Pelabelan Total Titik Ajaib Pada Graf Tangga

The labeling of a graph is a mapping that pairs the elements in the graph into positive integers. In this thesis, it discusses how the magic total point labeling algorithm on the  ladder graph and the  ladder graph and how the magic total point labeling on the  ladder graph and the adder graph uses the magic square matrix modification using the durer method. Where the elements of the result of this magic square matrix modification will be used as point labels on the  ladder graph and the ladder graph.&nbsp

A Study on Integer Additive Set-Valuations of Signed Graphs

Let $\N$ denote the set of all non-negative integers and \cP(\N) be its power set. An integer additive set-labeling (IASL) of a graph $G$ is an injective set-valued function f:V(G)\to \cP(\N)-\{\emptyset\} such that the induced function f^+:E(G) \to \cP(\N)-\{\emptyset\} is defined by $f^+ (uv) = f(u)+ f(v)$, where $f(u)+f(v)$ is the sumset of $f(u)$ and $f(v)$. A graph which admits an IASL is usually called an IASL-graph. An IASL $f$ of a graph $G$ is said to be an integer additive set-indexer (IASI) of $G$ if the associated function $f^+$ is also injective. In this paper, we define the notion of integer additive set-labeling of signed graphs and discuss certain properties of signed graphs which admits certain types of integer additive set-labelings.Comment: 12 pages, Carpathian Mathematical Publications, Vol. 8, Issue 2, 2015, 12 page

On the Implementation of the Probabilistic Logic Programming Language ProbLog

The past few years have seen a surge of interest in the field of probabilistic logic learning and statistical relational learning. In this endeavor, many probabilistic logics have been developed. ProbLog is a recent probabilistic extension of Prolog motivated by the mining of large biological networks. In ProbLog, facts can be labeled with probabilities. These facts are treated as mutually independent random variables that indicate whether these facts belong to a randomly sampled program. Different kinds of queries can be posed to ProbLog programs. We introduce algorithms that allow the efficient execution of these queries, discuss their implementation on top of the YAP-Prolog system, and evaluate their performance in the context of large networks of biological entities.Comment: 28 pages; To appear in Theory and Practice of Logic Programming (TPLP

A generic operational metatheory for algebraic effects

We provide a syntactic analysis of contextual preorder and equivalence for a polymorphic programming language with effects. Our approach applies uniformly across a range of algebraic effects, and incorporates, as instances: errors, input/output, global state, nondeterminism, probabilistic choice, and combinations thereof. Our approach is to extend Plotkin and Power’s structural operational semantics for algebraic effects (FoSSaCS 2001) with a primitive “basic preorder” on ground type computation trees. The basic preorder is used to derive notions of contextual preorder and equivalence on program terms. Under mild assumptions on this relation, we prove fundamental properties of contextual preorder (hence equivalence) including extensionality properties and a characterisation via applicative contexts, and we provide machinery for reasoning about polymorphism using relational parametricity

Thermal quantum spacetime

The intersection of thermodynamics, quantum theory and gravity has revealed many profound insights, all the while posing new puzzles. In this article, we discuss an extension of equilibrium statistical mechanics and thermodynamics potentially compatible with a key feature of general relativity, background independence; and we subsequently use it in a candidate quantum gravity system, thus providing a preliminary formulation of a thermal quantum spacetime. Specifically, we emphasise on an information-theoretic characterisation of generalised Gibbs equilibrium that is shown to be particularly suited to background independent settings, and in which the status of entropy is elevated to being more fundamental than energy. We also shed light on its intimate connections with the thermal time hypothesis. Based on this we outline a framework for statistical mechanics of quantum gravity degrees of freedom of combinatorial and algebraic type, and apply it in several examples. In particular, we provide a quantum statistical basis for the origin of covariant group field theories, shown to arise as effective statistical field theories of the underlying quanta of space in a certain class of generalised Gibbs states

Sum index and difference index of graphs

Let $G$ be a nonempty simple graph with a vertex set $V(G)$ and an edge set $E(G)$. For every injective vertex labeling $f:V(G)\to\mathbb{Z}$, there are two induced edge labelings, namely $f^+:E(G)\to\mathbb{Z}$ defined by $f^+(uv)=f(u)+f(v)$, and $f^-:E(G)\to\mathbb{Z}$ defined by $f^-(uv)=|f(u)-f(v)|$. The sum index and the difference index are the minimum cardinalities of the ranges of $f^+$ and $f^-$, respectively. We provide upper and lower bounds on the sum index and difference index, and determine the sum index and difference index of various families of graphs. We also provide an interesting conjecture relating the sum index and the difference index of graphs

Synthesis of graphical choreographies

Graphical choreographies, or global graphs, are general multiparty session specifications featuring expressive constructs such as forking, merging, and joining for representing application-level protocols. Global graphs can be directly translated into modelling notations such as BPMN and UML. This paper presents an algorithm whereby a global graph can be synthesised from asynchronous buffered behaviours represented by communicating finite state machines (CFSMs). Our results include: a sound and complete characterisation of a subset of safe CFSMs from which global graphs can be synthesised; a synthesis algorithm to translate CFSMs to global graphs; a time complexity analysis; and an implementation of our theory, as well as an experimental evaluation