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Wet paper codes (WPCs) are designed for steganography, in which the sender and recipient do not need to share the changeable positions. In this paper, we propose the N-page construction for wet paper coding, which can generate a family of WPCs following the upper bound on embedding efficiency from one single WPC. The Paper Folding method, one of our previous methods, is a special case of the N-page construction with N=2^k. We deduce recursions for calculating embedding efficiency of N-page construction, and obtain explicit expression on embedding efficiency of 2^k-page construction. Furthermore, we derive the limit of distance between the embedding efficiency of 2^k-page construction and the upper bound of embedding efficiency as k tends to infinity. Based on the limit, we analyze how the embedding efficiency is influenced by the proportion of wet pixels (wet ratio) in the cover, showing that embedding efficiency only drops about 0.32 as the wet ratio increases to 0.9999. [ABSTRACT FROM PUBLISHER]

This paper explores the conditions which make a regular balanced random (k,2s)-CNF formula (1,0)-unsatisfiable with high probability. The conditions also make a random instance of the regular balanced (k − 1,2(k − 1)s)-SAT problem unsatisfiable with high probability, where the instance obeys a distribution which differs from the distribution obeyed by a regular balanced random (k − 1,2(k − 1)s)-CNF formula. Let F be a regular balanced random (k,2s)-CNF formula where k ⩾ 3, then there exists a number s0 such that F is (1,0)-unsatisfiable with high probability if s > s0. A numerical solution of the number s0 when k ∈ {5, 6,..., 14} is given to conduct simulated experiments. The simulated experiments verify the theoretical result. Besides, the experiments also suggest that F is (1,0)-satisfiable with high probability if s is less than a certain value. [ABSTRACT FROM AUTHOR]

In this paper, we consider encoding strategies for the Z-channel with noiseless feedback. We analyze the combinatorial setting where the maximum number of errors inflicted by an adversary is proportional to the number of transmissions, which goes to infinity. Without feedback, it is known that the rate of optimal asymmetric-error-correcting codes for the error fraction $\tau \ge 1/4$ vanishes as the blocklength grows. In this paper, we give an efficient feedback encoding scheme with $n$ transmissions that achieves a positive rate for any fraction of errors $\tau < 1$ and $n\to \infty $. Additionally, we state an upper bound on the rate of asymptotically long feedback asymmetric error-correcting codes. [ABSTRACT FROM AUTHOR]

In this paper, we characterize the capacity of a new class of discrete memoryless multicast networks having a tree topology. For achievability, a novel coding scheme is constructed where some relays employ a combination of decode-and-forward and compress-and-forward and the other relays perform a random binning such that codebook constructions and relay operations are independent for each node and do not depend on the network topology. For converse, a new technique of iteratively manipulating inequalities exploiting the tree topology is used. This class of multicast tree networks includes the class of diamond networks studied by Kang and Ulukus as a special case. [ABSTRACT FROM PUBLISHER]

In this paper, we extend the localized error correction code introduced by L. A. Bassalygo and coworkers from Hamming space to projective space. For constant dimensional localized error correction codes in projective space, we have a lower bound and an upper bound of the capacity, which are asymptotically tight when z< x\leq n-z\over 2, where x, z, and n are dimensions of codewords, error configurations, and the ground space, respectively. We determine the capacity of nonconstant dimensional localized error correction codes when z < n\over 3. [ABSTRACT FROM PUBLISHER]

In this paper, the sequence families of which maximum correlation is determined by the Weil bound of exponential sums are revisited. Using the same approach, two new constructions with large family sizes and low maximum correlation are given. The first construction is an analog of one recent result derived from the interleaved structure of Sidel'nikov sequences. For a prime p and an integer M\vert (p-1), the new M-ary sequence families of period p are obtained from irreducible quadratic polynomials and known power residue-based sequence families. The new sequence families increase family sizes of the known power residue-based sequence families, but keep the maximum correlation unchanged. In the second construction, the sequences derived from the Weil representation are generalized, where each new sequence is the elementwise product of a modulated Sidel'nikov sequence and a modulated trace sequence. For positive integers d

The study of analytical solutions for the bearing capacity of reinforced soil foundations is a very important topic in engineering mathematics. Existing evaluations of the foundation-bearing capacity on reinforced soils are based on dry conditions, while many foundations are located on unsaturated soils in real engineering. In this paper, a new formula for the bearing capacity of reinforced strip footings on unsaturated soils is presented. Two sliding failure mechanisms are constructed based on the position of the reinforcement layer relative to the sliding surface. The distribution of apparent cohesion in the depth direction is calculated by considering the effect of matrix suction. By additionally considering the work conducted by the reinforcement and the contribution of the apparent cohesion, the bearing capacity formula is obtained using the upper bound theorem of limit analysis. The bearing capacity solution is obtained by adopting the sequential quadratic programming (SQP) algorithm. Comparing the results under two failure mechanisms, the optimal bearing capacity and the optimal embedment depth of reinforcement are obtained. The results of this paper are consistent with those of the existing literature. Finally, the effects of reinforcement embedment depth, effective internal friction angle, uniform load, and unsaturated soil parameters on the optimal bearing capacity are investigated through parametric analysis. This paper provides useful recommendations for the engineering application of reinforced strip footings on unsaturated soils. [ABSTRACT FROM AUTHOR]

Primality generation is the cornerstone of several essential cryptographic systems. The problem has been a subject of deep investigations, but there is still a substantial room for improvements. Typically, the algorithms used have two parts – trial divisions aimed at eliminating numbers with small prime factors and primality tests based on an easy-to-compute statement that is valid for primes and invalid for composites. In this paper, we will showcase a technique that will eliminate the first phase of the primality testing algorithms. The computational simulations show a reduction of the primality generation time by about 30 percent in the case of 1024-bit RSA key pairs. This can be particularly beneficial in the case of decentralized environments for shared RSA keys as the initial trial division part of the key generation algorithms can be avoided at no cost. This also significantly reduces the communication complexity. Another essential contribution of the paper is the introduction of a new one-way function that is computationally simpler than the existing ones used in public-key cryptography. This function can be used to create new random number generators, and it also could be potentially used for designing entirely new public-key encryption systems. [ABSTRACT FROM AUTHOR]

This paper considers an assembly problem. Let there be two interlocking parts, only one of which may be cut into pieces. How many pieces should we cut the divisible part into to separate the parts using a sequence of rigid-body motions? In this initial exploration, we primarily consider 2-D polygonal parts. This paper presents an algorithm that computes a lower bound on the number of pieces that the divisible part must be cut into. This paper also presents a complete algorithm that constructs a set of cuts and a motion plan for disassembly, yielding an upper bound on the required number of pieces. Applications of the future extension of this paper to 3-D may include robot self-assembly, interlocking 3-D model design, search-and-rescue, packaging, and robotic surgery. Note to Practitioners—This paper presents an opposite problem of immobilization or caging. Given two interlocking parts, only one of which may be cut into pieces. How can we unimmobilize or uncage one from another? We explore this problem in two aspects: the lower bound and the upper bound on the number of pieces that the divisible part must be cut into. This paper is an early theoretical exploration of this problem. We verified our methods in a virtual 2-D environment instead of building physical structures. Extension of this paper to 3-D could have many applications, including robot self-assembly, 3-D fabrication model design, search-and-rescue, packaging, and robotic surgery. [ABSTRACT FROM AUTHOR]

In this paper, we estimate sharp bounds for certain Hankel determinants, H2,3(f), H3,1(f) and Zalcman functional |a²3 -- a5| for the class of convex function with respect to symmetric points, hence proving the recent conjecture made by Virendra et al., that affirms the sharp bound for the third Hankel determinant in the classes of convex functions with respect to symmetric points is 4/135. [ABSTRACT FROM AUTHOR]

This paper proposes an upper bound for mine productivity (useful for long-term planning) and also a simple truck dispatch rule (useful for short-term operations) that demonstrates how tight the upper bound can be using a simulation. It also proposes a greedy search to approximate the productivity upper bound, which is faster and often exact. Uncertainty is added to the simulation in order to verify how the productivity responds to it. Typically, the productivity's upper bound is less tight close to its saturation point as a function of the number of trucks, where adding more trucks only increases queues. Furthermore, more uncertainty in the model typically leads to a less tight upper bound. The results conducted using real data from an open pit mine in Brazil show that the gap between the productivity upper bound and the productivity realization using the proposed dispatch rule for a homogeneous fleet can be less than 2% , but it can be as large as 12% near the productivity saturation point without uncertainty. Even though this gap seems to become arbitrarily small as the number of trucks and the simulation horizon increase, the productivity upper bound is never violated, which validates it as an upper bound and induces optimality for the dispatch rule. [ABSTRACT FROM AUTHOR]

Multiuser diversity has attracted significant attention recently. In this letter, we propose a greedy algorithm based on QR decomposition of the channel and dirty paper precoding to exploit the multiuser diversity of the Gaussian vector broadcast channel. Simulations show the approach provides performance which is extremely close to a well-known upper bound on the sum rate. Further, exploiting multiuser diversity can provide large gain over approaches ignoring this resource. [ABSTRACT FROM PUBLISHER]

We consider a variable-length source coding problem subject to local decodability constraints. In particular, we investigate the blocklength scaling behavior attainable by encodings of $r$ -sparse binary sequences, under the constraint that any source bit can be correctly decoded upon probing at most $d$ codeword bits. We consider both adaptive and non-adaptive access models, and derive upper and lower bounds that often coincide up to constant factors. Such a characterization for the fixed-blocklength analog of our problem, known as the bit probe complexity of static membership, remains unknown despite considerable attention from researchers over the last few decades. We also show that locally decodable schemes for sparse sequences are able to decode 0s (frequent source symbols) of the source with far fewer probes on average than they can decode 1s (infrequent source symbols), thus rigorizing the notion that infrequent symbols require high probe complexity, even on average. Connections to the fixed-blocklength model and to communication complexity are also briefly discussed. [ABSTRACT FROM AUTHOR]

The problem of universal source coding for binary trees is considered. Zhang, Yang, and Kieffer derived upper bounds on the average-case redundancy of codes based on directed acyclic graph (DAG) compression for binary tree sources with certain properties. In this paper, a natural class of binary tree sources is presented such that the demanded properties are fulfilled. Moreover, for both subclasses considered in the paper of Zhang, Yang, and Kieffer, their result is improved by deriving bounds on the maximal pointwise redundancy (or worst-case redundancy) instead of the average-case redundancy. Finally, using context-free tree grammars instead of DAGs, upper bounds on the maximal pointwise redundancy for certain binary tree sources are derived. This yields universal codes for new classes of binary tree sources. [ABSTRACT FROM AUTHOR]

Label corruption leads to a significant challenge in supervised learning, particularly in deep neural networks. This paper considers recovering a small corrupted subset of data samples which are typically caused by non-expert sources, such as automatic classifiers. Our aim is to recover the corrupted data samples by exploiting a finite query-testing system as an additional expert. The task involves identifying the corrupted data samples with minimal expert queries and finding them to their true label values. The proposed query-testing system uses a random selection of a subset of data samples and utilizes finite field operations to construct combined responses. In this paper, we demonstrate an information-theoretic lower bound on the minimum number of queries required for recovering corrupted labels. The lower bound can be represented as a function of joint entropy with an imbalanced rate of data samples and mislabeled probability. In addition, we find an upper bound on the error probability using maximum a posteriori decoding. [ABSTRACT FROM AUTHOR]

The standard formulation of the upper bound theorem is incompatible with the Coulomb friction law. However, this law is widely used in metal forming processes analysis. An alternative formulation based on non-kinematically admissible velocity fields can evaluate the load required to deform the material. The present paper adopts this formulation for evaluating the compression force in solid and hollow cylinder compression processes. The trial velocity fields are continuous. The field for the solid cylinder involves no parameter for minimization, and the field for the hollow cylinder involves one parameter. Parametric analyses of the solutions are provided. The compression forces found are compared to available results at small friction coefficients. The solution is also in agreement with physical expectations. In particular, the solution for the hollow cylinder compression predicts that the radial velocity is everywhere positive in the friction coefficient is small enough. For larger friction coefficients, the radius where the radial velocity vanishes propagates from the inner radius as the friction coefficient increases. The final result can be used in conjunction with standard procedures for evaluating the friction coefficient. [ABSTRACT FROM AUTHOR]

We show that the discrete Painlevé II equation with starting value $ a_{-1}=-1 $ a − 1 = − 1 has a unique solution for which $ -1 { \lt } a_n { \lt } 1 $ − 1 < a n < 1 for every $ n \geq ~0 $ n ≥ 0. This solution corresponds to the Verblunsky coefficients of a family of orthogonal polynomials on the unit circle. This result was already proved for certain values of the parameter in the equation and recently a full proof was given by Duits and Holcomb [A double scaling limit for the d-PII equation with boundary conditions. arXiv:2304.02918 [math.CA]]. In the present paper we give a different proof that is based on an idea put forward by Tomas Lasic Latimer [Unique positive solutions to q-discrete equations associated with orthogonal polynomials, J. Difference Equ. Appl. 27 (2021), pp. 763–775.] which uses orthogonal polynomials. We also give an upper bound for this special solution. [ABSTRACT FROM AUTHOR]

This paper introduced a smoothing algorithm for calculating the maximal eigenvalue of non-defective positive matrices. Two special matrices were constructed to provide monotonically increasing lower-bound estimates and monotonically decreasing upper-bound estimates of the maximal eigenvalue. The monotonicity and convergence of these estimations was also proven. Finally, the effectiveness of the algorithm was demonstrated with numerical examples. [ABSTRACT FROM AUTHOR]

In this paper, we define new subclasses of analytic functions related to a modified sigmoid function and analytic univalent function. Then, we attempt to investigate the upper bounds of the third and fourth Hankel determinant in the special case. Further, bound on third Hankel determinant of its inverse function is also investigated. In addition, we attempt to obtain the Fekete-Szegö inequality for the classes. Then, we estimate the bounds of initial coefficients for the function belongs to some kind of new subclasses when its inverse function also belongs to these new subclasses. [ABSTRACT FROM AUTHOR]

The main purpose of this paper is to investigate the upper bound and H¨older continuity for a general class of parametric elliptical variational-hemivariational inequalities via regularized gap functions. More precisely, we deliver a formulation of the elliptical variational-hemivariational inequalities in the case of the perturbed parameters governed by both the set of constraints and the mappings (for brevity, PEVHI (CM)). Based on the arguments of monotonicity and properties of the Clarke's generalized directional derivative, we establish an upper bound result for the PEVHI (CM) and provide the H¨older continuity of the solution mapping for the PEVHI (CM) under suitable assumptions on the data. [ABSTRACT FROM AUTHOR]

List decoding of insertions and deletions in the Levenshtein metric is considered. The Levenshtein distance between two sequences is the minimum number of insertions and deletions needed to turn one of the sequences into the other. In this paper, a Johnson-like upper bound on the maximum list size when list decoding in the Levenshtein metric is derived. This bound depends only on the length and minimum Levenshtein distance of the code, the length of the received word, and the alphabet size. It shows that polynomial-time list decoding beyond half the Levenshtein distance is possible for many parameters. Further, we also prove a lower bound on list decoding of deletions with the well-known binary Varshamov–Tenengolts codes, which shows that the maximum list size grows exponentially with the number of deletions. Finally, an efficient list decoding algorithm for two insertions/deletions with VT codes is given. This decoder can be modified to a polynomial-time list decoder of any constant number of insertions/deletions. [ABSTRACT FROM AUTHOR]

Owning to the sub-standards being developed by IEEE Time-Sensitive Networking (TSN) Task Group, the traditional IEEE 802.1 Ethernet is enhanced to support real-time dependable communications for future time- and safety-critical applications. Several sub-standards have been recently proposed that introduce various traffic shapers (e.g., Time-Aware Shaper (TAS), Asynchronous Traffic Shaper (ATS), Credit-Based Shaper (CBS), Strict Priority (SP)) for flow control mechanisms of queuing and scheduling, targeting different application requirements. These shapers can be used in isolation or combination and there is limited work that analyzes, evaluates, and compares their performance, which makes it challenging for end-users to choose the right combination for their applications. This paper aims at (i) quantitatively comparing various traffic shapers and their combinations, (ii) summarizing, classifying, and extending the architectures of individual and combined traffic shapers and their Network calculus (NC)-based performance analysis methods, and (iii) filling the gap in the timing analysis research on handling ATS and CBS used for different priority queues, and two novel hybrid architectures of combined traffic shapers, i.e., TAS+ATS+SP and TAS+ATS+CBS when ATS and CBS used at the same queue. A large number of experiments, using both synthetic and realistic test cases, are carried out for quantitative performance comparisons of various individual and combined traffic shapers, from the perspective of upper bounds of delay, backlog, and jitter. To the best of our knowledge, we are the first to quantitatively compare the performance of the main traffic shapers in TSN. The paper aims at supporting the researchers and practitioners in the selection of suitable TSN sub-protocols for their use cases. [ABSTRACT FROM AUTHOR]

We investigate the state-dependent Gaussian wiretap channel with noncausal channel state information at the transmitter (GWTC-N-CSIT), and explore whether three strategies (i.e., taking action on the state, legitimate receiver’s channel output feedback, and combining the former two strategies together) help to enhance the secrecy capacity of the GWTC-N-CSIT. To be specific, we first determine the secrecy capacity of the GWTC-N-CSIT with noiseless feedback. Next, we derive lower and upper bounds on the secrecy capacity of the GWTC-N-CSIT with action-dependent state. Finally, we derive lower and upper bounds on the secrecy capacity of the GWTC-N-CSIT with both action-dependent state and noiseless feedback, and show that these bounds meet for a special case. Numerical results of this paper indicate that all three strategies enhance the secrecy capacity of the GWTC-N-CSIT. The study of this paper offers new options for enhancing the secrecy rates of the state-dependent wiretap channel models. [ABSTRACT FROM AUTHOR]

This paper considers distribution systems with a high penetration of distributed, renewable generation and addresses the problem of incorporating the associated uncertainty into the optimal operation of these networks. Joint chance constraints, which satisfy multiple constraints simultaneously with a prescribed probability, are one way to incorporate uncertainty across sets of constraints, leading to a chance-constrained optimal power flow problem. Departing from the computationally heavy scenario-based approaches or approximations that transform the joint constraint into conservative deterministic constraints; this paper develops a scalable, data-driven approach which learns operational trends in a power network, eliminates zero-probability events (e.g., inactive constraints), and accurately and efficiently approximates bounds on the joint chance constraint iteratively. In particular, the proposed framework improves upon the classic methods based on the union bound (or Boole’s inequality) by generating a much less conservative set of single chance constraints that also guarantees the satisfaction of the original joint constraint. The proposed framework is evaluated numerically using the IEEE 37-node test feeder, focusing on the problem of voltage regulation in distribution grids. [ABSTRACT FROM AUTHOR]

There has been much recent interest in private information retrieval (PIR) in models where a database is stored across several servers using coding techniques from distributed storage, rather than being a simply replicated. In particular, a recent breakthrough result of Fazelli, Vardy, and Yaakobi introduces the notion of a PIR code and a PIR array code, and uses this notion to produce efficient PIR protocols. In this paper, we are interested in designing PIR array codes. We consider the case when we have $m$ servers, with each server storing a fraction $(1/s)$ of the bits of the database; here $s$ is a fixed rational number with $s > 1$. A PIR array code with the $k$ -PIR property enables a $k$ -server PIR protocol (with $k\leq m$) to be emulated on $m$ servers, with the overall storage requirements of the protocol being reduced. The communication complexity of a PIR protocol reduces as $k$ grows, so the virtual server rate, defined to be $k/m$ , is an important parameter. We study the maximum virtual server rate of a PIR array code with the $k$ -PIR property. We present upper bounds on the achievable virtual server rate, some constructions, and ideas how to obtain the PIR array codes with the highest possible virtual server rate. In particular, we present constructions that asymptotically meet our upper bounds and the exact largest virtual server rate is obtained when $1 < s \leq 2$. A $k$ -PIR code (and similarly a $k$ -PIR array code) is also a locally repairable code with symbol availability $k-1$. Such a code ensures $k$ parallel reads for each information symbol. So the virtual server rate is very closely related to the symbol availability of the code when used as a locally repairable code. The results of this paper are discussed also in this context where subspace codes also have an important role. [ABSTRACT FROM AUTHOR]

This paper studies the subcarrier allocation and precoder design problem for downlink multiple-input-multiple-output-orthogonal frequency-division multiple access systems. The criterion is to maximize the energy efficiency (EE) of the system. We adopt the time-sharing concept to allocate each subcarrier to one user, which results in a criterion similar with that of rate maximization. However, this approach does not make it possible to solve the problem for any value of the transmit power. We found that there exist gaps along the direction of total transmit power when the user selection switches for each subcarrier, which leads to a discontinuous EE function, for which quasi-concavity has to be checked. We first show that the sufficient conditions obtained for the subcarrier allocation approach are the optimal ones among all possibilities with the same transmit power. Then, we show that the proposed subcarrier allocation results in a discontinuous and quasi-concave EE function. We also give an upper bound of the EE function when the proposed sufficient conditions are not met. Finally, we propose an algorithm to find the maximal EE and its performance is illustrated by means of numerical results. [ABSTRACT FROM PUBLISHER]

Tunneling in soft clay requires accurate estimation of the inner support pressure to prevent undesired ground settlement and maintain the overall soil stability. Previous researchers have shown that the stability factor approach, which is analogous to Terzaghi's bearing capacity factors [critical stability number (Nc), Ns, and Nγ)], is effective and efficient to determine the limit loads of many geotechnical stability problems. Therefore, this paper aims to study the stability factors of four various tunnel shapes in undrained clay: the two-dimensional (2D) tunnels of circular, square, and heading in plane strain, and the three-dimensional (3D) circular tunnel heading. Using the advanced finite-element limit analysis (FELA), rigorous upper-bound (UB) solutions of the undrained stability factors (Fc, Fs and Fγ) will be produced for various tunnel depth ratios (C/D). Numerical UB results are compared with lower bound (LB) solutions. Comprehensive design charts, tables, and equations will be presented for practitioners to estimate the critical tunnel support pressure at collapse. [ABSTRACT FROM AUTHOR]

A common method for reading information stored in DNA molecules is shotgun sequencing. This method outputs a histogram of the frequencies of all the molecules’ substrings of a given length $\ell $. To protect against noisy readings, the rank-modulation scheme encodes the information in the relative ranking of the substring frequencies, instead of their absolute values. However, the best rank-modulation codes for shotgun sequencing have low rates which are asymptotically vanishing. In this paper we propose new constructions of rank-modulation codes for shotgun sequencing. The first code construction is systematic, allowing the user to arbitrarily set the frequencies of a large subset of the substrings, which the encoder then completes to a permutation that may be realized by a DNA molecule. The construction is then improved by allowing the user to set the frequencies of additional substrings, at the cost of imposing constraints on the frequencies. The resulting codes have higher, non-vanishing rates, compared with previously known codes. As an example, for histograms of substrings of length $\ell =2$ , and an alphabet of size 4 (as in DNA molecules), we are able to construct a code with rate $\approx 0.909$ , whereas previously, the best construction resulted in a code with rate $\approx 0.654$. Additionally, the encoded information in our construction may be written to shorter DNA molecules than possible before. We also prove that the systematic codes constructed in this paper are the largest possible among all systematic codes. [ABSTRACT FROM AUTHOR]

In this paper, we study the initial boundary value problem for a class of higher-order nonlinear pseudo-parabolic equations with a memory term. First, the blow-up results of the solution when the initial energy is negative or positive are obtained by using concavity analysis, and an upper bound on the blow-up time T ∗ is given. Second, a lower bound on the blow-up time T ∗ is obtained by applying differential inequalities when the solutions blow up. [ABSTRACT FROM AUTHOR]

In this paper, we study the class of graphs G m , n that have the same degree sequence as two disjoint cliques K m and K n , as well as the class G ¯ m , n of the complements of such graphs. The problems of finding a maximum clique and a maximum independent set are NP-hard on G m , n . Therefore, looking for upper and lower bounds for the clique and independence numbers of such graphs is a challenging task. In this article, we obtain such bounds, as well as other related results. In particular, we consider the class of regular graphs, which are degree-equivalent to arbitrarily many identical cliques, as well as such graphs of bounded degree. [ABSTRACT FROM AUTHOR]

In this paper, we defined a new generalized Cochrane sum with Dirichlet characters, and gave the upper bound of the generalized Cochrane sum with Dirichlet characters. Moreover, we studied the asymptotic estimation problem of the mean value of the generalized Cochrane sum with Dirichlet characters and obtained a sharp asymptotic formula for it. By using this asymptotic formula, we also gave the mean value of the generalized Dedekind sum. [ABSTRACT FROM AUTHOR]

Reconfigurable intelligent surfaces (RISs) appear as one of the most promising paradigms for future wireless communications, because of their high adjustability for diverse communication demands and the additional information-carrying capability by reflecting patterns. This paper investigates the capacity of RIS-assisted multiple-input multiple-output (MIMO) symbiotic communications utilizing multiple reflecting patterns, where each reflecting pattern is non-uniformly activated to carry additional information. To enhance transmission performance, the reflecting patterns, reflecting activation probability, and the transmit covariance matrix are jointly designed. Since the exact expression of the system capacity is intractable, the lower and upper bounds on the capacity are derived and used for optimization in this paper. Based on the lower bound on the capacity, a gradient ascent algorithm is developed to find the optimal reflecting patterns, reflecting activation probability, and the transmit covariance matrix. By taking advantage of the concise-form upper bound on the capacity, closed-form solutions of the reflecting activation probability and transmit covariance matrix can be derived after optimizing the reflecting patterns. The superiority of the proposed design is investigated and verified by computer simulations. Some selected numerical results demonstrate that the proposed design can achieve a higher capacity than the benchmark adopting only one reflecting pattern. [ABSTRACT FROM AUTHOR]

The Resource-Constrained Project Scheduling Problem (RCPSP) is a significant and important issue in the field of project management. It arises during project planning when resources must be allocated among tasks with specific time constraints. Solving this problem enables the optimization of project execution time, minimization of resource costs, and increased efficiency of the entire team's work. Due to the increasing complexity of projects, the development of new methods and algorithms to solve RCPSP is relevant nowadays. The existing methods for obtaining approximate solutions with guaranteed accuracy are characterized by high computational complexity and are often ineffective in considering the specific constraints of the problem. Fast heuristic approaches also have several drawbacks related to fine-tuning algorithm parameters and strong dependence on the quality of the initial solution. This paper investigates the features of the linear integer programming (LIP) model to solve RCPSP. The proposed LIP model is universal and scalable, enabling it to fully consider all specific aspects of the problem. The paper provides a construction algorithm of a functional space of the model and discusses the estimation of complexity. From the estimation of the mentioned algorithm's complexity, it is observed that the general complexity of the proposed approach is proportional to a controlled parameter of the LIP. Increasing this controlled parameter can significantly reduce the dimensionality of the initial problem, thus leading to the effectiveness of the LIP model-based approach in terms of computational resources. An upper bound for the value of this parameter is obtained for a special case of the RCPSP. Using the obtained balanced value, a numerical experiment was carried out on real-world samples. [ABSTRACT FROM AUTHOR]

This paper attempts to investigate the bearing capacity of a strip footing that rested on unsaturated homogenous sands and used upper bound finite-element limit analysis in association with linear optimization. The analysis is based on suction stress-based (σs) effective stress (σ′) analysis. Unlike the saturated soil, the size of the yield surface varies with the vertical position, and therefore, proper modifications are carried out in the upper bound formulations to incorporate the unsaturated soil property functions. A detailed investigation is carried out to estimate the load-carrying capacity of a strip footing that vary the mechanical strength, unsaturated soil properties, water table depth (hw), and climatic conditions. The numerical solutions are presented in terms of bearing capacity factors [BCF (Nγs, Nqs)] for the unit weight (γw) and surcharge pressure (qs). The nodal velocity patterns are drawn for several cases, and the presented solutions are compared with the available results. The design charts provided in this paper might be useful to design engineers. [ABSTRACT FROM AUTHOR]

Computation of reliability function of a coherent system is a difficult task especially when the system's configuration is complex. Hence, sometimes, we should simply work with some approximations, as bounds reliability. The computation of these bounds has been widely studied in the case of coherent systems with independent and identically distributed (i.i.d) components. However, few results have been obtained in the case of heterogeneous (non i.d) dependent components. In this paper, we derive sharp bounds for the reliability of circular consecutive -out-of- systems consisting by dependent components with identical or arbitrary distribution functions. Also some stochastic comparisons are made. Illustrative examples are included. [ABSTRACT FROM AUTHOR]

In a paper by Guruswami et al., it was shown that the length $n$ of a $q$ -ary linear locally recoverable code with distance $d \geqslant 5$ is upper bounded by $O(dq^{3})$. Thus, it is a challenging problem to construct $q$ -ary locally recoverable codes with distance $d \geqslant 5$ and length approaching the upper bound. The same paper also gave an algorithmic construction of $q$ -ary locally recoverable codes with locality $r$ and length $n=\Omega _{r}(q^{2})$ for $d=5$ and 6, where $\Omega _{r}$ means that the implicit constant depends on locality $r$. In this paper, we present an explicit construction of $q$ -ary locally recoverable codes of distance $d= 5$ and 6 via binary constant weight codes. It turns out that 1) our construction is simpler and more explicit and 2) the length of our codes is greater than previously known. [ABSTRACT FROM AUTHOR]

This paper studies the capacity of an $n$ -dimensional vector Gaussian noise channel subject to the constraint that an input must lie in the ball of radius $R$ centered at the origin. It is known that in this setting, the optimizing input distribution is supported on a finite number of concentric spheres. However, the number, the positions, and the probabilities of the spheres are generally unknown. This paper characterizes necessary and sufficient conditions on the constraint $R$ , such that the input distribution supported on a single sphere is optimal. The maximum $\bar {R}_{n}$ , such that using only a single sphere is optimal, is shown to be a solution of an integral equation. Moreover, it is shown that $\bar {R}_{n}$ scales as $\sqrt {n}$ and the exact limit of $\frac {\bar {R}_{n}}{\sqrt {n}}$ is found. [ABSTRACT FROM AUTHOR]

A generalized framework of spectrum sensing disruption for a power-limited adversary is proposed in this paper. In the literature, a conventional sensing attack typically assumes that the adversary has perfect knowledge of the spectral usage status. The framework in this paper considers a more general case where there are uncertainties in the estimates at the adversary. These uncertainties are modeled utilizing the probability of detection and the probability of false alarm. Then, the sum of the conditional probabilities of false detection at the secondary within the spectral range of interest, conditioned on the adversary’s estimated spectrum usage status, is maximized. It is shown that the optimal sensing attack, given perfect estimation is a special case of the proposed framework. When the adversary has perfect spectrum usage information, this framework reduces to a previously demonstrated optimal sensing disruption. When the adversary has imperfect information on the spectral status, the proposed framework is significantly more robust than conventional sensing attacks. Further, when the adversary’s power budget increases, it asymptotically approaches the sensing disruption performance upper bound. [ABSTRACT FROM AUTHOR]

Zero correlation zone (ZCZ) sequence sets and Golay complementary sets (GCSs) have different correlation properties and hence have different engineering applications. A number of constructions of ZCZ sequence sets and GCSs have been proposed, respectively, in the literature. In addition, some ZCZ sequence sets can be constructed from mutually orthogonal GCSs. In this paper, the relationship between GCSs and ZCZ sets is discovered further. We propose a new type of sequence sets which are ZCZ sequence sets and also GCSs. They are called the Golay-ZCZ sequence sets in this paper. Therefore, they have low peak-to-average power ratios when employed in OFDM systems due to the good autocorrelation properties of GCSs. Besides, the Golay-ZCZ sets possess zero autocorrelations and cross-correlations within their ZCZ and hence have the potential application to synchronization. Furthermore, a construction of Golay-ZCZ sequence family with flexible set sizes, various sequence lengths, and large ZCZ widths is proposed in this paper. [ABSTRACT FROM AUTHOR]

The zero-error capacity of a channel is defined as the maximum rate at which it is possible to transmit information with zero probability of error. In this paper, we settle all previously unsolved cases for the zero-error capacity of binary channels with one memory. [ABSTRACT FROM AUTHOR]

We revisit and take a closer look at a (not so well known) result of a 2017 paper, showing that the differential uniformity of any vectorial function is bounded from below by an expression depending on the size of its image set. We make explicit the resulting tight lower bound on the image set size of differentially $\delta $ -uniform functions (which is the only currently known non-trivial lower bound on the image set size of such functions). We also significantly improve an upper bound on the nonlinearity of vectorial functions obtained in the same reference and involving their image set size. We study when the resulting bound is sharper than the covering radius bound. We obtain as a by-product a lower bound on the Hamming distance between differentially $\delta $ -uniform functions and affine functions, which we improve significantly with a second bound. This leads us to study what can be the maximum Hamming distance between vectorial functions and affine functions. We provide an upper bound which is slightly sharper than a bound by Liu, Mesnager and Chen when $m < n$ , and a second upper bound, which is much stronger in the case (happening in practice) where $m$ is near $n$ ; we study the tightness of this latter bound; this leads to an interesting question on APN functions, which we address (negatively). We finally derive an upper bound on the nonlinearity of vectorial functions by means of their Hamming distance to affine functions and make more precise the bound on the differential uniformity which was the starting point of the paper. [ABSTRACT FROM AUTHOR]

Volume estimates of metric balls in manifolds find diverse applications in information and coding theory. In this paper, new results for the volume of a metric ball in unitary group are derived via tools from random matrix theory. The first result is an integral representation of the exact volume, which involves a Toeplitz determinant of Bessel functions. A simple but accurate limiting volume formula is then obtained by invoking Szegő’s strong limit theorem for large Toeplitz matrices. The derived asymptotic volume formula enables analytical evaluation of some coding-theoretic bounds of unitary codes. In particular, the Gilbert–Varshamov lower bound and the Hamming upper bound on the cardinality as well as the resulting bounds on code rate and minimum distance are derived. Moreover, bounds on the scaling law of code rate are found. Finally, a closed-form bound on the diversity sum relevant to unitary space-time codes is obtained, which was only computed numerically in the literature. [ABSTRACT FROM AUTHOR]

The state-dependent point-to-point Gaussian channel with a helper is first studied, in which a transmitter communicates with a receiver via a state-corrupted channel. The state is not known to the transmitter nor to the receiver, but known to a helper noncausally, which then wishes to assist the receiver to cancel the state. Differently from the previous work that characterized the capacity only in the infinite state power regime, this paper explores the general case with arbitrary state power. A lower bound on the capacity is derived based on an achievable scheme that integrates direct state subtraction and single-bin dirty paper coding. By analyzing this lower bound and further comparing it with the existing upper bounds, the capacity of the channel is characterized for a wide range of channel parameters. Such an idea of characterizing the capacity is further extended to study the two-user state-dependent multiple access channel with a helper. By comparing the derived inner and outer bounds, the channel parameters are partitioned into appropriate cases, and for each case, either segments on the capacity region boundary or the full capacity region are characterized. [ABSTRACT FROM PUBLISHER]

This paper proposes a novel fault tolerant consensus-based secondary voltage and frequency restoration method considering disturbances and actuator faults by using the sliding mode control for islanded microgrids (MGs). Existing distributed methods commonly design restoration layer based on the ideal condition that the actuators of distributed generations (DGs) function healthily and there are no faults and disturbances, whereas MGs are exposed to actuator faults of biased fault and partial loss of effectiveness fault. Faults and disturbances have a great impact on control of MG, which terribly reduce the stability and quality of it. To eliminate the adverse effects of them, this paper explicitly addresses the consensus problem for frequency and voltage restoration of MGs, whereas providing stringent real power sharing, in the presence of actuation/propulsion faults and disturbances. To this end, we derive the consensus restoration proof using rigorous Lyapunov analysis. As a result, the suggested method decreases the sensitivity of the system to failures and increases its reliability. Unlike conventional distributed controllers, the proposed approach quickly reaches consensus and exhibits a more accurate robust performance. Finally, we have performed several simulation scenarios in MATLAB/SimPowerSystems Toolbox to illustrate the efficiency of the theoretical results. [ABSTRACT FROM AUTHOR]

This paper considers a multiple-access system with multiple-packet reception (MPR) capability $\gamma $ , i.e., a packet can be successfully received as long as it overlaps with $\gamma -1$ or fewer other packets at any instant during its lifetime. To efficiently utilize the MPR capability, this paper generalizes $p$ -persistent carrier-sense multiple access (CSMA) to consider that a user with carrier sensing capability $c$ adopts the transmission probability $p_{n}$ if this user has sensed $n$ ongoing transmissions for $n=0,1,\ldots ,c-1$. This paper aims to model the characteristics of such CSMA and to design transmission probabilities for achieving maximum saturation throughput. To this end, we first formulate such CSMA as a parameterized Markov decision process (MDP) and use the long-run average performance to evaluate the saturation throughput. Second, by observing that the exact values of optimal transmission probabilities are in general infeasible to find, we modify this MDP to establish an upper bound on the maximum throughput, and modify this MDP again to propose a heuristic design with near-optimal performance. Simulations with respect to a wide range of configurations are provided to validate our study. The throughput performance under more general models and the robustness of our design are also investigated. [ABSTRACT FROM AUTHOR]

The capacity of noisy channels with memory and finite input has been difficult to characterize explicitly in many cases. In this paper, we consider single-tap binary-input Gaussian channels with inter-symbol interference (ISI). The dual capacity method is used to obtain upper bounds using Markov test distributions. The bound, expressed as a single-letter optimization problem, is solved numerically. For higher memory, the notion of cycle basis is used to provide an exponential reduction in the computational complexity of the optimization problem. Bounds were obtained for the important case of the dicode channel, and these are better than the previously known upper bounds and are close to achievable rates over a wide range of SNRs. [ABSTRACT FROM AUTHOR]