Computing with Membranes and Picture Arrays

Splicing systems were introduced by Tom Head [3] on biological considerations to model certain recombinant behaviour of DNA molecules. An effective extension of this operation to images was introduced by Helen Chandra et al. [5] and H array splicing systems were considered. A new method of applying the splicing operation on images of hexagonal arrays was introduced by Thomas et al. [12] and generated a new class of hexagonal array languages HASSL. On the other hand, P systems, introduced by Paun [6] generating rectangular arrays and hexagonal arrays have been studied in the literature, bringing together the two areas of theoretical computer science namely membrane computing and picture languages. P system with array objects and parallel splicing operation on arrays is introduced as a simple and effective extension of P system with operation of splicing on strings and this new class of array languages is compared with the existing families of array languages. Also we propose another P system with hexagonal array objects and parallel splicing operation on hexagonal arrays is introduced and this new class of hexagonal array languages is compared with the existing families of hexagonal array languages

Adjunct hexagonal array token Petri nets and hexagonal picture languages

Adjunct Hexagonal Array Token Petri Net Structures (AHPN) are re- cently introduced hexagonal picture generating devices which extended the Hexag- onal Array Token Petri Net Structures . In this paper we consider AHPN model along with a control feature called inhibitor arcs and compare it with some ex- pressive hexagonal picture generating and recognizing models with respect to the generating power

Pure 2D picture grammars and languages

A new syntactic model, called pure two-dimensional (2D) context-free grammar (P2DCFG), is introduced based on the notion of pure context-free string grammar. The rectangular picture generative power of this 2D grammar model is investigated. Certain closure properties are obtained. An analogue of this 2D grammar model called pure 2D hexagonal context-free grammar (P2DHCFG) is also considered to generate hexagonal picture arrays on triangular grids

Variants Of Array-Rewriting P Systems For Generating Picture Arrays

Bidang pengkomputeran membran dimulakan sekitar tahun 2000, berinspirasikan struktur dan fungsi sel-sel hidup. Model teori pengkomputeran membran ini dipanggil sistem P dan variannya dan penggunaan model ini dalam pelbagai masalah telah disiasat secara intensif sejak itu. Sistem P tatasusunan menghubungkan tatabahasa tatasusunan bahasa formal dengan sistem P. Dalam teori bahasa formal, salah satu kajian utama adalah terhadap keupayaan tatabahasa untuk menjana bahasa, yang disebut sebagai keupayaan generatif, yang bergantung kepada jenis-jenis peraturan yang digunakan. Kami menyiasat keupayaan generatif sistem P tatasusunan dengan memperkenalkan dalam peraturan sistem ciri-ciri benar, tatabahasa dengan penulisan semula selari dan kaedah mengumpul peraturan. Di sini dengan mengaitkan simbol benar dalam kaedah sistem P tatasusunan, kami memperkenalkan varian baru, yang dinamakan sebagai sistem P tatasusunan dengan ciri-ciri benar. Kami membuktikan bahawa jumlah membran yang digunakan dalam pembinaan itu dapat dikurangkan berbanding sistem P tatasusunan. Kami menggabungkan penulisan semula selari dalam sistem P rentetan di dalam sistem P tatasusuan, dengan itu memperkenalkan satu lagi varian baru dalam sistem P tatasusunan dan dinamakan sebagai sistem P tatasusunan selari. Inspired by the structure and functioning of the living cells, the field of membrane computing was initiated around the year 2000. Since then the theoretical model introduced in this area, called P system has been intensively investigated for properties and applications. One such P system known as array-rewriting P systems provides a link between two dimensional formal language theory and membrane computing. In formal language theory, one of the main studies is on the language generating capability of the grammars, referred to as the generative capacity, which depends on the types of rules. Also a standard technique to increase the generative capacity is to endow the rules with additional features. Here the array-rewriting P system is investigated by endowing the grammatical rules of the system with three such features, namely, permitting symbols, parallel rewriting and grouping of rules. Thus this thesis introduces and develops three such variants of the array-rewriting P system and brings out their advantages

Interactive specification of data displays

On-line graphical language for computer data displa

A multiscale generative model to understand disorder in domain boundaries

A continuing challenge in atomic resolution microscopy is to identify significant structural motifs and their assembly rules in synthesized materials with limited observations. Here we propose and validate a simple and effective hybrid generative model capable of predicting unseen domain boundaries in a potassium sodium niobate thin film from only a small number of observations, without expensive first-principles calculation. Our results demonstrate that complicated domain boundary structures can arise from simple interpretable local rules, played out probabilistically. We also found new significant tileable boundary motifs and evidence that our system creates domain boundaries with the highest entropy. More broadly, our work shows that simple yet interpretable machine learning models can help us describe and understand the nature and origin of disorder in complex materials

Mutual Composite Fermion and composite Boson approaches to balanced and imbalanced bilayer quantum Hall system: an electronic analogy of the Helium 4 system

We use both Mutual Composite Fermion (MCF) and Composite Boson (CB) approach to study balanced and im-balanced Bi-Layer Quantum Hall systems (BLQH) and make critical comparisons between the two approaches. We find the CB approach is superior to the MCF approach in studying ground states with different kinds of broken symmetries. In the phase representation of the CB theory, we first study the Excitonic superfluid state (ESF). The theory puts spin and charge degree freedoms in the same footing, explicitly bring out the spin-charge connection and classify all the possible excitations in a systematic way. Then in the dual density representation of the CB theory, we study possible intermediate phases as the distance increases. We propose there are two critical distances $d_{c1} < d_{c2}$ and three phases as the distance increases. When $0 < d < d_{c1}$, the system is in the ESF state which breaks the internal $U(1)$ symmetry, when $d_{c1} < d < d_{c2}$, the system is in an Pseudo-spin density wave (PSDW) state which breaks the translational symmetry, there is a first order transition at $d_{c1}$ driven by the collapsing of magneto-roton minimum at a finite wavevector in the pseudo-spin channel. When $d_{c2} < d < \infty$, the system becomes two weakly coupled $\nu =1/2$ Composite Fermion Fermi Liquid (FL) state. There is also a first order transition at $d= d_{c2}$. We construct a quantum Ginzburg Landau action to describe the transition from ESF to PSDW which break the two completely different symmetries. By using the QGL action, we explicitly show that the PSDW takes a square lattice and analyze in detail the properties of the PSDW at zero and finite temperature.Comment: 29 PRB pages, 18 figures, 2 tables, REVTEX

Inferring Pattern and Disorder in Close-Packed Structures from X-ray Diffraction Studies, Part I: epsilon-Machine Spectral Reconstruction Theory

In a recent publication [D. P. Varn, G. S. Canright, and J. P. Crutchfield, Phys. Rev. B {\bf 66}:17, 156 (2002)] we introduced a new technique for discovering and describing planar disorder in close-packed structures (CPSs) directly from their diffraction spectra. Here we provide the theoretical development behind those results, adapting computational mechanics to describe one-dimensional structure in materials. By way of contrast, we give a detailed analysis of the current alternative approach, the fault model (FM), and offer several criticisms. We then demonstrate that the computational mechanics description of the stacking sequence--in the form of an epsilon-machine--provides the minimal and unique description of the crystal, whether ordered, disordered, or some combination. We find that we can detect and describe any amount of disorder, as well as materials that are mixtures of various kinds of crystalline structure. Underlying this approach is a novel method for epsilon-machine reconstruction that uses correlation functions estimated from diffraction spectra, rather than sequences of microscopic configurations, as is typically used in other domains. The result is that the methods developed here can be adapted to a wide range of experimental systems in which spectroscopic data is available.Comment: 26 pages, 23 figures, 8 tables, 110 citations; http://www.santafe.edu/projects/CompMech/papers/ipdcpsi.htm