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.

The symbolic, socio-economic and exchange value of Imperial German and National Socialist medals and badges, 1701 to the present

This thesis examines the manufacture, use, exchange (including gift exchange), collecting and commodification of German medals and badges from the early 18th century until the present-day, with particular attention being given to the symbols that were deployed by the National Socialist German Workers’ Party (NSDAP) between 1919 and 1945. It does so by focusing in particular on the construction of value through insignia, and how such badges and their symbolic and monetary value changed over time. In order to achieve this, the thesis adopts a chronological structure, which encompasses the creation of Prussia in 1701, the Napoleonic wars and the increased democratisation of military awards such as the Iron Cross during the Great War. The collapse of the Kaiserreich in 1918 was the major factor that led to the creation of the NSDAP under the eventual strangle-hold of Hitler, a fundamentally racist and anti-Semitic movement that continued the German tradition of awarding and wearing badges. The traditional symbols of Imperial Germany, such as the eagle, were then infused with the swastika, an emblem that was meant to signify anti-Semitism, thus creating a hybrid identity. This combination was then replicated en-masse, and eventually eclipsed all the symbols that had possessed symbolic significance in Germany’s past. After Hitler was appointed Chancellor in 1933, millions of medals and badges were produced in an effort to create a racially based “People’s Community”, but the steel and iron that were required for munitions eventually led to substitute materials being utilised and developed in order to manufacture millions of politically oriented badges. The Second World War unleashed Nazi terror across Europe, and the conscripts and volunteers who took part in this fight for living-space were rewarded with medals that were modelled on those that had been instituted during Imperial times. The colonial conquest and occupation of the East by the Wehrmacht, the Order Police and the Waffen-SS surpassed the brutality of former wars that finally culminated in the Holocaust, and some of these horrific crimes and the perpetrators of them were perversely rewarded with medals and badges. Despite Nazism being thoroughly discredited, many of the Allied soldiers who occupied Germany took part in the age-old practice of obtaining trophies of war, which reconfigured the meaning of Nazi badges as souvenirs, and began the process of their increased commodification on an emerging secondary collectors’ market. In order to analyse the dynamics of this market, a “basket” of badges is examined that enables a discussion of the role that aesthetics, scarcity and authenticity have in determining the price of the artefacts. In summary, this thesis demonstrates how the symbolic, socio-economic and exchange value of German military and political medals and badges has changed substantially over time, provides a stimulus for scholars to conduct research in this under-developed area, and encourages collectors to investigate the artefacts that they collect in a more historically contextualised manner.

Towards a Bourdieusian analysis of the disabled body and practice: embodying negative symbolic capitals and the uneasy experience of hysteresis

Within the last few years, disabled people have become the target of government austerity measures through drastic cuts to welfare justified through the portrayal of benefit claimants as inactive, problem citizens who are wilfully unemployed. For all that is wrong with these cuts, they are one of many aspects of exclusion that disabled people face. Attitudes towards disability are deteriorating (Scope, 2011) and disabled people are devalued and negatively positioned in a myriad of ways, meaning that an understanding of the perceptions and positioning of disability and the power of disabling practices is critical. This thesis will examine how Bourdieu’s theoretical repertoire may be applied to the area of Disability Studies in order to discern how society produces oppressive and exclusionary systems of classification which structures the social position and perceptions of disability. The composite nature of disability and multiple forms of exclusion and inequality associated with it benefits from a multipronged approach which acknowledges personal, embodied and psychological aspects of disability alongside socio-political and cultural conceptualisations. Bourdieu’s approach is one in which the micro and macro aspects of social life are brought together through their meso interplay and provides a thorough analysis of the many aspects of disability.

Efficient Secure Computation for Real-world Settings and Security Models

Secure computation involves multiple parties computing a common function while keeping their inputs private, and is a growing field of cryptography due to its potential for maintaining privacy guarantees in real-world applications. However, current secure computation protocols are not yet efficient enough to be used in practice. We argue that this is due to much of the research effort being focused on generality rather than specificity. Namely, current research tends to focus on constructing and improving protocols for the strongest notions of security or for an arbitrary number of parties. However, in real-world deployments, these security notions are often too strong, or the number of parties running a protocol would be smaller. In this thesis we make several steps towards bridging the efficiency gap of secure computation by focusing on constructing efficient protocols for specific real-world settings and security models. In particular, we make the following four contributions: - We show an efficient (when amortized over multiple runs) maliciously secure two-party secure computation (2PC) protocol in the multiple-execution setting, where the same function is computed multiple times by the same pair of parties. - We improve the efficiency of 2PC protocols in the publicly verifiable covert security model, where a party can cheat with some probability but if it gets caught then the honest party obtains a certificate proving that the given party cheated. - We show how to optimize existing 2PC protocols when the function to be computed includes predicate checks on its inputs. - We demonstrate an efficient maliciously secure protocol in the three-party setting.

Processing of laser Doppler flowmetry signals from healthy subjects and patients with varicose veins: information categorization approach based on intrinsic mode functions and entropy computation

International audience

A MATLAB program for the computation of the confluent hypergeometric function Φ2

We here present a sample MATLAB program for the numerical evaluation of the confluent hypergeometric function Φ2. This program is based on the calculation of the inverse Laplace transform using the algorithm suggested by Simon and Alouini in their reference textbook [1].

The potential of symbolic approximation. Disentangling the effects of approximation vs. calculation demands in nonsymbolic and symbolic representations.

Mathematical skills that we acquire during formal education mostly entail exact numerical processing. Besides this specifically human faculty, an additional system exists to represent and manipulate quantities in an approximate manner. We share this innate approximate number system (ANS) with other nonhuman animals and are able to use it to process large numerosities long before we can master the formal algorithms taught in school. Dehaene´s (1992) Triple Code Model (TCM) states that also after the onset of formal education, approximate processing is carried out in this analogue magnitude code no matter if the original problem was presented nonsymbolically or symbolically. Despite the wide acceptance of the model, most research only uses nonsymbolic tasks to assess ANS acuity. Due to this silent assumption that genuine approximation can only be tested with nonsymbolic presentations, up to now important implications in research domains of high practical relevance remain unclear, and existing potential is not fully exploited. For instance, it has been found that nonsymbolic approximation can predict math achievement one year later (Gilmore, McCarthy, & Spelke, 2010), that it is robust against the detrimental influence of learners´ socioeconomic status (SES), and that it is suited to foster performance in exact arithmetic in the short-term (Hyde, Khanum, & Spelke, 2014). We provided evidence that symbolic approximation might be equally and in some cases even better suited to generate predictions and foster more formal math skills independently of SES. In two longitudinal studies, we realized exact and approximate arithmetic tasks in both a nonsymbolic and a symbolic format. With first graders, we demonstrated that performance in symbolic approximation at the beginning of term was the only measure consistently not varying according to children´s SES, and among both approximate tasks it was the better predictor for math achievement at the end of first grade. In part, the strong connection seems to come about from mediation through ordinal skills. In two further experiments, we tested the suitability of both approximation formats to induce an arithmetic principle in elementary school children. We found that symbolic approximation was equally effective in making children exploit the additive law of commutativity in a subsequent formal task as a direct instruction. Nonsymbolic approximation on the other hand had no beneficial effect. The positive influence of the symbolic approximate induction was strongest in children just starting school and decreased with age. However, even third graders still profited from the induction. The results show that also symbolic problems can be processed as genuine approximation, but that beyond that they have their own specific value with regard to didactic-educational concerns. Our findings furthermore demonstrate that the two often con-founded factors ꞌformatꞌ and ꞌdemanded accuracyꞌ cannot be disentangled easily in first graders numerical understanding, but that children´s SES also influences existing interrelations between the different abilities tested here.

A symbolic approach to nonlinearly perturbed heat equation

We consider a system described by the linear heat equation with adiabatic boundary conditions which is perturbed periodicaly. This perturbation is nonlinear and is characterized by a one-parameter family of quadratic maps. The system, depending on the parameters, presents very complex behaviour. We introduce a symbolic framework to analyze the system and resume its most important features.

Symbolic dynamics generated by a hybrid chaotic systems

We consider piecewise defined differential dynamical systems which can be analysed through symbolic dynamics and transition matrices. We have a continuous regime, where the time flow is characterized by an ordinary differential equation (ODE) which has explicit solutions, and the singular regime, where the time flow is characterized by an appropriate transformation. The symbolic codification is given through the association of a symbol for each distinct regular system and singular system. The transition matrices are then determined as linear approximations to the symbolic dynamics. We analyse the dependence on initial conditions, parameter variation and the occurrence of global strange attractors.

Detailed analysis of a conservative difference approximation for the time fractional diffusion equation

Diffusion equations that use time fractional derivatives are attractive because they describe a wealth of problems involving non-Markovian Random walks. The time fractional diffusion equation (TFDE) is obtained from the standard diffusion equation by replacing the first-order time derivative with a fractional derivative of order α ∈ (0, 1). Developing numerical methods for solving fractional partial differential equations is a new research field and the theoretical analysis of the numerical methods associated with them is not fully developed. In this paper an explicit conservative difference approximation (ECDA) for TFDE is proposed. We give a detailed analysis for this ECDA and generate discrete models of random walk suitable for simulating random variables whose spatial probability density evolves in time according to this fractional diffusion equation. The stability and convergence of the ECDA for TFDE in a bounded domain are discussed. Finally, some numerical examples are presented to show the application of the present technique.

On the zeros of the Abelian integrals for a class of Liénard systems

A planar polynomial differential system has a finite number of limit cycles. However, finding the upper bound of the number of limit cycles is an open problem for the general nonlinear dynamical systems. In this paper, we investigated a class of Liénard systems of the form x'=y, y'=f(x)+y g(x) with deg f=5 and deg g=4. We proved that the related elliptic integrals of the Liénard systems have at most three zeros including multiple zeros, which implies that the number of limit cycles bifurcated from the periodic orbits of the unperturbed system is less than or equal to 3.

Implicit difference approximation for the time fractional diffusion equation

In this paper, we consider a time fractional diffusion equation on a finite domain. The equation is obtained from the standard diffusion equation by replacing the first-order time derivative by a fractional derivative (of order $0<\alpha<1$ ). We propose a computationally effective implicit difference approximation to solve the time fractional diffusion equation. Stability and convergence of the method are discussed. We prove that the implicit difference approximation (IDA) is unconditionally stable, and the IDA is convergent with $O(\tau+h^2)$, where $\tau$ and $h$ are time and space steps, respectively. Some numerical examples are presented to show the application of the present technique.

A Petrov-Galerkin method for a singularly perturbed ordinary differential equation with non-smooth data

In this paper, a singularly perturbed ordinary differential equation with non-smooth data is considered. The numerical method is generated by means of a Petrov-Galerkin finite element method with the piecewise-exponential test function and the piecewise-linear trial function. At the discontinuous point of the coefficient, a special technique is used. The method is shown to be first-order accurate and singular perturbation parameter uniform convergence. Finally, numerical results are presented, which are in agreement with theoretical results.