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Blockchain networks are consistently challenged with security and accessibility issues, and technological developments call for the need for their security and integrity more than ever. Security vulnerabilities such as distributed denial-of-service (DDoS) attacks and Eclipse attacks influence public and private blockchains imposing significant losses to the network. Considering the key distribution and management service as a major part of the blockchain architecture, the present study proposes a combinatorial design-based token management system (CD-TMS) while offering optimum accessibility for the blockchain network. Our combinatorial design-based, clustered tokenization system enables the blockchain to prevent DDoS attacks. We also offer a leader selection mechanism relying on a probabilistic tokenization system that reduces communication overhead compared to voting-based systems. In this regard, CD-TMS integrates Balanced incomplete block designs and transversal designs (TD), as well as Eschenauer and Gligor (EG) designs, to distribute tokens on a public blockchain framework (i.e., Bitcoin), though it focuses mainly on DDoS and Eclipse attacks. The performance function, evaluated in terms of security, resiliency, communication overhead, connectivity, reliability, availability, and scalability, has shown the proposed architecture's superiority over conventional methods. [ABSTRACT FROM AUTHOR]

Software components such as application programming interfaces (APIs) provided by external developers are vital to online digital platforms. Although APIs generally increase the variety of products according to anecdote, the precise relationship between the categories of APIs and product variety is not yet known. We find that APIs, regarding their use frequency, are categorized into three groups. The core is a group of frequently used APIs, whereas the periphery is a group of sparsely used APIs. In a large and mature platform ecosystem, an additional group of APIs, the regular core, mainly provided by third-party developers, emerges. APIs in the regular core are the main driver of product variety. However, we also find that the strength of this effect diminishes in a newly created product category when most of the new products are built by duplicating the usage of APIs from other products. A platform owner can stimulate developers' creativity by acting as a bridge between digital product providers and third-party developers. It can collect functional needs from third-party developers and then share them with product providers. Therefore, the latter can build APIs that developers need. Software components, such as application programming interfaces (APIs), provided by both the platform owner and external developers in a platform ecosystem are vital to online digital platforms. These APIs are associated with functionality provided by the platform. A larger number of APIs used is generally associated with an increase in the platform ecosystem's variety of products. However, the precise nature of the relationship between the use of APIs and product variety in a platform ecosystem is not yet known because of the lack of appropriate methodologies to analyze the complex data generated in such platform ecosystems. Drawing on a recombinatorial design perspective, we use a dynamic network model to create metrics for product variety in a digital ecosystem and study how the use of different types of APIs affects product variety. In particular, we theorize that, contrary to existing models, the structure of APIs in a large platform ecosystem is not limited to a core–periphery structure, but includes an additional third layer that we refer to as the regular core. We further hypothesize that external APIs in the regular core play a crucial role in increasing product variety in the ecosystem. To test our hypothesis, we conduct an empirical study using longitudinal data of all available digital product (i.e., plug-in) source codes on WordPress.org, the world's largest content management system and one of the most extensive digital platform ecosystems. By analyzing all of the plug-ins on WordPress over 10 years from its inception, we find the support of our three-layer structure of APIs in a platform ecosystem: complete core, regular core, and periphery. Our empirical analysis further supports the role of external APIs in the regular core in increasing product variety. We, however, find that the strength of this effect diminishes in a newly created product category. History: Param Singh, Senior Editor; Pallab Sanyal, Associate Editor. Funding: This work was supported by the Ministry of Education Singapore [Grants R-253-000-122-133 and T1-251RES1916], the National Science Foundation [Grants 1261977 and 1120966], and Club Informatique des Grandes Entreprises Françaises. Supplemental Material: The e-companion is available at https://doi.org/10.1287/isre.2022.1172. [ABSTRACT FROM AUTHOR]

Design of mechanical metamaterials is typically realized by repeating microstructured building blocks or unit cells. Microstructures of these unit cells can be identical, whereas individual design of each cell and various combinations of unit cells definitely offer more freedoms and possibilities for combinatorial design of metamaterials. Unfortunately, this combinatorial design problem is prohibitively challenging, if not impossible, due mainly to its huge number of combinatorial cases. This paper poses and addresses the combinatorial optimization of a metabeam, aiming at maximizing its critical buckling load. The problem was conceptualized and solved by combination of ML accelerated surrogate modeling and optimization algorithm, and buckling and post-buckling performance of the optimal design was validated by high-fidelity simulations and experiments. The efforts provide efficient tools for combinatorial design of mechanical metamaterials. We publicly share all the data and codes for implementation. [ABSTRACT FROM AUTHOR]

Abstract Background Grouping samples with low prevalence of positives into pools and testing these pools can achieve considerable savings in testing resources compared with individual testing in the context of COVID-19. We review published pooling matrices, which encode the assignment of samples into pools and describe decoding algorithms, which decode individual samples from pools. Based on the findings we propose new one-round pooling designs with high compression that can efficiently be decoded by combinatorial algorithms. This expands the admissible parameter space for the construction of pooling matrices compared to current methods. Results By arranging samples in a grid and using polynomials to construct pools, we develop direct formulas for an Algorithm (Polynomial Pools (PP)) to generate assignments of samples into pools. Designs from PP guarantee to correctly decode all samples with up to a specified number of positive samples. PP includes recent combinatorial methods for COVID-19, and enables new constructions that can result in more effective designs. Conclusion For low prevalences of COVID-19, group tests can save resources when compared to individual testing. Constructions from the recent literature on combinatorial methods have gaps with respect to the designs that are available. We develop a method (PP), which generalizes previous constructions and enables new designs that can be advantageous in various situations.

Non-orthogonal multiple-access (NOMA) is designed to transmit massive amounts of user communications. The incidence matrix manages the relationship between users and resources. This study focused on increasing user supportability and complexity reduction using larger incidence matrices. Our approach to optimizing the incidence matrix to improve system capacity and reduce complexity is based on two critical mathematical concepts: Parallel classes in hypergraph theory and combinatorial designs allow us to explore and extend incidence matrices. Frame theory is used to estimate matrix structures. Then, we investigate applications utilizing our incidence matrix designs–Simple Orthogonal Multi-Arrays (SOMA). The characteristics of SOMA reflect the unique Latin Square pattern, allowing us to produce a highly flexible and fair resource allocation matrix. SOMA designs let us support overload factors over 500%. The theoretical performance analysis equations of our NOMA system were established to support dynamic adaptability and optimization. We implemented and evaluated security methods for eavesdroppers. The prototype of the user hierarchy allows a higher-priority group to have a lower error rate without significantly affecting the system’s performance. Finally, the Monte Carlo simulation indicated that our NOMA systems allow higher degrees of freedom and lower complexity than other NOMA schemes while maintaining graceful error rates with a maximum 33% improvement.

Current societal challenges, such as climate change and resource depletion, highlight an unprecedented need for disruptive innovation in materials science. Significant breakthroughs are expected in multinary materials whose efficient exploration necessitates dedicated strategies. The exploration of a refractory high entropy alloy Nb-Ti-Zr-Cr-Mo is proposed here as test case for a new strategy. Based on the proven methodology of mixture design and on combinatorial thin film metallurgy, the composition space is explored by a limited number of chosen gradients to build an alloy library comprising hardness and ductility, two antagonistic properties. The workflow is showcased here by studying the properties of the as-grown graded film, which presents wide amorphous domains and contrasted mechanical properties. This experimental dataset then trains machine learning models to provide continuous predictions of the alloy properties over the entire composition space. We show that optimal alloy properties are expected close to the binary edges of the quinary.

Background: Grouping samples with low prevalence of positives into pools and testing these pools can achieve considerable savings in testing resources compared with individual testing in the context of COVID-19. We review published pooling matrices, which encode the assignment of samples into pools and describe decoding algorithms, which decode individual samples from pools. Based on the findings we propose new one-round pooling designs with high compression that can efficiently be decoded by combinatorial algorithms. This expands the admissible parameter space for the construction of pooling matrices compared to current methods. Results: By arranging samples in a grid and using polynomials to construct pools, we develop direct formulas for an Algorithm (Polynomial Pools (PP)) to generate assignments of samples into pools. Designs from PP guarantee to correctly decode all samples with up to a specified number of positive samples. PP includes recent combinatorial methods for COVID-19, and enables new constructions that can result in more effective designs. Conclusion: For low prevalences of COVID-19, group tests can save resources when compared to individual testing. Constructions from the recent literature on combinatorial methods have gaps with respect to the designs that are available. We develop a method (PP), which generalizes previous constructions and enables new designs that can be advantageous in various situations. [ABSTRACT FROM AUTHOR]

Given the sensitivity of applications and the sensor node's resource constraints, key management is an important security concern in Wireless Sensor Networks (WSNs). Combinatorial Design based schemes are used to propose key pre-distribution in WSNs as they have patterns that can be mapped to the WSNs. We employ Combinatorial Designs to pre-distribute the keys to the sensor nodes. The deployment area is divided into equal-sized regions called cells. The network comprises two types of sensor nodes: ordinary sensor nodes and cell masters. The ordinary sensor nodes within a cell can communicate with each other directly. The inter-cell communication is through the cell masters, which have higher resource capabilities than the ordinary sensor nodes. To take into account the Radio Frequency range of cell masters, we use Lee sphere region around each cell (Ruj in ACM Transactions on Sensor Networks (TOSN) 6:4, 2009, Rui Key predistribution using partially balanced designs in wireless sensor networks, 2007). The proposed key pre-distribution scheme for cell masters provides high network scalability with low key storage overhead compared to other schemes. The model's performance is measured in terms of key storage overhead and the number of sensor nodes supported. A detailed analysis of resiliency in terms of fractions of links disrupted is also presented. Also, the proposed scheme achieved better resiliency and requires much less number of keys to be stored in sensor nodes than the existing schemes. [ABSTRACT FROM AUTHOR]

This paper revisits a combinatorial structure called the large set of ordered design ( L O D ). Among others, we introduce a novel structure called Latin matching and prove that a Latin matching of order n leads to an L O D (n − 1 ,   n ,   2 n − 1) ; thus, we obtain constructions for L O D (1 ,   2 ,   3) , L O D (2 ,   3 ,   5) , and L O D (4 ,   5 ,   9) . Moreover, we show that constructing a Latin matching of order n is at least as hard as constructing a Steiner system S (n − 2 ,   n − 1 ,   2 n − 2) ; therefore, the order of a Latin matching must be prime. We also show some applications in multiagent systems. [ABSTRACT FROM AUTHOR]

Resource-constrained Devices are extensively used on the Internet of Things (IoT). WSN, RFID, and embedded systems are examples of these devices that have processing and communication power, memory capacity, and energy constraints. One of the lightweight methods in key distribution in these devices is to use Key Pre-Distribution Schemes (KPSs). A feature of a combinatorial key pre-distribution scheme, which is considered a deterministic scheme in key distribution, can be kept constant, while that feature may only occur in random key distribution schemes with a certain probability. In this paper, a new key pre-distribution scheme based on combinatorial designs was introduced, and using theoretical analysis, it was shown that such a scheme had high scalability and resilience compared to schemes introduced in recent years. They also enjoyed a good connectivity. [ABSTRACT FROM AUTHOR]

This paper is a contribution to the classification of parallelisms in three-dimensional projective spaces over small finite fields of order q by computer. The smallest space in which parallelisms have not yet been classified is for q = 4. Partial results are available. The parallelisms admitting a nontrivial automorphism of odd prime order are known. Moreover, much is known about the case of parallelisms of PG (3 , 4) whose automorphism group is a two group. Namely, everything is known for two of the three possible groups of order two, as well as for cyclic groups of order 4. The present paper will settle the case of parallelisms whose automorphism group is elementary abelian of order 4. This leaves open the cases of parallelisms whose full automorphism groups are either trivial or a specific group of order two. [ABSTRACT FROM AUTHOR]

The classification of unitals with parameters 2-(28, 4, 1) according to the 2-rank of their incidence matrices was initiated by McGuire, Tonchev and Ward, who proved that the 2-rank of any unital on 28 points is greater than or equal to 19, and up to isomorphism, there is a unique unital with 2-rank equal to 19. Jaffe and Tonchev investigated the next two 2-ranks, 20 and 21, and showed that there are no unitals on 28 points with 2-rank equal to 20, and there are exactly 4 isomorphism classes of unitals of rank 21. The subject of this paper is the classification of unitals having 2-rank 22, 23 and 24. [ABSTRACT FROM AUTHOR]

[Display omitted] • Modular combination design of multifunctional polymers for DNA delivery. • Rapid synthesis and screening of biodegradable polyaspartic acid polymers. • Heterocyclic substitution of polymers showed excellent transfection effects. • Polyplexes stimulate cellular immunity and antibody production in mice and chickens. It is crucial to develop non-viral gene vectors that can efficiently and safely transfect plasmid DNA into cells. Low transfection efficiency and high cytotoxicity of cationic polymers hinder their application as gene carriers. Modification of cationic polymers has emerged as an attractive strategy for efficient and safe nucleic acids delivery. In this study, a simple and rapid method is developed to synthesize a series of multifunctional polymers by utilizing biodegradable polyaspartic acid as the backbone and modifying it with three modules. This one-component polymer possesses capabilities for nucleic acid condensation, cellular uptake, and endosomal escape. Polymers containing imidazole, triazole, or pyridine group exhibited promising transfection activity. Substituted with dodecylamine or 2-hexyldecan-1-amine enhance cellular uptake and subsequent transfection. Furthermore, the influence of ionizable amine side chains on gene delivery is investigated. Two optimal polymers, combined with the avian encephalomyelitis virus (AEV) plasmid vaccine, induced robust specific antibody responses and cellular immune responses in mice and chickens. Through module-combination design and screening of polyaspartamide polymers, this study presents a paradigm for the development of gene delivery vectors. [ABSTRACT FROM AUTHOR]

It is a well-known fact that a graph of diameter d has at least d + 1 eigenvalues. A graph is d-extremal (resp. d α -extremal) if it has diameter d and exactly d + 1 distinct eigenvalues (resp. α -eigenvalues), and a graph is split if its vertex set can be partitioned into a clique and a stable set. Such graphs have a diameter of at most three. If all vertex degrees in a split graph are either d ˜ or d ^ , then we say it is (d ˜ , d ^) -bidegreed. In this paper, we present a complete classification of the connected bidegreed 3 α -extremal split graphs using the association of split graphs with combinatorial designs. This result is a natural generalization of Theorem 4.6 proved by Goldberg et al. and Proposition 3.8 proved by Song et al., respectively. [ABSTRACT FROM AUTHOR]

Several constructions of Mutually Unbiased Bases (MUBs) borrow tools from combinatorial objects. In this paper we focus on how one can construct Approximate Real MUBs (ARMUBs) with improved parameters using results from the domain of Resolvable Block Designs (RBDs). We first explain the generic idea of our strategy in relating the RBDs with MUBs/ARMUBs, which are sparse (the basis vectors have small number of non-zero co-ordinates). Then specific parameters are presented, for which we can obtain new classes and improve the existing results. To be specific, we present an infinite family of ⌈ d ⌉ many ARMUBs for dimension d = q(q + 1), where q ≡ 3 mod 4 and it is a prime power, such that for any two vectors v1,v2 belonging to different bases, | 〈 v 1 | v 2 〉 | < 2 d . We also demonstrate certain cases, such as d = sq2, where q is a prime power and sq ≡ 0 mod 4. These findings subsume and improve our earlier results in [Cryptogr. Commun. 13, 321-329, January 2021]. This present construction idea provides several infinite families of such objects, not known in the literature, which can find efficient applications in quantum information processing for the sparsity, apart from suggesting that parallel classes of RBDs are intimately linked with MUBs/ARMUBs. [ABSTRACT FROM AUTHOR]

To remain competitive in currently unpredictable markets, the enterprises must adapt their manufacturing systems to frequent market changes and high product variety. Reconfigurable manufacturing systems (RMSs) promise to offer a rapid and cost-effective response to production fluctuations under the condition that their configuration is attentively studied and optimised. This paper presents a decision support tool for designing reconfigurable machining systems to be used for family part production. The objective is to elaborate a cost-effective solution for production of several part families. This design issue is modelled as a combinatorial optimisation problem. An illustrative example and computational experiments are discussed to reveal the application of the proposed methodology. Insight gained would be useful to the decision-makers managing the configuration of manufacturing systems for diversified products. [ABSTRACT FROM AUTHOR]

It is a well-known fact that a graph of diameter d has at least d + 1 eigenvalues (A.E. Brouwer, W.H. Haemers (2012) [2]). A graph is d -extremal (resp. d S L -extremal) if it has diameter d and exactly d + 1 distinct eigenvalues (resp. signless Laplacian eigenvalues), and a graph is split if its vertex set can be partitioned into a clique and a stable set. Such graphs have diameter at most three. If all vertex degrees in a split graph are either d ˜ or d ˆ , then we say it is (d ˜ , d ˆ) -bidegreed. In this paper, we present a complete classification of the connected bidegreed 3 S L -extremal split graphs using the association of split graphs with combinatorial designs. [ABSTRACT FROM AUTHOR]

This paper revisits a combinatorial structure called the large set of ordered design (LOD). Among others, we introduce a novel structure called Latin matching and prove that a Latin matching of order n leads to an LOD(n−1, n, 2n−1); thus, we obtain constructions for LOD(1, 2, 3), LOD(2, 3, 5), and LOD(4, 5, 9). Moreover, we show that constructing a Latin matching of order n is at least as hard as constructing a Steiner system S(n−2, n−1, 2n−2); therefore, the order of a Latin matching must be prime. We also show some applications in multiagent systems.

• Automate non-periodic integral 3D woven candidate generation with a game theory-inspired algorithm. • This method has potential to be used for designing 3D woven composites at any scale. • The method uses a manufacturing-based parameterization to ensure fabricability. Three-dimensional non-periodic woven composite preforms have sufficient design flexibility that tows can be aligned along principal loading paths even in shaped structural components with detailed local features. While this promises competitive performance, the feasible design space is combinatorially large, far beyond exhaustive search. Seeking a design space that is compact and easily searched yet can span the full potential of 3D weaving, we propose a method for generating candidate designs called the Background Vector Method (BVM) which treats weaving tows as agents in a game competing to match background vectors derived from different design requirements. The BVM generates candidate designs that adapt local architecture to global design goals by adjusting scalar weights. A manufacturing-based parameterization assures fabricability. The scope of possible designs and the speed of the BVM are illustrated by re-creating common periodic 3D weaving patterns and novel complex non-periodic architectures, with a route demonstrated to forming cavities, ducts, and other open volumes. How the BVM might be incorporated within an optimization algorithm is outlined and pathways are shown for systematically enlarging the design space as individual design problems may require. [ABSTRACT FROM AUTHOR]

Erdős and Lovász noticed that an r‐uniform intersecting hypergraph H with maximal covering number, that is, τ(H)=r, must have at least 83r−3 edges. There has been no improvement on this lower bound for 45 years. We try to understand the reason by studying some small cases to see whether the truth lies very close to this simple bound. Let q(r) denote the minimum number of edges in an intersecting r‐uniform hypergraph. It was known that q(3)=6 and q(4)=9. We obtain the following new results: The extremal example for uniformity 4 is unique. Somewhat surprisingly it is not symmetric by any means. For uniformity 5, q(5)=13, and we found three examples, none of them being some known graph. We use both theoretical arguments and computer searches. In the footsteps of Erdős and Lovász, we also consider the special case, when the hypergraph is part of a finite projective plane. We determine the exact answer for r∈{3,4,5,6}. For uniformity 6, there is a unique extremal example. In a related question, we try to find 2‐intersecting r‐uniform hypergraphs with maximal covering number, that is, τ(H)=r−1. An infinite family of examples is to take all possible r‐sets of a (2r−2)‐vertex set. There is also a geometric candidate: biplanes. These are symmetric 2‐designs with λ=2. We determined that only three biplanes of the 18 known examples are extremal. [ABSTRACT FROM AUTHOR]

There are two construction methods of designs from $(n,m)$ -bent functions, known as translation and addition designs. In this article we analyze, which equivalence relation for Boolean bent functions, i.e. $(n,1)$ -bent functions, and vectorial bent functions, i.e. $(n,m)$ -bent functions with $2\le m\le n/2$ , is coarser: extended-affine equivalence or isomorphism of associated translation and addition designs. First, we observe that similar to the Boolean bent functions, extended-affine equivalence of vectorial $(n,m)$ -bent functions and isomorphism of addition designs are the same concepts for all even $n$ and $m\le n/2$. Further, we show that extended-affine inequivalent Boolean bent functions in $n$ variables, whose translation designs are isomorphic, exist for all $n\ge 6$. This implies, that isomorphism of translation designs for Boolean bent functions is a coarser equivalence relation than extended-affine equivalence. However, we do not observe the same phenomenon for vectorial bent functions in a small number of variables. We classify and enumerate all vectorial bent functions in six variables and show, that in contrast to the Boolean case, one cannot exhibit isomorphic translation designs from extended-affine inequivalent vectorial $(6,m)$ -bent functions with $m\in \{ 2,3 \}$. [ABSTRACT FROM AUTHOR]

It is a well-known fact that a graph of diameter d has at least d+1 eigenvalues. A graph is d-extremal (resp. dα-extremal) if it has diameter d and exactly d+1 distinct eigenvalues (resp. α-eigenvalues), and a graph is split if its vertex set can be partitioned into a clique and a stable set. Such graphs have a diameter of at most three. If all vertex degrees in a split graph are either d˜ or d^, then we say it is (d˜,d^)-bidegreed. In this paper, we present a complete classification of the connected bidegreed 3α-extremal split graphs using the association of split graphs with combinatorial designs. This result is a natural generalization of Theorem 4.6 proved by Goldberg et al. and Proposition 3.8 proved by Song et al., respectively.

Techniques of producing new combinatorial structures from old ones are commonly called trades. The switching principle applies for a broad class of designs: it is a local transformation that modifies two columns of the incidence matrix. In this paper, we present a construction, which is a generalization of the switching transform for the class of Steiner 2-designs. We call this construction paramodification of Steiner 2-designs, since it modifies the parallelism of a subsystem. We study in more detail the paramodifications of affine planes, Steiner triple systems, and abstract unitals. Computational results show that paramodification can construct many new unitals. [ABSTRACT FROM AUTHOR]

Compromised sensor nodes can be used to inject false reports (bogus reports) in wireless ssensor networks (WSNs). This can cause the sink to take wrong decisions. En-route filtering is a method to detect and filter false reports from WSNs. Most of the existing en-route filtering schemes use probabilistic approaches to filter false reports from the network, where filtering of false reports is based on a fixed probability. Thus false reports can travel multiple hops before being dropped. In this article we seek to overcome limitations of the existing schemes and reduce the overall key storage overhead in the cluster heads. In this article we propose a combinatorial design based partial en-route filtering scheme (CD-PEFS) which filters the fabricated reports deterministically. CD-PEFS reduces the energy requirements in the network by early detection and elimination of the false reports. Adoption of combinatorial design based keys get rid of shared key discovery phase from the network. This considerably reduces the communication overhead in the network. We carried out a detailed analysis of CD-PEFS against an increasing number of compromised sensor nodes in the network. We found that our scheme performs better than existing schemes in terms of filtering efficiency while maintaining low key storage overhead in the network. Further the performance of CD-PEFS is at par with existing schemes in terms of other protocol overheads. [ABSTRACT FROM AUTHOR]

It is well known to us that a graph of diameter l has at least l+1 eigenvalues. A graph is said to be Laplacian (resp, normalized Laplacian) l‐extremal if it is of diameter l having exactly l+1 distinct Laplacian (resp, normalized Laplacian) eigenvalues. A graph is split if its vertex set can be partitioned into a clique and a stable set. Each split graph is of diameter at most 3. In this paper, we completely classify the connected bidegreed Laplacian (resp, normalized Laplacian) 2‐extremal (resp, 3‐extremal) split graphs using the association of split graphs with combinatorial designs. Furthermore, we identify connected bidegreed split graphs of diameter 2 having just four Laplacian (resp, normalized Laplacian) eigenvalues. [ABSTRACT FROM AUTHOR]

We study the problem of identity testing for depth-3 circuits of top fanin k and degree d. We give a new structure theorem for such identities that improves the known deterministic …-time blackbox identity test over rationals [Kayal and Saraf, 2009] to one that takes …-time. Our structure theorem essentially says that the number of independent variables in a real depth-3 identity is very small. This theorem affirmatively settles the strong rank conjecture posed by Dvir and Shpilka [2006]. We devise various algebraic tools to study depth-3 identities, and use these tools to show that any depth-3 identity contains a much smaller nucleus identity that contains most of the "complexity" of the main identity. The special properties of this nucleus allow us to get near optimal rank bounds for depth-3 identities. The most important aspect of this work is relating a field-dependent quantity, the Sylvester-Gallai rank bound, to the rank of depth-3 identities. We also prove a high-dimensional Sylvester-Gallai theorem for all fields, and get a general depth-3 identity rank bound (slightly improving previous bounds). [ABSTRACT FROM AUTHOR]

In this paper we show the usability of the Gray code with constant weight words for computing linear combinations of codewords.This can lead to a big improvement of the computation time for finding the minimum distance of a code.We have also considered the usefulness of combinatorial 2-(t,k,1) designs when there are memory limitations to the number of objects (linear codes in particular) that can be tested for equivalence.

Wireless sensor networks are an easy target for report fabrication attack, where compromised sensor nodes can be used by an adversary to flood the network with bogus/false reports. En-route filtering is a mechanism where intermediate forwarding nodes identify and drop false reports while they are being forwarded toward the sink. Most of the existing en-route filtering schemes are probabilistic, where sensor nodes in each cell share secret keys with a fixed probability with intermediate nodes. Thus, forwarded reports are verified probabilistically by intermediate nodes, because of which false reports can travel several hops before being dropped. Few deterministic en-route filtering schemes have also been proposed in the literature, but all such schemes require a source to send the reports through a fixed path to reach the sink. In this paper, we propose a novel deterministic en-route filtering scheme based on a combinatorial design to overcome the above-mentioned limitations of the existing schemes. The use of combinatorial design-based keys ensures direct communication between all the sensor nodes while maintaining low key storage overhead in the network. We provide a comprehensive analysis of the proposed scheme. The proposed scheme notably performs better than the existing schemes in terms of the expected filtering position of false reports. Furthermore, the proposed scheme improves data authenticity in the network and is more buoyant to selective forwarding and report disruption attacks.

With the deep study of the Hamming distances of orthogonal arrays (OAs), the application of OAs has penetrated into many fields, one of which is to construct the key predistribution schemes (KPSs) for distributed sensor networks. In this paper, we define the Hamming distance distribution (HDD) of an OA and its uniqueness. Furthermore, we present some OAs with unique HDD. In KPSs based on these OAs, the calculations of metrics for evaluating connectivity and resilience can be simplified. We also illustrate that KPSs based on them have a wider application and better connectivity and resilience than the existing ones. [ABSTRACT FROM AUTHOR]

This paper studies the Pliable Index CODing problem (PICOD), which models content-type distribution networks. In the PICOD $({t})$ problem there are ${m}$ messages, ${n}$ users and each user has a distinct message side information set, as in the classical Index Coding problem (IC). Differently from IC, where each user has a pre-specified set of messages to decode, in the PICOD $({t})$ a user is “pliable” and is satisfied if it can decode any ${t}$ messages that are not in its side information set. The goal is to find a code with the shortest length that satisfies all the users. This flexibility in determining the desired message sets makes the PICOD $({t})$ behave quite differently compared to the IC, and its analysis even more challenging. This paper mainly focuses on the complete– ${S}$ PICOD $({t})$ with ${m}$ messages, where the set ${S}\subset [{m}]$ contains the sizes of the side information sets, and the number of users is ${n}=\sum _{s\in {S}}\binom {m} {s}$ , with no two users having the same side information set. Capacity results are shown for: (i) the consecutive complete– ${S}$ PICOD $({t})$ , where ${S}=[{s}_{\text {min}}:{s}_{\text {max}}]$ for some $0 \leqslant {s}_{\text {min}}\leqslant {s}_{\text {max}} \leqslant {m}-{t}$ , and (ii) the complement-consecutive complete– ${S}$ PICOD $({t})$ , where ${S}=[0: {m}-{t}]\backslash [{s}_{\text {min}}:{s}_{\text {max}}]$ , for some $0 < {s}_{\text {min}}\leqslant {s}_{\text {max}} < {m}-{t}$. The novel converse proof is inspired by combinatorial design techniques and the key insight is to consider all messages that a user can eventually decode successfully, even those in excess of the ${t}$ required ones. This allows one to circumvent the need to consider all possible desired message set assignments at the users in order to find the one that leads to the shortest code length. The core of the novel proof is to solve the critical complete– ${S}$ PICOD $({t})$ with ${m} = 2{s}+{t}$ messages and ${S}=\{{s}\}$ , by showing the existence of a user who can decode ${s}+{t}$ messages regardless of the desired message set assignment. All other tight converse results for the complete– ${S}$ PICOD $({t})$ can be deduced from this critical case. The converse results show the information theoretic optimality of simple linear coding schemes. By similar reasoning, all complete– ${S}$ PICOD $({t})$ where the number of messages is ${m}\leqslant 5$ can be fully characterized. In addition, tight converse results are also shown for the PICOD(1) with circular-arc network topology hypergraph. [ABSTRACT FROM AUTHOR]

It is a well-known fact that a graph of diameter d has at least d + 1 eigenvalues. A graph is d -extremal, if it has diameter d and exactly d + 1 eigenvalues. A graph is split if its vertex set can be partitioned into a clique and a stable set. Such graphs have diameter at most 3. We obtain a complete classification of the connected bidegreed 3-extremal split graphs using the association of split graphs with combinatorial designs. We also construct certain families of non-bidegreed 3-extremal split graphs. [ABSTRACT FROM AUTHOR]

The radical S-adenosylmethionine (SAM) enzyme NifB occupies a central and essential position in nitrogenase biogenesis. NifB catalyzes the formation of an [8Fe-9S-C] cluster, called NifB-co, which constitutes the core of the active-site cofactors for all 3 nitrogenase types. Here, we produce functional NifB in aerobically cultured Saccharomyces cerevisiae. Combinatorial pathway design was employed to construct 62 strains in which transcription units driving different expression levels of mitochondria-targeted nif genes (nifUSXB and fdxN) were integrated into the chromosome. Two combinatorial libraries totaling 0.7 Mb were constructed: An expression library of 6 partial clusters, including nifUSX and fdxN, and a library consisting of 28 different nifB genes mined from the Structure-Function Linkage Database and expressed at different levels according to a factorial design. We show that coexpression in yeast of the nitrogenase maturation proteins NifU, NifS, and FdxN from Azotobacter vinelandii with NifB from the archaea Methanocaldococcus infernus or Methanothermobacter thermautotrophicus yields NifB proteins equipped with [Fe-S] clusters that, as purified, support in vitro formation of NifB-co. Proof of in vivo NifB-co formation was additionally obtained. NifX as purified from aerobically cultured S. cerevisiae coexpressing M. thermautotrophicus NifB with A. vinelandii NifU, NifS, and FdxN, and engineered yeast SAM synthase supported FeMo-co synthesis, indicative of NifX carrying in vivo-formed NifB-co. This study defines the minimal genetic determinants for the formation of the key precursor in the nitrogenase cofactor biosynthetic pathway in a eukaryotic organism. [ABSTRACT FROM AUTHOR]

A new scheme for the problem of centralized coded caching with non-uniform demands is proposed. The distinguishing feature of the proposed placement strategy is that it admits equal sub-packetization for all files while allowing the users to allocate more cache to the files which are more popular. This creates natural broadcasting opportunities in the delivery phase which are simultaneously helpful for the users who have requested files of different popularities. For the case of two files, we propose a new delivery strategy based on interference alignment which enables each user to decode his desired file following a two-layer peeling decoder. Furthermore, we extend the existing converse bounds for uniform demands under uncoded placement to the nonuniform case. To accomplish this, we construct $N!$ auxiliary users, corresponding to all permutations of the $N$ files, each caching carefully selected sub-packets of the files. Each auxiliary user provides a different converse bound. The overall converse bound is the maximum of all these $N!$ bounds. We prove that our achievable delivery rate for the case of two files meets this converse, thereby establishing the optimal expected memory-rate trade-off for the case of $K$ users and two files with arbitrary popularities under uncoded placement. [ABSTRACT FROM AUTHOR]

This article summarizes a series of interconnected researches exploring the potential of applying topological interlocking methodologies to the field of architectural design and fabrication. Specifically, it describes two concurrent approaches to design with interlocking units: the first relying on parametric design logics and mass-customized fabrication processes and the second implementing discrete combinatorial processes for both design and fabrication using modular units. We first outline the historical background of combinatorial thinking in architectural computing and describe the emergence of computational design and digital fabrication. We further present the recent evolution of a combinatorial design paradigm, which challenges the acquired parametric design methodologies in computational architecture research. We then present our research in the field of topological interlocking, focusing on a parametric design approach. We further describe implications of a shift from parametric to combinatorial design logics in architecture. Finally, we present the transition of the topological interlocking research from parametric to combinational logics. In these three sections, we describe design and fabrication methodologies for both approaches and evaluate the potentials and limitations of both. We present recent work in the development of software for combinatorial design within caad software, and its first application is to design topological interlocking systems. We conclude by outlining the future research directions and possibilities of integration between parametric and combinatorial processes in design, fabrication, and assembly of interlocking systems. [ABSTRACT FROM AUTHOR]

In this paper, using group actions, we introduce a new method for constructing partial geometric designs (sometimes referred to as 1 1 2 -designs). Using this new method, we construct several infinite families of partial geometric designs by investigating the actions of various linear groups of degree two on certain subsets of F q 2 . Moreover, by computing the stabilizers of such subsets in various linear groups of degree two, we are also able to construct a new infinite family of balanced incomplete block designs. [ABSTRACT FROM AUTHOR]

• Orthogonal array with strength 3 has few applications in cryptography to date, although it possesses some excellent cryptographic properties. This paper tries an image encryption algorithm based on this configuration. Simulation results demonstrate the proposed algorithm has good statistical characteristics and strong diffusivity. • The algorithm can encrypt multiple images simultaneously. The cipher images in the same batch are highly correlated, which makes the attacks more difficult. Moreover, if one cipher image is lost, its partial information can be recovered by other cipher images in the same batch. • Unlike other algorithms based on combinatorial configurations, the proposed algorithm doesn't generate the whole configuration. It generates the designated element in orthogonal arrays only when needed. This strategy is more time-saving, and makes the algorithm not limited by the size of encrypted images. In recent years, remote working and studying lead to numerous images being transmitted on the Internet. Many of these images need protection from illegal obtaining or malicious peeping. Under the circumstances, the demand for image encryption algorithms with sufficient capacity and high efficiency is increasing. Multiple-image encryption algorithms can suit the demand well. This paper proposes a multiple-image encryption algorithm based on orthogonal arrays with strength 3. Orthogonal array is a typical configuration in combinatorial design theory, but the application research of orthogonal arrays with strength 3 in image encryption is still a blank. The proposed algorithm combines orthogonal arrays and chaotic maps perfectly to generate multiple 3D permutation maps and substitution maps, then multiple images can be encrypted efficiently. In simulation experiments, the average value of information entropy is 7.9993, the average value of PSNR is 8.884, the average value of MSD is 50, the average values of NPCR and UACI are 99.6127% and 33.4765% respectively. The numerical results demonstrate that the algorithm has enough ability to resist common attacks. [ABSTRACT FROM AUTHOR]