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Motivated by the sequence reconstruction problem initiated by Levenshtein, reconstruction codes were introduced by Cai et al. to combat errors when a fixed number of noisy channels are available. The central problem on this topic is to design codes with sizes as large as possible, such that every codeword can be uniquely reconstructed from any N distinct noisy reads, where N is fixed. In this paper, we study binary reconstruction codes with the constraint that every codeword is balanced, which is a fundamental requirement in the technique of DNA-based storage. For all possible channels with a single edit error and their variants, we design asymptotically optimal balanced reconstruction codes for all N, and show that the number of their redundant symbols decreases from 3 2 log 2 n + O (1) to 1 2 log 2 n + log 2 log 2 n + O (1) , and finally to 1 2 log 2 n + O (1) but with different speeds, where n is the length of the code. Compared with the unbalanced case, our results imply that the balanced property does not reduce the rate of the reconstruction code in the corresponding codebook. [ABSTRACT FROM AUTHOR]

In this paper, we first generalize the polycyclic codes over finite fields to polycyclic codes over the mixed alphabet Z 2 Z 4 , and we show that these codes can be identified as Z 4 [ x ] -submodules of R α , β with R α , β = Z 2 [ x ] / ⟨ t 1 (x) ⟩ × Z 4 [ x ] / ⟨ t 2 (x) ⟩ , where t 1 (x) and t 2 (x) are monic polynomials over Z 2 and Z 4 , respectively. Then we provide the generator polynomials and minimal generating sets for this family of codes based on the strong Gröbner basis. In particular, under the proper defined inner product, we study the dual of Z 2 Z 4 -additive polycyclic codes. Finally, we focus on the characterization of the Z 2 Z 4 -MDSS and MDSR codes, and as examples, we also present some (almost) optimal binary codes derived from the Z 2 Z 4 -additive polycyclic codes. [ABSTRACT FROM AUTHOR]

Quasi-polycyclic (QP for short) codes over a finite chain ring R are a generalization of quasi-cyclic codes, and these codes can be viewed as an R[x]-submodule of R m ℓ , where R m : = R [ x ] / ⟨ f ⟩ , and f is a monic polynomial of degree m over R. If f factors uniquely into monic and coprime basic irreducibles, then their algebraic structure allow us to characterize the generator polynomials and the minimal generating sets of 1-generator QP codes as R-modules. In addition, we also determine the parity check polynomials for these codes by using the strong Gröbner bases. In particular, via Magma system, some quaternary codes with new parameters are derived from these 1-generator QP codes. [ABSTRACT FROM AUTHOR]

In this paper, a class of additive codes which is referred to as ℤ 2 ℤ 2 [ u , v ] -additive codes is introduced. This is a generalization towards another direction of recently introduced ℤ 2 ℤ 4 codes (Doughterty et al., Appl. Algebra Eng. Commun. Comput. 27(2), 123–138, 7). A MacWilliams-type identity that relates the weight enumerator of a code with its dual is proved. Furthermore, the structure and possible weights for all one-weight and two-weight ℤ 2 ℤ 2 [ u , v ] -additive codes are described. Additionally, we also construct some one-weight and two-weight ℤ 2 ℤ 2 [ u , v ] -additive codes to illustrate our obtained results. [ABSTRACT FROM AUTHOR]

In this paper, several classes of three-weight codes and two-weight codes for the homogeneous metric over the chain ring R = F p + u F p + ⋯ + u k - 1 F p , with u k = 0 , are constructed that generalize the construction of Shi et al. (IEEE Commun. Lett. 20(12):2346–2349, 2016), which is the special case of p = k = 2. These codes are defined as trace codes. In some cases of their defining sets, they are abelian. Their homogeneous weight distributions are computed by using exponential sums. In particular, in the two-weight case, we give some conditions of optimality of their Gray images by using the Griesmer bound. Their dual homogeneous distance is also given. The codewords of these codes are shown to be minimal for inclusion of supports, a fact favorable to an application to secret sharing schemes. [ABSTRACT FROM AUTHOR]

We construct an infinite family of three-Lee-weight codes of dimension 2 m, where m is singly-even, over the ring $\mathbb {F}_{p}+u\mathbb {F}_{p}$ with u =0. These codes are defined as trace codes. They have the algebraic structure of abelian codes. Their Lee weight distribution is computed by using Gauss sums. By Gray mapping, we obtain an infinite family of abelian p-ary three-weight codes. When m is odd, and p≡3 (mod 4), we obtain an infinite family of two-weight codes which meets the Griesmer bound with equality. An application to secret sharing schemes is given. [ABSTRACT FROM AUTHOR]

A coupled air-sea model for tropical cyclones (TCs) is constructed by coupling the Pennsylvania State University/National Center for Atmospheric Research mesoscale model (MM5) with the Princeton Ocean Model. Four numerical simulations of tropical cyclone development have been conducted using different configurations of the coupled model on the f-plane. When coupled processes are excluded, a weak initial vortex spins up into a mature symmetric TC that strongly resembles those observed and simulated in prior research. The coupled model reproduces the reduction in sea temperature induced by the TC reasonably well, as well as changes in the minimum central pressure of the TC that result from negative atmosphere-ocean feedbacks. Asymmetric structures are successfully simulated under conditions of uniform environmental flow. The coupled ocean-atmosphere model is suitable for simulating air-sea interactions under TC conditions. The effects of the ocean on the track of the TC and changes in its intensity under uniform environmental flow are also investigated. TC intensity responds nonlinearly to sea surface temperature (SST). The TC intensification rate becomes smaller once the SST exceeds a certain threshold. Oceanic stratification also influences TC intensity, with stronger stratification responsible for a larger decrease in intensity. The value of oceanic enthalpy is small when the ocean is weakly stratified and large when the ocean is strongly stratified, demonstrating that the oceanic influence on TC intensity results not only from SST distributions but also from stratification. Air-sea interaction has only a slight influence on TC movement in this model. [ABSTRACT FROM AUTHOR]

Recent publications have investigated the interactions between the extratropical transitions (ETs) of tropical cyclones (TCs) and midlatitude circulations; however, studies of ET events have rarely considered the relationship between the storm and the nearby subtropical high. The TC best-track data provided by the Regional Specialized Meteorological Center-Tokyo Typhoon Center of the Japan Meteorology Agency are used in conjunction with the NCEP/NCAR reanalysis data to discuss the potential effects of the subtropical high on ETs over the western North Pacific basin. When the western Pacific subtropical high (WPSH) is weakened and withdrawn toward the east, more TCs follow recurving paths and the midlatitude trough activity is intensified. These changes lead to enhanced ET activity. By contrast, when the WPSH strengthens and extends westward, the number of TCs that follow direct westward paths increases and the midlatitude trough is relatively inactive. These conditions lead to reduced occurrences of ET cases. Abnormal activity of the WPSH should be considered as an important factor in determining ET activity. [ABSTRACT FROM AUTHOR]

Newtonian jerky dynamics is applied to inertial instability analysis to study the nonlinear features of atmospheric motion under the action of variable forces. Theoretical analysis of the Newtonian jerky function is used to clarify the criteria for inertial instability, including the influences of the meridional distributions of absolute vorticity ( ζ) and planetary vorticity (the β effect). The results indicate that the meridional structure of absolute vorticity plays a fundamental role in the dynamic features of inertial motion. Including only the β effect (with the assumption of constant ζ) does not change the instability criteria or the dynamic features of the flow, but combining the β effect with meridional variations of ζ introduces nonlinearities that significantly influence the instability criteria. Numerical analysis is used to derive time series of position, velocity, and acceleration under different sets of parameters, as well as their trajectories in phase space. The time evolution of kinematic variables indicates that a regular wave-like change in acceleration corresponds to steady wave-like variations in position and velocity, while a rapid growth in acceleration (caused by a rapid intensification in the force acting on the parcel) corresponds to track shifts and abrupt changes in direction. Stable limiting cases under the f- and β-plane approximations yield periodic wave-like solutions, while unstable limiting cases yield exponential growth in all variables. Perturbing the value of absolute vorticity at the initial position ( ζ) results in significant changes in the stability and dynamic features of the motion. Enhancement of the nonlinear term may cause chaotic behavior to emerge, suggesting a limit to the predictability of inertial motion. [ABSTRACT FROM AUTHOR]

The changes of tropical cyclone (TC) activities in response to influencing environmental conditions have been paid more and more attention to in recent years. The potential contributions of single and multivariate environmental variables to annual TC frequency and intensity from 1970 to 2009 are investigated in this study. Instead of using correlation coefficient that assumes a set of samples satisfying the normal distribution, a quantitative measurement is formulated based on the information theory. The results show that dynamic environmental variables play an important role in variations of TC activities over the western North Pacific, North Atlantic, and eastern Pacific. These dynamic factors include wind shear between 850 and 200 hPa and 850-hPa relative vorticity. However, the effects of thermal factors on TC activities are distinct over different basins. The thermal environmental variables only have significant contributions to TC frequency and intensity over the eastern Pacific as well as to TC frequency over the North Atlantic. It is found that the primary factors influencing TC activities are indeed not the same over different basins because of the differences in atmospheric conditions and their changes across different areas. The effects of dynamic variables should be considered more in the regions such as the western North Pacific where the thermal conditions are always satisfied. [ABSTRACT FROM AUTHOR]

The atmospheric and oceanic conditions are examined during different stages of the lifecycle of western North Pacific tropical cyclones (TCs), with the intention to understand how the environment affects the intensity change of TCs in this area. It is found that the intensification usually occurs when the underlying sea surface temperature (SST) is higher than 26°C. TCs usually experience a rapid intensification when the SST is higher than 27.5°C while lower than 29.5°C. However, TCs decay or only maintain its intensity when the SST is lower than 26°C. The intensifying TCs usually experience a low-to-moderate vertical wind shear (2-10 m s). The larger the vertical wind shear, the slower the TCs strengthen. In addition, the convective available potential energy (CAPE) is much smaller in the developing stage than in the formation stage of TCs. For the rapidly intensifying TCs, the changes of SST, CAPE, and vertical wind shear are usually small, indicating that the rapid intensification of TCs occurs when the evolution of the environment is relatively slow. [ABSTRACT FROM AUTHOR]

The adaptive wavelet collocation method (AWCM) is a variable grid technology for solving partial differential equations (PDEs) with high singularities. Based on interpolating wavelets, the AWCM adapts the grid so that a higher resolution is automatically attributed to domain regions with high singularities. Accuracy problems with the AWCM have been reported in the literature, and in this paper problems of efficiency with the AWCM are discussed in detail through a simple one-dimensional (1D) nonlinear advection equation whose analytic solution is easily obtained. A simple and efficient implementation of the AWCM is investigated. Through studying the maximum errors at the moment of frontogenesis of the 1D nonlinear advection equation with different initial values and a comparison with the finite difference method (FDM) on a uniform grid, the AWCM shows good potential for modeling the front efficiently. The AWCM is also applied to a two-dimensional (2D) unbalanced frontogenesis model in its first attempt at numerical simulation of a meteorological front. Some important characteristics about the model are revealed by the new scheme. [ABSTRACT FROM AUTHOR]

When tropical cyclones (hereafter referred as TCs) are over the ocean, surface friction plays a dual role in the development of TCs. From the viewpoint of water vapor supply, frictional convergence and Ekman pumping provide a source of moisture for organized cumulus convection and is propitious to the spin-up of TCs. On the other hand, surface friction leads to a dissipation of kinetic energy that impedes the intensification of TCs. Which role is dominant in the developing stage of TCs is a controversial issue. In the present work, the influence of surface friction on the growth of TCs is re-examined in detail by conducting two sets of numerical experiments initialized with different cyclonic disturbances. Results indicate that, because of the inherent complexities of TCs, the impact of surface friction on the evolution of TCs can not be simply boiled down to being positive or negative. In the case that a TC starts from a low-level vortex with a warm core, surface friction and the resultant vertical motion makes an important contribution to the convection in the early developing stage of the TC by accelerating the build-up of convective available potential energy (CAPE) and ensuring moisture supply and the lifting of air parcels. This effect is so prominent that it dominates the friction-induced dissipation and makes surface friction a facilitative factor in the spin-up of the TC. However, for a TC formed from a mesoscale convective vortex (MCV) spawned in a long-lasting mesoscale convective system (MCS), the initial fields, and especially the low-level humidity and cold core, enable the prerequisites of convection (i.e., conditional instability, moisture, and lifting), to be easily achieved even without the help of boundary-layer pumping induced by surface friction. Accordingly, the reliance of the development of TCs on surface friction is not as heavy as that derived from a lowlevel vortex. The positive effect of surface friction on the development of TCs realized through facilitating favorable conditions for convection is nearly cancelled out by the friction-induced dissipation. However, as SST is enhanced in the latter case, the situation may be changed, and different development speeds may emerge between model TCs with and without surface friction considered. In short, owing to the fact that TC development is a complicated process affected by many factors such as initial perturbations, SST, etc., the importance of surface friction to the intensification of TCs may vary enormously from case to case. [ABSTRACT FROM AUTHOR]

This paper reviews the main theoretical progress of mesoscale weather dynamics since 2003, including: (1) The dynamic mechanisms of balanced and unbalanced flow are applied to study the genesis and development problems of mesoscale circulation. The symmetric instability and transverse-wave instability are analyzed in line and vortex atmosphere convection, and further research has been done on nonlinear convective symmetric instability. The interaction between forced convection and unstable convection and the wave characteristics of mesoscale motion are also discussed. (2) Intermediate atmosphere dynamic boundary layer models are developed. The complicated nonlinear interaction is analyzed theoretically between the atmospheric boundary layer and the free atmosphere. The structure of the topography boundary layer, atmospheric frontogenesis, the structure and circulation of the low-level front and other boundary layer dynamic problems are discussed. (3) The formation and development of meso- β-scale rainstorms under the background of the East-Asia atmosphere circulation are diagnosed with the variation of MPV (moist potential vorticity) anomalies. And some physical vectors are modified and applied in the moist atmosphere. [ABSTRACT FROM AUTHOR]

Helicity is defined as H = V · ω, where V and ω velocity and vorticity vectors, respectively. Many works have pointed out that the larger the helicity is, the longer the life cycle of the weather system is. However, the direct relationship of the helicity to the evolution of the weather system is not quite clear. In this paper, the concept of helicity is generalized as shearing wind helicity (SWH). Dynamically, it is found that the average SWH is directly related to the increase of the average cyclonic rotation of the weather system. Physically, it is also pointed out that the SWH, as a matter of fact, is the sum of the torsion terms and the divergence term in the vorticity equation. Thermal wind helicity (TWH), as a derivative of SWH, is also discussed here because it links the temperature field and the vertical wind field. These two quantities may be effective for diagnosing a weather system. This paper applies these two quantities in cylindrical coordinates to study the development of Hurricane Andrew to validate their practical use. Through analyzing the hurricane, it is found that TWH can well describe the characteristics of the hurricane such as the strong convection and release of latent heat, SWH is not only a good quantity for diagnosing the weather system, but also an effective one for diagnosing the development of the hurricane. [ABSTRACT FROM AUTHOR]

Numerical results indicate that advection of momentum in the boundary layer may significantly alter both the structure of the planetary boundary layer and its influence on the overlying free atmosphere. However, due to the nonlinearity of the inertial terms, it is always difficult to obtain the analytical solution of the boundary-layer model that retains the flow acceleration. In order to overcome this difficulty, the geostrophic momentum (hereafter GM) approximation has been introduced into boundary-layer models. By replacing the advected momentum with the geostrophic wind, the effect of the flow acceleration is partially considered and the original nonlinear partial differential equation set is converted to ordinary differential equations, the solutions of which can be obtained easily with standard techniques. However, the model employing GM fails to capture the features of the boundary layer when the spatio-temporal variation of the boundary-layer flow cannot be properly approximated by the geostrophic wind. In the present work, a modified boundary-layer model with the inertial acceleration in a different approximate form is proposed, in which the advecting wind instead of the advected momentum is approximated by the geostrophic wind (hereafter GAM). Comparing the horizontal velocity and boundary-layer pumping obtained from the classical Ekman theory, and the model incorporating (i) GM and (ii) GAM, it is found that the model with GAM describes most facets of the steady well-mixed layer beneath a north-westerly flow with embedded mesoscale perturbations that is considered in the present work. Inspection of the solution of the model with GAM shows that, within the limit of the validation of the model (i.e., the Rossby number RO is not very large and the drag coefficient CD is not too small), the horizontal convergence (divergence) is strengthened by the effect of the inertial acceleration in the region of maximum positive (negative) geostrophic vorticity. Consequently, the boundary-layer pumping there is intensified. It is found that the intensification is firstly strengthened and then weakened as RO or CD increases. [ABSTRACT FROM AUTHOR]

In the present work, the data assimilation problem in meteorology and physical oceanography is re-examined using the variational optimal control approaches in combination with regularization techniques in inverse problem. Here the estimations of the initial condition, boundary condition and model parameters are performed simultaneously in the framework of variational data assimilation. To overcome the difficulty of ill-posedness, especially for the model parameters distributed in space and time, an additional term is added into the cost functional as a stabilized functional. Numerical experiments show that even with noisy observations the initial conditions and model parameters are recovered to an acceptable degree of accuracy. [ABSTRACT FROM AUTHOR]

A limited-area primitive equation model is used to study the role of the β-effect and a uniform current on tropical cyclone (TC) intensity. It is found that TC intensity is reduced in a non-quiescent environment compared with the case of no uniform current. On an f-plane, the rate of intensification of a tropical cyclone is larger than that of the uniform flow. A TC on a β-plane intensifies slower than one on an f-plane. The main physical characteristic that distinguishes the experiments is the asymmetric thermodynamic (including convective) and dynamic structures present when either a uniform flow or β-effect is introduced. But a fairly symmetric TC structure is simulated on an f-plane. The magnitude of the warm core and the associated subsidence are found to be responsible for such simulated intensity changes. On an f-plane, the convection tends to be symmetric, which results in strong upper-level convergence near the center and hence strong forced subsidence and a very warm core. On the other hand, horizontal advection of temperature cancels part of the adiabatic heating and results in less warming of the core, and hence the TC is not as intense. This advective process is due to the tilt of the vortex as a result of the β-effect. A similar situation occurs in the presence of a uniform flow. Thus, the asymmetric horizontal advection of temperature plays an important role in the temperature distribution. Dynamically, the asymmetric angular momentum (AM) flux is very small on an f-plane throughout the troposphere. However, the total AM exports at the upper levels for a TC either on a β-plane or with a uniform flow environment are larger because of an increase of the asymmetric as well as symmetric AM export on the plane at radii >450 km, and hence there is a lesser intensification. [ABSTRACT FROM AUTHOR]

In this paper, the influences of orography on the boundary layer flow with the approximation of geostrophic momentum are studied. The wind velocity at the lower boundary will not always be zero when the orography exists. So the structure of the boundary layer flow, as well as the vertical velocity at the top of the boundary layer, is affected. There are three factors affecting the vertical motion at the top of the boundary layer: lifting due to orography; divergence due to Ekman flow, and advection of the geostrophic momentum. These effects and the features of the flow within the boundary layer are discussed in detail. [ABSTRACT FROM AUTHOR]

A correction to the article "Numerical Simulation of Changes in Tropical Cyclone Intensity Using a Coupled Air-Sea Model" in a 2014 issue of the "Journal of Meteorological Research" is presented.