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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]

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 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]

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]

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]

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]

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]

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]

This paper is concerned with detecting an integer parameter vector inside a box from a linear model that is corrupted with a noise vector following the Gaussian distribution. One of the commonly used detectors is the maximum likelihood detector, which is obtained by solving a box-constrained integer least squares problem, that is NP-hard. Two other popular detectors are the box-constrained rounding and Babai detectors due to their high efficiency of implementation. In this paper, we first present formulas for the success probabilities (the probabilities of correct detection) of these three detectors for two different situations: the integer parameter vector is deterministic and is uniformly distributed over the constraint box. Then, we give two simple examples to respectively show that the success probability of the box-constrained rounding detector can be larger than that of the box-constrained Babai detector and the latter can be larger than the success probability of the maximum likelihood detector when the parameter vector is deterministic, and prove that the success probability of the box-constrained rounding detector is always not larger than that of the box-constrained Babai detector when the parameter vector is uniformly distributed over the constraint box. Some relations between the results for the box constrained and ordinary cases are presented, and two bounds on the success probability of the maximum likelihood detector, which can easily be computed, are developed. Finally, simulation results are provided to illustrate our main theoretical findings. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new subclass of H-matrices called S DDk matrices, which contains S DD matrices and S DD1 matrices as special cases, and present some properties of S DDk matrices. Based on these properties, we also provide new infinity norm bounds for the inverse of S DD matrices and S DDk matrices. It is proved that these new bounds are better than some existing results in some cases. Numerical examples demonstrate the effectiveness of the obtained results. [ABSTRACT FROM AUTHOR]

The concept of covering energy of a poset is known and its McClelland type bounds are available in the literature. In this paper, we establish formulas for the covering energy of a crown with 2n elements and a fence with n elements. A lower bound for the largest eigenvalue of a poset is established. Using this lower bound, we improve the McClelland type bounds for the covering energy for some special classes of posets. [ABSTRACT FROM AUTHOR]

This paper studies low-latency streaming codes for the multi-hop network. The source transmits a sequence of messages to a destination through a chain of relays, and requires the destination to reconstruct each message by its deadline. We assume that each communication link is subjected to a certain maximum number of packet erasures. The case of a single relay (a three-node network) was considered in Fong et al. (2020). A coding scheme known as symbol-wise decode and forward was proposed. In the present work, we propose an alternative scheme that is different from Fong et al. (2020) and still achieves the same rate as in Fong et al. (2020) for the one hop case as the field-size goes to infinity. Furthermore, our proposed scheme naturally generalizes to the case of multiple-relay nodes yielding new achievable rates for this setting. The main difference with Fong et al. (2020) is that our proposed scheme exploits the ability of the relay nodes to adapt the transmission based on the erasures on the previous link. Hence, we refer to our scheme as “state-dependent” and contrast it with the scheme in Fong et al. (2020) that is state-independent. Our scheme requires the relay nodes to append a header to the transmitted packets, and we show that the size of the header does not depend on the field-size of the code. We also derive an upper bound on the maximal streaming rate achievable over a network with an arbitrary number of relays. We show that this upper bound matches our achievable rate in the special case when the maximal number of erasures on the first link is greater than or equal to the maximal number of erasures on each of the following links, and the field size goes to infinity. [ABSTRACT FROM AUTHOR]

In this paper, we consider variable-length coding over the memoryless binary asymmetric channel (BAC) with full noiseless feedback, including the binary symmetric channel (BSC) as a special case. In 2012, Naghshvar et al. introduced a coding scheme, which we refer to as the small-enough-difference (SED) coding scheme. For symmetric binary-input channels, the deterministic variable-length feedback (VLF) code constructed with the SED coding scheme asymptotically achieves both capacity and Burnashev’s optimal error exponent. Building on the work of Naghshvar et al., this paper extends the SED coding scheme to the BAC and develops a non-asymptotic VLF achievability bound that is shown to achieve both capacity and the optimal error exponent. For the specific case of the BSC, we develop an additional non-asymptotic VLF achievability bound using a two-phase analysis that leverages both a submartingale synthesis and a Markov chain time of first passage analysis. Numerical evaluations show that both new VLF achievability bounds outperform Polyanskiy’s achievability bound for variable-length stop-feedback codes. [ABSTRACT FROM AUTHOR]

In sequential decision-making, imitation learning (IL) trains a policy efficiently by mimicking expert demonstrations. Various imitation methods were proposed and empirically evaluated, meanwhile, their theoretical understandings need further studies, among which the compounding error in long-horizon decisions is a major issue. In this paper, we first analyze the value gap between the expert policy and imitated policies by two imitation methods, behavioral cloning (BC) and generative adversarial imitation. The results support that generative adversarial imitation can reduce the compounding error compared to BC. Furthermore, we establish the lower bounds of IL under two settings, suggesting the significance of environment interactions in IL. By considering the environment transition model as a dual agent, IL can also be used to learn the environment model. Therefore, based on the bounds of imitating policies, we further analyze the performance of imitating environments. The results show that environment models can be more effectively imitated by generative adversarial imitation than BC. Particularly, we obtain a policy evaluation error that is linear with the effective planning horizon w.r.t. the model bias, suggesting a novel application of adversarial imitation for model-based reinforcement learning (MBRL). We hope these results could inspire future advances in IL and MBRL. [ABSTRACT FROM AUTHOR]

This paper presents a unifying framework to construct low-density parity-check (LDPC) codes with associated Tanner graphs of desired girth. Towards this goal, we highlight the role that a certain square matrix that appears in the product of the parity-check matrix with its transpose has in the construction of codes with graphs of desired girth and further explore it in order to generate the set of necessary and sufficient conditions for a Tanner graph to have a given girth between 6 and 12. For each such girth, we present algorithms to construct codes of the desired girth and we show how to use them to compute the minimum necessary value of the lifting factor. For girth larger than 12, we show how to use multi-step graph lifting methods to deterministically modify codes in order to increase their girth. We also give a new perspective on LDPC protograph-based parity-check matrices by viewing them as rows of a parity-check matrix equal to the sum of certain permutation matrices and obtain an important connection between all protographs and those with variable nodes of degree 2. We also show that the results and methodology that we develop for the all-one protograph can be used and adapted to analyze the girth of the Tanner graph of any parity-check matrix and demonstrate how this can be done using a well-known irregular, multi-edge protograph specified by the NASA Consultative Committee for Space Data Systems (CCSDS). Throughout the paper, we exemplify our theoretical results with constructions of LDPC codes with Tanner graphs of any girth between 6 and 14 and give sufficient conditions for a multi-step lifted parity-check matrix to have girth between 14 and 22. [ABSTRACT FROM AUTHOR]

Sidelnikov sequences, a kind of cyclotomic sequences with many desired properties such as low correlation and variable alphabet sizes, can be employed to construct a polyphase sequence family that has many applications in high-speed data communications. Recently, cyclotomic numbers have been used to investigate the linear complexity of Sidelnikov sequences, mainly about binary ones, although the limitation on the orders of the available cyclotomic numbers makes it difficult. This paper continues to study the linear complexity over $\mathbb {F}_{M}$ of $M$ -ary Sidelnikov sequence of period $q-1$ using Hasse derivative, which implies $q=p^{m}$ , $m\geq 1$ and $M|(q-1)$. The $t$ th Hasse derivative formulas are presented in terms of cyclotomic numbers, and some upper bounds on the linear complexity for $M=2$ and 3 are obtained only with some additional restrictions on $q$. Furthermore, concrete illustrations for several families of these sequences, such as $q\equiv 1\pmod {2}$ and $q\equiv 1\pmod {3}$ , show these upper bounds are tight and reachable; especially for $q=2\times 3^{\lambda }+1 (1\leq \lambda \leq 20)$ , the exact linear complexities over $\mathbb {F}_{3}$ of the ternary Sidelnikov sequences are determined; and it turns out that all the linear complexities of the sequences considered are very close to their periods. [ABSTRACT FROM AUTHOR]

For fixed integers $n$ and $b\geq k$ , let $A(b,k,n)$ the largest size of a subset of $\{1,2,\ldots,b\}^{n}$ such that, for any $k$ distinct elements in the set, there is a coordinate where they all differ. Bounding $A(b,k,n)$ is a problem of relevant interest in information theory and computer science, relating to the zero-error capacity with list decoding and to the study of $(b, k)$ -hash families of functions. It is known that, for fixed $b$ and $k$ , $A(b,k,n)$ grows exponentially in $n$. In this paper, we determine new exponential upper bounds for different values of $b$ and $k$. A first bound on $A(b,k,n)$ for general $b$ and $k$ was derived by Fredman and Komlós in the ’80s and improved for certain $b\neq k$ by Körner and Marton and by Arikan. Only very recently better bounds were derived for general $b$ and $k$ by Guruswami and Riazanov, while stronger results for small values of $b=k$ were obtained by Arikan, by Dalai, Guruswami and Radhakrishnan, and by Costa and Dalai. In this paper, we strengthen the bounds for some specific values of $b$ and $k$. Our contribution is a new computational method for obtaining upper bounds on the values of a quadratic form defined over discrete probability distributions in arbitrary dimensions, which emerged as a central ingredient in recent works. The proposed method reduces an infinite-dimensional problem to a finite one, which we manage to further simplify by means of a series of optimality conditions. [ABSTRACT FROM AUTHOR]

The family of Goppa codes is one of the most interesting subclasses of linear codes. As the McEliece cryptosystem often chooses a random Goppa code as its key, knowledge of the number of inequivalent Goppa codes for fixed parameters may facilitate in the evaluation of the security of such a cryptosystem. In this paper we present a new approach to give an upper bound on the number of inequivalent extended irreducible binary Goppa codes. To be more specific, let $n>3$ be an odd prime number and $q=2^{n}$ ; let $r\geq 3$ be a positive integer satisfying $\gcd (r,n)=1$ and $\gcd \big (r,q(q^{2}-1)\big)=1$. We obtain an upper bound for the number of inequivalent extended irreducible binary Goppa codes of length $q+1$ and degree $r$. [ABSTRACT FROM AUTHOR]

Many unsupervised domain adaptation (UDA) methods have been developed and have achieved promising results in various pattern recognition tasks. However, most existing methods assume that raw source data are available in the target domain when transferring knowledge from the source to the target domain. Due to the emerging regulations on data privacy, the availability of source data cannot be guaranteed when applying UDA methods in a new domain. The lack of source data makes UDA more challenging, and most existing methods are no longer applicable. To handle this issue, this paper analyzes the cross-domain representations in source-data-free unsupervised domain adaptation (SF-UDA). A new theorem is derived to bound the target-domain prediction error using the trained source model instead of the source data. On the basis of the proposed theorem, information bottleneck theory is introduced to minimize the generalization upper bound of the target-domain prediction error, thereby achieving domain adaptation. The minimization is implemented in a variational inference framework using a newly developed latent alignment variational autoencoder (LA-VAE). The experimental results show good performance of the proposed method in several cross-dataset classification tasks without using source data. Ablation studies and feature visualization also validate the effectiveness of our method in SF-UDA. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the linear precoder design for three dimensional (3D) massive multi-input multi-output (MIMO) downlink with uniform planar array (UPA) and imperfect channel state information (CSI). We introduce a beam based statistical channel model (BSCM) by using sampled steering vectors, and then an a posteriori channel model which includes the channel aging is established. On the basis of the a posteriori channel model, we consider the robust precoder design by maximizing an upper bound of the expected weighted sum-rate under a total power constraint. We derive two concave minorizing functions of the objective function. With these minorizing functions and the minorize-maximization (MM) methodology, we derive two iterative algorithms that converge to stationary points of the optimization problem. Simulation results show that the proposed precoders can achieve a significant performance gain than the widely used regularized zero forcing (RZF) precoder and the signal to leakage noise ratio (SLNR) precoder in median to high mobility scenarios. [ABSTRACT FROM AUTHOR]

The strong secrecy transmission problem of the arbitrarily varying wiretap channel (AVWC) with input and state constraints is investigated in this paper. First, a stochastic-encoder code lower bound of the strong secrecy capacity is established by applying the type argument and Csiszár’s almost independent coloring lemma. Then, a superposition stochastic-encoder code lower bound of the secrecy capacity is provided. The superposition stochastic-encoder code lower bound can be larger than the ordinary stochastic-encoder code lower bound. Random code lower and upper bounds of the secrecy capacity of the AVWC with constraints are further provided. Based on these results, we further consider a special case of the model, namely severely less noisy AVWC, and give the stochastic-encoder code and random code capacities. It is proved that the stochastic-encoder code capacity of the AVWC with constraints is either equal to or strictly smaller than the corresponding random code capacity, which is consistent with the property of the ordinary AVC. Finally, some numerical examples are presented to better illustrate our capacity results. Compared to the soft covering lemma that requires the codewords to be generated i.i.d., our method has more relaxed requirements regarding codebooks. It is proved that the good codebooks for secure transmission can be generated by choosing codewords randomly from a given type set, which is critical when considering the AVWC with constraints. [ABSTRACT FROM AUTHOR]

This paper describes new, simple, recursive methods of construction for orientable sequences, i.e. periodic binary sequences in which any $n$ -tuple occurs at most once in a period in either direction. As has been previously described, such sequences have potential applications in automatic position-location systems, where the sequence is encoded onto a surface and a reader needs only examine $n$ consecutive encoded bits to determine its location and orientation on the surface. The only previously described method of construction (due to Dai et al.) is somewhat complex, whereas the new techniques are simple to both describe and implement. The methods of construction cover both the standard ‘infinite periodic’ case, and also the aperiodic, finite sequence, case. Both the new methods build on the Lempel homomorphism, first introduced as a means of recursively generating de Bruijn sequences. [ABSTRACT FROM AUTHOR]

A block code is called a locally recoverable code (LRC for short) with $(r,\delta)$ -locality, if subject to any $\delta -1$ erasure failures, every symbol in the encoding can still be recovered by accessing at most $r$ other symbols. Recently, it was discovered by several authors that a $q$ -ary optimal $(r,\delta)$ -LRC, i.e., an LRC achieving the generalized Singleton-type bound, can have length much bigger than $q+1$. This is quite different from the classical $q$ -ary MDS codes where it is conjectured that the code length is upper bounded by $q+1$ (or $q+2$ for some special cases). In this paper, we further investigate constructions of optimal $(r,\delta)$ -LRCs along the line of using parity-check matrices. Inspired by classical Reed-Solomon codes and the work in Jin (2019), we equip parity-check matrices with the Vandermonde structure. It turns out that a parity-check matrix with the Vandermonde structure that produces an optimal LRC must obey certain disjoint property for subsets of $\mathbb {F}_{q}$. We manage to show the existence of these disjoint subsets. Thus, this yields an optimal $(r,\delta)$ -LRC with code length $\Omega \left({q^{\frac {\delta }{2}\left({1+\frac {1}{\lfloor \frac {d-1}{\delta }\rfloor -1}}\right)}}\right)\vphantom {\bigg)_{j}}$ , where $d$ is the minimum distance. In particular, to our surprise, for $\delta =2$ this disjoint condition is equivalent to a well-studied problem in extremal graph theory. With the help of extremal graph theory, we succeed to improve all of the best known results in Guruswami et al. (2018) for $d\geq 7$. In addition, for $d=6$ , we are able to remove the constraint required in Jin (2019) that $q$ is even. [ABSTRACT FROM AUTHOR]

The one-dimensional (1-D) Golay complementary set (GCS) has many well-known properties and has been widely employed in communications engineering. The concept of 1-D GCS can be extended to the two-dimensional (2-D) Golay complementary array set (GCAS) where the 2-D aperiodic autocorrelations of constituent arrays sum to zero except for the 2-D zero shift. The 2-D GCAS includes the 2-D Golay complementary array pair (GCAP) as a special case when the set size is 2. In this paper, 2-D generalized Boolean functions are introduced and constructions of 2-D GCAPs, 2-D GCASs, and 2-D Golay complementary array mates based on generalized Boolean functions are proposed. Explicit expressions of 2-D Boolean functions for 2-D GCAPs and 2-D GCASs are given. Therefore, they are all direct constructions without the aid of other existing 1-D or 2-D sequences. Moreover, the peak-to-average power ratio (PAPR) properties of the column sequences and row sequences of the constructed 2-D GCAPs and 2-D GCASs are investigated and the PAPRs are proved to be upper bounded. [ABSTRACT FROM AUTHOR]

Mining a weighted single large graph has recently attracted many researchers. The WeGraMi algorithm is considered the state-of-the-art among current approaches. It uses a MaxMin measure to calculate weights for all mined subgraphs. However, if all values in the domain have the same role and the user needs an average value of that domain, then we have to use another measure. In this paper, we introduce a novel algorithm called AWeGraMi (Average Weighted Graph Mining) to solve the above problem, and our method calculates the weight based on the average of all values in the domain. We also apply the MaxMin measure as an upper-bound to prune the search space. The new algorithm can mine all frequent weighted subgraphs effectively. Our experiments on the directed and undirected datasets have shown that AWeGraMi has better performance in comparison to post-processing GraMi for all three criteria: search space (the number of candidate subgraphs), running time, and memory consumption. [ABSTRACT FROM AUTHOR]

In engineering mathematics, the unsaturated nature of soil has a significant impact on the seismic bearing capacity solution. However, it has generally been neglected in the published literature to date. Based on the kinematic approach of limit analysis, the present study proposes a method for calculating the bearing capacity of shallow strip footings located in unsaturated soils, taking four common types of soils as examples. The modified pseudo-dynamic (MPD) approach is used to calculate the seismic forces varying with time and space, and the layerwise summation method is used to derive the power generated by the seismic forces. In the calculation of internal energy dissipation, this paper introduces the effective stress based on the suction stress to derive the cohesion expression at different depths. The analytical formula of bearing capacity is obtained by the principle of virtual work, and its value is optimized by the Sequential Quadratic Programming (SQP) algorithm. In order to verify the validity of the proposed method, the present results are compared with the solutions published so far and a good agreement is obtained. Finally, a parametric study is performed to investigate the influence of different types of parameters on the bearing capacity. [ABSTRACT FROM AUTHOR]

Discovering high utility sequences in a quantitative database is a popular data mining task. The goal is to enumerate all sequences of items (symbols) that have a high value for the user, as measured by a utility function. A representative application of high utility sequence mining is the identification of profitable sequences of purchases in transactions from online stores. Though useful, a drawback of that task is that the cost of items is not considered. However, cost is a key factor for decision-making in that domain and many others. To consider both the cost and utility of items for sequence mining, this paper defines a novel problem FLCHUSM of mining frequent sequences having a high average utility and a low average cost. Though the proposed problem is a generalization of the traditional problem of frequent sequence mining, it is more challenging because the average utility and average cost functions do not satisfy the downward-closure property traditionally used to reduce the search space. To offer a solution to this issue, this paper presents a lower bound on the cost and two novel upper bounds on the utility. Besides, four width, depth pruning, reducing and tightening strategies are devised to eliminate unpromising patterns from the search space. Taking these theoretical results as a foundation, a new CUL (Cost-Utility List) data structure is conceived for storing and quickly updating the utility and cost information of patterns, and a novel algorithm named FLCHUSPM is proposed for FLCHUSM . Results from several experiments show that FLCHUSPM is efficient in terms of memory usage and runtime, and that interesting patterns can be discovered in real data. [ABSTRACT FROM AUTHOR]

Sparse code multiple access (SCMA), as a codebook-based non-orthogonal multiple access (NOMA) technique, has received research attention in recent years. The codebook design problem for SCMA has also been studied to some extent since codebook choices are highly related to the system’s error rate performance. In this paper, we approach the SCMA codebook design problem by formulating an optimization problem to maximize the minimum Euclidean distance (MED) of superimposed codewords under power constraints. While SCMA codebooks with a larger MED are expected to obtain a better BER performance, no optimal SCMA codebook in terms of MED maximization, to the authors’ best knowledge, has been reported in the SCMA literature yet. In this paper, a new iterative algorithm based on alternating maximization with exact penalty is proposed for the MED maximization problem. The proposed algorithm, when supplied with appropriate initial points and parameters, achieves a set of codebooks of all users whose MED is larger than any previously reported results. A Lagrange dual problem is derived which provides an upper bound of MED of any set of codebooks. Even though there is still a nonzero gap between the achieved MED and the upper bound given by the dual problem, simulation results demonstrate clear advantages in error rate performances of the proposed set of codebooks over all existing ones not only in AWGN channels but also in some downlink scenarios that fit in 5G/NR applications, making it a good codebook candidate thereof. The proposed set of SCMA codebooks, however, are not shown to outperform existing ones in uplink channels or in the case where non-consecutive OFDMA subcarriers are used. The correctness and accuracy of error curves in the simulation results are further confirmed by the coincidences with the theoretical upper bounds of error rates derived for any given set of codebooks. [ABSTRACT FROM AUTHOR]

Insertion–deletion codes (insdel codes for short) play an important role in synchronization error correction. The higher the minimum insdel distance, the more insdel errors the code can correct. Haeupler and Shahrasbi established the Singleton bound for insdel codes: the minimum insdel distance of any $[n,k]$ linear code over $\mathbb {F}_{q}$ satisfies $d\leq 2n-2k+2$. There have been some constructions of insdel codes through Reed-Solomon codes with high capabilities, but none has come close to this bound. Recently, Do Duc et al. showed that the minimum insdel distance of any $[n,k]$ Reed-Solomon code is no more than $2n-2k$ if $q$ is large enough compared to the code length $n$ ; optimal codes that meet the new bound were also constructed explicitly. The contribution of this paper is twofold. We first show that the minimum insdel distance of any $[n,k]$ linear code over $\mathbb {F}_{q}$ satisfies $d\leq 2n-2k$ if $n > k > 1$. This result improves and generalizes the previously known results in the literature. We then give a sufficient condition under which the minimum insdel distance of a 2-D Reed-Solomon code of length $n$ over $\mathbb {F}_{q}$ is exactly equal to $2n-4$. As a consequence, we show that the sufficient condition is not hard to achieve; we explicitly construct an infinite family of optimal 2-D Reed-Somolom codes meeting the bound. [ABSTRACT FROM AUTHOR]

High utility sequence mining is a popular data mining task, which aims at finding sequences having a high utility (importance) in a quantitative sequence database. Though it has several applications, state-of-the-art algorithms have one or more of the following limitations: (1) they rely on a utility function that tends to be biased toward finding long patterns, (2) some algorithms do take pattern length into account using an average-utility function but they adopt an optimistic perspective that can be risky or misleading for some applications, (3) they do not let the user specify additional constraints on patterns to be found. To address these three limitations, this paper defines a novel task of mining frequent high minimum average-utility sequences (FHAUS) with constraints in a quantitative sequence database. This task has the following benefits. First, it uses the average-utility au function based on the minimum utility, which takes the length of a pattern into account to calculate its utility. This helps finding short patterns missed by traditional algorithms and it is based on more safe pessimistic utility calculations. Second, the user can specify a set of monotonic and anti-monotonic constraints C on patterns to filter irrelevant patterns and improve the performance of the mining process. To efficiently find all FHAUSs with constraints, this paper first proposes some novel upper bounds (UBs) and weak upper bounds (WUBs) on the average-utility, which satisfy downward-closure (DC) properties or DC-like properties. Then, to effectively reduce the search space, the paper designs novel width pruning, depth pruning, reducing, and tightening strategies based on the proposed bounds. These proposed novel theoretical results are integrated into an algorithm named C-FHAUSPM (Constrained Frequent High minimum Average-Utility Sequential Pattern Mining) for efficiently discovering all FHAUSs with constraints. Results from extensive experiments on both real-life and synthetic quantitative sequence databases show that C-FHAUSPM is highly efficient in terms of runtime and memory usage. [ABSTRACT FROM AUTHOR]

Conventional design methods of polar-coded modulation schemes aim to minimize the block error rate (BLER) under successive cancellation (SC) decoding. However, codes designed by conventional methods are not competitive under successive cancellation list (SCL) decoding. This paper presents a new design method based on the BLER upper bound under maximum-likelihood (ML) decoding (ML-BLER upper bound). The ML-BLER upper bound depends on the weight enumerating function (WEF) of the polar-coded modulation scheme over the squared Euclidean distance. In this paper, the polar-coded modulation is randomized by the concept of interleaved polar (i-polar) codes, and the WEF averaged over the ensemble of the polar-coded modulation schemes can be derived. Three polar-coded modulation schemes are considered, i.e., the bit-interleaved polar-coded modulation with a single interleaver (BIPCM-SI), the bit-interleaved polar-coded modulation with multiple interleavers (BIPCM-MI), and the multi-level polar-coded modulation (MLPCM). A new bit channel selection algorithm for polar-coded modulation schemes is proposed, which takes the polarization effect and the ML-BLER upper bound as design criteria. Design examples show that, under SCL decoding, the polar-coded modulation schemes (without CRC) with the proposed channel selection algorithm outperform those with conventional algorithms and are competitive as compared to the state-of-the-art 5G LDPC codes. [ABSTRACT FROM AUTHOR]

Depletion and deforestation of forest resources are mainly due to industrialization, population, pollution, forest fire, improper commercial logging, and illegal logging in the world. In this paper, we consider two dynamic models. A mathematical Model 1 is proposed considering the forest biomass density x(t), the density of wood‐based industries y(t) with unknown parameter h. Model 2 is an extension of Model 1 with the density of illegal logging z(t) with unknown parameter n. It is assumed that the density of forest biomass grows logistically in the absence of wood‐based industries and illegal logging. In the proposed models, the controlling parameters h and n are crucial parameters for the local stable conditions of the equilibrium points and system control. We also show in this paper that it is possible to control illegal logging by increasing the level of logging by selecting system parameters efficiently and effectively. Recommendations for Resource ManagersDepletion and deforestation of Mongolian forest resource are mainly due to forest fire, illegal logging. We consider mathematical models of forest depletion due to forest operation and illegal logging.Mongolian forest's current situation is that the rate of illegal logging is higher than the wood‐based industries. We show that this situation can be changed by changing the parameters.Based on the mathematical modeling and statistical analysis, we define the upper bound of the rate of resources of the wood‐based industries.We also presented that it is possible to control the parameters efficiently. The result suggests that to approximate the limit of wood utilized for the nationwide supply from the government it is necessary to increase the current amount of forest utility considering the actual forest resources and demands. [ABSTRACT FROM AUTHOR]

In this paper we improve the upper bound of the third order Hankel determinant for the class of Ozaki close-to-convex functions. The sharp bound is conjectured. [ABSTRACT FROM AUTHOR]

This paper studies the problem of constructing codes correcting deletions in arrays. Under this model, it is assumed that an $n \times n$ array can experience deletions of rows and columns. These deletion errors are referred to as $({t_{\mathrm {r}}}, {t_{\mathrm {c}}})$ -criss-cross deletions if ${t_{\mathrm {r}}}$ rows and ${t_{\mathrm {c}}}$ columns are deleted, while a code correcting these deletion patterns is called a $({t_{\mathrm {r}}}, {t_{\mathrm {c}}})$ -criss-cross deletion correction code. The definitions for criss-cross insertions are similar. It is first shown that when $t_{r}=t_{c}$ the problems of correcting criss-cross deletions and criss-cross insertions are equivalent. The focus of this paper lies on the case of (1, 1)-criss-cross deletions. A non-asymptotic upper bound on the cardinality of (1, 1)-criss-cross deletion correction codes is shown which assures that the redundancy is at least $2n-3+2\log n$ bits. A code construction with an existential encoding and an explicit decoding algorithm is presented. The redundancy of the construction is at most $2n+4 \log n + 7 +2 \log e$. A construction with explicit encoder and decoder is presented. The explicit encoder adds an extra $5\log n + 5$ bits of redundancy to the construction. [ABSTRACT FROM AUTHOR]

The Maximum Clique Problem (MCP) is a classic NP-hard problem, which has the goal of finding the largest possible clique. It is known to have direct applications in a wide spectrum of fields such as data association problems appearing in bioinformatics and computational biology, computer vision and robotics. Solutions like using brute force, backtracking and branch and bound are designed to deal with the maximum problem. In the branch and bound method, a branch is pruned if the currently found largest clique is better than its upper bound. However, the upper bound obtained by current methods is often not close enough to the ω (G) , leading to large inefficient search space. This paper discusses the branch and bound procedure to solve the maximum clique problem in large and sparse graphs and proposes a new efficient branch and bound maximum clique algorithm named SMC-BRB. SMC-BRB solves the maximum clique problem in heuristic search stage and exact search stage. It simultaneously utilizes the s + -index and color-based upper bound in heuristic search stage, which effectively reduces the number of branches in the exact search stage. This method is beneficial to the solution of MCP because it provides a scale reduction on heuristic search stage. Experimental results show that SMC-BRB has better performance than the state-of-the-art algorithm MC-BRB, which demonstrates the efficiency of the proposed approach. [ABSTRACT FROM AUTHOR]

The yield criterion of many metallic materials differs from the von Mises yield criterion. However, the available upper bound solutions are almost all restricted to this criterion. The objective of the present paper was to derive an upper bound solution based on a generalized yield criterion for evaluating the extrusion and drawing force, assuming a conical die. The solution method differs from the conventional method used in conjunction with the von Mises yield criterion. The development of this method is necessary, since the work function is not readily expressed as an explicit function of strain rate invariants if the generalized yield criterion is adopted. The solution is illustrated using numerical examples, which show the effect of the yield criterion on the limit load. [ABSTRACT FROM AUTHOR]

Radio antennas switch signals in the form of radio waves using different frequency bands of the electromagnetic spectrum. To avoid interruption, each radio station is assigned a unique number. The channel assignment problem refers to this application. A radio geometric mean labeling of a connected graph G is an injective function h from the vertex set, V (G) to the set of natural numbers N such that for any two distinct vertices x and y of G , h (x) · h (y) ≥ d i a m + 1 − d (x , y) . The radio geometric mean number of h , r g m n (h) , is the maximum number assigned to any vertex of G. The radio geometric mean number of G, r g m n (G) is the minimum value of r g m n (h) , taken over all radio geometric mean labeling h of G . In this paper, we present two theorems for calculating the exact radio geometric mean number of paths and cycles. We also present a novel algorithm for determining the upper bound for the radio geometric mean number of a given graph. We verify that the upper bounds obtained from this algorithm coincide with the exact value of the radio geometric mean number for paths, cycles, stars, and bi-stars. [ABSTRACT FROM AUTHOR]

Due to the advantage of capacity-achieving, polar codes have been extended to the block fading channel whereas most constructions involve complex iterative-calculation. In this paper, we establish a systematic framework to analyze the error performance of polar codes in the case of block mapping and random mapping. For both the mappings, by introducing the new concept, named split polar spectrum, we derive the upper bound on the error probability of polarized channel which explicitly reveals the relationship between the diversity order $L$ and the block-wise weight distribution of the codeword. For the special case $L=2$ in the block mapping, we design the enumeration algorithm to calculate the exact split polar spectrum based on the general MacWilliams identities. For arbitrary diversity order in the random mapping, with the help of uniform interleaving, we derive the approximate split polar spectrum by combining the polar spectrum and the probability of fading pattern for a specific weight. Furthermore, we propose the design criteria to construct polar codes over the block fading channel. The full diversity criterion is the primary target to achieve the diversity gain and the product distance criterion requires to maximize the product of the block-wise Hamming distance whereby obtain the coding gain. Guided by these design criteria, the construction metrics, respectively named polarized diversity weight (PDW) and simplified PDW (SPDW) are proposed to designpolar codes in both mappings. Such simple metrics can construct polar codes with similar or better performance over those based on traditional methods in block fading channel. [ABSTRACT FROM AUTHOR]

Multiple-input-multiple-output (MIMO) systems significantly increase the network throughput and coverage probability for short-packet communications. In this paper, a tight lower bound on the average achievable rate of MIMO short-packet communication systems is theoretically derived, considering flat uncorrelated Rayleigh fading MIMO channels. The derivations are based on the eigenvalue analysis of a Wishart matrix and Jensen's inequality. Given the actual transmission rate, a tight approximation on the average block error rate (BLER) of MIMO short-packet communication systems is also provided, which is based on the moment generating function and inverse Laplace transform. Numerical results demonstrate that both our theoretically derived analytical average achievable rate lower bound and approximate average BLER are almost the same as the simulation results. [ABSTRACT FROM AUTHOR]

The notion of correlation immune functions has been introduced by Siegenthaler (1984) in symmetric cryptography in the framework of stream ciphers. At the conference CRYPTO’91 by Camion et al., it has been pointed out that this notion existed in statistics and combinatorics. It has recently been highlighted that such functions also play an important role in a new framework related to side-channel attack counter-measures. Since then, the interest in correlation immune Boolean functions has been renewed, and new challenges regarding these functions have appeared. Specifically, low Hamming weight correlation immune functions have been selected as useful for counter-measures to side-channel attacks. Despite their importance, the literature is not abundant in this research direction. Two very interesting articles in which such correlation immune functions were nicely explored, given this novel use of them. Carlet initiated the first one in 2013, and the second one is due to Carlet and Chen (2018). This paper deals with correlation immune Boolean functions aiming to produce more candidates of those processing low Hamming weights. We shall focus on correlation immune Boolean functions with Hamming weights power of 2 (which offer a flexibility to control the correlation immunity aspects) and present several methods of designing them. Some design methods are efficient and could be employed to derive such functions. Consequently, given two positive integers $n$ and $m$ , we derive new effective constructions of correlation immune Boolean functions with Hamming weight power of 2. Furthermore, an upper bound on the correlation immunity of the newly constructed $n$ -variable Boolean functions with Hamming weight $2^{m}$ was determined for $n-m\ge 0$. Besides, exact values and lower bounds on the maximum correlation immunity of those functions are explored and discussed, mainly when the values of $n$ and $m$ are very close. This paper also exhibits explicit examples of those correlation immune functions that illustrate our methods. [ABSTRACT FROM AUTHOR]