227 research outputs found
Dynamical order, disorder and propagating defects in homogeneous system of relaxation oscillators
Reaction-diffusion (RD) mechanisms in chemical and biological systems can
yield a variety of patterns that may be functionally important. We show that
diffusive coupling through the inactivating component in a generic model of
coupled relaxation oscillators give rise to a wide range of spatio-temporal
phenomena. Apart from analytically explaining the genesis of anti-phase
synchronization and spatially patterned oscillatory death regimes in the model
system, we report the existence of a chimera state, characterized by spatial
co-occurrence of patches with distinct dynamics. We also observe propagating
phase defects in both one- and two-dimensional media resembling persistent
structures in cellular automata, whose interactions may be used for computation
in RD systems.Comment: 6 pages, 4 figure
Combinatorial Games with a Pass: A dynamical systems approach
By treating combinatorial games as dynamical systems, we are able to address
a longstanding open question in combinatorial game theory, namely, how the
introduction of a "pass" move into a game affects its behavior. We consider two
well known combinatorial games, 3-pile Nim and 3-row Chomp. In the case of Nim,
we observe that the introduction of the pass dramatically alters the game's
underlying structure, rendering it considerably more complex, while for Chomp,
the pass move is found to have relatively minimal impact. We show how these
results can be understood by recasting these games as dynamical systems
describable by dynamical recursion relations. From these recursion relations we
are able to identify underlying structural connections between these "games
with passes" and a recently introduced class of "generic (perturbed) games."
This connection, together with a (non-rigorous) numerical stability analysis,
allows one to understand and predict the effect of a pass on a game.Comment: 39 pages, 13 figures, published versio
A new heap game
Given heaps of tokens. The moves of the 2-player game introduced
here are to either take a positive number of tokens from at most heaps,
or to remove the {\sl same} positive number of tokens from all the heaps.
We analyse this extension of Wythoff's game and provide a polynomial-time
strategy for it.Comment: To appear in Computer Games 199
Analysis of reaction and timing attacks against cryptosystems based on sparse parity-check codes
In this paper we study reaction and timing attacks against cryptosystems
based on sparse parity-check codes, which encompass low-density parity-check
(LDPC) codes and moderate-density parity-check (MDPC) codes. We show that the
feasibility of these attacks is not strictly associated to the quasi-cyclic
(QC) structure of the code but is related to the intrinsically probabilistic
decoding of any sparse parity-check code. So, these attacks not only work
against QC codes, but can be generalized to broader classes of codes. We
provide a novel algorithm that, in the case of a QC code, allows recovering a
larger amount of information than that retrievable through existing attacks and
we use this algorithm to characterize new side-channel information leakages. We
devise a theoretical model for the decoder that describes and justifies our
results. Numerical simulations are provided that confirm the effectiveness of
our approach
An efficient quantum algorithm for finding hidden parabolic subgroups in the general linear group
Codes for the Quantum Erasure Channel
The quantum erasure channel (QEC) is considered. Codes for the QEC have to
correct for erasures, i. e., arbitrary errors at known positions. We show that
four qubits are necessary and sufficient to encode one qubit and correct one
erasure, in contrast to five qubits for unknown positions. Moreover, a family
of quantum codes for the QEC, the quantum BCH codes, that can be efficiently
decoded is introduced.Comment: 6 pages, RevTeX, no figures, submitted to Physical Review A, code
extended to encode 2 qubits, references adde
Strategic Insights From Playing the Quantum Tic-Tac-Toe
In this paper, we perform a minimalistic quantization of the classical game
of tic-tac-toe, by allowing superpositions of classical moves. In order for the
quantum game to reduce properly to the classical game, we require legal quantum
moves to be orthogonal to all previous moves. We also admit interference
effects, by squaring the sum of amplitudes over all moves by a player to
compute his or her occupation level of a given site. A player wins when the
sums of occupations along any of the eight straight lines we can draw in the grid is greater than three. We play the quantum tic-tac-toe first
randomly, and then deterministically, to explore the impact different opening
moves, end games, and different combinations of offensive and defensive
strategies have on the outcome of the game. In contrast to the classical
tic-tac-toe, the deterministic quantum game does not always end in a draw. In
contrast also to most classical two-player games of no chance, it is possible
for Player 2 to win. More interestingly, we find that Player 1 enjoys an
overwhelming quantum advantage when he opens with a quantum move, but loses
this advantage when he opens with a classical move. We also find the quantum
blocking move, which consists of a weighted superposition of moves that the
opponent could use to win the game, to be very effective in denying the
opponent his or her victory. We then speculate what implications these results
might have on quantum information transfer and portfolio optimization.Comment: 20 pages, 3 figures, and 3 tables. LaTeX 2e using iopart class, and
braket, color, graphicx, multirow, subfig, url package
LEDAkem: a post-quantum key encapsulation mechanism based on QC-LDPC codes
This work presents a new code-based key encapsulation mechanism (KEM) called
LEDAkem. It is built on the Niederreiter cryptosystem and relies on
quasi-cyclic low-density parity-check codes as secret codes, providing high
decoding speeds and compact keypairs. LEDAkem uses ephemeral keys to foil known
statistical attacks, and takes advantage of a new decoding algorithm that
provides faster decoding than the classical bit-flipping decoder commonly
adopted in this kind of systems. The main attacks against LEDAkem are
investigated, taking into account quantum speedups. Some instances of LEDAkem
are designed to achieve different security levels against classical and quantum
computers. Some performance figures obtained through an efficient C99
implementation of LEDAkem are provided.Comment: 21 pages, 3 table
An iterative algorithm for parametrization of shortest length shift registers over finite rings
The construction of shortest feedback shift registers for a finite sequence
S_1,...,S_N is considered over the finite ring Z_{p^r}. A novel algorithm is
presented that yields a parametrization of all shortest feedback shift
registers for the sequence of numbers S_1,...,S_N, thus solving an open problem
in the literature. The algorithm iteratively processes each number, starting
with S_1, and constructs at each step a particular type of minimal Gr\"obner
basis. The construction involves a simple update rule at each step which leads
to computational efficiency. It is shown that the algorithm simultaneously
computes a similar parametrization for the reciprocal sequence S_N,...,S_1.Comment: Submitte
Computing with Liquid Crystal Fingers: Models of geometric and logical computation
When a voltage is applied across a thin layer of cholesteric liquid crystal,
fingers of cholesteric alignment can form and propagate in the layer. In
computer simulation, based on experimental laboratory results, we demonstrate
that these cholesteric fingers can solve selected problems of computational
geometry, logic and arithmetics. We show that branching fingers approximate a
planar Voronoi diagram, and non-branching fingers produce a convex subdivision
of concave polygons. We also provide a detailed blue-print and simulation of a
one-bit half-adder functioning on the principles of collision-based computing,
where the implementation is via collision of liquid crystal fingers with
obstacles and other fingers.Comment: submitted Sept 201
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