6,777 research outputs found
On the Anti-Wishart distribution
We provide the probability distribution function of matrix elements each of
which is the inner product of two vectors.
The vectors we are considering here are independently distributed but not
necessarily Gaussian variables.
When the number of components M of each vector is greater than the number of
vectors N, one has a symmetric matrix.
When and the components of each vector are independent Gaussian
variables, the distribution function of the matrix elements was
obtained by Wishart in 1928.
When N > M, what we called the ``Anti-Wishart'' case, the matrix elements are
no longer completely independent because the true degrees of freedom becomes
smaller than the number of matrix elements. Due to this singular nature,
analytical derivation of the probability distribution function is much more
involved than the corresponding Wishart case. For a class of general random
vectors, we obtain the analytical distribution function in a closed form, which
is a product of various factors and delta function constraints, composed of
various determinants. The distribution function of the matrix element for the
case with the same class of random vectors is also obtained as a
by-product. Our result is closely related to and should be valuable for the
study of random magnet problem and information redundancy problem.Comment: to appear in Physica
Decoding Information from noisy, redundant, and intentionally-distorted sources
Advances in information technology reduce barriers to information
propagation, but at the same time they also induce the information overload
problem. For the making of various decisions, mere digestion of the relevant
information has become a daunting task due to the massive amount of information
available. This information, such as that generated by evaluation systems
developed by various web sites, is in general useful but may be noisy and may
also contain biased entries. In this study, we establish a framework to
systematically tackle the challenging problem of information decoding in the
presence of massive and redundant data. When applied to a voting system, our
method simultaneously ranks the raters and the ratees using only the evaluation
data, consisting of an array of scores each of which represents the rating of a
ratee by a rater. Not only is our appraoch effective in decoding information,
it is also shown to be robust against various hypothetical types of noise as
well as intentional abuses.Comment: 19 pages, 5 figures, accepted for publication in Physica
Qubit Mapping Toward Quantum Advantage
Qubit Mapping is a pivotal stage in quantum compilation flow. Its goal is to
convert logical circuits into physical circuits so that a quantum algorithm can
be executed on real-world non-fully connected quantum devices. Qubit Mapping
techniques nowadays still lack the key to quantum advantage, scalability.
Several studies have proved that at least thousands of logical qubits are
required to achieve quantum computational advantage. However, to our best
knowledge, there is no previous research with the ability to solve the qubit
mapping problem with the necessary number of qubits for quantum advantage in a
reasonable time. In this work, we provide the first qubit mapping framework
with the scalability to achieve quantum advantage while accomplishing a fairly
good performance. The framework also boasts its flexibility for quantum
circuits of different characteristics. Experimental results show that the
proposed mapping method outperforms the state-of-the-art methods on quantum
circuit benchmarks by improving over 5% of the cost complexity in one-tenth of
the program running time. Moreover, we demonstrate the scalability of our
method by accomplishing mapping of an 11,969-qubit Quantum Fourier Transform
within five hours
Heat Conduction Process on Community Networks as a Recommendation Model
Using heat conduction mechanism on a social network we develop a systematic
method to predict missing values as recommendations. This method can treat very
large matrices that are typical of internet communities. In particular, with an
innovative, exact formulation that accommodates arbitrary boundary condition,
our method is easy to use in real applications. The performance is assessed by
comparing with traditional recommendation methods using real data.Comment: 4 pages, 2 figure
KINETIC ANALYSIS OF THE UPPER EXTREMITY BETWEEN DIFFERENT STANCES IN TENNIS TWO-HANDED BACKHAND
INTRODUCTION: Now the tennis players could explore more racket capabilities through the change of racket materials and design. The open stance comes out in modern tennis relative to the traditional square stance. This study was conducted to analyze the upper extremity joint forces and moments between the different stances in advanced and intermediate athletes, who separated from ITN rating system, during two-handed stroke
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