Combinatorial Set Research Articles

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 novel approach for optimizing data pre-processing is proposed in this work. Unlike simultaneous hyperparameter optimization, COPS employs a priori optimization to reduce computational time while refining the search space for preprocessing sequences and combinations. It allows for setting a maximum number of pre-processing methods, while efficiently searching through combinations of methods with chemically relevant knowledge. In this work, 67 calibration datasets across various analytical techniques, including fluorescence spectroscopy, gas chromatography (GC), near-infrared spectroscopy (NIR), mid-infrared spectroscopy (MIR), visible-near-infrared spectroscopy (Vis-NIR), Raman spectroscopy, nuclear magnetic resonance (NMR) spectroscopy, and voltammetry were evaluated. COPS yielded significant improvements over existing methodologies based on design of experiment and compounded pre-processing approaches. The COPS outperformed the other methods, resulting in an average root mean square error of prediction (RMSEP) reduction of 31.7%, while also reduced the complexity (number of latent variables) of the model which allows for easier interpretation. This underscores the importance of combinatorial order set theory for the search of pre-processing method combinations (without fixing the sequence of pre-processing methods) to enhance model performance and interpretation. The novel COPS approach can be employed in process analytical technology (such as inline, online or at-line chemical sensing analytics) to enhance predictive accuracy and operational efficiency, fundamentally transforming the quality and reliability of chemical process monitoring and control.

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

Portfolios employing a (factor) risk model are usually constructed using a two step process: first, the risk model parameters are estimated, then the portfolio is constructed. Recent works have shown that this decoupled approach may be improved using an integrated framework that takes the downstream portfolio optimization into account during parameter estimation. In this work we implement an integrated, end-to-end, predict-&-optimize framework to the cardinality-constrained portfolio optimization problem. To the best of our knowledge, we are the first to implement the framework to a nonlinear mixed integer programming problem. Since the feasible region of the problem is discontinuous, we are unable to directly differentiate through it. Thus, we compare three different continuous relaxations of increasing tightness to the problem which are placed as an implicit layers in a neural network. The parameters of the factor model governing the problem’s covariance matrix structure are learned using a loss function that directly corresponds to the decision quality made based on the factor model’s predictions. Using real world financial data, our proposed end-to-end, decision based model is compared to two decoupled alternatives. Results show significant improvements over the traditional decoupled approaches across all cardinality sizes and model variations while highlighting the need of additional research into the interplay between experimental design, problem size and structure, and relaxation tightness in a combinatorial setting.

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

In this note we prove linear independence of the combinatorial spanning set for standard Cℓ(1)-module L(kΛ0) by establishing a connection with the combinatorial basis of Feigin-Stoyanovsky's type subspace W(kΛ0) of C2ℓ(1)-module L(kΛ0). It should be noted that the proof of linear independence for the basis of W(kΛ0) is obtained by using simple currents and intertwining operators in the vertex operator algebra L(kΛ0).

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.

Morphological and Phylogenetic Analyses Reveal Three New Species of Phyllosticta (Botryosphaeriales, Phyllostictaceae) in China.

The genus Phyllosticta has been reported worldwide and contains many pathogenic and endophytic species isolated from a wide range of plant hosts. A multipoint phylogeny based on gene coding combinatorial data sets for the internal transcribed spacer (ITS), large subunit of ribosomal RNA (LSU rDNA), translation elongation factor 1α (TEF1α), actin (ACT), and glycerol-3-phosphate dehydrogenase (GPDH), combined with morphological characteristics, was performed. We describe three new species, P. fujianensis sp. nov., P. saprophytica sp. nov., and P. turpiniae sp. nov., and annotate and discusse their similarities and differences in morphological relationships and phylogenetic phases with closely related species.

Robust planning for multi-stage forceful manipulation

Multi-step forceful manipulation tasks, such as opening a push-and-twist childproof bottle, require a robot to make various planning choices that are substantially impacted by the requirement to exert force during the task. The robot must reason over discrete and continuous choices relating to the sequence of actions, such as whether to pick up an object, and the parameters of each of those actions, such how to grasp the object. To enable planning and executing forceful manipulation, we augment an existing task and motion planner with constraints that explicitly consider torque and frictional limits, captured through the proposed forceful kinematic chain constraint. In three domains, opening a childproof bottle, twisting a nut and cutting a vegetable, we demonstrate how the system selects from among a combinatorial set of strategies. We also show how cost-sensitive planning can be used to find strategies and parameters that are robust to uncertainty in the physical parameters.

MET overexpression in ovarian cancer via CD24-induced downregulation of miR-181a: A signalling for cellular quiescence-like state and chemoresistance in ovarian CSCs.

Increased expression of CD24 and MET, markers for cancer stem-like cells (CSCs), are each associated with ovarian cancer severity. However, whether CD24 and MET are co-expressed in ovarian CSCs and, if so, how they are related to CSC phenotype manifestation remains unknown. Our immunohistochemistry analysis showed that the co-expression of CD24 and MET was associated with poorer patient survival in ovarian cancer than those without. In addition, analyses using KM plotter and ROC plotter presented that the overexpression of CD24 or MET in ovarian cancer patients was associated with resistance to platinum-based chemotherapy. In our miRNA transcriptome and putative target genes analyses, miR-181a was downregulated in CD24-high ovarian cancer cells compared to CD24-low and predicted to bind to CD24 and MET 3'UTRs. In OV90 and SK-OV-3 cells, CD24 downregulated miR-181a expression by Src-mediated YY1 activation, leading to increased expression of MET. And, CD24 or MET knockdown or miR-181a overexpression inhibited the manifestation of CSC phenotypes, cellular quiescence-like state and chemoresistance, in OV90 and SK-OV-3 cells: increased colony formation, decreased G0/G1 phase cell population and increased sensitivity to Cisplatin and Carboplatin. Our findings suggest that CD24-miR-181a-MET may consist of a signalling route for ovarian CSCs, therefore being a combinatory set of markers and therapeutic targets for ovarian CSCs.

A Workflow for Accelerating Multimodal Data Collection for Electrodeposited Films

Future machine learning strategies for materials process optimization will likely replace human capital-intensive artisan research with autonomous and/or accelerated approaches. Such automation enables accelerated multimodal characterization that simultaneously minimizes human errors, lowers costs, enhances statistical sampling, and allows scientists to allocate their time to critical thinking instead of repetitive manual tasks. Previous acceleration efforts to synthesize and evaluate materials have often employed elaborate robotic self-driving laboratories or used specialized strategies that are difficult to generalize. Herein we describe an implemented workflow for accelerating the multimodal characterization of a combinatorial set of 915 electroplated Ni and Ni–Fe thin films resulting in a data cube with over 160,000 individual data files. Our acceleration strategies do not require manufacturing-scale resources and are thus amenable to typical materials research facilities in academic, government, or commercial laboratories. The workflow demonstrated the acceleration of six characterization modalities: optical microscopy, laser profilometry, X-ray diffraction, X-ray fluorescence, nanoindentation, and tribological (friction and wear) testing, each with speedup factors ranging from 13–46x. In addition, automated data upload to a repository using FAIR data principles was accelerated by 64x.

Numerically efficient and robust interior-point algorithm for finite strain rate-independent crystal plasticity

The challenges of classic rate-independent crystal plasticity models regarding the determination of active slip systems and computation of solutions due to linear dependent slip systems are still a field of active research. In that regard, interior-point methods are promising approaches because a logarithmic barrier term naturally avoids the combinatorial active set search, and these methods are applicable even when the gradient of inequality constraints is linearly dependent. In this paper, a new interior-point algorithm suitable for rate-independent crystal plasticity at finite strains is developed. For that purpose, the postulate of maximum dissipation is recast as a constrained optimization problem whose optimality conditions are derived by utilizing interior-point approaches. This optimization problem is discretized in time by means of an exponential time integration of the flow rule, and the time-discrete equations are solved by a Newton scheme. The focus of this paper is the efficiency and robustness of the implementation of this approach. In particular, the effect of different line search procedures, favorable residual forms, preconditioning methods, barrier parameter updates and the consistent algorithmic tangent modulus are discussed and further elaborated. In addition, aspects regarding uniqueness and well-posedness of the algorithm are analyzed in a geometrically linearized setting. Efficiency and robustness of the developed algorithm are shown by numerical examples of an FCC crystal including finite element simulations without stabilizing hardening or rate-dependent effects. Furthermore, the results are compared to the well-established augmented Lagrangian formulation.

Flip paths between lattice triangulations

We present a O(n32)-time algorithm for the shortest (diagonal) flip path problem for lattice triangulations with n points, improving over previous O(n2)-time algorithms. For a large, natural class of inputs, our bound is tight in the sense that our algorithm runs in time linear in the number of flips in the output flip path. Our results rely on an independently interesting structural elucidation of shortest flip paths as the linear orderings of a unique partially ordered set, called a minimum flip plan, constructed by a novel use of Farey sequences from elementary number theory. Flip paths between general (not necessarily lattice) triangulations have been studied in the combinatorial setting for nearly a century. In the Euclidean geometric setting, finding a shortest flip path between two triangulations is NP-complete. However, for lattice triangulations, which are studied as spin systems, there are known On2-time algorithms to find shortest flip paths. These algorithms, as well as ours, apply to constrained flip paths that ensure a set of constraint edges are present in every triangulation along the path. Implications for determining simultaneously flippable edges, i.e. finding optimal simultaneous flip paths between lattice triangulations, and for counting lattice triangulations are discussed.