Symbolic Computation

This paper proposes a method to automatically detect equivalent mutants using symbolic computation. Mutation
analysis is an evaluation method of the software test cases set
quality. In mutation analysis, mutant programs are generated
by intentionally embedding bugs in the original program to
evaluate the quality of the test cases set by determining
whether bugs are detected by it. However, equivalent mutant
programs, which generate exactly the same output as their
original program, disturb the accurate assessment of a test
cases set. To precisely evaluate the quality of the test set, we
must remove equivalent mutants.
In this paper, symbolic computation is adopted to detect
equivalent mutants. Symbolic computation executes a given
program by providing symbolic values instead of concrete
values, such as numbers. The result of symbolic computation
is a set of a pair of expressions: a symbolic value and a path
condition, both of which may contain symbols. Since the output
of equivalent mutants is identical to its original for any input,
a mutant is proved to be an equivalent mutant if its symbolic
output is identical to that of the original.
Our proposed system is designed for Java programming
language. First, the system converts an original and its mutants
written in Java programming language to JavaML, a markup
language for Java. Then both of the programs represented in
JavaML are executed symbolically, and outputs are generated
for arbitrary inputs. If the mutant ’ s output is equivalent to
that of the original, the system determines that the mutant
is an equivalent mutant. Evaluation experiments proved that
our proposed method detects more equivalent mutants than
existing methods.

In this paper, we introduce the notion of isoclinism among crossed modules and describe various properties of the notion. We give an algorithm for checking isoclinism among crossed modules and apply the algorithm (implemented in GAP) to classify certain crossed modules.

Since many years, theoretical concepts of Data Mining have been developed and improved. Data Mining has become applied to many academic and industrial situations, and recently, soundings of public opinion about privacy have been carried out. However, a consistent and standardized definition is still missing, and the initial explanation given by Frawley et al. has pragmatically often changed over the years. Furthermore, alternative terms like Knowledge Discovery have been conjured and forged, and a necessity of a Data Warehouse has been endeavoured to persuade the users. In this work, we pick up current definitions and introduce an unified definition that covers existing attempted explanations. For this, we appeal to the natural original of chemical states of aggregation.

In this essay, we examine the feasibility of quantum computation of Gr\"obner basis which is a fundamental tool of algebraic geometry. The classical method for computing Gr\"obner basis is based on Buchberger's algorithm, and our question is how to adopt quantum algorithm there. A Quantum algorithm for finding the maximum is usable for detecting head terms of polynomials, which are required for the computation of S-polynomials. The reduction of S-polynomials with respect to a Gr\"obner basis could be done by the quantum version of Gauss-Jordan elimination of echelon which represents polynomials. However, the frequent occurrence of zero-reductions of polynomials is an obstacle to the effective application of quantum algorithms. This is because zero-reductions of polynomials occur in non-full-rank echelons, for which quantum linear systems algorithms (through the inversion of matrices) are inadequate, as ever-known quantum linear solvers (such as Harrow-Hassidim-Lloyd) require the clandestine computations of the inverses of eigenvalues. Such algorithms should be used in limited situations with the guarantee that the matrices could be inverted. For example, the transformation from the non-reduced Gr\"obner basis to the reduced one is of this sort, and the quantum algorithms surely achieve the partial speedup of the computations.

Herein, it is shown that by exploiting integral definitions of well known special functions, through generalizations and differentiations, broad classes of definite integrals can be solved in closed form or in terms of special functions. This is especially useful when there is no closed form solution to the indefinite form of the integral. In this paper, three such classes of definite integrals are presented. Two of these classes incorporate and supercede all of Kölbig's integration formulae [11], including his formulation for the computation of Cauchy principal values. Also presented are the mathematical derivations that support the implementation of a third class which exploits the incomplete Gamma function. The resulting programs, based on pattern matching, differentiation, and occasionally limits, are very efficient.

It is often thought that consciousness has a qualitative dimension that cannot be tracked by science. Recently, however, some philosophers have argued that this worry stems not from an elusive feature of the mind, but from the special nature of the concepts used to describe conscious states. Marc Champagne draws on the neglected branch of philosophy of signs or semiotics to develop a new take on this strategy. 

The term “semiotics” was introduced by John Locke in the modern period – its etymology is ancient Greek, and its theoretical underpinnings are medieval. Charles Sanders Peirce made major advances in semiotics, so he can act as a pipeline for these forgotten ideas. Most philosophers know Peirce as the founder of American pragmatism, but few know that he also coined the term “qualia,” which is meant to capture the intrinsic feel of an experience. Since pragmatic verification and qualia are now seen as conflicting commitments, Champagne endeavors to understand how Peirce could (or thought he could) have it both ways. The key, he suggests, is to understand how humans can insert distinctions between features that are always bound.

Recent attempts to take qualities seriously have resulted in versions of panpsychism, but Champagne outlines a more plausible way to achieve this. So, while semiotics has until now been the least known branch of philosophy ending in –ics, his book shows how a better understanding of that branch can move one of the liveliest debates in philosophy forward.

(PhD Dissertation, Stanford Mathematics 2001)
What sort of geometric creation and performance can or cannot be supported in a writing technology that spans freehand sketching, manipulable graphics, text, symbolic computation and simulation? How do we work with and gain intuitions about supposedly abstract things like a Riemannian manifold or an infinite-dimensional function space by manipulating material marks using chalk, pencil or computer? How do we exteriorize thought using the technologies of writing and sketching when it is about processes or objects that could not be embedded in a naive space-time?

I analyze in detail what differential geometric work can or cannot be performed easily in a hybrid medium provided by a generalized multi-modal writing and sketching technology. The critical part of this project is informed by insights from literary and performance studies as well as the mathematical sciences. Focusing on differential geometry through the lens of practice, I examine a-linguistic semiotic usage, and through the lens of phenomenological investigation, I examine how geometers work with continuous, smooth, or infinite structures and processes.

This investigation promises both pragmatic as well as conceptual results. Concretely, this study provides a design for future technologies of mathematical writing that will better augment the working practices of differential geometers.  Conceptually, my proposed materialized phenomenological view of mathematics as a performance practice eliminates three problems in philosophy and in critical studies of symbolic systems: (1) how do we represent continuity and smoothness using discrete symbolic systems? (2) how do we represent infinite things or processes? (3) why do symbolic systems have explanatory or generative power? These conundrums have occupied philosophers of mathematics, and have driven some to propose strict finitist or radically fictionalist theories of mathematics. Moreover, approaches to their resolution underwrite all the technologies that serve mathematical practice today, so these problems fundamentally affect the design of technologies for the working mathematician as well.

The present paper, being the first part of two relevant studies, deals with the evaluation of the stress distribution under steel base-plate connections, acted upon statically by axial forces and bending moments. The whole approach is formulated on the basis of the proper equilibrium equations that are valid for both elastic and plastic plate behaviour adopting a nonlinear stress distribution function under the base plate of catenary type, depending on only one parameter. Taking into account the compatibility and geometric conditions valid for all the connection components, the aforementioned equations are fully assessed, considering the base-plate connection as semi-rigid. Numerical results, parametric studies and comparison with existing relevant investigations will be demonstrated in the companion paper, being the product of advances symbolic computations of the theoretical findings of the present work.

Lattice structures can be developed for operating in high temperature environments. Ceramic-metal FGMs (Functionally graded materials) can be considered for manufacturing lattice plates. In the current study, an exact material modeling using Heaviside distribution functions is performed for lattice FGM plates. Using the classical theory, motion governing equations for lattice FGM plates under uniform temperature field has been derived. Free vibration problem of lattice FGM plates subjected to initial thermal loading and considering simply-supported boundary conditions has been solved using closed form Galerkin method. The analytical results are verified through comparison by those obtained from ABAQUS FEM (finite element method) commercial software. The solution presented here could be treated as a benchmark for future studies about FGM stiffened plates.

This paper is a preliminary overview of advanced mathematical techniques employed by Rabbi Elozor of Worms, a great German Kabbalist of the 13th century. The methods and concepts discussed include integer partition functions and set operations; elements of graph theory; algorithms
for constructing finite and infinite trees; generative grammars of formal languages; finite state automata; elements of chaos theory; list processing and higher-order functions. The development of these devices and theories in the Kabbalistic circles started long before their rediscovery and rigorous formulation by the great European mathematicians in the last two centuries. This paper also demonstrates that
Rabbi Elozor’s worldview can be considered an early form of digital philosophy.

We present a novel scheme to the coverage problem, introducing a quantitative way to estimate the interaction between a block and its enviroment.This is achieved by setting a discrete version of Green`s theorem, specially adapted for Model Checking based verification of integrated circuits.This method is best suited for the coverage problem since it enables one to quantify the incompleteness or, on the other hand, the redundancy of a set of rules, describing the model under verification.Moreover this can be done continuously throughout the verification process, thus enabling the user to pinpoint the stages at which incompleteness/redundancy occurs. Although the method is presented locally on a small hardware example, we additionally show its possibility to provide precise coverage estimation also for large scale systems. We compare this method to others by checking it on the same test-cases.

Abstract: In the last years, there has been an increasing demand of a variety of logical systems, prompted mostly by applications of logic in AI and other related areas. Labeled Deductive Systems (LDS) were developed as a flexible methodology to formalize such a kind of complex logical systems. Defeasible argumentation has proven to be a successful approach to formalizing commonsense reasoning, encompassing many other alternative formalisms for defeasible reasoning. Argument-based frameworks share some common ...