Dynamics of a diffusive predator–prey model with herd behavior

This paper is devoted to considering a diffusive predator–prey model with Leslie–Gower term and herd behavior subject to the homogeneous Neumann boundary conditions. Concretely, by choosing the proper bifurcation parameter, the local stability of constant equilibria of this model without diffusion and the existence of Hopf bifurcation are investigated by analyzing the distribution of the eigenvalues. Furthermore, the explicit formula for determining the direction of Hopf bifurcation and the stability of the bifurcating periodic solutions are also derived by applying the normal form theory. Next, we show the stability of positive constant equilibrium, the existence and stability of periodic solutions near positive constant equilibrium for the diffusive model. Finally, some numerical simulations are carried out to support the analytical results

Design and analysis of bent functions using M\mathcal{M}-subspaces

In this article, we provide the first systematic analysis of bent functions $f$ on $\mathbb{F}_2^{n}$ in the Maiorana-McFarland class $\mathcal{MM}$ regarding the origin and cardinality of their $\mathcal{M}$-subspaces, i.e., vector subspaces on which the second-order derivatives of $f$ vanish. By imposing restrictions on permutations $\pi$ of $\mathbb{F}_2^{n/2}$, we specify the conditions, such that Maiorana-McFarland bent functions $f(x,y)=x\cdot \pi(y) + h(y)$ admit a unique $\mathcal{M}$-subspace of dimension $n/2$. On the other hand, we show that permutations $\pi$ with linear structures give rise to Maiorana-McFarland bent functions that do not have this property. In this way, we contribute to the classification of Maiorana-McFarland bent functions, since the number of $\mathcal{M}$-subspaces is invariant under equivalence. Additionally, we give several generic methods of specifying permutations $\pi$ so that $f\in\mathcal{MM}$ admits a unique $\mathcal{M}$-subspace. Most notably, using the knowledge about $\mathcal{M}$-subspaces, we show that using the bent 4-concatenation of four suitably chosen Maiorana-McFarland bent functions, one can in a generic manner generate bent functions on $\mathbb{F}_2^{n}$ outside the completed Maiorana-McFarland class $\mathcal{MM}^\#$ for any even $n\geq 8$. Remarkably, with our construction methods it is possible to obtain inequivalent bent functions on $\mathbb{F}_2^8$ not stemming from two primary classes, the partial spread class $\mathcal{PS}$ and $\mathcal{MM}$. In this way, we contribute to a better understanding of the origin of bent functions in eight variables, since only a small fraction, of which size is about $2^{76}$, stems from $\mathcal{PS}$ and $\mathcal{MM}$, whereas the total number of bent functions on $\mathbb{F}_2^8$ is approximately $2^{106}$

Hard Fault Analysis of Trivium

Fault analysis is a powerful attack to stream ciphers. Up to now, the major idea of fault analysis is to simplify the cipher system by injecting some soft faults. We call it soft fault analysis. As a hardware--oriented stream cipher, Trivium is weak under soft fault analysis. In this paper we consider another type of fault analysis of stream cipher, which is to simplify the cipher system by injecting some hard faults. We call it hard fault analysis. We present the following results about such attack to Trivium. In Case 1 with the probability not smaller than 0.2396, the attacker can obtain 69 bits of 80--bits--key. In Case 2 with the probability not smaller than 0.2291, the attacker can obtain all of 80--bits--key. In Case 3 with the probability not smaller than 0.2291, the attacker can partially solve the key. In Case 4 with non--neglectable probability, the attacker can obtain a simplified cipher, with smaller number of state bits and slower non--linearization procedure. In Case 5 with non--neglectable probability, the attacker can obtain another simplified cipher. Besides, these 5 cases can be checked out by observing the key--stream

Effect of supercritical CO2 extraction on pore characteristics of coal and its mechanism

Abundant pore space in coal is not only the place for the accumulation of coalbed methane (CBM), but also the tunnel for gas migration. In this study, five sets of coal samples before and after the second coalification were selected from the eastern margin of Ordos Basin to simulate supercritical CO2 (Sc-CO2) extraction in supercritical extraction equipment. The evolutions of pore structure and porosity were tested by mercury intrusion porosimetry and nuclear magnetic resonance spectroscopy to compare the changes of pore structure and porosity due to the Sc-CO2 extraction, and to explain the related mechanism. The results show that: (1) Pore volume, pore specific surface area, and connectivity characteristics changed significantly due to Sc-CO2 extraction, and the increment of pore volume and pore specific surface area presented a law of increase–decrease–increase with the increase in the coal rank, and the turning point was near the second coalification. (2) The porosity increment change trend due to Sc-CO2 extraction was increase–decrease–increase with increasing coal rank, and the turning point was again near the second coalification, which supports the mercury intrusion porosimetry results. (3) The changes were observed in the porosity characteristics due to Sc-CO2 extraction through pore-increasing and expanding effects. Before the second coalification, the pore-increasing and expanding effects co-existed in the micropores, and after the second coalification, the pore-expanding effect mainly existed in the transitional pores and above. (4) The variation model for the pore structure of coal due to Sc-CO2 extraction was established. The conclusions offer not only important theoretical significance for the CO2-enhanced CBM (CO2-ECBM) mechanism but also important significance for CO2-ECBM engineering

Immune Efficacy of a Genetically Engineered Vaccine against Lymphocystis Disease Virus: Analysis of Different Immunization Strategies

Here, we report the construction of a vaccine against lymphocystis disease virus (LCDV) using nucleic acid vaccination technology. A fragment of the major capsid protein encoding gene from an LCDV isolated from China (LCDV-cn) was cloned into an eukaryotic expression vector pEGFP-N2, yielding a recombinant plasmid pEGFP-N2-LCDV-cn0.6 kb. This plasmid was immediately expressed after liposomal transfer into the Japanese flounder embryo cell line. The recombinant plasmid was inoculated into Japanese flounder via two routes (intramuscular injection and hypodermic injection) at three doses (0.1, 5, and 15 μg), and then T-lymphopoiesis in different tissues and antibodies raised against LCDV were evaluated. The results indicated that this recombinant plasmid induced unique humoral or cell-mediated immune responses depending on the inoculation route and conferred immune protection. Furthermore, the humoral immune responses and protective effects were significantly increased at higher vaccine doses via the two injection routes. Plasmid pEGFP-N2-LCDV0.6 kb is therefore a promising vaccine candidate against LCDV in Japanese flounder

Constructing new superclasses of bent functions from known ones

Some recent research articles [23, 24] addressed an explicit specification of indicators that specify bent functions in the so-called $\mathcal{C}$ and $\mathcal{D}$ classes, derived from the Maiorana- McFarland ($\mathcal{M}$) class by C. Carlet in 1994 [5]. Many of these bent functions that belong to $\mathcal{C}$ or $\mathcal{D}$ are provably outside the completed $\mathcal{M}$ class. Nevertheless, these modifications are performed on affine subspaces, whereas modifying bent functions on suitable subsets may provide us with further classes of bent functions. In this article, we exactly specify new families of bent functions obtained by adding together indicators typical for the $\mathcal{C}$ and $\mathcal{D}$ class, thus essentially modifying bent functions in $\mathcal{M}$ on suitable subsets instead of subspaces. It is shown that the modification of certain bent functions in $\mathcal{M}$ gives rise to new bent functions which are provably outside the completed $\mathcal{M}$ class. Moreover, we consider the so-called 4-bent concatenation (using four different bent functions on the same variable space) of the (non)modified bent functions in $\mathcal{M}$ and show that we can generate new bent functions in this way which do not belong to the completed $\mathcal{M}$ class either. This result is obtained by specifying explicitly the duals of four constituent bent functions used in the concatenation. The question whether these bent functions are also excluded from the completed versions of $\mathcal{PS}$, $\mathcal{C}$ or $\mathcal{D}$ remains open and is considered difficult due to the lack of membership indicators for these classes

Minimal pp-ary codes from non-covering permutations

In this article, we propose several generic methods for constructing minimal linear codes over the field $\mathbb{F}_p$. The first construction uses the method of direct sum of an arbitrary function $f:\mathbb{F}_{p^r}\to \mathbb{F}_{p}$ and a bent function $g:\mathbb{F}_{p^s}\to \mathbb{F}_p$ to induce minimal codes with parameters $[p^{r+s}-1,r+s+1]$ and minimum distance larger than $p^r(p-1)(p^{s-1}-p^{s/2-1})$. For the first time, we provide a general construction of linear codes from a subclass of non-weakly regular plateaued functions, which partially answers an open problem posed in [22]. The second construction deals with a bent function $g:\mathbb{F}_{p^m}\to \mathbb{F}_p$ and a subspace of suitable derivatives $U$ of $g$, i.e., functions of the form $g(y+a)-g(y)$ for some $a\in \mathbb{F}_{p^m}^*$. We also provide a sound generalization of the recently introduced concept of non-covering permutations [45]. Some important structural properties of this class of permutations are derived in this context. The most remarkable observation is that the class of non-covering permutations contains the class of APN power permutations (characterized by having two-to-one derivatives). Finally, the last general construction combines the previous two methods (direct sum, non-covering permutations and subspaces of derivatives) together with a bent function in the Maiorana-McFarland class to construct minimal codes (even those violating the Ashikhmin-Barg bound) with a larger dimension. This last method proves to be quite flexible since it can lead to several non-equivalent codes, depending to a great extent on the choice of the underlying non-covering permutation