Mathematical models of short-range dispersal in defoliating lepidopterans

The gypsy moth (Lymantria dispar) is among the most destructive invasive species in North America, responsible for defoliating millions of hectares of oak forest. The spatial dynamics of defoliating lepidopteran populations, such as those of the gypsy moth, are thus of great interest to forestry and conservation efforts. Despite numerous studies on the long-range dispersal patterns of defoliators, there is comparatively little theoretical understanding or field research concerning short-range dispersal via ballooning. Previous studies of ballooning have assumed random diffusion, but these models cannot account for non-random biases, such as the effect of wind on the angle of dispersal.Here, I develop models of short-range dispersal in larvae via ballooning, informed by methods from the seed dispersal kernel literature. I then fit models to field data of gypsy moth larvae dispersal using MCMC to perform Bayesian inference, and PSIS-LOO to perform model selection. I found that dispersal kernel models are able to reliably detect biases in angle of dispersal due to wind direction, and allow for testing of correlations between experimental variables and measures of dispersal. These modeling methods can help inform future studies into short-range larval dispersal and provide a novel framework with which to analyze dispersal data.

Determining travel fluxes in epidemic areas

Infectious diseases attack humans from time to time and threaten the lives and survival of people all around the world. An important strategy to prevent the spatial spread of infectious diseases is to restrict population travel. With the reduction of the epidemic situation, when and where travel restrictions can be lifted, and how to organize orderly movement patterns become critical and fall within the scope of this study. We define a novel diffusion distance derived from the estimated mobility network, based on which we provide a general model to describe the spatiotemporal spread of infectious diseases with a random diffusion process and a deterministic drift process of the population. We consequently develop a multi-source data fusion method to determine the population flow in epidemic areas. In this method, we first select available subregions in epidemic areas, and then provide solutions to initiate new travel flux among these subregions. To verify our model and method, we analyze the multi-source data from mainland China and obtain a new travel flux triggering scheme in the selected 29 cities with the most active population movements in mainland China. The testable predictions in these selected cities show that reopening the borders in accordance with our proposed travel flux will not cause a second outbreak of COVID-19 in these cities. The finding provides a methodology of re-triggering travel flux during the weakening spread stage of the epidemic.

Structural Attack (and Repair) of Diffused-Input-Blocked-Output White-Box Cryptography

In some practical enciphering frameworks, operational constraints may require that a secret key be embedded into the cryptographic algorithm. Such implementations are referred to as White-Box Cryptography (WBC). One technique consists of the algorithm’s tabulation specialized for its key, followed by obfuscating the resulting tables. The obfuscation consists of the application of invertible diffusion and confusion layers at the interface between tables so that the analysis of input/output does not provide exploitable information about the concealed key material.Several such protections have been proposed in the past and already cryptanalyzed thanks to a complete WBC scheme analysis. In this article, we study a particular pattern for local protection (which can be leveraged for robust WBC); we formalize it as DIBO (for Diffused-Input-Blocked-Output). This notion has been explored (albeit without having been nicknamed DIBO) in previous works. However, we notice that guidelines to adequately select the invertible diffusion ∅and the blocked bijections B were missing. Therefore, all choices for ∅ and B were assumed as suitable. Actually, we show that most configurations can be attacked, and we even give mathematical proof for the attack. The cryptanalysis tool is the number of zeros in a Walsh-Hadamard spectrum. This “spectral distinguisher” improves on top of the previously known one (Sasdrich, Moradi, Güneysu, at FSE 2016). However, we show that such an attack does not work always (even if it works most of the time).Therefore, on the defense side, we give a straightforward rationale for the WBC implementations to be secure against such spectral attacks: the random diffusion part ∅ shall be selected such that the rank of each restriction to bytes is full. In AES’s case, this seldom happens if ∅ is selected at random as a linear bijection of F322. Thus, specific care shall be taken. Notice that the entropy of the resulting ∅ (suitable for WBC against spectral attacks) is still sufficient to design acceptable WBC schemes.

The effects of diffusion on the principal eigenvalue for age-structured models with random diffusion

In this paper, we study the principal spectral theory of age-structured models with random diffusion. First, we provide an equivalent characteristic for the principal eigenvalue, the strong maximum principle and a positive strict super-solution. Then, we use the result to investigate the effects of diffusion rate on the principal eigenvalue. Finally, we study how the principal eigenvalue affects the global dynamics of the KPP model and verify that the principal eigenvalue being zero is a critical value.

Qualitative Dynamics and Pattern Formation of COVID-19 in the Modified SIR Model

SIR (susceptible-infective-recovery) model is a widely investigated model to explain the time evolution of infectious diseases. Outbreak of infectious diseases is affected by diffusion of infected, which is true especially in COVID-19 outbreak. Therefore, it is imperative to construct a diffusion network in the model for spatial consideration; However, the inclusion of a diffusion network is seldom considered for the studies. In this work, we first modified the SIR model for COVID-19 and then performed its stability and bifurcation analysis in qualitative research. Based on our analysis, we propose some of the advice to mitigate the spread of COVID-19. Then, a random diffusion network is constructed, which shows its vital role in the Turing instability and bifurcation. We noticed that the stability of network-organized SIR could be determined by the maximum of eigenvalues of the network matrix. The maximum of eigenvalues of the network matrix is proportional to network connection rate and infection rate of the network. Therefore, these two rates play a critical role in Turing instability. We perform the numerical simulations to verify the analytical results. We try to explain the spread mechanism of infectious diseases and provide some feasible strategies based on our analysis of these two models. Also, the reduced system method for a network-organized system is proposed, which is a novel approach to investigate the complex system.

Does Altered Probability of Real Time Diffusional Collisions of Membrane Molecules Trigger or Delay Alzheimers Disease

Understanding stochastic events that control the molecular events leading to the onset of neurodegenerative diseases such as Alzheimer's Disease (AD) is not well understood. Though the bulk of the attention is attributed to the increased burden of detrimental proteoforms generated by the processing of Amyloid Precursor Protein, there lacks a clear consensus on how the molecular events that control the localization and trafficking contribute to the onset. Here, we discuss emerging evidence that indicate the role of nanoscale compositionality of the membrane and random diffusion at the millisecond time scale that contribute to the onset of AD. We believe that intuitive knowledge of nanobiology controlling the local rates of product formation holds the clue for next-generation therapeutics that might delay or halt the onset of AD.

Derivation of Kolmogorov-Chapman type equations with Fokker-Planck operator

In this paper we obtain the differential equation of the type Kolmogorov-Chapman with differential operator of the Fokker-Planck, having theoretical and practical value in the differential equations theory. Equations concerning non-stationary and stationary characteristics of the number of applications obtained for a class of Queuing systems (QS) with an infinite storage device, one service device with exponential service, the input of which is supplied twice stochastic a Poisson flow whose intensity is a random diffusion process with springy boundaries and a non-zero drift coefficient. Service systems with diffusion intensity of the input flow are used for modeling of global computer networks nodes.