Search

Self-avoiding conformational sampling (SACS) is proposed as an enhanced conformational sampling method for proteins. In SACS, the following conformational resampling is repeated for a given protein: (1) identification of newly visited states in a subspace and (2) conformational resampling by restarting short-time molecular dynamics (MD) simulations from the newly visited states. To identify the newly visited states, a set of history-dependent histograms projected onto the subspace is used. One is constructed from the trajectories sampled at the current (ith) cycle, and the other is constructed from all of the trajectories accumulated up through the previous ((i - 1)th) cycle. By reference to the history-dependent histograms, the newly visited states appearing at the current (ith) cycle are defined as a difference set between them. By repeating the cycle of conformational resampling, SACS prevents the system from revisiting states that have already been visited for previous cycles, promoting structural transitions via resampling from the newly visited states. To verify the conformational sampling efficiency of SACS, the present method was applied to reveal underlying mechanisms of biologically important domain motions of maltodextrin binding protein in explicit water and successfully reproduced the open-closed transition with a reasonable (nanosecond-order) computational cost.

In this paper, we construct a novel coarray named as the difference and sum (diff–sum) coarray by exploiting an improved Conjugate Augmented MUSIC (CAM) estimator, which utilizes both the temporal information and the spatial information. The diff–sum coarray is the union of the difference coarray and the sum coarray. When taking the coprime array as the array model, we find that the elements of the sum coarray can fill up all the holes in the difference coarray. Besides, the sum coarray contains bonus uniform linear array (ULA) segments which extend the consecutive range of the difference coarray. As a result, the consecutive lags of the diff–sum coarray are much more than those of the difference coarray. For analysis, we derive the hole locations and consecutive ranges of the difference set and the sum set, discuss the complementarity of the two sets, and provide the analytical expression of the diff–sum virtual aperture. Simulations verify the effectivity of the improved method and show the high DOF of the diff–sum coarray.

In this note we prove the non-existence of two types of partial difference sets in Abelian groups of order 216 . This completes the classification of parameters for which a partial difference set of size at most 100 exists in an Abelian group.

This paper addresses the question of whether triple arrays can be constructed from Youden squares developed from difference sets. We prove that if the difference set is abelian, then having −1 as multiplier is both a necessary and sufficient condition for the construction to work. Using this, we are able to give a new infinite family of triple arrays. We use an alternative version of the construction to analyze the case of non-abelian difference sets, for which we prove a sufficient condition for giving triple arrays. We do a computer search for such non-abelian difference sets, but have not found any examples satisfying the given condition.

We present a new construction of almost difference sets. The construction occurs in nonabelian groups of order 4N with a subgroup H of order N so that H has an (N,\(\frac{N-1}{2}\),\(\frac{N-3}{4}\)) difference set (and hence N must be an integer that is 3 (mod 4)).

By further exploring some ideas in Buratti (1999), Chang and Ding (2006) several new infinite classes of difference families from finite fields are obtained and some results of Chang and Ding (2006) are extended.

In this paper we extend previous results regarding SL2(k) over any finite field k by investigating the structure of the symmetric spaces for the family of special linear groups SLn(k) for any integer n>2. Specifically, we discuss the generalized and extended symmetric spaces of SLn(k) for all conjugacy classes of involutions over a finite field of odd or even characteristic. We characterize the structure of these spaces and provide an explicit difference set in cases where the two spaces are not equal.

Multiple-compression detection is of particular importance in video forensics, as it reveals possible manipulations to the content. However, methods for detecting multiple compressions with same quantisation parameters (QPs) are rarely reported. To deal with this issue, a novel method is presented in this study to detect multiple H.264/advanced video coding compressions with the same QPs. First, a new set, named ratio difference set (RDS), is proposed, which is calculated by identifying the quantised DCT coefficients whose values will be changed after re-compression. Then, a discriminative and fixed statistical feature set extracted from RDS of each video is obtained to serve as input for classification. With the aid of support vector machines, the extracted feature set is used to classify the videos that have undergone H.264 compressions twice or more from those compressed just once. Experimental results show that high classification accuracy and robustness against copy-move attack and frame-deletion attack can be achieved with the authors’ proposed method.

The problem of packing n-dimensional subspaces of m-dimensional Euclidean space such that these subspaces are as far apart as possible was introduced by Conway, Hardin and Sloane. It can be seen as a higher dimensional version of spherical codes or equiangular lines. In this paper, we first give a general construction of equiangular lines, and then present a family of equiangular lines with large size from direct product difference sets. Meanwhile, for packing higher dimensional subspaces, we give three constructions of optimal packings in Grassmannian spaces based on difference sets and Latin squares. As a consequence, we obtain many new classes of optimal Grassmannian packings.

Zhou (J. Combin. Des. 21(12), 563–584, 2013) introduced modified planar functions in order to describe (2n, 2n, 2n, 1) relative difference sets R as a graph of a function on the finite field \(\mathbb {F}_{2^{n}}\), and pointed out that projections of R are difference sets that can be described by negabent or bent4 functions, which are Boolean functions given in multivariate form. One of the objectives of this paper is to contribute to the understanding of these component functions of modified planar functions. We identify the versions of the Walsh transforms that apply to modified planar functions on \(\mathbb {F}_{2^{n}}\) and their components, obtain a description of modified planar functions by their components which is similar to that of the classical planar functions in odd characteristic as a vectorial bent function, and point out some further properties of these components. Finally we introduce vectorial bent4 functions (over finite fields), which correspond to relative difference sets in certain groups. We give conditions under which Maiorana-McFarland functions are such functions, hence give rise to relative difference sets in \(\mathbb {Z}_{2}^{n/2}\times \mathbb {Z}_{4}^{n/2}\).

The problem of constructing polynomials with all coefficients $1$ or $-1$ and large merit factor (equivalently with small $L^4$ norm on the unit circle) arises naturally in complex analysis, condensed matter physics, and digital communications engineering. Most known constructions arise (sometimes in a subtle way) from difference sets, in particular from Paley and Singer difference sets. We consider the asymptotic merit factor of polynomials constructed from other difference sets, providing the first essentially new examples since 1991. In particular we prove a general theorem on the asymptotic merit factor of polynomials arising from cyclotomy, which includes results on Hall and Paley difference sets as special cases. In addition, we establish the asymptotic merit factor of polynomials derived from Gordon-Mills-Welch difference sets and Sidelnikov almost difference sets, proving two recent conjectures., 22 pages, this revision contains a more general version of Thm. 2.1

Generalizing a result of Ko and Ray-Chaudhuri (Discrete Math. 39 (1982), 37–58), we show the following: Assume the existence of an affine difference set in G relative to N of even order n≠2. If G is of the form G = N ⊕ H, where N is abelian, then n is actually a multiple of 4, say n = 4k, and there exists a (4k − 1, 2k − 1, k − 1)-Hadamard difference set in N. More detailed considerations lead to variations of this result (under appropriate assumptions) which yield even stronger non-existence theorems. In particular, we show the non-existence of abelian affine difference sets of order n ≡ 4 mod 8 (with the exception n = 4) and of nilpotent affine difference sets of order n ≡ 2 mod 4 (n ≠ 2). The latter result is the first general non-existence theorem in the non-abelian case.

A theorem of Steinhaus states that if $E\subset \mathbb R^d$ has positive Lebesgue measure, then the difference set $E-E$ contains a neighborhood of $0$. Similarly, if $E$ merely has Hausdorff dimension $\dim_{\mathcal H}(E)>(d+1)/2$, a result of Mattila and Sj\"olin states that the distance set $\Delta(E)\subset\mathbb R$ contains an open interval. In this work, we study such results from a general viewpoint, replacing $E-E$ or $\Delta(E)$ with more general $\Phi\,$-configurations for a class of $\Phi:\mathbb R^d\times\mathbb R^d\to\mathbb R^k$, and showing that, under suitable lower bounds on $\dim_{\mathcal H}(E)$ and a regularity assumption on the family of generalized Radon transforms associated with $\Phi$, it follows that the set $\Delta_\Phi(E)$ of $\Phi$-configurations in $E$ has nonempty interior in $\mathbb R^k$. Further extensions hold for $\Phi\,$-configurations generated by two sets, $E$ and $F$, in spaces of possibly different dimensions and with suitable lower bounds on $\dim_{\mathcal H}(E)+\dim_{\mathcal H}(F)$., Comment: 19 pages, no figures. Added references and commentary, and corrected a more few typos for publication

A T -user UD k-ary codes for MAAC is proposed. First, a coding scheme for a Tf+g-user UD k-ary code with code length f + g is proposed that is constructed from a Tf-user UD k-ary code and a Tg-user UD (2k − 1)-ary difference set. In fact, the Tg-user UD (2k − 1)-ary difference set is associated with Tg-user UD (2k − 1)-ary code. Second, originally from the multi-user UD (2i(k − 1) + 1)-ary (i = 0, 1, 2,…, m) codes with unitary code length, by recursively employing the coding scheme, 2m+1-user k-ary code with code length 2m is obtained. Finally, by recursively employing the coding scheme, 2n-user UD k-ary code with arbitrary code length n from the codes with length 2i (i = 0, 1,…, ⌊log 2 n⌋) is given. Since introducing the high-order multiary difference sets, the total rates of the proposed codes are higher those of conventional codes.

We present a construction that gives an infinite series of divisible design graphs which are Cayley graphs., Some minor mistakes were fixed in this version

We construct finite sets of real numbers that have a small difference set and strong local properties. In particular, we construct a set A of n real numbers such that | A − A | = n log 2 3 and that every subset A ′ ⊆ A of size k satisfies | A ′ − A ′ | ≥ k log 2 3 . This construction leads to the first non-trivial upper bound for the problem of distinct distances with local properties.

We revisit the problem of constructing Menon-Hadamard difference sets. In 1997, Wilson and Xiang gave a general framework for constructing Menon-Hadamard difference sets by using a combination of a spread and four projective sets of type Q in ${\mathrm{PG}}(3,q)$. They also found examples of suitable spreads and projective sets of type Q for $q=5,13,17$. Subsequently, Chen (1997) succeeded in finding a spread and four projective sets of type Q in ${\mathrm{PG}}(3,q)$ satisfying the conditions in the Wilson-Xiang construction for all odd prime powers $q$. Thus, he showed that there exists a Menon-Hadamard difference set of order $4q^4$ for all odd prime powers $q$. However, the projective sets of type Q found by Chen have automorphisms different from those of the examples constructed by Wilson and Xiang. In this paper, we first generalize Chen's construction of projective sets of type Q by using `semi-primitive' cyclotomic classes. This demonstrates that the construction of projective sets of type Q satisfying the conditions in the Wilson-Xiang construction is much more flexible than originally thought. Secondly, we give a new construction of spreads and projective sets of type Q in ${\mathrm{PG}}(3,q)$ for all odd prime powers $q$, which generalizes the examples found by Wilson and Xiang. This solves a problem left open in Section 5 of the Wilson-Xiang paper from 1997., Comment: 21 pages

This paper proposes a new level set based multi-material topology optimization method, where a difference-set-based multi-material level set (DS-MMLS) model is developed for topology description and an alternating active-phase algorithm is implemented. Based on the alternating active-phase algorithm, a multi-material topology optimization problem with N + 1 phases is split into N(N + 1)/2 binary-phase topology optimization sub-problems. Compared with the initial multi-material problem, each sub-problem involves fewer design variables and volume constraints. In the DS-MMLS model, N + 1 phases are represented by the sequential difference set of N level set functions . Based on this model, the topological evolution of two active phases can be easily achieved by updating a single level set function in a fixed domain, which contributes a great convenience to the implementation of the alternating active-phase algorithm with level set method. Therefore, the proposed method can be easily extended to topology optimization problems with more material phases. To demonstrate its effectiveness, some 2D and 3D numerical examples with different material phases are presented. The results reveal that the proposed method is effective for multi-material topology optimization problems.

Simple Summary There is a growing interest in using milk mid-infrared (MIR) spectrometry to obtain new phenotypes to assist in the complex management of dairy farms. These predictive values can be erroneous for many reasons, even if the prediction equations used are accurate. Unfortunately, there is no quality protocol routinely implemented to detect those abnormal predictive values in the database recorded by dairy herd improvement (DHI) organizations, except for fat and protein contents. However, for financial and practical reasons, it is unfeasible to adapt the quality protocol commonly used in milk laboratories to improve the accuracy of those traits. So, this study proposes three different statistical methods that would be easy to implement by DHI organizations to detect abnormal values and limit the spectral extrapolation in order to improve the accuracy of MIR-based predictive values. Abstract The use of abnormal milk mid-infrared (MIR) spectrum strongly affects prediction quality, even if the prediction equations used are accurate. So, this record must be detected after or before the prediction process to avoid erroneous spectral extrapolation or the use of poor-quality spectral data by dairy herd improvement (DHI) organizations. For financial or practical reasons, adapting the quality protocol currently used to improve the accuracy of fat and protein contents is unfeasible. This study proposed three different statistical methods that would be easy to implement by DHI organizations to solve this issue: the deletion of 1% of the extreme high and low predictive values (M1), the deletion of records based on the Global-H (GH) distance (M2), and the deletion of records based on the absolute fat residual value (M3). Additionally, the combinations of these three methods were investigated. A total of 346,818 milk samples were analyzed by MIR spectrometry to predict the contents of fat, protein, and fatty acids. Then, the same traits were also predicted externally using their corresponded standardized MIR spectra. The interest in cleaning procedures was assessed by estimating the root mean square differences (RMSDs) between those internal and external predicted phenotypes. All methods allowed for a decrease in the RMSD, with a gain ranging from 0.32% to 41.39%. Based on the obtained results, the “M1 and M2” combination should be preferred to be more parsimonious in the data loss, as it had the higher ratio of RMSD gain to data loss. This method deleted the records based on the 2% extreme predictions and a GH threshold set at 5. However, to ensure the lowest RMSD, the “M2 or M3” combination, considering a GH threshold of 5 and an absolute fat residual difference set at 0.30 g/dL of milk, was the most relevant. Both combinations involved M2 confirming the high interest of calculating the GH distance for all samples to predict. However, if it is impossible to estimate the GH distance due to a lack of relevant information to compute this statistical parameter, the obtained results recommended the use of M1 combined with M3. The limitation used in M3 must be adapted by the DHI, as this will depend on the spectral data and the equation used. The methodology proposed in this study can be generalized for other MIR-based phenotypes.

Non-maximum suppression (NMS) as a post-processing step for object detection is mainly used to remove redundant bounding boxes in the object and plays a vital role in many detectors. Its positioning accuracy mainly depends on the bounding box with the highest score, and this strategy is difficult to eliminate the false positive. In order to solve the problem, this paper regards the post-processing step as a combinatorial optimization problem and combines the chaotic whale optimization algorithm and non-maximum suppression. The chaotic search method is used to generate an initial combinatorial solution, and the whale optimization algorithm is discretized to create an updated combinatorial strategy. Under the guidance of the fitness function, the optimal combination is searched. In addition, the method of difference set area (DSA) is proposed to optimize the final detection result. The experiment uses the current mainstream framework Faster R-CNN as the detector on PASCAL VOC2012, COCO2017 and the Warships datasets. The experimental results show that the proposed method can significantly improve the average precision (AP) of detectors compared with the most advanced methods.

A finite group G is called a Schur group if every Schur ring over G is the transitivity module of a point stabilizer in a subgroup of Sym(G) that contains all permutations induced by the right multiplications in G. It is proved that the group $$ {\mathrm{\mathbb{Z}}}_2\times {\mathrm{\mathbb{Z}}}_{2^n} $$ is Schur, which completes the classification of Abelian Schur 2-groups. It is also proved that any non-Abelian Schur 2-group of order larger than 32 is dihedral (the Schur 2-groups of smaller orders are known). Finally, the Schur rings over a dihedral 2-group G are studied. It turns out that among such rings of rank at most 5, the only obstacle for G to be a Schur group is a hypothetical ring of rank 5 associated with a divisible difference set.

We consider the problem of sampling a node-valued graph. The objective is to infer the values of all nodes from that of a minimum subset of nodes by exploiting correlations in node values. We first introduce the concept of information dominating set (IDS). A subset of nodes in a given graph is an IDS if the values of these nodes are sufficient to infer the values of all nodes. We focus on two fundamental algorithmic problems: (i) how to determine whether a given subset of nodes is an IDS; (ii) how to construct a minimum IDS. Assuming binary node values and the local majority rule for information correlation, we first show that in acyclic graphs, both problems admit linear-complexity solutions by establishing a connection between the IDS problems and the vertex cover problem. We then show that in a general graph, the first problem is co-NP-complete and the second problem is NP-hard. We develop two approaches to solve the IDS problems: one reduces the problems to a hitting set problem based on the concept of essential difference set , the other a gradient-based approach with a tunable parameter that trades off performance with time complexity. The concept of IDS finds applications in opinion sampling such as political polling and market survey, identifying critical nodes in information networks, and inferring epidemics and cascading failures in communication and infrastructure networks.

It is shown that, if D is a nontrivial 2-(v,k,λ) symmetric design, with (k,λ)=1, admitting a flag-transitive automorphism group G of affine type, then v=pd, p an odd prime, and G is a point-primitive, block-primitive subgroup of AΓL1(pd). Moreover, O(G) acts flag-transitively, point-primitively on D, and D is isomorphic to the development of a difference set whose parameters and structure are also provided.