Loss of Accuracy in Numerical Computations

Михаил М. Константинов, Петко Х. Петков - Разгледани са възможните катастрофални ефекти от неправилното използване на крайна машинна аритметика с плаваща точка. За съжаление, тази тема не винаги се разбира достатъчно добре от студентите по приложна и изчислителна математика, като положението в инженерните и икономическите специалности в никакъв случай не е по-добро. За преодоляване на този образователен пропуск тук сме разгледали главните виновници за загубата на точност при числените компютърни пресмятания. Надяваме се, че представените резултати ще помогнат на студентите и лекторите за по-добро разбиране и съответно за избягване на основните фактори, които могат да разрушат точността при компютърните числени пресмятания. Последното не е маловажно – числените катастрофи понякога стават истински, с големи щети и човешки жертви.

Symbolic Solving of Partial Differential Equation Systems and Compatibility Conditions

An algorithm is produced for the symbolic solving of systems of partial differential equations by means of multivariate Laplace–Carson transform. A system of K equations with M as the greatest order of partial derivatives and right-hand parts of a special type is considered. Initial conditions are input. As a result of a Laplace–Carson transform of the system according to initial condition we obtain an algebraic system of equations. A method to obtain compatibility conditions is discussed.

On Optimal Quadratic Lagrange Interpolation: Extremal Node Systems with Minimal Lebesgue Constant via Symbolic Computation

ACM Computing Classification System (1998): G.1.1, G.1.2.

Weitzenböck Derivations and Classical Invariant Theory II: The Symbolic Method

2000 Mathematics Subject Classification: 13N15, 13A50, 13F20.

A quantitative application of symbolic interactionism to advance directive completion by older adults

This study examined contextual and situational influences on older adults' decision to complete advance directives by means of a conceptual framework derived from symbolic interactionist theory and a cross-sectional, correlational research design. It was hypothesized that completion of advance directives among older adults would be associated with visiting or participating in the care of a terminally ill or permanently incompetent individual sustained by technology. Using a 53-item questionnaire, computer assisted telephone interviews (CATI) were conducted with 398 community dwelling adults between September and October 2003. Respondents were contacted using random-select dialing from a listed sample of 99% of household telephone numbers in one South Florida census tract. Over 90% of households in this tract include an individual age 65 or older. ^ The results revealed that contrary to most reports in the literature a substantial proportion of older adults (82%) had completed advance directives and that the link between older adults and document completion was mainly through attorneys and not mandated agents, health care professionals. Further, more than one third of older adults reported that religion/spirituality was not an important part of their life, suggesting that the recommended practice of offering religious/spiritual counseling to all those approaching death be reexamined. The hypothesis was not supported (p > .05) and is explained by the situational emphasis on the variables rather than on structural influences. In logistic regression analysis, only increasing age (p = .001) and higher education (p = < .001) were significant but explained only 10% of the variance in document completion. ^ Based on the findings, increased interdisciplinary collaboration is suggested with regard to the advance directive agenda. Since attorneys play a key role in document completion, other professions should seek their expertise and collaboration. In addition, the inclusion of a religious/spiritual preference section in all living wills should be considered as an essential part of a holistic and individually appropriate document. Implications for social work education, practice, and advocacy are discussed as well as suggestions for further research. ^

A software tool that generates symbolic model verifier (SMV) input language from a predicate transition net

The purpose of this research was to apply model checking by using a symbolic model checker on Predicate Transition Nets (PrT Nets). A PrT Net is a formal model of information flow which allows system properties to be modeled and analyzed. The aim of this thesis was to use the modeling and analysis power of PrT nets to provide a mechanism for the system model to be verified. Symbolic Model Verifier (SMV) was the model checker chosen in this thesis, and in order to verify the PrT net model of a system, it was translated to SMV input language. A software tool was implemented which translates the PrT Net into SMV language, hence enabling the process of model checking. The system includes two parts: the PrT net editor where the representation of a system can be edited, and the translator which converts the PrT net into an SMV program.

Design as Symbolic Violence. Design for Social Justice.

Design embeds ideas in communication and artefacts in subtle and psychologically powerful ways. Sociologist Pierre Bourdieu coined the term ‘symbolic violence’ to describe how powerful ideologies, priorities, values and even sensibilities are constructed and reproduced through cultural institutions, processes and practices. Through symbolic violence, individuals learn to consider unjust conditions as natural and even come to value customs and ideas that are oppressive. Symbolic violence normalises structural violence and enables real violence to take place, often preceding it and later justifying it. Feminist, class, race and indigenous scholars and activists describe how oppressions (how patriarchy, racism, colonialism, etc.) exist within institutions and structures, and also within cultural practices that embed ideologies into everyday life. The theory of symbolic violence sheds light on how design can function to naturalise oppressions and then obfuscate power relations around this process. Through symbolic violence, design can function as an enabler for the exploitation of certain groups of people and the environment they (and ultimately ‘we’) depend on to live. Design functions as symbolic violence when it is involved with the creation and reproduction of ideas, practices, tools and processes that result in structural and other types of violence (including ecocide). Breaking symbolic violence involves discovering how it works and building capacities to challenge and transform dysfunctional ideologies, structures and institutions. This conversation will give participants an opportunity to discuss, critique and/or develop the theory of design as symbolic violence as a basis for the development of design strategies for social justice.

An Empirical Evaluation of Preconditioning Data for Accelerating Convex Hull Computations

The convex hull describes the extent or shape of a set of data and is used ubiquitously in computational geometry. Common algorithms to construct the convex hull on a finite set of n points (x,y) range from O(nlogn) time to O(n) time. However, it is often the case that a heuristic procedure is applied to reduce the original set of n points to a set of s < n points which contains the hull and so accelerates the final hull finding procedure. We present an algorithm to precondition data before building a 2D convex hull with integer coordinates, with three distinct advantages. First, for all practical purposes, it is linear; second, no explicit sorting of data is required and third, the reduced set of s points is constructed such that it forms an ordered set that can be directly pipelined into an O(n) time convex hull algorithm. Under these criteria a fast (or O(n)) pre-conditioner in principle creates a fast convex hull (approximately O(n)) for an arbitrary set of points. The paper empirically evaluates and quantifies the acceleration generated by the method against the most common convex hull algorithms. An extra acceleration of at least four times when compared to previous existing preconditioning methods is found from experiments on a dataset.

An Empirical Evaluation of Preconditioning Data for Accelerating Convex Hull Computations

The convex hull describes the extent or shape of a set of data and is used ubiquitously in computational geometry. Common algorithms to construct the convex hull on a finite set of n points (x,y) range from O(nlogn) time to O(n) time. However, it is often the case that a heuristic procedure is applied to reduce the original set of n points to a set of s < n points which contains the hull and so accelerates the final hull finding procedure. We present an algorithm to precondition data before building a 2D convex hull with integer coordinates, with three distinct advantages. First, for all practical purposes, it is linear; second, no explicit sorting of data is required and third, the reduced set of s points is constructed such that it forms an ordered set that can be directly pipelined into an O(n) time convex hull algorithm. Under these criteria a fast (or O(n)) pre-conditioner in principle creates a fast convex hull (approximately O(n)) for an arbitrary set of points. The paper empirically evaluates and quantifies the acceleration generated by the method against the most common convex hull algorithms. An extra acceleration of at least four times when compared to previous existing preconditioning methods is found from experiments on a dataset.

Sneakerheads and Custom Kicks: Insights into Symbolic Mass Customization

This chapter presents an exploratory study involving a group of athletic shoe enthusiasts and their feelings towards customized footwear. These "sneakerheads" demonstrate their infatuation with sneakers via activities ranging from creating catalogs of custom shoes to buying and selling rare athletic footwear online. The key characteristic these individuals share is that, for them, athletic shoes are a fundamental fashion accessory stepped in symbolism and meaning. A series of in-depth interviews utilizing the Zaltman Metaphor Elicitation Technique (ZMET) provide a better understanding of how issues such as art, self-expression, exclusivity, peer recognition, and counterfeit goods interact with the mass customization of symbolic products by category experts.

On T-Semisimplicity of Iwasawa Modules and Some Computations with Z3-Extensions

Thesis (Ph.D.)--University of Washington, 2016-08

FRAMEWORK SYNTHESIS FOR SYMBOLIC EXECUTION OF EVENT-DRIVEN FRAMEWORKS

Symbolic execution is a powerful program analysis technique, but it is very challenging to apply to programs built using event-driven frameworks, such as Android. The main reason is that the framework code itself is too complex to symbolically execute. The standard solution is to manually create a framework model that is simpler and more amenable to symbolic execution. However, developing and maintaining such a model by hand is difficult and error-prone. We claim that we can leverage program synthesis to introduce a high-degree of automation to the process of framework modeling. To support this thesis, we present three pieces of work. First, we introduced SymDroid, a symbolic executor for Android. While Android apps are written in Java, they are compiled to Dalvik bytecode format. Instead of analyzing an app’s Java source, which may not be available, or decompiling from Dalvik back to Java, which requires significant engineering effort and introduces yet another source of potential bugs in an analysis, SymDroid works directly on Dalvik bytecode. Second, we introduced Pasket, a new system that takes a first step toward automatically generating Java framework models to support symbolic execution. Pasket takes as input the framework API and tutorial programs that exercise the framework. From these artifacts and Pasket's internal knowledge of design patterns, Pasket synthesizes an executable framework model by instantiating design patterns, such that the behavior of a synthesized model on the tutorial programs matches that of the original framework. Lastly, in order to scale program synthesis to framework models, we devised adaptive concretization, a novel program synthesis algorithm that combines the best of the two major synthesis strategies: symbolic search, i.e., using SAT or SMT solvers, and explicit search, e.g., stochastic enumeration of possible solutions. Adaptive concretization parallelizes multiple sub-synthesis problems by partially concretizing highly influential unknowns in the original synthesis problem. Thanks to adaptive concretization, Pasket can generate a large-scale model, e.g., thousands lines of code. In addition, we have used an Android model synthesized by Pasket and found that the model is sufficient to allow SymDroid to execute a range of apps.

Non-Symbolic Fragmentation

This paper reports on the use of non-symbolic fragmentation of data for securing communications. Non-symbolic fragmentation, or NSF, relies on breaking up data into non-symbolic fragments, which are (usually irregularly-sized) chunks whose boundaries do not necessarily coincide with the boundaries of the symbols making up the data. For example, ASCII data is broken up into fragments which may include 8-bit fragments but also include many other sized fragments. Fragments are then separated with a form of path diversity. The secrecy of the transmission relies on the secrecy of one or more of a number of things: the ordering of the fragments, the sizes of the fragments, and the use of path diversity. Once NSF is in place, it can help secure many forms of communication, and is useful for exchanging sensitive information, and for commercial transactions. A sample implementation is described with an evaluation of the technology.

Original sin: divine and symbolic violence in the turn to the Apostle Paul

When we take a step back from the imposing figure of physical violence, it becomes possible to examine other structurally violent forces that constantly shape our cultural and political landscapes. One of the driving interests in the “turn to Paul” in recent continental philosophy stems from wrestling with questions about the real nature of contemporary violence. Paul is positioned as a thinker whose messianic experience began to cut through the violent masquerade of the existing order. The crucifixion and resurrection of the Messiah (a slave and a God co-existing in one body) exposed the empty grounding upon which power resided. The Christ-event signifies a moment of violent interruption in the existing order which Paul enjoins the Gentiles to participate in through a dedication of love for the neighbour. This divine violence aims to reveal and subvert the “powers,” epitomised in the Roman Empire, in order to fulfil the labour of the Messianic now-time which had arrived. The impetus behind this research comes from a typically enigmatic and provocative section of text by the Slovene philosopher, cultural critic, and Christian atheist Slavoj Žižek. He claims that 'the notion of love should be given here all its Paulinian weight: the domain of pure violence… is the domain of love' (2008a, 173). In this move he links Paul’s idea of love to that of Walter Benjamin’s divine violence; the sublime and the cataclysmic come together in this seemingly perverse notion. At stake here is the way in which uncovering violent forces in the “zero-level” of our narrative worldviews aids the diagnosis of contemporary political and ethical issues. It is not enough to imagine Paul’s encounter with the Christ-event as non-violent. This Jewish apocalyptic movement was engaged in a violent struggle within an existing order that God’s wrath will soon dismantle. Paul’s weak violence, inspired by his fidelity to the Christ-event, places all responsibility over creation in the role of the individual within the collective body. The centre piece of this re-imagined construction of the Pauline narrative comes in Romans 13: the violent dedication to love understood in the radical nature of the now-time. 3 This research examines the role that narratives play in the creation and diagnosis of these violent forces. In order to construct a new genealogy of violence in Christianity it is crucial to understand the role of the slave of Christ (the revolutionary messianic subject). This turn in the Symbolic is examined through creating a literary structure in which we can approach a radical Nietzschean shift in Pauline thought. The claim here, a claim which is also central to Paul’s letters, is that when the symbolic violence which manipulates our worldviews is undone by a divine violence, if even for a moment, new possibilities are created in the opening for a transvaluation of values. Through this we uncover the nature of original sin: the consequences of the interconnected reality of our actions. The role of literature is vital in the construction of this narrative; starting with Cormac McCarthy’s No Country for Old Men, and continuing through works such as Melville’s Bartleby the Scrivener, this thesis draws upon the power of literature in the shaping of our narrative worlds. Typical of the continental philosophy at the heart of this work, a diverse range of illustrations and inspirations from fiction is pulled into its narrative to reflect the symbolic universe that this work was forged through. What this work attempts to do is give this theory a greater grounding in Paul’s letters by demonstrating this radical kenotic power at the heart of the Christ-event. Romans 13 reveals, in a way that has not yet been picked up by Critchley, Žižek, and others, that Paul opposed the biopolitical power of the Roman Empire through the weak violence of love that is the labour of the slaves of Christ on the “now-time” that had arrived.