Combinatorial Applications Research Articles

Cuminaldehyde in combination with tetracycline shows promising antibiofilm activity against drug-resistant Pseudomonas aeruginosa

Pseudomonas aeruginosa, an opportunistic pathogen often causes biofilm-linked infections. A combinatorial approach involving tetracycline (antibiotic) and cuminaldehyde (phytochemical) was explored to combat this infectious pathogen. The results showed that both tetracycline and cuminaldehyde individually demonstrated antibacterial effects. However, when the compounds were applied together, there was a significant increase in their antimicrobial potential. The determined fractional inhibitory concentration index of 0.43 indicated a synergistic interaction between the two compounds. Furthermore, a series of experiments demonstrated that the combined application of cuminaldehyde and tetracycline could lead to a significant enhancement of their antibiofilm potential. This enhanced antibiofilm potential was attributed to the accumulation of reactive oxygen species and increased cell membrane permeability. Besides, this combinatorial application reduced the secretion of various virulence factors from P. aeruginosa. Therefore, this combined approach holds promise for effectively treating P. aeruginosa biofilms.

Advancing Anticancer Drug Discovery: Leveraging Metabolomics and Machine Learning for Mode of Action Prediction by Pattern Recognition.

A bottleneck in the development of new anti-cancer drugs is the recognition of their mode of action (MoA). Metabolomics combined with machine learning allowed to predict MoAs of novel anti-proliferative drug candidates, focusing on human prostate cancer cells (PC-3). As proof of concept, 38 drugs are studied with known effects on 16 key processes of cancer metabolism, profiling low molecular weight intermediates of the central carbon and cellular energy metabolism (CCEM) by LC-MS/MS. These metabolic patterns unveiled distinct MoAs, enabling accurate MoA predictions for novel agents by machine learning. The transferability of MoA predictions based on PC-3 cell treatments is validated with two other cancer cell models, i.e., breast cancer and Ewing's sarcoma, and show that correct MoA predictions for alternative cancer cells are possible, but still at some expense of prediction quality. Furthermore, metabolic profiles of treated cells yield insights into intracellular processes, exemplified for drugs inducing different types of mitochondrial dysfunction. Specifically, it is predicted that pentacyclic triterpenes inhibit oxidative phosphorylation and affect phospholipid biosynthesis, as confirmed by respiration parameters, lipidomics, and molecular docking. Using biochemical insights from individual drug treatments, this approach offers new opportunities, including the optimization of combinatorial drug applications.

In-Materia Annealing and Combinatorial Optimization Based on Vertical Memristive Array.

Due to its area and energy efficiency, a memristive crossbar array (CBA) has been extensively studied for various combinatorial optimization applications, from network problems to circuit design. However, conventional approaches include heavily burdening software fine-tuning for the annealing process. Instead, this study introduces the "in-materia annealing" method, where the inter-layer interference of vertically stacked memristive CBA is utilized as an annealing method. When mapping combinatorial optimization problems into the configuration layer of the CBA, exponentially decaying annealing profiles are generated in nearby noise layers. Moreover, in-materia annealing profiles can be controlled by changing compliance current, read voltage, and read pulse width. Therefore, the annealing profiles can be arbitrarily controlled and generated individually for each cell, providing rich noise sources to solve the problem efficiently. Consequently, the experimental and simulation of Max-Cut and weighted Max-Cut problems achieve notable results with the minimum software burden.

Individual and combinatorial application of nanosilica and carbon nanoparticles alleviate nickel stress in barley (Hordeum vulgare L.): Impacts on gene expression, AsA − GSH cycle, cellular fractionation, and proline metabolism

Nanotechnology is grabbing great attention all over the world because of its stimulating use in numerous fields, and the nanosilica (nSi) and carbon nanoparticles (CNPs) application has been examined in various studies. Conversely, the nSi and CNPs combinatorial use is a new method and researched in limited literature. For this purpose, a pot experiment was conducted to examine various growth and biochemical parameters in barley (Hordeum vulgare L.) under the toxic concentration of nickel (Ni) i.e., 200 mg kg−1 which were primed with combined application of two NPs of nSi at 3 mM and CNPs i.e., 200 μM respectively. The results showed that the Ni toxicity in the soil showed a significantly (P < 0.05) declined in the growth, gas exchange attributes, sugars, AsA-GSH cycle, cellular fractionation, proline metabolism in H. vulgare. However, Ni toxicity significantly (P < 0.05) increased oxidative stress biomarkers, enzymatic and nonenzymatic antioxidants including their gene expression in H. vulgare. Although, the application of nSi and CNPs showed a significant (P < 0.05) increase in the plant growth and biomass, gas exchange characteristics, enzymatic and non-enzymatic compounds and their gene expression and also decreased the oxidative stress, and Ni uptake. In addition, individual or combined application of nSi and CNPs enhanced the cellular fractionation and decreases the proline metabolism and AsA−GSH cycle in H. vulgare. These results open new insights for sustainable agriculture practices and hold immense promise in addressing the pressing challenges of heavy metal contamination in agricultural soils.

Exploring the antibacterial efficacy of Satureja hortensis and Bacillus subtilis extracts in combating Xanthomonas citri

Biofilm plays a critical role in protecting the associated bacterial colonies. Citrus canker caused by Xanthomonas citri, resulted in remarkable yield reduction in citrus orchards. This study aims to evaluate the anti-biofilm properties of S. hortensis and B. subtilis extracts against X. citri. The antibacterial effects of both extracts were evaluated using the disk diffusion method and 96-well microdilution plates. Crystal violet and XTT procedures were employed to assess the inhibition of adhesion and antibiofilm effects of both extracts. The checkboard titration method was applied to determine the synergistic effects of the plant-bacterial extracts. The antibiofilm effects were confirmed by the light microscopy method. The results showed that the antibacterial and antibiofilm properties of both extracts varied. The MIC values of S. hortensis and B. subtilis extracts were 6.25 and 50 mg/ml, respectively. In these concentrations the inhibition of adhesion effects of S. hortensis and B. subtilis were 70% and 80%, whereas their antibiofilm effects were 60% and 72%. S. hortensis and B. subtilis extracts showed 63% and 76% antibiofilm activity, respectively, using the XTT test. The extracts showed synergistic effects, resulting in higher inhibition rates in combinatorial applications. Molecular docking results also confirmed that the secondary metabolites of S. hortensis could interact with different X. citri proteins differentially. Further large-scale studies on combinatorial antibiofilm effects of plant and bacterial extracts against citrus pathogens will provide new opportunities to develop safe and applicable reagents to control these destructive diseases.

Next-generation mapping of the salicylic acid signaling hub and transcriptional cascade

For over 60 years, salicylic acid (SA) has been known as a plant immune signal required for basal and systemic acquired resistance. SA activates these immune responses by reprogramming ∼20% of the transcriptome through NPR1. However, components in the NPR1 signaling hub, which appears as nuclear condensates, and the NPR1 signaling cascade have remained elusive due to difficulties in studying this transcriptional cofactor, whose chromatin association is indirect and likely transient. To overcome this challenge, we applied TurboID to divulge the NPR1 proxiome, which detected almost all known NPR1 interactors as well as new components of transcription-related complexes. Testing of new components showed that chromatin remodeling and histone demethylation contribute to SA-induced resistance. Globally, the NPR1 proxiome has a striking similarity to the proxiome of GBPL3 that is involved in SA synthesis, except for associated transcription factors (TFs), suggesting that common regulatory modules are recruited to reprogram specific transcriptomes by transcriptional cofactors, like NPR1, through binding to unique TFs. Stepwise green fluorescent protein-tagged factor cleavage under target and release using nuclease (greenCUT&RUN) analyses showed that, upon SA induction, NPR1 initiates the transcriptional cascade primarily through association with TGACG-binding TFs to induce expression of secondary TFs, predominantly WRKYs. Further, WRKY54 and WRKY70 were identified to play a major role in inducing immune-output genes without interacting with NPR1 at the chromatin. Moreover, loss of condensate formation function of NPR1 decreases its chromatin association and transcriptional activity, indicating the importance of condensates in organizing the NPR1 signaling hub and initiating the transcriptional cascade. Collectively, this study demonstrates how combinatorial applications of TurboID and stepwise greenCUT&RUN transcend traditional genetic methods to globally map signaling hubs and transcriptional cascades for in-depth explorations.

Design and Synthesis of Cyclic Dinucleotide Analogues Containing Triazolyl C-Nucleosides.

Natural cyclic dinucleotide (CDN) is the secondary messenger involved in bacterial hemostasis, human innate immunity, and bacterial antiphage immunity. Synthetic CDN and its analogues are key molecular probes and potential immunotherapeutic agents. Several CDN analogues are under clinical research for antitumor immunotherapy. A myriad of synthetic methods have been developed and reported for the preparation of CDN and its analogues. However, most of the protocols require multiple steps, and only one CDN or its analogue is prepared at a time. In this study, a strategy based on a macrocyclic ribose phosphate skeleton containing a 1'-alkynyl group was designed and developed to prepare CDN analogues containing triazolyl C-nucleosides by click chemistry. Combinatorial application of click chemistry and the sulfenylation cascade to the macrocyclic skeleton expanded the diversity of the CDN analogues. This macrocyclic skeleton strategy rapidly and efficiently provides CDN analogues to facilitate research on microbiology, immunology, and immunotherapy.

A note on the k-restriction problem

Consider a set of demands, each taking length-k strings as input. The k-restriction problem is to construct a small set of length-m strings, such that given any k positions and any demand, there exists a string in the set satisfying the demand at these positions. The k-restriction problem relates to many problems, such as k-independent sets, covering arrays, and many other combinatorial applications. By considering the VC-dimension of demands, we prove bounds independent of the number of demands with the Lovász Local Lemma. As a result, we can prove better bounds for demands with finite VC-dimension.

Uniform syndeticity in multiple recurrence

Abstract The main theorem of this paper establishes a uniform syndeticity result concerning the multiple recurrence of measure-preserving actions on probability spaces. More precisely, for any integers $d,l\geq 1$ and any $\varepsilon&gt; 0$ , we prove the existence of $\delta&gt;0$ and $K\geq 1$ (dependent only on d, l, and $\varepsilon $ ) such that the following holds: Consider a solvable group $\Gamma $ of derived length l, a probability space $(X, \mu )$ , and d pairwise commuting measure-preserving $\Gamma $ -actions $T_1, \ldots , T_d$ on $(X, \mu )$ . Let E be a measurable set in X with $\mu (E) \geq \varepsilon $ . Then, K many (left) translates of $$ \begin{align*} \big\{\gamma\in\Gamma\colon \mu(T_1^{\gamma^{-1}}(E)\cap T_2^{\gamma^{-1}} \circ T^{\gamma^{-1}}_1(E)\cap \cdots \cap T^{\gamma^{-1}}_d\circ T^{\gamma^{-1}}_{d-1}\circ \cdots \circ T^{\gamma^{-1}}_1(E))\geq \delta \big\} \end{align*} $$ cover $\Gamma $ . This result extends and refines uniformity results by Furstenberg and Katznelson. As a combinatorial application, we obtain the following uniformity result. For any integers $d,l\geq 1$ and any $\varepsilon&gt; 0$ , there are $\delta&gt;0$ and $K\geq 1$ (dependent only on d, l, and $\varepsilon $ ) such that for all finite solvable groups G of derived length l and any subset $E\subset G^d$ with $m^{\otimes d}(E)\geq \varepsilon $ (where m is the uniform measure on G), we have that K-many (left) translates of $$ \begin{align*} \{g\in G\colon &amp;m^{\otimes d}(\{(a_1,\ldots,a_n)\in G^d\colon \\ &amp; (a_1,\ldots,a_n),(ga_1,a_2,\ldots,a_n),\ldots,(ga_1,ga_2,\ldots, ga_n)\in E\})\geq \delta \} \end{align*} $$ cover G. The proof of our main result is a consequence of an ultralimit version of Austin’s amenable ergodic Szeméredi theorem.

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.

Near MDS and near quantum MDS codes via orthogonal arrays

Near maximum distance separable (NMDS) codes are closely related to interesting objects in finite geometry and have nice applications in combinatorics and cryptography. But there are many unsolved problems about construction of NMDS codes. In this paper, by using symmetrical orthogonal arrays (OAs), we construct a lot of NMDS, m-MDS and almost extremal NMDS codes. Quantum error-correcting codes (QECCs) play a central role in quantum information processing and can protect quantum information from various quantum noises. We present a general method for constructing QECCs over mixed alphabets through asymmetrical OAs. Since quantum maximum distance separable (QMDS) codes over mixed alphabets with the dimension equal to one have not been found in all the literature so far, the definition of a near QMDS code over mixed alphabets is proposed. By using asymmetrical OAs, we obtain many such codes.

A Twin Learning Framework for Traveling Salesman Problem Based on Autoencoder, Graph Filter, and Transfer Learning

Efficient solvers for traveling salesman problem (TSP) have great significance in the field of consumer electronic systems and devices. Existing studies require independent and repetitive runs for similar TSPs. To utilize useful knowledge buried in the twin TSP which is similar to the target TSP, a twin learning framework based on task matching and mapping strategy is proposed. We use an autoencoder to extract the feature vectors of the historical tasks and the target task to find the twin task. If not found, construct a twin task based on a graph-filter. Further, we get the solution of the target task with the optimized twin task by learning a mapping matrix from the twin task to the target task. Finally, we incorporate local search algorithms into the twin learning framework, which called strategy mapping solver (SMS) to further improve the quality of the solution. The efficacy of the SMS is evaluated through comprehensive empirical studies with commonly used TSP benchmarks, against meta-heuristic algorithms and a learning improvement heuristics algorithm, demonstrating its effectiveness for TSP. Moreover, a real-world combinatorial optimization application, laser engraving path planning, is presented to further confirm the efficacy of SMS.

Lorentzian polynomials, Segre classes, and adjoint polynomials of convex polyhedral cones

We consider polynomials expressing the cohomology classes of subvarieties of products of projective spaces, and limits of positive real multiples of such polynomials. We study the relation between these covolume polynomials and Lorentzian polynomials. While these are distinct notions, we prove that, like Lorentzian polynomials, covolume polynomials have M-convex support and generalize the notion of log-concave sequences. In fact, we prove that covolume polynomials are ‘sectional log-concave’, that is, the coefficients of suitable restrictions of these polynomials form log-concave sequences.We observe that Chern classes of globally generated bundles give rise to covolume polynomials, and use this fact to prove that certain polynomials associated with Segre classes of subschemes of products of projective spaces are covolume polynomials. We conjecture that the same polynomials may be Lorentzian after a standard normalization operation.Finally, we obtain a combinatorial application of a particular case of our Segre class result. We prove that the adjoint polynomial of a convex polyhedral cone contained in the nonnegative orthant, and sharing a face with it, is a covolume polynomials. This implies that these adjoint polynomials are M-convex and sectional log-concave, and in fact dually Lorentzian, that is, Lorentzian after a certain change of variables.

Improved cooperative Ant Colony Optimization for the solution of binary combinatorial optimization applications

AbstractBinary combinatorial optimization plays a crucial role in various scientific and engineering fields. While deterministic approaches have traditionally been used to solve these problems, stochastic methods, particularly metaheuristics, have gained popularity in recent years for efficiently handling large problem instances. Ant Colony Optimization (ACO) is among the most successful metaheuristics and is frequently employed in non‐binary combinatorial problems due to its adaptability. Although for binary combinatorial problems ACO can suffer from issues such as rapid convergence to local minima, its eminently parallel structure means that it can be exploited to solve large and complex problems also in this field. In order to provide a versatile ACO implementation that achieves competitive results across a wide range of binary combinatorial optimization problems, we introduce a parallel multicolony strategy with an improved cooperation scheme to maintain search diversity. We evaluate our proposal (Binary Parallel Cooperative ACO, BiPCACO) using a comprehensive benchmark framework, showcasing its performance and, most importantly, its flexibility as a successful all‐purpose solver for binary combinatorial problems.

A Novel Anti-CD47 Nanobody Tetramer for Cancer Therapy.

CD47 acts as a defense mechanism for tumor cells by sending a "don't eat me" signal via its bond with SIRPα. With CD47's overexpression linked to poor cancer outcomes, its pathway has become a target in cancer immunotherapy. Though monoclonal antibodies offer specificity, they have limitations like the large size and production costs. Nanobodies, due to their small size and unique properties, present a promising therapeutic alternative. In our study, a high-affinity anti-CD47 nanobody was engineered from an immunized alpaca. We isolated a specific VHH from the phage library, which has nanomolar affinity to SIRPα, and constructed a streptavidin-based tetramer. The efficacy of the nanobody and its derivative was evaluated using various assays. The new nanobody demonstrated higher affinity than the monoclonal anti-CD47 antibody, B6H12.2. The nanobody and its derivatives also stimulated substantial phagocytosis of tumor cell lines and induced apoptosis in U937 cells, a response confirmed in both in vitro and in vivo settings. Our results underscore the potential of the engineered anti-CD47 nanobody as a promising candidate for cancer immunotherapy. The derived nanobody could offer a more effective, cost-efficient alternative to conventional antibodies in disrupting the CD47-SIRPα axis, opening doors for its standalone or combinatorial therapeutic applications in oncology.

Relative rank and regularization

Abstract We introduce a new concept of rank – relative rank associated to a filtered collection of polynomials. When the filtration is trivial, our relative rank coincides with Schmidt rank (also called strength). We also introduce the notion of relative bias. The main result of the paper is a relation between these two quantities over finite fields (as a special case, we obtain a new proof of the results in [21]). This relation allows us to get an accurate estimate for the number of points on an affine variety given by a collection of polynomials which is of high relative rank (Lemma 3.2). The key advantage of relative rank is that it allows one to perform an efficient regularization procedure which is polynomial in the initial number of polynomials (the regularization process with Schmidt rank is far worse than tower exponential). The main result allows us to replace Schmidt rank with relative rank in many key applications in combinatorics, algebraic geometry, and algebra. For example, we prove that any collection of polynomials $\mathcal P=(P_i)_{i=1}^c$ of degrees $\le d$ in a polynomial ring over an algebraically closed field of characteristic $&gt;d$ is contained in an ideal $\mathcal I({\mathcal Q})$ , generated by a collection ${\mathcal Q}$ of polynomials of degrees $\le d$ which form a regular sequence, and ${\mathcal Q}$ is of size $\le A c^{A}$ , where $A=A(d)$ is independent of the number of variables.

Formula omitted]-Stirling numbers in type [formula omitted

Stirling numbers of the first and second kind, which respectively count permutations in the symmetric group and partitions of a set, have found extensive application in combinatorics, geometry, and algebra. We study analogues and q-analogues of these numbers corresponding to the Coxeter group of type B. In particular, we show how they are related to complete homogeneous and elementary symmetric polynomials; demonstrate how they q-count signed partitions and permutations; compute their ordinary, exponential, and q-exponential generating functions; and prove various identities about them. Ordered analogues of the q-Stirling numbers of the second kind have recently appeared in conjectures of Zabrocki and of Swanson–Wallach concerning the Hilbert series of certain super coinvariant algebras. We provide conjectural bases for these algebras and show that they have the correct Hilbert series.

A rooted variant of Stanley's chromatic symmetric function

Richard Stanley defined the chromatic symmetric function XG of a graph G and asked whether there are non-isomorphic trees T and U with XT=XU. We study variants of the chromatic symmetric function for rooted graphs, where we require the root vertex to either use or avoid a specified color. We present combinatorial identities and recursions satisfied by these rooted chromatic polynomials, explain their relation to pointed chromatic functions and rooted U-polynomials, and prove three main theorems. First, for all non-empty connected graphs G, Stanley's polynomial XG(x1,…,xN) is irreducible in Q[x1,…,xN] for all large enough N. The same result holds for our rooted variant where the root node must avoid a specified color. We prove irreducibility by a novel combinatorial application of Eisenstein's Criterion. Second, we prove the rooted version of Stanley's Conjecture: two rooted trees are isomorphic as rooted graphs if and only if their rooted chromatic polynomials are equal. In fact, we prove that a one-variable specialization of the rooted chromatic polynomial (obtained by setting x0=x1=q, x2=x3=1, and xn=0 for n>3) already distinguishes rooted trees. Third, we answer a question of Pawlowski by providing a combinatorial interpretation of the monomial expansion of pointed chromatic functions.

Some identities on degenerate poly-Euler polynomials arising from degenerate polylogarithm functions

Our main focus here is a new type of degenerate poly-Euler polynomials and numbers. This focus stems from their nascent importance for applications in combinatorics, number theory and in other aspects of applied mathematics. We construct a new type of degenerate poly-Euler polynomials by using the degenerate polylogarithm functions. We also show several combinatorial identities related to this polynomials and numbers.

Hopf Monoids and Generalized Permutahedra

Generalized permutahedra are polytopes that arise in combinatorics, algebraic geometry, representation theory, topology, and optimization. They possess a rich combinatorial structure. Out of this structure we build a Hopf monoid in the category of species.Species provide a unifying framework for organizing families of combinatorial objects. Many species carry a Hopf monoid structure and are related to generalized permutahedra by means of morphisms of Hopf monoids. This includes the species of graphs, matroids, posets, set partitions, linear graphs, hypergraphs, simplicial complexes, and building sets, among others. We employ this algebraic structure to define and study polynomial invariants of the various combinatorial structures.We pay special attention to the antipode of each Hopf monoid. This map is central to the structure of a Hopf monoid, and it interacts well with its characters and polynomial invariants. It also carries information on the values of the invariants on negative integers. For our Hopf monoid of generalized permutahedra, we show that the antipode maps each polytope to the alternating sum of its faces. This fact has numerous combinatorial consequences.We highlight some main applications:We obtain uniform proofs of numerous old and new results about the Hopf algebraic and combinatorial structures of these families. In particular, we give optimal formulas for the antipode of graphs, posets, matroids, hypergraphs, and building sets. They are optimal in the sense that they provide explicit descriptions for the integers entering in the expansion of the antipode, after all coefficients have been collected and all cancellations have been taken into account.We show that reciprocity theorems of Stanley and Billera–Jia–Reiner (BJR) on chromatic polynomials of graphs, order polynomials of posets, and BJR-polynomials of matroids are instances of one such result for generalized permutahedra.We explain why the formulas for the multiplicative and compositional inverses of power series are governed by the face structure of permutahedra and associahedra, respectively, providing an answer to a question of Loday.We answer a question of Humpert and Martin on certain invariants of graphs and another of Rota on a certain class of submodular functions.We hope our work serves as a quick introduction to the theory of Hopf monoids in species, particularly to the reader interested in combinatorial applications. It may be supplemented with Marcelo Aguiar and Swapneel Mahajan’s 2010 and 2013 works, which provide longer accounts with a more algebraic focus.