Combinatorial Set Research Articles

Algorithms for ranking and unranking the combinatorial set of RNA secondary structures

In this paper, we study the combinatorial set of RNA secondary structures. The main contribution of this paper is the developed ranking and unranking algorithms for the combinatorial set of pseudoknot-free RNA secondary structures of length [Formula: see text] with [Formula: see text] base-pairs. The developed algorithms are based on a bijection between the set of RNA structures and the variants of the corresponding AND/OR tree structure. Assuming a unit-cost RAM model, the developed algorithms have polynomial time complexity [Formula: see text] for [Formula: see text] and [Formula: see text] for [Formula: see text]. In contrast to the existing algorithms, the new algorithms do not require preprocessing steps and have better overall time complexity.

Prophet Inequalities via the Expected Competitive Ratio

We consider prophet inequalities under general downward-closed constraints. In a prophet inequality problem, a decision-maker sees a series of online elements with values and needs to decide immediately and irrevocably whether or not to select each element upon its arrival, subject to an underlying feasibility constraint. Traditionally, the decision-maker’s expected performance has been compared to the expected performance of the prophet , i.e., the expected offline optimum. We refer to this measure as the Ratio of Expectations (or, in short, RoE ). However, a major limitation of the RoE measure is that it only gives a guarantee against what the optimum would be on average, while, in theory, algorithms still might perform poorly compared to the realized ex-post optimal value. Hence, we study alternative performance measures. In particular, we suggest the Expectation of Ratio (or, in short, EoR ), which is the expectation of the ratio between the value of the algorithm and the value of the prophet. This measure yields desirable guarantees, e.g., a constant EoR implies achieving a constant fraction of the ex-post offline optimum with constant probability. Moreover, in the single-choice setting, we show that the EoR is equivalent (in the worst case) to the probability of selecting the maximum, a well-studied measure in the literature. However, the probability of selecting the maximum does not generalize meaningfully to combinatorial constraints (beyond single-choice), since its direct equivalent is the probability of selecting an optimal overall set. We, thus, introduce the EoR as a cardinal variant of the probability of selecting the maximum, which extends naturally to combinatorial settings. Our main goal is to understand the relation between RoE and EoR in combinatorial settings. Specifically, we establish two reductions: For every feasibility constraint, the RoE and the EoR are at most a constant factor apart on worst-case instances. Additionally, we show that the EoR is a stronger benchmark than the RoE in that, for every instance (feasibility constraint and product distribution), the RoE is at least a constant fraction of the EoR but not vice versa. Both these reductions imply a wealth of EoR results in multiple settings where RoE results are known.

The Competition Complexity of Prophet Inequalities

We study the classic single-choice prophet inequality problem through a resource augmentation lens. Our goal is to bound the [Formula: see text]-competition complexity of different types of online algorithms. This metric asks for the smallest k such that the expected value of the online algorithm on k copies of the original instance is at least a [Formula: see text]-approximation to the expected off-line optimum on a single copy. We show that block threshold algorithms, which set one threshold per copy, are optimal and give a tight bound of [Formula: see text]. This shows that block threshold algorithms approach the off-line optimum doubly exponentially fast. For single threshold algorithms, we give a tight bound of [Formula: see text], establishing an exponential gap between block threshold algorithms and single threshold algorithms. Our model and results pave the way for exploring resource-augmented prophet inequalities in combinatorial settings. In line with this, we present preliminary findings for bipartite matching with one-sided vertex arrivals as well as in XOS combinatorial auctions. Our results have a natural competition complexity interpretation in mechanism design and pricing applications. Funding: J. Correa was partially funded by Anillo Information and Computation in Market Design [Agencia Nacional de Investigación y Desarrollo (ANID) Grant ACT210005] and the Center for Mathematical Modeling [ANID Grant FB210005]. T. Ezra is supported by the Harvard University Center of Mathematical Sciences and Applications. M. Feldman was partially funded by the European Research Council under the European Union’s Horizon 2020 research and innovation program [Grant 866132], by an Amazon Research Award, by the United States-Israel Binational Science Foundation [Grant 2020788], and by a grant from the TAU Center for AI and Data Science. V. Verdugo was partially funded by Anillo ICMD [ANID Grant ACT210005] and Fondecyt [ANID Grant 1241846].

Blood proteomics and multimodal risk profiling of human volunteers after incision injury: A translational study for advancing personalized pain management after surgery.

Blood proteomics and multimodal risk profiling of human volunteers after incision injury: A translational study for advancing personalized pain management after surgery.

Dynamics on the $\mathrm {SU}(2,1)$ -character variety of the one-holed torus

Abstract We study the relative $\mathrm {SU}(2,1)$ -character varieties of the one-holed torus, and the action of the mapping class group on them. We use an explicit description of the character variety of the free group of rank two in $\mathrm {SU}(2,1)$ in terms of traces, which allow us to describe the topology of the character variety. We then combine this description with a generalization of the Farey graph adapted to this new combinatorial setting, using ideas introduced by Bowditch. Using these tools, we can describe an open domain of discontinuity for the action of the mapping class group which strictly contains the set of convex cocompact characters, and we give several characterizations of representations in this domain.

Bactericidal Metal-Organic Gallium Frameworks - Synthesis to Application.

Gallium, a trace metal not found in its elemental form in nature, has garnered significant interest as a biocide, given its ability to interfere with iron metabolism in bacteria. Consequently, several gallium compounds have been developed and studied for their antimicrobial properties but face challenges of poor solubility and formulation for delivery. Organizing the metal into three-dimensional, hybrid scaffolds, termed metal-organic frameworks (MOFs), is an emerging platform with potential to address many of these limitations. Gallium MOFs show improved solubility and antibacterial potency relative to the free metal due to their ability to coload antibiotics and functional biomolecules. Synthetic strategies are equally versatile, with several rapid, cost-effective, and scalable methods available. In this review, we present the advantages and disadvantages of these various synthetic strategies with respect to their antibacterial efficiency, product purity, and reaction control. The activity of gallium-based MOFs against Gram-positive and Gram-negative pathogens in mono- and combinatorial therapeutic settings is discussed in the context of their mechanisms of action and structure-function-performance relationships collated from recent studies. While gallium MOF development as antibacterials is still in its nascent stages, the examples discussed here highlight their potential as a novel class of therapeutics poised to impact the fight against pan-drug-resistant bacterial pathogens.

Predicative Classes and Strict Potentialism

Abstract While sets are combinatorial collections, defined by their elements, classes are logical collections, defined by their membership conditions. We develop, in a potentialist setting, a predicative approach to (logical) classes of (combinatorial) sets. Some reasons emerge to adopt a stricter form of potentialism, which insists, not only that each object is generated at some stage of an incompletable process, but also that each truth is “made true” at some such stage. The natural logic of this strict form of potentialism is semi-intuitionistic: where each set-sized domain is classical, the domain of all sets or all classes is intuitionistic.

CO2 transport in supercritical state: Nikiski, Alaska pipeline study

AbstractCarbon dioxide (CO2) in the supercritical state, being denser yet less viscous, is suitable for long‐distance transportation. Despite this well‐known principle, implementing an operational scheme with appropriate inlet pressure and mass flow rate for supercritical CO2 (srCO2) transportation is challenging due to the complex interplay among state variables, fluid properties, pipeline dimensions and materials, and the intricate boundary and ambient conditions surrounding the pipeline. This paper utilizes PIPESIM software to conduct a feasibility study of srCO2 transportation over a 10‐mile‐long model pipeline in the Cook Inlet region of Alaska, USA. The study aims to understand the limitations of operational parameters and develop a scheme for selecting feasible parameters for srCO2 transportation. Considering geographic location, elevation profiles, and ambient conditions, the simulations calculated pressure and temperature profiles, erosion kinetics, and fluid states for various conditions derived from a combinatorial set of pipeline diameters ranging from 11 to 16 in, inlet pressures between 1,400 and 1,900 psia, and mass flow rates from 10 to 275 lbm/s, with an inlet temperature of 200 °F. The major findings indicate that larger pressure losses are expected in smaller pipelines that are well‐insulated and/or operated at lower inlet pressures. Turbulent flow is more likely to occur in smaller pipelines and at higher mass flow rates, potentially altering the state of the transported fluid. The parametric modeling results provide a scenario‐driven approach to determining a feasible range of mass flow rates, pipeline inner diameters, and inlet pressures for srCO2 transportation. © 2024 Society of Chemical Industry and John Wiley & Sons, Ltd.

Nonlinear Dynamics for the Ising Model

We introduce and analyze a natural class of nonlinear dynamics for spin systems such as the Ising model. This class of dynamics is based on the framework of mass action kinetics, which models the evolution of systems of entities under pairwise interactions, and captures a number of important nonlinear models from various fields, including chemical reaction networks, Boltzmann’s model of an ideal gas, recombination in population genetics and genetic algorithms. In the context of spin systems, it is a natural generalization of linear dynamics based on Markov chains, such as Glauber dynamics and block dynamics, which are by now well understood. However, the inherent nonlinearity makes the dynamics much harder to analyze, and rigorous quantitative results so far are limited to processes which converge to essentially trivial stationary distributions that are product measures. In this paper we provide the first quantitative convergence analysis for natural nonlinear dynamics in a combinatorial setting where the stationary distribution contains non-trivial correlations, namely spin systems at high temperatures. We prove that nonlinear versions of both the Glauber dynamics and the block dynamics converge to the Gibbs distribution of the Ising model (with given external fields) in times O(nlogn)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$O(n\\log n)$$\\end{document} and O(logn)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$O(\\log n)$$\\end{document} respectively, where n is the size of the underlying graph (number of spins). Given the lack of general analytical methods for such nonlinear systems, our analysis is unconventional, and combines tools such as information percolation (due in the linear setting to Lubetzky and Sly), a novel coupling of the Ising model with Erdős-Rényi random graphs, and non-traditional branching processes augmented by a “fragmentation” process. Our results extend immediately to any spin system with a finite number of spins and bounded interactions.

Combinatorial Order Pre-processing Search (COPS): A new pre-processing strategy for large-scale interpretable data analysis in process analytical technologies

Combinatorial Order Pre-processing Search (COPS): A new pre-processing strategy for large-scale interpretable data analysis in process analytical technologies

End-to-end, decision-based, cardinality-constrained portfolio optimization

End-to-end, decision-based, cardinality-constrained portfolio optimization

Linear independence for [formula omitted] by using [formula omitted]

Linear independence for [formula omitted] by using [formula omitted]

P53 at the crossroads of tumor immunity.

The p53 tumor suppressor protein has a plethora of cell-intrinsic functions and consequences that impact diverse cell types and tissues. Recent studies are beginning to unravel how wild-type and mutant p53 work in distinct ways to modulate tumor immunity. This sets up a disequilibrium between tumor immunosurveillance and escape therefrom. The ability to exploit this emerging knowledge for translational approaches may shape immunotherapy and targeted therapeutics in the future, especially in combinatorial settings.

Synergistic Polymer Blending Informs Efficient Terpolymer Design and Machine Learning Discerns Performance Trends for pDNA Delivery.

Cationic polymers offer an alternative to viral vectors in nucleic acid delivery. However, the development of polymer vehicles capable of high transfection efficiency and minimal toxicity has remained elusive, and continued exploration of the vast design space is required. Traditional single polymer syntheses with large monomer bases are very time-intensive, limiting the speed at which new formulations are identified. In this work, we present an experimental method for the quick probing of the design space, utilizing a combinatorial set of 90 polymer blends, derived from 6 statistical copolymers, to deliver pDNA. This workflow facilitated rapid screening of polyplex compositions, successfully tailoring polyplex hydrophobicity, particle size, and payload binding affinity. This workflow identified blended polyplexes with high levels of transfection efficiency and cell viability relative to single copolymer controls and commercial JetPEI, indicating synergistic benefits from copolymer blending. Polyplex composition was coupled with biological outputs to guide the synthesis of single terpolymer vehicles, with high-performing polymers P10 and M20, providing superior transfection of HEK293T cells in serum-free and serum-containing media, respectively. Machine learning coupled with SHapley Additive exPlanations (SHAP) was used to identify polymer/polyplex attributes that most impact transfection efficiency, viability, and overall effective efficiency. Subsequent transfections on ARPE-19 and HDFn cells found that P10 and M20 were surpassed in performance by M10, contrasting with results in HEK293T cells. This cell type dependency reinforced the need to evaluate transfection conditions with multiple cell models to potentially identify moieties more beneficial to delivery in certain tissues. Overall, the workflow employed can be used to expedite the exploration of the polymer design space, bypassing extensive synthesis, and to develop improved polymer delivery vehicles more readily for nucleic acid therapies.

Beyond benchmarking and towards predictive models of dataset-specific single-cell RNA-seq pipeline performance

BackgroundThe advent of single-cell RNA-sequencing (scRNA-seq) has driven significant computational methods development for all steps in the scRNA-seq data analysis pipeline, including filtering, normalization, and clustering. The large number of methods and their resulting parameter combinations has created a combinatorial set of possible pipelines to analyze scRNA-seq data, which leads to the obvious question: which is best? Several benchmarking studies compare methods but frequently find variable performance depending on dataset and pipeline characteristics. Alternatively, the large number of scRNA-seq datasets along with advances in supervised machine learning raise a tantalizing possibility: could the optimal pipeline be predicted for a given dataset?ResultsHere, we begin to answer this question by applying 288 scRNA-seq analysis pipelines to 86 datasets and quantifying pipeline success via a range of measures evaluating cluster purity and biological plausibility. We build supervised machine learning models to predict pipeline success given a range of dataset and pipeline characteristics. We find that prediction performance is significantly better than random and that in many cases pipelines predicted to perform well provide clustering outputs similar to expert-annotated cell type labels. We identify characteristics of datasets that correlate with strong prediction performance that could guide when such prediction models may be useful.ConclusionsSupervised machine learning models have utility for recommending analysis pipelines and therefore the potential to alleviate the burden of choosing from the near-infinite number of possibilities. Different aspects of datasets influence the predictive performance of such models which will further guide users.

Strictly monotone sequences of lower and upper bounds on Perron values and their combinatorial applications

In this paper, we present monotone sequences of lower and upper bounds on the Perron value of a nonnegative matrix, and we study their strict monotonicity. Using those sequences, we provide two combinatorial applications. One is to improve bounds on Perron values of rooted trees in combinatorial settings, in order to find characteristic sets of trees. The other is to generate log-concave and log-convex sequences through the monotone sequences.

Online Submodular Maximization via Online Convex Optimization

We study monotone submodular maximization under general matroid constraints in the online setting. We prove that online optimization of a large class of submodular functions, namely, threshold potential functions, reduces to online convex optimization (OCO). This is precisely because functions in this class admit a concave relaxation; as a result, OCO policies, coupled with an appropriate rounding scheme, can be used to achieve sublinear regret in the combinatorial setting. We also show that our reduction extends to many different versions of the online learning problem, including the dynamic regret, bandit, and optimistic-learning settings.

Abstract 2902: CA-4948 (emavusertib) improves treatment response of preclinical metastatic brain melanoma to anti-PD-1 immune checkpoint blockade

Abstract Background: Although recent advances in immunotherapy for metastatic melanoma have transformed the treatment paradigm for a disease that once carried a grim prognosis, nearly 50% of patients fail to reach a complete response to immune checkpoint blockade (ICB) due to multiple mechanisms of tumor-induced immune resistance. These challenges are amplified in the CNS tumor microenvironment (TME) where metastatic brain melanoma (MBM) demonstrates diminished clinical benefit to ICB treatment. A deeper understanding of these mechanisms are required to improve therapeutic response to ICB for these patients. Our group has previously identified that aberrant activation of the myddosomal cascade through downstream interleukin (IL)-1 receptor-associated kinase (IRAK-4) signaling results in chronic stimulation of MAPK and NF-κB in MBM. Further investigation reveals myddosome signaling emanates in large part from the TME, resulting in reflexive immune suppression. CA-4948 (emavusertib), a small molecule inhibitor of IRAK-4, is capable of reaching therapeutic dose levels in the brain where it demonstrates on-target inhibition of this pathway. These data highlight a unique therapeutic opportunity where selective inhibition of immune-suppressive signaling via targeted IRAK-4 blockade may sensitize MBM to anti-PD-1 ICB. Methods Multispectral imaging of patient MBM samples were analyzed for myddosome expression in the TME. Melanoma preclinical models, including both primary site (cutaneous) and metastatic brain disease, were evaluated for tumor burden and survival in response to CA-4948 treatment alone and in combination with anti-PD-1 ICB. Immunological responses of tumor to treatment were evaluated in two transgenic reporter models, CCR2RFPCX3CR1GFP and IFNγIRES-EYFP, to determine both the distribution and activation of infiltrating immune cells. Tumor-associated myeloid cells were assessed for phenotypic markers by multiparameter flow cytometry. Results Myddosome signaling was found to be elevated in tumor-associated immune cells in patient MBM specimens. Treatment of preclinical melanoma with CA-4948 combined with anti-PD-1 ICB resulted in significantly reduced tumor growth and improved survival in three independent models. CA-4948 treatment was associated with reduced tumor recruitment of peripherally derived tumor-associated macrophages, as well as increased lymphocyte infiltration and improved pro-inflammatory signaling measured by increased IFNγ expression in the combinatorial setting. Conclusion Targeted inhibition of IRAK-4 with CA-4948 improves immune surveillance and activation in preclinical models when combined with anti-PD-1 ICB, resulting in reduced tumor growth and increased survival. Thus, CA-4948 may be an effective adjuvant treatment strategy alongside anti-PD-1 ICB for the treatment of metastatic melanoma. Citation Format: Christina A. von Roemeling, Bently P. Doonan, Amanda M. Acevedo, Jeet A. Patel, Savannah L. Carpenter, Alisha Bhatia, Reinhard W. von Roemeling, Jamison Hoffman, Maureen Lane, Duane A. Mitchell. CA-4948 (emavusertib) improves treatment response of preclinical metastatic brain melanoma to anti-PD-1 immune checkpoint blockade [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2024; Part 1 (Regular Abstracts); 2024 Apr 5-10; San Diego, CA. Philadelphia (PA): AACR; Cancer Res 2024;84(6_Suppl):Abstract nr 2902.

Full-Combinatorial Concentration Gradient Array with 3D Micro/Nanofluidics for Antibiotic Susceptibility Testing.

Recent advancements in micro/nanofluidics have facilitated on-chip microscopy of cellular responses in a high-throughput and controlled microenvironment with the desired physicochemical properties. Despite its potential benefits to combination drug discovery, generating a complete combinatorial set of concentration gradients for multiple reagents in an array format remains challenging. The main reason is limited layouts of conventional micro/nanofluidic systems based on two-dimensional channel networks. In this paper, we present a device with three-dimensional (3D) interconnection of micro/nanochannels capable of generating a complete combinatorial set of concentration gradients for two reagents. The device was readily fabricated by laminating a pair of multilayered monolithic films containing a Christmas tree-like mixer, a cell culture chamber array, and through-holes, all within each single film. We assessed the reliable generation of a full-combinatorial concentration gradient array and validated it by using numerical analysis. We applied the proposed device to test the antibiotic susceptibility of bacterial cells in a convenient one-step manner. Furthermore, we explored the potential of the device to accommodate the arrayed complete combinatorial set for two or more drugs, while extending the capabilities of our laminated object manufacturing method for realizing 3D micro/nanofluidic systems.

Systematic Evaluation of Protein-Small Molecule Hybrids on the Yeast Surface.

Protein-small molecule hybrids are structures that have the potential to combine the inhibitory properties of small molecules and the specificities of binding proteins. However, achieving such synergies is a substantial engineering challenge with fundamental principles yet to be elucidated. Recent work has demonstrated the power of the yeast display-based discovery of hybrids using a combination of fibronectin-binding domains and thiol-mediated conjugations to introduce small-molecule warheads. Here, we systematically study the effects of expanding the chemical diversity of these hybrids on the yeast surface by investigating a combinatorial set of fibronectins, noncanonical amino acid (ncAA) substitutions, and small-molecule pharmacophores. Our results show that previously discovered thiol-fibronectin hybrids are generally tolerant of a range of ncAA substitutions and retain binding functions to carbonic anhydrases following click chemistry-mediated assembly of hybrids with diverse linker structures. Most surprisingly, we identified several cases where replacement of a potent acetazolamide warhead with a substantially weaker benzenesulfonamide warhead still resulted in the assembly of multiple functional hybrids. In addition to these unexpected findings, we expanded the throughput of our system by validating a 96-well plate-based format to produce yeast-displayed hybrid conjugates in parallel. These efficient explorations of hybrid chemical diversity demonstrate that there are abundant opportunities to expand the functions of protein-small molecule hybrids and elucidate principles that dictate their efficient discovery and design.