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 $N\times N$ symmetric matrix. When $M\ge N$ and the components of each vector are independent Gaussian variables, the distribution function of the $N(N+1)/2$ 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 $M\ge N$ 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

The role of thrombomodulin lectin-like domain in inflammation

Thrombomodulin (TM) is a cell surface glycoprotein which is widely expressed in a variety of cell types. It is a cofactor for thrombin binding that mediates protein C activation and inhibits thrombin activity. In addition to its anticoagulant activity, recent evidence has revealed that TM, especially its lectin-like domain, has potent anti-inflammatory function through a variety of molecular mechanisms. The lectin-like domain of TM plays an important role in suppressing inflammation independent of the TM anticoagulant activity. This article makes an extensive review of the role of TM in inflammation. The molecular targets of TM lectin-like domain have also been elucidated. Recombinant TM protein, especially the TM lectin-like domain may play a promising role in the management of sepsis, glomerulonephritis and arthritis. These data demonstrated the potential therapeutic role of TM in the treatment of inflammatory diseases

Emergence of topological phases from the extension of two-dimensional lattice with nonsymmorphic symmetries

Young and Kane have given a great insight for 2D Dirac semimetals with nontrivial topology in the presence of nonsymmorphic crystalline symmetry. Based on one of 2D nonsymmorphic square lattice structures they proposed, we further construct a set of 3D minimal tight-binding models via vertically stacking the 2D nonsymmorphic lattice. Specifically, our model provides a platform to generate three topologically semimetallic phases such as Dirac nodal line semimetals, Weyl nodal line semimetals and Weyl semimetals. The off-centered mirror symmetry sufficiently protects nodal lines emerging within mirror-invariant plane with a nontrivial mirror invariant $n_{M\mathbb{Z}}$, whereas twofold screw rotational symmetry protects nontrivial Weyl nodal points with topological charge $C=2$. Interestingly, Weyl nodal loops are generated without mirror symmetry protection, where nontrivial "drumhead" surface states emerge within loops. In the presence of both time-reversal and inversion symmetries, the emergence of weak topological insulator phases is discussed as well.Comment: 8 pages, 6 figures and 1 tabl