1,182 research outputs found
Dense packing crystal structures of physical tetrahedra
We present a method for discovering dense packings of general convex hard
particles and apply it to study the dense packing behavior of a one-parameter
family of particles with tetrahedral symmetry representing a deformation of the
ideal mathematical tetrahedron into a less ideal, physical, tetrahedron and all
the way to the sphere. Thus, we also connect the two well studied problems of
sphere packing and tetrahedron packing on a single axis. Our numerical results
uncover a rich optimal-packing behavior, compared to that of other continuous
families of particles previously studied. We present four structures as
candidates for the optimal packing at different values of the parameter,
providing an atlas of crystal structures which might be observed in systems of
nano-particles with tetrahedral symmetry
On the security of a new image encryption scheme based on chaotic map lattices
This paper reports a detailed cryptanalysis of a recently proposed encryption
scheme based on the logistic map. Some problems are emphasized concerning the
key space definition and the implementation of the cryptosystem using
floating-point operations. It is also shown how it is possible to reduce
considerably the key space through a ciphertext-only attack. Moreover, a timing
attack allows the estimation of part of the key due to the existent
relationship between this part of the key and the encryption/decryption time.
As a result, the main features of the cryptosystem do not satisfy the demands
of secure communications. Some hints are offered to improve the cryptosystem
under study according to those requirements.Comment: 8 pages, 8 Figure
On Adversarial Examples and Stealth Attacks in Artificial Intelligence Systems
In this work we present a formal theoretical framework for assessing and
analyzing two classes of malevolent action towards generic Artificial
Intelligence (AI) systems. Our results apply to general multi-class classifiers
that map from an input space into a decision space, including artificial neural
networks used in deep learning applications. Two classes of attacks are
considered. The first class involves adversarial examples and concerns the
introduction of small perturbations of the input data that cause
misclassification. The second class, introduced here for the first time and
named stealth attacks, involves small perturbations to the AI system itself.
Here the perturbed system produces whatever output is desired by the attacker
on a specific small data set, perhaps even a single input, but performs as
normal on a validation set (which is unknown to the attacker). We show that in
both cases, i.e., in the case of an attack based on adversarial examples and in
the case of a stealth attack, the dimensionality of the AI's decision-making
space is a major contributor to the AI's susceptibility. For attacks based on
adversarial examples, a second crucial parameter is the absence of local
concentrations in the data probability distribution, a property known as
Smeared Absolute Continuity. According to our findings, robustness to
adversarial examples requires either (a) the data distributions in the AI's
feature space to have concentrated probability density functions or (b) the
dimensionality of the AI's decision variables to be sufficiently small. We also
show how to construct stealth attacks on high-dimensional AI systems that are
hard to spot unless the validation set is made exponentially large
Information mobility in complex networks
The concept of information mobility in complex networks is introduced on the basis of a stochastic process taking place in the network. The transition matrix for this process represents the probability that the information arising at a given node is transferred to a target one. We use the fractional powers of this transition matrix to investigate the stochastic process at fractional time intervals. The mobility coefficient is then introduced on the basis of the trace of these fractional powers of the stochastic matrix. The fractional time at which a network diffuses 50% of the information contained in its nodes (1/ k50 ) is also introduced. We then show that the scale-free random networks display better spread of information than the non scale-free ones. We study 38 real-world networks and analyze their performance in spreading information from their nodes. We find that some real-world networks perform even better than the scale-free networks with the same average degree and we point out some of the structural parameters that make this possible
Solution of the Multi-Channel Anderson Impurity Model: Ground state and thermodynamics
We present the solution of the SU(N) x SU(M) Anderson impurity model using
the Bethe-Ansatz. We first explain what extensions to the formalism were
required for the solution. Subsequently we determine the ground state and
derive the thermodynamics over the full range of temperature and fields. We
identify the different regimes of valence fluctuation at high temperatures,
followed by moment formation or intrinsic mixed valence at intermediate
temperatures and a low temperature non-Fermi liquid phase. Among other things
we obtain the impurity entropy, charge valence and specific heat over the full
range of temperature. We show that the low-energy physics is governed by a line
of fixed points. This describes non-Fermi-liquid behavior in the integral
valence regime, associated with moment formation, as well as in the mixed
valence regime where no moment forms.Comment: 28 pages, 8 figures, 1 tabl
Algorithms and literate programs for weighted low-rank approximation with missing data
Linear models identification from data with missing values is posed as a weighted low-rank approximation problem with weights related to the missing values equal to zero. Alternating projections and variable projections methods for solving the resulting problem are outlined and implemented in a literate programming style, using Matlab/Octave's scripting language. The methods are evaluated on synthetic data and real data from the MovieLens data sets
Taking the Pressure Off the Patient - Understanding Digital Rectal Examinations on a Real Subject.
Better understanding of palpation techniques during unsighted physical examinations has mostly been limited to qualitative and quantitative studies of performance of experts whilst conducting examinations on plastic benchtop models. However, little is known about their performance when conducting such examinations on real subjects. OBJECTIVE: The aim of this paper is to better understand palpation techniques of experts whilst conducting a Digital Rectal Examination on a real subject. METHODS: We recruited four consultants from relevant specialties and asked them to conduct two DREs on a Rectal Teaching Assistant whilst wearing small position and pressure sensors on their examining finger. We segmented the relevant anatomy from an MRI taken of the pelvic region, registered 3D models and analysed retrospectively performance in relation to executed tasks, supination/pronation, palpation convex hull and pressure applied. RESULTS: Primary care consultants examined the anatomy more holistically compared to secondary care experts, the maximum pressure applied across experiments is 3.3N, overall the pressure applied on the prostate is higher than that applied to rectal walls, and the urologist participant not only applied the highest pressure but also did so with the highest most prominent frequency (15.4 and 25.3Â Hz). CONCLUSIONS: The results of our research allow for better understanding of experts' technical performance from relevant specialities when conducting a DRE, and suggest the range of pressure applied whilst palpating anatomy. SIGNIFICANCE: This research will be valuable in improving the design of haptics-based learning tools, as well as in encouraging reflection on palpation styles across different specialities to develop metrics of performance
Projection methods in conic optimization
There exist efficient algorithms to project a point onto the intersection of
a convex cone and an affine subspace. Those conic projections are in turn the
work-horse of a range of algorithms in conic optimization, having a variety of
applications in science, finance and engineering. This chapter reviews some of
these algorithms, emphasizing the so-called regularization algorithms for
linear conic optimization, and applications in polynomial optimization. This is
a presentation of the material of several recent research articles; we aim here
at clarifying the ideas, presenting them in a general framework, and pointing
out important techniques
Fast linear algebra is stable
In an earlier paper, we showed that a large class of fast recursive matrix
multiplication algorithms is stable in a normwise sense, and that in fact if
multiplication of -by- matrices can be done by any algorithm in
operations for any , then it can be done
stably in operations for any . Here we extend
this result to show that essentially all standard linear algebra operations,
including LU decomposition, QR decomposition, linear equation solving, matrix
inversion, solving least squares problems, (generalized) eigenvalue problems
and the singular value decomposition can also be done stably (in a normwise
sense) in operations.Comment: 26 pages; final version; to appear in Numerische Mathemati
An algorithm to compute the polar decomposition of a 3 Ă 3 matrix
We propose an algorithm for computing the polar decomposition of a 3 Ă 3 real matrix that is based on the connection between orthogonal matrices and quaternions. An important application is to 3D transformations in the level 3 Cascading Style Sheets specification used in web browsers. Our algorithm is numerically reliable and requires fewer arithmetic operations than the alternative of computing the polar decomposition via the singular value decomposition
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