Strongly Universal Reversible Gate Sets

It is well-known that the Toffoli gate and the negation gate together yield a universal gate set, in the sense that every permutation of $\{0,1\}^n$ can be implemented as a composition of these gates. Since every bit operation that does not use all of the bits performs an even permutation, we need to use at least one auxiliary bit to perform every permutation, and it is known that one bit is indeed enough. Without auxiliary bits, all even permutations can be implemented. We generalize these results to non-binary logic: If $A$ is a finite set of odd cardinality then a finite gate set can generate all permutations of $A^n$ for all $n$, without any auxiliary symbols. If the cardinality of $A$ is even then, by the same argument as above, only even permutations of $A^n$ can be implemented for large $n$, and we show that indeed all even permutations can be obtained from a finite universal gate set. We also consider the conservative case, that is, those permutations of $A^n$ that preserve the weight of the input word. The weight is the vector that records how many times each symbol occurs in the word. It turns out that no finite conservative gate set can, for all $n$, implement all conservative even permutations of $A^n$ without auxiliary bits. But we provide a finite gate set that can implement all those conservative permutations that are even within each weight class of $A^n$.Comment: Submitted to Rev Comp 201

Recruitment Market Trend Analysis with Sequential Latent Variable Models

Recruitment market analysis provides valuable understanding of industry-specific economic growth and plays an important role for both employers and job seekers. With the rapid development of online recruitment services, massive recruitment data have been accumulated and enable a new paradigm for recruitment market analysis. However, traditional methods for recruitment market analysis largely rely on the knowledge of domain experts and classic statistical models, which are usually too general to model large-scale dynamic recruitment data, and have difficulties to capture the fine-grained market trends. To this end, in this paper, we propose a new research paradigm for recruitment market analysis by leveraging unsupervised learning techniques for automatically discovering recruitment market trends based on large-scale recruitment data. Specifically, we develop a novel sequential latent variable model, named MTLVM, which is designed for capturing the sequential dependencies of corporate recruitment states and is able to automatically learn the latent recruitment topics within a Bayesian generative framework. In particular, to capture the variability of recruitment topics over time, we design hierarchical dirichlet processes for MTLVM. These processes allow to dynamically generate the evolving recruitment topics. Finally, we implement a prototype system to empirically evaluate our approach based on real-world recruitment data in China. Indeed, by visualizing the results from MTLVM, we can successfully reveal many interesting findings, such as the popularity of LBS related jobs reached the peak in the 2nd half of 2014, and decreased in 2015.Comment: 11 pages, 30 figure, SIGKDD 201

Administration of Interleukin-15 Peptide Improves Cardiac Function in a Mouse Model of Myocardial Infarction.

Interleukin-15 is a pleotropic factor, capable of modulating metabolism, survival, proliferation, and differentiation in many different cell types. The rationale behind this study relates to previous work demonstrating that IL-15 is a major factor present in stem cell extracts, which protects cardiomyocytes subjected to hypoxic stress in vitro. The objective of this current study was to assess whether administration of IL-15 peptide will also show protective effects in vivo. The data indicate that administration of IL-15 reduces cell death, increases vascularity, decreases scar size, and significantly improves left ventricular ejection fraction in a mouse model of myocardial infarction

Plasmon Resonances in Nanoparticles, Their Applications to Magnetics and Relation to the Riemann Hypothesis

The review of the mathematical treatment of plasmon resonances as an eigenvalue problem for specific boundary integral equations is presented and general properties of plasmon spectrum are outlined. Promising applications of plasmon resonances to magnetics are described. Interesting relation of eigenvalue treatment of plasmon resonances to the Riemann hypothesis is discussed.Comment: 10 pages; misprints corrected, some explanations added. Physica B (2011

Theory of Dicke narrowing in coherent population trapping

The Doppler effect is one of the dominant broadening mechanisms in thermal vapor spectroscopy. For two-photon transitions one would naively expect the Doppler effect to cause a residual broadening, proportional to the wave-vector difference. In coherent population trapping (CPT), which is a narrow-band phenomenon, such broadening was not observed experimentally. This has been commonly attributed to frequent velocity-changing collisions, known to narrow Doppler-broadened one-photon absorption lines (Dicke narrowing). Here we show theoretically that such a narrowing mechanism indeed exists for CPT resonances. The narrowing factor is the ratio between the atom's mean free path and the wavelength associated with the wave-vector difference of the two radiation fields. A possible experiment to verify the theory is suggested.Comment: 6 pages, 2 figures; Introduction revise

Noncommutativity and Discrete Physics

The purpose of this paper is to present an introduction to a point of view for discrete foundations of physics. In taking a discrete stance, we find that the initial expression of physical theory must occur in a context of noncommutative algebra and noncommutative vector analysis. In this way the formalism of quantum mechanics occurs first, but not necessarily with the usual interpretations. The basis for this work is a non-commutative discrete calculus and the observation that it takes one tick of the discrete clock to measure momentum.Comment: LaTeX, 23 pages, no figure

On-line construction of position heaps

We propose a simple linear-time on-line algorithm for constructing a position heap for a string [Ehrenfeucht et al, 2011]. Our definition of position heap differs slightly from the one proposed in [Ehrenfeucht et al, 2011] in that it considers the suffixes ordered from left to right. Our construction is based on classic suffix pointers and resembles the Ukkonen's algorithm for suffix trees [Ukkonen, 1995]. Using suffix pointers, the position heap can be extended into the augmented position heap that allows for a linear-time string matching algorithm [Ehrenfeucht et al, 2011].Comment: to appear in Journal of Discrete Algorithm

The ideal energy of classical lattice dynamics

We define, as local quantities, the least energy and momentum allowed by quantum mechanics and special relativity for physical realizations of some classical lattice dynamics. These definitions depend on local rates of finite-state change. In two example dynamics, we see that these rates evolve like classical mechanical energy and momentum.Comment: 12 pages, 4 figures, includes revised portion of arXiv:0805.335

Clifford algebras and universal sets of quantum gates

In this paper is shown an application of Clifford algebras to the construction of computationally universal sets of quantum gates for $n$-qubit systems. It is based on the well-known application of Lie algebras together with the especially simple commutation law for Clifford algebras, which states that all basic elements either commute or anticommute.Comment: 4 pages, REVTeX (2 col.), low-level language corrections, PR