In tracking-by-detection paradigm for multi-target tracking, target association is modeled as an optimization problem that is usually solved through network flow formulation. In this paper, we proposed combinatorial optimization formulation and used a bipartite graph matching for associating the targets in the consecutive frames. Usually, the target of interest is represented in a bounding box and track the whole box as a single entity. However, in the case of humans, the body goes through complex articulation and occlusion that severely deteriorate the tracking performance. To partially tackle the problem of occlusion, we argue that tracking the rigid body organ could lead to better tracking performance compared to the whole body tracking. Based on this assumption, we generated the target hypothesis of only the spatial locations of person’s heads in every frame. After the localization of head location, a constant velocity motion model is used for the temporal evolution of the targets in the visual scene. Qualitative results are evaluated on four challenging video surveillance dataset and promising results has been achieved.

In light of advancing technology, the conventional clock network architecture has become inadequate for addressing the intricacies inherent in modern System-on-Chip (SoC) designs. While clock mesh topology offers resilience against On-Chip Variation (OCV) fluctuations, it still necessitates manual intervention. Therefore, substantial scope exists for methodological enhancements and the refinement of rapid analytical techniques. This paper introduces a novel clock mesh synthesis approach, underpinned by dynamic programming algorithms, that guarantees latency constraints. Our experimental findings demonstrate that our algorithm achieves an additional 26.6% reduction in power consumption compared to the baseline methodology. Furthermore, it substantially reduces runtime by an average of 78.0% when contrasted with traditional simulation methods. These results highlight the potential of our methodology for enhancing the efficiency and power management of clock mesh.

Many combinatorial optimization problems are hard to solve within the polynomial computational time or NP-hard problems. Therefore, developing new optimization techniques or improving existing ones still grab attention. This paper presents an improved variant of the Ant Colony Optimization meta-heuristic called Enhanced Hyper Cube Framework ACO (EHCFACO). This variant has an enhanced exploitation feature that works through two added local search movements of insertion and bit flip. In order to examine the performance of the improved meta-heuristic, a well-known structural optimization problem of laminate Stacking Sequence Design (SSD) for maximizing critical buckling load has been used. Furthermore, five different ACO variants were concisely presented and implemented to solve the same optimization problem. The performance assessment results reveal that EHCFACO outperforms the other ACO variants and produces a cost-effective solution with considerable quality.

Electrochromic measurements have been performed to optimize the composition of reactive magnetron-sputtered mixed layers of Zinc oxide and Tin oxide (ZnO-SnO2). A combinatorial material synthesis approach was applied throughout the deposition experiments, and the samples represented the full composition range of the binary SnO2-ZnO system. The Coloration Efficiency (CE) of the mixed oxide films were determined with simultaneous measurement of layer transmittance and applied electric current through the using organic propylene carbonate electrolyte cells in a conventional three-electrode configuration. Optical parameters and composition have been determined and mapped by using Spectroscopic Ellipsometry (SE). Scanning Electron Microscopy (SEM) with Energy-Dispersive X-ray Spectroscopy (EDS) has been used to check the SE results as it was used in our earlier paper [N. T. Ismaeel et al, Materials 2023, 16(12), 4204] for (TiO2-SnO2). Zn and Sn targets were put separately from each other, and the Indium-Tin-Oxide (ITO) covered glass and Si-probes on a glass substrate (30 cm × 30 cm) were moved under the two separated targets (Zn and Sn) in a reactive Argon-Oxygen (Ar-O2) gas mixture. By using this combinatorial process, all the compositions (from 0 to 100%) were achieved in the same sputtering chamber after one sputtering process. CE data evaluated from the primary data plotted against the composition displayed a characteristic maximum at around 29 % ZnO. Our combinatorial approach allows the localization of the maximum at 5% accuracy.

This article introduces a novel three-phase angular perturbation technique for solving the School Bus Problem (SBP), an NP-hard combinatorial optimization challenge. The three phases—initial solution, global and local search, and solution exploration—focus on optimizing school bus routes by minimizing sharp turns and reducing travel distances. The performance of three metaheuristic algorithms (GAACOSA-AP, BFSPSO-AP, RL-AP) is evaluated, and significant improvements in routing efficiency are observed. we evaluated the performance of our hybrid algorithm against the industry-leading optimization software, CPLEX, and other optimization techniques across multiple school scenarios. The results show that the GAACOSA-AP algorithm consistently outperforms its counterparts, achieving substantial reductions in travel distances, particularly for complex routes with numerous stops. The integration of Angular Perturbation was key to improving route geometry by, reducing sharp turns, and enhancing overall path optimization by an average reduction of 27.12% compared to 22.37% without Angular Perturbation.

The quadratic unconstrained binary optimization (QUBO) is a classic NP-hard problem with an enormous number of applications. Local search strategy (LSS) is one of the most fundamental algorithmic concepts that has been successfully applied to a wide range of hard combinatorial optimization problems. One LSS that has gained the attention of researchers is the r-flip (also known as r-Opt) strategy. Given a binary solution with n variables, the r-flip strategy ‘flips’ r binary variables to get a new solution if the changes improve the objective function. The main purpose of this paper is to develop several results for implementation of r-flip moves in QUBO, including a necessary and sufficient condition that when a 1-flip search reaches local optimality, the number of candidates for implementation of the r-flip moves can be reduced significantly. The results of the substantial computational experiments are reported to compare an r-flip strategy embedded algorithm and a multiple start tabu search algorithm on a set of benchmark instances and three very-large-scale QUBO instances. The r-flip strategy implemented within the algorithm makes the algorithm very efficient, very high-quality solutions within a short CPU time.

Due to advancement in hacking/reverse engineering tools, threat against transfer of sensitive data or highly classified information is always at risk of being intercepted by an attacker. Covert communication outwit this malicious breach of privacy act better than cryptography as it camouflage secret information inside another innocent looking information, while cryptography shows scrambled information that might arouse attention of an attacker. However, the challenges in Steganography are the modification of carrier that causes some abnormalities, which is detectable and often the methods are not optimize. This paper presents an approach in Covert communication Chanel, which utilizes mathematical concept of combination to optimize time of transmission using sets of multiple transmitter’s, and receiver’s addresses where each abstractly represents a set of bits or characters combination without modifying the address. To minimize the number of physical address to be use, a combinatorial and permutation concept of virtual address generation from physical address is introduce. The paper in addition presents some technique like relationship and their application in both re-enforcing resistivity against Steganalysis and generating combinations. Furthermore, a concept of dynamical clockwise and anti-clockwise rotation of combination over addresses after every transmission is introduce to further improve on resistivity against Steganalysis. A simple test was performed for demonstrating relay address, combination and permutation concepts. Based on test results and analysis, the method is effective as expected and it is quite easy to use as it can be implemented in different platform without much difficulties.

Triple-negative breast cancer (TNBC), lacking specific receptors found in other breast cancer subtypes, poses significant treatment challenges due to limited therapeutic options. Therefore, it is necessary to develop novel treatment approaches for TNBC. In the last few decades, many attempts have been reported for alternative tools for TNBC treatment: immunotherapy, radiotherapy, targeted therapy, combination therapy, and nanotechnology-based therapy. Among them, combination therapy and nanotechnology-based therapy show the most promise for TNBC treatment. This review outlines recent advancements in these areas, highlighting the efficacy of combination therapy (immunotherapy paired with chemotherapy, targeted therapy, or radiotherapy) in both preclinical and clinical stages and nanotechnology-based therapies utilizing various nanoparticles loaded with anticancer agents, nucleic acids, immunotherapeutics, or CRISPRs in preclinical stages for TNBC treatment.

In recent years, the emergence of cancer drug resistance is one of the crucial tumor hallmarks which is supported by the level of genetic heterogeneity and complexities at cellular levels. Oxidative stress, immune evasion, metabolic reprogramming, overexpression of ABC transporters and stemness are among the several key contributing molecular and cellular response mechanisms. Topo-active drugs, e.g., doxorubicin and topotecan, are clinically active and are utilized extensively against a wide variety of human tumors and often results in the development of resistance and failure to therapy. Thus, there is an urgent need for an incremental and comprehensive understanding of mechanisms of cancer drug resistance specifically in the context of topo-active drugs. This review delves into the intricate mechanistic aspects of these intracellular and extracellular topo-active drug resistance mechanisms and explores use of potential combinatorial approaches by utilizing various topo-active drugs and inhibitors of pathways involved in drug resistance. We believe that this review will help guide basic scientists, pre-clinicians, clinicians, and policymakers toward holistic and interdisciplinary strategies that transcend resistance, renewing optimism in the ongoing battle against cancer.

The process of testing software is examining the artifacts and behavior of the software under test by validating and verifying it. Testing can provide valuable information about the software. Given an input to the system, there is a challenge of distinguishing correct from potentially incorrect behavior, which is the test oracle problem. Although the combinatorial testing approach can effectively reduce the number of test cases, the manual inspection of the outputs is still required. In this paper, we propose an approach to automatically classify the return pages with conducting combinatorial testing based on page similarities and hierarchical clustering, by which potential output anomalies can be identified. In the experiment, we apply our approach to a real-world e-commerce website, an anomaly can be found with the visualization of the clustering hierarchy, which suggests the potential of the applicability of the approach.

Effective prediction of wastewater treatment is beneficial for precise control of wastewater treatment processes. The nonlinearity of pollutant indicators such as COD and TP makes the model difficult to fit and has low prediction accuracy. The classical deep learning methods have been shown to perform nonlinear modeling. However, there are enormous numerical differences between multi-dimensional data in the prediction problem of wastewater treatment, such as COD above 3000 mg/L and TP around 30 mg/L. It will make current normalization methods challenging to handle effectively, leading to the training failing to converge and the gradient disappears or exploding. This paper proposes a multi-factor prediction model based on deep learning. The model consists of a combined normalization layer and a codec. The combined normalization layer combines the advantages of three normalization calculation methods: z-score, Interval, and Max, which can realize the adaptive processing of multi-factor data, fully retain the characteristics of the data, and finally cooperate with the codec to learn the data characteristics and output the prediction results. Experiments show that the proposed model can overcome data differences and complex nonlinearity in predicting industrial wastewater pollutant indicators and achieve better prediction accuracy than classical models.

The capacitated team orienteering problem with time windows (CTOPTW) is a NP-hard combinatorial optimization problem. In the CTOPTW, a set of customers is given each with a profit, a demand, a service time and a time window. A homogeneous fleet of vehicles is available for serving customers and collecting their associated profits. Each vehicle is constrained by a maximum tour duration and a limited capacity. The CTOPTW is concerned with the determination of a preset number of vehicle tours that begin and end at a depot, visit each customer no more than once while satisfying the time duration, time window and vehicle capacity constraints on each tour. The objective is to maximize the total profit collected. In this study we propose an iterated local search (ILS) algorithm to deal with the CTOPTW. ILS is a single solution based meta-heuristic that successively invokes a local search procedure to explore the solution space. A perturbation operator is used to modify the current local optimum solution in order to provide a starting solution for the local search procedure. As different problems and instances have different characteristics, the success of the ILS is highly dependent on the local search procedure, the perturbation operator(s) and the perturbation strength. The basic ILS uses a single perturbation operator and the perturbation strength remains the same during the optimization process. To address these issues, we use three different perturbation operators and a varying perturbation strength which changes as the algorithm progresses. The idea is to assign a larger perturbation strength in the early stages of the search in order to focus on exploring the search space. The perturbation strength is gradually decreased so that we focus more on exploitation. The computational results show that the proposed ILS algorithm is able to generate high quality solutions on the CTOPTW benchmark instances taken from the scientific literature, demonstrating its efficiency in terms of both the solution quality and computational time. Moreover, the proposed ILS produces 21 best known results and 5 new best solutions.

The up-and-coming microfluidic technology is the most promising platform for designing anti-cancer drugs and new point-of-care diagnostics. Compared to conventional drug screening methods based on Petri dishes and animal studies, drug delivery in microfluidic systems has many advantages. For instance, these platforms offer high throughput drug screening, require a small amount of samples, provide an in vivo-like microenvironment for cells, and eliminate ethical issues associated with animal studies. Multiple cell cultures in microfluidic chips could better mimic the 3D tumor environment using low reagents consumption. The clinical experiments have shown that combinatorial drug treatments have a better therapeutic effect than monodrug therapy. So many attempts were performed in this field in the last decade. This review highlights the applications of microfluidic chips in anti-cancer drug screening and systematically categorizes these systems as a function of sample size and combination of drug screening. Finally, it provides a perspective on the future of the clinical applications of microfluidic systems for anti-cancer drug development.

With the rapid growth of large language models (LLMs), there is increasing demand for memory and computation in LLMs. Recent efforts on post-training pruning of LLMs aim to reduce the model size and computation requirements, yet the performance is still sub-optimal. In this paper, we present a plug-and-play solution for post-training pruning of LLMs. The proposed solution has two innovative components: 1) Relative Importance and Activations (RIA), a new pruning metric that jointly considers the weight and activations efficiently on LLMs; and 2) Channel Permutation, a new approach to maximally preserve important weights under N:M sparsity. The two proposed components can be readily combined to further enhance the N:M semi-structured pruning of LLMs. Our empirical experiments show that RIA alone can already surpass all existing post-training pruning methods on prevalent LLMs, e.g., LLaMA ranging from 7B to 65B. Furthermore, N:M semi-structured pruning with channel permutation can even outperform the original LLaMA2-70B on zero-shot tasks, together with practical speed-up on specific hardware. Our code is available at: https://github.com/biomedical-cybernetics/Relative-importance-and-activation-pruning

$P$ versus $NP$ is considered as one of the most important open problems in computer science. This consists in knowing the answer of the following question: Is $P$ equal to $NP$? The precise statement of the $P$ versus $NP$ problem was introduced independently by Stephen Cook and Leonid Levin. Since that date, all efforts to find a proof for this problem have failed. Another major complexity class is $\textit{P-Sel}$. $\textit{P-Sel}$ is the class of decision problems for which there is a polynomial time algorithm (called a selector) with the following property: Whenever it's given two instances, a $``yes"$ and a $``no"$ instance, the algorithm can always decide which is the $``yes"$ instance. It is known that if $NP$ is contained in $\textit{P-Sel}$, then $P = NP$. We consider the problem of computing the sum of the weighted densities of states of a Boolean formula in $3CNF$. Given a Boolean formula $\phi$ with $m$ clauses, the density of states $n(E)$ for some integer $0 \leq E \leq m$ counts the number of truth assignments that leave exactly $E$ clauses unsatisfied in $\phi$. The weighted density of states $m(E)$ is equal to $E \times n(E)$. The sum of the weighted densities of states of a Boolean formula in $3CNF$ with $m$ clauses is equal to $\sum_{E = 0}^{m} m(E)$. We prove that we can calculate the sum of the weighted densities of states in polynomial time. Given two Boolean formulas $\phi_{1}$ and $\phi_{2}$ in $3CNF$ with $n$ variables and $m$ clauses, the combinatorial optimization problem $\textit{SELECTOR-3SAT}$ consists in selecting the formula which is satisfiable, where every clause from $\phi_{1}$ and $\phi_{2}$ can be unsatisfied for some truth assignment. We assume that the formula that is satisfiable has the minimum sum of the weighted densities of states. In this way, we solve $\textit{SELECTOR-3SAT}$ with an exact polynomial time algorithm. We claim this problem is a selector of $3SAT$ and thus, $P = NP$.

3D city models are being extensively used in applications such as evacuation scenarios and energy consumption estimation. The main standard for 3D city models is the CityGML data model which can be encoded through the CityJSON data format. CityGML and CityJSON use polygonal modelling in order to represent geometries. True topological data structures have proven to be more computationally efficient for geometric analysis compared to polygonal modelling. In a previous study, we have introduced a method to topologically reconstruct CityGML models while maintaining the semantic information of the dataset, based solely on the combinatorial map (C-Map) data structure. As a result of the limitations of C-Map's semantic representation mechanism, the resulting datasets could suffer either from semantic information loss or the redundant repetition of them. In this article, we propose a solution for a more efficient representation of both geometry, topology and semantics by incorporating the C-Map data structure in the CityGML data model and implementing a CityJSON extension to encode the C-Map data. In addition, we provide an algorithm for the topological reconstruction of CityJSON datasets to append them according to this extension. Finally, we apply our methodology to three open datasets in order to validate our approach when applied to real-world data. Our results show that the proposed CityJSON extension can represent all geometric information of a city model in a lossless way, providing additional topological information for the objects of the model.

Electrochromic measurements have been performed throughout the full composition range of reactive magnetron-sputtered mixed Titanium oxide and Molybdenum oxide (TiO2-MoO3) to search for enhanced Coloration Efficiency (CE). Optical parameters and composition have been determined and mapped by using Spectroscopic Ellipsometry (SE). Scanning Electron Microscopy (SEM) with Energy-Dispersive X-ray Spectroscopy (EDS). EDS has been used to check the SE results as it was used in our earlier paper [N. T. Ismaeel et al, Materials 2023, 16(12), 4204] for (TiO2-SnO2). Ti and Mo targets were put separately from each other, and the Indium-Tin-Oxide (ITO) covered glass and Si-probes on a glass substrate (30 cm × 30 cm) were moved under the two separated targets (Ti and Mo) in a reactive Argon-Oxygen (Ar-O2) gas mixture. By using this combinatorial process, all the compositions (from 0 to 100%) were achieved in the same sputtering chamber after one sputtering process. The CE (the change of light transmission for the unit electric charge) of mixed metal oxides (TiO2-MoO3) that are deposited by reactive sputtering has been studied in an electrochemical cell. This paper aims to assess the results of investigations of such materials showing the enhanced electrochromic behavior compared to the pure materials and to enhance the Coloration Efficiency.

: Multimodal Large Language Models (MLLMs) harness comprehensive knowledge spanning text, images, and audio to adeptly tackle complex problems, including zero-shot in-context learning scenarios. This study explores the ability of MLLMs in visually solving the Traveling Salesman Problem (TSP) and Multiple Traveling Salesman Problem (mTSP) using images that portray point distributions on a two-dimensional plane. We introduce a novel approach employing multiple specialized agents within the MLLM framework, each dedicated to optimizing solutions for these combinatorial challenges. Our experimental investigation includes rigorous evaluations across zero-shot settings and introduces innovative multi-agent zero-shot in-context scenarios. The re-sults demonstrated that both multi-agent models—Multi-Agent 1, which includes the Initializer, Critic, and Scorer agents, and Multi-Agent 2, which comprises only the Initializer and Critic agents—significantly improved solution quality for TSP and mTSP problems. Multi-Agent 1 ex-celled in environments requiring detailed route refinement and evaluation, providing a robust framework for sophisticated optimizations. In contrast, Multi-Agent 2, focusing on iterative re-finements by the Initializer and Critic, proved effective for rapid decision-making scenarios. These experiments yield promising outcomes, showcasing the robust visual reasoning capabilities of MLLMs in addressing diverse combinatorial problems. The findings underscore the potential of MLLMs as powerful tools in computational optimization, offering insights that could inspire further advancements in this promising field.

The construction time of concrete structures in hydraulic tunnels is long, the construction environment is complex, and there are many influencing factors. The requirements for construction quality are high, not only to meet the strength requirements, but also to meet the design requirements of erosion resistance, crack resistance, and seepage resistance according to its specific operating environment. Therefore, evaluating the construction quality of concrete structures in hydraulic tunnels is of great significance. Considering the randomness and fuzziness of factors affecting the construction quality of concrete structures in hydraulic tunnels, this paper proposes a comprehensive evaluation model based on Combined Weighting (CWM) and Uncertainty Measurement Theory (UM). The IAHP method and CRITIC method are used to determine the subjective and objective weights of evaluation indicators, combined weighting is based on the principle of minimum entropy, and the UM method is used to evaluate the construction quality level. Finally, taking a hydraulic tunnel as an example, its construction quality grade is calculated to be III according to the evaluation model proposed in this paper, which matches with the engineering reality, and a comparative study is made with the mixture element topology theory at the same time. It is verified that the evaluation model can scientifically and reasonably evaluate the construction quality level of concrete structures in hydraulic tunnels.

Dendritic cell (DC) cancer vaccines are a promising therapeutic approach, leveraging the immune system to fight tumors. These vaccines utilize DCs' ability to present tumor-associated antigens to T cells, triggering a robust immune response. DC vaccine development has progressed through three generations. The first generation involved priming DCs with tumor-associated antigens or messenger RNA outside the body, showing limited clinical success. The second generation improved efficacy by using cytokine mixtures and specialized DC subsets to enhance immunogenicity. The third generation uses blood-derived DCs to elicit a stronger immune response. Clinical trials indicate that cancer vaccines have lower toxicity than traditional cytotoxic treatments. However, achieving significant clinical responses with DC immunotherapy remains challenging. Combining DC vaccines with immune checkpoint inhibitors (ICIs) such as anti-cytotoxic T-lymphocyte Antigen 4 and anti-programmed Death-1 antibodies has shown promise by enhancing T cell responses and improving clinical outcomes. These combinations can transform non-inflamed tumors into inflamed ones, boosting ICIs' efficacy. Current research is exploring new checkpoint targets like LAG-3, TIM-3, and TIGIT, considering their potential with DC vaccines. Additionally, engineering T cells with chimeric antigen receptors or T cell receptors could further augment the anti-tumor response. This comprehensive strategy aims to enhance cancer immunotherapy, focusing on increased efficacy and improved patient survival rates.

In this paper, we mainly show that generalized hyperharmonic number sums with reciprocal binomial coefficients can be expressed in terms of classical (alternating) Euler sums, zeta values and generalized (alternating) harmonic numbers.

The minimum vertex cover (MVC) problem is a canonical NP-hard combinatorial optimization problem, aiming to find a smallest set of vertices such that every edge has at least one endpoint in the set, which has extensive applications in cyber security, scheduling, and monitoring link failures in wireless sensor networks (WSNs). Numerous local search algorithms have been proposed to obtain a “good” vertex cover. However, due to the NP-hard nature, it is challenging to efficiently solve the MVC problem, especially on large graphs. In this paper, we propose an efficient local search algorithm for MVC called TIVC, which is based on two main ideas: A 3-improvements (TI) framework with tiny perturbation, and an edge selection strategy. We conducted experiments on real-world large instances of a massive graph benchmark. Compared with two state-of-the-art MVC algorithms, TIVC shows superior performance in accuracy and possesses a remarkable ability to identify significantly smaller vertex covers on many graphs.

In the paper, by virtue of techniques in combinatorial analysis, the authors simplify two families of nonlinear ordinary differential equations in terms of the Stirling numbers of the first kind.

The existence of multiple copies of genes is a well-known phenomenon. A gene family is a set of sufficiently similar genes, formed by gene duplication. In earlier works conducted on limited number of completely sequenced and annotated genomes it was found that size of gene family and size of genome are positively correlated. Additionally, it was found that several atypical microbes deviated from the observed general trend. In this study, we reexamined these associations on a larger dataset consisting of 1484 prokaryotic genomes and using several ranking approaches. We applied ranking methods in such a way that genomes with lower number of paralogs would have lower rank. Until now only simple ranking methods were used; we applied the Kemeny optimal aggregation approach as well. Regression and correlation analysis were utilized in order to accurately quantify and characterize the relationships between measures of paralog indices and genome size. In addition, boxplot analysis was employed as a method for outlier detection. We found that, in general, all paralog indexes positively correlate with an increase of genome size. As expected, different groups of atypical prokaryotic genomes were found for different types of paralog quantities.

We introduce derangetropy, a novel functional measure designed to characterize the dynamics of information within probability distributions. Unlike scalar measures such as Shannon entropy, derangetropy offers a functional representation that captures the dispersion of information across the entire support of a distribution. By incorporating self-referential and periodic properties, it provides deeper insights into information dynamics governed by differential equations and equilibrium states. Through combinatorial justifications and empirical analysis, we demonstrate the utility of derangetropy in depicting distribution behavior and evolution, providing a new tool for analyzing complex and hierarchical systems in information theory.

The Vehicle Routing Problem (VRP) and its variants are found in many fields, especially logistics. In this study, we introduced an adaptive method to a complex VRP. It combines multi-objective optimization and several forms of VRPs with practical requirements for an urban shipment system. The optimizer needs to consider terrain and traffic conditions. The proposed model also considers customers' expectations, shipper considerations as goals, and the common goal like transportation cost. We offered compromise programming to approach the multi-objective problem by decomposing the original multi-objective problem into a minimized distance-based problem. We designed a hybrid version of the Genetic algorithm with the Local Search algorithm to solve the proposed problem. We evaluate the effectiveness of the proposed algorithm with the Tabu Search algorithm, the original Genetic algorithm on the tested dataset. The results show that our method is an effective decision-making tool for the multi-objective VRP and an effective solver for the new variation of VRP.

Often, in biology, we are faced with the problem of exploring relevant unknown biological hypotheses in the form of myriads of combination of factors that might be affecting the pathway under certain conditions. Currently, a major persisting problem is to cherry pick the combinations based on expert advice, literature survey or guesses for investigation. This entails investment in time, energy and expenses at various levels of research. To address these issues, a search engine design was recently been developed, which showed promise by revealing existing confirmatory published wet lab results. Additionally and of import, the engine mined up a range of unexplored/untested/unknown combinations of genetic factors in the Wnt pathway that were affected by ETC-1922159 enantiomer, a PORCN-WNT inhibitor, after the colorectal cancer cells were treated with the inhibitor drug. As an example, MYC is known to upregulate PRC2 complex. PRC2 complex contains EZH2, which suppresses tumor suppressor genes via epigenetic modifications. MYC and HOXB8 are up regulated in colorectal cancer, however, the dual working mechanism of the same is not known. The in silico engine showed positioning which correctly approximates and assigns to this 3rd order combination of MYC-HOXB8-EZH2, pointing to the in vitro/in vivo down regulation by ETC-1922159. If the protein interaction of MYC-HOXB8 can be established and a study be done apropos EZH2, it will establish at in vitro/in vivo level, the in silico ranking also. The potential of this engine is immense given the problem faced in biology and other fields. Here we elucidate the R code to understand the mechanics of the search engine in a fluid manner for systems biologists. Though the search engine is in the developmental stage, we share the detailed mechanism of the working principles of the same as it can be generalized to problems in other fields.

This article presents a new methodology for modeling and analyzing discrete dynamic systems through the construction of inverse algebraic models, giving rise to the Theory of Inverse Discrete Dynamical Systems. Key concepts such as inverse modeling, structural analysis in inverse algebraic trees, and the establishment of topological equivalences for the analytical transfer of properties between the canonical system and its inverted counterpart are introduced. Central theorems on homeomorphic invariance and topological transport are demonstrated, consolidating the validity of transferring cardinal attributes between both equivalent dynamic representations. As a concrete application, an alternative proof of the historic Collatz Conjecture is presented through the rigorous construction of the associated inverse model and the analytical transfer of properties exhibited in the inverted tree structure. Furthermore, evidence has been presented on Conway's Conjecture in the Game of Life through meticulous inverse modeling in bounded cases, overcoming initial limitations of the theory in combinatorial explosions. Although a complete proof of the conjecture is not achieved, this positively expands the modeling and analysis capacity of the methodology. The impact of properly applying this novel theory to expand understanding and solve open problems in discrete dynamical systems seems vast and profound.

Wind power is one of the most important sources of renewable energy available today. A large part of the wind energy cost is due to the cost of maintaining wind power equipment. When a wind turbine component fails to function, it might need to be replaced under the less than ideal circumstances. This is known as corrective maintenance. To minimize unnecessary costs, a more active maintenance policy based on the life expectancy of the key components is preferred. Optimal scheduling of preventive maintenance activities requires advanced mathematical modeling. In this paper, an optimal preventive maintenance algorithm is designed using the renewal-reward theorem. In the multi-component setting, our approach involves a new idea of virtual maintenance which allows us to treat each replacement event as a renewal event even if some components are not replaced by new ones. The proposed optimization algorithm is applied to a four-component model of a wind turbine and the optimal maintenance plans are computed for various initial conditions. The modeling results showed clearly the benefit of PM planning compared to pure CM strategy (about 30% lower maintenance cost).

In this article, the usual factorials and binomial coefficients have been generalized and extended to the negative integers. Basing on this generalization and extension, a new kind of polynomials has been proposed, which led directly to the non-classical hypergeometric orthogonal polynomials and the non-classical second-order hypergeometric linear DEs. The resulting polynomials can be used in non-relativistic and relativistic QM, particularly, in the case of the Schrödinger equation, and Dirac equations for an electron in a Coulomb potential field.

WNT10B belongs to the family of WNT proteins that are implicated in a range of phenomena that are affected by the Wnt signaling pathway. Recent studies have shown that WNT10B plays a role in colorectal cancer. WNTs have been found to directly affect the stemness of the tumor cells via regulation of ASCL2. Switching off the ASCL2 literally blocks the stemness process of the tumor cells and vice versa. Furthermore, recent findings suggest BVES to be highly suppressed in malignancies and in vitro deletions of BVES show higher Wnt signaling activity to induce stem- ness. WNT10B was found to be highly expressed in such cases. Often, in biology, we are faced with the problem of exploring relevant unknown biological hypotheses in the form of myriads of combination of factors that might be affecting the pathway under certain conditions. For example, WNT10B-ASCL2 is one such 2^nd order combination whose relation needs to be tested under the influence of recently developed porcupine-WNT inhibitor ETC-1922159. The inhibitor is known to suppress PORCN (porcupine) and thus inhibit a range of oncogenes known to be directly or indirectly affected by the Wnts. In a recent unpublished work in bioRxiv, Sinha 1, we had the opportunity to rank these unknown biological hypotheses for down regulated genes at 2^nd order level after the drug was administered. The in silico observations showed that the combination of WNT10B-ASCL2 was assigned a relatively lower rank, thus validating the pipeline’s efficacy with the confirmed wet lab experiment that indicate that both WNT10B and ASCL2 were down regulated after treatment in cancer cells. Here, we take one step further by in silico analysis of the 3rd order combinations of WNT10B-X-X (X can be known or unknown factor), from a range of 100 randomly picked down regulated genes after ETC-1922159 treatment. The pipeline uses the density based HSIC (Hilbert Schmidt Information Criterion) sensitivity index with an rbf (ra- dial basis function) kernel, which is known to be highly effective in sensitivity analysis. Various unknown/unexplored/untested 3^rd order biological hypotheses emerge some of which are con- firmed in wet lab, while others need to be tested. The potential of such ranking is indispensable in the current era of search in a vast combinatorial forest.

Peptide-based opioid ligands are important candidates for the development of novel, safer, and more effective analgesics to treat pain. To develop peptide-based safer analgesics, we synthesized a mixture-based cyclic pentapeptide library containing a total of 24,624 pentapeptides and screened the mixture-based library samples using a 55 °C warm-water tail-withdrawal assay. Using this phenotypic screening approach, we deconvoluted the mixture-based samples to identify a novel cyclic peptide Tyr-[D-Lys-Dap(Ant)-Thr-Gly] (CycloAnt), which produced dose- and time-dependent antinociception with an ED50 (and 95% confidence interval) of 0.70 (0.52-0.97) mg/kg i.p. mediated by the mu-opioid receptor (MOR). Additionally, higher doses (≥ 3 mg/kg, i.p.) of CycloAnt antagonized delta-opioid receptors (DOR) at least 3 hours. Pharmacological characterization of CycloAnt showed the cyclic peptide did not reduce breathing rate in mice at doses up to 15 times the analgesic ED50 value, and dramatically less hyperlocomotion than the MOR agonist, morphine. While chronic administration of CycloAnt resulted in antinociceptive tolerance, it was without opioid-induced hyperalgesia and significantly reduced signs of naloxone-precipitated withdrawal suggestive of reduced physical dependence as compared to morphine. Collectively, the results suggest this dual MOR/DOR multifunctional ligand is an excellent lead for the development of peptide-based safer analgesics.

DNA repair helps in maintaining the proper and healthy functioning for the cells in the human body. Failure in DNA repair process can lead to aberrations as well as tumorous stages. There are various types of damages that a DNA can go through, one of which is the DNA double strand breaks (DSB) that can be repaired via homologous recombination (HR). RAD51 plays a central role in HR and has been implicated as a negative/poor prognostic marker for colorectal adenocarcinoma, with high expression in colorectal cancer. Mechanistically, RAD51AP1 facilitates RAD51 during the repairing process by binding with RAD51 via two DNA binding sites, thus helping in the D-loop formation in the HR process. Often, in biology, we are faced with the problem of exploring relevant unknown biological hypotheses in the form of myriads of combination of factors that might be affecting the pathway under certain conditions. For example, RAD51AP1-XRCC2 is one such 2^nd order combination whose relation needs to be tested under the influence recently developed Porcupine-WNT inhibitor ETC-1922159. The x-ray repair cross complementing XRCC family is known to work as a mediator or stabilizer for RAD51 during the HR process. The inhibitor is known to suppress Porcupine and thus inhibit a range of oncogenes known to be directly or indirectly affected by the Wnts. In a recent unpublished work in bioRxiv, we had the opportunity to rank these unknown biological hypotheses for down regulated genes at 2^nd order level after the drug was administered. The in silico observations showed that the combination of RAD51AP1-XRCC2 was assigned a relatively lower rank, thus validating the pipeline's efficacy with the confirmed wet lab experiment that indicate that both RAD51AP1 and XRCC2 were down regulated after treatment in cancer cells. Here, we take one step further by in silico analysis of the 3^rd order combinations of RAD51-X-X & RAD51AP1-X-X (X can be known or unknown factor), from a range of 100 randomly picked down regulated genes after ETC-1922159 treatment. The pipeline uses the density based HSIC (Hibert Schmidth Information Criterion) sensitivity index with an rbf (radial basis function) kernel, which is known to be highly effective in sensitivity analysis. Various unknown/unexplored/untested RAD51/RAD51AP1 related 3^rd order biological hypotheses emerge some of which are confirmed in wet lab, while others need to be tested.

Often, in biology, we are faced with the problem of exploring relevant unknown biological hypotheses in the form of myriads of combination of factors that might be affecting the pathway under certain conditions. For example, Brancati et al.1 observe that mutations in poliovirus receptor related protein 4 (PVRL4), encoding cell adhesion molecule nectin-4, causes Ectodermal dysplasia-syndactyly syndrome. Interaction with cad- herins also implies an influence of nectin-4 on Wnt signaling, which plays a relevant role in limb development (Brancati et al.1). However, not much work has been done to explore the relation of Wnts and PVR family. In CRC cells treated with ETC-1922159, both were found up regulated. In a recent unpublished work in Open Science Framework, Sinha2, we had the opportunity to rank these unknown biological hypotheses for both up and down regulated genes at 2nd order level after drug administration. The search engine alloted high nu- merical valued rankings to some combinations of PVR-WNT, thus indicating a possibility of high combinatorial synergy also. The in-silico derived influences can be represented graphically as - PVR w.r.t WNT with PVR <- WNT9A; and WNT w.r.t PVR with WNT-7B/9A <- PVR and WNT4 <- PVRL2; In the light of the recent findings of PVR with IFN (interferon) and the known interactions between IFN and Wnts, there might be a possibilty to explore the bridge of PVR, IFN and WNTs. The 3 fold (PVR - IFN; IFN - WNT; WNT - PVR), 2 way cross family analysis might shed light on the possible combinations that might be of import. Here, we present a 2-way cross family analysis of multiple, such in-silico ranked 2nd order synergistic combinations, after ETC-1922159 treatment of CRC cells. Via this 2-way cross family analysis, we are able to discover through majority voting, the combinations that might of interest to biologists and also derive plausible influences of components of combinations among themselves. Note that these form biological hypotheses which indicate whether a particular combination and the direction of influence within the combination, exist synergistically in CRC cells. Wet lab tests will indicate the veracity of these combinations and if proven true, will lead to further study of mechanism between the components.

\textsc{Background} Often, in biology, we are faced with the problem of exploring relevant unknown biological hypotheses in the form of myriads of combination of factors that might be affecting the pathway under certain conditions. Currently, a major problem in biology is to cherry pick the combinations based on expert advice, literature survey or guesses for investigation. The search and wet lab testing of these combinations costs a lot in terms of time, investment and energy. In a recent development of the PORCN-WNT inhibitor ETC-1922159 for colorectal cancer, a list of down-regulated genes were recorded in a time buffer after the administration of the drug. The regulation of the genes were recorded individually but for a majority, it is still not known which higher ($\geq 2$) order combinations might be playing a greater role in the pathway. \textsc{Results} The pipeline provides a prioritised list of important $2^{nd}$ order combinations of a range of family of genes involved in the Wnt pathway. More specifically, it reveals the various unexplored FZD-WNT combinations that have been untested till now in the pathway. In relation to ETC-1922159 affected combinations, the down-regulation of LGR-RNF family after the drug treatment is evident in these rankings as it takes bottom priorities for LGR5-RNF43 combination. The LGR6-RNF43 takes higher ranking than LGR5-RNF43, indicating that it might not be playing a greater role as LGR5 during the Wnt enhancing signals. These rankings confirm the efficacy of the proposed search engine design. \textsc{Conclusion} A pipeline has been developed to prioritise an $n^{th}$ order combination of factors that affect a signaling pathway. It takes into account the sensitivity indices computed from variance based (SOBOL) and density-kernel based (HSIC) methods to estimate the influence of each factor or combination of factors. These are then fed as feature vectors into a powerful support vector ranking algorithm that produces a ranked list of the interactions/combinations.