Abstract: A new decomposition form is introduced in this report
to establish a criterion for the bi-partite separability of Bell diagonal
states. A such criterion takes a quadratic inequality of the coefficients
of a given Bell diagonal states and can be derived via a simple
algorithmic calculation of its invariants. In addition, the criterion can
be extended to a quantum system of higher dimension.
Abstract: This paper is motivated by the aspect of uncertainty in
financial decision making, and how artificial intelligence and soft
computing, with its uncertainty reducing aspects can be used for
algorithmic trading applications that trade in high frequency.
This paper presents an optimized high frequency trading system that
has been combined with various moving averages to produce a hybrid
system that outperforms trading systems that rely solely on moving
averages. The paper optimizes an adaptive neuro-fuzzy inference
system that takes both the price and its moving average as input,
learns to predict price movements from training data consisting of
intraday data, dynamically switches between the best performing
moving averages, and performs decision making of when to buy or
sell a certain currency in high frequency.
Abstract: Clustering in high dimensional space is a difficult
problem which is recurrent in many fields of science and
engineering, e.g., bioinformatics, image processing, pattern
reorganization and data mining. In high dimensional space some of
the dimensions are likely to be irrelevant, thus hiding the possible
clustering. In very high dimensions it is common for all the objects in
a dataset to be nearly equidistant from each other, completely
masking the clusters. Hence, performance of the clustering algorithm
decreases.
In this paper, we propose an algorithmic framework which
combines the (reduct) concept of rough set theory with the k-means
algorithm to remove the irrelevant dimensions in a high dimensional
space and obtain appropriate clusters. Our experiment on test data
shows that this framework increases efficiency of the clustering
process and accuracy of the results.
Abstract: Groups where the discrete logarithm problem (DLP) is believed to be intractable have proved to be inestimable building blocks for cryptographic applications. They are at the heart of numerous protocols such as key agreements, public-key cryptosystems, digital signatures, identification schemes, publicly verifiable secret sharings, hash functions and bit commitments. The search for new groups with intractable DLP is therefore of great importance.The goal of this article is to study elliptic curves over the ring Fq[], with Fq a finite field of order q and with the relation n = 0, n ≥ 3. The motivation for this work came from the observation that several practical discrete logarithm-based cryptosystems, such as ElGamal, the Elliptic Curve Cryptosystems . In a first time, we describe these curves defined over a ring. Then, we study the algorithmic properties by proposing effective implementations for representing the elements and the group law. In anther article we study their cryptographic properties, an attack of the elliptic discrete logarithm problem, a new cryptosystem over these curves.