Exponential Number Research Articles

Can Massive Religious Festival Celebrations Encourage a Faster Spread of a Pandemic? The Case of COVID-19 in Israel.

This paper attempts to evaluate how massive religious festivalcelebrations can encourage the faster spread of any pandemic according to our problem statement, such as the case of COVID-19. For example, we evaluate Israel's three major religions, namely Judaism, Christianity, and the Islamic festival celebrations, respectively. Firstly, we have the traditional Jewish festivities such asHanukkah, Yom Kippur, Sukkot, and Rosh Hashanah. In the Christian's traditional festivities celebrations, we identified Christmas, Easter Day, and All Saints Day. Finally, the Muslim festivities ofMuharram and the Birthday of theHoly Prophet Mohamad. Thepurpose of thisstudy wasto evaluate if these nine massive religious festival celebrations are the main reasons for the large spread of COVID-19 in Israel directly or indirectly. In fact, we propose a new methodology to evaluate the impact of any massive religious festivalcelebration andthe fast spread of any pandemic everywhere and anytime. The new indicator is entitled "The National Spread Levels of Infectious Diseases Risk from Massive Religious Festivities Index" (National-SLIDRMRF-Index). Finally, the major finding in this research is that any massive religious events can generate an exponential number of COVID-19 cases constantly. Therefore, this research concluded that we urgentlyneed a standardized index to monitor and control the expansion of any pandemic such as COVID-19 among different religious groups in the same country. At the same time, we give different policy recommendations to the Israeli government to constantlykeep major controls and measures ofdifferent religious events inJerusalem.

Language Acceptors with a Pushdown: Characterizations and Complexity

We study one-way nondeterministic pushdown automata ([Formula: see text]), optionally with reversal-bounded counters. Finite-turn pushdown automata are pushdown automata with a bound on the number of switches between pushing and popping. We give new characterizations for finite-turn pushdown automata, and for finite-turn pushdown automata augmented with reversal-bounded counters. The first is in terms of multi-tape nondeterministic finite automata ([Formula: see text]), and the second is in terms of multi-tape [Formula: see text] with reversal-bounded counters. We then use the characterizations to determine the complexity of the languages defined by these automata. In particular, we show that languages accepted by finite-turn [Formula: see text] augmented with reversal-bounded counters are in [Formula: see text]. For the non-finite-turn case, the languages are in [Formula: see text] and in [Formula: see text]. We also look at the space complexity of languages accepted by two-way machines. In particular, we show that every language accepted by a two-way [Formula: see text] with reversal-bounded counters that makes a polynomial (resp., exponential) number of input head reversals is in [Formula: see text] (resp., [Formula: see text]). This remains true if the pushdown can flip its contents a bounded number of times.

Physical layer security for confidential transmissions in frequency hopping-based downlink NOMA networks

Facing the exponential number of Internet of Things (IoT) devices and the scarcity of available resources, next-generation wireless networks have to meet very challenging performance targets in terms of providing massive access and ensuring higher spectral efficiency. In this vein, Non-Orthogonal Multiple Access (NOMA) has been widely recognized as one of the advantageous techniques to handle the proliferation of the IoT. Nevertheless, from a security standpoint, enabling a user to decode the signals of the other users, while using Successive Interference Cancellation (SIC), raises serious concerns regarding confidentiality and vulnerability to malicious attacks. Meanwhile, conventional security paradigms, such as upper-layer encryption and sophisticated authentication mechanisms, require high computational complexity and additional processing, which impose an overwhelming burden on energy-efficient IoT devices. Alternatively, Physical layer Security (PLS) has sparked a significant interest as a promising complement to cryptographic techniques. The key idea of PLS is to avail wireless communication properties to secure communications without adding complex encryption mechanisms at higher layers. In this paper, we propose a PLS approach based on a network coding technique to prevent eavesdroppers from decoding users’ information transmitted through a downlink-based NOMA system. This results in correlating the packets to be transmitted with each other, making the interception of a single packet useless. We demonstrate that the eavesdropper’s decoding complexity increases exponentially with the sequence length, making the task intractable for relatively long ones.

Expert label for explainable fault diagnosis and for unknown fault generalization

This study proposes the expert label that incorporates specific process knowledge into sample labels to enhance the explainability of diagnostic results. Traditional sample label is a one-hot encoding vector without inherent physical meaning, limiting the diagnostic scope to predefined fault types without explainability. In contrast, expert label as multi-label provides multi-dimensional information including disturbance type, unit location, and associated variable type. Since multi-label can accommodate an exponential number of fault types, the diagnosis models based on expert label have the potential to generalize unknown faults. Meanwhile, we develop the process multi-scale feature mixture network (PMFMN), which excels in deep feature extraction through modules including multi-scale decomposition, multiple pattern representation, and Fourier attention mechanism. The effectiveness of PMFMN with expert label is validated through case studies in two chemical processes, which further improves the fault diagnosis rate, provides reliable diagnostic results with explainability, and can diagnose unknown faults.

Improving Quantum Optimization Algorithms by Constraint Relaxation

Quantum optimization is a significant area of quantum computing research with anticipated near-term quantum advantages. Current quantum optimization algorithms, most of which are hybrid variational-Hamiltonian-based algorithms, struggle to present quantum devices due to noise and decoherence. Existing techniques attempt to mitigate these issues through employing different Hamiltonian encodings or Hamiltonian clause pruning, but they often rely on optimistic assumptions rather than a deep analysis of the problem structure. We demonstrate how to formulate the problem Hamiltonian for a quantum approximate optimization algorithm that satisfies all the requirements to correctly describe the considered tactical aircraft deconfliction problem, achieving higher probabilities for finding solutions compared to previous works. Our results indicate that constructing Hamiltonians from an unconventional, quantum-specific perspective with a high degree of entanglement results in a linear instead of exponential number of entanglement gates instead and superior performance compared to standard formulations. Specifically, we achieve a higher probability of finding feasible solutions: finding solutions in nine out of nine instances compared to standard Hamiltonian formulations and quadratic programming formulations known from quantum annealers, which only found solutions in seven out of nine instances. These findings suggest that there is substantial potential for further research in quantum Hamiltonian design and that gate-based approaches may offer superior optimization performance over quantum annealers in the future.

Symmetry-free routing and spectrum assignment: a universal algorithm based on first-fit

First-fit (FF) is a well-known and widely deployed algorithm for spectrum assignment (SA), but until our recent study [J. Opt. Commun. Netw. 14, 165 (2022)JOCNBB1943-062010.1364/JOCN.445492], investigations of the algorithm had been experimental in nature and no formal properties of the algorithm with respect to SA were known. In this work, we make two contributions. First, we show that FF is a universal algorithm for the SA problem in the sense that, for any variant, 1) it can be used to construct solutions equivalent to, or better than, any solution obtained by any other algorithm, and 2) it can construct an optimal solution. This universality property applies to both the min-max and min-frag objectives and to variants of the SA problem with or without guard band constraints. Consequently, the spectrum symmetry-free model of our recent study [J. Opt. Commun. Netw. 14, 165 (2022)JOCNBB1943-062010.1364/JOCN.445492] extends to all known SA variants, which therefore reduce to permutation problems. Second, we extend the spectrum symmetry-free model to the routing and spectrum assignment (RSA) problem in general topologies. This model allows for the design of more efficient algorithms as it eliminates from consideration an exponential number of equivalent symmetric solutions. By sidestepping symmetry, the RSA solution space is naturally and optimally decomposed into a routing space and a connection permutation space. Building upon this property, we introduce a two-parameter, symmetry-free universal algorithm that can be used to tackle any RSA variant in a uniform manner. The algorithm is amenable to multi-threaded execution to speed up the search process, and the value of the parameters can be adjusted to strike a balance between running time and solution quality. Our evaluation provides insight into the relative benefits of path diversity (which determines the size of the routing space) and connection diversity (which determines the size of the permutation space).

Improving the food safety of bakery products by simultaneously monitoring the occurrence of pyrrolizidine, tropane and opium alkaloids

The exponential number of food alerts about concerning levels of some plant-alkaloids, such as pyrrolizidine, tropane and opium alkaloids, have stressed the need to monitor their occurrence in foods to avoid toxic health effects derived from their intake. Therefore, analytical strategies to simultaneously monitor the occurrence of these alkaloids should be developed to ensure food safety an comply with regulations. Accordingly, this work proposes an efficient multicomponent analytical strategy for the simultaneous extraction of these alkaloids from commercial bakery products. The analytical method was validated and applied to the analysis of 15 samples, revealing that 100% of them contained at least one of the target alkaloids, in some cases exceeding the maximum limits legislated. Moreover, in two samples the 3 different alkaloid families were detected. These results confirm the importance of simultaneously monitoring these alkaloids in food and highlight also considering some opium alkaloids in current legislation.

Importance of Hospital Performance Indicators in Contracting and Financing Medical Services in Surgical Wards.

In the Romanian healthcare system, public hospitals' contract for the provision of healthcare services with the National Health Insurance Services (NHIS) is the main source of revenue in a hospital's income and expenditure budget. In Romania, for acute diseases, payment is made on a per-case basis for hospitals financed under the diagnostic-related groups (DRG) system, which is calculated according to the indicators achieved. The main objective of the study aimed at the quantitative and comparative analysis of hospital performance indicators used in the calculation of the contracted amount with NHIS, in order to quantify the results and evaluate the effectiveness of the measures taken in the surgical wards of the Emergency Clinical County Hospital of Oradea (ECCHO) compared to the annual average values at the national level, in the period 2012-2022. The indicators, such as the number of beds, number of cases, average length of hospitalization (LOH), and case complexity index (CCI), were analyzed at the level of the ECCHO, a tertiary care hospital in the surgical wards. Rehabilitation and modernization of wards, laboratories, operating theatres, and high-performance equipment have been made possible through efficient management and monthly monitoring of medical and financial activity. The average LOH actually carried out on the surgical wards has been decreasing over the 11 years analyzed, with a lower number of hospital days than at the national level. The CCI achieved by the hospital's surgical wards has had an increasing evolution throughout the period analyzed, higher than the national value. The maximum amount contracted and the amount contracted by the hospital is higher when the LOH and CCI indicators achieved by each section are included in the formula than the indicators established at the national level. A lower LOH and a higher CCI than the national values facilitated the contracting of a higher amount. Optimization of the indicators by hospital performance is correlated with improved funding by the NHIS. Increasing the contracted amount facilitates the contracting of an exponential annual number of cases, resulting in more efficient medical services in the surgical wards.

A Model-Free Approach for Solving Choice-Based Competitive Facility Location Problems Using Simulation and Submodularity

This paper considers facility location problems in which a firm entering a market seeks to open facilities on a subset of candidate locations so as to maximize its expected market share, assuming that customers choose the available alternative that maximizes a random utility function. We introduce a deterministic equivalent reformulation of this stochastic problem as a maximum covering location problem with an exponential number of demand points, each of which is covered by a different set of candidate locations. Estimating the prevalence of these preference profiles through simulation generalizes a sample average approximation method from the literature and results in a maximum covering location problem of manageable size. To solve it, we develop a partial Benders reformulation in which the contribution to the objective of the least influential preference profiles is aggregated and bounded by submodular cuts. This set of profiles is selected by a knee detection method that seeks to identify the best tradeoff between the fraction of the demand that is retained in the master problem and the size of the model. We develop a theoretical analysis of our approach and show that the solution quality it provides for the original stochastic problem, its computational performance, and the automatic profile-retention strategy it exploits are directly connected to the entropy of the preference profiles in the population. Computational experiments on existing and new benchmark sets indicate that our approach dominates the classical sample average approximation method on large instances of the competitive facility location problem, can outperform the best heuristic method from the literature under the multinomial logit model, and achieves state-of-the-art results under the mixed multinomial logit model. We characterize a broader class of problems, which includes assortment optimization, to which the solving methodology and the analyses developed in this paper can be extended. History: Accepted by Andrea Lodi, Area Editor for Design & Analysis of Algorithms—Discrete. Funding: This research was supported by Fonds de Recherche du Québec-Nature et Technologies and Institut de Valorisation des Données through scholarships to R. Legault. E. Frejinger was partially supported by the Canada Research Chair program [Grant 950-232244]. Supplemental Material: The online appendices are available at https://doi.org/10.1287/ijoc.2023.0280 .

Combining the analytical hierarchy process, fuzzy expert systems, and the exponential risk priority number for the holistic evaluation of innovation projects in manufacturing

ABSTRACT Manufacturing companies operate in a complex environment and need efficient manufacturing processes to remain competitive. Therefore, evaluation methods are essential for decision makers when selecting manufacturing innovation projects (MIPs). However, most approaches are not suitable for strategic use and do not consider all relevant evaluation dimensions. To address this issue, this work presents an approach to evaluate and select MIPs holistically, considering potential, effort, and risk. The approach enables the analysis of the strategic impact of an MIP using a fuzzy expert system, and further evaluates the implementation effort and risk using a combination of the Analytical Hierarchy Process and the Exponential Risk Priority Number. The approach was developed using the results of a systematic literature review and expert-based methods. Finally, the approach was validated in an industrial case study and enabled a transparent evaluation of the strategic potential, effort, and risk of two MIPs, leading to informed project selection.

A Branch-Price-and-Cut algorithm for the Multi-Commodity two-echelon Distribution Problem

In the Multi-Commodity two-echelon Distribution Problem (MC2DP), multiple commodities are distributed in a two-echelon distribution system involving suppliers, distribution centres and customers. Each supplier may provide different commodities and each customer may request several commodities as well. In the first echelon, capacitated vehicles perform direct trips to transport the commodities from the suppliers to the distribution centres for consolidation purposes. In the second echelon, each distribution centre owns a fleet of capacitated vehicles to deliver the commodities to the customers through multi-stop routes. Commodities are compatible, i.e., they can be mixed in the vehicles. Finally, customer requests can be split by commodities, that is, a customer can be visited by several vehicles, but the total amount of each commodity has to be delivered by a single vehicle. The aim of the MC2DP is to minimize the total transportation cost to satisfy customer demands.We propose a set covering formulation for the MC2DP where the exponential number of variables relates to the routes in the delivery echelon. We develop a Branch-Price-and-Cut algorithm (BPC) to solve the problem. The pricing problem results in solving an Elementary Shortest Path Problem with Resource Constraints (ESPPRC) per distribution centre. We tackle the ESPPRC with a label setting dynamic programming algorithm which incorporates ng-path relaxation and a bidirectional labelling search. Pricing heuristics are invoked to speed up the procedure. In addition, the formulation is strengthened by integrating capacity cuts and two families of valid inequalities specific for the multiple commodities aspect of the problem.Our approach solves to optimality 439 over the 736 benchmark instances from the literature. The optimality gap of the unsolved instances is 2.1%, on average.

A mixed-initiative design framework for procedural content generation using reinforcement learning

Currently, there are a significant and growing number of games and players. Creating digital games becomes a challenging task, as manual game development is costly and time-consuming. A technique known as procedural content generation (PCG) can potentially reduce both the time and production costs of games. It is feasible to automate the creation process by utilizing artificial intelligence techniques and PCG, assisting game designers in their tasks. PCG is not a novel concept, and there is a diverse range of algorithms aimed at automatically generating content in games. However, a significant number of these techniques do not incorporate artificial intelligence. This paper introduces the PCGRLPuzzle framework used to generate procedural scenarios through reinforcement learning agents trained with the policy proximal optimization algorithm. The process of building scenarios poses a challenging problem due to the existence of an exponential number of possibilities. The framework employs a mixed-initiative design, where humans and computers collaborate to create levels for 2D dungeon crawler games. We apply this framework to generate levels for three different games and analyze the results based on their expressive range, evaluating linearity and lenience. The conducted experiments demonstrate that utilizing reinforcement learning in conjunction with procedural content generation and mixed-initiative enables the generation of highly diverse levels.

Mixed-model sequencing with stochastic failures: A case study for automobile industry

In the automotive industry, the sequence of vehicles to be produced is determined ahead of the production day. However, there are some vehicles, failed vehicles, that cannot be produced due to some reasons such as material shortage or paint failure. These vehicles are pulled out of the sequence, and the vehicles in the succeeding positions are moved forward, potentially resulting in challenges for logistics or other scheduling concerns. This paper proposes a two-stage stochastic program for the mixed-model sequencing (MMS) problem with stochastic product failures, and provides improvements to the second-stage problem. To tackle the exponential number of scenarios, we employ the sample average approximation approach and two solution methodologies. On one hand, we develop an L-shaped decomposition-based algorithm, where the computational experiments show its superiority over solving the extensive equivalent formulation with an off-the-shelf solver. Moreover, we provide a tabu search algorithm in addition to a greedy heuristic to tackle case study instances inspired by our car manufacturer partner. Numerical experiments show that the proposed solution methodologies generate high-quality solutions by utilizing a sample of scenarios. Particularly, a robust sequence that is generated by considering car failures can decrease the expected work overload by more than 20% for both small- and large-sized instances.

STG-MTL: scalable task grouping for multi-task learning using data maps

Multi-Task Learning (MTL) is a powerful technique that has gained popularity due to its performance improvement over traditional Single-Task Learning (STL). However, MTL is often challenging because there is an exponential number of possible task groupings, which can make it difficult to choose the best one because some groupings might produce performance degradation due to negative interference between tasks. That is why existing solutions are severely suffering from scalability issues, limiting any practical application. In our paper, we propose a new data-driven method that addresses these challenges and provides a scalable and modular solution for classification task grouping based on a re-proposed data-driven features, Data Maps, which capture the training dynamics for each classification task during the MTL training. Through a theoretical comparison with other techniques, we manage to show that our approach has the superior scalability. Our experiments show a better performance and verify the method’s effectiveness, even on an unprecedented number of tasks (up to 100 tasks on CIFAR100). Being the first to work on such number of tasks, our comparisons on the resulting grouping shows similar grouping to the mentioned in the dataset, CIFAR100. Finally, we provide a modular implementation 3 3 https://github.com/ammarSherif/STG-MTL. for easier integration and testing, with examples from multiple datasets and tasks.

IR.WoT: An Architecture and Vision for a Unified Web of Things Search Engine.

The revolution of the Internet of Things (IoT) and the Web of Things (WoT) has brought new opportunities and challenges for the information retrieval (IR) field. The exponential number of interconnected physical objects and real-time data acquisition requires new approaches and architectures for IR systems. Research and prototypes can be crucial in designing and developing new systems and refining architectures for IR in the WoT. This paper proposes a unified and holistic approach for IR in the WoT, called IR.WoT. The proposed system contemplates the critical indexing, scoring, and presentation stages applied to some smart cities' use cases and scenarios. Overall, this paper describes the research, architecture, and vision for advancing the field of IR in the WoT and addresses some of the remaining challenges and opportunities in this exciting area. The article also describes the design considerations, cloud implementation, and experimentation based on a simulated collection of synthetic XML documents with technical efficiency measures. The experimentation results show promising outcomes, whereas further studies are required to improve IR.WoT effectiveness, considering the WoT dynamic characteristics and, more importantly, the heterogeneity and divergence of WoT modeling proposals in the IR domain.

Convex Bodies of Constant Width with Exponential Illumination Number

Convex Bodies of Constant Width with Exponential Illumination Number

Mechanism design for public projects via three machine learning based approaches

We study mechanism design for nonexcludable and excludable binary public project problems. Our aim is to maximize the expected number of consumers and the expected agents’ welfare. We first show that for the nonexcludable public project model, there is no need for machine learning based mechanism design. We identify a sufficient condition on the prior distribution for the existing conservative equal costs mechanism to be the optimal strategy-proof and individually rational mechanism. For general distributions, we propose a dynamic program that solves for the optimal mechanism. For the excludable public project model, we identify a similar sufficient condition for the existing serial cost sharing mechanism to be optimal for 2 and 3 agents. We derive a numerical upper bound and use it to show that for several common distributions, the serial cost sharing mechanism is close to optimality. The serial cost sharing mechanism is not optimal in general. We propose three machine learning based approaches for designing better performing mechanisms. We focus on the family of largest unanimous mechanisms, which characterizes all strategy-proof and individually rational mechanisms for the excludable public project model. A largest unanimous mechanism describes an iterative mechanism, which is defined by an exponential number of mechanism parameters. Our first approach describes the largest unanimous mechanism family using a neural network and training is carried out by minimizing a cost function that combines the mechanism design objective and the constraint violation penalty. We interpret the largest unanimous mechanisms as price-oriented rationing-free (PORF) mechanisms, which enables us to move the mechanisms’ iterative decision making off the neural network, to a separate simulation process, therefore avoiding the vanishing gradient problem. We also feed the prior distribution’s analytical form into the cost function to achieve high-quality gradients for efficient training. Our second approach treats the mechanism design task as a Markov Decision Process with an exponential number of states. During the Markov decision process, the non-consumers are gradually removed from the system. We train multiple neural networks, each for a different number of remaining agents, to learn the optimal value function on the states. Training is carried out by supervised learning toward a set of manually prepared base cases and the Bellman equation. Our third approach is based on reinforcement learning for a Partially Observable Markov Decision Process. Each RL episode randomly draws a type profile, which is hidden from the RL agent (mechanism designer). The RL agent only observes which cost share offers have been accepted under the largest unanimous mechanism under discussion. We use a continuous action space reinforcement learning approach to adjust the offer policy (i.e., adjust mechanism parameters). Lastly, our first two approaches use “supervision to manual mechanisms” as a systematic way for network initialization, which is potentially valuable for machine learning based mechanism design in general.

Transformable lattice with in-situ changeable elastic modulus arising from structural interaction

Many efforts have been made for lattice design and fabrication for various applications, but most lattices possess fixed elastic modulus after fabrication, which impedes the development of multifunctional lattices. Here we propose a new lattice type that enables in-situ structural transformation and changeable elastic modulus. The structural interaction arises from opposite rotations of the rings from Yin and Yang patch of a lattice under compressive force. The distance between the Yin and Yang patch determines if interaction occurs and the lattice elastic modulus, which is decoupled with volume fraction. Here, numerical and experimental investigation were carried out to reveal the relationship between the interaction type, distance and stress-strain curve. Results show that the ratio of maximum to minimum elastic modulus of a lattice is 81.4 with six interaction bars on the ring, and we can obtain an exponential number of reprogrammable elastic moduli when combining multiple lattices as units to construct a cellular structure. Our work shows a potential for constructing intelligent lattices that can adapt to the surroundings.

Theoretical and Empirical Analysis of Cost-Function Merging for Implicit Hitting Set WCSP Solving

The Implicit Hitting Set (HS) approach has shown very effective for MaxSAT solving. However, only preliminary promising results have been obtained for the very similar Weighted CSP framework. In this paper we contribute towards both a better theoretical understanding of the HS approach and a more effective HS-based solvers for WCSP. First, we bound the minimum number of iterations of HS thanks to what we call distinguished cores. Then, we show a source of inefficiency by introducing two simple problems where HS is unfeasible. Next, we propose two reformulation methods that merge cost-functions to overcome the problem. We provide a theoretical analysis that quantifies the magnitude of the improvement of each method with respect to the number of iterations of the algorithm. In particular, we show that the reformulations can bring an exponential number of iterations down to a constant number in our working examples. Finally, we complement our theoretical analysis with two sets of experiments. First, we show that our results are aligned with real executions. Second, and most importantly, we conduct experiments on typical benchmark problems and show that cost-function merging may be heuristically applied and it may accelerate HS algorithms by several orders of magnitude. In some cases, it even outperforms state-of-the-art solvers.

A Dual Bounding Framework Through Cost Splitting for Binary Quadratic Optimization

Binary quadratic programming (BQP) is a class of combinatorial optimization problems comprising binary variables, quadratic objective functions, and linear/nonlinear constraints. This paper examines a unified framework to reformulate a BQP problem with linear constraints to a new BQP with an exponential number of variables defined on a graph. This framework relies on the concept of stars in the graph to split the quadratic costs into adjacent and nonadjacent components indicating in-star and out-of-star interactions. We exploit the star-based structure of the new reformulation to develop a decomposition-based column generation algorithm. In our computational experiments, we evaluate the performance of our methodology on different applications with different quadratic structures. The quadratic component of the problem is dealt with in the column generation master problem and its subproblem. Results indicate the superiority of the framework over one of the state-of-the-art solvers, GUROBI, when applied to various benchmark reformulations with adjacent-only or sparse quadratic cost matrices. The framework outperforms GUROBI in terms of both dual bound and computational time in almost all instances. History: Accepted by Andrea Lodi, Area Editor for Design & Analysis of Algorithms—Discrete. Funding: The authors thank the Mitacs Accelerate Program for providing funding for this project. In addition, B. Rostami gratefully acknowledges the funding provided by the Canadian Natural Sciences and Engineering Research Council (NSERC) under a Discovery Grant [Grant RGPIN-2020-05395]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/ijoc.2021.0186 .