A systematic construction of integrable delay-difference and delay-differential analogues of soliton equations

We propose a systematic method for constructing integrable delay-difference and delay-differential analogues of known soliton equations such as the Lotka-Volterra, Toda lattice, and sine-Gordon equations and their multi-soliton solutions. It is carried out by applying a reduction and delay-differential limit to the discrete KP or discrete two-dimensional Toda lattice equations. Each of the delay-difference and delay-differential equations has the N-soliton solution, which depends on the delay parameter and converges to an N-soliton solution of a known soliton equation as the delay parameter approaches 0.Comment: 15 page

A delay analogue of the box and ball system arising from the ultra-discretization of the delay discrete Lotka-Volterra equation

A delay analogue of the box and ball system (BBS) is presented. This new soliton cellular automaton is constructed by the ultra-discretization of the delay discrete Lotka-Volterra equation, which is an integrable delay analogue of the discrete Lotka-Volterra equation. This delay BBS requires multiple time initial states for time evolution, thus it has various types of soliton patterns. Soliton patterns generated by the delay BBS are classified into normal solitons and abnormal solitons. Normal solitons can be discussed analytically, while abnormal solitons show various phenomena which are not explained easily. Finally, we show that the delay BBS is equivalent to the BBS with K kinds of balls if we consider only normal solitons

An IPW-based Unbiased Ranking Metric in Two-sided Markets

In modern recommendation systems, unbiased learning-to-rank (LTR) is crucial for prioritizing items from biased implicit user feedback, such as click data. Several techniques, such as Inverse Propensity Weighting (IPW), have been proposed for single-sided markets. However, less attention has been paid to two-sided markets, such as job platforms or dating services, where successful conversions require matching preferences from both users. This paper addresses the complex interaction of biases between users in two-sided markets and proposes a tailored LTR approach. We first present a formulation of feedback mechanisms in two-sided matching platforms and point out that their implicit feedback may include position bias from both user groups. On the basis of this observation, we extend the IPW estimator and propose a new estimator, named two-sided IPW, to address the position bases in two-sided markets. We prove that the proposed estimator satisfies the unbiasedness for the ground-truth ranking metric. We conducted numerical experiments on real-world two-sided platforms and demonstrated the effectiveness of our proposed method in terms of both precision and robustness. Our experiments showed that our method outperformed baselines especially when handling rare items, which are less frequently observed in the training data

Quantum key distribution with an efficient countermeasure against correlated intensity fluctuations in optical pulses

Quantum key distribution (QKD) allows two distant parties to share secret keys with the proven security even in the presence of an eavesdropper with unbounded computational power. Recently, GHz-clock decoy QKD systems have been realized by employing ultrafast optical communication devices. However, security loopholes of high-speed systems have not been fully explored yet. Here we point out a security loophole at the transmitter of the GHz-clock QKD, which is a common problem in high-speed QKD systems using practical band-width limited devices. We experimentally observe the inter-pulse intensity correlation and modulation-pattern dependent intensity deviation in a practical high-speed QKD system. Such correlation violates the assumption of most security theories. We also provide its countermeasure which does not require significant changes of hardware and can generate keys secure over 100 km fiber transmission. Our countermeasure is simple, effective and applicable to wide range of high-speed QKD systems, and thus paves the way to realize ultrafast and security-certified commercial QKD systems

Investigation of simulated annealing method and its application to optimal design of die mold for orientation of magnetic powder

Factors affecting the convergence characteristics and results obtained by the optimal design method using the finite element method and simulated annealing are investigated systematically, and the optimal parameters for simulated annealing method are obtained. The optimal shape of the die mold for orientation of the magnetic powder (nonlinear magnetostatic problem) is obtained using finite elements and simulated annealing. The experimental verification is also carried out </p

On the evolution and environmental dependence of the star formation rate versus stellar mass relation since z ˜ 2.

This paper discusses the evolution of the correlation between galaxy star formation rates (SFRs) and stellar mass (M*) over the last ∼10 Gyr, particularly focusing on its environmental dependence. We first present the mid-infrared (MIR) properties of the Hα-selected galaxies in a rich cluster Cl 0939+4713 at z = 0.4. We use wide-field Spitzer/MIPS 24 μm data to show that the optically red Hα emitters, which are most prevalent in group-scale environments, tend to have higher SFRs and higher dust extinction than the majority population of blue Hα sources. With an MIR stacking analysis, we find that the median SFR of Hα emitters is higher in higher density environment at z = 0.4. We also find that star-forming galaxies in high-density environment tend to have higher specific SFR (SSFR), although the trend is much less significant compared to that of SFR. This increase of SSFR in high-density environment is not visible when we consider the SFR derived from Hα alone, suggesting that the dust attenuation in galaxies depends on environment; galaxies in high-density environment tend to be dustier (by up to ∼0.5 mag), probably reflecting a higher fraction of nucleated, dusty starbursts in higher density environments at z = 0.4. We then discuss the environmental dependence of the SFR–M* relation for star-forming galaxies since z ∼ 2, by compiling our comparable, narrow-band-selected, large Hα emitter samples in both distant cluster environments and field environments. We find that the SSFR of Hα-selected galaxies (at the fixed mass of log (M*/M⊙) = 10) rapidly evolves as (1 + z)3, but the SFR–M* relation is independent of the environment since z ∼ 2, as far as we rely on the Hα-based SFRs (with M*-dependent extinction correction). Even if we consider the possible environmental variation in the dust attenuation, we conclude that the difference in the SFR–M* relation between cluster and field star-forming galaxies is always small (≲0.2 dex level) at any time in the history of the Universe since z ∼ 2

Collagen gene expression during chondrogenesis from chick periosteum-derived cells

AbstractChick periosteum-derived cells, which do not enter the chondrogenic cell lineage during normal bone development and growth, exhibit chondrogenic potential in high cell density culture conditions. In such cultures, collagen gene expression was temporally analyzed at the mRNA level by a reverse transcription PCR (RT-PCR) procedure, which showed that α1(II) and α1(IX) collagen mRNAs are coordinately increased, coincident with the onset of overt chondrogenesis, and subsequently decreased as chondrocytes exhibited hypertrophic characteristics. α1(X) collagen mRNA was detected well before the onset of chondrogenesis and markedly increased along with the hypertrophic change. For α2(I) collagen, both the bone/tendon form and the cartilage form of mRNA were detected throughout the culture period. This culture system provides an experimental vehicle capable of investigating the molecular events involved in the full range of chondrogenic differentiation starting from uncommitted periosteum-derived mesenchymal stem cells