General Independence Sets in Random Strongly Sparse Hypergraphs

We analyze the asymptotic behavior of the j-independence number of a random k-uniform hypergraph H(n, k, p) in the binomial model. We prove that in the strongly sparse case, i.e., where \(p = c/\left( \begin{gathered} n - 1 \hfill \\ k - 1 \hfill \\ \end{gathered} \right)\) for a positive constant 0 < c ≤ 1/(k ? 1), there exists a constant γ(k, j, c) > 0 such that the j-independence number α _j (H(n, k, p)) obeys the law of large numbers \(\frac{{{\alpha _j}\left( {H\left( {n,k,p} \right)} \right)}}{n}\xrightarrow{P}\gamma \left( {k,j,c} \right)asn \to + \infty \) Moreover, we explicitly present γ(k, j, c) as a function of a solution of some transcendental equation.     

Cryptanalysis of an MOR cryptosystem based on a finite associative algebra基于有限结合代数的 MOR 公钥密码安全性分析

The Shor algorithm is effective for public-key cryptosystems based on an abelian group. At CRYPTO 2001, Paeng (2001) presented a MOR cryptosystem using a non-abelian group, which can be considered as a candidate scheme for post-quantum attack. This paper analyses the security of a MOR cryptosystem based on a finite associative algebra using a quantum algorithm. Specifically, let L be a finite associative algebra over a finite field F. Consider a homomorphism φ: Aut(L) → Aut(H)×Aut(I), where I is an ideal of L and H ? L/I. We compute dim Im(φ) and dim Ker(φ), and combine them by dim Aut(L) = dim Im(φ)+dim Ker(φ). We prove that Im(φ) = Stab_Comp(H,I)(μ + B²(H, I)) and Ker(φ) ? Z¹(H, I). Thus, we can obtain dim Im(φ), since the algorithm for the stabilizer is a standard algorithm among abelian hidden subgroup algorithms. In addition, Z¹(H, I) is equivalent to the solution space of the linear equation group over the Galois fields GF(p), and it is possible to obtain dim Ker(φ) by the enumeration theorem. Furthermore, we can obtain the dimension of the automorphism group Aut(L). When the map ? ∈ Aut(L), it is possible to effectively compute the cyclic group 〈?〉 and recover the private key a. Therefore, the MOR scheme is insecure when based on a finite associative algebra in quantum computation.     

Guaranteed strategies for escaping encirclement

This paper considers a conflict situation on the plane as follows. A fast evader E has to break out the encirclement of slow pursuers P _{j1,...,j n} = {P _j1,..., P _jn }, n ≥ 3, with a miss distance not smaller than r ≥ 0. First, we estimate the minimum guaranteed miss distance from E to a pursuer P _a , a ∈ {j ₁,..., j _n }, when the former moves along a given straight line. Then the obtained results are used to calculate the guaranteed estimates to a group of two pursuers P _b,c = {P _b , P _c }, b, c ∈ {j ₁,..., j _n }, b ≠ c, when E maneuvers by crossing the rectilinear segment P _b P _c , and the state passes to the domain of the game space where E applies a strategy under which the miss distance to any of the pursuers is not decreased. In addition, we describe an approach to the games with a group of pursuers P _{j1,... jn} , n ≥ 3, in which E seeks to break out the encirclement by passing between two pursuers P _b and P _c , entering the domain of the game space where E can increase the miss distance to all pursuers by straight motion. By comparing the guaranteed miss distances with r for all alternatives b, c ∈ {j ₁,..., j _n }, b ≠ c, and a ? {b, c}, it is possible to choose the best alternative and also to extract the histories of the game in which the designed evasion strategies guarantee a safe break out from the encirclement.     

A game-theoretic model of TV show “The Voice”

This paper proposes a game-theoretic model of the two-player best-choice problem with incomplete information. The players (experts) choose between objects by observing their quality in the form of two components forming a sequence of random variables (x_i, y_i), i = 1,..., n. By assumption, the first quality component x_i is known to the players and the second one y_i is hidden. A player accepts or declines an object based on the first quality component only. A player with the maximal sum of the components becomes the winner in the game. The optimal strategies are derived in the cases of independent and correlated quality components.     

On s-uniform property of compressing sequences derived from primitive sequences modulo odd prime powers

Let Z/(p^e) be the integer residue ring modulo p^e with p an odd prime and e ≥ 2. We consider the suniform property of compressing sequences derived from primitive sequences over Z/(p^e). We give necessary and sufficient conditions for two compressing sequences to be s-uniform with α provided that the compressing map is of the form ?(x₀, x₁,...,x_e?1) = g(x_e?1) + η(x₀, x₁,..., x_e?2), where g(x_e?1) is a permutation polynomial over Z/(p) and η is an (e ? 1)-variable polynomial over Z/(p).     

On the Number of Edges of a Uniform Hypergraph with a Range of Allowed Intersections

We study the quantity p(n, k, t₁, t₂) equal to the maximum number of edges in a k-uniform hypergraph having the property that all cardinalities of pairwise intersections of edges lie in the interval [t₁, t₂]. We present previously known upper and lower bounds on this quantity and analyze their interrelations. We obtain new bounds on p(n, k, t₁, t₂) and consider their possible applications in combinatorial geometry problems. For some values of the parameters we explicitly evaluate the quantity in question. We also give a new bound on the size of a constant-weight error-correcting code.     

A model of best choice under incomplete information

This paper suggests two approaches to the construction of a two-player game of best choice under incomplete information with the choice priority of one player and the equal weights of both players. We consider a sequence of independent identically distributed random variables (x _i , y _i ), i = 1..., n, which represent the quality of incoming objects. The first component is announced to the players and the second component is hidden. Each player chooses an object based on the information available. The winner is the player whose object has a greater sum of the quality components than the opponent’s object. We derive the optimal threshold strategies and compare them for both approaches.     

Observational constraints on a hyperbolic potential in brane-world inflation

We focus on the large field of a hyperbolic potential form, which is characterized by a parameter f, in the framework of the brane-world inflation in Randall-Sundrum-II model. From the observed form of the power spectrum P _R (k), the parameter f should be of order 0.1m _p to 0.001m _p , the brane tension must be in the range λ ~ (1?10)×10⁵⁷ GeV⁴, and the energy scale is around V₀ ^1/4 ~ 10¹⁵ GeV. We find that the inflationary parameters (n _s , r, and dn _s /d(ln k) depend only on the number of e-folds N. The compatibility of these parameters with the last Planck measurements is realized with large values of N.     

<Emphasis Type="Italic">α</Emphasis>-Systems of differential inclusions and their unification

This paper introduces α-systems of differential inclusions on a bounded time interval [t₀, ?] and defines α-weakly invariant sets in [t₀, ?] × ?_n, where ?_n is a phase space of the differential inclusions. We study the problems connected with bringing the motions (trajectories) of the differential inclusions from an α-system to a given compact set M ? ?_n at the moment ? (the approach problems). The issues of extracting the solvability set W ? [t₀, ?] × ?ⁿ in the problem of bringing the motions of an α-system to M and the issues of calculating the maximal α-weakly invariant set W^c ? [t₀, ?] × ?ⁿ are also discussed. The notion of the quasi-Hamiltonian of an α-system (α-Hamiltonian) is proposed, which seems important for the problems of bringing the motions of the α-system to M.     

Linear complexity problems of level sequences of Euler quotients and their related binary sequences欧拉商的权位序列及其二元序列的线性复杂度问题

The Euler quotient modulo an odd-prime power p^r (r > 1) can be uniquely decomposed as a p-adic number of the form \(\frac{{u^{(p - 1)p^{r - 1} } - 1}}{{p^r }} \equiv a_0 (u) + a_1 (u)p + \cdots + a_{r - 1} (u)p^{r - 1} (\bmod p^r ), \gcd (u,p) = 1,\) where 0 ? a_j (u) < p for 0 ? j ? r?1 and we set all a_j (u) = 0 if gcd(u, p) > 1. We firstly study certain arithmetic properties of the level sequences (a_j (u))_u?0 over \(\mathbb{F}_p \) via introducing a new quotient. Then we determine the exact values of linear complexity of (a_j (u))_u?0 and values of k-error linear complexity for binary sequences defined by (a_j (u))_u?0.     

<Emphasis Type="Italic">I</Emphasis><Subscript>DDT</Subscript>: Fundamentals and test generation

It is the time to explore the fundamentals ofI _DDT testing when extensive work has been done forI _DDT testing since it was proposed. This paper precisely defines the concept of average transient current (I _DDT) of CMOS digital ICs, and experimentally analyzes the feasibility ofI _DDT test generation at gate level. Based on the SPICE simulation results, the paper suggests a formula to calculateI _DDT by means of counting only logical up-transitions, which enablesI _DDT test generation at logic level. The Bayesian optimization algorithm is utilized forI _DDT test generation. Experimental results show that about 25% stuck-open faults are withI _DDT test generation. 2.5, and likely to beI _DDT testable. It is also found that mostI _DDT testable faults are located near the primary inputs of a circuit under test.I _DDT test generation does not require fault sensitization procedure compared with stuck-at fault test generation. Furthermore, some redundant stuck-at faults can be detected by usingI _DDT testing.     

Expansion of Self-Similar Functions in the Faber–Schauder System

Let Ω = A^N be a space of right-sided infinite sequences drawn from a finite alphabet A = {0,1}, N = {1,2,…}. Let ρ(x, y)Σ_k=1^∞|x _k ? y _k |2^?k be a metric on Ω = AN, and μ the Bernoulli measure on Ω with probabilities p₀, p₁ > 0, p₀ + p₁ = 1. Denote by B(x,ω) an open ball of radius r centered at ω. The main result of this paper \(\mu (B(\omega ,r))r + \sum\nolimits_{n = 0}^\infty {\sum\nolimits_{j = 0}^{{2^n} - 1} {{\mu _{n,j}}} } (\omega )\tau ({2^n}r - j)\), where τ(x) = 2min {x,1 ? x}, 0 ≤ x ≤ 1, (τ(x) = 0, if x < 0 or x > 1 ), \({\mu _{n,j}}(\omega ) = (1 - {p_{{\omega _{n + 1}}}})\prod _{k = 1}^n{p_{{\omega _k}}} \oplus {j_k}\), \(j = {j_1}{2^{n - 1}} + {j_2}{2^{n - 2}} + ... + {j_n}\). The family of functions 1, x, τ(2 ⁿ r ? j), j = 0,1,…, 2 ⁿ ? 1, n = 0,1,…, is the Faber–Schauder system for the space C([0,1]) of continuous functions on [0, 1]. We also obtain the Faber–Schauder expansion for Lebesgue’s singular function, Cezaro curves, and Koch–Peano curves. Article is published in the author’s wording.     

Reverse Furthest Neighbors Query in Road Networks

Given a road network G = (V,E), where V (E) denotes the set of vertices(edges) in G, a set of points of interest P and a query point q residing in G, the reverse furthest neighbors (Rfn _R ) query in road networks fetches a set of points p ∈ P that take q as their furthest neighbor compared with all points in P ∪ {q}. This is the monochromatic Rfn _R (Mrfn _R ) query. Another interesting version of Rfn _R query is the bichromatic reverse furthest neighbor (Brfn _R ) query. Given two sets of points P and Q, and a query point q ∈ Q, a Brfn _R query fetches a set of points p ∈ P that take q as their furthest neighbor compared with all points in Q. This paper presents efficient algorithms for both Mrfn _R and Brfn _R queries, which utilize landmarks and partitioning-based techniques. Experiments on real datasets confirm the efficiency and scalability of proposed algorithms.     

Research on axial bearing capacity of rectangular concrete-filled steel tubular columns based on artificial neural networks

Design of rectangular concrete-filled steel tubular (CFT) columns has been a big concern owing to their complex constraint mechanism. Generally, most existing methods are based on simplified mechanical model with limited experimental data, which is not reliable under many conditions, e.g., columns using high strength materials. Artificial neural network (ANN) models have shown the effectiveness to solve complex problems in many areas of civil engineering in recent years. In this paper, ANN models were employed to predict the axial bearing capacity of rectangular CFT columns based on the experimental data. 305 experimental data from articles were collected, and 275 experimental samples were chosen to train the ANN models while 30 experimental samples were used for testing. Based on the comparison among different models, artificial neural network model1 (ANN1) and artificial neural network model2 (ANN2) with a 20-neuron hidden layer were chosen as the fit prediction models. ANN1 has five inputs: the length (D) and width (B) of cross section, the thickness of steel (t), the yield strength of steel (f _y), the cylinder strength of concrete (f′_c). ANN2 has ten inputs: D, B, t, f _y, f′_c, the length to width ratio (D/B), the length to thickness ratio (D/t), the width to thickness ratio (B/t), restraint coefficient (ξ), the steel ratio (α). The axial bearing capacity is the output data for both models.The outputs from ANN1 and ANN2 were verified and compared with those from EC4, ACI, GJB4142 and AISC360-10. The results show that the implemented models have good prediction and generalization capacity. Parametric study was conducted using ANN1 and ANN2 which indicates that effect law of basic parameters of columns on the axial bearing capacity of rectangular CFT columns differs from design codes.The results also provide convincing design reference to rectangular CFT columns.     

On finite groups with large degrees of irreducible character

Let G be a finite nontrivial group with an irreducible complex character χ of degree d = χ(1). According to the orthogonality relation, the sum of the squared degrees of irreducible characters of G is the order of G. N. Snyder proved that, if G = d(d + e), then the order of the group G is bounded in terms of e for e > 1. Y. Berkovich demonstrated that, in the case e = 1, the group G is Frobenius with the complement of order d. This paper studies a finite nontrivial group G with an irreducible complex character Θ such that G ≤ 2Θ(1)² and Θ(1) = pq where p and q are different primes. In this case, we have shown that G is a solvable group with an Abelian normal subgroup K of index pq. Using the classification of finite simple groups, we have established that the simple non-Abelian group, the order of which is divisible by the prime p and not greater than 2p ⁴ is isomorphic to one of the following groups: L ₂(q), L ₃(q), U ₃(q), S _z(8), A ₇, M ₁₁, and J ₁.     

Independence Numbers of Random Subgraphs of Some Distance Graph

The distance graph G(n, 2, 1) is a graph where vertices are identified with twoelement subsets of {1, 2,..., n}, and two vertices are connected by an edge whenever the corresponding subsets have exactly one common element. A random subgraph G _p (n, 2, 1) in the Erd?os–Rényi model is obtained by selecting each edge of G(n, 2, 1) with probability p independently of other edges. We find a lower bound on the independence number of the random subgraph G_1/2(n, 2, 1).     

Complexity of ideals in finite semigroups and finite-state machines

# _G (S) denotes the complexity of a finite semigroup as introduced by Krohn and Rhodes. IfI is a maximal ideal or maximal left ideal of a semigroupS, then# _G (I) ? # _G (S) ? # _G (I) + 1. Thus, ifV is an ideal ofS with# _G (S) = n ? k = # _G (V), then there is a chain of ideals ofS

$$V = V_k \subset V_{k + 1} \subset ... \subset V_n \subseteq S$$     

Tracking frequent items over distributed probabilistic data

Tracking frequent items (also called heavy hitters) is one of the most fundamental queries in real-time data due to its wide applications, such as logistics monitoring, association rule based analysis, etc. Recently, with the growing popularity of Internet of Things (IoT) and pervasive computing, a large amount of real-time data is usually collected from multiple sources in a distributed environment. Unfortunately, data collected from each source is often uncertain due to various factors: imprecise reading, data integration from multiple sources (or versions), transmission errors, etc. In addition, due to network delay and limited by the economic budget associated with large-scale data communication over a distributed network, an essential problem is to track the global frequent items from all distributed uncertain data sites with the minimum communication cost. In this paper, we focus on the problem of tracking distributed probabilistic frequent items (TDPF). Specifically, given k distributed sites S = {S ₁, … , S _k }, each of which is associated with an uncertain database \(\mathcal {D}_{i}\) of size n _i , a centralized server (or called a coordinator) H, a minimum support ratio r, and a probabilistic threshold t, we are required to find a set of items with minimum communication cost, each item X of which satisfies P r(s u p(X) ≥ r × N) > t, where s u p(X) is a random variable to describe the support of X and \(N={\sum }_{i=1}^{k}n_{i}\). In order to reduce the communication cost, we propose a local threshold-based deterministic algorithm and a sketch-based sampling approximate algorithm, respectively. The effectiveness and efficiency of the proposed algorithms are verified with extensive experiments on both real and synthetic uncertain datasets.     

The formula of the solution for some classes of initial boundary value problems for the hyperbolic equation with two independent variables

A new representation is proved of the solutions of initial boundary value problems for the equation of the form u _xx (x, t) + r(x)u _x (x, t) ? q(x)u(x, t) = u _tt (x, t) + μ(x)u _t (x, t) in the section (under boundary conditions of the 1st, 2nd, or 3rd type in any combination). This representation has the form of the Riemann integral dependent on the x and t over the given section.     

(<Emphasis Type="Italic">a</Emphasis>, <Emphasis Type="Italic">d</Emphasis>)-Distance Antimagic Labeling of Some Types of Graphs

We analyze the necessary existence conditions for (a, d)-distance antimagic labeling of a graph G = (V, E) of order n. We obtain theorems that expand the family of not (a, d) -distance antimagic graphs. In particular, we prove that the crown P _n ○ P ₁ does not admit an (a, 1)-distance antimagic labeling for n ≥ 2 if a ≥ 2. We determine the values of a at which path P _n can be an (a, 1)-distance antimagic graph. Among regular graphs, we investigate the case of a circulant graph.