416 research outputs found
Mathematical Model of Strong Physically Unclonable Functions Based on Hybrid Boolean Networks
We introduce a mathematical framework for simulating Hybrid Boolean Network
(HBN) Physically Unclonable Functions (PUFs, HBN-PUFs). We verify that the
model is able to reproduce the experimentally observed PUF statistics for
uniqueness and reliability obtained from
experiments of HBN-PUFs on Cyclone V FPGAs. Our results suggest that the
HBN-PUF is a true `strong' PUF in the sense that its security properties depend
exponentially on both the manufacturing variation and the challenge-response
space. Our Python simulation methods are open-source and available at
https://github.com/Noeloikeau/networkm.Comment: Presented at HOST 2022 conference. This work has been submitted to
the IEEE for possible publication. Copyright may be transferred without
notice, after which this version may no longer be accessibl
Feedback control of unstable cellular solidification fronts
We present a numerical and experimental study of feedback control of unstable
cellular patterns in directional solidification (DS). The sample, a dilute
binary alloy, solidifies in a 2D geometry under a control scheme which applies
local heating close to the cell tips which protrude ahead of the other. For the
experiments, we use a real-time image processing algorithm to track cell tips,
coupled with a movable laser spot array device, to heat locally. We show,
numerically and experimentally, that spacings well below the threshold for a
period-doubling instability can be stabilized. As predicted by the numerical
calculations, cellular arrays become stable, and the spacing becomes uniform
through feedback control which is maintained with minimal heating.Comment: 4 pages, 4 figures, 1 tabl
A hyperelliptic smoothness test, I
Wetensch. publicatieFaculteit der Wiskunde en Natuurwetenschappe
Multiplicative Structure of Values of the Euler Function
This is a preprint of a book chapter published in High Primes and Misdemeanours: Lectures in Honour of the 60th Birthday of Hugh Cowie Williams, Fields Institute Communications, AMS (2004). © American Mathematical Society.We establish upper bounds for the number of smooth values of the Euler function. In particular, although the Euler function has
a certain “smoothing” effect on its integer arguments, our results show that, in fact, most values produced by the Euler function are not smooth. We apply our results to study the distribution of “strong primes”, which are commonly encountered in cryptography. We also consider the problem of obtaining upper and lower bounds for the number of positive integers n ≤ x for which the value of the Euler function φ (n) is a perfect square and also for the number of n ≤ x such that φ (n) is squarefull. We give similar bounds for the Carmichael function λ (n)
On the Directional Derivative of Kemeny's Constant
In a connected graph, Kemeny's constant gives the expected time of a random
walk from an arbitrary vertex to reach a randomly-chosen vertex .
Because of this, Kemeny's constant can be interpreted as a measure of how well
a graph is connected. It is generally unknown how the addition or removal of
edges affects Kemeny's constant. Inspired by the directional derivative of the
normalized Laplacian, we derive the directional derivative of Kemeny's constant
for several graph families. In addition, we find sharp bounds for the
directional derivative of an eigenvalue of the normalized Laplacian and bounds
for the directional derivative of Kemeny's constant
A Quantum Mechanical Model of Spherical Supermembranes
We present a quantum mechanical model of spherical supermembranes. Using
superfields to represent the cartesian coordinates of the membrane, we are able
to exactly determine its supersymmetric vacua. We find there are two classical
vacua, one corresponding to an extended membrane and one corresponding to a
point-like membrane. For the case, instanton effects then
lift these vacua to massive states. For the case, there is
no instanton tunneling, and the vacua remain massless. Similarities to
spherical supermembranes as giant gravitons and in Matrix theory on pp-waves is
discussed.Comment: 9 page
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