Throughput optimization for micro-factories subject to task and machine failures

In this paper, we study the problem of optimizing the throughput for micro-factories subject to failures. The challenge is to map several tasks of different types onto a set of machines. The originality of our approach is the failure model for such applications in which not only the machines are subject to failures but the reliability of a task may depend on its type. The failure rate is unrelated: a probability of failure is associated to each couple (task type, machine). We consider different kind of mappings: in one-to-one mappings, each machine can process only a single task, while several tasks of the same type can be processed by the same machine in specialized mappings. Finally, general mappings have no constraints. The optimal one-to-one mapping can be found in polynomial time for particular problem instances, but the problem is NP- hard in most of the cases. For the most realistic case of specialized mappings, which turns out to be NP-hard, we design several polynomial time heuristics and a linear program allows us to find the optimal solution (in exponential time) for small problem instances. Experimental results show that the best heuristics obtain a good throughput, much better than the throughput achieved with a random mapping. Moreover, we obtain a throughput close to the optimal solution in the particular cases where the optimal throughput can be computed

Sampling From Autoencoders' Latent Space via Quantization And Probability Mass Function Concepts

In this study, we focus on sampling from the latent space of generative models built upon autoencoders so as the reconstructed samples are lifelike images. To do to, we introduce a novel post-training sampling algorithm rooted in the concept of probability mass functions, coupled with a quantization process. Our proposed algorithm establishes a vicinity around each latent vector from the input data and then proceeds to draw samples from these defined neighborhoods. This strategic approach ensures that the sampled latent vectors predominantly inhabit high-probability regions, which, in turn, can be effectively transformed into authentic real-world images. A noteworthy point of comparison for our sampling algorithm is the sampling technique based on Gaussian mixture models (GMM), owing to its inherent capability to represent clusters. Remarkably, we manage to improve the time complexity from the previous $\mathcal{O}(n\times d \times k \times i)$ associated with GMM sampling to a much more streamlined $\mathcal{O}(n\times d)$, thereby resulting in substantial speedup during runtime. Moreover, our experimental results, gauged through the Fr\'echet inception distance (FID) for image generation, underscore the superior performance of our sampling algorithm across a diverse range of models and datasets. On the MNIST benchmark dataset, our approach outperforms GMM sampling by yielding a noteworthy improvement of up to $0.89$ in FID value. Furthermore, when it comes to generating images of faces and ocular images, our approach showcases substantial enhancements with FID improvements of $1.69$ and $0.87$ respectively, as compared to GMM sampling, as evidenced on the CelebA and MOBIUS datasets. Lastly, we substantiate our methodology's efficacy in estimating latent space distributions in contrast to GMM sampling, particularly through the lens of the Wasserstein distance

Molecular phylogenetics of the Metazoan clade Lophotrochozoa

Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution September 2003DNA sequencing and phylogenetic analyses were conducted to investigate evolutionary relationships between taxa within the metazoan clade Lophotrochozoa. Chapter 1 presents an introduction to phylogenetics of the Metazoa and the clade Lophotrochozoa. Chapter 2 analyzes higher level relationships between the major groups within the phylum Mollusca using sequences of the nuclear ribosomal large-subunit RNA gene (LSD rDNA). Results presented provide the first molecular evidence for a close relationship between the Scaphopoda and Cephalopoda. Phylogenetic trees with this topology were found to have likelihood scores significantly better than those for phylogenies constrained to fit the Diasoma hypothesis grouping Scaphopoda and Bivalvia as sister taxa. Chapter 3 utilizes LSU rDNA sequences to analyze relationships between diverse phyla within the clade Lophotrochozoa. LSU rDNA sequences were found to provide greater resolution than has been provided by previous analyses of the nuclear small-subunit ribosomal RNA gene (SSU rDNA). Analysis ofLSU rDNA sequences recovered the monophyly of several phyla, such as Mollusca and Anelida, whose members are found to be paraphyletic using SSU rDNA sequences alone. Results also suggest that the clade Platyzoa, including rotifers and platyhelminthes, may have arisen within the Lophotrochozoa, rather than as a sister group to lophotrochozoans. Chapter 4 investigates the Hox gene complement of the bryozoan Bugula turrita. Six Hox genes were recovered, including an ortholog of the posterior class gene Post2, which is a synapomorphy for the Lophotrochozoa. The identification of a Post2 ortholog provides evidence of a close relationship between the Bryozoa and other lophotrochozoan phyla.This work was supported by a grant from the National Science Foundation, DEB-0075618 "Genomic approaches to metazoan evolution; lophotrochozoans and Hox genes" to Kenneth Halanych. Bryozoan Hox research was supported by a Doctoral dissertation Improvement Grant from the National Science Foundation, DEB-OI04984 "Phylogenetic inference from bryozoan Hox genes" to Kenneth Halanych and Yale Passamaneck. Additional support was provided by the Woods Hole Oceanographic Institution Education Office