The Randomized Competitive Ratio of Weighted k-Server Is at Least Exponential

The weighted k-server problem is a natural generalization of the k-server problem in which the cost incurred in moving a server is the distance traveled times the weight of the server. Even after almost three decades since the seminal work of Fiat and Ricklin (1994), the competitive ratio of this problem remains poorly understood even on the simplest class of metric spaces - the uniform metric spaces. In particular, in the case of randomized algorithms against the oblivious adversary, neither a better upper bound that the doubly exponential deterministic upper bound, nor a better lower bound than the logarithmic lower bound of unweighted k-server, is known. In this paper, we make significant progress towards understanding the randomized competitive ratio of weighted k-server on uniform metrics. We cut down the triply exponential gap between the upper and lower bound to a singly exponential gap by proving that the competitive ratio is at least exponential in k, substantially improving on the previously known lower bound of about ln k

On Minimizing Generalized Makespan on Unrelated Machines

We consider the Generalized Makespan Problem (GMP) on unrelated machines, where we are given n jobs and m machines and each job j has arbitrary processing time p_{ij} on machine i. Additionally, there is a general symmetric monotone norm ?_i for each machine i, that determines the load on machine i as a function of the sizes of jobs assigned to it. The goal is to assign the jobs to minimize the maximum machine load. Recently, Deng, Li, and Rabani [Deng et al., 2023] gave a 3 approximation for GMP when the ?_i are top-k norms, and they ask the question whether an O(1) approximation exists for general norms ?? We answer this negatively and show that, under natural complexity assumptions, there is some fixed constant ? > 0, such that GMP is ?(log^? n) hard to approximate. We also give an ?(log^{1/2} n) integrality gap for the natural configuration LP

Development of an automated robotic deburring workcell

This thesis deals with the development of an automated robotic deburring workcell for refurbished components with intricate geometry. Deburring of a refurbished workpiece involves establishing the location of the workpiece, establishing its geometry using surface digitizing and mathematical splining algorithms, extrapolating the reconstructed surface to get the edge profile, determining and executing the tool path. The robot chosen for the workcell is YAMAHA Zeta-1 robot designed specifically for deburring. A displacement sensor with an accuracy of 0.004 mm is interfaced to the workcell. The limited computational ability of the robot controller and its closed architecture have necessitated the development of an external controller to coordinate the activities of the workcell. The robot controller neither provides for communication with external computing systems, nor does it allow interfacing external sensors

A Simple and Interpretable Predictive Model for Healthcare

Deep Learning based models are currently dominating most state-of-the-art solutions for disease prediction. Existing works employ RNNs along with multiple levels of attention mechanisms to provide interpretability. These deep learning models, with trainable parameters running into millions, require huge amounts of compute and data to train and deploy. These requirements are sometimes so huge that they render usage of such models as unfeasible. We address these challenges by developing a simpler yet interpretable non-deep learning based model for application to EHR data. We model and showcase our work's results on the task of predicting first occurrence of a diagnosis, often overlooked in existing works. We push the capabilities of a tree based model and come up with a strong baseline for more sophisticated models. Its performance shows an improvement over deep learning based solutions (both, with and without the first-occurrence constraint) all the while maintaining interpretability.Comment: 7 pages, 10 figure

A Narrow Quantitative Trait Locus in C. elegans Coordinately Affects Longevity, Thermotolerance, and Resistance to Paraquat

By linkage mapping of quantitative trait loci, we previously identified at least 11 natural genetic variants that significantly modulate Caenorhabditis elegans life-span (LS), many of which would have eluded discovery by knock-down or mutation screens. A region on chromosome IV between markers stP13 and stP35 had striking effects on longevity in three inter-strain crosses (each P < 10−9). In order to define the limits of that interval, we have now constructed two independent lines by marker-based selection during 20 backcross generations, isolating the stP13–stP35 interval from strain Bergerac-BO in a CL2a background. These congenic lines differed significantly from CL2a in LS, assayed in two environments (each P < 0.001). We then screened for exchange of flanking markers to isolate recombinants that partition this region, because fine-mapping the boundaries for overlapping heteroallelic spans can greatly narrow the implicated interval. Recombinants carrying the CL2a allele at stP35 were consistently long-lived compared to those retaining the Bergerac-BO allele (P < 0.001), and more resistant to temperature elevation and paraquat (each ∼1.7-fold, P < 0.0001), but gained little protection from ultraviolet or peroxide stresses. Two rounds of recombinant screening, followed by fine-mapping of break-points and survival testing, narrowed the interval to 0.18 Mb (13.35–13.53 Mb) containing 26 putative genes and six small-nuclear RNAs – a manageable number of targets for functional assessment

A genome-wide library of CB4856/N2 introgression lines of Caenorhabditis elegans

Recombinant inbred lines (RILs) derived from Caenorhabditis elegans wild-type N2 and CB4856 are increasingly being used for mapping genes underlying complex traits. To speed up mapping and gene discovery, introgression lines (ILs) offer a powerful tool for more efficient QTL identification. We constructed a library of 90 ILs, each carrying a single homozygous CB4856 genomic segment introgressed into the genetic background of N2. The ILs were genotyped by 123 single-nucleotide polymorphism (SNP) markers. The proportion of the CB4856 segments in most lines does not exceed 3%, and together the introgressions cover 96% of the CB4856 genome. The value of the IL library was demonstrated by identifying novel loci underlying natural variation in two ageing-related traits, i.e. lifespan and pharyngeal pumping rate. Bin mapping of lifespan resulted in six QTLs, which all have a lifespan-shortening effect on the CB4856 allele. We found five QTLs for the decrease in pumping rate, of which four colocated with QTLs found for average lifespan. This suggests pleiotropic or closely linked QTL associated with lifespan and pumping rate. Overall, the presented IL library provides a versatile resource toward easier and efficient fine mapping and functional analyses of loci and genes underlying complex traits in C. elegans

A fluorescence based sensor assay that monitors general protein aggregation in human cells

Protein conformational disorders are characterized by disruption of protein folding and toxic accumulation of protein aggregates. Here we describe a sensitive and simple method to follow and monitor general protein aggregation in human cells. Heat shock protein 27 (HSP27) is an oligomeric small heat shock protein that binds and keeps unfolded proteins in a folding competent state. This high specificity of HSP27 for aggregated proteins can be explored to monitor aggregation in living cells by fusing it to a fluorescent protein as Green Fluorescent Protein (GFP). We have constructed a HeLa stable cell line expressing a HSP27:GFP chimeric reporter protein and after validation, this stable cell line is exposed to different agents that interfere with proteostasis, namely Arsenite, MG132, and Aβ-peptide. Exposure to proteome destabilizers lead to re-localization of HSP27:GFP fluorescence to foci, confirming that our reporter system is functional and can be used to detect and follow protein aggregation in living cells. This reporter is a valuable tool to setup wide-genetic screens to identify genes and pathways involved in protein misfolding and aggregation.publishe