Searcharxiv⌕ Search

arXiv subjects

Christian Seifert

Publications and source records attributed to Christian Seifert.

At least 37 records · Page 2Linked to original sources

Living-Off-The-Land Command Detection Using Active Learning

In recent years, enterprises have been targeted by advanced adversaries who leverage creative ways to infiltrate their systems and move laterally to gain access to critical data. One increasingly common evasive method is to hide the malicious activity behind a benign program by using tools that are already installed on user computers. These programs are usually part of the operating system distribution or another user-installed binary, therefore this type of attack is called "Living-Off-The-Land". Detecting these attacks is challenging, as adversaries may not create malicious files on the victim computers and anti-virus scans fail to detect them. We propose the design of an Active Learning framework called LOLAL for detecting Living-Off-the-Land attacks that iteratively selects a set of uncertain and anomalous samples for labeling by a human analyst. LOLAL is specifically designed to work well when a limited number of labeled samples are available for training machine learning models to detect attacks. We investigate methods to represent command-line text using word-embedding techniques, and design ensemble boosting classifiers to distinguish malicious and benign samples based on the embedding representation. We leverage a large, anonymized dataset collected by an endpoint security product and demonstrate that our ensemble classifiers achieve an average F1 score of 0.96 at classifying different attack classes. We show that our active learning method consistently improves the classifier performance, as more training data is labeled, and converges in less than 30 iterations when starting with a small number of labeled instances.

cs.CR↗

Sufficient criteria for stabilization properties in Banach spaces

We study abstract sufficient criteria for open-loop stabilizability of linear control systems in a Banach space with a bounded control operator, which build up and generalize a sufficient condition for null-controllability in Banach spaces given by an uncertainty principle and a dissipation estimate. For stabilizability these estimates are only needed for a single spectral parameter and, in particular, their constants do not depend on the growth rate w.r.t. this parameter. Our result unifies and generalizes earlier results obtained in the context of Hilbert spaces. As an application we consider fractional powers of elliptic differential operators with constant coefficients in $L_p(\mathbb{R}^d)$ for $p\in [1,\infty)$ and thick control sets.

math.OC↗

Subordination for sequentially equicontinuous equibounded $C_0$-semigroups

We consider operators $A$ on a sequentially complete Hausdorff locally convex space $X$ such that $-A$ generates a (sequentially) equicontinuous equibounded $C_0$-semigroup. For every Bernstein function $f$ we show that $-f(A)$ generates a semigroup which is of the same `kind' as the one generated by $-A$. As a special case we obtain that fractional powers $-A^α$, where $α\in (0,1)$, are generators.

math.FA↗

Sufficient criteria and sharp geometric conditions for observability in Banach spaces

Let $X,Y$ be Banach spaces, $(S_t)_{t \geq 0}$ a $C_0$-semigroup on $X$, $-A$ the corresponding infinitesimal generator on $X$, $C$ a bounded linear operator from $X$ to $Y$, and $T > 0$. We consider the system \[ \dot{x}(t) = -Ax(t), \quad y(t) = Cx(t) \quad t\in (0,T], \quad x(0) = x_0 \in X. \] We provide sufficient conditions such that this system satisfies a final state observability estimate in $L_r ((0,T) ; Y)$, $r \in [1,\infty]$. These sufficient conditions are given by an uncertainty relation and a dissipation estimate. Our approach unifies and generalizes the respective advantages from earlier results obtained in the context of Hilbert spaces. As an application we consider the example where $A$ is an elliptic operator in $L_p(\mathbb{R}^d)$ for $1<p<\infty$, and where $C = \mathbf{1}_ω$ is the restriction onto a thick set $ω\subset \mathbb{R}^d$. In this case, we show that the above system satisfies a final state observability estimate if and only if $ω\subset \mathbb{R}^d$ is a thick set. Finally, we make use of the well-known relation between observability and null-controllability of the predual system, and investigate bounds on the corresponding control costs.

math.FA↗

On the harmonic extension approach to fractional powers in Banach spaces

We show that fractional powers of general sectorial operators on Banach spaces can be obtained by the harmonic extension approach. Moreover, for the corresponding second order ordinary differential equation with incomplete data describing the harmonic extension we prove existence and uniqueness of a bounded solution (i.e. of the harmonic extension).

math.FA↗

Limit operators techniques on general metric measure spaces of bounded geometry

We study band-dominated operators on (subspaces of) $L_p$-spaces over metric measure spaces of bounded geometry satisfying an additional property. We single out core assumptions to obtain, in an abstract setting, definitions of limit operators, characterizations of compactness and Fredholmness using limit operators; and thus also spectral consequences. In this way, we recover and unify the classical and recent results on limit operator techniques, but also gain new insights and are able to treat further applications.

math.FA↗

Evolutionary Equations

This is the final version of the lecture notes of the 23rd Internet Seminar on Evolutionary Equations, see also https://www.mat.tuhh.de/isem23/.

math.AP↗

On the construction and convergence of traces of forms

We elaborate a new method for constructing traces of quadratic forms in the framework of Hilbert and Dirichlet spaces. Our method relies on monotone convergence of quadratic forms and the canonical decomposition into regular and singular part. We give various situations where the trace can be described more explicitly and compute it for some illustrating examples. We then show that Mosco convergence of Dirichlet forms implies Mosco convergence of a subsequence of their approximating traces and that asymptotic compactness of Dirichlet forms yields asymptotic compactness of their traces.

math.FA↗

Spectral monotonicity for Schrödinger operators on metric graphs

We study the influence of certain geometric perturbations on the spectra of self-adjoint Schrödinger operators on compact metric graphs. Results are obtained for permutation invariant vertex conditions, which, amongst others, include $δ$ and $δ'$-type conditions. We show that adding edges to the graph or joining vertices changes the eigenvalues monotonically. However, the monotonicity properties may differ from what is known for the previously studied cases of Kirchhoff (or standard) and $δ$-conditions and may depend on the signs of the coefficients in the vertex conditions.

math.SP↗

A note on perturbations of $C_0$-semigroups

This article deals with a variation of constants type inequality for semigroups acting consistently on a scale of Banach spaces. This inequality can be characterized by a corresponding (easy to verify) inequality for their generators. The results have applications to heat kernel estimates and provide a unified perspective to estimates of these type. Moreover, bi-continuous semigroups can be treated as well.

math.FA↗

The linearized Korteweg-de-Vries equa- tion on general metric graphs

We consider the linearized Korteweg-de-Vries equa- tions, sometimes called Airy equation, on general metric graphs with edge lengths bounded away from zero. We show that pro- perties of the induced dynamics can be obtained by studying boundary operators in the corresponding boundary space indu- ced by the vertices of the graph. In particular, we characterize unitary dynamics and contractive dynamics. We demonstrate our results on various special graphs, including those recently treated in the literature.

math-ph↗

Absolutely continuous spectrum for Laplacians on radial metric trees and periodicity

On an infinite, radial metric tree graph we consider the corresponding Laplacian equipped with self-adjoint vertex conditions from a large class including $δ$- and weighted $δ'$-couplings. Assuming the numbers of different edge lengths, branching numbers and different coupling conditions to be finite, we prove that the presence of absolutely continuous spectrum implies that the sequence of geometric data of the tree as well as the coupling conditions are eventually periodic. On the other hand, we provide examples of self-adjoint, non-periodic couplings which admit absolutely continuous spectrum.

math.SP↗

On the spectrum of operator families on discrete groups over minimal dynamical systems

It is well known that, given an equivariant and continuous (in a suitable sense) family of selfadjoint operators in a Hilbert space over a minimal dynamical system, the spectrum of all operators from that family coincides. As shown recently similar results also hold for suitable families of non-selfadjoint operators in $\ell^p (\ZM)$. Here, we generalize this to a large class of bounded linear operator families on Banach-space valued $\ell^p$-spaces over countable discrete groups. We also provide equality of the pseudospectra for operators in such a family. A main tool for our analysis are techniques from limit operator theory.

math.SP↗

Gordon type Theorem for measure perturbation

Generalizing the concept of Gordon potentials to measures we prove a version of Gordon's theorem for measures as potentials and show absence of eigenvalues for these one-dimensional Schrödinger operators.

math-ph↗

Dirichlet forms for singular diffusion on graphs

We describe operators driving the time evolution of singular diffusion on finite graphs whose vertices are allowed to carry masses. The operators are defined by the method of quadratic forms on suitable Hilbert spaces. The model also covers quantum graphs and discrete Laplace operators.

math.FA↗

Almost sure purely singular continuous spectrum for quasicrystal models

We review recent developments in the spectral theory of continuum one-dimensional quasicystals, yielding purely singular continuous spectrum for these Schrödinger operators. Allowing measures as potentials we can generalize some results to very singular potentials, including Kronig-Penney type models.

math-ph↗

On eigenvalue bounds for a general class of Sturm-Liouville operators

We consider Sturm-Liouville operators with measure-valued weight and potential, and positive, bounded diffusion coefficient which is bounded away from zero. By means of a local periodicity condition, which can be seen as a quantitative Gordon condition, we prove a bound on eigenvalues for the corresponding operator in $L_p$, for $1\leq p<\infty$. We also explain the sharpness of our quantitative bound, and provide an example for quasiperiodic operators.

math.SP↗