation in technical-scientific knowledge.

Blockchain State Machine Representation

We present a formalization of blockchain as a state machine, focusing upon permissionless blockchains due to general audience awareness of its most popular implementation, Bitcoin (permissioned blockchains are treated similarly without loss of generality). After presenting a typical Bitcoin transaction workflow, a general blockchain state representation is derived. It is demonstrated that the proper mathematical object defining the state of a blockchain is a topological fiber bundle, because it is not possible to globally `parametrize' blocks (or ledgers of blocks) by time due to their dependence upon cryptographic hash functions. In addition, we specify a general transition function between blockchain states that is agnostic to the consensus mechanism used to write blocks into the ledger, and which is probabilistic in nature, so that blockchain may be regarded as a probabilistic state machine. We then interpret agents (both human and code-based, such as `chaincode', `smart contracts', or other artificial intelligence) as automata interacting with blockchain technology, drawing upon the theory of non-cooperative repeated interaction games. Finally, blockchain as a hierarchy of state machines is defined, and future research directions are presented using this hierarchy as a point of departure for modeling blockchain dynamics.

Calculation of Gaussian Quadrature with High Accuracy Mathematics Package

We are checking here the dependence of numerical integration accuracy on the quantity of integration points and the accuracy of machine representation of numbers. For this purpose, the package HAHMath is applied. This package allows one to carry out calculations with arbitrary long machine decimal numbers, presented as vectors of integers. Integrals are substituted for Gaussian sums where Hermite polynomials zeros and corresponding weights, computed by the same package are used. It is shown that the chosen case accuracy of final calculations depends on the used machine numbers’ length more strictly than on the quantity of the integration points.

RealText-lex: A Lexicalization Framework for RDF Triples

The online era has made available almost cosmic amounts of information in the public and semi-restricted domains, prompting development of corresponding host of technologies to organize and navigate this information. One of these developing technologies deals with encoding information from free form natural language into a structured form as RDF triples. This representation enables machine processing of the data, however the processed information can not be directly converted back to human language. This has created a need to be able to lexicalize machine processed data existing as triples into a natural language, so that there is seamless transition between machine representation of information and information meant for human consumption. This paper presents a framework to lexicalize RDF triples extracted from DBpedia, a central interlinking hub for the emerging Web of Data. The framework comprises of four pattern mining modules which generate lexicalization patterns to transform triples to natural language sentences. Among these modules, three are based on lexicons and the other works on extracting relations by exploiting unstructured text to generate lexicalization patterns. A linguistic accuracy evaluation and a human evaluation on a sub-sample showed that the framework can produce patterns which are accurate and emanate human generated qualities.

Uniform Model of Representation Heterogeneous Data Hydrometeorological Observations

The article discusses the uniform model of representation heterogeneous data hydrometeorological observations from international codes used for transmission. Physical this model simply shows the machine representation of aggregate tables with variable-length strings. A list of keys creates for all tables and this list of keys allows to carry out a targeted search for the required data.