Linear span ≈ Linear span
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SpanConv: A New Convolution via Spanning Kernel Space for Lightweight Pansharpening Open
Standard convolution operations can effectively perform feature extraction and representation but result in high computational cost, largely due to the generation of the original convolution kernel corresponding to the channel dimension of…
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Zero-Correlation Attacks on Tweakable Block Ciphers with Linear Tweakey Expansion Open
The design and analysis of dedicated tweakable block ciphers is a quite recent and very active research field that provides an ongoing stream of new insights. For instance, results of Kranz, Leander, and Wiemer from FSE 2017 show that the …
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Linear sets from projection of Desarguesian spreads Open
Every linear set in a projective space is the projection of a subgeometry, and most known characterizations of linear sets are given under this point of view. For instance, scattered linear sets of pseudoregulus type are obtained by consid…
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Identification information sensors of robot systems Open
At the present time, the complexity of identification is to find such a description, in which the image (information) of each class would have identified similar properties. The task is to make the transformed description includes the whol…
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On cyclic and negacyclic codes with one-dimensional hulls and their applications Open
Linear codes over finite fields with small dimensional hulls have received much attention due to their applications in cryptology and quantum computing. In this paper, we study cyclic and negacyclic codes with one-dimensional hulls. We det…
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On the Differential-Linear Connectivity Table of Vectorial Boolean Functions Open
Vectorial Boolean functions are crucial building-blocks in symmetric ciphers. Different known attacks on block ciphers have resulted in diverse cryptographic criteria for vectorial Boolean functions, such as differential uniformity and non…
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Constructions of linear codes with small hulls from association schemes Open
The intersection of a linear code and its dual is called the hull of this code. The code is a linear complementary dual (LCD) code if the dimension of its hull is zero. In this paper, we develop a method to construct LCD codes and linear c…
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To Each Optimizer a Norm, To Each Norm its Generalization Open
We study the implicit regularization of optimization methods for linear models interpolating the training data in the under-parametrized and over-parametrized regimes. Since it is difficult to determine whether an optimizer converges to so…
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Local Instruction Theories at the University Level: An Example in a Linear Algebra Course Open
In order to promote the design of innovative instructional activities at the Linear Algebra, we perform a design-based research project to explore how to teach Linear Algebra at the university level. In this article, we present the results…
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Learning Functions over Sets via Permutation Adversarial Networks Open
In this paper, we consider the problem of learning functions over sets, i.e., functions that are invariant to permutations of input set items. Recent approaches of pooling individual element embeddings can necessitate extremely large embed…
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Pre-Schauder Bases in Topological Vector Spaces Open
A Schauder basis in a real or complex Banach space X is a sequence ( e n ) n ∈ N in X such that for every x ∈ X there exists a unique sequence of scalars ( λ n ) n ∈ N satisfying that x = ∑ n = 1 ∞ λ n e n . Schauder bases were first intro…
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The Linear Span of Uniform Matrix Product States Open
The variety of uniform matrix product states arises both in algebraic geometry as a natural generalization of the Veronese variety, and in quantum many-body physics as a model for a translation-invariant system of sites placed on a ring. U…
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On spanning sets and generators of near-vector spaces Open
CITATION: Howell, K.-T. & Sanon, S. P. 2018. On spanning sets and generators of near-vector spaces. Turkish Journal of Mathematics, 42(6):3232 – 3241, doi:10.3906/mat-1807-155.
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Homogeneous Components of a CDH Fuzzy Space Open
We prove that fuzzy homogeneous components of a CDH fuzzy topological space (X,T) are clopen and also they are CDH topological subspaces of its 0-cut topological space (X,T0).
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A Further Understanding of Differential‐Linear Cryptanalysis Open
Differential-linear cryptanalysis has attracted much attention since proposed to attack DES in 1994, and then some generalized theories are developed to complement and unify the method. However, the links between differential-linear crypta…
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Differential-Linear Cryptanalsis on SIMECK32/64 and SIMON32/64 Open
In this paper, we give differential-linear cryptanalysis of SIMON, which is a family of lightweight block ciphers published by the National Security Agency, and SIMECK, which is a family of lightweight block ciphers proposed by Yang et al.…
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Numerical Range Inclusion, Dilation, and Operator Systems Open
Researchers have identified complex matrices $A$ such that a bounded linear operator $B$ acting on a Hilbert space will admit a dilation of the form $A \otimes I$ whenever the numerical range inclusion relation $W(B) \subseteq W(A)$ holds.…
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New Linear Trails and Linear Hulls of CHAM Open
CHAM is a family of lightweight block ciphers with block sizes of 64 bits and 128 bits. CHAM performs very well in lightweight environments and is known to be one of the block ciphers that can be implemented with the smallest hardware area…
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Maltsev equal-norm tight frames Open
A frame in $\mathbb{R}^d$ is a set of $n\geqslant d$ vectors whose linear span coincides with $\mathbb{R}^d$. A frame is said to be equal-norm if the norms of all its vectors are equal. Tight frames enable one to represent vectors in $\mat…
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Automatic Search for the Linear (Hull) Characteristics of ARX Ciphers: Applied to SPECK, SPARX, Chaskey, and CHAM-64 Open
Linear cryptanalysis is an important evaluation method for cryptographic primitives against key recovery attack. In this paper, we revisit the Walsh transformation for linear correlation calculation of modular addition, and an efficient al…
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Closure of the linear span of an exponential system in a weighted Banach space Open
For a certain class of sequences with repeated terms,
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Joint numerical ranges and communtativity of matrices Open
The connection between the commutativity of a family of $n\times n$ matrices and the generalized joint numerical ranges is studied. For instance, it is shown that ${\cal F}$ is a family of mutually commuting normal matrices if and only if …
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Rebricking frames and bases Open
In 1949, Denis Gabor introduced the ``complex signal'' (nowadays called ``analytic signal'') by combining a real function $f$ with its Hilbert transform $Hf$ to a complex function $f+ iHf$. His aim was to extract phase information, an idea…
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Comment on mr-2021-26 Open
Abstract. The quantum state of a spin ensemble is described by a density operator, which corresponds to a point in the Liouville space of orthogonal spin operators. Valid density operators are confined to a particular region of Liouville s…
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Comment on bg-2020-448 Open
Abstract. The South China Sea (SCS) is the world's largest marginal sea, playing an important role in the regional biogeochemical cycling of carbon and oxygen. However, its overall metabolic balance, primary production rates and links to E…
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Reply on RC1 Open
Abstract. Information on soils' composition and physical, chemical and biological properties is paramount to elucidate agroecosystem functioning in space and over time. For this purpose, we developed a national Swiss soil spectral library …
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Comment on acp-2021-340 Open
Abstract. The oxidation of Î3-carene and one of its main oxidation products, caronaldehyde, by the OH radical and O3 was investigated in the atmospheric simulation chamber SAPHIR under atmospheric conditions for NOx mixing ratios below 2â…
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Comment on mr-2021-10 Open
Abstract. Double electron–electron resonance (DEER) is a pulse electron paramagnetic resonance (EPR) technique that measures distances between paramagnetic centres. It utilizes a four-pulse sequence based on the refocused Hahn spin echo. T…
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Reply on RC1 Open
Abstract. Accelerator mass spectrometry (AMS) is currently the standard technique to measure cosmogenic 10Be and 26Al concentrations, but the challenge with measuring low nuclide concentrations is to combine high AMS measurement efficiency…
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Comment on essd-2022-34 Open
Abstract. The characteristics of the CISE-LOCEAN seawater isotope dataset (δ18O, δ2H, referred to as δD) are presented (https://doi.org/10.17882/71186; Waterisotopes-CISE-LOCEAN, 2021). This dataset covers the time period from 1998 to 2…