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We study scheduling mechanisms that explore the trade-off between containing the spread of COVID-19 and performing in-person activity in organizations. Our mechanisms, referred to as group scheduling, are based on partitioning the population randomly into groups and scheduling each group on appropriate days with possible gaps (when no one is working and all are quarantined). Each group interacts with no other group and, importantly, any person who is symptomatic in a group is quarantined. We show that our mechanisms effectively trade-off in-person activity for more effective control of the COVID-19 virus spread. In particular, we show that a mechanism which partitions the population into two groups that alternatively work in-person for five days each, flatlines the number of COVID-19 cases quite effectively, while still maintaining in-person activity at 70% of pre-COVID-19 level. Other mechanisms that partitions into two groups with less continuous work days or more spacing or three groups achieve even more aggressive control of the virus at the cost of a somewhat lower in-person activity (about 50%). We demonstrate the efficacy of our mechanisms by theoretical analysis and extensive experimental simulations on various epidemiological models based on real-world data., Competing Interests: The authors have declared that no competing interests exist.

Structural motifs encapsulate local sequence-structure-function relationships characteristic of related proteins, enabling the prediction of functional characteristics of new proteins, providing molecular-level insights into how those functions are performed, and supporting the development of variants specifically maintaining or perturbing function in concert with other properties. Numerous computational methods have been developed to search through databases of structures for instances of specified motifs. However, it remains an open problem how best to leverage the local geometric and chemical constraints underlying structural motifs in order to develop motif-finding algorithms that are both theoretically and practically efficient. We present a simple, general, efficient approach, called Ballast (ball-based algorithm for structural motifs), to match given structural motifs to given structures. Ballast combines the best properties of previously developed methods, exploiting the composition and local geometry of a structural motif and its possible instances in order to effectively filter candidate matches. We show that on a wide range of motif-matching problems, Ballast efficiently and effectively finds good matches, and we provide theoretical insights into why it works well. By supporting generic measures of compositional and geometric similarity, Ballast provides a powerful substrate for the development of motif-matching algorithms.

Motivation: Complementing its traditional role in structural studies of proteins, nuclear magnetic resonance (NMR) spectroscopy is playing an increasingly important role in functional studies. NMR dynamics experiments characterize motions involved in target recognition, ligand binding, etc., while NMR chemical shift perturbation experiments identify and localize protein-protein and protein-ligand interactions. The key bottleneck in these studies is to determine the backbone resonance assignment, which allows spectral peaks to be mapped to specific atoms. This article develops a novel approach to address that bottleneck, exploiting an available X-ray structure or homology model to assign the entire backbone from a set of relatively fast and cheap NMR experiments., Results: We formulate contact replacement for resonance assignment as the problem of computing correspondences between a contact graph representing the structure and an NMR graph representing the data; the NMR graph is a significantly corrupted, ambiguous version of the contact graph. We first show that by combining connectivity and amino acid type information, and exploiting the random structure of the noise, one can provably determine unique correspondences in polynomial time with high probability, even in the presence of significant noise (a constant number of noisy edges per vertex). We then detail an efficient randomized algorithm and show that, over a variety of experimental and synthetic datasets, it is robust to typical levels of structural variation (1-2 AA), noise (250-600%) and missings (10-40%). Our algorithm achieves very good overall assignment accuracy, above 80% in alpha-helices, 70% in beta-sheets and 60% in loop regions., Availability: Our contact replacement algorithm is implemented in platform-independent Python code. The software can be freely obtained for academic use by request from the authors.

Motivation: Backbone resonance assignment is a critical bottleneck in studies of protein structure, dynamics and interactions by nuclear magnetic resonance (NMR) spectroscopy. A minimalist approach to assignment, which we call 'contact-based', seeks to dramatically reduce experimental time and expense by replacing the standard suite of through-bond experiments with the through-space (nuclear Overhauser enhancement spectroscopy, NOESY) experiment. In the contact-based approach, spectral data are represented in a graph with vertices for putative residues (of unknown relation to the primary sequence) and edges for hypothesized NOESY interactions, such that observed spectral peaks could be explained if the residues were 'close enough'. Due to experimental ambiguity, several incorrect edges can be hypothesized for each spectral peak. An assignment is derived by identifying consistent patterns of edges (e.g. for alpha-helices and beta-sheets) within a graph and by mapping the vertices to the primary sequence. The key algorithmic challenge is to be able to uncover these patterns even when they are obscured by significant noise., Results: This paper develops, analyzes and applies a novel algorithm for the identification of polytopes representing consistent patterns of edges in a corrupted NOESY graph. Our randomized algorithm aggregates simplices into polytopes and fixes inconsistencies with simple local modifications, called rotations, that maintain most of the structure already uncovered. In characterizing the effects of experimental noise, we employ an NMR-specific random graph model in proving that our algorithm gives optimal performance in expected polynomial time, even when the input graph is significantly corrupted. We confirm this analysis in simulation studies with graphs corrupted by up to 500% noise. Finally, we demonstrate the practical application of the algorithm on several experimental beta-sheet datasets. Our approach is able to eliminate a large majority of noise edges and to uncover large consistent sets of interactions., Availability: Our algorithm has been implemented in the platform-independent Python code. The software can be freely obtained for academic use by request from the authors.

Nuclear magnetic resonance (NMR) spectroscopy allows scientists to study protein structure, dynamics and interactions in solution. A necessary first step for such applications is determining the resonance assignment, mapping spectral data to atoms and residues in the primary sequence. Automated resonance assignment algorithms rely on information regarding connectivity (e.g., through-bond atomic interactions) and amino acid type, typically using the former to determine strings of connected residues and the latter to map those strings to positions in the primary sequence. Significant ambiguity exists in both connectivity and amino acid type information. This paper focuses on the information content available in connectivity alone and develops a novel random-graph theoretic framework and algorithm for connectivity-driven NMR sequential assignment. Our random graph model captures the structure of chemical shift degeneracy, a key source of connectivity ambiguity. We then give a simple and natural randomized algorithm for finding optimal assignments as sets of connected fragments in NMR graphs. The algorithm naturally and efficiently reuses substrings while exploring connectivity choices; it overcomes local ambiguity by enforcing global consistency of all choices. By analyzing our algorithm under our random graph model, we show that it can provably tolerate relatively large ambiguity while still giving expected optimal performance in polynomial time. We present results from practical applications of the algorithm to experimental datasets from a variety of proteins and experimental set-ups. We demonstrate that our approach is able to overcome significant noise and local ambiguity in identifying significant fragments of sequential assignments.

Ferric gluconate complex in sucrose (Ferrlecit) has been associated with less side-effects than iron dextran; however, the recommended dose of 62.5-125 mg per treatment is only suitable for haemodialysis (HD) patients. We retrospectively analysed the incidence of the side-effects associated with a high dose of Ferrlecit infusion (20 treatments in 13 patients; 10 treatments of 250 mg/3-4 h, and 10 treatments of 500 mg/5 h infusion). The patients were in the age range of 32-75 years old, seven with chronic renal failure (CRF), and six on dialysis treatment. One (10%) of the 10 treatments using a 250 mg dose was complicated with severe nausea/vomiting, diarrhoea and a burning sensation in the feet. Three (30%) of the 10 treatments using a 500 mg dose were complicated with: chills, severe nausea/vomiting, hypotension and syncope in one; severe nausea/vomiting, diarrhoea and hypotension in one; and an episode of vomiting in one patient. A single treatment with a 250 mg dose resulted in no significant change in haematological parameters. A single treatment with a 500 mg dose resulted in a significant increase in haemoglobin (Hgb) and haematocrit (Hct), but only a rising trend in serum iron,% transferrin saturation and ferritin pre versus 1-2 months postinfusion. In conclusion, Ferrlecit doses of 250 or 500 mg are complicated with significant untoward reactions in 10-30% of patients, in a dose-dependent fashion.