510 research outputs found
Weak randomness completely trounces the security of QKD
In usual security proofs of quantum protocols the adversary (Eve) is expected
to have full control over any quantum communication between any communicating
parties (Alice and Bob). Eve is also expected to have full access to an
authenticated classical channel between Alice and Bob. Unconditional security
against any attack by Eve can be proved even in the realistic setting of device
and channel imperfection. In this Letter we show that the security of QKD
protocols is ruined if one allows Eve to possess a very limited access to the
random sources used by Alice. Such knowledge should always be expected in
realistic experimental conditions via different side channels
The escape problem under stochastic volatility: the Heston model
We solve the escape problem for the Heston random diffusion model. We obtain
exact expressions for the survival probability (which ammounts to solving the
complete escape problem) as well as for the mean exit time. We also average the
volatility in order to work out the problem for the return alone regardless
volatility. We look over these results in terms of the dimensionless normal
level of volatility --a ratio of the three parameters that appear in the Heston
model-- and analyze their form in several assymptotic limits. Thus, for
instance, we show that the mean exit time grows quadratically with large spans
while for small spans the growth is systematically slower depending on the
value of the normal level. We compare our results with those of the Wiener
process and show that the assumption of stochastic volatility, in an apparent
paradoxical way, increases survival and prolongs the escape time.Comment: 29 pages, 12 figure
Quantum Sign Permutation Polytopes
Convex polytopes are convex hulls of point sets in the -dimensional space
\E^n that generalize 2-dimensional convex polygons and 3-dimensional convex
polyhedra. We concentrate on the class of -dimensional polytopes in \E^n
called sign permutation polytopes. We characterize sign permutation polytopes
before relating their construction to constructions over the space of quantum
density matrices. Finally, we consider the problem of state identification and
show how sign permutation polytopes may be useful in addressing issues of
robustness
2D pattern evolution constrained by complex network dynamics
Complex networks have established themselves along the last years as being
particularly suitable and flexible for representing and modeling several
complex natural and human-made systems. At the same time in which the
structural intricacies of such networks are being revealed and understood,
efforts have also been directed at investigating how such connectivity
properties define and constrain the dynamics of systems unfolding on such
structures. However, lesser attention has been focused on hybrid systems,
\textit{i.e.} involving more than one type of network and/or dynamics. Because
several real systems present such an organization (\textit{e.g.} the dynamics
of a disease coexisting with the dynamics of the immune system), it becomes
important to address such hybrid systems. The current paper investigates a
specific system involving a diffusive (linear and non-linear) dynamics taking
place in a regular network while interacting with a complex network of
defensive agents following Erd\"os-R\'enyi and Barab\'asi-Albert graph models,
whose nodes can be displaced spatially. More specifically, the complex network
is expected to control, and if possible to extinguish, the diffusion of some
given unwanted process (\textit{e.g.} fire, oil spilling, pest dissemination,
and virus or bacteria reproduction during an infection). Two types of pattern
evolution are considered: Fick and Gray-Scott. The nodes of the defensive
network then interact with the diffusing patterns and communicate between
themselves in order to control the spreading. The main findings include the
identification of higher efficiency for the Barab\'asi-Albert control networks.Comment: 18 pages, 32 figures. A working manuscript, comments are welcome
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Preface
Preface - The second International Conference on Mathematical Modeling in Physical Sciences (IC-MSQUARE) took place at Prague, Czech Republic, from Sunday 1 September to Thursday 5 September 2013
Rendering an Account: An Open-State Archive in Postgraduate Supervision
The paper begins with a brief account of the transformation of research degree studies under the pressures of global capitalism and neo-liberal governmentality. A parallel transformation is occurring in the conduct of research through the use of information and communication technologies. Yet the potential of ICTs to shape practices of surveillance or to produce new student-supervisor relations and enhance the processes of developing the dissertation has received almost no critical attention. As doctoral supervisor and student, we then describe the features and uses of a web-based open state archive of the student's work-in-progress, developed by the student and accessible to his supervisor. Our intention was to encourage more open conversations between data and theorising, student and supervisor, and ultimately between the student and professional community. However, we recognise that relations of accountability, as these have developed within a contemporary "audit revolution" (Power, 1994, 1997) in universities, create particular "lines of visibility" (Munro, 1996). Thus while the open-state archive may help to redefine in less managerial terms notions of quality, transparency, flexibility and accountability, it might also make possible greater supervisory surveillance. How should we think about the panoptical potential of this archive? We argue that the diverse kinds of interactional patterns and pedagogical intervention it encourages help to create shifting subjectivities. Moreover, the archive itself is multiple, in bringing together an array of diverse materials that can be read in various ways, by following multiple paths. It therefore constitutes a collage, which we identify as a mode of cognition and of accounting distinct from but related to argument and narrative. As a more "open" text (Iser, 1978) it has an indeterminacy which may render it less open to abuse for the technologies of managerial accountability
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Lookback option pricing using the Fourier transform B-spline method
We derive a new, efficient closed-form formula approximating the price of discrete lookback options, whose underlying asset price is driven by an exponential semimartingale process, which includes (jump) diffusions, LĂ©vy models, affine processes and other models. The derivation of our pricing formula is based on inverting the Fourier transform using B-spline approximation theory. We give an error bound for our formula and establish its fast rate of convergence to the true price. Our method provides lookback option prices across the quantum of strike prices with greater efficiency than for a single strike price under existing methods. We provide an alternative proof to the Spitzer formula for the characteristic function of the maximum of a discretely observed stochastic process, which yields a numerically efficient algorithm based on convolutions. This is an important result which could have a wide range of applications in which the Spitzer formula is utilized. We illustrate the numerical efficiency of our algorithm by applying it in pricing fixed and floating discrete lookback options under Brownian motion, jump diffusion models, and the variance gamma process
A finite difference method for pricing European and American options under a geometric LĂ©vy process
In this paper we develop a numerical approach to a fractional-order differential Linear Complementarity Problem (LCP) arising in pricing European and American options under a geometric LĂ©vy process. The LCP is first approximated by a nonlinear penalty fractional Black-Scholes (fBS) equation. We then propose a finite difference scheme for the penalty fBS equation. We show that both the continuous and the discretized fBS equations are uniquely solvable and establish the convergence of the numerical solution to the viscosity solution of the penalty fBS equation by proving the consistency, stability and monotonicity of the numerical scheme. We also show that the discretization has the 2nd-order truncation error in both the spatial and time mesh sizes. Numerical results are presented to demonstrate the accuracy and usefulness of the numerical method for pricing both European and American options under the geometric LĂ©vy process
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