Variational properties of a pumped dynamical system

We have earlier constructed a generalized entropy concept to show the direction of time in an evolution following from a Markov generator. In such a dynamical system, the entity found changes in a monotonic way starting from any initial state of the system. In this paper, we generalize the treatment to the case when population is pumped into the system from levels not explicitly considered. These populations then pass through the coupled levels and exit by decay to levels outside the system. We derive the form of the equation of motion and relate it to our earlier treatments. It turns out that the formalism can be generalized to the new situation. Its physically relevant features are demonstrated, and the behaviour obtained is illustrated by numerical treatment of the standard two-level system with pumping and relaxation included.Comment: 10 pages, 2 figure

Weak convergence for a spatial approximation of the nonlinear stochastic heat equation

We find the weak rate of convergence of the spatially semidiscrete finite element approximation of the nonlinear stochastic heat equation. Both multiplicative and additive noise is considered under different assumptions. This extends an earlier result of Debussche in which time discretization is considered for the stochastic heat equation perturbed by white noise. It is known that this equation has a solution only in one space dimension. In order to obtain results for higher dimensions, colored noise is considered here, besides white noise in one dimension. Integration by parts in the Malliavin sense is used in the proof. The rate of weak convergence is, as expected, essentially twice the rate of strong convergence.Comment: 19 page

Weak convergence for a spatial approximation of the nonlinear stochastic heat equation

We find the weak rate of convergence of approximate solutions of the nonlinear stochastic heat equation, when discretized in space by a standard finite element method. Both multiplicative and additive noise is considered under different assumptions. This extends an earlier result of Debussche in which time discretization is considered for the stochastic heat equation perturbed by white noise. It is known that this equation only has a solution in one space dimension. In order to get results for higher dimensions, colored noise is considered here, besides the white noise case where considerably weaker assumptions on the noise term is needed. Integration by parts in the Malliavin sense is used in the proof. The rate of weak convergence is, as expected, essentially twice the rate of strong convergence

Duality in refined Sobolev-Malliavin spaces and weak approximations of SPDE

We introduce a new family of refined Sobolev-Malliavin spaces that capture the integrability in time of the Malliavin derivative. We consider duality in these spaces and derive a Burkholder type inequality in a dual norm. The theory we develop allows us to prove weak convergence with essentially optimal rate for numerical approximations in space and time of semilinear parabolic stochastic evolution equations driven by Gaussian additive noise. In particular, we combine a standard Galerkin finite element method with backward Euler timestepping. The method of proof does not rely on the use of the Kolmogorov equation or the It\={o} formula and is therefore non-Markovian in nature. Test functions satisfying polynomial growth and mild smoothness assumptions are allowed, meaning in particular that we prove convergence of arbitrary moments with essentially optimal rate.Comment: 32 page

Detecting Network-Based Obfuscated Code Injection Attacks Using Sandboxing

Intrusion detection systems (IDSs) are widely recognised as the last line of defence often used to enable incident response when intrusion prevention mechanisms are ineffective, or have been compromised. A signature based network IDS (NIDS) which operates by comparing network traffic to a database of suspicious activity patterns (known as signatures) is a popular solution due to its ease of deployment and relatively low false positive (incorrect alert) rate. Lately, attack developers have focused on developing stealthy attacks designed to evade NIDS. One technique used to accomplish this is to obfuscate the shellcode (the executable component of an attack) so that it does not resemble the signatures the IDS uses to identify the attacks but is still logically equivalent to the clear-text attacks when executed. We present an approach to detect obfuscated code injection attacks, an approach which compensates for efforts to evade IDSs. This is achieved by executing those network traffic segments that are judged potentially to contain executable code and monitoring the execution to detect operating system calls which are a necessary component of any such code. This detection method is based not on how the injected code is represented but rather on the actions it performs. Correct configuration of the IDS at deployment time is crucial for correct operation when this approach is taken, in particular, the examined executable code must be executed in an environment identical to the execution environment of the host the IDS is monitoring with regards to both operating system and architecture. We have implemented a prototype detector that is capable of detecting obfuscated shellcodes in a Linux environment, and demonstrate how it can be used to detect new or previously unseen code injection attacks and obfuscated attacks as well as well known attacks

An energy-based deep splitting method for the nonlinear filtering problem

The purpose of this paper is to explore the use of deep learning for the solution of the nonlinear filtering problem. This is achieved by solving the Zakai equation by a deep splitting method, previously developed for approximate solution of (stochastic) partial differential equations. This is combined with an energy-based model for the approximation of functions by a deep neural network. This results in a computationally fast filter that takes observations as input and that does not require re-training when new observations are received. The method is tested on three examples, one linear Gaussian and two nonlinear. The method shows promising performance when benchmarked against the Kalman filter and the bootstrap particle filter.Comment: 20 pages, 5 figure

Rotgallnematoder

Rotgallnematoderna (släktet Meloidogyne) är en grupp av nematoder, som är närbesläktade med de hos oss mera kända cystnematoderna. Medan cystnematoderna är de viktigaste nematoderna i tempererat klimat, så är rotgallnematoderna mest betydelsefulla under tropiska och subtropiska förhållanden. Troligen är rotgallnematoderna globalt sett de ekonomiskt viktigaste av alla nematoder. Också hos oss kan vissa arter vara eller bli av mycket stor betydelse. Den for närvarande enda kända arten på friland här i landet, Meloidogyne hapla, har gjort sig starkt påmind under de allra senaste åren