Session: Cloud Computing, Transport, and AI
Chair: Julius Lohmann
Cluster: nan
Talk 1: An ϵ outer linear approximation optimization model for geo-distributed cloud applications
Speaker: Julio C Góez
Abstract: Cloud computing has become key for software providers aiming to serve a geographically distributed user base. As application demand changes and users become more latency sensitive, software providers need to adapt their deployments to reach latency-based service-level objectives while keeping costs low. In this paper, we propose a method to provision Cloud resources considering latency-based service-level constraints while minimizing operating costs. Our method is based on a latency model to capture the load balancing among resources. To solve the resulting mixed integer non-linear optimization model, we propose an outer linear approximation that is able to find feasible solutions faster than solving the non-linear problem. Experiments based on realistic deployment data reveal how the proposed method is able to deliver timely solutions to the provisioning problem. Further, the solutions adapt to key elements of the problem, such as the service-level objective defined and the characteristics of the software application deployed.
Talk 2: Integral representation of the h-mass
Speaker: Julius Lohmann
Abstract: The multi-material transport problem [1, 2] is convex optimization problem on normal 1-currents in ℝⁿ with coefficients in ℝᵐ. The prescribed boundary can be written μ⃗₋−μ⃗₊, where μ⃗₊ and μ⃗₋ are compactly supported ℝᵐ-valued Radon measures whose components μ⃗±ʲ are nonnegative and satisfy μ⃗₊ʲ(ℝⁿ) = μ⃗₋ʲ(ℝⁿ). For each j the measure μ⃗₊ʲ can be interpreted as the source distribution of some material j which has to be transported to the sink μ⃗₋ʲ. The objective in the above Plateau problem is the so-called h-mass ℳₕ with norm h on the coefficient group ℝᵐ. The value h(θ⃗) represents the transportation cost to move a material bundle θ⃗ per unit distance. The triangle inequality h(θ⃗+θ⃗) ≤ h(θ⃗)+h(θ⃗) implies that the joint transport of different materials may be more efficient. The h-mass ℳₕ(F) then indicates the total transportation cost of an admissible candidate F, that is ∂F = μ⃗₋−μ⃗₊, with respect to h (also called mass flux in this context). A candidate mass flux F for the Plateau problem inf ℳₕ(G), subject to ∂G=μ⃗₋−μ⃗₊, can alternatively be interpreted as a finite mass flat 1-chain with coefficients in ℝᵐ and boundary μ⃗₋−μ⃗₊ or as a matrix-valued Radon measure (row j being a mass flux describing the transport of material j) whose distributional divergence equals μ⃗₊−μ⃗₋. Each interpretation of F, as a current, flat chain, or measure, comes with its own natural notion of an h-mass ℳₕ, 𝕄ₕ, or |·|ₕ. In [3] it is shown that all these notions are equivalent. In particular, this result yields an integral representation of the h-mass which, so far, was only known for rectifiable currents [2, 4]. In addition, the proof motivates a new definition of so-called calibrations for multi-material transport. Calibrations are a classical tool in the study of Plateau problems. They can be used to certify optimality of candidate minimizers. The new definition of a calibration in [3] provides a sufficient and necessary criterion for optimality (opposed to just sufficient as in the classical case). Since, in addition, this notion ‘includes’ the classical definition, a sharp characterization of the regularity of calibrations for multi- material transport is obtained. In my talk, I will motivate the study of multi-material transport, explain the different h-masses, sketch the argument yielding their equality, and give examples of calibrations. [1] A. Marchese, A. Massaccesi, R. Tione. A multi-material transport problem and its convex relaxation via rectifiable G-currents. SIAM J. Math. Anal., 51(3):1965–1998, 2019. [2] A. Marchese, A. Massaccesi, S. Stuvard, R. Tione. A multi-material transport problem with arbitrary marginals. Calc. Var. Partial Differential Equations, 60(3):Paper No. 88, 2021. [3] J. Lohmann, B. Schmitzer, B. Wirth. Formulas for the h-mass on 1-currents with coefficients in Rm. Preprint: arXiv:2407.10158 [math.OC], 2024. [4] B. White. Rectifiability of flat chains. Ann. of Math., 150(1):165–184, 1999.
Talk 3: Detecting AI Generated Images through Texture and Frequency Analysis of Patches
Speaker: Maryam Yashtini
Abstract: The significant improvement in AI image generation in recent years poses serious threats to social security, as AI generated misinformation may infringe upon political stability, personal privacy, and digital copy rights of artists. Building an AI generated image detector that accurately identifies generated image is crucial to maintain the social security and property rights of artists. This paper introduces preprocessing pipeline that uses positional encoded azimuthal integrals for image patches to create fingerprints that encapsulate distinguishing features. We then trained a multi-head attention model with 97.5% accuracy on classification of the fingerprints. The model also achieved 80% accuracy on images generated by AI models not presented in the training dataset, demonstrating the robustness of our pipeline and the potential of broader application of our model.
